From 9548e52266e03d4465a32e77b8a1835bfef430c9 Mon Sep 17 00:00:00 2001
From: jysh1214 <jyxemperor@gmail.com>
Date: Mon, 1 Dec 2025 22:30:06 +0800
Subject: [PATCH 1/7] Refactor arithmetic ops to use std::variant + std::visit
 Remove Arithmetic_internal.hpp/cpp and Ari_ii from linalg_internal_interface

---
 .../Arithmetic_internal.cpp                   | 3042 -----------------
 .../Arithmetic_internal.hpp                   |  805 -----
 .../linalg_internal_cpu/CMakeLists.txt        |    2 -
 src/backend/linalg_internal_interface.cpp     |  134 -
 src/backend/linalg_internal_interface.hpp     |    8 +-
 src/linalg/Add.cpp                            |  171 +-
 src/linalg/Cpr.cpp                            |  171 +-
 src/linalg/Div.cpp                            |  308 +-
 src/linalg/Mod.cpp                            |  308 +-
 src/linalg/Mul.cpp                            |  171 +-
 src/linalg/Sub.cpp                            |  308 +-
 11 files changed, 1077 insertions(+), 4351 deletions(-)
 delete mode 100644 src/backend/linalg_internal_cpu/Arithmetic_internal.cpp
 delete mode 100644 src/backend/linalg_internal_cpu/Arithmetic_internal.hpp

diff --git a/src/backend/linalg_internal_cpu/Arithmetic_internal.cpp b/src/backend/linalg_internal_cpu/Arithmetic_internal.cpp
deleted file mode 100644
index fa83b7e9c..000000000
--- a/src/backend/linalg_internal_cpu/Arithmetic_internal.cpp
+++ /dev/null
@@ -1,3042 +0,0 @@
-#include "Arithmetic_internal.hpp"
-
-namespace cytnx {
-  namespace linalg_internal {
-
-    void Arithmetic_internal_cdtcd(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex128, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex128, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex128, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex128, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex128, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex128, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_cdtcf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex128, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex128, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex128, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex128, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex128, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex128, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_cdtd(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex128, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex128, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex128, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex128, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex128, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex128, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_cdtf(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex128, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex128, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex128, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex128, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex128, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex128, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_cdtu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex128, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex128, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex128, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex128, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex128, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex128, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_cdti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex128, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex128, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex128, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex128, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex128, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex128, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_cdtu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex128, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex128, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex128, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex128, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex128, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex128, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_cdti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex128, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex128, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex128, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex128, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex128, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex128, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_cdti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex128, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex128, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex128, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex128, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex128, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex128, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_cdtu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex128, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex128, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex128, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex128, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex128, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex128, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_cdtb(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex128, cytnx_bool>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex128, cytnx_bool>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex128, cytnx_bool>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex128, cytnx_bool>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex128, cytnx_bool>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex128, cytnx_bool>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    //-----------------------
-    void Arithmetic_internal_cftcd(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex64, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex64, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex64, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex64, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex64, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex64, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_cftcf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex64, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex64, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex64, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex64, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex64, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex64, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_cftd(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex64, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex64, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex64, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex64, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex64, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex64, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_cftf(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex64, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex64, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex64, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex64, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex64, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex64, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_cftu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex64, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex64, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex64, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex64, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex64, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex64, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_cfti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex64, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex64, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex64, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex64, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex64, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex64, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_cftu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex64, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex64, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex64, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex64, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex64, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex64, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_cfti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex64, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex64, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex64, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex64, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex64, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex64, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_cfti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex64, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex64, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex64, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex64, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex64, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex64, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_cftu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex64, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex64, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex64, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex64, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex64, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex64, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_cftb(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_complex64, cytnx_bool>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_complex64, cytnx_bool>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_complex64, cytnx_bool>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_complex64, cytnx_bool>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_complex64, cytnx_bool>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_complex64, cytnx_bool>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    //---------------------------
-    void Arithmetic_internal_dtcd(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_double, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_double, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_double, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_double, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_double, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_double, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_dtcf(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_double, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_double, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_double, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_double, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_double, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_double, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_dtd(boost::intrusive_ptr<Storage_base> &out,
-                                 boost::intrusive_ptr<Storage_base> &Lin,
-                                 boost::intrusive_ptr<Storage_base> &Rin,
-                                 const unsigned long long &len,
-                                 const std::vector<cytnx_uint64> &shape,
-                                 const std::vector<cytnx_uint64> &invmapper_L,
-                                 const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_double, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_double, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_double, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_double, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_double, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_double, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_dtf(boost::intrusive_ptr<Storage_base> &out,
-                                 boost::intrusive_ptr<Storage_base> &Lin,
-                                 boost::intrusive_ptr<Storage_base> &Rin,
-                                 const unsigned long long &len,
-                                 const std::vector<cytnx_uint64> &shape,
-                                 const std::vector<cytnx_uint64> &invmapper_L,
-                                 const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_double, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_double, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_double, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_double, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_double, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_double, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_dtu64(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_double, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_double, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_double, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_double, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_double, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_double, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_dti64(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_double, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_double, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_double, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_double, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_double, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_double, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_dtu32(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_double, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_double, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_double, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_double, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_double, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_double, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_dti32(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_double, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_double, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_double, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_double, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_double, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_double, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_dti16(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_double, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_double, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_double, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_double, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_double, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_double, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_dtu16(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_double, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_double, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_double, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_double, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_double, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_double, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_dtb(boost::intrusive_ptr<Storage_base> &out,
-                                 boost::intrusive_ptr<Storage_base> &Lin,
-                                 boost::intrusive_ptr<Storage_base> &Rin,
-                                 const unsigned long long &len,
-                                 const std::vector<cytnx_uint64> &shape,
-                                 const std::vector<cytnx_uint64> &invmapper_L,
-                                 const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_double, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_double, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_double, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_double, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_double, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_double, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    //----------------------
-    void Arithmetic_internal_ftcd(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_float, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_float, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_float, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_float, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_float, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_float, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_ftcf(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_float, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_float, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_float, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_float, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_float, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_float, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_ftd(boost::intrusive_ptr<Storage_base> &out,
-                                 boost::intrusive_ptr<Storage_base> &Lin,
-                                 boost::intrusive_ptr<Storage_base> &Rin,
-                                 const unsigned long long &len,
-                                 const std::vector<cytnx_uint64> &shape,
-                                 const std::vector<cytnx_uint64> &invmapper_L,
-                                 const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_float, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_float, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_float, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_float, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_float, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_float, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_ftf(boost::intrusive_ptr<Storage_base> &out,
-                                 boost::intrusive_ptr<Storage_base> &Lin,
-                                 boost::intrusive_ptr<Storage_base> &Rin,
-                                 const unsigned long long &len,
-                                 const std::vector<cytnx_uint64> &shape,
-                                 const std::vector<cytnx_uint64> &invmapper_L,
-                                 const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_float, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_float, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_float, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_float, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_float, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_float, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_ftu64(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_float, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_float, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_float, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_float, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_float, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_float, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_fti64(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_float, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_float, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_float, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_float, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_float, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_float, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_ftu32(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_float, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_float, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_float, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_float, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_float, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_float, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_fti32(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_float, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_float, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_float, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_float, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_float, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_float, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_fti16(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_float, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_float, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_float, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_float, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_float, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_float, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_ftu16(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_float, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_float, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_float, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_float, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_float, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_float, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_ftb(boost::intrusive_ptr<Storage_base> &out,
-                                 boost::intrusive_ptr<Storage_base> &Lin,
-                                 boost::intrusive_ptr<Storage_base> &Rin,
-                                 const unsigned long long &len,
-                                 const std::vector<cytnx_uint64> &shape,
-                                 const std::vector<cytnx_uint64> &invmapper_L,
-                                 const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_float, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_float, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_float, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_float, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_float, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_float, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-    }
-
-    //-----------------------
-    void Arithmetic_internal_u64tcd(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint64, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint64, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint64, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint64, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint64, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint64, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u64tcf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint64, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint64, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint64, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint64, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint64, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint64, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u64td(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint64, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint64, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint64, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint64, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint64, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint64, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u64tf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint64, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint64, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint64, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint64, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint64, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint64, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u64tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint64, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint64, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint64, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint64, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint64, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint64, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u64ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint64, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint64, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint64, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint64, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint64, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint64, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u64tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint64, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint64, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint64, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint64, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint64, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint64, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u64ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint64, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint64, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint64, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint64, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint64, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint64, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u64ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint64, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint64, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint64, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint64, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint64, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint64, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u64tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint64, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint64, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint64, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint64, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint64, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint64, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u64tb(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint64, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint64, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint64, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint64, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint64, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint64, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    //----------------------
-    void Arithmetic_internal_i64tcd(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int64, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int64, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int64, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int64, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int64, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int64, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i64tcf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int64, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int64, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int64, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int64, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int64, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int64, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i64td(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int64, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int64, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int64, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int64, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int64, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int64, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i64tf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int64, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int64, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int64, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int64, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int64, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int64, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i64tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int64, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int64, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int64, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int64, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int64, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int64, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i64ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int64, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int64, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int64, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int64, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int64, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int64, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i64tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int64, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int64, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int64, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int64, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int64, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int64, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i64ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int64, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int64, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int64, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int64, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int64, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int64, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i64ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int64, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int64, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int64, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int64, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int64, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i64tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int64, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int64, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int64, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int64, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int64, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int64, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i64tb(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int64, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int64, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int64, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int64, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int64, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int64, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-    }
-
-    //-------------------
-    void Arithmetic_internal_u32tcd(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint32, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint32, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint32, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint32, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint32, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint32, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u32tcf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint32, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint32, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint32, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint32, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint32, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint32, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u32td(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint32, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint32, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint32, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint32, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint32, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint32, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u32tf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint32, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint32, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint32, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint32, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint32, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint32, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u32tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint32, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint32, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint32, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint32, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint32, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint32, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u32ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint32, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint32, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint32, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint32, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint32, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint32, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u32tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint32, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint32, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint32, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint32, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint32, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint32, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u32ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint32, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint32, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint32, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint32, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint32, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint32, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u32ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint32, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint32, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint32, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint32, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint32, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint32, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u32tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint32, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint32, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint32, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint32, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint32, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint32, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u32tb(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint32, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint32, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint32, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint32, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint32, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint32, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-
-    //----------------------
-    void Arithmetic_internal_i32tcd(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int32, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int32, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int32, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int32, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int32, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int32, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i32tcf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int32, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int32, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int32, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int32, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int32, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int32, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i32td(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int32, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int32, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int32, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int32, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int32, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int32, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i32tf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int32, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int32, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int32, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int32, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int32, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int32, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i32tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int32, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int32, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int32, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int32, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int32, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int32, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i32ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int32, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int32, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int32, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int32, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int32, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int32, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i32tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int32, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int32, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int32, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int32, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int32, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int32, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i32ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int32, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int32, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int32, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int32, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int32, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int32, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i32ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int32, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int32, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int32, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int32, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int32, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int32, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i32tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int32, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int32, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int32, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int32, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int32, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i32tb(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int32, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int32, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int32, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int32, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int32, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int32, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-    }
-    //----------------------
-    void Arithmetic_internal_i16tcd(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int16, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int16, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int16, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int16, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int16, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int16, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i16tcf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int16, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int16, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int16, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int16, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int16, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int16, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i16td(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int16, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int16, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int16, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int16, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int16, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int16, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i16tf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int16, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int16, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int16, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int16, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int16, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int16, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i16tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int16, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int16, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int16, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int16, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int16, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int16, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i16ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int16, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int16, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int16, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int16, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int16, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int16, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i16tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int16, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int16, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int16, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int16, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int16, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int16, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i16ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int16, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int16, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int16, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int16, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int16, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int16, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i16ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int16, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int16, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int16, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int16, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int16, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int16, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i16tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int16, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int16, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int16, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int16, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int16, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int16, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_i16tb(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_int16, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_int16, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_int16, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_int16, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_int16, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_int16, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-    }
-
-    //----------------------
-    void Arithmetic_internal_u16tcd(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint16, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint16, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint16, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint16, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint16, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint16, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u16tcf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint16, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint16, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint16, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint16, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint16, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint16, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u16td(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint16, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint16, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint16, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint16, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint16, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint16, cytnx_double>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u16tf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint16, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint16, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint16, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint16, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint16, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint16, cytnx_float>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u16tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint16, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint16, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint16, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint16, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint16, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint16, cytnx_uint64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u16ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint16, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint16, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint16, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint16, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint16, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint16, cytnx_int64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u16tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint16, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint16, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint16, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint16, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint16, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint16, cytnx_uint32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u16ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint16, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint16, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint16, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint16, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint16, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint16, cytnx_int32>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u16ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint16, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint16, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint16, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint16, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint16, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint16, cytnx_int16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u16tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint16, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint16, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint16, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint16, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint16, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint16, cytnx_uint16>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_u16tb(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_uint16, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_uint16, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_uint16, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_uint16, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_uint16, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_uint16, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    //----------------------
-    void Arithmetic_internal_btcd(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_bool, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_bool, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_bool, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_bool, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_bool, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_bool, cytnx_complex128>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_btcf(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_bool, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_bool, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_bool, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_bool, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_bool, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_bool, cytnx_complex64>(
-          out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_btd(boost::intrusive_ptr<Storage_base> &out,
-                                 boost::intrusive_ptr<Storage_base> &Lin,
-                                 boost::intrusive_ptr<Storage_base> &Rin,
-                                 const unsigned long long &len,
-                                 const std::vector<cytnx_uint64> &shape,
-                                 const std::vector<cytnx_uint64> &invmapper_L,
-                                 const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_bool, cytnx_double>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_bool, cytnx_double>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_bool, cytnx_double>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_bool, cytnx_double>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_bool, cytnx_double>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_bool, cytnx_double>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_btf(boost::intrusive_ptr<Storage_base> &out,
-                                 boost::intrusive_ptr<Storage_base> &Lin,
-                                 boost::intrusive_ptr<Storage_base> &Rin,
-                                 const unsigned long long &len,
-                                 const std::vector<cytnx_uint64> &shape,
-                                 const std::vector<cytnx_uint64> &invmapper_L,
-                                 const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_bool, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_bool, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_bool, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_bool, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_bool, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_bool, cytnx_float>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_btu64(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_bool, cytnx_uint64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_bool, cytnx_uint64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_bool, cytnx_uint64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_bool, cytnx_uint64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_bool, cytnx_uint64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_bool, cytnx_uint64>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_bti64(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_bool, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_bool, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_bool, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_bool, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_bool, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_bool, cytnx_int64>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_btu32(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_bool, cytnx_uint32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_bool, cytnx_uint32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_bool, cytnx_uint32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_bool, cytnx_uint32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_bool, cytnx_uint32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_bool, cytnx_uint32>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_bti32(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_bool, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_bool, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_bool, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_bool, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_bool, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_bool, cytnx_int32>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_bti16(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_bool, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_bool, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_bool, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_bool, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_bool, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_bool, cytnx_int16>(out, Lin, Rin, len, shape,
-                                                                         invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_btu16(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_bool, cytnx_uint16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_bool, cytnx_uint16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_bool, cytnx_uint16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_bool, cytnx_uint16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_bool, cytnx_uint16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_bool, cytnx_uint16>(out, Lin, Rin, len, shape,
-                                                                          invmapper_L, invmapper_R);
-    }
-    void Arithmetic_internal_btb(boost::intrusive_ptr<Storage_base> &out,
-                                 boost::intrusive_ptr<Storage_base> &Lin,
-                                 boost::intrusive_ptr<Storage_base> &Rin,
-                                 const unsigned long long &len,
-                                 const std::vector<cytnx_uint64> &shape,
-                                 const std::vector<cytnx_uint64> &invmapper_L,
-                                 const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::AddInternalImpl<cytnx_bool, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                        invmapper_L, invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::MulInternalImpl<cytnx_bool, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                        invmapper_L, invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::SubInternalImpl<cytnx_bool, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                        invmapper_L, invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::DivInternalImpl<cytnx_bool, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                        invmapper_L, invmapper_R);
-      else if (type == 4)
-        cytnx::linalg_internal::CprInternalImpl<cytnx_bool, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                        invmapper_L, invmapper_R);
-      else
-        cytnx::linalg_internal::ModInternalImpl<cytnx_bool, cytnx_bool>(out, Lin, Rin, len, shape,
-                                                                        invmapper_L, invmapper_R);
-    }
-
-  }  // namespace linalg_internal
-}  // namespace cytnx
diff --git a/src/backend/linalg_internal_cpu/Arithmetic_internal.hpp b/src/backend/linalg_internal_cpu/Arithmetic_internal.hpp
deleted file mode 100644
index 0ed4add51..000000000
--- a/src/backend/linalg_internal_cpu/Arithmetic_internal.hpp
+++ /dev/null
@@ -1,805 +0,0 @@
-#ifndef CYTNX_BACKEND_LINALG_INTERNAL_CPU_ARITHMETIC_INTERNAL_H_
-#define CYTNX_BACKEND_LINALG_INTERNAL_CPU_ARITHMETIC_INTERNAL_H_
-
-#include "Type.hpp"
-#include "backend/Storage.hpp"
-#include "Add_internal.hpp"
-#include "Mul_internal.hpp"
-#include "Sub_internal.hpp"
-#include "Div_internal.hpp"
-#include "Cpr_internal.hpp"
-#include "Mod_internal.hpp"
-namespace cytnx {
-  namespace linalg_internal {
-
-    /// Arithmetic
-    void Arithmetic_internal_cdtcd(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_cdtcf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_cdtd(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_cdtf(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_cdti64(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_cdtu64(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_cdti32(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_cdtu32(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_cdtu16(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_cdti16(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_cdtb(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-    void Arithmetic_internal_cftcd(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_cftcf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_cftd(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_cftf(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_cfti64(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_cftu64(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_cfti32(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_cftu32(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_cftu16(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_cfti16(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_cftb(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-    void Arithmetic_internal_dtcd(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_dtcf(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_dtd(boost::intrusive_ptr<Storage_base> &out,
-                                 boost::intrusive_ptr<Storage_base> &Lin,
-                                 boost::intrusive_ptr<Storage_base> &Rin,
-                                 const unsigned long long &len,
-                                 const std::vector<cytnx_uint64> &shape,
-                                 const std::vector<cytnx_uint64> &invmapper_L,
-                                 const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_dtf(boost::intrusive_ptr<Storage_base> &out,
-                                 boost::intrusive_ptr<Storage_base> &Lin,
-                                 boost::intrusive_ptr<Storage_base> &Rin,
-                                 const unsigned long long &len,
-                                 const std::vector<cytnx_uint64> &shape,
-                                 const std::vector<cytnx_uint64> &invmapper_L,
-                                 const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_dti64(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_dtu64(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_dti32(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_dtu32(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_dtu16(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_dti16(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_dtb(boost::intrusive_ptr<Storage_base> &out,
-                                 boost::intrusive_ptr<Storage_base> &Lin,
-                                 boost::intrusive_ptr<Storage_base> &Rin,
-                                 const unsigned long long &len,
-                                 const std::vector<cytnx_uint64> &shape,
-                                 const std::vector<cytnx_uint64> &invmapper_L,
-                                 const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-    void Arithmetic_internal_ftcd(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_ftcf(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_ftd(boost::intrusive_ptr<Storage_base> &out,
-                                 boost::intrusive_ptr<Storage_base> &Lin,
-                                 boost::intrusive_ptr<Storage_base> &Rin,
-                                 const unsigned long long &len,
-                                 const std::vector<cytnx_uint64> &shape,
-                                 const std::vector<cytnx_uint64> &invmapper_L,
-                                 const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_ftf(boost::intrusive_ptr<Storage_base> &out,
-                                 boost::intrusive_ptr<Storage_base> &Lin,
-                                 boost::intrusive_ptr<Storage_base> &Rin,
-                                 const unsigned long long &len,
-                                 const std::vector<cytnx_uint64> &shape,
-                                 const std::vector<cytnx_uint64> &invmapper_L,
-                                 const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_fti64(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_ftu64(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_fti32(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_ftu32(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_ftu16(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_fti16(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_ftb(boost::intrusive_ptr<Storage_base> &out,
-                                 boost::intrusive_ptr<Storage_base> &Lin,
-                                 boost::intrusive_ptr<Storage_base> &Rin,
-                                 const unsigned long long &len,
-                                 const std::vector<cytnx_uint64> &shape,
-                                 const std::vector<cytnx_uint64> &invmapper_L,
-                                 const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-    void Arithmetic_internal_i64tcd(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i64tcf(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i64td(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i64tf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i64ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i64tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i64ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i64tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i64tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i64ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i64tb(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-    void Arithmetic_internal_u64tcd(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u64tcf(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u64td(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u64tf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u64ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u64tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u64ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u64tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u64ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u64tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u64tb(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-    void Arithmetic_internal_i32tcd(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i32tcf(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i32td(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i32tf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i32ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i32tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i32ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i32tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i32tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i32ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i32tb(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-    void Arithmetic_internal_u32tcd(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u32tcf(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u32td(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u32tf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u32ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u32tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u32ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u32tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u32tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u32ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u32tb(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-    void Arithmetic_internal_i16tcd(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i16tcf(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i16td(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i16tf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i16ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i16tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i16ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i16tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i16tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i16ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_i16tb(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-    void Arithmetic_internal_u16tcd(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u16tcf(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u16td(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u16tf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u16ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u16tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u16ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u16tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u16tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u16ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_u16tb(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-    void Arithmetic_internal_btcd(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_btcf(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_btd(boost::intrusive_ptr<Storage_base> &out,
-                                 boost::intrusive_ptr<Storage_base> &Lin,
-                                 boost::intrusive_ptr<Storage_base> &Rin,
-                                 const unsigned long long &len,
-                                 const std::vector<cytnx_uint64> &shape,
-                                 const std::vector<cytnx_uint64> &invmapper_L,
-                                 const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_btf(boost::intrusive_ptr<Storage_base> &out,
-                                 boost::intrusive_ptr<Storage_base> &Lin,
-                                 boost::intrusive_ptr<Storage_base> &Rin,
-                                 const unsigned long long &len,
-                                 const std::vector<cytnx_uint64> &shape,
-                                 const std::vector<cytnx_uint64> &invmapper_L,
-                                 const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_bti64(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_btu64(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_bti32(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_btu32(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_btu16(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_bti16(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void Arithmetic_internal_btb(boost::intrusive_ptr<Storage_base> &out,
-                                 boost::intrusive_ptr<Storage_base> &Lin,
-                                 boost::intrusive_ptr<Storage_base> &Rin,
-                                 const unsigned long long &len,
-                                 const std::vector<cytnx_uint64> &shape,
-                                 const std::vector<cytnx_uint64> &invmapper_L,
-                                 const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-  }  // namespace linalg_internal
-}  // namespace cytnx
-
-#endif  // CYTNX_BACKEND_LINALG_INTERNAL_CPU_ARITHMETIC_INTERNAL_H_
diff --git a/src/backend/linalg_internal_cpu/CMakeLists.txt b/src/backend/linalg_internal_cpu/CMakeLists.txt
index 29aa58257..3f00ecb4f 100644
--- a/src/backend/linalg_internal_cpu/CMakeLists.txt
+++ b/src/backend/linalg_internal_cpu/CMakeLists.txt
@@ -3,7 +3,6 @@ target_sources_local(cytnx
     Norm_internal.hpp
     Add_internal.hpp
     iAdd_internal.hpp
-    Arithmetic_internal.hpp
     iArithmetic_internal.hpp
     Conj_inplace_internal.hpp
     Cpr_internal.hpp
@@ -46,7 +45,6 @@ target_sources_local(cytnx
     memcpyTruncation.hpp
 
     iAdd_internal.cpp
-    Arithmetic_internal.cpp
     iArithmetic_internal.cpp
     Conj_inplace_internal.cpp
     Diag_internal.cpp
diff --git a/src/backend/linalg_internal_interface.cpp b/src/backend/linalg_internal_interface.cpp
index a2080c87a..fbb800d98 100644
--- a/src/backend/linalg_internal_interface.cpp
+++ b/src/backend/linalg_internal_interface.cpp
@@ -13,140 +13,6 @@ namespace cytnx {
 
     linalg_internal_interface::~linalg_internal_interface() {}
     linalg_internal_interface::linalg_internal_interface() {
-      Ari_ii = vector<vector<Arithmeticfunc_oii>>(N_Type, vector<Arithmeticfunc_oii>(N_Type, NULL));
-
-      Ari_ii[Type.ComplexDouble][Type.ComplexDouble] = Arithmetic_internal_cdtcd;
-      Ari_ii[Type.ComplexDouble][Type.ComplexFloat] = Arithmetic_internal_cdtcf;
-      Ari_ii[Type.ComplexDouble][Type.Double] = Arithmetic_internal_cdtd;
-      Ari_ii[Type.ComplexDouble][Type.Float] = Arithmetic_internal_cdtf;
-      Ari_ii[Type.ComplexDouble][Type.Int64] = Arithmetic_internal_cdti64;
-      Ari_ii[Type.ComplexDouble][Type.Uint64] = Arithmetic_internal_cdtu64;
-      Ari_ii[Type.ComplexDouble][Type.Int32] = Arithmetic_internal_cdti32;
-      Ari_ii[Type.ComplexDouble][Type.Uint32] = Arithmetic_internal_cdtu32;
-      Ari_ii[Type.ComplexDouble][Type.Uint16] = Arithmetic_internal_cdtu16;
-      Ari_ii[Type.ComplexDouble][Type.Int16] = Arithmetic_internal_cdti16;
-      Ari_ii[Type.ComplexDouble][Type.Bool] = Arithmetic_internal_cdtb;
-
-      Ari_ii[Type.ComplexFloat][Type.ComplexDouble] = Arithmetic_internal_cftcd;
-      Ari_ii[Type.ComplexFloat][Type.ComplexFloat] = Arithmetic_internal_cftcf;
-      Ari_ii[Type.ComplexFloat][Type.Double] = Arithmetic_internal_cftd;
-      Ari_ii[Type.ComplexFloat][Type.Float] = Arithmetic_internal_cftf;
-      Ari_ii[Type.ComplexFloat][Type.Int64] = Arithmetic_internal_cfti64;
-      Ari_ii[Type.ComplexFloat][Type.Uint64] = Arithmetic_internal_cftu64;
-      Ari_ii[Type.ComplexFloat][Type.Int32] = Arithmetic_internal_cfti32;
-      Ari_ii[Type.ComplexFloat][Type.Uint32] = Arithmetic_internal_cftu32;
-      Ari_ii[Type.ComplexFloat][Type.Uint16] = Arithmetic_internal_cftu16;
-      Ari_ii[Type.ComplexFloat][Type.Int16] = Arithmetic_internal_cfti16;
-      Ari_ii[Type.ComplexFloat][Type.Bool] = Arithmetic_internal_cftb;
-
-      Ari_ii[Type.Double][Type.ComplexDouble] = Arithmetic_internal_dtcd;
-      Ari_ii[Type.Double][Type.ComplexFloat] = Arithmetic_internal_dtcf;
-      Ari_ii[Type.Double][Type.Double] = Arithmetic_internal_dtd;
-      Ari_ii[Type.Double][Type.Float] = Arithmetic_internal_dtf;
-      Ari_ii[Type.Double][Type.Int64] = Arithmetic_internal_dti64;
-      Ari_ii[Type.Double][Type.Uint64] = Arithmetic_internal_dtu64;
-      Ari_ii[Type.Double][Type.Int32] = Arithmetic_internal_dti32;
-      Ari_ii[Type.Double][Type.Uint32] = Arithmetic_internal_dtu32;
-      Ari_ii[Type.Double][Type.Uint16] = Arithmetic_internal_dtu16;
-      Ari_ii[Type.Double][Type.Int16] = Arithmetic_internal_dti16;
-      Ari_ii[Type.Double][Type.Bool] = Arithmetic_internal_dtb;
-
-      Ari_ii[Type.Float][Type.ComplexDouble] = Arithmetic_internal_ftcd;
-      Ari_ii[Type.Float][Type.ComplexFloat] = Arithmetic_internal_ftcf;
-      Ari_ii[Type.Float][Type.Double] = Arithmetic_internal_ftd;
-      Ari_ii[Type.Float][Type.Float] = Arithmetic_internal_ftf;
-      Ari_ii[Type.Float][Type.Int64] = Arithmetic_internal_fti64;
-      Ari_ii[Type.Float][Type.Uint64] = Arithmetic_internal_ftu64;
-      Ari_ii[Type.Float][Type.Int32] = Arithmetic_internal_fti32;
-      Ari_ii[Type.Float][Type.Uint32] = Arithmetic_internal_ftu32;
-      Ari_ii[Type.Float][Type.Uint16] = Arithmetic_internal_ftu16;
-      Ari_ii[Type.Float][Type.Int16] = Arithmetic_internal_fti16;
-      Ari_ii[Type.Float][Type.Bool] = Arithmetic_internal_ftb;
-
-      Ari_ii[Type.Int64][Type.ComplexDouble] = Arithmetic_internal_i64tcd;
-      Ari_ii[Type.Int64][Type.ComplexFloat] = Arithmetic_internal_i64tcf;
-      Ari_ii[Type.Int64][Type.Double] = Arithmetic_internal_i64td;
-      Ari_ii[Type.Int64][Type.Float] = Arithmetic_internal_i64tf;
-      Ari_ii[Type.Int64][Type.Int64] = Arithmetic_internal_i64ti64;
-      Ari_ii[Type.Int64][Type.Uint64] = Arithmetic_internal_i64tu64;
-      Ari_ii[Type.Int64][Type.Int32] = Arithmetic_internal_i64ti32;
-      Ari_ii[Type.Int64][Type.Uint32] = Arithmetic_internal_i64tu32;
-      Ari_ii[Type.Int64][Type.Uint16] = Arithmetic_internal_i64tu16;
-      Ari_ii[Type.Int64][Type.Int16] = Arithmetic_internal_i64ti16;
-      Ari_ii[Type.Int64][Type.Bool] = Arithmetic_internal_i64tb;
-
-      Ari_ii[Type.Uint64][Type.ComplexDouble] = Arithmetic_internal_u64tcd;
-      Ari_ii[Type.Uint64][Type.ComplexFloat] = Arithmetic_internal_u64tcf;
-      Ari_ii[Type.Uint64][Type.Double] = Arithmetic_internal_u64td;
-      Ari_ii[Type.Uint64][Type.Float] = Arithmetic_internal_u64tf;
-      Ari_ii[Type.Uint64][Type.Int64] = Arithmetic_internal_u64ti64;
-      Ari_ii[Type.Uint64][Type.Uint64] = Arithmetic_internal_u64tu64;
-      Ari_ii[Type.Uint64][Type.Int32] = Arithmetic_internal_u64ti32;
-      Ari_ii[Type.Uint64][Type.Uint32] = Arithmetic_internal_u64tu32;
-      Ari_ii[Type.Uint64][Type.Uint16] = Arithmetic_internal_u64tu16;
-      Ari_ii[Type.Uint64][Type.Int16] = Arithmetic_internal_u64ti16;
-      Ari_ii[Type.Uint64][Type.Bool] = Arithmetic_internal_u64tb;
-
-      Ari_ii[Type.Int32][Type.ComplexDouble] = Arithmetic_internal_i32tcd;
-      Ari_ii[Type.Int32][Type.ComplexFloat] = Arithmetic_internal_i32tcf;
-      Ari_ii[Type.Int32][Type.Double] = Arithmetic_internal_i32td;
-      Ari_ii[Type.Int32][Type.Float] = Arithmetic_internal_i32tf;
-      Ari_ii[Type.Int32][Type.Int64] = Arithmetic_internal_i32ti64;
-      Ari_ii[Type.Int32][Type.Uint64] = Arithmetic_internal_i32tu64;
-      Ari_ii[Type.Int32][Type.Int32] = Arithmetic_internal_i32ti32;
-      Ari_ii[Type.Int32][Type.Uint32] = Arithmetic_internal_i32tu32;
-      Ari_ii[Type.Int32][Type.Uint16] = Arithmetic_internal_i32tu16;
-      Ari_ii[Type.Int32][Type.Int16] = Arithmetic_internal_i32ti16;
-      Ari_ii[Type.Int32][Type.Bool] = Arithmetic_internal_i32tb;
-
-      Ari_ii[Type.Uint32][Type.ComplexDouble] = Arithmetic_internal_u32tcd;
-      Ari_ii[Type.Uint32][Type.ComplexFloat] = Arithmetic_internal_u32tcf;
-      Ari_ii[Type.Uint32][Type.Double] = Arithmetic_internal_u32td;
-      Ari_ii[Type.Uint32][Type.Float] = Arithmetic_internal_u32tf;
-      Ari_ii[Type.Uint32][Type.Int64] = Arithmetic_internal_u32ti64;
-      Ari_ii[Type.Uint32][Type.Uint64] = Arithmetic_internal_u32tu64;
-      Ari_ii[Type.Uint32][Type.Int32] = Arithmetic_internal_u32ti32;
-      Ari_ii[Type.Uint32][Type.Uint32] = Arithmetic_internal_u32tu32;
-      Ari_ii[Type.Uint32][Type.Uint16] = Arithmetic_internal_u32tu16;
-      Ari_ii[Type.Uint32][Type.Int16] = Arithmetic_internal_u32ti16;
-      Ari_ii[Type.Uint32][Type.Bool] = Arithmetic_internal_u32tb;
-
-      Ari_ii[Type.Int16][Type.ComplexDouble] = Arithmetic_internal_i16tcd;
-      Ari_ii[Type.Int16][Type.ComplexFloat] = Arithmetic_internal_i16tcf;
-      Ari_ii[Type.Int16][Type.Double] = Arithmetic_internal_i16td;
-      Ari_ii[Type.Int16][Type.Float] = Arithmetic_internal_i16tf;
-      Ari_ii[Type.Int16][Type.Int64] = Arithmetic_internal_i16ti64;
-      Ari_ii[Type.Int16][Type.Uint64] = Arithmetic_internal_i16tu64;
-      Ari_ii[Type.Int16][Type.Int32] = Arithmetic_internal_i16ti32;
-      Ari_ii[Type.Int16][Type.Uint32] = Arithmetic_internal_i16tu32;
-      Ari_ii[Type.Int16][Type.Uint16] = Arithmetic_internal_i16tu16;
-      Ari_ii[Type.Int16][Type.Int16] = Arithmetic_internal_i16ti16;
-      Ari_ii[Type.Int16][Type.Bool] = Arithmetic_internal_i16tb;
-
-      Ari_ii[Type.Uint16][Type.ComplexDouble] = Arithmetic_internal_u16tcd;
-      Ari_ii[Type.Uint16][Type.ComplexFloat] = Arithmetic_internal_u16tcf;
-      Ari_ii[Type.Uint16][Type.Double] = Arithmetic_internal_u16td;
-      Ari_ii[Type.Uint16][Type.Float] = Arithmetic_internal_u16tf;
-      Ari_ii[Type.Uint16][Type.Int64] = Arithmetic_internal_u16ti64;
-      Ari_ii[Type.Uint16][Type.Uint64] = Arithmetic_internal_u16tu64;
-      Ari_ii[Type.Uint16][Type.Int32] = Arithmetic_internal_u16ti32;
-      Ari_ii[Type.Uint16][Type.Uint32] = Arithmetic_internal_u16tu32;
-      Ari_ii[Type.Uint16][Type.Uint16] = Arithmetic_internal_u16tu16;
-      Ari_ii[Type.Uint16][Type.Int16] = Arithmetic_internal_u16ti16;
-      Ari_ii[Type.Uint16][Type.Bool] = Arithmetic_internal_u16tb;
-
-      Ari_ii[Type.Bool][Type.ComplexDouble] = Arithmetic_internal_btcd;
-      Ari_ii[Type.Bool][Type.ComplexFloat] = Arithmetic_internal_btcf;
-      Ari_ii[Type.Bool][Type.Double] = Arithmetic_internal_btd;
-      Ari_ii[Type.Bool][Type.Float] = Arithmetic_internal_btf;
-      Ari_ii[Type.Bool][Type.Int64] = Arithmetic_internal_bti64;
-      Ari_ii[Type.Bool][Type.Uint64] = Arithmetic_internal_btu64;
-      Ari_ii[Type.Bool][Type.Int32] = Arithmetic_internal_bti32;
-      Ari_ii[Type.Bool][Type.Uint32] = Arithmetic_internal_btu32;
-      Ari_ii[Type.Bool][Type.Uint16] = Arithmetic_internal_btu16;
-      Ari_ii[Type.Bool][Type.Int16] = Arithmetic_internal_bti16;
-      Ari_ii[Type.Bool][Type.Bool] = Arithmetic_internal_btb;
-
       iAri_ii =
         vector<vector<Arithmeticfunc_oii>>(N_Type, vector<Arithmeticfunc_oii>(N_Type, NULL));
 
diff --git a/src/backend/linalg_internal_interface.hpp b/src/backend/linalg_internal_interface.hpp
index 5835a7ecb..df53fa504 100644
--- a/src/backend/linalg_internal_interface.hpp
+++ b/src/backend/linalg_internal_interface.hpp
@@ -8,11 +8,13 @@
 #include "backend/Scalar.hpp"
 #include "backend/Storage.hpp"
 #include "linalg_internal_cpu/Abs_internal.hpp"
-#include "linalg_internal_cpu/Arithmetic_internal.hpp"
+#include "linalg_internal_cpu/Add_internal.hpp"
 #include "linalg_internal_cpu/Axpy_internal.hpp"
 #include "linalg_internal_cpu/Conj_inplace_internal.hpp"
+#include "linalg_internal_cpu/Cpr_internal.hpp"
 #include "linalg_internal_cpu/Det_internal.hpp"
 #include "linalg_internal_cpu/Diag_internal.hpp"
+#include "linalg_internal_cpu/Div_internal.hpp"
 #include "linalg_internal_cpu/Eig_internal.hpp"
 #include "linalg_internal_cpu/Eigh_internal.hpp"
 #include "linalg_internal_cpu/Exp_internal.hpp"
@@ -27,11 +29,14 @@
 #include "linalg_internal_cpu/Matmul_internal.hpp"
 #include "linalg_internal_cpu/Matvec_internal.hpp"
 #include "linalg_internal_cpu/MaxMin_internal.hpp"
+#include "linalg_internal_cpu/Mod_internal.hpp"
+#include "linalg_internal_cpu/Mul_internal.hpp"
 #include "linalg_internal_cpu/Norm_internal.hpp"
 #include "linalg_internal_cpu/Outer_internal.hpp"
 #include "linalg_internal_cpu/Pow_internal.hpp"
 #include "linalg_internal_cpu/QR_internal.hpp"
 #include "linalg_internal_cpu/Sdd_internal.hpp"
+#include "linalg_internal_cpu/Sub_internal.hpp"
 #include "linalg_internal_cpu/Sum_internal.hpp"
 #include "linalg_internal_cpu/Trace_internal.hpp"
 #include "linalg_internal_cpu/Tridiag_internal.hpp"
@@ -212,7 +217,6 @@ namespace cytnx {
 #endif
     class linalg_internal_interface {
      public:
-      std::vector<std::vector<Arithmeticfunc_oii>> Ari_ii;
       std::vector<std::vector<Arithmeticfunc_oii>> iAri_ii;
       std::vector<Svdfunc_oii> Sdd_ii;
       std::vector<Svdfunc_oii> Gesvd_ii;
diff --git a/src/linalg/Add.cpp b/src/linalg/Add.cpp
index e0193e76f..4ee3bad05 100644
--- a/src/linalg/Add.cpp
+++ b/src/linalg/Add.cpp
@@ -41,9 +41,19 @@ namespace cytnx {
       if ((Lt.is_contiguous() && Rt.is_contiguous()) || icnst) {
         // contiguous section.
         if (Lt.device() == Device.cpu) {
-          cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Rt.dtype()](
-            out._impl->storage()._impl, Lt._impl->storage()._impl, Rt._impl->storage()._impl,
-            out._impl->storage()._impl->size(), {}, {}, {}, 0);
+          std::visit(
+            [&](auto *lptr) {
+              using TL = std::remove_pointer_t<decltype(lptr)>;
+              std::visit(
+                [&](auto *rptr) {
+                  using TR = std::remove_pointer_t<decltype(rptr)>;
+                  cytnx::linalg_internal::AddInternalImpl<TL, TR>(
+                    out._impl->storage()._impl, Lt._impl->storage()._impl,
+                    Rt._impl->storage()._impl, out._impl->storage()._impl->size(), {}, {}, {});
+                },
+                Rt.ptr());
+            },
+            Lt.ptr());
         } else {
   #ifdef UNI_GPU
           checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -58,10 +68,20 @@ namespace cytnx {
       } else {
         // non-contiguous section
         if (Lt.device() == Device.cpu) {
-          linalg_internal::lii.Ari_ii[Lt.dtype()][Rt.dtype()](
-            out._impl->storage()._impl, Lt._impl->storage()._impl, Rt._impl->storage()._impl,
-            Lt._impl->storage()._impl->size(), Lt._impl->shape(), Lt._impl->invmapper(),
-            Rt._impl->invmapper(), 0);
+          std::visit(
+            [&](auto *lptr) {
+              using TL = std::remove_pointer_t<decltype(lptr)>;
+              std::visit(
+                [&](auto *rptr) {
+                  using TR = std::remove_pointer_t<decltype(rptr)>;
+                  cytnx::linalg_internal::AddInternalImpl<TL, TR>(
+                    out._impl->storage()._impl, Lt._impl->storage()._impl,
+                    Rt._impl->storage()._impl, Lt._impl->storage()._impl->size(), Lt._impl->shape(),
+                    Lt._impl->invmapper(), Rt._impl->invmapper());
+                },
+                Rt.ptr());
+            },
+            Lt.ptr());
         } else {
   #ifdef UNI_GPU
           linalg_internal::lii.cuAri_ii[Lt.dtype()][Rt.dtype()](
@@ -88,9 +108,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.ComplexDouble,Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        linalg_internal::lii.Ari_ii[Type.ComplexDouble][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::AddInternalImpl<cytnx_complex128, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -119,9 +144,14 @@ namespace cytnx {
       // Rt.dtype()?Type.ComplexFloat:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        linalg_internal::lii.Ari_ii[Type.ComplexFloat][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::AddInternalImpl<cytnx_complex64, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -149,9 +179,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Double < Rt.dtype()?Type.Double:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        linalg_internal::lii.Ari_ii[Type.Double][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::AddInternalImpl<cytnx_double, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -178,9 +213,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Float < Rt.dtype()?Type.Float:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        linalg_internal::lii.Ari_ii[Type.Float][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::AddInternalImpl<cytnx_float, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -207,9 +247,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Int64 < Rt.dtype()?Type.Int64:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        linalg_internal::lii.Ari_ii[Type.Int64][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::AddInternalImpl<cytnx_int64, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -237,9 +282,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Uint64 < Rt.dtype()?Type.Uint64:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        linalg_internal::lii.Ari_ii[Type.Uint64][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::AddInternalImpl<cytnx_uint64, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -266,9 +316,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Int32 < Rt.dtype()?Type.Int32:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        linalg_internal::lii.Ari_ii[Type.Int32][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::AddInternalImpl<cytnx_int32, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -296,9 +351,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Uint32 < Rt.dtype()?Type.Uint32:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        linalg_internal::lii.Ari_ii[Type.Uint32][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::AddInternalImpl<cytnx_uint32, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -325,9 +385,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Int16 < Rt.dtype()?Type.Int16:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        linalg_internal::lii.Ari_ii[Type.Int16][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::AddInternalImpl<cytnx_int16, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -355,9 +420,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Uint16 < Rt.dtype()?Type.Uint16:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        linalg_internal::lii.Ari_ii[Type.Uint16][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::AddInternalImpl<cytnx_uint16, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -384,9 +454,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Bool < Rt.dtype()?Type.Bool:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        linalg_internal::lii.Ari_ii[Type.Bool][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::AddInternalImpl<cytnx_bool, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -413,9 +488,19 @@ namespace cytnx {
         Rt._impl->storage().size(), lc.dtype() < Rt.dtype() ? lc.dtype() : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        linalg_internal::lii.Ari_ii[lc.dtype()][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            std::visit(
+              [&](auto *rptr) {
+                using TR = std::remove_pointer_t<decltype(rptr)>;
+                cytnx::linalg_internal::AddInternalImpl<TL, TR>(
+                  out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+                  Rt._impl->storage()._impl->size(), {}, {}, {});
+              },
+              Rt.ptr());
+          },
+          Tensor::from_storage(Cnst).ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
diff --git a/src/linalg/Cpr.cpp b/src/linalg/Cpr.cpp
index e6214b3a6..6692ca870 100644
--- a/src/linalg/Cpr.cpp
+++ b/src/linalg/Cpr.cpp
@@ -22,9 +22,19 @@ namespace cytnx {
       if (Lt.is_contiguous() && Rt.is_contiguous()) {
         // contiguous section.
         if (Lt.device() == Device.cpu) {
-          cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Rt.dtype()](
-            out._impl->storage()._impl, Lt._impl->storage()._impl, Rt._impl->storage()._impl,
-            Lt._impl->storage()._impl->size(), {}, {}, {}, 4);
+          std::visit(
+            [&](auto *lptr) {
+              using TL = std::remove_pointer_t<decltype(lptr)>;
+              std::visit(
+                [&](auto *rptr) {
+                  using TR = std::remove_pointer_t<decltype(rptr)>;
+                  cytnx::linalg_internal::CprInternalImpl<TL, TR>(
+                    out._impl->storage()._impl, Lt._impl->storage()._impl,
+                    Rt._impl->storage()._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
+                },
+                Rt.ptr());
+            },
+            Lt.ptr());
         } else {
   #ifdef UNI_GPU
           checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -39,10 +49,20 @@ namespace cytnx {
       } else {
         // non-contiguous section
         if (Lt.device() == Device.cpu) {
-          cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Rt.dtype()](
-            out._impl->storage()._impl, Lt._impl->storage()._impl, Rt._impl->storage()._impl,
-            Lt._impl->storage()._impl->size(), Lt._impl->shape(), Lt._impl->invmapper(),
-            Rt._impl->invmapper(), 4);
+          std::visit(
+            [&](auto *lptr) {
+              using TL = std::remove_pointer_t<decltype(lptr)>;
+              std::visit(
+                [&](auto *rptr) {
+                  using TR = std::remove_pointer_t<decltype(rptr)>;
+                  cytnx::linalg_internal::CprInternalImpl<TL, TR>(
+                    out._impl->storage()._impl, Lt._impl->storage()._impl,
+                    Rt._impl->storage()._impl, Lt._impl->storage()._impl->size(), Lt._impl->shape(),
+                    Lt._impl->invmapper(), Rt._impl->invmapper());
+                },
+                Rt.ptr());
+            },
+            Lt.ptr());
         } else {
   #ifdef UNI_GPU
           cytnx_error_msg(true,
@@ -67,9 +87,14 @@ namespace cytnx {
       Tensor out(Rt.shape(), Type.Bool, Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.ComplexDouble][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 4);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::CprInternalImpl<cytnx_complex128, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -93,9 +118,14 @@ namespace cytnx {
       Tensor out(Rt.shape(), Type.Bool, Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.ComplexFloat][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 4);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::CprInternalImpl<cytnx_complex64, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -119,9 +149,14 @@ namespace cytnx {
       Tensor out(Rt.shape(), Type.Bool, Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Double][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 4);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::CprInternalImpl<cytnx_double, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -145,9 +180,14 @@ namespace cytnx {
       Tensor out(Rt.shape(), Type.Bool, Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Float][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 4);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::CprInternalImpl<cytnx_float, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -171,9 +211,14 @@ namespace cytnx {
       Tensor out(Rt.shape(), Type.Bool, Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Int64][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 4);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::CprInternalImpl<cytnx_int64, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -197,9 +242,14 @@ namespace cytnx {
       Tensor out(Rt.shape(), Type.Bool, Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Uint64][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 4);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::CprInternalImpl<cytnx_uint64, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -223,9 +273,14 @@ namespace cytnx {
       Tensor out(Rt.shape(), Type.Bool, Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Int32][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 4);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::CprInternalImpl<cytnx_int32, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -249,9 +304,14 @@ namespace cytnx {
       Tensor out(Rt.shape(), Type.Bool, Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Uint32][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 4);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::CprInternalImpl<cytnx_uint32, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -275,9 +335,14 @@ namespace cytnx {
       Tensor out(Rt.shape(), Type.Bool, Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Int16][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 4);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::CprInternalImpl<cytnx_int16, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -301,9 +366,14 @@ namespace cytnx {
       Tensor out(Rt.shape(), Type.Bool, Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Uint16][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 4);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::CprInternalImpl<cytnx_uint16, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -327,9 +397,14 @@ namespace cytnx {
       Tensor out(Rt.shape(), Type.Bool, Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Bool][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 4);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::CprInternalImpl<cytnx_bool, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -353,9 +428,19 @@ namespace cytnx {
       Tensor out(Rt.shape(), Type.Bool, Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[lc.dtype()][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 4);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            std::visit(
+              [&](auto *rptr) {
+                using TR = std::remove_pointer_t<decltype(rptr)>;
+                cytnx::linalg_internal::CprInternalImpl<TL, TR>(
+                  out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+                  Rt._impl->storage()._impl->size(), {}, {}, {});
+              },
+              Rt.ptr());
+          },
+          Tensor::from_storage(Cnst).ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
diff --git a/src/linalg/Div.cpp b/src/linalg/Div.cpp
index 2dad1e956..80d7fa0af 100644
--- a/src/linalg/Div.cpp
+++ b/src/linalg/Div.cpp
@@ -37,9 +37,19 @@ namespace cytnx {
       if ((Lt.is_contiguous() && Rt.is_contiguous()) || icnst) {
         // contiguous section
         if (Lt.device() == Device.cpu) {
-          cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Rt.dtype()](
-            out._impl->storage()._impl, Lt._impl->storage()._impl, Rt._impl->storage()._impl,
-            out._impl->storage()._impl->size(), {}, {}, {}, 3);
+          std::visit(
+            [&](auto *lptr) {
+              using TL = std::remove_pointer_t<decltype(lptr)>;
+              std::visit(
+                [&](auto *rptr) {
+                  using TR = std::remove_pointer_t<decltype(rptr)>;
+                  cytnx::linalg_internal::DivInternalImpl<TL, TR>(
+                    out._impl->storage()._impl, Lt._impl->storage()._impl,
+                    Rt._impl->storage()._impl, out._impl->storage()._impl->size(), {}, {}, {});
+                },
+                Rt.ptr());
+            },
+            Lt.ptr());
         } else {
   #ifdef UNI_GPU
           checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -54,10 +64,20 @@ namespace cytnx {
       } else {
         // non-contiguous section
         if (Lt.device() == Device.cpu) {
-          cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Rt.dtype()](
-            out._impl->storage()._impl, Lt._impl->storage()._impl, Rt._impl->storage()._impl,
-            Lt._impl->storage()._impl->size(), Lt._impl->shape(), Lt._impl->invmapper(),
-            Rt._impl->invmapper(), 3);
+          std::visit(
+            [&](auto *lptr) {
+              using TL = std::remove_pointer_t<decltype(lptr)>;
+              std::visit(
+                [&](auto *rptr) {
+                  using TR = std::remove_pointer_t<decltype(rptr)>;
+                  cytnx::linalg_internal::DivInternalImpl<TL, TR>(
+                    out._impl->storage()._impl, Lt._impl->storage()._impl,
+                    Rt._impl->storage()._impl, Lt._impl->storage()._impl->size(), Lt._impl->shape(),
+                    Lt._impl->invmapper(), Rt._impl->invmapper());
+                },
+                Rt.ptr());
+            },
+            Lt.ptr());
         } else {
   #ifdef UNI_GPU
           cytnx_error_msg(true,
@@ -84,9 +104,14 @@ namespace cytnx {
       out._impl->storage() = Storage(Rt._impl->storage().size(), Type.ComplexDouble, Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.ComplexDouble][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::DivInternalImpl<cytnx_complex128, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -116,9 +141,14 @@ namespace cytnx {
       // Rt.dtype()?Type.ComplexFloat:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.ComplexFloat][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::DivInternalImpl<cytnx_complex64, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -146,9 +176,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Double < Rt.dtype()?Type.Double:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Double][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::DivInternalImpl<cytnx_double, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         cytnx::linalg_internal::lii.cuAri_ii[Type.Double][Rt.dtype()](
@@ -174,9 +209,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Float < Rt.dtype()?Type.Float:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Float][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::DivInternalImpl<cytnx_float, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -203,9 +243,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Int64 < Rt.dtype()?Type.Int64:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Int64][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::DivInternalImpl<cytnx_int64, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         cytnx::linalg_internal::lii.cuAri_ii[Type.Int64][Rt.dtype()](
@@ -232,9 +277,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Uint64 < Rt.dtype()?Type.Uint64:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Uint64][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::DivInternalImpl<cytnx_uint64, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -261,9 +311,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Int32 < Rt.dtype()?Type.Int32:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Int32][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::DivInternalImpl<cytnx_int32, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -291,9 +346,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Uint32 < Rt.dtype()?Type.Uint32:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Uint32][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::DivInternalImpl<cytnx_uint32, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -320,9 +380,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Int16 < Rt.dtype()?Type.Int16:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Int16][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::DivInternalImpl<cytnx_int16, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -350,9 +415,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Uint16 < Rt.dtype()?Type.Uint16:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Uint16][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::DivInternalImpl<cytnx_uint16, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -379,9 +449,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Bool < Rt.dtype()?Type.Bool:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Bool][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::DivInternalImpl<cytnx_bool, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -408,9 +483,19 @@ namespace cytnx {
         Rt._impl->storage().size(), lc.dtype() < Rt.dtype() ? lc.dtype() : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        linalg_internal::lii.Ari_ii[lc.dtype()][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            std::visit(
+              [&](auto *rptr) {
+                using TR = std::remove_pointer_t<decltype(rptr)>;
+                cytnx::linalg_internal::DivInternalImpl<TL, TR>(
+                  out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+                  Rt._impl->storage()._impl->size(), {}, {}, {});
+              },
+              Rt.ptr());
+          },
+          Tensor::from_storage(Cnst).ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -436,9 +521,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(),Type.ComplexDouble,Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.ComplexDouble](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::DivInternalImpl<TL, cytnx_complex128>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -466,9 +556,14 @@ namespace cytnx {
       // Lt.dtype()?Type.ComplexFloat:Lt.dtype(),Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.ComplexFloat](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::DivInternalImpl<TL, cytnx_complex64>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -496,9 +591,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(),Type.Double < Lt.dtype()?Type.Double:Lt.dtype(),Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Double](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::DivInternalImpl<TL, cytnx_double>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -524,9 +624,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(),Type.Float < Lt.dtype()?Type.Float:Lt.dtype(),Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Float](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::DivInternalImpl<TL, cytnx_float>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -552,9 +657,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(),Type.Int64 < Lt.dtype()?Type.Int64:Lt.dtype(),Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Int64](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::DivInternalImpl<TL, cytnx_int64>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -581,9 +691,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(),Type.Uint64 < Lt.dtype()?Type.Uint64:Lt.dtype(),Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Uint64](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::DivInternalImpl<TL, cytnx_uint64>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -610,9 +725,14 @@ namespace cytnx {
 
       if (Lt.device() == Device.cpu) {
         // std::cout << "chk" << std::endl;
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Int32](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::DivInternalImpl<TL, cytnx_int32>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -639,9 +759,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(),Type.Uint32 < Lt.dtype()?Type.Uint32:Lt.dtype(),Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Uint32](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::DivInternalImpl<TL, cytnx_uint32>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -668,9 +793,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(),Type.Int16 < Lt.dtype()?Type.Int16:Lt.dtype(),Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Int16](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::DivInternalImpl<TL, cytnx_int16>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -697,9 +827,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(),Type.Uint16 < Lt.dtype()?Type.Uint16:Lt.dtype(),Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Uint16](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::DivInternalImpl<TL, cytnx_uint16>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -725,9 +860,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(),Type.Bool < Lt.dtype()?Type.Bool:Lt.dtype(),Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Bool](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::DivInternalImpl<TL, cytnx_bool>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -754,9 +894,19 @@ namespace cytnx {
         Lt._impl->storage().size(), Lt.dtype() < rc.dtype() ? Lt.dtype() : rc.dtype(), Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        linalg_internal::lii.Ari_ii[Lt.dtype()][rc.dtype()](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            std::visit(
+              [&](auto *rptr) {
+                using TR = std::remove_pointer_t<decltype(rptr)>;
+                cytnx::linalg_internal::DivInternalImpl<TL, TR>(
+                  out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+                  Lt._impl->storage()._impl->size(), {}, {}, {});
+              },
+              Tensor::from_storage(Cnst).ptr());
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
diff --git a/src/linalg/Mod.cpp b/src/linalg/Mod.cpp
index 80880a20f..e26496ead 100644
--- a/src/linalg/Mod.cpp
+++ b/src/linalg/Mod.cpp
@@ -30,9 +30,19 @@ namespace cytnx {
       if ((Lt.is_contiguous() && Rt.is_contiguous()) || icnst) {
         // contiguous section
         if (Lt.device() == Device.cpu) {
-          cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Rt.dtype()](
-            out._impl->storage()._impl, Lt._impl->storage()._impl, Rt._impl->storage()._impl,
-            out._impl->storage()._impl->size(), {}, {}, {}, 5);
+          std::visit(
+            [&](auto *lptr) {
+              using TL = std::remove_pointer_t<decltype(lptr)>;
+              std::visit(
+                [&](auto *rptr) {
+                  using TR = std::remove_pointer_t<decltype(rptr)>;
+                  cytnx::linalg_internal::ModInternalImpl<TL, TR>(
+                    out._impl->storage()._impl, Lt._impl->storage()._impl,
+                    Rt._impl->storage()._impl, out._impl->storage()._impl->size(), {}, {}, {});
+                },
+                Rt.ptr());
+            },
+            Lt.ptr());
         } else {
   #ifdef UNI_GPU
           checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -47,10 +57,20 @@ namespace cytnx {
       } else {
         // non-contiguous section
         if (Lt.device() == Device.cpu) {
-          cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Rt.dtype()](
-            out._impl->storage()._impl, Lt._impl->storage()._impl, Rt._impl->storage()._impl,
-            Lt._impl->storage()._impl->size(), Lt._impl->shape(), Lt._impl->invmapper(),
-            Rt._impl->invmapper(), 5);
+          std::visit(
+            [&](auto *lptr) {
+              using TL = std::remove_pointer_t<decltype(lptr)>;
+              std::visit(
+                [&](auto *rptr) {
+                  using TR = std::remove_pointer_t<decltype(rptr)>;
+                  cytnx::linalg_internal::ModInternalImpl<TL, TR>(
+                    out._impl->storage()._impl, Lt._impl->storage()._impl,
+                    Rt._impl->storage()._impl, Lt._impl->storage()._impl->size(), Lt._impl->shape(),
+                    Lt._impl->invmapper(), Rt._impl->invmapper());
+                },
+                Rt.ptr());
+            },
+            Lt.ptr());
         } else {
   #ifdef UNI_GPU
           cytnx_error_msg(true,
@@ -77,9 +97,14 @@ namespace cytnx {
       out._impl->storage() = Storage(Rt._impl->storage().size(), Type.ComplexDouble, Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.ComplexDouble][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::ModInternalImpl<cytnx_complex128, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -109,9 +134,14 @@ namespace cytnx {
       // Rt.dtype()?Type.ComplexFloat:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.ComplexFloat][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::ModInternalImpl<cytnx_complex64, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -139,9 +169,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Double < Rt.dtype()?Type.Double:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Double][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::ModInternalImpl<cytnx_double, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         cytnx::linalg_internal::lii.cuAri_ii[Type.Double][Rt.dtype()](
@@ -167,9 +202,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Float < Rt.dtype()?Type.Float:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Float][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::ModInternalImpl<cytnx_float, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -196,9 +236,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Int64 < Rt.dtype()?Type.Int64:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Int64][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::ModInternalImpl<cytnx_int64, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         cytnx::linalg_internal::lii.cuAri_ii[Type.Int64][Rt.dtype()](
@@ -225,9 +270,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Uint64 < Rt.dtype()?Type.Uint64:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Uint64][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::ModInternalImpl<cytnx_uint64, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -254,9 +304,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Int32 < Rt.dtype()?Type.Int32:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Int32][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::ModInternalImpl<cytnx_int32, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -284,9 +339,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Uint32 < Rt.dtype()?Type.Uint32:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Uint32][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::ModInternalImpl<cytnx_uint32, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -313,9 +373,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Int16 < Rt.dtype()?Type.Int16:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Int16][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::ModInternalImpl<cytnx_int16, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -343,9 +408,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Uint16 < Rt.dtype()?Type.Uint16:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Uint16][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::ModInternalImpl<cytnx_uint16, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -372,9 +442,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Bool < Rt.dtype()?Type.Bool:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Bool][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::ModInternalImpl<cytnx_bool, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -402,9 +477,19 @@ namespace cytnx {
       // Tensor out(Rt.shape(),Type.Bool < Rt.dtype()?Type.Bool:Rt.dtype(),Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[lc.dtype()][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            std::visit(
+              [&](auto *rptr) {
+                using TR = std::remove_pointer_t<decltype(rptr)>;
+                cytnx::linalg_internal::ModInternalImpl<TL, TR>(
+                  out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+                  Rt._impl->storage()._impl->size(), {}, {}, {});
+              },
+              Rt.ptr());
+          },
+          Tensor::from_storage(Cnst).ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -431,9 +516,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(),Type.ComplexDouble,Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.ComplexDouble](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::ModInternalImpl<TL, cytnx_complex128>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -461,9 +551,14 @@ namespace cytnx {
       // Lt.dtype()?Type.ComplexFloat:Lt.dtype(),Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.ComplexFloat](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::ModInternalImpl<TL, cytnx_complex64>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -491,9 +586,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(),Type.Double < Lt.dtype()?Type.Double:Lt.dtype(),Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Double](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::ModInternalImpl<TL, cytnx_double>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -519,9 +619,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(),Type.Float < Lt.dtype()?Type.Float:Lt.dtype(),Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Float](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::ModInternalImpl<TL, cytnx_float>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -547,9 +652,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(),Type.Int64 < Lt.dtype()?Type.Int64:Lt.dtype(),Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Int64](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::ModInternalImpl<TL, cytnx_int64>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -576,9 +686,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(),Type.Uint64 < Lt.dtype()?Type.Uint64:Lt.dtype(),Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Uint64](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::ModInternalImpl<TL, cytnx_uint64>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -604,9 +719,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(),Type.Int32 < Lt.dtype()?Type.Int32:Lt.dtype(),Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Int32](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::ModInternalImpl<TL, cytnx_int32>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -633,9 +753,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(),Type.Uint32 < Lt.dtype()?Type.Uint32:Lt.dtype(),Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Uint32](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::ModInternalImpl<TL, cytnx_uint32>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -662,9 +787,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(),Type.Int16 < Lt.dtype()?Type.Int16:Lt.dtype(),Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Int16](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::ModInternalImpl<TL, cytnx_int16>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -691,9 +821,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(),Type.Uint16 < Lt.dtype()?Type.Uint16:Lt.dtype(),Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Uint16](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::ModInternalImpl<TL, cytnx_uint16>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -719,9 +854,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(),Type.Bool < Lt.dtype()?Type.Bool:Lt.dtype(),Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Bool](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::ModInternalImpl<TL, cytnx_bool>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -749,9 +889,19 @@ namespace cytnx {
       // Tensor out(Lt.shape(),Type.Bool < Lt.dtype()?Type.Bool:Lt.dtype(),Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][rc.dtype()](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 5);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            std::visit(
+              [&](auto *rptr) {
+                using TR = std::remove_pointer_t<decltype(rptr)>;
+                cytnx::linalg_internal::ModInternalImpl<TL, TR>(
+                  out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+                  Lt._impl->storage()._impl->size(), {}, {}, {});
+              },
+              Tensor::from_storage(Cnst).ptr());
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
diff --git a/src/linalg/Mul.cpp b/src/linalg/Mul.cpp
index 7469a3747..76555a127 100644
--- a/src/linalg/Mul.cpp
+++ b/src/linalg/Mul.cpp
@@ -37,9 +37,19 @@ namespace cytnx {
       if ((Lt.is_contiguous() && Rt.is_contiguous()) || icnst) {
         // contiguous section
         if (Lt.device() == Device.cpu) {
-          cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Rt.dtype()](
-            out._impl->storage()._impl, Lt._impl->storage()._impl, Rt._impl->storage()._impl,
-            out._impl->storage()._impl->size(), {}, {}, {}, 1);
+          std::visit(
+            [&](auto *lptr) {
+              using TL = std::remove_pointer_t<decltype(lptr)>;
+              std::visit(
+                [&](auto *rptr) {
+                  using TR = std::remove_pointer_t<decltype(rptr)>;
+                  cytnx::linalg_internal::MulInternalImpl<TL, TR>(
+                    out._impl->storage()._impl, Lt._impl->storage()._impl,
+                    Rt._impl->storage()._impl, out._impl->storage()._impl->size(), {}, {}, {});
+                },
+                Rt.ptr());
+            },
+            Lt.ptr());
         } else {
   #ifdef UNI_GPU
           checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -54,10 +64,20 @@ namespace cytnx {
       } else {
         // non-contiguous section
         if (Lt.device() == Device.cpu) {
-          cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Rt.dtype()](
-            out._impl->storage()._impl, Lt._impl->storage()._impl, Rt._impl->storage()._impl,
-            Lt._impl->storage()._impl->size(), Lt._impl->shape(), Lt._impl->invmapper(),
-            Rt._impl->invmapper(), 1);
+          std::visit(
+            [&](auto *lptr) {
+              using TL = std::remove_pointer_t<decltype(lptr)>;
+              std::visit(
+                [&](auto *rptr) {
+                  using TR = std::remove_pointer_t<decltype(rptr)>;
+                  cytnx::linalg_internal::MulInternalImpl<TL, TR>(
+                    out._impl->storage()._impl, Lt._impl->storage()._impl,
+                    Rt._impl->storage()._impl, Lt._impl->storage()._impl->size(), Lt._impl->shape(),
+                    Lt._impl->invmapper(), Rt._impl->invmapper());
+                },
+                Rt.ptr());
+            },
+            Lt.ptr());
         } else {
   #ifdef UNI_GPU
           cytnx_error_msg(true,
@@ -85,9 +105,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(), Type.ComplexDouble, Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.ComplexDouble][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::MulInternalImpl<cytnx_complex128, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -116,9 +141,14 @@ namespace cytnx {
       // Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.ComplexFloat][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::MulInternalImpl<cytnx_complex64, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -146,9 +176,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(), Type.Double < Rt.dtype() ? Type.Double : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Double][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::MulInternalImpl<cytnx_double, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -175,9 +210,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(), Type.Float < Rt.dtype() ? Type.Float : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Float][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::MulInternalImpl<cytnx_float, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -204,9 +244,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(), Type.Int64 < Rt.dtype() ? Type.Int64 : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Int64][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::MulInternalImpl<cytnx_int64, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -234,9 +279,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(), Type.Uint64 < Rt.dtype() ? Type.Uint64 : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Uint64][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::MulInternalImpl<cytnx_uint64, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -263,9 +313,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(), Type.Int32 < Rt.dtype() ? Type.Int32 : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Int32][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::MulInternalImpl<cytnx_int32, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -293,9 +348,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(), Type.Uint32 < Rt.dtype() ? Type.Uint32 : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Uint32][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::MulInternalImpl<cytnx_uint32, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -322,9 +382,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(), Type.Int16 < Rt.dtype() ? Type.Int16 : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Int16][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::MulInternalImpl<cytnx_int16, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -352,9 +417,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(), Type.Uint16 < Rt.dtype() ? Type.Uint16 : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Uint16][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::MulInternalImpl<cytnx_uint16, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -381,9 +451,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(), Type.Bool < Rt.dtype() ? Type.Bool : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Bool][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::MulInternalImpl<cytnx_bool, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -410,9 +485,19 @@ namespace cytnx {
         Rt._impl->storage().size(), lc.dtype() < Rt.dtype() ? lc.dtype() : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        linalg_internal::lii.Ari_ii[lc.dtype()][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            std::visit(
+              [&](auto *rptr) {
+                using TR = std::remove_pointer_t<decltype(rptr)>;
+                cytnx::linalg_internal::MulInternalImpl<TL, TR>(
+                  out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+                  Rt._impl->storage()._impl->size(), {}, {}, {});
+              },
+              Rt.ptr());
+          },
+          Tensor::from_storage(Cnst).ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
diff --git a/src/linalg/Sub.cpp b/src/linalg/Sub.cpp
index 1f5d068a4..0947733b6 100644
--- a/src/linalg/Sub.cpp
+++ b/src/linalg/Sub.cpp
@@ -35,9 +35,19 @@ namespace cytnx {
       if ((Lt.is_contiguous() && Rt.is_contiguous()) || icnst) {
         // contiguous section
         if (Lt.device() == Device.cpu) {
-          cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Rt.dtype()](
-            out._impl->storage()._impl, Lt._impl->storage()._impl, Rt._impl->storage()._impl,
-            out._impl->storage()._impl->size(), {}, {}, {}, 2);
+          std::visit(
+            [&](auto *lptr) {
+              using TL = std::remove_pointer_t<decltype(lptr)>;
+              std::visit(
+                [&](auto *rptr) {
+                  using TR = std::remove_pointer_t<decltype(rptr)>;
+                  cytnx::linalg_internal::SubInternalImpl<TL, TR>(
+                    out._impl->storage()._impl, Lt._impl->storage()._impl,
+                    Rt._impl->storage()._impl, out._impl->storage()._impl->size(), {}, {}, {});
+                },
+                Rt.ptr());
+            },
+            Lt.ptr());
         } else {
   #ifdef UNI_GPU
           checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -52,10 +62,20 @@ namespace cytnx {
       } else {
         // non-contiguous section
         if (Lt.device() == Device.cpu) {
-          cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Rt.dtype()](
-            out._impl->storage()._impl, Lt._impl->storage()._impl, Rt._impl->storage()._impl,
-            Rt._impl->storage()._impl->size(), Lt._impl->shape(), Lt._impl->invmapper(),
-            Rt._impl->invmapper(), 2);
+          std::visit(
+            [&](auto *lptr) {
+              using TL = std::remove_pointer_t<decltype(lptr)>;
+              std::visit(
+                [&](auto *rptr) {
+                  using TR = std::remove_pointer_t<decltype(rptr)>;
+                  cytnx::linalg_internal::SubInternalImpl<TL, TR>(
+                    out._impl->storage()._impl, Lt._impl->storage()._impl,
+                    Rt._impl->storage()._impl, Rt._impl->storage()._impl->size(), Lt._impl->shape(),
+                    Lt._impl->invmapper(), Rt._impl->invmapper());
+                },
+                Rt.ptr());
+            },
+            Lt.ptr());
         } else {
   #ifdef UNI_GPU
           checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -83,9 +103,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(), Type.ComplexDouble, Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.ComplexDouble][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::SubInternalImpl<cytnx_complex128, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -114,9 +139,14 @@ namespace cytnx {
       // Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.ComplexFloat][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::SubInternalImpl<cytnx_complex64, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -144,9 +174,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(), Type.Double < Rt.dtype() ? Type.Double : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Double][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::SubInternalImpl<cytnx_double, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -173,9 +208,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(), Type.Float < Rt.dtype() ? Type.Float : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Float][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::SubInternalImpl<cytnx_float, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -202,9 +242,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(), Type.Int64 < Rt.dtype() ? Type.Int64 : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Int64][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::SubInternalImpl<cytnx_int64, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -232,9 +277,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(), Type.Uint64 < Rt.dtype() ? Type.Uint64 : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Uint64][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::SubInternalImpl<cytnx_uint64, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -261,9 +311,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(), Type.Int32 < Rt.dtype() ? Type.Int32 : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Int32][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::SubInternalImpl<cytnx_int32, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -291,9 +346,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(), Type.Uint32 < Rt.dtype() ? Type.Uint32 : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Uint32][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::SubInternalImpl<cytnx_uint32, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -320,9 +380,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(), Type.Int16 < Rt.dtype() ? Type.Int16 : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Int16][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::SubInternalImpl<cytnx_int16, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -350,9 +415,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(), Type.Uint16 < Rt.dtype() ? Type.Uint16 : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Uint16][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::SubInternalImpl<cytnx_uint16, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -379,9 +449,14 @@ namespace cytnx {
       // Tensor out(Rt.shape(), Type.Bool < Rt.dtype() ? Type.Bool : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Type.Bool][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *rptr) {
+            using TR = std::remove_pointer_t<decltype(rptr)>;
+            cytnx::linalg_internal::SubInternalImpl<cytnx_bool, TR>(
+              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+              Rt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Rt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -408,9 +483,19 @@ namespace cytnx {
         Rt._impl->storage().size(), lc.dtype() < Rt.dtype() ? lc.dtype() : Rt.dtype(), Rt.device());
 
       if (Rt.device() == Device.cpu) {
-        linalg_internal::lii.Ari_ii[lc.dtype()][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            std::visit(
+              [&](auto *rptr) {
+                using TR = std::remove_pointer_t<decltype(rptr)>;
+                cytnx::linalg_internal::SubInternalImpl<TL, TR>(
+                  out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+                  Rt._impl->storage()._impl->size(), {}, {}, {});
+              },
+              Rt.ptr());
+          },
+          Tensor::from_storage(Cnst).ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -437,9 +522,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(), Type.ComplexDouble, Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.ComplexDouble](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::SubInternalImpl<TL, cytnx_complex128>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -468,9 +558,14 @@ namespace cytnx {
       // Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.ComplexFloat](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::SubInternalImpl<TL, cytnx_complex64>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -498,9 +593,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(), Type.Double < Lt.dtype() ? Type.Double : Lt.dtype(), Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Double](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::SubInternalImpl<TL, cytnx_double>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -527,9 +627,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(), Type.Float < Lt.dtype() ? Type.Float : Lt.dtype(), Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Float](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::SubInternalImpl<TL, cytnx_float>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -556,9 +661,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(), Type.Int64 < Lt.dtype() ? Type.Int64 : Lt.dtype(), Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Int64](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::SubInternalImpl<TL, cytnx_int64>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -586,9 +696,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(), Type.Uint64 < Lt.dtype() ? Type.Uint64 : Lt.dtype(), Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Uint64](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::SubInternalImpl<TL, cytnx_uint64>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -615,9 +730,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(), Type.Int32 < Lt.dtype() ? Type.Int32 : Lt.dtype(), Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Int32](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::SubInternalImpl<TL, cytnx_int32>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -645,9 +765,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(), Type.Uint32 < Lt.dtype() ? Type.Uint32 : Lt.dtype(), Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Uint32](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::SubInternalImpl<TL, cytnx_uint32>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -674,9 +799,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(), Type.Int16 < Lt.dtype() ? Type.Int16 : Lt.dtype(), Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Int16](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::SubInternalImpl<TL, cytnx_int16>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -704,9 +834,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(), Type.Uint16 < Lt.dtype() ? Type.Uint16 : Lt.dtype(), Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Uint16](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::SubInternalImpl<TL, cytnx_uint16>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -733,9 +868,14 @@ namespace cytnx {
       // Tensor out(Lt.shape(), Type.Bool < Lt.dtype() ? Type.Bool : Lt.dtype(), Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        cytnx::linalg_internal::lii.Ari_ii[Lt.dtype()][Type.Bool](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            cytnx::linalg_internal::SubInternalImpl<TL, cytnx_bool>(
+              out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+              Lt._impl->storage()._impl->size(), {}, {}, {});
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
@@ -762,9 +902,19 @@ namespace cytnx {
         Lt._impl->storage().size(), Lt.dtype() < rc.dtype() ? Lt.dtype() : rc.dtype(), Lt.device());
 
       if (Lt.device() == Device.cpu) {
-        linalg_internal::lii.Ari_ii[Lt.dtype()][rc.dtype()](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            std::visit(
+              [&](auto *rptr) {
+                using TR = std::remove_pointer_t<decltype(rptr)>;
+                cytnx::linalg_internal::SubInternalImpl<TL, TR>(
+                  out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
+                  Lt._impl->storage()._impl->size(), {}, {}, {});
+              },
+              Tensor::from_storage(Cnst).ptr());
+          },
+          Lt.ptr());
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));

From c483252c77f525b3964118a6df769e2eee40817e Mon Sep 17 00:00:00 2001
From: Ying-Jer Kao <yjkao@phys.ntu.edu.tw>
Date: Mon, 30 Mar 2026 14:56:05 +0800
Subject: [PATCH 2/7] linalg: use std::visit for inplace cpu arithmetic
 dispatch

---
 src/linalg/iAdd.cpp              |  16 ++---
 src/linalg/iArithmetic_visit.hpp | 111 +++++++++++++++++++++++++++++++
 src/linalg/iDiv.cpp              |  13 ++--
 src/linalg/iMul.cpp              |  13 ++--
 src/linalg/iSub.cpp              |  13 ++--
 5 files changed, 132 insertions(+), 34 deletions(-)
 create mode 100644 src/linalg/iArithmetic_visit.hpp

diff --git a/src/linalg/iAdd.cpp b/src/linalg/iAdd.cpp
index ab062fcbb..183163404 100644
--- a/src/linalg/iAdd.cpp
+++ b/src/linalg/iAdd.cpp
@@ -5,6 +5,7 @@
 #ifdef BACKEND_TORCH
 #else
   #include "backend/linalg_internal_interface.hpp"
+  #include "iArithmetic_visit.hpp"
 
 namespace cytnx {
   namespace linalg {
@@ -19,9 +20,6 @@ namespace cytnx {
                         Lt.shape().size(), Rt.shape().size(), "\n");
       }
 
-      // std::cout << "iadd entry" << std::endl;
-      Storage nulls;
-
       Tensor R;
       if (Lt._impl->storage()._impl == Rt._impl->storage()._impl) {
         R = Rt.clone();
@@ -29,13 +27,13 @@ namespace cytnx {
         R = Rt;
       }
 
+      static const std::vector<cytnx_uint64> empty_mapper;
+
       // if contiguous, then no need to calculate the mappers
       if ((Lt.is_contiguous() && Rt.is_contiguous())) {
         // contiguous section.
         if (Lt.device() == Device.cpu) {
-          cytnx::linalg_internal::lii.iAri_ii[Lt.dtype()][Rt.dtype()](
-            nulls._impl, Lt._impl->storage()._impl, R._impl->storage()._impl,
-            Lt._impl->storage()._impl->size(), {}, {}, {}, 0);
+          detail::DispatchInplaceArithmeticCPU<0>(Lt, R, empty_mapper, empty_mapper, empty_mapper);
         } else {
   #ifdef UNI_GPU
           checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -59,10 +57,8 @@ namespace cytnx {
       } else {
         // non-contiguous section
         if (Lt.device() == Device.cpu) {
-          linalg_internal::lii.iAri_ii[Lt.dtype()][Rt.dtype()](
-            nulls._impl, Lt._impl->storage()._impl, R._impl->storage()._impl,
-            Lt._impl->storage()._impl->size(), Lt._impl->shape(), Lt._impl->invmapper(),
-            Rt._impl->invmapper(), 0);
+          detail::DispatchInplaceArithmeticCPU<0>(Lt, R, Lt._impl->shape(), Lt._impl->invmapper(),
+                                                  Rt._impl->invmapper());
         } else {
   #ifdef UNI_GPU
           checkCudaErrors(cudaSetDevice(Rt.device()));
diff --git a/src/linalg/iArithmetic_visit.hpp b/src/linalg/iArithmetic_visit.hpp
new file mode 100644
index 000000000..33225edb3
--- /dev/null
+++ b/src/linalg/iArithmetic_visit.hpp
@@ -0,0 +1,111 @@
+#ifndef CYTNX_LINALG_IARITHMETIC_VISIT_HPP_
+#define CYTNX_LINALG_IARITHMETIC_VISIT_HPP_
+
+#include <type_traits>
+#include <vector>
+
+#include "Tensor.hpp"
+#include "utils/utils.hpp"
+
+namespace cytnx {
+  namespace linalg {
+    namespace detail {
+
+      template <char op_code, typename TLin, typename TRin>
+      inline void ApplyInplaceArithmeticOp(TLin &lhs, const TRin &rhs) {
+        if constexpr (!cytnx::is_complex_v<TLin> && cytnx::is_complex_v<TRin>) {
+          if constexpr (op_code == 0) {
+            cytnx_error_msg(true, "[ERROR][iadd] Cannot perform real+=complex%s", "\n");
+          } else if constexpr (op_code == 1) {
+            cytnx_error_msg(true, "[ERROR][imul] Cannot perform real+=complex%s", "\n");
+          } else if constexpr (op_code == 2) {
+            cytnx_error_msg(true, "[ERROR][isub] Cannot perform real+=complex%s", "\n");
+          } else if constexpr (op_code == 3) {
+            cytnx_error_msg(true, "[ERROR][idiv] Cannot perform real+=complex%s", "\n");
+          }
+        } else {
+          if constexpr (op_code == 0) {
+            lhs += rhs;
+          } else if constexpr (op_code == 1) {
+            lhs *= rhs;
+          } else if constexpr (op_code == 2) {
+            lhs -= rhs;
+          } else if constexpr (op_code == 3) {
+            lhs /= rhs;
+          }
+        }
+      }
+
+      template <char op_code, typename TLin, typename TRin>
+      inline void ApplyInplaceArithmeticKernel(
+        TLin *lhs, const TRin *rhs, const cytnx_uint64 &len, const bool &rhs_is_scalar,
+        const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
+        const std::vector<cytnx_uint64> &invmapper_R) {
+        if (rhs_is_scalar) {
+          for (cytnx_uint64 i = 0; i < len; i++) {
+            ApplyInplaceArithmeticOp<op_code>(lhs[i], rhs[0]);
+          }
+          return;
+        }
+
+        if (shape.empty()) {
+          for (cytnx_uint64 i = 0; i < len; i++) {
+            ApplyInplaceArithmeticOp<op_code>(lhs[i], rhs[i]);
+          }
+          return;
+        }
+
+        std::vector<cytnx_uint64> accu_shape(shape.size());
+        std::vector<cytnx_uint64> old_accu_shapeL(shape.size()), old_accu_shapeR(shape.size());
+        cytnx_uint64 tmp1 = 1, tmp2 = 1, tmp3 = 1;
+        for (cytnx_uint64 i = 0; i < shape.size(); i++) {
+          accu_shape[shape.size() - 1 - i] = tmp1;
+          tmp1 *= shape[shape.size() - 1 - i];
+
+          old_accu_shapeL[shape.size() - 1 - i] = tmp2;
+          tmp2 *= shape[invmapper_L[shape.size() - 1 - i]];
+
+          old_accu_shapeR[shape.size() - 1 - i] = tmp3;
+          tmp3 *= shape[invmapper_R[shape.size() - 1 - i]];
+        }
+
+        for (cytnx_uint64 i = 0; i < len; i++) {
+          std::vector<cytnx_uint64> tmpv = cytnx::c2cartesian(i, accu_shape);
+          cytnx_uint64 idx_L =
+            cytnx::cartesian2c(cytnx::vec_map(tmpv, invmapper_L), old_accu_shapeL);
+          cytnx_uint64 idx_R =
+            cytnx::cartesian2c(cytnx::vec_map(tmpv, invmapper_R), old_accu_shapeR);
+          ApplyInplaceArithmeticOp<op_code>(lhs[idx_L], rhs[idx_R]);
+        }
+      }
+
+      template <char op_code>
+      inline void DispatchInplaceArithmeticCPU(Tensor &Lt, const Tensor &Rt,
+                                               const std::vector<cytnx_uint64> &shape,
+                                               const std::vector<cytnx_uint64> &invmapper_L,
+                                               const std::vector<cytnx_uint64> &invmapper_R) {
+        const cytnx_uint64 len = Lt._impl->storage()._impl->size();
+        const bool rhs_is_scalar = (Rt._impl->storage()._impl->size() == 1);
+
+        std::visit(
+          [&](auto *lptr) {
+            using TL = std::remove_pointer_t<decltype(lptr)>;
+            static_assert(!std::is_same_v<TL, void>);
+
+            std::visit(
+              [&](auto *rptr) {
+                using TR = std::remove_pointer_t<decltype(rptr)>;
+                static_assert(!std::is_same_v<TR, void>);
+                ApplyInplaceArithmeticKernel<op_code, TL, TR>(lptr, rptr, len, rhs_is_scalar, shape,
+                                                               invmapper_L, invmapper_R);
+              },
+              Rt.ptr());
+          },
+          Lt.ptr());
+      }
+
+    }  // namespace detail
+  }  // namespace linalg
+}  // namespace cytnx
+
+#endif  // CYTNX_LINALG_IARITHMETIC_VISIT_HPP_
diff --git a/src/linalg/iDiv.cpp b/src/linalg/iDiv.cpp
index 0cb35a999..89abe4b29 100644
--- a/src/linalg/iDiv.cpp
+++ b/src/linalg/iDiv.cpp
@@ -5,6 +5,7 @@
 #ifdef BACKEND_TORCH
 #else
   #include "backend/linalg_internal_interface.hpp"
+  #include "iArithmetic_visit.hpp"
 
 namespace cytnx {
   namespace linalg {
@@ -27,14 +28,12 @@ namespace cytnx {
         R = Rt;
       }
 
-      Storage nulls;
+      static const std::vector<cytnx_uint64> empty_mapper;
       // if contiguous, then no need to calculate the mappers
       if ((Lt.is_contiguous() && Rt.is_contiguous())) {
         // contiguous section.
         if (Lt.device() == Device.cpu) {
-          cytnx::linalg_internal::lii.iAri_ii[Lt.dtype()][Rt.dtype()](
-            nulls._impl, Lt._impl->storage()._impl, Rt._impl->storage()._impl,
-            Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+          detail::DispatchInplaceArithmeticCPU<3>(Lt, R, empty_mapper, empty_mapper, empty_mapper);
         } else {
   #ifdef UNI_GPU
           checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -58,10 +57,8 @@ namespace cytnx {
       } else {
         // non-contiguous section
         if (Lt.device() == Device.cpu) {
-          linalg_internal::lii.iAri_ii[Lt.dtype()][Rt.dtype()](
-            nulls._impl, Lt._impl->storage()._impl, R._impl->storage()._impl,
-            Lt._impl->storage()._impl->size(), Lt._impl->shape(), Lt._impl->invmapper(),
-            Rt._impl->invmapper(), 3);
+          detail::DispatchInplaceArithmeticCPU<3>(Lt, R, Lt._impl->shape(), Lt._impl->invmapper(),
+                                                  Rt._impl->invmapper());
         } else {
   #ifdef UNI_GPU
           cytnx_error_msg(true,
diff --git a/src/linalg/iMul.cpp b/src/linalg/iMul.cpp
index b6d8e47dd..b54993ccf 100644
--- a/src/linalg/iMul.cpp
+++ b/src/linalg/iMul.cpp
@@ -5,6 +5,7 @@
 #ifdef BACKEND_TORCH
 #else
   #include "backend/linalg_internal_interface.hpp"
+  #include "iArithmetic_visit.hpp"
 namespace cytnx {
   namespace linalg {
 
@@ -27,14 +28,12 @@ namespace cytnx {
         R = Rt;
       }
 
-      Storage nulls;
+      static const std::vector<cytnx_uint64> empty_mapper;
       // if contiguous, then no need to calculate the mappers
       if ((Lt.is_contiguous() && Rt.is_contiguous())) {
         // contiguous section.
         if (Lt.device() == Device.cpu) {
-          cytnx::linalg_internal::lii.iAri_ii[Lt.dtype()][Rt.dtype()](
-            nulls._impl, Lt._impl->storage()._impl, R._impl->storage()._impl,
-            Lt._impl->storage()._impl->size(), {}, {}, {}, 1);
+          detail::DispatchInplaceArithmeticCPU<1>(Lt, R, empty_mapper, empty_mapper, empty_mapper);
         } else {
   #ifdef UNI_GPU
           checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -58,10 +57,8 @@ namespace cytnx {
       } else {
         // non-contiguous section
         if (Lt.device() == Device.cpu) {
-          linalg_internal::lii.iAri_ii[Lt.dtype()][Rt.dtype()](
-            nulls._impl, Lt._impl->storage()._impl, R._impl->storage()._impl,
-            Lt._impl->storage()._impl->size(), Lt._impl->shape(), Lt._impl->invmapper(),
-            Rt._impl->invmapper(), 1);
+          detail::DispatchInplaceArithmeticCPU<1>(Lt, R, Lt._impl->shape(), Lt._impl->invmapper(),
+                                                  Rt._impl->invmapper());
         } else {
   #ifdef UNI_GPU
           cytnx_error_msg(true,
diff --git a/src/linalg/iSub.cpp b/src/linalg/iSub.cpp
index f1a8c52c4..f98a5ad45 100644
--- a/src/linalg/iSub.cpp
+++ b/src/linalg/iSub.cpp
@@ -5,6 +5,7 @@
 #ifdef BACKEND_TORCH
 #else
   #include "backend/linalg_internal_interface.hpp"
+  #include "iArithmetic_visit.hpp"
 
 namespace cytnx {
   namespace linalg {
@@ -27,14 +28,12 @@ namespace cytnx {
         R = Rt;
       }
 
-      Storage nulls;
+      static const std::vector<cytnx_uint64> empty_mapper;
       // if contiguous, then no need to calculate the mappers
       if ((Lt.is_contiguous() && Rt.is_contiguous())) {
         // contiguous section.
         if (Lt.device() == Device.cpu) {
-          cytnx::linalg_internal::lii.iAri_ii[Lt.dtype()][Rt.dtype()](
-            nulls._impl, Lt._impl->storage()._impl, R._impl->storage()._impl,
-            Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+          detail::DispatchInplaceArithmeticCPU<2>(Lt, R, empty_mapper, empty_mapper, empty_mapper);
         } else {
   #ifdef UNI_GPU
           checkCudaErrors(cudaSetDevice(Rt.device()));
@@ -58,10 +57,8 @@ namespace cytnx {
       } else {
         // non-contiguous section
         if (Lt.device() == Device.cpu) {
-          linalg_internal::lii.iAri_ii[Lt.dtype()][Rt.dtype()](
-            nulls._impl, Lt._impl->storage()._impl, R._impl->storage()._impl,
-            Lt._impl->storage()._impl->size(), Lt._impl->shape(), Lt._impl->invmapper(),
-            Rt._impl->invmapper(), 2);
+          detail::DispatchInplaceArithmeticCPU<2>(Lt, R, Lt._impl->shape(), Lt._impl->invmapper(),
+                                                  Rt._impl->invmapper());
         } else {
   #ifdef UNI_GPU
           checkCudaErrors(cudaSetDevice(Rt.device()));

From 17b60364d02505fb989cb11ae0c7d90cda426765 Mon Sep 17 00:00:00 2001
From: Ying-Jer Kao <yjkao@phys.ntu.edu.tw>
Date: Mon, 30 Mar 2026 16:00:33 +0800
Subject: [PATCH 3/7] linalg: remove dead inplace arithmetic dispatch table

---
 .../linalg_internal_cpu/CMakeLists.txt        |    2 -
 .../iArithmetic_internal.cpp                  | 2239 -----------------
 .../iArithmetic_internal.hpp                  |  755 ------
 src/backend/linalg_internal_interface.cpp     |  135 -
 src/backend/linalg_internal_interface.hpp     |    2 -
 5 files changed, 3133 deletions(-)
 delete mode 100644 src/backend/linalg_internal_cpu/iArithmetic_internal.cpp
 delete mode 100644 src/backend/linalg_internal_cpu/iArithmetic_internal.hpp

diff --git a/src/backend/linalg_internal_cpu/CMakeLists.txt b/src/backend/linalg_internal_cpu/CMakeLists.txt
index 3f00ecb4f..0c0bc89c7 100644
--- a/src/backend/linalg_internal_cpu/CMakeLists.txt
+++ b/src/backend/linalg_internal_cpu/CMakeLists.txt
@@ -3,7 +3,6 @@ target_sources_local(cytnx
     Norm_internal.hpp
     Add_internal.hpp
     iAdd_internal.hpp
-    iArithmetic_internal.hpp
     Conj_inplace_internal.hpp
     Cpr_internal.hpp
     Diag_internal.hpp
@@ -45,7 +44,6 @@ target_sources_local(cytnx
     memcpyTruncation.hpp
 
     iAdd_internal.cpp
-    iArithmetic_internal.cpp
     Conj_inplace_internal.cpp
     Diag_internal.cpp
     iDiv_internal.cpp
diff --git a/src/backend/linalg_internal_cpu/iArithmetic_internal.cpp b/src/backend/linalg_internal_cpu/iArithmetic_internal.cpp
deleted file mode 100644
index 1b42efecf..000000000
--- a/src/backend/linalg_internal_cpu/iArithmetic_internal.cpp
+++ /dev/null
@@ -1,2239 +0,0 @@
-#include "iArithmetic_internal.hpp"
-
-namespace cytnx {
-  namespace linalg_internal {
-
-    void iArithmetic_internal_cdtcd(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cdtcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cdtcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cdtcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cdtcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_cdtcf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cdtcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cdtcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cdtcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cdtcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_cdtd(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cdtd(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cdtd(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cdtd(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cdtd(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-    }
-    void iArithmetic_internal_cdtf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cdtf(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cdtf(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cdtf(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cdtf(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-    }
-    void iArithmetic_internal_cdtu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cdtu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cdtu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cdtu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cdtu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_cdti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cdti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cdti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cdti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cdti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_cdtu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cdtu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cdtu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cdtu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cdtu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_cdti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cdti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cdti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cdti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cdti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_cdti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cdti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cdti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cdti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cdti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_cdtu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cdtu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cdtu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cdtu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cdtu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_cdtb(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cdtb(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cdtb(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cdtb(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cdtb(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-    }
-    //-----------------------
-    void iArithmetic_internal_cftcd(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cftcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cftcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cftcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cftcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_cftcf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cftcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cftcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cftcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cftcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_cftd(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cftd(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cftd(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cftd(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cftd(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-    }
-    void iArithmetic_internal_cftf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cftf(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cftf(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cftf(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cftf(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-    }
-    void iArithmetic_internal_cftu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cftu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cftu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cftu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cftu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_cfti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cfti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cfti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cfti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cfti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_cftu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cftu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cftu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cftu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cftu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_cfti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cfti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cfti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cfti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cfti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_cfti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cfti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cfti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cfti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cfti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_cftu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cftu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cftu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cftu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cftu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_cftb(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_cftb(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_cftb(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_cftb(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_cftb(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-    }
-    //---------------------------
-    void iArithmetic_internal_dtcd(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_dtcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_dtcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_dtcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_dtcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-    }
-    void iArithmetic_internal_dtcf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_dtcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_dtcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_dtcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_dtcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-    }
-    void iArithmetic_internal_dtd(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_dtd(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_dtd(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_dtd(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_dtd(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-    }
-    void iArithmetic_internal_dtf(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_dtf(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_dtf(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_dtf(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_dtf(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-    }
-    void iArithmetic_internal_dtu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_dtu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_dtu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_dtu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_dtu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_dti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_dti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_dti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_dti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_dti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_dtu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_dtu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_dtu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_dtu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_dtu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_dti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_dti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_dti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_dti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_dti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_dti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_dti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_dti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_dti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_dti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_dtu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_dtu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_dtu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_dtu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_dtu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_dtb(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_dtb(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_dtb(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_dtb(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_dtb(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-    }
-    //----------------------
-    void iArithmetic_internal_ftcd(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_ftcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_ftcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_ftcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_ftcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-    }
-    void iArithmetic_internal_ftcf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_ftcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_ftcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_ftcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_ftcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-    }
-    void iArithmetic_internal_ftd(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_ftd(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_ftd(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_ftd(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_ftd(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-    }
-    void iArithmetic_internal_ftf(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_ftf(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_ftf(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_ftf(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_ftf(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-    }
-    void iArithmetic_internal_ftu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_ftu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_ftu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_ftu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_ftu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_fti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_fti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_fti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_fti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_fti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_ftu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_ftu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_ftu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_ftu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_ftu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_fti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_fti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_fti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_fti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_fti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_fti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_fti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_fti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_fti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_fti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_ftu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_ftu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_ftu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_ftu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_ftu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_ftb(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_ftb(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_ftb(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_ftb(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_ftb(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-    }
-
-    //-----------------------
-    void iArithmetic_internal_u64tcd(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u64tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u64tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u64tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u64tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_u64tcf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u64tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u64tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u64tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u64tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_u64td(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u64td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u64td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u64td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u64td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_u64tf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u64tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u64tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u64tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u64tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_u64tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u64tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u64tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u64tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u64tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_u64ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u64ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u64ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u64ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u64ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_u64tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u64tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u64tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u64tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u64tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_u64ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u64ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u64ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u64ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u64ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_u64ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u64ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u64ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u64ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u64ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_u64tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u64tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u64tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u64tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u64tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_u64tb(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u64tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u64tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u64tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u64tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    //----------------------
-    void iArithmetic_internal_i64tcd(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i64tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i64tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i64tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i64tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_i64tcf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i64tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i64tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i64tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i64tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_i64td(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i64td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i64td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i64td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i64td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_i64tf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i64tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i64tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i64tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i64tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_i64tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i64tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i64tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i64tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i64tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_i64ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i64ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i64ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i64ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i64ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_i64tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i64tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i64tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i64tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i64tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_i64ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i64ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i64ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i64ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i64ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_i64ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i64ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i64ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i64ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_i64tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i64tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i64tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i64tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i64tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_i64tb(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i64tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i64tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i64tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i64tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-
-    //-------------------
-    void iArithmetic_internal_u32tcd(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u32tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u32tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u32tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u32tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_u32tcf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u32tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u32tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u32tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u32tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_u32td(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u32td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u32td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u32td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u32td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_u32tf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u32tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u32tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u32tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u32tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_u32tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u32tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u32tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u32tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u32tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_u32ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u32ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u32ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u32ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u32ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_u32tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u32tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u32tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u32tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u32tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_u32ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u32ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u32ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u32ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u32ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_u32ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u32ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u32ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u32ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u32ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_u32tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u32tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u32tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u32tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u32tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_u32tb(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u32tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u32tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u32tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u32tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-
-    //----------------------
-    void iArithmetic_internal_i32tcd(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i32tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i32tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i32tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i32tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_i32tcf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i32tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i32tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i32tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i32tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_i32td(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i32td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i32td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i32td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i32td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_i32tf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i32tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i32tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i32tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i32tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_i32tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i32tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i32tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i32tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i32tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_i32ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i32ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i32ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i32ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i32ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_i32tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i32tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i32tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i32tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i32tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_i32ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i32ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i32ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i32ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i32ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_i32ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i32ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i32ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i32ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i32ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_i32tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i32tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i32tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i32tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i32tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_i32tb(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i32tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i32tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i32tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i32tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    //----------------------
-    void iArithmetic_internal_i16tcd(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i16tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i16tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i16tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i16tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_i16tcf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i16tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i16tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i16tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i16tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_i16td(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i16td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i16td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i16td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i16td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_i16tf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i16tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i16tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i16tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i16tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_i16tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i16tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i16tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i16tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i16tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_i16ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i16ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i16ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i16ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i16ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_i16tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i16tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i16tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i16tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i16tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_i16ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i16ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i16ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i16ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i16ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_i16ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i16ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i16ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i16ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i16ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_i16tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i16tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i16tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i16tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i16tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_i16tb(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_i16tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_i16tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_i16tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_i16tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-
-    //----------------------
-    void iArithmetic_internal_u16tcd(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u16tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u16tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u16tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u16tcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_u16tcf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u16tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u16tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u16tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u16tcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                     invmapper_R);
-    }
-    void iArithmetic_internal_u16td(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u16td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u16td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u16td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u16td(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_u16tf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u16tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u16tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u16tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u16tf(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_u16tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u16tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u16tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u16tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u16tu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_u16ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u16ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u16ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u16ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u16ti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_u16tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u16tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u16tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u16tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u16tu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_u16ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u16ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u16ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u16ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u16ti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_u16ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u16ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u16ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u16ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u16ti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_u16tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u16tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u16tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u16tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u16tu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                      invmapper_R);
-    }
-    void iArithmetic_internal_u16tb(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_u16tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_u16tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_u16tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_u16tb(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    //----------------------
-    void iArithmetic_internal_btcd(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_btcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_btcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_btcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_btcd(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-    }
-    void iArithmetic_internal_btcf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_btcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_btcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_btcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_btcf(out, Lin, Rin, len, shape, invmapper_L,
-                                                   invmapper_R);
-    }
-    void iArithmetic_internal_btd(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_btd(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_btd(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_btd(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_btd(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-    }
-    void iArithmetic_internal_btf(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_btf(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_btf(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_btf(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_btf(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-    }
-    void iArithmetic_internal_btu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_btu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_btu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_btu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_btu64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_bti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_bti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_bti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_bti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_bti64(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_btu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_btu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_btu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_btu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_btu32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_bti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_bti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_bti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_bti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_bti32(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_bti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_bti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_bti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_bti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_bti16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_btu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_btu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_btu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_btu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_btu16(out, Lin, Rin, len, shape, invmapper_L,
-                                                    invmapper_R);
-    }
-    void iArithmetic_internal_btb(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type) {
-      if (type == 0)
-        cytnx::linalg_internal::iAdd_internal_btb(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 1)
-        cytnx::linalg_internal::iMul_internal_btb(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 2)
-        cytnx::linalg_internal::iSub_internal_btb(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-      else if (type == 3)
-        cytnx::linalg_internal::iDiv_internal_btb(out, Lin, Rin, len, shape, invmapper_L,
-                                                  invmapper_R);
-    }
-
-  }  // namespace linalg_internal
-}  // namespace cytnx
diff --git a/src/backend/linalg_internal_cpu/iArithmetic_internal.hpp b/src/backend/linalg_internal_cpu/iArithmetic_internal.hpp
deleted file mode 100644
index 1460c172c..000000000
--- a/src/backend/linalg_internal_cpu/iArithmetic_internal.hpp
+++ /dev/null
@@ -1,755 +0,0 @@
-#ifndef CYTNX_BACKEND_LINALG_INTERNAL_CPU_IARITHMETIC_INTERNAL_H_
-#define CYTNX_BACKEND_LINALG_INTERNAL_CPU_IARITHMETIC_INTERNAL_H_
-
-#include "Type.hpp"
-#include "backend/Storage.hpp"
-#include "iAdd_internal.hpp"
-#include "iMul_internal.hpp"
-#include "iSub_internal.hpp"
-#include "iDiv_internal.hpp"
-namespace cytnx {
-  namespace linalg_internal {
-
-    /// iArithmetic
-    void iArithmetic_internal_cdtcd(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_cdtcf(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_cdtd(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_cdtf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_cdti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_cdtu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_cdti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_cdtu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_cdtu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_cdti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_cdtb(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-    void iArithmetic_internal_cftcd(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_cftcf(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_cftd(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_cftf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_cfti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_cftu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_cfti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_cftu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_cftu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_cfti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_cftb(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-    void iArithmetic_internal_dtcd(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_dtcf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_dtd(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_dtf(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_dti64(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_dtu64(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_dti32(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_dtu32(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_dtu16(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_dti16(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_dtb(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-    void iArithmetic_internal_ftcd(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_ftcf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_ftd(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_ftf(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_fti64(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_ftu64(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_fti32(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_ftu32(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_ftu16(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_fti16(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_ftb(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-    void iArithmetic_internal_i64tcd(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i64tcf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i64td(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i64tf(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i64ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i64tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i64ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i64tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i64tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i64ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i64tb(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-    void iArithmetic_internal_u64tcd(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u64tcf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u64td(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u64tf(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u64ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u64tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u64ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u64tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u64ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u64tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u64tb(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-    void iArithmetic_internal_i32tcd(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i32tcf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i32td(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i32tf(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i32ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i32tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i32ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i32tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i32tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i32ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i32tb(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-    void iArithmetic_internal_u32tcd(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u32tcf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u32td(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u32tf(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u32ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u32tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u32ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u32tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u32tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u32ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u32tb(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-    void iArithmetic_internal_i16tcd(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i16tcf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i16td(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i16tf(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i16ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i16tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i16ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i16tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i16tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i16ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_i16tb(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-    void iArithmetic_internal_u16tcd(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u16tcf(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u16td(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u16tf(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u16ti64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u16tu64(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u16ti32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u16tu32(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u16tu16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u16ti16(
-      boost::intrusive_ptr<Storage_base> &out, boost::intrusive_ptr<Storage_base> &Lin,
-      boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
-      const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-      const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_u16tb(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-    void iArithmetic_internal_btcd(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_btcf(boost::intrusive_ptr<Storage_base> &out,
-                                   boost::intrusive_ptr<Storage_base> &Lin,
-                                   boost::intrusive_ptr<Storage_base> &Rin,
-                                   const unsigned long long &len,
-                                   const std::vector<cytnx_uint64> &shape,
-                                   const std::vector<cytnx_uint64> &invmapper_L,
-                                   const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_btd(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_btf(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_bti64(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_btu64(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_bti32(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_btu32(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_btu16(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_bti16(boost::intrusive_ptr<Storage_base> &out,
-                                    boost::intrusive_ptr<Storage_base> &Lin,
-                                    boost::intrusive_ptr<Storage_base> &Rin,
-                                    const unsigned long long &len,
-                                    const std::vector<cytnx_uint64> &shape,
-                                    const std::vector<cytnx_uint64> &invmapper_L,
-                                    const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-    void iArithmetic_internal_btb(boost::intrusive_ptr<Storage_base> &out,
-                                  boost::intrusive_ptr<Storage_base> &Lin,
-                                  boost::intrusive_ptr<Storage_base> &Rin,
-                                  const unsigned long long &len,
-                                  const std::vector<cytnx_uint64> &shape,
-                                  const std::vector<cytnx_uint64> &invmapper_L,
-                                  const std::vector<cytnx_uint64> &invmapper_R, const char &type);
-
-  }  // namespace linalg_internal
-}  // namespace cytnx
-
-#endif  // CYTNX_BACKEND_LINALG_INTERNAL_CPU_IARITHMETIC_INTERNAL_H_
diff --git a/src/backend/linalg_internal_interface.cpp b/src/backend/linalg_internal_interface.cpp
index fbb800d98..18925dea8 100644
--- a/src/backend/linalg_internal_interface.cpp
+++ b/src/backend/linalg_internal_interface.cpp
@@ -13,141 +13,6 @@ namespace cytnx {
 
     linalg_internal_interface::~linalg_internal_interface() {}
     linalg_internal_interface::linalg_internal_interface() {
-      iAri_ii =
-        vector<vector<Arithmeticfunc_oii>>(N_Type, vector<Arithmeticfunc_oii>(N_Type, NULL));
-
-      iAri_ii[Type.ComplexDouble][Type.ComplexDouble] = iArithmetic_internal_cdtcd;
-      iAri_ii[Type.ComplexDouble][Type.ComplexFloat] = iArithmetic_internal_cdtcf;
-      iAri_ii[Type.ComplexDouble][Type.Double] = iArithmetic_internal_cdtd;
-      iAri_ii[Type.ComplexDouble][Type.Float] = iArithmetic_internal_cdtf;
-      iAri_ii[Type.ComplexDouble][Type.Int64] = iArithmetic_internal_cdti64;
-      iAri_ii[Type.ComplexDouble][Type.Uint64] = iArithmetic_internal_cdtu64;
-      iAri_ii[Type.ComplexDouble][Type.Int32] = iArithmetic_internal_cdti32;
-      iAri_ii[Type.ComplexDouble][Type.Uint32] = iArithmetic_internal_cdtu32;
-      iAri_ii[Type.ComplexDouble][Type.Uint16] = iArithmetic_internal_cdtu16;
-      iAri_ii[Type.ComplexDouble][Type.Int16] = iArithmetic_internal_cdti16;
-      iAri_ii[Type.ComplexDouble][Type.Bool] = iArithmetic_internal_cdtb;
-
-      iAri_ii[Type.ComplexFloat][Type.ComplexDouble] = iArithmetic_internal_cftcd;
-      iAri_ii[Type.ComplexFloat][Type.ComplexFloat] = iArithmetic_internal_cftcf;
-      iAri_ii[Type.ComplexFloat][Type.Double] = iArithmetic_internal_cftd;
-      iAri_ii[Type.ComplexFloat][Type.Float] = iArithmetic_internal_cftf;
-      iAri_ii[Type.ComplexFloat][Type.Int64] = iArithmetic_internal_cfti64;
-      iAri_ii[Type.ComplexFloat][Type.Uint64] = iArithmetic_internal_cftu64;
-      iAri_ii[Type.ComplexFloat][Type.Int32] = iArithmetic_internal_cfti32;
-      iAri_ii[Type.ComplexFloat][Type.Uint32] = iArithmetic_internal_cftu32;
-      iAri_ii[Type.ComplexFloat][Type.Uint16] = iArithmetic_internal_cftu16;
-      iAri_ii[Type.ComplexFloat][Type.Int16] = iArithmetic_internal_cfti16;
-      iAri_ii[Type.ComplexFloat][Type.Bool] = iArithmetic_internal_cftb;
-
-      iAri_ii[Type.Double][Type.ComplexDouble] = iArithmetic_internal_dtcd;
-      iAri_ii[Type.Double][Type.ComplexFloat] = iArithmetic_internal_dtcf;
-      iAri_ii[Type.Double][Type.Double] = iArithmetic_internal_dtd;
-      iAri_ii[Type.Double][Type.Float] = iArithmetic_internal_dtf;
-      iAri_ii[Type.Double][Type.Int64] = iArithmetic_internal_dti64;
-      iAri_ii[Type.Double][Type.Uint64] = iArithmetic_internal_dtu64;
-      iAri_ii[Type.Double][Type.Int32] = iArithmetic_internal_dti32;
-      iAri_ii[Type.Double][Type.Uint32] = iArithmetic_internal_dtu32;
-      iAri_ii[Type.Double][Type.Uint16] = iArithmetic_internal_dtu16;
-      iAri_ii[Type.Double][Type.Int16] = iArithmetic_internal_dti16;
-      iAri_ii[Type.Double][Type.Bool] = iArithmetic_internal_dtb;
-
-      iAri_ii[Type.Float][Type.ComplexDouble] = iArithmetic_internal_ftcd;
-      iAri_ii[Type.Float][Type.ComplexFloat] = iArithmetic_internal_ftcf;
-      iAri_ii[Type.Float][Type.Double] = iArithmetic_internal_ftd;
-      iAri_ii[Type.Float][Type.Float] = iArithmetic_internal_ftf;
-      iAri_ii[Type.Float][Type.Int64] = iArithmetic_internal_fti64;
-      iAri_ii[Type.Float][Type.Uint64] = iArithmetic_internal_ftu64;
-      iAri_ii[Type.Float][Type.Int32] = iArithmetic_internal_fti32;
-      iAri_ii[Type.Float][Type.Uint32] = iArithmetic_internal_ftu32;
-      iAri_ii[Type.Float][Type.Uint16] = iArithmetic_internal_ftu16;
-      iAri_ii[Type.Float][Type.Int16] = iArithmetic_internal_fti16;
-      iAri_ii[Type.Float][Type.Bool] = iArithmetic_internal_ftb;
-
-      iAri_ii[Type.Int64][Type.ComplexDouble] = iArithmetic_internal_i64tcd;
-      iAri_ii[Type.Int64][Type.ComplexFloat] = iArithmetic_internal_i64tcf;
-      iAri_ii[Type.Int64][Type.Double] = iArithmetic_internal_i64td;
-      iAri_ii[Type.Int64][Type.Float] = iArithmetic_internal_i64tf;
-      iAri_ii[Type.Int64][Type.Int64] = iArithmetic_internal_i64ti64;
-      iAri_ii[Type.Int64][Type.Uint64] = iArithmetic_internal_i64tu64;
-      iAri_ii[Type.Int64][Type.Int32] = iArithmetic_internal_i64ti32;
-      iAri_ii[Type.Int64][Type.Uint32] = iArithmetic_internal_i64tu32;
-      iAri_ii[Type.Int64][Type.Uint16] = iArithmetic_internal_i64tu16;
-      iAri_ii[Type.Int64][Type.Int16] = iArithmetic_internal_i64ti16;
-      iAri_ii[Type.Int64][Type.Bool] = iArithmetic_internal_i64tb;
-
-      iAri_ii[Type.Uint64][Type.ComplexDouble] = iArithmetic_internal_u64tcd;
-      iAri_ii[Type.Uint64][Type.ComplexFloat] = iArithmetic_internal_u64tcf;
-      iAri_ii[Type.Uint64][Type.Double] = iArithmetic_internal_u64td;
-      iAri_ii[Type.Uint64][Type.Float] = iArithmetic_internal_u64tf;
-      iAri_ii[Type.Uint64][Type.Int64] = iArithmetic_internal_u64ti64;
-      iAri_ii[Type.Uint64][Type.Uint64] = iArithmetic_internal_u64tu64;
-      iAri_ii[Type.Uint64][Type.Int32] = iArithmetic_internal_u64ti32;
-      iAri_ii[Type.Uint64][Type.Uint32] = iArithmetic_internal_u64tu32;
-      iAri_ii[Type.Uint64][Type.Uint16] = iArithmetic_internal_u64tu16;
-      iAri_ii[Type.Uint64][Type.Int16] = iArithmetic_internal_u64ti16;
-      iAri_ii[Type.Uint64][Type.Bool] = iArithmetic_internal_u64tb;
-
-      iAri_ii[Type.Int32][Type.ComplexDouble] = iArithmetic_internal_i32tcd;
-      iAri_ii[Type.Int32][Type.ComplexFloat] = iArithmetic_internal_i32tcf;
-      iAri_ii[Type.Int32][Type.Double] = iArithmetic_internal_i32td;
-      iAri_ii[Type.Int32][Type.Float] = iArithmetic_internal_i32tf;
-      iAri_ii[Type.Int32][Type.Int64] = iArithmetic_internal_i32ti64;
-      iAri_ii[Type.Int32][Type.Uint64] = iArithmetic_internal_i32tu64;
-      iAri_ii[Type.Int32][Type.Int32] = iArithmetic_internal_i32ti32;
-      iAri_ii[Type.Int32][Type.Uint32] = iArithmetic_internal_i32tu32;
-      iAri_ii[Type.Int32][Type.Uint16] = iArithmetic_internal_i32tu16;
-      iAri_ii[Type.Int32][Type.Int16] = iArithmetic_internal_i32ti16;
-      iAri_ii[Type.Int32][Type.Bool] = iArithmetic_internal_i32tb;
-
-      iAri_ii[Type.Uint32][Type.ComplexDouble] = iArithmetic_internal_u32tcd;
-      iAri_ii[Type.Uint32][Type.ComplexFloat] = iArithmetic_internal_u32tcf;
-      iAri_ii[Type.Uint32][Type.Double] = iArithmetic_internal_u32td;
-      iAri_ii[Type.Uint32][Type.Float] = iArithmetic_internal_u32tf;
-      iAri_ii[Type.Uint32][Type.Int64] = iArithmetic_internal_u32ti64;
-      iAri_ii[Type.Uint32][Type.Uint64] = iArithmetic_internal_u32tu64;
-      iAri_ii[Type.Uint32][Type.Int32] = iArithmetic_internal_u32ti32;
-      iAri_ii[Type.Uint32][Type.Uint32] = iArithmetic_internal_u32tu32;
-      iAri_ii[Type.Uint32][Type.Uint16] = iArithmetic_internal_u32tu16;
-      iAri_ii[Type.Uint32][Type.Int16] = iArithmetic_internal_u32ti16;
-      iAri_ii[Type.Uint32][Type.Bool] = iArithmetic_internal_u32tb;
-
-      iAri_ii[Type.Int16][Type.ComplexDouble] = iArithmetic_internal_i16tcd;
-      iAri_ii[Type.Int16][Type.ComplexFloat] = iArithmetic_internal_i16tcf;
-      iAri_ii[Type.Int16][Type.Double] = iArithmetic_internal_i16td;
-      iAri_ii[Type.Int16][Type.Float] = iArithmetic_internal_i16tf;
-      iAri_ii[Type.Int16][Type.Int64] = iArithmetic_internal_i16ti64;
-      iAri_ii[Type.Int16][Type.Uint64] = iArithmetic_internal_i16tu64;
-      iAri_ii[Type.Int16][Type.Int32] = iArithmetic_internal_i16ti32;
-      iAri_ii[Type.Int16][Type.Uint32] = iArithmetic_internal_i16tu32;
-      iAri_ii[Type.Int16][Type.Uint16] = iArithmetic_internal_i16tu16;
-      iAri_ii[Type.Int16][Type.Int16] = iArithmetic_internal_i16ti16;
-      iAri_ii[Type.Int16][Type.Bool] = iArithmetic_internal_i16tb;
-
-      iAri_ii[Type.Uint16][Type.ComplexDouble] = iArithmetic_internal_u16tcd;
-      iAri_ii[Type.Uint16][Type.ComplexFloat] = iArithmetic_internal_u16tcf;
-      iAri_ii[Type.Uint16][Type.Double] = iArithmetic_internal_u16td;
-      iAri_ii[Type.Uint16][Type.Float] = iArithmetic_internal_u16tf;
-      iAri_ii[Type.Uint16][Type.Int64] = iArithmetic_internal_u16ti64;
-      iAri_ii[Type.Uint16][Type.Uint64] = iArithmetic_internal_u16tu64;
-      iAri_ii[Type.Uint16][Type.Int32] = iArithmetic_internal_u16ti32;
-      iAri_ii[Type.Uint16][Type.Uint32] = iArithmetic_internal_u16tu32;
-      iAri_ii[Type.Uint16][Type.Uint16] = iArithmetic_internal_u16tu16;
-      iAri_ii[Type.Uint16][Type.Int16] = iArithmetic_internal_u16ti16;
-      iAri_ii[Type.Uint16][Type.Bool] = iArithmetic_internal_u16tb;
-
-      iAri_ii[Type.Bool][Type.ComplexDouble] = iArithmetic_internal_btcd;
-      iAri_ii[Type.Bool][Type.ComplexFloat] = iArithmetic_internal_btcf;
-      iAri_ii[Type.Bool][Type.Double] = iArithmetic_internal_btd;
-      iAri_ii[Type.Bool][Type.Float] = iArithmetic_internal_btf;
-      iAri_ii[Type.Bool][Type.Int64] = iArithmetic_internal_bti64;
-      iAri_ii[Type.Bool][Type.Uint64] = iArithmetic_internal_btu64;
-      iAri_ii[Type.Bool][Type.Int32] = iArithmetic_internal_bti32;
-      iAri_ii[Type.Bool][Type.Uint32] = iArithmetic_internal_btu32;
-      iAri_ii[Type.Bool][Type.Uint16] = iArithmetic_internal_btu16;
-      iAri_ii[Type.Bool][Type.Int16] = iArithmetic_internal_bti16;
-      iAri_ii[Type.Bool][Type.Bool] = iArithmetic_internal_btb;
-
       //=====================
       QR_ii = vector<Qrfunc_oii>(5);
 
diff --git a/src/backend/linalg_internal_interface.hpp b/src/backend/linalg_internal_interface.hpp
index df53fa504..91916f60c 100644
--- a/src/backend/linalg_internal_interface.hpp
+++ b/src/backend/linalg_internal_interface.hpp
@@ -41,7 +41,6 @@
 #include "linalg_internal_cpu/Trace_internal.hpp"
 #include "linalg_internal_cpu/Tridiag_internal.hpp"
 #include "linalg_internal_cpu/Vectordot_internal.hpp"
-#include "linalg_internal_cpu/iArithmetic_internal.hpp"
 #include "linalg_internal_cpu/memcpyTruncation.hpp"
 
 #ifdef UNI_GPU
@@ -217,7 +216,6 @@ namespace cytnx {
 #endif
     class linalg_internal_interface {
      public:
-      std::vector<std::vector<Arithmeticfunc_oii>> iAri_ii;
       std::vector<Svdfunc_oii> Sdd_ii;
       std::vector<Svdfunc_oii> Gesvd_ii;
       std::vector<Eighfunc_oii> Eigh_ii;

From 965a109ebb631d88c83845a6ef6b05dddeb9111b Mon Sep 17 00:00:00 2001
From: Ying-Jer Kao <yjkao@phys.ntu.edu.tw>
Date: Mon, 30 Mar 2026 16:31:58 +0800
Subject: [PATCH 4/7] style: clang-format inplace arithmetic visit helper

---
 src/linalg/iArithmetic_visit.hpp | 11 ++++++-----
 1 file changed, 6 insertions(+), 5 deletions(-)

diff --git a/src/linalg/iArithmetic_visit.hpp b/src/linalg/iArithmetic_visit.hpp
index 33225edb3..a456dfc20 100644
--- a/src/linalg/iArithmetic_visit.hpp
+++ b/src/linalg/iArithmetic_visit.hpp
@@ -37,10 +37,11 @@ namespace cytnx {
       }
 
       template <char op_code, typename TLin, typename TRin>
-      inline void ApplyInplaceArithmeticKernel(
-        TLin *lhs, const TRin *rhs, const cytnx_uint64 &len, const bool &rhs_is_scalar,
-        const std::vector<cytnx_uint64> &shape, const std::vector<cytnx_uint64> &invmapper_L,
-        const std::vector<cytnx_uint64> &invmapper_R) {
+      inline void ApplyInplaceArithmeticKernel(TLin *lhs, const TRin *rhs, const cytnx_uint64 &len,
+                                               const bool &rhs_is_scalar,
+                                               const std::vector<cytnx_uint64> &shape,
+                                               const std::vector<cytnx_uint64> &invmapper_L,
+                                               const std::vector<cytnx_uint64> &invmapper_R) {
         if (rhs_is_scalar) {
           for (cytnx_uint64 i = 0; i < len; i++) {
             ApplyInplaceArithmeticOp<op_code>(lhs[i], rhs[0]);
@@ -97,7 +98,7 @@ namespace cytnx {
                 using TR = std::remove_pointer_t<decltype(rptr)>;
                 static_assert(!std::is_same_v<TR, void>);
                 ApplyInplaceArithmeticKernel<op_code, TL, TR>(lptr, rptr, len, rhs_is_scalar, shape,
-                                                               invmapper_L, invmapper_R);
+                                                              invmapper_L, invmapper_R);
               },
               Rt.ptr());
           },

From bc6f6d92e9f92951a54dae49e5ffadd4aed953aa Mon Sep 17 00:00:00 2001
From: Ying-Jer Kao <yjkao@phys.ntu.edu.tw>
Date: Mon, 30 Mar 2026 18:45:54 +0800
Subject: [PATCH 5/7] Refactor Add scalar dispatch and enforce CPU type
 promotion

---
 src/linalg/Add.cpp                | 526 ++++++------------------------
 tests/linalg_test/linalg_test.cpp |  23 ++
 2 files changed, 116 insertions(+), 433 deletions(-)

diff --git a/src/linalg/Add.cpp b/src/linalg/Add.cpp
index 4ee3bad05..15a0553bb 100644
--- a/src/linalg/Add.cpp
+++ b/src/linalg/Add.cpp
@@ -8,25 +8,75 @@
   #include "backend/linalg_internal_interface.hpp"
 namespace cytnx {
   namespace linalg {
+    namespace detail {
+      inline unsigned int SelectAddOutputType(const unsigned int lhs_dtype,
+                                              const unsigned int rhs_dtype, const int device) {
+  #ifdef UNI_GPU
+        // Current GPU arithmetic tables still assume legacy min(lhs, rhs) promotion.
+        if (device != Device.cpu) {
+          return lhs_dtype < rhs_dtype ? lhs_dtype : rhs_dtype;
+        }
+  #else
+        (void)device;
+  #endif
+        return Type.type_promote(lhs_dtype, rhs_dtype);
+      }
+
+      template <typename TL>
+      Tensor AddScalarTensorImpl(const TL &lc, const Tensor &Rt) {
+        const unsigned int lhs_dtype = Type.cy_typeid_v<TL>;
+        Storage Cnst(1, lhs_dtype);
+        Cnst.at<TL>(0) = lc;
+
+        Tensor out;
+        out._impl = Rt._impl->_clone_meta_only();
+        out._impl->storage() =
+          Storage(Rt._impl->storage().size(),
+                  SelectAddOutputType(lhs_dtype, Rt.dtype(), Rt.device()), Rt.device());
+
+        if (Rt.device() == Device.cpu) {
+          std::visit(
+            [&](auto *rptr) {
+              using TR = std::remove_pointer_t<decltype(rptr)>;
+              cytnx::linalg_internal::AddInternalImpl<TL, TR>(
+                out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+                Rt._impl->storage()._impl->size(), {}, {}, {});
+            },
+            Rt.ptr());
+        } else {
+  #ifdef UNI_GPU
+          checkCudaErrors(cudaSetDevice(Rt.device()));
+          linalg_internal::lii.cuAri_ii[lhs_dtype][Rt.dtype()](
+            out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
+            Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
+  #else
+          cytnx_error_msg(true, "[Add] fatal error, the tensor is on GPU without CUDA support.%s",
+                          "\n");
+  #endif
+        }
+
+        return out;
+      }
+    }  // namespace detail
+
     Tensor Add(const Tensor &Lt, const Tensor &Rt) {
       cytnx_error_msg(Lt.device() != Rt.device(),
                       "[Add] The two tensors cannot be on different devices.%s", "\n");
 
+      const unsigned int out_dtype =
+        detail::SelectAddOutputType(Lt.dtype(), Rt.dtype(), Lt.device());
+
       Tensor out;
       bool icnst = false;
 
       if (Lt.shape().size() == 1 && Lt.shape()[0] == 1) {
         out._impl = Rt._impl->_clone_meta_only();
-        out._impl->storage() = Storage(
-          Rt.storage().size(), Lt.dtype() < Rt.dtype() ? Lt.dtype() : Rt.dtype(), Rt.device());
-        // out.Init(Rt.shape(),Lt.dtype() < Rt.dtype()?Lt.dtype():Rt.dtype(),Lt.device());
+        out._impl->storage() = Storage(Rt.storage().size(), out_dtype, Rt.device());
         icnst = true;
 
       } else if (Rt.shape().size() == 1 && Rt.shape()[0] == 1) {
-        // out.Init(Lt.shape(),Lt.dtype() < Rt.dtype()?Lt.dtype():Rt.dtype(),Lt.device());
         out._impl = Lt._impl->_clone_meta_only();
-        out._impl->storage() = Storage(
-          Lt.storage().size(), Lt.dtype() < Rt.dtype() ? Lt.dtype() : Rt.dtype(), Lt.device());
+        out._impl->storage() = Storage(Lt.storage().size(), out_dtype, Lt.device());
         icnst = true;
 
       } else {
@@ -34,7 +84,7 @@ namespace cytnx {
                         "[Add] The two tensors do not have the same shape. Lt rank: [%d] "
                         "Rt rank: [%d] %s",
                         Lt.shape().size(), Rt.shape().size(), "\n");
-        out.Init(Lt.shape(), Lt.dtype() < Rt.dtype() ? Lt.dtype() : Rt.dtype(), Lt.device());
+        out.Init(Lt.shape(), out_dtype, Lt.device());
       }
 
       // if contiguous, then no need to calculate the mappers
@@ -98,383 +148,11 @@ namespace cytnx {
     }
 
     //-----------------------------------------------------------------------------------
-    template <>
-    Tensor Add<cytnx_complex128>(const cytnx_complex128 &lc, const Tensor &Rt) {
-      Storage Cnst(1, Type.ComplexDouble);
-      Cnst.at<cytnx_complex128>(0) = lc;
-      Tensor out;
-      out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(Rt._impl->storage().size(), Type.ComplexDouble, Rt.device());
-      // Tensor out(Rt.shape(),Type.ComplexDouble,Rt.device());
-
-      if (Rt.device() == Device.cpu) {
-        std::visit(
-          [&](auto *rptr) {
-            using TR = std::remove_pointer_t<decltype(rptr)>;
-            cytnx::linalg_internal::AddInternalImpl<cytnx_complex128, TR>(
-              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-              Rt._impl->storage()._impl->size(), {}, {}, {});
-          },
-          Rt.ptr());
-      } else {
-  #ifdef UNI_GPU
-        checkCudaErrors(cudaSetDevice(Rt.device()));
-        linalg_internal::lii.cuAri_ii[Type.ComplexDouble][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
-  #else
-        cytnx_error_msg(true, "[Add] fatal error, the tensor is on GPU without CUDA support.%s",
-                        "\n");
-  #endif
-      }
-
-      return out;
-    }
-
-    template <>
-    Tensor Add<cytnx_complex64>(const cytnx_complex64 &lc, const Tensor &Rt) {
-      Storage Cnst(1, Type.ComplexFloat);
-      Cnst.at<cytnx_complex64>(0) = lc;
-      Tensor out;
-      out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Rt._impl->storage().size(),
-                Type.ComplexFloat < Rt.dtype() ? Type.ComplexFloat : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(),Type.ComplexFloat <
-      // Rt.dtype()?Type.ComplexFloat:Rt.dtype(),Rt.device());
-
-      if (Rt.device() == Device.cpu) {
-        std::visit(
-          [&](auto *rptr) {
-            using TR = std::remove_pointer_t<decltype(rptr)>;
-            cytnx::linalg_internal::AddInternalImpl<cytnx_complex64, TR>(
-              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-              Rt._impl->storage()._impl->size(), {}, {}, {});
-          },
-          Rt.ptr());
-      } else {
-  #ifdef UNI_GPU
-        checkCudaErrors(cudaSetDevice(Rt.device()));
-        linalg_internal::lii.cuAri_ii[Type.ComplexFloat][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
-  #else
-        cytnx_error_msg(true, "[Add] fatal error, the tensor is on GPU without CUDA support.%s",
-                        "\n");
-  #endif
-      }
-
-      return out;
-    }
-
-    template <>
-    Tensor Add<cytnx_double>(const cytnx_double &lc, const Tensor &Rt) {
-      Storage Cnst(1, Type.Double);
-      Cnst.at<cytnx_double>(0) = lc;
-      Tensor out;
-      out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Rt._impl->storage().size(), Type.Double < Rt.dtype() ? Type.Double : Rt.dtype(),
-                Rt.device());
-      // Tensor out(Rt.shape(),Type.Double < Rt.dtype()?Type.Double:Rt.dtype(),Rt.device());
-
-      if (Rt.device() == Device.cpu) {
-        std::visit(
-          [&](auto *rptr) {
-            using TR = std::remove_pointer_t<decltype(rptr)>;
-            cytnx::linalg_internal::AddInternalImpl<cytnx_double, TR>(
-              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-              Rt._impl->storage()._impl->size(), {}, {}, {});
-          },
-          Rt.ptr());
-      } else {
-  #ifdef UNI_GPU
-        checkCudaErrors(cudaSetDevice(Rt.device()));
-        linalg_internal::lii.cuAri_ii[Type.Double][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
-  #else
-        cytnx_error_msg(true, "[Add] fatal error, the tensor is on GPU without CUDA support.%s",
-                        "\n");
-  #endif
-      }
-
-      return out;
-    }
-
-    template <>
-    Tensor Add<cytnx_float>(const cytnx_float &lc, const Tensor &Rt) {
-      Storage Cnst(1, Type.Float);
-      Cnst.at<cytnx_float>(0) = lc;
-      Tensor out;
-      out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Rt._impl->storage().size(), Type.Float < Rt.dtype() ? Type.Float : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(),Type.Float < Rt.dtype()?Type.Float:Rt.dtype(),Rt.device());
-
-      if (Rt.device() == Device.cpu) {
-        std::visit(
-          [&](auto *rptr) {
-            using TR = std::remove_pointer_t<decltype(rptr)>;
-            cytnx::linalg_internal::AddInternalImpl<cytnx_float, TR>(
-              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-              Rt._impl->storage()._impl->size(), {}, {}, {});
-          },
-          Rt.ptr());
-      } else {
-  #ifdef UNI_GPU
-        checkCudaErrors(cudaSetDevice(Rt.device()));
-        linalg_internal::lii.cuAri_ii[Type.Float][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
-  #else
-        cytnx_error_msg(true, "[Add] fatal error, the tensor is on GPU without CUDA support.%s",
-                        "\n");
-  #endif
-      }
-
-      return out;
-    }
-
-    template <>
-    Tensor Add<cytnx_int64>(const cytnx_int64 &lc, const Tensor &Rt) {
-      Storage Cnst(1, Type.Int64);
-      Cnst.at<cytnx_int64>(0) = lc;
-      Tensor out;
-      out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Rt._impl->storage().size(), Type.Int64 < Rt.dtype() ? Type.Int64 : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(),Type.Int64 < Rt.dtype()?Type.Int64:Rt.dtype(),Rt.device());
-
-      if (Rt.device() == Device.cpu) {
-        std::visit(
-          [&](auto *rptr) {
-            using TR = std::remove_pointer_t<decltype(rptr)>;
-            cytnx::linalg_internal::AddInternalImpl<cytnx_int64, TR>(
-              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-              Rt._impl->storage()._impl->size(), {}, {}, {});
-          },
-          Rt.ptr());
-      } else {
-  #ifdef UNI_GPU
-        checkCudaErrors(cudaSetDevice(Rt.device()));
-        linalg_internal::lii.cuAri_ii[Type.Int64][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
-  #else
-        cytnx_error_msg(true, "[Add] fatal error, the tensor is on GPU without CUDA support.%s",
-                        "\n");
-  #endif
-      }
-
-      return out;
-    }
-
-    template <>
-    Tensor Add<cytnx_uint64>(const cytnx_uint64 &lc, const Tensor &Rt) {
-      Storage Cnst(1, Type.Uint64);
-      Cnst.at<cytnx_uint64>(0) = lc;
-      Tensor out;
-      out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Rt._impl->storage().size(), Type.Uint64 < Rt.dtype() ? Type.Uint64 : Rt.dtype(),
-                Rt.device());
-      // Tensor out(Rt.shape(),Type.Uint64 < Rt.dtype()?Type.Uint64:Rt.dtype(),Rt.device());
-
-      if (Rt.device() == Device.cpu) {
-        std::visit(
-          [&](auto *rptr) {
-            using TR = std::remove_pointer_t<decltype(rptr)>;
-            cytnx::linalg_internal::AddInternalImpl<cytnx_uint64, TR>(
-              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-              Rt._impl->storage()._impl->size(), {}, {}, {});
-          },
-          Rt.ptr());
-      } else {
-  #ifdef UNI_GPU
-        checkCudaErrors(cudaSetDevice(Rt.device()));
-        linalg_internal::lii.cuAri_ii[Type.Uint64][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
-  #else
-        cytnx_error_msg(true, "[Add] fatal error, the tensor is on GPU without CUDA support.%s",
-                        "\n");
-  #endif
-      }
-
-      return out;
-    }
-
-    template <>
-    Tensor Add<cytnx_int32>(const cytnx_int32 &lc, const Tensor &Rt) {
-      Storage Cnst(1, Type.Int32);
-      Cnst.at<cytnx_int32>(0) = lc;
-      Tensor out;
-      out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Rt._impl->storage().size(), Type.Int32 < Rt.dtype() ? Type.Int32 : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(),Type.Int32 < Rt.dtype()?Type.Int32:Rt.dtype(),Rt.device());
-
-      if (Rt.device() == Device.cpu) {
-        std::visit(
-          [&](auto *rptr) {
-            using TR = std::remove_pointer_t<decltype(rptr)>;
-            cytnx::linalg_internal::AddInternalImpl<cytnx_int32, TR>(
-              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-              Rt._impl->storage()._impl->size(), {}, {}, {});
-          },
-          Rt.ptr());
-      } else {
-  #ifdef UNI_GPU
-        checkCudaErrors(cudaSetDevice(Rt.device()));
-        linalg_internal::lii.cuAri_ii[Type.Int32][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
-  #else
-        cytnx_error_msg(true, "[Add] fatal error, the tensor is on GPU without CUDA support.%s",
-                        "\n");
-  #endif
-      }
-
-      return out;
-    }
-
-    template <>
-    Tensor Add<cytnx_uint32>(const cytnx_uint32 &lc, const Tensor &Rt) {
-      Storage Cnst(1, Type.Uint32);
-      Cnst.at<cytnx_uint32>(0) = lc;
-      Tensor out;
-      out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Rt._impl->storage().size(), Type.Uint32 < Rt.dtype() ? Type.Uint32 : Rt.dtype(),
-                Rt.device());
-      // Tensor out(Rt.shape(),Type.Uint32 < Rt.dtype()?Type.Uint32:Rt.dtype(),Rt.device());
-
-      if (Rt.device() == Device.cpu) {
-        std::visit(
-          [&](auto *rptr) {
-            using TR = std::remove_pointer_t<decltype(rptr)>;
-            cytnx::linalg_internal::AddInternalImpl<cytnx_uint32, TR>(
-              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-              Rt._impl->storage()._impl->size(), {}, {}, {});
-          },
-          Rt.ptr());
-      } else {
-  #ifdef UNI_GPU
-        checkCudaErrors(cudaSetDevice(Rt.device()));
-        linalg_internal::lii.cuAri_ii[Type.Uint32][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
-  #else
-        cytnx_error_msg(true, "[Add] fatal error, the tensor is on GPU without CUDA support.%s",
-                        "\n");
-  #endif
-      }
-
-      return out;
-    }
-
-    template <>
-    Tensor Add<cytnx_int16>(const cytnx_int16 &lc, const Tensor &Rt) {
-      Storage Cnst(1, Type.Int16);
-      Cnst.at<cytnx_int16>(0) = lc;
-      Tensor out;
-      out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Rt._impl->storage().size(), Type.Int16 < Rt.dtype() ? Type.Int16 : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(),Type.Int16 < Rt.dtype()?Type.Int16:Rt.dtype(),Rt.device());
-
-      if (Rt.device() == Device.cpu) {
-        std::visit(
-          [&](auto *rptr) {
-            using TR = std::remove_pointer_t<decltype(rptr)>;
-            cytnx::linalg_internal::AddInternalImpl<cytnx_int16, TR>(
-              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-              Rt._impl->storage()._impl->size(), {}, {}, {});
-          },
-          Rt.ptr());
-      } else {
-  #ifdef UNI_GPU
-        checkCudaErrors(cudaSetDevice(Rt.device()));
-        linalg_internal::lii.cuAri_ii[Type.Int16][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
-  #else
-        cytnx_error_msg(true, "[Add] fatal error, the tensor is on GPU without CUDA support.%s",
-                        "\n");
-  #endif
-      }
-
-      return out;
-    }
-
-    template <>
-    Tensor Add<cytnx_uint16>(const cytnx_uint16 &lc, const Tensor &Rt) {
-      Storage Cnst(1, Type.Uint16);
-      Cnst.at<cytnx_uint16>(0) = lc;
-      Tensor out;
-      out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Rt._impl->storage().size(), Type.Uint16 < Rt.dtype() ? Type.Uint16 : Rt.dtype(),
-                Rt.device());
-      // Tensor out(Rt.shape(),Type.Uint16 < Rt.dtype()?Type.Uint16:Rt.dtype(),Rt.device());
-
-      if (Rt.device() == Device.cpu) {
-        std::visit(
-          [&](auto *rptr) {
-            using TR = std::remove_pointer_t<decltype(rptr)>;
-            cytnx::linalg_internal::AddInternalImpl<cytnx_uint16, TR>(
-              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-              Rt._impl->storage()._impl->size(), {}, {}, {});
-          },
-          Rt.ptr());
-      } else {
-  #ifdef UNI_GPU
-        checkCudaErrors(cudaSetDevice(Rt.device()));
-        linalg_internal::lii.cuAri_ii[Type.Uint16][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
-  #else
-        cytnx_error_msg(true, "[Add] fatal error, the tensor is on GPU without CUDA support.%s",
-                        "\n");
-  #endif
-      }
-
-      return out;
-    }
-
-    template <>
-    Tensor Add<cytnx_bool>(const cytnx_bool &lc, const Tensor &Rt) {
-      Storage Cnst(1, Type.Bool);
-      Cnst.at<cytnx_bool>(0) = lc;
-      Tensor out;
-      out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(Rt._impl->storage().size(),
-                                     Type.Bool < Rt.dtype() ? Type.Bool : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(),Type.Bool < Rt.dtype()?Type.Bool:Rt.dtype(),Rt.device());
-
-      if (Rt.device() == Device.cpu) {
-        std::visit(
-          [&](auto *rptr) {
-            using TR = std::remove_pointer_t<decltype(rptr)>;
-            cytnx::linalg_internal::AddInternalImpl<cytnx_bool, TR>(
-              out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-              Rt._impl->storage()._impl->size(), {}, {}, {});
-          },
-          Rt.ptr());
-      } else {
-  #ifdef UNI_GPU
-        checkCudaErrors(cudaSetDevice(Rt.device()));
-        linalg_internal::lii.cuAri_ii[Type.Bool][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
-  #else
-        cytnx_error_msg(true, "[Add] fatal error, the tensor is on GPU without CUDA support.%s",
-                        "\n");
-  #endif
-      }
-
-      return out;
+    template <class T>
+    Tensor Add(const T &lc, const Tensor &Rt) {
+      static_assert(!std::is_same_v<T, Scalar>,
+                    "Add<Scalar>(const Scalar&, const Tensor&) is specialized separately.");
+      return detail::AddScalarTensorImpl(lc, Rt);
     }
 
     template <>
@@ -484,8 +162,9 @@ namespace cytnx {
 
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Rt._impl->storage().size(), lc.dtype() < Rt.dtype() ? lc.dtype() : Rt.dtype(), Rt.device());
+      out._impl->storage() =
+        Storage(Rt._impl->storage().size(),
+                detail::SelectAddOutputType(lc.dtype(), Rt.dtype(), Rt.device()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -516,57 +195,38 @@ namespace cytnx {
     }
 
     //-----------------------------------------------------------------------------------
-    template <>
-    Tensor Add<cytnx_complex128>(const Tensor &Lt, const cytnx_complex128 &rc) {
-      return Add(rc, Lt);
-    }
-    template <>
-    Tensor Add<cytnx_complex64>(const Tensor &Lt, const cytnx_complex64 &rc) {
-      return Add(rc, Lt);
-    }
-    template <>
-    Tensor Add<cytnx_double>(const Tensor &Lt, const cytnx_double &rc) {
-      return Add(rc, Lt);
-    }
-    template <>
-    Tensor Add<cytnx_float>(const Tensor &Lt, const cytnx_float &rc) {
-      return Add(rc, Lt);
-    }
-    template <>
-    Tensor Add<cytnx_int64>(const Tensor &Lt, const cytnx_int64 &rc) {
-      return Add(rc, Lt);
-    }
-    template <>
-    Tensor Add<cytnx_uint64>(const Tensor &Lt, const cytnx_uint64 &rc) {
-      return Add(rc, Lt);
-    }
-    template <>
-    Tensor Add<cytnx_int32>(const Tensor &Lt, const cytnx_int32 &rc) {
-      return Add(rc, Lt);
-    }
-    template <>
-    Tensor Add<cytnx_uint32>(const Tensor &Lt, const cytnx_uint32 &rc) {
-      return Add(rc, Lt);
-    }
-    template <>
-    Tensor Add<cytnx_int16>(const Tensor &Lt, const cytnx_int16 &rc) {
-      return Add(rc, Lt);
-    }
-    template <>
-    Tensor Add<cytnx_uint16>(const Tensor &Lt, const cytnx_uint16 &rc) {
-      return Add(rc, Lt);
-    }
-    template <>
-    Tensor Add<cytnx_bool>(const Tensor &Lt, const cytnx_bool &rc) {
-      return Add(rc, Lt);
-    }
-    template <>
-    Tensor Add<Scalar>(const Tensor &Lt, const Scalar &rc) {
+    template <class T>
+    Tensor Add(const Tensor &Lt, const T &rc) {
       return Add(rc, Lt);
     }
 
-  }  // namespace linalg
+    template Tensor Add<cytnx_complex128>(const cytnx_complex128 &lc, const Tensor &Rt);
+    template Tensor Add<cytnx_complex64>(const cytnx_complex64 &lc, const Tensor &Rt);
+    template Tensor Add<cytnx_double>(const cytnx_double &lc, const Tensor &Rt);
+    template Tensor Add<cytnx_float>(const cytnx_float &lc, const Tensor &Rt);
+    template Tensor Add<cytnx_int64>(const cytnx_int64 &lc, const Tensor &Rt);
+    template Tensor Add<cytnx_uint64>(const cytnx_uint64 &lc, const Tensor &Rt);
+    template Tensor Add<cytnx_int32>(const cytnx_int32 &lc, const Tensor &Rt);
+    template Tensor Add<cytnx_uint32>(const cytnx_uint32 &lc, const Tensor &Rt);
+    template Tensor Add<cytnx_int16>(const cytnx_int16 &lc, const Tensor &Rt);
+    template Tensor Add<cytnx_uint16>(const cytnx_uint16 &lc, const Tensor &Rt);
+    template Tensor Add<cytnx_bool>(const cytnx_bool &lc, const Tensor &Rt);
+    template Tensor Add<Scalar>(const Scalar &lc, const Tensor &Rt);
+
+    template Tensor Add<cytnx_complex128>(const Tensor &Lt, const cytnx_complex128 &rc);
+    template Tensor Add<cytnx_complex64>(const Tensor &Lt, const cytnx_complex64 &rc);
+    template Tensor Add<cytnx_double>(const Tensor &Lt, const cytnx_double &rc);
+    template Tensor Add<cytnx_float>(const Tensor &Lt, const cytnx_float &rc);
+    template Tensor Add<cytnx_int64>(const Tensor &Lt, const cytnx_int64 &rc);
+    template Tensor Add<cytnx_uint64>(const Tensor &Lt, const cytnx_uint64 &rc);
+    template Tensor Add<cytnx_int32>(const Tensor &Lt, const cytnx_int32 &rc);
+    template Tensor Add<cytnx_uint32>(const Tensor &Lt, const cytnx_uint32 &rc);
+    template Tensor Add<cytnx_int16>(const Tensor &Lt, const cytnx_int16 &rc);
+    template Tensor Add<cytnx_uint16>(const Tensor &Lt, const cytnx_uint16 &rc);
+    template Tensor Add<cytnx_bool>(const Tensor &Lt, const cytnx_bool &rc);
+    template Tensor Add<Scalar>(const Tensor &Lt, const Scalar &rc);
 
+  }  // namespace linalg
   //===================
   // operators:
   //===================
diff --git a/tests/linalg_test/linalg_test.cpp b/tests/linalg_test/linalg_test.cpp
index e4deeaf49..a01f42bc3 100644
--- a/tests/linalg_test/linalg_test.cpp
+++ b/tests/linalg_test/linalg_test.cpp
@@ -318,6 +318,29 @@ TEST_F(linalg_Test, Tensor_Norm) {
   EXPECT_EQ(linalg::Norm(arange3x3cd).item(), ans);
 }
 
+TEST_F(linalg_Test, Tensor_Add_mixed_dtype_type_promote_cpu) {
+  Tensor lhs = arange(0, 4, 1, Type.Uint32).reshape(2, 2);
+  Tensor rhs = arange(0, 4, 1, Type.Int16).reshape(2, 2);
+
+  Tensor out = linalg::Add(lhs, rhs);
+  EXPECT_EQ(out.dtype(), Type.type_promote(lhs.dtype(), rhs.dtype()));
+  EXPECT_EQ((cytnx_int64)out(1, 1).item().real(), 6);
+}
+
+TEST_F(linalg_Test, Tensor_Add_scalar_mixed_dtype_type_promote_cpu) {
+  Tensor rhs = arange(0, 4, 1, Type.Int16).reshape(2, 2);
+  const cytnx_uint32 lhs_scalar = 5;
+
+  Tensor out_lhs = linalg::Add(lhs_scalar, rhs);
+  Tensor out_rhs = linalg::Add(rhs, lhs_scalar);
+  const unsigned int promoted = Type.type_promote(Type.Uint32, rhs.dtype());
+
+  EXPECT_EQ(out_lhs.dtype(), promoted);
+  EXPECT_EQ(out_rhs.dtype(), promoted);
+  EXPECT_EQ((cytnx_int64)out_lhs(1, 1).item().real(), 8);
+  EXPECT_EQ((cytnx_int64)out_rhs(1, 1).item().real(), 8);
+}
+
 TEST_F(linalg_Test, DenseUt_Norm) {
   cytnx_double ans = 0;
   for (cytnx_uint64 i = 0; i < 9; i++) {

From d2c38818ca6a6be79fffb3222bb5f2954ff0ae52 Mon Sep 17 00:00:00 2001
From: Ying-Jer Kao <yjkao@phys.ntu.edu.tw>
Date: Tue, 31 Mar 2026 08:44:51 +0800
Subject: [PATCH 6/7] CUDA: typed Add dispatch + CUDA13 CCCL include detection

---
 CytnxBKNDCMakeLists.cmake                     |  27 ++
 .../linalg_internal_gpu/cuAdd_internal.cu     | 274 ++++++++++++++++++
 .../linalg_internal_gpu/cuAdd_internal.hpp    |   7 +
 src/linalg/Add.cpp                            |  34 +--
 tests/gpu/linalg_test/Add_test.cpp            |  35 +++
 5 files changed, 357 insertions(+), 20 deletions(-)

diff --git a/CytnxBKNDCMakeLists.cmake b/CytnxBKNDCMakeLists.cmake
index 1beaeada1..3cda74010 100644
--- a/CytnxBKNDCMakeLists.cmake
+++ b/CytnxBKNDCMakeLists.cmake
@@ -126,6 +126,33 @@ if(USE_CUDA)
     #      -gencode=arch=compute_75,code=compute_75 ")
     target_compile_definitions(cytnx PUBLIC UNI_GPU)
     target_include_directories(cytnx PRIVATE ${CUDAToolkit_INCLUDE_DIRS})
+    # CUDA 12+/13 may place Thrust/CUB headers under include/cccl.
+    set(_cytnx_cccl_candidates)
+    if(DEFINED CUDAToolkit_TARGET_DIR AND NOT "${CUDAToolkit_TARGET_DIR}" STREQUAL "")
+      list(APPEND _cytnx_cccl_candidates "${CUDAToolkit_TARGET_DIR}/include/cccl")
+    endif()
+    foreach(_cuda_inc IN LISTS CUDAToolkit_INCLUDE_DIRS)
+      list(APPEND _cytnx_cccl_candidates
+        "${_cuda_inc}/cccl"
+        "${_cuda_inc}/../include/cccl"
+        "${_cuda_inc}/../../include/cccl"
+        "${_cuda_inc}/../../../include/cccl")
+    endforeach()
+    list(REMOVE_DUPLICATES _cytnx_cccl_candidates)
+
+    set(_cytnx_cccl_dir "")
+    foreach(_cccl_candidate IN LISTS _cytnx_cccl_candidates)
+      get_filename_component(_cccl_candidate_abs "${_cccl_candidate}" ABSOLUTE)
+      if(EXISTS "${_cccl_candidate_abs}")
+        set(_cytnx_cccl_dir "${_cccl_candidate_abs}")
+        break()
+      endif()
+    endforeach()
+    if(NOT "${_cytnx_cccl_dir}" STREQUAL "")
+      target_include_directories(cytnx PRIVATE "${_cytnx_cccl_dir}")
+      message(STATUS "Detected CCCL headers at: ${_cytnx_cccl_dir}")
+    endif()
+
     target_link_libraries(cytnx PUBLIC CUDA::toolkit)
     target_link_libraries(cytnx PUBLIC CUDA::cudart CUDA::cublas CUDA::cusparse CUDA::curand CUDA::cusolver)
     target_link_libraries(cytnx PUBLIC -lcudadevrt)
diff --git a/src/backend/linalg_internal_gpu/cuAdd_internal.cu b/src/backend/linalg_internal_gpu/cuAdd_internal.cu
index 57cc32631..e97f0121b 100644
--- a/src/backend/linalg_internal_gpu/cuAdd_internal.cu
+++ b/src/backend/linalg_internal_gpu/cuAdd_internal.cu
@@ -5,6 +5,280 @@ namespace cytnx {
 
   namespace linalg_internal {
 
+    namespace {
+
+      template <typename T>
+      __device__ inline cuDoubleComplex CuToComplexDouble(const T &v) {
+        return make_cuDoubleComplex(static_cast<cytnx_double>(v), 0.0);
+      }
+
+      __device__ inline cuDoubleComplex CuToComplexDouble(const cuDoubleComplex &v) { return v; }
+
+      __device__ inline cuDoubleComplex CuToComplexDouble(const cuComplex &v) {
+        return cuComplexFloatToDouble(v);
+      }
+
+      template <typename T>
+      __device__ inline cuComplex CuToComplexFloat(const T &v) {
+        return make_cuFloatComplex(static_cast<cytnx_float>(v), 0.0f);
+      }
+
+      __device__ inline cuComplex CuToComplexFloat(const cuComplex &v) { return v; }
+
+      __device__ inline cuComplex CuToComplexFloat(const cuDoubleComplex &v) {
+        return make_cuFloatComplex(static_cast<cytnx_float>(cuCreal(v)),
+                                   static_cast<cytnx_float>(cuCimag(v)));
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __device__ inline TO CuAddDispatchOp(const TL &lhs, const TR &rhs) {
+        if constexpr (std::is_same_v<TO, cuDoubleComplex>) {
+          return cuCadd(CuToComplexDouble(lhs), CuToComplexDouble(rhs));
+        } else if constexpr (std::is_same_v<TO, cuComplex>) {
+          return cuCaddf(CuToComplexFloat(lhs), CuToComplexFloat(rhs));
+        } else {
+          return static_cast<TO>(lhs) + static_cast<TO>(rhs);
+        }
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __global__ void cuAdd_dispatch_constconst_kernel(TO *out, const TL lhs, const cytnx_uint64 n,
+                                                       const TR rhs) {
+        const cytnx_uint64 idx = blockIdx.x * blockDim.x + threadIdx.x;
+        if (idx < n) out[idx] = CuAddDispatchOp<TO>(lhs, rhs);
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __global__ void cuAdd_dispatch_lconst_kernel(TO *out, const TL lhs, const cytnx_uint64 n,
+                                                   const TR *rhs) {
+        const cytnx_uint64 idx = blockIdx.x * blockDim.x + threadIdx.x;
+        if (idx < n) out[idx] = CuAddDispatchOp<TO>(lhs, rhs[idx]);
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __global__ void cuAdd_dispatch_rconst_kernel(TO *out, const TL *lhs, const cytnx_uint64 n,
+                                                   const TR rhs) {
+        const cytnx_uint64 idx = blockIdx.x * blockDim.x + threadIdx.x;
+        if (idx < n) out[idx] = CuAddDispatchOp<TO>(lhs[idx], rhs);
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __global__ void cuAdd_dispatch_tn_kernel(TO *out, const TL *lhs, const cytnx_uint64 n,
+                                               const TR *rhs) {
+        const cytnx_uint64 idx = blockIdx.x * blockDim.x + threadIdx.x;
+        if (idx < n) out[idx] = CuAddDispatchOp<TO>(lhs[idx], rhs[idx]);
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __global__ void cuAdd_dispatch_tn_kernel_nonconti(
+        TO *out, const TL *lhs, const cytnx_uint64 n, const TR *rhs, const cytnx_uint64 *accu_shape,
+        const cytnx_uint64 *old_accu_shapeL, const cytnx_uint64 *old_accu_shapeR,
+        const cytnx_uint64 *invmapper_L, const cytnx_uint64 *invmapper_R,
+        const cytnx_uint64 shapesize) {
+        extern __shared__ cytnx_uint64 tmpv[];
+
+        const cytnx_uint64 idx = blockIdx.x * blockDim.x + threadIdx.x;
+        if (idx < n) {
+          cytnx_uint64 tmp = idx;
+          const cytnx_uint64 offset = threadIdx.x * shapesize;
+          cytnx_uint64 Lidx = 0, Ridx = 0;
+
+          for (cytnx_uint64 j = 0; j < shapesize; j++) {
+            tmpv[offset + j] = tmp / accu_shape[j];
+            tmp = tmp % accu_shape[j];
+          }
+          for (cytnx_uint64 j = 0; j < shapesize; j++) {
+            Lidx += tmpv[offset + invmapper_L[j]] * old_accu_shapeL[j];
+            Ridx += tmpv[offset + invmapper_R[j]] * old_accu_shapeR[j];
+          }
+          out[idx] = CuAddDispatchOp<TO>(lhs[Lidx], rhs[Ridx]);
+        }
+      }
+
+      template <typename TL, typename TR>
+      void cuAdd_dispatch_typed(boost::intrusive_ptr<Storage_base> &out,
+                                boost::intrusive_ptr<Storage_base> &Lin,
+                                boost::intrusive_ptr<Storage_base> &Rin,
+                                const unsigned long long &len,
+                                const std::vector<cytnx_uint64> &shape,
+                                const std::vector<cytnx_uint64> &invmapper_L,
+                                const std::vector<cytnx_uint64> &invmapper_R) {
+        using TO = Type_class::type_promote_gpu_t<TL, TR>;
+        cytnx_error_msg(out->dtype() != Type_class::cy_typeid_gpu_v<TO>,
+                        "[cuAdd_dispatch] output dtype mismatch. got=%d expected=%d%s",
+                        out->dtype(), Type_class::cy_typeid_gpu_v<TO>, "\n");
+
+        TO *_out = reinterpret_cast<TO *>(out->data());
+        const TL *_Lin = reinterpret_cast<const TL *>(Lin->data());
+        const TR *_Rin = reinterpret_cast<const TR *>(Rin->data());
+
+        cytnx_uint32 NBlocks = len / 512;
+        if (len % 512) NBlocks += 1;
+
+        if (Lin->size() == 1 and Rin->size() == 1) {
+          cuAdd_dispatch_constconst_kernel<<<NBlocks, 512>>>(_out, _Lin[0], len, _Rin[0]);
+        } else if (Lin->size() == 1) {
+          cuAdd_dispatch_lconst_kernel<<<NBlocks, 512>>>(_out, _Lin[0], len, _Rin);
+        } else if (Rin->size() == 1) {
+          cuAdd_dispatch_rconst_kernel<<<NBlocks, 512>>>(_out, _Lin, len, _Rin[0]);
+        } else {
+          if (shape.size() == 0) {
+            cuAdd_dispatch_tn_kernel<<<NBlocks, 512>>>(_out, _Lin, len, _Rin);
+          } else {
+            cytnx_uint64 *m_accu_shape = reinterpret_cast<cytnx_uint64 *>(
+              utils_internal::cuCalloc_gpu(shape.size(), sizeof(cytnx_uint64)));
+            cytnx_uint64 *m_old_accu_shapeL = reinterpret_cast<cytnx_uint64 *>(
+              utils_internal::cuCalloc_gpu(shape.size(), sizeof(cytnx_uint64)));
+            cytnx_uint64 *m_old_accu_shapeR = reinterpret_cast<cytnx_uint64 *>(
+              utils_internal::cuCalloc_gpu(shape.size(), sizeof(cytnx_uint64)));
+            cytnx_uint64 *m_invmapper_L = reinterpret_cast<cytnx_uint64 *>(
+              utils_internal::cuMalloc_gpu(invmapper_L.size() * sizeof(cytnx_uint64)));
+            cytnx_uint64 *m_invmapper_R = reinterpret_cast<cytnx_uint64 *>(
+              utils_internal::cuMalloc_gpu(invmapper_R.size() * sizeof(cytnx_uint64)));
+
+            checkCudaErrors(cudaMemcpy(m_invmapper_L, &invmapper_L[0],
+                                       sizeof(cytnx_uint64) * invmapper_L.size(),
+                                       cudaMemcpyHostToDevice));
+            checkCudaErrors(cudaMemcpy(m_invmapper_R, &invmapper_R[0],
+                                       sizeof(cytnx_uint64) * invmapper_R.size(),
+                                       cudaMemcpyHostToDevice));
+
+            cytnx_uint64 tmp1 = 1, tmp2 = 1, tmp3 = 1;
+            for (cytnx_uint64 i = 0; i < shape.size(); i++) {
+              m_accu_shape[shape.size() - 1 - i] = tmp1;
+              tmp1 *= shape[shape.size() - 1 - i];
+
+              m_old_accu_shapeL[shape.size() - 1 - i] = tmp2;
+              tmp2 *= shape[invmapper_L[shape.size() - 1 - i]];
+
+              m_old_accu_shapeR[shape.size() - 1 - i] = tmp3;
+              tmp3 *= shape[invmapper_R[shape.size() - 1 - i]];
+            }
+
+            cuAdd_dispatch_tn_kernel_nonconti<<<NBlocks, 512,
+                                                512 * shape.size() * sizeof(cytnx_uint64)>>>(
+              _out, _Lin, len, _Rin, m_accu_shape, m_old_accu_shapeL, m_old_accu_shapeR,
+              m_invmapper_L, m_invmapper_R, shape.size());
+
+            checkCudaErrors(cudaFree(m_accu_shape));
+            checkCudaErrors(cudaFree(m_old_accu_shapeL));
+            checkCudaErrors(cudaFree(m_old_accu_shapeR));
+            checkCudaErrors(cudaFree(m_invmapper_L));
+            checkCudaErrors(cudaFree(m_invmapper_R));
+          }
+        }
+      }
+
+      template <typename TL>
+      void cuAdd_dispatch_rhs(boost::intrusive_ptr<Storage_base> &out,
+                              boost::intrusive_ptr<Storage_base> &Lin,
+                              boost::intrusive_ptr<Storage_base> &Rin,
+                              const unsigned long long &len, const std::vector<cytnx_uint64> &shape,
+                              const std::vector<cytnx_uint64> &invmapper_L,
+                              const std::vector<cytnx_uint64> &invmapper_R) {
+        switch (Rin->dtype()) {
+          case Type.ComplexDouble:
+            cuAdd_dispatch_typed<TL, cuDoubleComplex>(out, Lin, Rin, len, shape, invmapper_L,
+                                                      invmapper_R);
+            break;
+          case Type.ComplexFloat:
+            cuAdd_dispatch_typed<TL, cuComplex>(out, Lin, Rin, len, shape, invmapper_L,
+                                                invmapper_R);
+            break;
+          case Type.Double:
+            cuAdd_dispatch_typed<TL, cytnx_double>(out, Lin, Rin, len, shape, invmapper_L,
+                                                   invmapper_R);
+            break;
+          case Type.Float:
+            cuAdd_dispatch_typed<TL, cytnx_float>(out, Lin, Rin, len, shape, invmapper_L,
+                                                  invmapper_R);
+            break;
+          case Type.Int64:
+            cuAdd_dispatch_typed<TL, cytnx_int64>(out, Lin, Rin, len, shape, invmapper_L,
+                                                  invmapper_R);
+            break;
+          case Type.Uint64:
+            cuAdd_dispatch_typed<TL, cytnx_uint64>(out, Lin, Rin, len, shape, invmapper_L,
+                                                   invmapper_R);
+            break;
+          case Type.Int32:
+            cuAdd_dispatch_typed<TL, cytnx_int32>(out, Lin, Rin, len, shape, invmapper_L,
+                                                  invmapper_R);
+            break;
+          case Type.Uint32:
+            cuAdd_dispatch_typed<TL, cytnx_uint32>(out, Lin, Rin, len, shape, invmapper_L,
+                                                   invmapper_R);
+            break;
+          case Type.Int16:
+            cuAdd_dispatch_typed<TL, cytnx_int16>(out, Lin, Rin, len, shape, invmapper_L,
+                                                  invmapper_R);
+            break;
+          case Type.Uint16:
+            cuAdd_dispatch_typed<TL, cytnx_uint16>(out, Lin, Rin, len, shape, invmapper_L,
+                                                   invmapper_R);
+            break;
+          case Type.Bool:
+            cuAdd_dispatch_typed<TL, cytnx_bool>(out, Lin, Rin, len, shape, invmapper_L,
+                                                 invmapper_R);
+            break;
+          default:
+            cytnx_error_msg(true, "[cuAdd_dispatch] unsupported rhs dtype: %d%s", Rin->dtype(),
+                            "\n");
+        }
+      }
+
+    }  // namespace
+
+    void cuAdd_dispatch(boost::intrusive_ptr<Storage_base> &out,
+                        boost::intrusive_ptr<Storage_base> &Lin,
+                        boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
+                        const std::vector<cytnx_uint64> &shape,
+                        const std::vector<cytnx_uint64> &invmapper_L,
+                        const std::vector<cytnx_uint64> &invmapper_R) {
+      const unsigned int expected_dtype = Type.type_promote(Lin->dtype(), Rin->dtype());
+      cytnx_error_msg(out->dtype() != expected_dtype,
+                      "[cuAdd_dispatch] output dtype mismatch. got=%d expected=%d%s", out->dtype(),
+                      expected_dtype, "\n");
+
+      switch (Lin->dtype()) {
+        case Type.ComplexDouble:
+          cuAdd_dispatch_rhs<cuDoubleComplex>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.ComplexFloat:
+          cuAdd_dispatch_rhs<cuComplex>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Double:
+          cuAdd_dispatch_rhs<cytnx_double>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Float:
+          cuAdd_dispatch_rhs<cytnx_float>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Int64:
+          cuAdd_dispatch_rhs<cytnx_int64>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Uint64:
+          cuAdd_dispatch_rhs<cytnx_uint64>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Int32:
+          cuAdd_dispatch_rhs<cytnx_int32>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Uint32:
+          cuAdd_dispatch_rhs<cytnx_uint32>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Int16:
+          cuAdd_dispatch_rhs<cytnx_int16>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Uint16:
+          cuAdd_dispatch_rhs<cytnx_uint16>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Bool:
+          cuAdd_dispatch_rhs<cytnx_bool>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        default:
+          cytnx_error_msg(true, "[cuAdd_dispatch] unsupported lhs dtype: %d%s", Lin->dtype(), "\n");
+      }
+    }
+
     //====================================================================
     // generic R+R kernel
 
diff --git a/src/backend/linalg_internal_gpu/cuAdd_internal.hpp b/src/backend/linalg_internal_gpu/cuAdd_internal.hpp
index ca8997145..860bae9ea 100644
--- a/src/backend/linalg_internal_gpu/cuAdd_internal.hpp
+++ b/src/backend/linalg_internal_gpu/cuAdd_internal.hpp
@@ -13,6 +13,13 @@ namespace cytnx {
   namespace linalg_internal {
 
     /// cuAdd
+    void cuAdd_dispatch(boost::intrusive_ptr<Storage_base> &out,
+                        boost::intrusive_ptr<Storage_base> &Lin,
+                        boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
+                        const std::vector<cytnx_uint64> &shape,
+                        const std::vector<cytnx_uint64> &invmapper_L,
+                        const std::vector<cytnx_uint64> &invmapper_R);
+
     void cuAdd_internal_cdtcd(boost::intrusive_ptr<Storage_base> &out,
                               boost::intrusive_ptr<Storage_base> &Lin,
                               boost::intrusive_ptr<Storage_base> &Rin,
diff --git a/src/linalg/Add.cpp b/src/linalg/Add.cpp
index 15a0553bb..4bb555a4d 100644
--- a/src/linalg/Add.cpp
+++ b/src/linalg/Add.cpp
@@ -11,14 +11,7 @@ namespace cytnx {
     namespace detail {
       inline unsigned int SelectAddOutputType(const unsigned int lhs_dtype,
                                               const unsigned int rhs_dtype, const int device) {
-  #ifdef UNI_GPU
-        // Current GPU arithmetic tables still assume legacy min(lhs, rhs) promotion.
-        if (device != Device.cpu) {
-          return lhs_dtype < rhs_dtype ? lhs_dtype : rhs_dtype;
-        }
-  #else
         (void)device;
-  #endif
         return Type.type_promote(lhs_dtype, rhs_dtype);
       }
 
@@ -46,9 +39,9 @@ namespace cytnx {
         } else {
   #ifdef UNI_GPU
           checkCudaErrors(cudaSetDevice(Rt.device()));
-          linalg_internal::lii.cuAri_ii[lhs_dtype][Rt.dtype()](
-            out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-            Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
+          linalg_internal::cuAdd_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                          Rt._impl->storage()._impl,
+                                          Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
           cytnx_error_msg(true, "[Add] fatal error, the tensor is on GPU without CUDA support.%s",
                           "\n");
@@ -107,9 +100,9 @@ namespace cytnx {
         } else {
   #ifdef UNI_GPU
           checkCudaErrors(cudaSetDevice(Rt.device()));
-          linalg_internal::lii.cuAri_ii[Lt.dtype()][Rt.dtype()](
-            out._impl->storage()._impl, Lt._impl->storage()._impl, Rt._impl->storage()._impl,
-            out._impl->storage()._impl->size(), {}, {}, {}, 0);
+          linalg_internal::cuAdd_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                          Rt._impl->storage()._impl,
+                                          out._impl->storage()._impl->size(), {}, {}, {});
   #else
           cytnx_error_msg(true, "[Add] fatal error, the tensor is on GPU without CUDA support.%s",
                           "\n");
@@ -134,10 +127,11 @@ namespace cytnx {
             Lt.ptr());
         } else {
   #ifdef UNI_GPU
-          linalg_internal::lii.cuAri_ii[Lt.dtype()][Rt.dtype()](
-            out._impl->storage()._impl, Lt._impl->storage()._impl, Rt._impl->storage()._impl,
-            Lt._impl->storage()._impl->size(), Lt._impl->shape(), Lt._impl->invmapper(),
-            Rt._impl->invmapper(), 0);
+          checkCudaErrors(cudaSetDevice(Rt.device()));
+          linalg_internal::cuAdd_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                          Rt._impl->storage()._impl,
+                                          Lt._impl->storage()._impl->size(), Lt._impl->shape(),
+                                          Lt._impl->invmapper(), Rt._impl->invmapper());
   #else
           cytnx_error_msg(true, "[Add] fatal error, the tensor is on GPU without CUDA support.%s",
                           "\n");
@@ -183,9 +177,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        linalg_internal::lii.cuAri_ii[lc.dtype()][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 0);
+        linalg_internal::cuAdd_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Add] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
diff --git a/tests/gpu/linalg_test/Add_test.cpp b/tests/gpu/linalg_test/Add_test.cpp
index f125d8012..de5baa853 100644
--- a/tests/gpu/linalg_test/Add_test.cpp
+++ b/tests/gpu/linalg_test/Add_test.cpp
@@ -126,6 +126,41 @@ namespace AddTest {
     }
   }
 
+  TEST(AddMixedDtypeTest, gpu_tensor_add_tensor_mixed_unsigned_signed_type_promote) {
+    cytnx::Tensor lhs = cytnx::arange(0, 6, 1, cytnx::Type.Uint32).reshape({2, 3});
+    cytnx::Tensor rhs = cytnx::arange(0, 6, 1, cytnx::Type.Int16).reshape({2, 3});
+    lhs = lhs.to(cytnx::Device.cuda);
+    rhs = rhs.to(cytnx::Device.cuda);
+
+    cytnx::Tensor gpu_result = cytnx::linalg::Add(lhs, rhs);
+    cytnx::Tensor expected_cpu =
+      cytnx::linalg::Add(lhs.to(cytnx::Device.cpu), rhs.to(cytnx::Device.cpu));
+    cytnx::Tensor gpu_result_cpu = gpu_result.to(cytnx::Device.cpu);
+
+    EXPECT_EQ(gpu_result.dtype(), expected_cpu.dtype());
+    EXPECT_TRUE(cytnx::TestTools::AreNearlyEqTensor(gpu_result_cpu, expected_cpu, 1e-6));
+  }
+
+  TEST(AddMixedDtypeTest, gpu_scalar_add_tensor_mixed_unsigned_signed_type_promote) {
+    const cytnx::cytnx_uint32 scalar = 5;
+    cytnx::Tensor rhs =
+      cytnx::arange(0, 6, 1, cytnx::Type.Int16).reshape({2, 3}).to(cytnx::Device.cuda);
+
+    cytnx::Tensor gpu_result_l = cytnx::linalg::Add(scalar, rhs);
+    cytnx::Tensor gpu_result_r = cytnx::linalg::Add(rhs, scalar);
+
+    cytnx::Tensor rhs_cpu = rhs.to(cytnx::Device.cpu);
+    cytnx::Tensor expected_l = cytnx::linalg::Add(scalar, rhs_cpu);
+    cytnx::Tensor expected_r = cytnx::linalg::Add(rhs_cpu, scalar);
+    cytnx::Tensor gpu_result_l_cpu = gpu_result_l.to(cytnx::Device.cpu);
+    cytnx::Tensor gpu_result_r_cpu = gpu_result_r.to(cytnx::Device.cpu);
+
+    EXPECT_EQ(gpu_result_l.dtype(), expected_l.dtype());
+    EXPECT_EQ(gpu_result_r.dtype(), expected_r.dtype());
+    EXPECT_TRUE(cytnx::TestTools::AreNearlyEqTensor(gpu_result_l_cpu, expected_l, 1e-6));
+    EXPECT_TRUE(cytnx::TestTools::AreNearlyEqTensor(gpu_result_r_cpu, expected_r, 1e-6));
+  }
+
   INSTANTIATE_TEST_SUITE_P(AddTests, AddTestAllShapes, ::testing::ValuesIn(GetTestShapes()));
 
   ::testing::AssertionResult CheckAddResult(const cytnx::Tensor& gpu_result,

From d60ea7ffebaa6576e3ebba0b552e33e33934b4d6 Mon Sep 17 00:00:00 2001
From: Ying-Jer Kao <yjkao@phys.ntu.edu.tw>
Date: Tue, 31 Mar 2026 09:01:26 +0800
Subject: [PATCH 7/7] CUDA: typed dispatch for Sub/Mul/Div with mixed-dtype
 tests

---
 .../linalg_internal_gpu/CMakeLists.txt        |   3 +
 .../linalg_internal_gpu/cuDiv_dispatch.cu     | 283 +++++++++++++++++
 .../linalg_internal_gpu/cuDiv_internal.hpp    |   7 +
 .../linalg_internal_gpu/cuMul_dispatch.cu     | 283 +++++++++++++++++
 .../linalg_internal_gpu/cuMul_internal.hpp    |   7 +
 .../linalg_internal_gpu/cuSub_dispatch.cu     | 283 +++++++++++++++++
 .../linalg_internal_gpu/cuSub_internal.hpp    |   7 +
 src/linalg/Div.cpp                            | 286 ++++++++---------
 src/linalg/Mul.cpp                            | 161 +++++-----
 src/linalg/Sub.cpp                            | 298 ++++++++----------
 tests/gpu/linalg_test/Div_test.cpp            |  38 +++
 tests/gpu/linalg_test/Mul_test.cpp            |  35 ++
 tests/gpu/linalg_test/Sub_test.cpp            |  35 ++
 13 files changed, 1329 insertions(+), 397 deletions(-)
 create mode 100644 src/backend/linalg_internal_gpu/cuDiv_dispatch.cu
 create mode 100644 src/backend/linalg_internal_gpu/cuMul_dispatch.cu
 create mode 100644 src/backend/linalg_internal_gpu/cuSub_dispatch.cu

diff --git a/src/backend/linalg_internal_gpu/CMakeLists.txt b/src/backend/linalg_internal_gpu/CMakeLists.txt
index c3ca5f0ca..ef8eb9ef2 100644
--- a/src/backend/linalg_internal_gpu/CMakeLists.txt
+++ b/src/backend/linalg_internal_gpu/CMakeLists.txt
@@ -36,6 +36,9 @@ target_sources_local(cytnx
 
     cuAbs_internal.cu
     cuAdd_internal.cu
+    cuSub_dispatch.cu
+    cuMul_dispatch.cu
+    cuDiv_dispatch.cu
     cuGer_internal.cu
     cuArithmetic_internal.cu
     cuConj_inplace_internal.cu
diff --git a/src/backend/linalg_internal_gpu/cuDiv_dispatch.cu b/src/backend/linalg_internal_gpu/cuDiv_dispatch.cu
new file mode 100644
index 000000000..5eb9b6731
--- /dev/null
+++ b/src/backend/linalg_internal_gpu/cuDiv_dispatch.cu
@@ -0,0 +1,283 @@
+#include "cuDiv_internal.hpp"
+#include "backend/utils_internal_interface.hpp"
+
+namespace cytnx {
+
+  namespace linalg_internal {
+
+    namespace {
+
+      template <typename T>
+      __device__ inline cuDoubleComplex CuToComplexDouble(const T &v) {
+        return make_cuDoubleComplex(static_cast<cytnx_double>(v), 0.0);
+      }
+
+      __device__ inline cuDoubleComplex CuToComplexDouble(const cuDoubleComplex &v) { return v; }
+
+      __device__ inline cuDoubleComplex CuToComplexDouble(const cuComplex &v) {
+        return cuComplexFloatToDouble(v);
+      }
+
+      template <typename T>
+      __device__ inline cuComplex CuToComplexFloat(const T &v) {
+        return make_cuFloatComplex(static_cast<cytnx_float>(v), 0.0f);
+      }
+
+      __device__ inline cuComplex CuToComplexFloat(const cuComplex &v) { return v; }
+
+      __device__ inline cuComplex CuToComplexFloat(const cuDoubleComplex &v) {
+        return make_cuFloatComplex(static_cast<cytnx_float>(cuCreal(v)),
+                                   static_cast<cytnx_float>(cuCimag(v)));
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __device__ inline TO CuDivDispatchOp(const TL &lhs, const TR &rhs) {
+        if constexpr (std::is_same_v<TO, cuDoubleComplex>) {
+          return cuCdiv(CuToComplexDouble(lhs), CuToComplexDouble(rhs));
+        } else if constexpr (std::is_same_v<TO, cuComplex>) {
+          return cuCdivf(CuToComplexFloat(lhs), CuToComplexFloat(rhs));
+        } else {
+          return static_cast<TO>(lhs) / static_cast<TO>(rhs);
+        }
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __global__ void cuDiv_dispatch_constconst_kernel(TO *out, const TL lhs, const cytnx_uint64 n,
+                                                       const TR rhs) {
+        const cytnx_uint64 idx = blockIdx.x * blockDim.x + threadIdx.x;
+        if (idx < n) out[idx] = CuDivDispatchOp<TO>(lhs, rhs);
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __global__ void cuDiv_dispatch_lconst_kernel(TO *out, const TL lhs, const cytnx_uint64 n,
+                                                   const TR *rhs) {
+        const cytnx_uint64 idx = blockIdx.x * blockDim.x + threadIdx.x;
+        if (idx < n) out[idx] = CuDivDispatchOp<TO>(lhs, rhs[idx]);
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __global__ void cuDiv_dispatch_rconst_kernel(TO *out, const TL *lhs, const cytnx_uint64 n,
+                                                   const TR rhs) {
+        const cytnx_uint64 idx = blockIdx.x * blockDim.x + threadIdx.x;
+        if (idx < n) out[idx] = CuDivDispatchOp<TO>(lhs[idx], rhs);
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __global__ void cuDiv_dispatch_tn_kernel(TO *out, const TL *lhs, const cytnx_uint64 n,
+                                               const TR *rhs) {
+        const cytnx_uint64 idx = blockIdx.x * blockDim.x + threadIdx.x;
+        if (idx < n) out[idx] = CuDivDispatchOp<TO>(lhs[idx], rhs[idx]);
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __global__ void cuDiv_dispatch_tn_kernel_nonconti(
+        TO *out, const TL *lhs, const cytnx_uint64 n, const TR *rhs, const cytnx_uint64 *accu_shape,
+        const cytnx_uint64 *old_accu_shapeL, const cytnx_uint64 *old_accu_shapeR,
+        const cytnx_uint64 *invmapper_L, const cytnx_uint64 *invmapper_R,
+        const cytnx_uint64 shapesize) {
+        extern __shared__ cytnx_uint64 tmpv[];
+
+        const cytnx_uint64 idx = blockIdx.x * blockDim.x + threadIdx.x;
+        if (idx < n) {
+          cytnx_uint64 tmp = idx;
+          const cytnx_uint64 offset = threadIdx.x * shapesize;
+          cytnx_uint64 Lidx = 0, Ridx = 0;
+
+          for (cytnx_uint64 j = 0; j < shapesize; j++) {
+            tmpv[offset + j] = tmp / accu_shape[j];
+            tmp = tmp % accu_shape[j];
+          }
+          for (cytnx_uint64 j = 0; j < shapesize; j++) {
+            Lidx += tmpv[offset + invmapper_L[j]] * old_accu_shapeL[j];
+            Ridx += tmpv[offset + invmapper_R[j]] * old_accu_shapeR[j];
+          }
+          out[idx] = CuDivDispatchOp<TO>(lhs[Lidx], rhs[Ridx]);
+        }
+      }
+
+      template <typename TL, typename TR>
+      void cuDiv_dispatch_typed(boost::intrusive_ptr<Storage_base> &out,
+                                boost::intrusive_ptr<Storage_base> &Lin,
+                                boost::intrusive_ptr<Storage_base> &Rin,
+                                const unsigned long long &len,
+                                const std::vector<cytnx_uint64> &shape,
+                                const std::vector<cytnx_uint64> &invmapper_L,
+                                const std::vector<cytnx_uint64> &invmapper_R) {
+        using TO = Type_class::type_promote_gpu_t<TL, TR>;
+        cytnx_error_msg(out->dtype() != Type_class::cy_typeid_gpu_v<TO>,
+                        "[cuDiv_dispatch] output dtype mismatch. got=%d expected=%d%s",
+                        out->dtype(), Type_class::cy_typeid_gpu_v<TO>, "\n");
+
+        TO *_out = reinterpret_cast<TO *>(out->data());
+        const TL *_Lin = reinterpret_cast<const TL *>(Lin->data());
+        const TR *_Rin = reinterpret_cast<const TR *>(Rin->data());
+
+        cytnx_uint32 NBlocks = len / 512;
+        if (len % 512) NBlocks += 1;
+
+        if (Lin->size() == 1 and Rin->size() == 1) {
+          cuDiv_dispatch_constconst_kernel<<<NBlocks, 512>>>(_out, _Lin[0], len, _Rin[0]);
+        } else if (Lin->size() == 1) {
+          cuDiv_dispatch_lconst_kernel<<<NBlocks, 512>>>(_out, _Lin[0], len, _Rin);
+        } else if (Rin->size() == 1) {
+          cuDiv_dispatch_rconst_kernel<<<NBlocks, 512>>>(_out, _Lin, len, _Rin[0]);
+        } else {
+          if (shape.size() == 0) {
+            cuDiv_dispatch_tn_kernel<<<NBlocks, 512>>>(_out, _Lin, len, _Rin);
+          } else {
+            cytnx_uint64 *m_accu_shape = reinterpret_cast<cytnx_uint64 *>(
+              utils_internal::cuCalloc_gpu(shape.size(), sizeof(cytnx_uint64)));
+            cytnx_uint64 *m_old_accu_shapeL = reinterpret_cast<cytnx_uint64 *>(
+              utils_internal::cuCalloc_gpu(shape.size(), sizeof(cytnx_uint64)));
+            cytnx_uint64 *m_old_accu_shapeR = reinterpret_cast<cytnx_uint64 *>(
+              utils_internal::cuCalloc_gpu(shape.size(), sizeof(cytnx_uint64)));
+            cytnx_uint64 *m_invmapper_L = reinterpret_cast<cytnx_uint64 *>(
+              utils_internal::cuMalloc_gpu(invmapper_L.size() * sizeof(cytnx_uint64)));
+            cytnx_uint64 *m_invmapper_R = reinterpret_cast<cytnx_uint64 *>(
+              utils_internal::cuMalloc_gpu(invmapper_R.size() * sizeof(cytnx_uint64)));
+
+            checkCudaErrors(cudaMemcpy(m_invmapper_L, &invmapper_L[0],
+                                       sizeof(cytnx_uint64) * invmapper_L.size(),
+                                       cudaMemcpyHostToDevice));
+            checkCudaErrors(cudaMemcpy(m_invmapper_R, &invmapper_R[0],
+                                       sizeof(cytnx_uint64) * invmapper_R.size(),
+                                       cudaMemcpyHostToDevice));
+
+            cytnx_uint64 tmp1 = 1, tmp2 = 1, tmp3 = 1;
+            for (cytnx_uint64 i = 0; i < shape.size(); i++) {
+              m_accu_shape[shape.size() - 1 - i] = tmp1;
+              tmp1 *= shape[shape.size() - 1 - i];
+
+              m_old_accu_shapeL[shape.size() - 1 - i] = tmp2;
+              tmp2 *= shape[invmapper_L[shape.size() - 1 - i]];
+
+              m_old_accu_shapeR[shape.size() - 1 - i] = tmp3;
+              tmp3 *= shape[invmapper_R[shape.size() - 1 - i]];
+            }
+
+            cuDiv_dispatch_tn_kernel_nonconti<<<NBlocks, 512,
+                                                512 * shape.size() * sizeof(cytnx_uint64)>>>(
+              _out, _Lin, len, _Rin, m_accu_shape, m_old_accu_shapeL, m_old_accu_shapeR,
+              m_invmapper_L, m_invmapper_R, shape.size());
+
+            checkCudaErrors(cudaFree(m_accu_shape));
+            checkCudaErrors(cudaFree(m_old_accu_shapeL));
+            checkCudaErrors(cudaFree(m_old_accu_shapeR));
+            checkCudaErrors(cudaFree(m_invmapper_L));
+            checkCudaErrors(cudaFree(m_invmapper_R));
+          }
+        }
+      }
+
+      template <typename TL>
+      void cuDiv_dispatch_rhs(boost::intrusive_ptr<Storage_base> &out,
+                              boost::intrusive_ptr<Storage_base> &Lin,
+                              boost::intrusive_ptr<Storage_base> &Rin,
+                              const unsigned long long &len, const std::vector<cytnx_uint64> &shape,
+                              const std::vector<cytnx_uint64> &invmapper_L,
+                              const std::vector<cytnx_uint64> &invmapper_R) {
+        switch (Rin->dtype()) {
+          case Type.ComplexDouble:
+            cuDiv_dispatch_typed<TL, cuDoubleComplex>(out, Lin, Rin, len, shape, invmapper_L,
+                                                      invmapper_R);
+            break;
+          case Type.ComplexFloat:
+            cuDiv_dispatch_typed<TL, cuComplex>(out, Lin, Rin, len, shape, invmapper_L,
+                                                invmapper_R);
+            break;
+          case Type.Double:
+            cuDiv_dispatch_typed<TL, cytnx_double>(out, Lin, Rin, len, shape, invmapper_L,
+                                                   invmapper_R);
+            break;
+          case Type.Float:
+            cuDiv_dispatch_typed<TL, cytnx_float>(out, Lin, Rin, len, shape, invmapper_L,
+                                                  invmapper_R);
+            break;
+          case Type.Int64:
+            cuDiv_dispatch_typed<TL, cytnx_int64>(out, Lin, Rin, len, shape, invmapper_L,
+                                                  invmapper_R);
+            break;
+          case Type.Uint64:
+            cuDiv_dispatch_typed<TL, cytnx_uint64>(out, Lin, Rin, len, shape, invmapper_L,
+                                                   invmapper_R);
+            break;
+          case Type.Int32:
+            cuDiv_dispatch_typed<TL, cytnx_int32>(out, Lin, Rin, len, shape, invmapper_L,
+                                                  invmapper_R);
+            break;
+          case Type.Uint32:
+            cuDiv_dispatch_typed<TL, cytnx_uint32>(out, Lin, Rin, len, shape, invmapper_L,
+                                                   invmapper_R);
+            break;
+          case Type.Int16:
+            cuDiv_dispatch_typed<TL, cytnx_int16>(out, Lin, Rin, len, shape, invmapper_L,
+                                                  invmapper_R);
+            break;
+          case Type.Uint16:
+            cuDiv_dispatch_typed<TL, cytnx_uint16>(out, Lin, Rin, len, shape, invmapper_L,
+                                                   invmapper_R);
+            break;
+          case Type.Bool:
+            cuDiv_dispatch_typed<TL, cytnx_bool>(out, Lin, Rin, len, shape, invmapper_L,
+                                                 invmapper_R);
+            break;
+          default:
+            cytnx_error_msg(true, "[cuDiv_dispatch] unsupported rhs dtype: %d%s", Rin->dtype(),
+                            "\n");
+        }
+      }
+
+    }  // namespace
+
+    void cuDiv_dispatch(boost::intrusive_ptr<Storage_base> &out,
+                        boost::intrusive_ptr<Storage_base> &Lin,
+                        boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
+                        const std::vector<cytnx_uint64> &shape,
+                        const std::vector<cytnx_uint64> &invmapper_L,
+                        const std::vector<cytnx_uint64> &invmapper_R) {
+      const unsigned int expected_dtype = Type.type_promote(Lin->dtype(), Rin->dtype());
+      cytnx_error_msg(out->dtype() != expected_dtype,
+                      "[cuDiv_dispatch] output dtype mismatch. got=%d expected=%d%s", out->dtype(),
+                      expected_dtype, "\n");
+
+      switch (Lin->dtype()) {
+        case Type.ComplexDouble:
+          cuDiv_dispatch_rhs<cuDoubleComplex>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.ComplexFloat:
+          cuDiv_dispatch_rhs<cuComplex>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Double:
+          cuDiv_dispatch_rhs<cytnx_double>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Float:
+          cuDiv_dispatch_rhs<cytnx_float>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Int64:
+          cuDiv_dispatch_rhs<cytnx_int64>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Uint64:
+          cuDiv_dispatch_rhs<cytnx_uint64>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Int32:
+          cuDiv_dispatch_rhs<cytnx_int32>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Uint32:
+          cuDiv_dispatch_rhs<cytnx_uint32>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Int16:
+          cuDiv_dispatch_rhs<cytnx_int16>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Uint16:
+          cuDiv_dispatch_rhs<cytnx_uint16>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Bool:
+          cuDiv_dispatch_rhs<cytnx_bool>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        default:
+          cytnx_error_msg(true, "[cuDiv_dispatch] unsupported lhs dtype: %d%s", Lin->dtype(), "\n");
+      }
+    }
+
+  }  // namespace linalg_internal
+}  // namespace cytnx
diff --git a/src/backend/linalg_internal_gpu/cuDiv_internal.hpp b/src/backend/linalg_internal_gpu/cuDiv_internal.hpp
index 2b6c220b3..a4bee2e61 100644
--- a/src/backend/linalg_internal_gpu/cuDiv_internal.hpp
+++ b/src/backend/linalg_internal_gpu/cuDiv_internal.hpp
@@ -13,6 +13,13 @@ namespace cytnx {
   namespace linalg_internal {
 
     /// cuDiv
+    void cuDiv_dispatch(boost::intrusive_ptr<Storage_base> &out,
+                        boost::intrusive_ptr<Storage_base> &Lin,
+                        boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
+                        const std::vector<cytnx_uint64> &shape,
+                        const std::vector<cytnx_uint64> &invmapper_L,
+                        const std::vector<cytnx_uint64> &invmapper_R);
+
     void cuDiv_internal_cdtcd(boost::intrusive_ptr<Storage_base> &out,
                               boost::intrusive_ptr<Storage_base> &Lin,
                               boost::intrusive_ptr<Storage_base> &Rin,
diff --git a/src/backend/linalg_internal_gpu/cuMul_dispatch.cu b/src/backend/linalg_internal_gpu/cuMul_dispatch.cu
new file mode 100644
index 000000000..e2bba1362
--- /dev/null
+++ b/src/backend/linalg_internal_gpu/cuMul_dispatch.cu
@@ -0,0 +1,283 @@
+#include "cuMul_internal.hpp"
+#include "backend/utils_internal_interface.hpp"
+
+namespace cytnx {
+
+  namespace linalg_internal {
+
+    namespace {
+
+      template <typename T>
+      __device__ inline cuDoubleComplex CuToComplexDouble(const T &v) {
+        return make_cuDoubleComplex(static_cast<cytnx_double>(v), 0.0);
+      }
+
+      __device__ inline cuDoubleComplex CuToComplexDouble(const cuDoubleComplex &v) { return v; }
+
+      __device__ inline cuDoubleComplex CuToComplexDouble(const cuComplex &v) {
+        return cuComplexFloatToDouble(v);
+      }
+
+      template <typename T>
+      __device__ inline cuComplex CuToComplexFloat(const T &v) {
+        return make_cuFloatComplex(static_cast<cytnx_float>(v), 0.0f);
+      }
+
+      __device__ inline cuComplex CuToComplexFloat(const cuComplex &v) { return v; }
+
+      __device__ inline cuComplex CuToComplexFloat(const cuDoubleComplex &v) {
+        return make_cuFloatComplex(static_cast<cytnx_float>(cuCreal(v)),
+                                   static_cast<cytnx_float>(cuCimag(v)));
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __device__ inline TO CuMulDispatchOp(const TL &lhs, const TR &rhs) {
+        if constexpr (std::is_same_v<TO, cuDoubleComplex>) {
+          return cuCmul(CuToComplexDouble(lhs), CuToComplexDouble(rhs));
+        } else if constexpr (std::is_same_v<TO, cuComplex>) {
+          return cuCmulf(CuToComplexFloat(lhs), CuToComplexFloat(rhs));
+        } else {
+          return static_cast<TO>(lhs) * static_cast<TO>(rhs);
+        }
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __global__ void cuMul_dispatch_constconst_kernel(TO *out, const TL lhs, const cytnx_uint64 n,
+                                                       const TR rhs) {
+        const cytnx_uint64 idx = blockIdx.x * blockDim.x + threadIdx.x;
+        if (idx < n) out[idx] = CuMulDispatchOp<TO>(lhs, rhs);
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __global__ void cuMul_dispatch_lconst_kernel(TO *out, const TL lhs, const cytnx_uint64 n,
+                                                   const TR *rhs) {
+        const cytnx_uint64 idx = blockIdx.x * blockDim.x + threadIdx.x;
+        if (idx < n) out[idx] = CuMulDispatchOp<TO>(lhs, rhs[idx]);
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __global__ void cuMul_dispatch_rconst_kernel(TO *out, const TL *lhs, const cytnx_uint64 n,
+                                                   const TR rhs) {
+        const cytnx_uint64 idx = blockIdx.x * blockDim.x + threadIdx.x;
+        if (idx < n) out[idx] = CuMulDispatchOp<TO>(lhs[idx], rhs);
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __global__ void cuMul_dispatch_tn_kernel(TO *out, const TL *lhs, const cytnx_uint64 n,
+                                               const TR *rhs) {
+        const cytnx_uint64 idx = blockIdx.x * blockDim.x + threadIdx.x;
+        if (idx < n) out[idx] = CuMulDispatchOp<TO>(lhs[idx], rhs[idx]);
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __global__ void cuMul_dispatch_tn_kernel_nonconti(
+        TO *out, const TL *lhs, const cytnx_uint64 n, const TR *rhs, const cytnx_uint64 *accu_shape,
+        const cytnx_uint64 *old_accu_shapeL, const cytnx_uint64 *old_accu_shapeR,
+        const cytnx_uint64 *invmapper_L, const cytnx_uint64 *invmapper_R,
+        const cytnx_uint64 shapesize) {
+        extern __shared__ cytnx_uint64 tmpv[];
+
+        const cytnx_uint64 idx = blockIdx.x * blockDim.x + threadIdx.x;
+        if (idx < n) {
+          cytnx_uint64 tmp = idx;
+          const cytnx_uint64 offset = threadIdx.x * shapesize;
+          cytnx_uint64 Lidx = 0, Ridx = 0;
+
+          for (cytnx_uint64 j = 0; j < shapesize; j++) {
+            tmpv[offset + j] = tmp / accu_shape[j];
+            tmp = tmp % accu_shape[j];
+          }
+          for (cytnx_uint64 j = 0; j < shapesize; j++) {
+            Lidx += tmpv[offset + invmapper_L[j]] * old_accu_shapeL[j];
+            Ridx += tmpv[offset + invmapper_R[j]] * old_accu_shapeR[j];
+          }
+          out[idx] = CuMulDispatchOp<TO>(lhs[Lidx], rhs[Ridx]);
+        }
+      }
+
+      template <typename TL, typename TR>
+      void cuMul_dispatch_typed(boost::intrusive_ptr<Storage_base> &out,
+                                boost::intrusive_ptr<Storage_base> &Lin,
+                                boost::intrusive_ptr<Storage_base> &Rin,
+                                const unsigned long long &len,
+                                const std::vector<cytnx_uint64> &shape,
+                                const std::vector<cytnx_uint64> &invmapper_L,
+                                const std::vector<cytnx_uint64> &invmapper_R) {
+        using TO = Type_class::type_promote_gpu_t<TL, TR>;
+        cytnx_error_msg(out->dtype() != Type_class::cy_typeid_gpu_v<TO>,
+                        "[cuMul_dispatch] output dtype mismatch. got=%d expected=%d%s",
+                        out->dtype(), Type_class::cy_typeid_gpu_v<TO>, "\n");
+
+        TO *_out = reinterpret_cast<TO *>(out->data());
+        const TL *_Lin = reinterpret_cast<const TL *>(Lin->data());
+        const TR *_Rin = reinterpret_cast<const TR *>(Rin->data());
+
+        cytnx_uint32 NBlocks = len / 512;
+        if (len % 512) NBlocks += 1;
+
+        if (Lin->size() == 1 and Rin->size() == 1) {
+          cuMul_dispatch_constconst_kernel<<<NBlocks, 512>>>(_out, _Lin[0], len, _Rin[0]);
+        } else if (Lin->size() == 1) {
+          cuMul_dispatch_lconst_kernel<<<NBlocks, 512>>>(_out, _Lin[0], len, _Rin);
+        } else if (Rin->size() == 1) {
+          cuMul_dispatch_rconst_kernel<<<NBlocks, 512>>>(_out, _Lin, len, _Rin[0]);
+        } else {
+          if (shape.size() == 0) {
+            cuMul_dispatch_tn_kernel<<<NBlocks, 512>>>(_out, _Lin, len, _Rin);
+          } else {
+            cytnx_uint64 *m_accu_shape = reinterpret_cast<cytnx_uint64 *>(
+              utils_internal::cuCalloc_gpu(shape.size(), sizeof(cytnx_uint64)));
+            cytnx_uint64 *m_old_accu_shapeL = reinterpret_cast<cytnx_uint64 *>(
+              utils_internal::cuCalloc_gpu(shape.size(), sizeof(cytnx_uint64)));
+            cytnx_uint64 *m_old_accu_shapeR = reinterpret_cast<cytnx_uint64 *>(
+              utils_internal::cuCalloc_gpu(shape.size(), sizeof(cytnx_uint64)));
+            cytnx_uint64 *m_invmapper_L = reinterpret_cast<cytnx_uint64 *>(
+              utils_internal::cuMalloc_gpu(invmapper_L.size() * sizeof(cytnx_uint64)));
+            cytnx_uint64 *m_invmapper_R = reinterpret_cast<cytnx_uint64 *>(
+              utils_internal::cuMalloc_gpu(invmapper_R.size() * sizeof(cytnx_uint64)));
+
+            checkCudaErrors(cudaMemcpy(m_invmapper_L, &invmapper_L[0],
+                                       sizeof(cytnx_uint64) * invmapper_L.size(),
+                                       cudaMemcpyHostToDevice));
+            checkCudaErrors(cudaMemcpy(m_invmapper_R, &invmapper_R[0],
+                                       sizeof(cytnx_uint64) * invmapper_R.size(),
+                                       cudaMemcpyHostToDevice));
+
+            cytnx_uint64 tmp1 = 1, tmp2 = 1, tmp3 = 1;
+            for (cytnx_uint64 i = 0; i < shape.size(); i++) {
+              m_accu_shape[shape.size() - 1 - i] = tmp1;
+              tmp1 *= shape[shape.size() - 1 - i];
+
+              m_old_accu_shapeL[shape.size() - 1 - i] = tmp2;
+              tmp2 *= shape[invmapper_L[shape.size() - 1 - i]];
+
+              m_old_accu_shapeR[shape.size() - 1 - i] = tmp3;
+              tmp3 *= shape[invmapper_R[shape.size() - 1 - i]];
+            }
+
+            cuMul_dispatch_tn_kernel_nonconti<<<NBlocks, 512,
+                                                512 * shape.size() * sizeof(cytnx_uint64)>>>(
+              _out, _Lin, len, _Rin, m_accu_shape, m_old_accu_shapeL, m_old_accu_shapeR,
+              m_invmapper_L, m_invmapper_R, shape.size());
+
+            checkCudaErrors(cudaFree(m_accu_shape));
+            checkCudaErrors(cudaFree(m_old_accu_shapeL));
+            checkCudaErrors(cudaFree(m_old_accu_shapeR));
+            checkCudaErrors(cudaFree(m_invmapper_L));
+            checkCudaErrors(cudaFree(m_invmapper_R));
+          }
+        }
+      }
+
+      template <typename TL>
+      void cuMul_dispatch_rhs(boost::intrusive_ptr<Storage_base> &out,
+                              boost::intrusive_ptr<Storage_base> &Lin,
+                              boost::intrusive_ptr<Storage_base> &Rin,
+                              const unsigned long long &len, const std::vector<cytnx_uint64> &shape,
+                              const std::vector<cytnx_uint64> &invmapper_L,
+                              const std::vector<cytnx_uint64> &invmapper_R) {
+        switch (Rin->dtype()) {
+          case Type.ComplexDouble:
+            cuMul_dispatch_typed<TL, cuDoubleComplex>(out, Lin, Rin, len, shape, invmapper_L,
+                                                      invmapper_R);
+            break;
+          case Type.ComplexFloat:
+            cuMul_dispatch_typed<TL, cuComplex>(out, Lin, Rin, len, shape, invmapper_L,
+                                                invmapper_R);
+            break;
+          case Type.Double:
+            cuMul_dispatch_typed<TL, cytnx_double>(out, Lin, Rin, len, shape, invmapper_L,
+                                                   invmapper_R);
+            break;
+          case Type.Float:
+            cuMul_dispatch_typed<TL, cytnx_float>(out, Lin, Rin, len, shape, invmapper_L,
+                                                  invmapper_R);
+            break;
+          case Type.Int64:
+            cuMul_dispatch_typed<TL, cytnx_int64>(out, Lin, Rin, len, shape, invmapper_L,
+                                                  invmapper_R);
+            break;
+          case Type.Uint64:
+            cuMul_dispatch_typed<TL, cytnx_uint64>(out, Lin, Rin, len, shape, invmapper_L,
+                                                   invmapper_R);
+            break;
+          case Type.Int32:
+            cuMul_dispatch_typed<TL, cytnx_int32>(out, Lin, Rin, len, shape, invmapper_L,
+                                                  invmapper_R);
+            break;
+          case Type.Uint32:
+            cuMul_dispatch_typed<TL, cytnx_uint32>(out, Lin, Rin, len, shape, invmapper_L,
+                                                   invmapper_R);
+            break;
+          case Type.Int16:
+            cuMul_dispatch_typed<TL, cytnx_int16>(out, Lin, Rin, len, shape, invmapper_L,
+                                                  invmapper_R);
+            break;
+          case Type.Uint16:
+            cuMul_dispatch_typed<TL, cytnx_uint16>(out, Lin, Rin, len, shape, invmapper_L,
+                                                   invmapper_R);
+            break;
+          case Type.Bool:
+            cuMul_dispatch_typed<TL, cytnx_bool>(out, Lin, Rin, len, shape, invmapper_L,
+                                                 invmapper_R);
+            break;
+          default:
+            cytnx_error_msg(true, "[cuMul_dispatch] unsupported rhs dtype: %d%s", Rin->dtype(),
+                            "\n");
+        }
+      }
+
+    }  // namespace
+
+    void cuMul_dispatch(boost::intrusive_ptr<Storage_base> &out,
+                        boost::intrusive_ptr<Storage_base> &Lin,
+                        boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
+                        const std::vector<cytnx_uint64> &shape,
+                        const std::vector<cytnx_uint64> &invmapper_L,
+                        const std::vector<cytnx_uint64> &invmapper_R) {
+      const unsigned int expected_dtype = Type.type_promote(Lin->dtype(), Rin->dtype());
+      cytnx_error_msg(out->dtype() != expected_dtype,
+                      "[cuMul_dispatch] output dtype mismatch. got=%d expected=%d%s", out->dtype(),
+                      expected_dtype, "\n");
+
+      switch (Lin->dtype()) {
+        case Type.ComplexDouble:
+          cuMul_dispatch_rhs<cuDoubleComplex>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.ComplexFloat:
+          cuMul_dispatch_rhs<cuComplex>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Double:
+          cuMul_dispatch_rhs<cytnx_double>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Float:
+          cuMul_dispatch_rhs<cytnx_float>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Int64:
+          cuMul_dispatch_rhs<cytnx_int64>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Uint64:
+          cuMul_dispatch_rhs<cytnx_uint64>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Int32:
+          cuMul_dispatch_rhs<cytnx_int32>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Uint32:
+          cuMul_dispatch_rhs<cytnx_uint32>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Int16:
+          cuMul_dispatch_rhs<cytnx_int16>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Uint16:
+          cuMul_dispatch_rhs<cytnx_uint16>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Bool:
+          cuMul_dispatch_rhs<cytnx_bool>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        default:
+          cytnx_error_msg(true, "[cuMul_dispatch] unsupported lhs dtype: %d%s", Lin->dtype(), "\n");
+      }
+    }
+
+  }  // namespace linalg_internal
+}  // namespace cytnx
diff --git a/src/backend/linalg_internal_gpu/cuMul_internal.hpp b/src/backend/linalg_internal_gpu/cuMul_internal.hpp
index 6837e6f43..8f393e4d7 100644
--- a/src/backend/linalg_internal_gpu/cuMul_internal.hpp
+++ b/src/backend/linalg_internal_gpu/cuMul_internal.hpp
@@ -13,6 +13,13 @@ namespace cytnx {
   namespace linalg_internal {
 
     /// cuMul
+    void cuMul_dispatch(boost::intrusive_ptr<Storage_base> &out,
+                        boost::intrusive_ptr<Storage_base> &Lin,
+                        boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
+                        const std::vector<cytnx_uint64> &shape,
+                        const std::vector<cytnx_uint64> &invmapper_L,
+                        const std::vector<cytnx_uint64> &invmapper_R);
+
     void cuMul_internal_cdtcd(boost::intrusive_ptr<Storage_base> &out,
                               boost::intrusive_ptr<Storage_base> &Lin,
                               boost::intrusive_ptr<Storage_base> &Rin,
diff --git a/src/backend/linalg_internal_gpu/cuSub_dispatch.cu b/src/backend/linalg_internal_gpu/cuSub_dispatch.cu
new file mode 100644
index 000000000..b0b593299
--- /dev/null
+++ b/src/backend/linalg_internal_gpu/cuSub_dispatch.cu
@@ -0,0 +1,283 @@
+#include "cuSub_internal.hpp"
+#include "backend/utils_internal_interface.hpp"
+
+namespace cytnx {
+
+  namespace linalg_internal {
+
+    namespace {
+
+      template <typename T>
+      __device__ inline cuDoubleComplex CuToComplexDouble(const T &v) {
+        return make_cuDoubleComplex(static_cast<cytnx_double>(v), 0.0);
+      }
+
+      __device__ inline cuDoubleComplex CuToComplexDouble(const cuDoubleComplex &v) { return v; }
+
+      __device__ inline cuDoubleComplex CuToComplexDouble(const cuComplex &v) {
+        return cuComplexFloatToDouble(v);
+      }
+
+      template <typename T>
+      __device__ inline cuComplex CuToComplexFloat(const T &v) {
+        return make_cuFloatComplex(static_cast<cytnx_float>(v), 0.0f);
+      }
+
+      __device__ inline cuComplex CuToComplexFloat(const cuComplex &v) { return v; }
+
+      __device__ inline cuComplex CuToComplexFloat(const cuDoubleComplex &v) {
+        return make_cuFloatComplex(static_cast<cytnx_float>(cuCreal(v)),
+                                   static_cast<cytnx_float>(cuCimag(v)));
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __device__ inline TO CuSubDispatchOp(const TL &lhs, const TR &rhs) {
+        if constexpr (std::is_same_v<TO, cuDoubleComplex>) {
+          return cuCsub(CuToComplexDouble(lhs), CuToComplexDouble(rhs));
+        } else if constexpr (std::is_same_v<TO, cuComplex>) {
+          return cuCsubf(CuToComplexFloat(lhs), CuToComplexFloat(rhs));
+        } else {
+          return static_cast<TO>(lhs) - static_cast<TO>(rhs);
+        }
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __global__ void cuSub_dispatch_constconst_kernel(TO *out, const TL lhs, const cytnx_uint64 n,
+                                                       const TR rhs) {
+        const cytnx_uint64 idx = blockIdx.x * blockDim.x + threadIdx.x;
+        if (idx < n) out[idx] = CuSubDispatchOp<TO>(lhs, rhs);
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __global__ void cuSub_dispatch_lconst_kernel(TO *out, const TL lhs, const cytnx_uint64 n,
+                                                   const TR *rhs) {
+        const cytnx_uint64 idx = blockIdx.x * blockDim.x + threadIdx.x;
+        if (idx < n) out[idx] = CuSubDispatchOp<TO>(lhs, rhs[idx]);
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __global__ void cuSub_dispatch_rconst_kernel(TO *out, const TL *lhs, const cytnx_uint64 n,
+                                                   const TR rhs) {
+        const cytnx_uint64 idx = blockIdx.x * blockDim.x + threadIdx.x;
+        if (idx < n) out[idx] = CuSubDispatchOp<TO>(lhs[idx], rhs);
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __global__ void cuSub_dispatch_tn_kernel(TO *out, const TL *lhs, const cytnx_uint64 n,
+                                               const TR *rhs) {
+        const cytnx_uint64 idx = blockIdx.x * blockDim.x + threadIdx.x;
+        if (idx < n) out[idx] = CuSubDispatchOp<TO>(lhs[idx], rhs[idx]);
+      }
+
+      template <typename TO, typename TL, typename TR>
+      __global__ void cuSub_dispatch_tn_kernel_nonconti(
+        TO *out, const TL *lhs, const cytnx_uint64 n, const TR *rhs, const cytnx_uint64 *accu_shape,
+        const cytnx_uint64 *old_accu_shapeL, const cytnx_uint64 *old_accu_shapeR,
+        const cytnx_uint64 *invmapper_L, const cytnx_uint64 *invmapper_R,
+        const cytnx_uint64 shapesize) {
+        extern __shared__ cytnx_uint64 tmpv[];
+
+        const cytnx_uint64 idx = blockIdx.x * blockDim.x + threadIdx.x;
+        if (idx < n) {
+          cytnx_uint64 tmp = idx;
+          const cytnx_uint64 offset = threadIdx.x * shapesize;
+          cytnx_uint64 Lidx = 0, Ridx = 0;
+
+          for (cytnx_uint64 j = 0; j < shapesize; j++) {
+            tmpv[offset + j] = tmp / accu_shape[j];
+            tmp = tmp % accu_shape[j];
+          }
+          for (cytnx_uint64 j = 0; j < shapesize; j++) {
+            Lidx += tmpv[offset + invmapper_L[j]] * old_accu_shapeL[j];
+            Ridx += tmpv[offset + invmapper_R[j]] * old_accu_shapeR[j];
+          }
+          out[idx] = CuSubDispatchOp<TO>(lhs[Lidx], rhs[Ridx]);
+        }
+      }
+
+      template <typename TL, typename TR>
+      void cuSub_dispatch_typed(boost::intrusive_ptr<Storage_base> &out,
+                                boost::intrusive_ptr<Storage_base> &Lin,
+                                boost::intrusive_ptr<Storage_base> &Rin,
+                                const unsigned long long &len,
+                                const std::vector<cytnx_uint64> &shape,
+                                const std::vector<cytnx_uint64> &invmapper_L,
+                                const std::vector<cytnx_uint64> &invmapper_R) {
+        using TO = Type_class::type_promote_gpu_t<TL, TR>;
+        cytnx_error_msg(out->dtype() != Type_class::cy_typeid_gpu_v<TO>,
+                        "[cuSub_dispatch] output dtype mismatch. got=%d expected=%d%s",
+                        out->dtype(), Type_class::cy_typeid_gpu_v<TO>, "\n");
+
+        TO *_out = reinterpret_cast<TO *>(out->data());
+        const TL *_Lin = reinterpret_cast<const TL *>(Lin->data());
+        const TR *_Rin = reinterpret_cast<const TR *>(Rin->data());
+
+        cytnx_uint32 NBlocks = len / 512;
+        if (len % 512) NBlocks += 1;
+
+        if (Lin->size() == 1 and Rin->size() == 1) {
+          cuSub_dispatch_constconst_kernel<<<NBlocks, 512>>>(_out, _Lin[0], len, _Rin[0]);
+        } else if (Lin->size() == 1) {
+          cuSub_dispatch_lconst_kernel<<<NBlocks, 512>>>(_out, _Lin[0], len, _Rin);
+        } else if (Rin->size() == 1) {
+          cuSub_dispatch_rconst_kernel<<<NBlocks, 512>>>(_out, _Lin, len, _Rin[0]);
+        } else {
+          if (shape.size() == 0) {
+            cuSub_dispatch_tn_kernel<<<NBlocks, 512>>>(_out, _Lin, len, _Rin);
+          } else {
+            cytnx_uint64 *m_accu_shape = reinterpret_cast<cytnx_uint64 *>(
+              utils_internal::cuCalloc_gpu(shape.size(), sizeof(cytnx_uint64)));
+            cytnx_uint64 *m_old_accu_shapeL = reinterpret_cast<cytnx_uint64 *>(
+              utils_internal::cuCalloc_gpu(shape.size(), sizeof(cytnx_uint64)));
+            cytnx_uint64 *m_old_accu_shapeR = reinterpret_cast<cytnx_uint64 *>(
+              utils_internal::cuCalloc_gpu(shape.size(), sizeof(cytnx_uint64)));
+            cytnx_uint64 *m_invmapper_L = reinterpret_cast<cytnx_uint64 *>(
+              utils_internal::cuMalloc_gpu(invmapper_L.size() * sizeof(cytnx_uint64)));
+            cytnx_uint64 *m_invmapper_R = reinterpret_cast<cytnx_uint64 *>(
+              utils_internal::cuMalloc_gpu(invmapper_R.size() * sizeof(cytnx_uint64)));
+
+            checkCudaErrors(cudaMemcpy(m_invmapper_L, &invmapper_L[0],
+                                       sizeof(cytnx_uint64) * invmapper_L.size(),
+                                       cudaMemcpyHostToDevice));
+            checkCudaErrors(cudaMemcpy(m_invmapper_R, &invmapper_R[0],
+                                       sizeof(cytnx_uint64) * invmapper_R.size(),
+                                       cudaMemcpyHostToDevice));
+
+            cytnx_uint64 tmp1 = 1, tmp2 = 1, tmp3 = 1;
+            for (cytnx_uint64 i = 0; i < shape.size(); i++) {
+              m_accu_shape[shape.size() - 1 - i] = tmp1;
+              tmp1 *= shape[shape.size() - 1 - i];
+
+              m_old_accu_shapeL[shape.size() - 1 - i] = tmp2;
+              tmp2 *= shape[invmapper_L[shape.size() - 1 - i]];
+
+              m_old_accu_shapeR[shape.size() - 1 - i] = tmp3;
+              tmp3 *= shape[invmapper_R[shape.size() - 1 - i]];
+            }
+
+            cuSub_dispatch_tn_kernel_nonconti<<<NBlocks, 512,
+                                                512 * shape.size() * sizeof(cytnx_uint64)>>>(
+              _out, _Lin, len, _Rin, m_accu_shape, m_old_accu_shapeL, m_old_accu_shapeR,
+              m_invmapper_L, m_invmapper_R, shape.size());
+
+            checkCudaErrors(cudaFree(m_accu_shape));
+            checkCudaErrors(cudaFree(m_old_accu_shapeL));
+            checkCudaErrors(cudaFree(m_old_accu_shapeR));
+            checkCudaErrors(cudaFree(m_invmapper_L));
+            checkCudaErrors(cudaFree(m_invmapper_R));
+          }
+        }
+      }
+
+      template <typename TL>
+      void cuSub_dispatch_rhs(boost::intrusive_ptr<Storage_base> &out,
+                              boost::intrusive_ptr<Storage_base> &Lin,
+                              boost::intrusive_ptr<Storage_base> &Rin,
+                              const unsigned long long &len, const std::vector<cytnx_uint64> &shape,
+                              const std::vector<cytnx_uint64> &invmapper_L,
+                              const std::vector<cytnx_uint64> &invmapper_R) {
+        switch (Rin->dtype()) {
+          case Type.ComplexDouble:
+            cuSub_dispatch_typed<TL, cuDoubleComplex>(out, Lin, Rin, len, shape, invmapper_L,
+                                                      invmapper_R);
+            break;
+          case Type.ComplexFloat:
+            cuSub_dispatch_typed<TL, cuComplex>(out, Lin, Rin, len, shape, invmapper_L,
+                                                invmapper_R);
+            break;
+          case Type.Double:
+            cuSub_dispatch_typed<TL, cytnx_double>(out, Lin, Rin, len, shape, invmapper_L,
+                                                   invmapper_R);
+            break;
+          case Type.Float:
+            cuSub_dispatch_typed<TL, cytnx_float>(out, Lin, Rin, len, shape, invmapper_L,
+                                                  invmapper_R);
+            break;
+          case Type.Int64:
+            cuSub_dispatch_typed<TL, cytnx_int64>(out, Lin, Rin, len, shape, invmapper_L,
+                                                  invmapper_R);
+            break;
+          case Type.Uint64:
+            cuSub_dispatch_typed<TL, cytnx_uint64>(out, Lin, Rin, len, shape, invmapper_L,
+                                                   invmapper_R);
+            break;
+          case Type.Int32:
+            cuSub_dispatch_typed<TL, cytnx_int32>(out, Lin, Rin, len, shape, invmapper_L,
+                                                  invmapper_R);
+            break;
+          case Type.Uint32:
+            cuSub_dispatch_typed<TL, cytnx_uint32>(out, Lin, Rin, len, shape, invmapper_L,
+                                                   invmapper_R);
+            break;
+          case Type.Int16:
+            cuSub_dispatch_typed<TL, cytnx_int16>(out, Lin, Rin, len, shape, invmapper_L,
+                                                  invmapper_R);
+            break;
+          case Type.Uint16:
+            cuSub_dispatch_typed<TL, cytnx_uint16>(out, Lin, Rin, len, shape, invmapper_L,
+                                                   invmapper_R);
+            break;
+          case Type.Bool:
+            cuSub_dispatch_typed<TL, cytnx_bool>(out, Lin, Rin, len, shape, invmapper_L,
+                                                 invmapper_R);
+            break;
+          default:
+            cytnx_error_msg(true, "[cuSub_dispatch] unsupported rhs dtype: %d%s", Rin->dtype(),
+                            "\n");
+        }
+      }
+
+    }  // namespace
+
+    void cuSub_dispatch(boost::intrusive_ptr<Storage_base> &out,
+                        boost::intrusive_ptr<Storage_base> &Lin,
+                        boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
+                        const std::vector<cytnx_uint64> &shape,
+                        const std::vector<cytnx_uint64> &invmapper_L,
+                        const std::vector<cytnx_uint64> &invmapper_R) {
+      const unsigned int expected_dtype = Type.type_promote(Lin->dtype(), Rin->dtype());
+      cytnx_error_msg(out->dtype() != expected_dtype,
+                      "[cuSub_dispatch] output dtype mismatch. got=%d expected=%d%s", out->dtype(),
+                      expected_dtype, "\n");
+
+      switch (Lin->dtype()) {
+        case Type.ComplexDouble:
+          cuSub_dispatch_rhs<cuDoubleComplex>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.ComplexFloat:
+          cuSub_dispatch_rhs<cuComplex>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Double:
+          cuSub_dispatch_rhs<cytnx_double>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Float:
+          cuSub_dispatch_rhs<cytnx_float>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Int64:
+          cuSub_dispatch_rhs<cytnx_int64>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Uint64:
+          cuSub_dispatch_rhs<cytnx_uint64>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Int32:
+          cuSub_dispatch_rhs<cytnx_int32>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Uint32:
+          cuSub_dispatch_rhs<cytnx_uint32>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Int16:
+          cuSub_dispatch_rhs<cytnx_int16>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Uint16:
+          cuSub_dispatch_rhs<cytnx_uint16>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        case Type.Bool:
+          cuSub_dispatch_rhs<cytnx_bool>(out, Lin, Rin, len, shape, invmapper_L, invmapper_R);
+          break;
+        default:
+          cytnx_error_msg(true, "[cuSub_dispatch] unsupported lhs dtype: %d%s", Lin->dtype(), "\n");
+      }
+    }
+
+  }  // namespace linalg_internal
+}  // namespace cytnx
diff --git a/src/backend/linalg_internal_gpu/cuSub_internal.hpp b/src/backend/linalg_internal_gpu/cuSub_internal.hpp
index 5073e3ea6..8dc83d66d 100644
--- a/src/backend/linalg_internal_gpu/cuSub_internal.hpp
+++ b/src/backend/linalg_internal_gpu/cuSub_internal.hpp
@@ -13,6 +13,13 @@ namespace cytnx {
   namespace linalg_internal {
 
     /// cuSub
+    void cuSub_dispatch(boost::intrusive_ptr<Storage_base> &out,
+                        boost::intrusive_ptr<Storage_base> &Lin,
+                        boost::intrusive_ptr<Storage_base> &Rin, const unsigned long long &len,
+                        const std::vector<cytnx_uint64> &shape,
+                        const std::vector<cytnx_uint64> &invmapper_L,
+                        const std::vector<cytnx_uint64> &invmapper_R);
+
     void cuSub_internal_cdtcd(boost::intrusive_ptr<Storage_base> &out,
                               boost::intrusive_ptr<Storage_base> &Lin,
                               boost::intrusive_ptr<Storage_base> &Rin,
diff --git a/src/linalg/Div.cpp b/src/linalg/Div.cpp
index 80d7fa0af..d31b0a606 100644
--- a/src/linalg/Div.cpp
+++ b/src/linalg/Div.cpp
@@ -16,22 +16,22 @@ namespace cytnx {
       bool icnst = false;
       if (Lt.shape().size() == 1 && Lt.shape()[0] == 1) {
         out._impl = Rt._impl->_clone_meta_only();
-        out._impl->storage() = Storage(
-          Rt.storage().size(), Lt.dtype() < Rt.dtype() ? Lt.dtype() : Rt.dtype(), Rt.device());
-        // out.Init(Rt.shape(),Lt.dtype() < Rt.dtype()?Lt.dtype():Rt.dtype(),Lt.device());
+        out._impl->storage() =
+          Storage(Rt.storage().size(), Type.type_promote(Lt.dtype(), Rt.dtype()), Rt.device());
+        // out.Init(Rt.shape(),Type.type_promote(Lt.dtype(), Rt.dtype()),Lt.device());
         icnst = true;
 
       } else if (Rt.shape().size() == 1 && Rt.shape()[0] == 1) {
-        // out.Init(Lt.shape(),Lt.dtype() < Rt.dtype()?Lt.dtype():Rt.dtype(),Lt.device());
+        // out.Init(Lt.shape(),Type.type_promote(Lt.dtype(), Rt.dtype()),Lt.device());
         out._impl = Lt._impl->_clone_meta_only();
-        out._impl->storage() = Storage(
-          Lt.storage().size(), Lt.dtype() < Rt.dtype() ? Lt.dtype() : Rt.dtype(), Lt.device());
+        out._impl->storage() =
+          Storage(Lt.storage().size(), Type.type_promote(Lt.dtype(), Rt.dtype()), Lt.device());
         icnst = true;
 
       } else {
         cytnx_error_msg(Lt.shape() != Rt.shape(),
                         "[Div] The two tensors do not have the same shape.%s", "\n");
-        out.Init(Lt.shape(), Lt.dtype() < Rt.dtype() ? Lt.dtype() : Rt.dtype(), Lt.device());
+        out.Init(Lt.shape(), Type.type_promote(Lt.dtype(), Rt.dtype()), Lt.device());
       }
 
       if ((Lt.is_contiguous() && Rt.is_contiguous()) || icnst) {
@@ -53,9 +53,9 @@ namespace cytnx {
         } else {
   #ifdef UNI_GPU
           checkCudaErrors(cudaSetDevice(Rt.device()));
-          cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Rt.dtype()](
-            out._impl->storage()._impl, Lt._impl->storage()._impl, Rt._impl->storage()._impl,
-            out._impl->storage()._impl->size(), {}, {}, {}, 3);
+          linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                          Rt._impl->storage()._impl,
+                                          out._impl->storage()._impl->size(), {}, {}, {});
   #else
           cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                           "\n");
@@ -115,9 +115,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.ComplexDouble][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -134,9 +134,8 @@ namespace cytnx {
 
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();  //(Rt.shape(),Type.ComplexDouble,Rt.device());
-      out._impl->storage() =
-        Storage(Rt._impl->storage().size(),
-                Type.ComplexFloat < Rt.dtype() ? Type.ComplexFloat : Rt.dtype(), Rt.device());
+      out._impl->storage() = Storage(Rt._impl->storage().size(),
+                                     Type.type_promote(Type.ComplexFloat, Rt.dtype()), Rt.device());
       // Tensor out(Rt.shape(),Type.ComplexFloat <
       // Rt.dtype()?Type.ComplexFloat:Rt.dtype(),Rt.device());
 
@@ -152,9 +151,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.ComplexFloat][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -170,10 +169,9 @@ namespace cytnx {
       Cnst.at<cytnx_double>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();  //(Rt.shape(),Type.ComplexDouble,Rt.device());
-      out._impl->storage() =
-        Storage(Rt._impl->storage().size(), Type.Double < Rt.dtype() ? Type.Double : Rt.dtype(),
-                Rt.device());
-      // Tensor out(Rt.shape(),Type.Double < Rt.dtype()?Type.Double:Rt.dtype(),Rt.device());
+      out._impl->storage() = Storage(Rt._impl->storage().size(),
+                                     Type.type_promote(Type.Double, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(),Type.type_promote(Type.Double, Rt.dtype()),Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -186,9 +184,9 @@ namespace cytnx {
           Rt.ptr());
       } else {
   #ifdef UNI_GPU
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Double][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -204,9 +202,9 @@ namespace cytnx {
       Cnst.at<cytnx_float>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();  //(Rt.shape(),Type.ComplexDouble,Rt.device());
-      out._impl->storage() = Storage(
-        Rt._impl->storage().size(), Type.Float < Rt.dtype() ? Type.Float : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(),Type.Float < Rt.dtype()?Type.Float:Rt.dtype(),Rt.device());
+      out._impl->storage() =
+        Storage(Rt._impl->storage().size(), Type.type_promote(Type.Float, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(),Type.type_promote(Type.Float, Rt.dtype()),Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -220,9 +218,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Float][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -238,9 +236,9 @@ namespace cytnx {
       Cnst.at<cytnx_int64>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();  //(Rt.shape(),Type.ComplexDouble,Rt.device());
-      out._impl->storage() = Storage(
-        Rt._impl->storage().size(), Type.Int64 < Rt.dtype() ? Type.Int64 : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(),Type.Int64 < Rt.dtype()?Type.Int64:Rt.dtype(),Rt.device());
+      out._impl->storage() =
+        Storage(Rt._impl->storage().size(), Type.type_promote(Type.Int64, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(),Type.type_promote(Type.Int64, Rt.dtype()),Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -253,9 +251,9 @@ namespace cytnx {
           Rt.ptr());
       } else {
   #ifdef UNI_GPU
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Int64][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -271,10 +269,9 @@ namespace cytnx {
       Cnst.at<cytnx_uint64>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();  //(Rt.shape(),Type.ComplexDouble,Rt.device());
-      out._impl->storage() =
-        Storage(Rt._impl->storage().size(), Type.Uint64 < Rt.dtype() ? Type.Uint64 : Rt.dtype(),
-                Rt.device());
-      // Tensor out(Rt.shape(),Type.Uint64 < Rt.dtype()?Type.Uint64:Rt.dtype(),Rt.device());
+      out._impl->storage() = Storage(Rt._impl->storage().size(),
+                                     Type.type_promote(Type.Uint64, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(),Type.type_promote(Type.Uint64, Rt.dtype()),Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -288,9 +285,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Uint64][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -306,9 +303,9 @@ namespace cytnx {
       Cnst.at<cytnx_int32>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();  //(Rt.shape(),Type.ComplexDouble,Rt.device());
-      out._impl->storage() = Storage(
-        Rt._impl->storage().size(), Type.Int32 < Rt.dtype() ? Type.Int32 : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(),Type.Int32 < Rt.dtype()?Type.Int32:Rt.dtype(),Rt.device());
+      out._impl->storage() =
+        Storage(Rt._impl->storage().size(), Type.type_promote(Type.Int32, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(),Type.type_promote(Type.Int32, Rt.dtype()),Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -322,9 +319,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Int32][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -340,10 +337,9 @@ namespace cytnx {
       Cnst.at<cytnx_uint32>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();  //(Rt.shape(),Type.ComplexDouble,Rt.device());
-      out._impl->storage() =
-        Storage(Rt._impl->storage().size(), Type.Uint32 < Rt.dtype() ? Type.Uint32 : Rt.dtype(),
-                Rt.device());
-      // Tensor out(Rt.shape(),Type.Uint32 < Rt.dtype()?Type.Uint32:Rt.dtype(),Rt.device());
+      out._impl->storage() = Storage(Rt._impl->storage().size(),
+                                     Type.type_promote(Type.Uint32, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(),Type.type_promote(Type.Uint32, Rt.dtype()),Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -357,9 +353,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Uint32][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -375,9 +371,9 @@ namespace cytnx {
       Cnst.at<cytnx_int16>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();  //(Rt.shape(),Type.ComplexDouble,Rt.device());
-      out._impl->storage() = Storage(
-        Rt._impl->storage().size(), Type.Int16 < Rt.dtype() ? Type.Int16 : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(),Type.Int16 < Rt.dtype()?Type.Int16:Rt.dtype(),Rt.device());
+      out._impl->storage() =
+        Storage(Rt._impl->storage().size(), Type.type_promote(Type.Int16, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(),Type.type_promote(Type.Int16, Rt.dtype()),Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -391,9 +387,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Int16][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -409,10 +405,9 @@ namespace cytnx {
       Cnst.at<cytnx_uint16>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();  //(Rt.shape(),Type.ComplexDouble,Rt.device());
-      out._impl->storage() =
-        Storage(Rt._impl->storage().size(), Type.Uint16 < Rt.dtype() ? Type.Uint16 : Rt.dtype(),
-                Rt.device());
-      // Tensor out(Rt.shape(),Type.Uint16 < Rt.dtype()?Type.Uint16:Rt.dtype(),Rt.device());
+      out._impl->storage() = Storage(Rt._impl->storage().size(),
+                                     Type.type_promote(Type.Uint16, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(),Type.type_promote(Type.Uint16, Rt.dtype()),Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -426,9 +421,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Uint16][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -444,9 +439,9 @@ namespace cytnx {
       Cnst.at<cytnx_bool>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();  //(Rt.shape(),Type.ComplexDouble,Rt.device());
-      out._impl->storage() = Storage(Rt._impl->storage().size(),
-                                     Type.Bool < Rt.dtype() ? Type.Bool : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(),Type.Bool < Rt.dtype()?Type.Bool:Rt.dtype(),Rt.device());
+      out._impl->storage() =
+        Storage(Rt._impl->storage().size(), Type.type_promote(Type.Bool, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(),Type.type_promote(Type.Bool, Rt.dtype()),Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -460,9 +455,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Bool][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -479,8 +474,8 @@ namespace cytnx {
 
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Rt._impl->storage().size(), lc.dtype() < Rt.dtype() ? lc.dtype() : Rt.dtype(), Rt.device());
+      out._impl->storage() =
+        Storage(Rt._impl->storage().size(), Type.type_promote(lc.dtype(), Rt.dtype()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -499,9 +494,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        linalg_internal::lii.cuAri_ii[lc.dtype()][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -532,9 +527,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.ComplexDouble](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -549,9 +543,8 @@ namespace cytnx {
       Cnst.at<cytnx_complex64>(0) = rc;
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Lt._impl->storage().size(),
-                Type.ComplexFloat < Lt.dtype() ? Type.ComplexFloat : Lt.dtype(), Lt.device());
+      out._impl->storage() = Storage(Lt._impl->storage().size(),
+                                     Type.type_promote(Type.ComplexFloat, Lt.dtype()), Lt.device());
       // Tensor out(Lt.shape(),Type.ComplexFloat <
       // Lt.dtype()?Type.ComplexFloat:Lt.dtype(),Lt.device());
 
@@ -567,9 +560,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.ComplexFloat](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -585,10 +577,9 @@ namespace cytnx {
 
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();  //(Rt.shape(),Type.ComplexDouble,Rt.device());
-      out._impl->storage() =
-        Storage(Lt._impl->storage().size(), Type.Double < Lt.dtype() ? Type.Double : Lt.dtype(),
-                Lt.device());
-      // Tensor out(Lt.shape(),Type.Double < Lt.dtype()?Type.Double:Lt.dtype(),Lt.device());
+      out._impl->storage() = Storage(Lt._impl->storage().size(),
+                                     Type.type_promote(Type.Double, Lt.dtype()), Lt.device());
+      // Tensor out(Lt.shape(),Type.type_promote(Type.Double, Lt.dtype()),Lt.device());
 
       if (Lt.device() == Device.cpu) {
         std::visit(
@@ -602,9 +593,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.Double](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -619,9 +609,9 @@ namespace cytnx {
       Cnst.at<cytnx_float>(0) = rc;
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Lt._impl->storage().size(), Type.Float < Lt.dtype() ? Type.Float : Lt.dtype(), Lt.device());
-      // Tensor out(Lt.shape(),Type.Float < Lt.dtype()?Type.Float:Lt.dtype(),Lt.device());
+      out._impl->storage() =
+        Storage(Lt._impl->storage().size(), Type.type_promote(Type.Float, Lt.dtype()), Lt.device());
+      // Tensor out(Lt.shape(),Type.type_promote(Type.Float, Lt.dtype()),Lt.device());
 
       if (Lt.device() == Device.cpu) {
         std::visit(
@@ -635,9 +625,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.Float](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -652,9 +641,9 @@ namespace cytnx {
       Cnst.at<cytnx_int64>(0) = rc;
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Lt._impl->storage().size(), Type.Int64 < Lt.dtype() ? Type.Int64 : Lt.dtype(), Lt.device());
-      // Tensor out(Lt.shape(),Type.Int64 < Lt.dtype()?Type.Int64:Lt.dtype(),Lt.device());
+      out._impl->storage() =
+        Storage(Lt._impl->storage().size(), Type.type_promote(Type.Int64, Lt.dtype()), Lt.device());
+      // Tensor out(Lt.shape(),Type.type_promote(Type.Int64, Lt.dtype()),Lt.device());
 
       if (Lt.device() == Device.cpu) {
         std::visit(
@@ -668,9 +657,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.Int64](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -685,10 +673,9 @@ namespace cytnx {
       Cnst.at<cytnx_uint64>(0) = rc;
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Lt._impl->storage().size(), Type.Uint64 < Lt.dtype() ? Type.Uint64 : Lt.dtype(),
-                Lt.device());
-      // Tensor out(Lt.shape(),Type.Uint64 < Lt.dtype()?Type.Uint64:Lt.dtype(),Lt.device());
+      out._impl->storage() = Storage(Lt._impl->storage().size(),
+                                     Type.type_promote(Type.Uint64, Lt.dtype()), Lt.device());
+      // Tensor out(Lt.shape(),Type.type_promote(Type.Uint64, Lt.dtype()),Lt.device());
 
       if (Lt.device() == Device.cpu) {
         std::visit(
@@ -702,9 +689,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.Uint64](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -719,9 +705,9 @@ namespace cytnx {
       Cnst.at<cytnx_int32>(0) = rc;
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Lt._impl->storage().size(), Type.Int32 < Lt.dtype() ? Type.Int32 : Lt.dtype(), Lt.device());
-      // Tensor out(Lt.shape(),Type.Int32 < Lt.dtype()?Type.Int32:Lt.dtype(),Lt.device());
+      out._impl->storage() =
+        Storage(Lt._impl->storage().size(), Type.type_promote(Type.Int32, Lt.dtype()), Lt.device());
+      // Tensor out(Lt.shape(),Type.type_promote(Type.Int32, Lt.dtype()),Lt.device());
 
       if (Lt.device() == Device.cpu) {
         // std::cout << "chk" << std::endl;
@@ -736,9 +722,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.Int32](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -753,10 +738,9 @@ namespace cytnx {
       Cnst.at<cytnx_uint32>(0) = rc;
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Lt._impl->storage().size(), Type.Uint32 < Lt.dtype() ? Type.Uint32 : Lt.dtype(),
-                Lt.device());
-      // Tensor out(Lt.shape(),Type.Uint32 < Lt.dtype()?Type.Uint32:Lt.dtype(),Lt.device());
+      out._impl->storage() = Storage(Lt._impl->storage().size(),
+                                     Type.type_promote(Type.Uint32, Lt.dtype()), Lt.device());
+      // Tensor out(Lt.shape(),Type.type_promote(Type.Uint32, Lt.dtype()),Lt.device());
 
       if (Lt.device() == Device.cpu) {
         std::visit(
@@ -770,9 +754,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.Uint32](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -788,9 +771,9 @@ namespace cytnx {
       Cnst.at<cytnx_int16>(0) = rc;
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Lt._impl->storage().size(), Type.Int16 < Lt.dtype() ? Type.Int16 : Lt.dtype(), Lt.device());
-      // Tensor out(Lt.shape(),Type.Int16 < Lt.dtype()?Type.Int16:Lt.dtype(),Lt.device());
+      out._impl->storage() =
+        Storage(Lt._impl->storage().size(), Type.type_promote(Type.Int16, Lt.dtype()), Lt.device());
+      // Tensor out(Lt.shape(),Type.type_promote(Type.Int16, Lt.dtype()),Lt.device());
 
       if (Lt.device() == Device.cpu) {
         std::visit(
@@ -804,9 +787,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.Int16](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -821,10 +803,9 @@ namespace cytnx {
       Cnst.at<cytnx_uint16>(0) = rc;
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Lt._impl->storage().size(), Type.Uint16 < Lt.dtype() ? Type.Uint16 : Lt.dtype(),
-                Lt.device());
-      // Tensor out(Lt.shape(),Type.Uint16 < Lt.dtype()?Type.Uint16:Lt.dtype(),Lt.device());
+      out._impl->storage() = Storage(Lt._impl->storage().size(),
+                                     Type.type_promote(Type.Uint16, Lt.dtype()), Lt.device());
+      // Tensor out(Lt.shape(),Type.type_promote(Type.Uint16, Lt.dtype()),Lt.device());
 
       if (Lt.device() == Device.cpu) {
         std::visit(
@@ -838,9 +819,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.Uint16](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -855,9 +835,9 @@ namespace cytnx {
       Cnst.at<cytnx_bool>(0) = rc;
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(Lt._impl->storage().size(),
-                                     Type.Bool < Lt.dtype() ? Type.Bool : Lt.dtype(), Lt.device());
-      // Tensor out(Lt.shape(),Type.Bool < Lt.dtype()?Type.Bool:Lt.dtype(),Lt.device());
+      out._impl->storage() =
+        Storage(Lt._impl->storage().size(), Type.type_promote(Type.Bool, Lt.dtype()), Lt.device());
+      // Tensor out(Lt.shape(),Type.type_promote(Type.Bool, Lt.dtype()),Lt.device());
 
       if (Lt.device() == Device.cpu) {
         std::visit(
@@ -871,9 +851,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.Bool](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -890,8 +869,8 @@ namespace cytnx {
 
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Lt._impl->storage().size(), Lt.dtype() < rc.dtype() ? Lt.dtype() : rc.dtype(), Lt.device());
+      out._impl->storage() =
+        Storage(Lt._impl->storage().size(), Type.type_promote(Lt.dtype(), rc.dtype()), Lt.device());
 
       if (Lt.device() == Device.cpu) {
         std::visit(
@@ -910,9 +889,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        linalg_internal::lii.cuAri_ii[Lt.dtype()][rc.dtype()](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 3);
+        linalg_internal::cuDiv_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Div] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
diff --git a/src/linalg/Mul.cpp b/src/linalg/Mul.cpp
index 76555a127..daf88a94f 100644
--- a/src/linalg/Mul.cpp
+++ b/src/linalg/Mul.cpp
@@ -16,22 +16,22 @@ namespace cytnx {
       bool icnst = false;
       if (Lt.shape().size() == 1 && Lt.shape()[0] == 1) {
         out._impl = Rt._impl->_clone_meta_only();
-        out._impl->storage() = Storage(
-          Rt.storage().size(), Lt.dtype() < Rt.dtype() ? Lt.dtype() : Rt.dtype(), Rt.device());
-        // out.Init(Rt.shape(),Lt.dtype() < Rt.dtype()?Lt.dtype():Rt.dtype(),Lt.device());
+        out._impl->storage() =
+          Storage(Rt.storage().size(), Type.type_promote(Lt.dtype(), Rt.dtype()), Rt.device());
+        // out.Init(Rt.shape(),Type.type_promote(Lt.dtype(), Rt.dtype()),Lt.device());
         icnst = true;
 
       } else if (Rt.shape().size() == 1 && Rt.shape()[0] == 1) {
-        // out.Init(Lt.shape(),Lt.dtype() < Rt.dtype()?Lt.dtype():Rt.dtype(),Lt.device());
+        // out.Init(Lt.shape(),Type.type_promote(Lt.dtype(), Rt.dtype()),Lt.device());
         out._impl = Lt._impl->_clone_meta_only();
-        out._impl->storage() = Storage(
-          Lt.storage().size(), Lt.dtype() < Rt.dtype() ? Lt.dtype() : Rt.dtype(), Lt.device());
+        out._impl->storage() =
+          Storage(Lt.storage().size(), Type.type_promote(Lt.dtype(), Rt.dtype()), Lt.device());
         icnst = true;
 
       } else {
         cytnx_error_msg(Lt.shape() != Rt.shape(),
                         "[Mul] The two tensors do not have the same shape.%s", "\n");
-        out.Init(Lt.shape(), Lt.dtype() < Rt.dtype() ? Lt.dtype() : Rt.dtype(), Lt.device());
+        out.Init(Lt.shape(), Type.type_promote(Lt.dtype(), Rt.dtype()), Lt.device());
       }
 
       if ((Lt.is_contiguous() && Rt.is_contiguous()) || icnst) {
@@ -53,9 +53,9 @@ namespace cytnx {
         } else {
   #ifdef UNI_GPU
           checkCudaErrors(cudaSetDevice(Rt.device()));
-          cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Rt.dtype()](
-            out._impl->storage()._impl, Lt._impl->storage()._impl, Rt._impl->storage()._impl,
-            out._impl->storage()._impl->size(), {}, {}, {}, 1);
+          linalg_internal::cuMul_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                          Rt._impl->storage()._impl,
+                                          out._impl->storage()._impl->size(), {}, {}, {});
   #else
           cytnx_error_msg(true, "[Mul] fatal error, the tensor is on GPU without CUDA support.%s",
                           "\n");
@@ -116,9 +116,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.ComplexDouble][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        linalg_internal::cuMul_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Mul] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -134,10 +134,9 @@ namespace cytnx {
       Cnst.at<cytnx_complex64>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Rt._impl->storage().size(),
-                Type.ComplexFloat < Rt.dtype() ? Type.ComplexFloat : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(), Type.ComplexFloat < Rt.dtype() ? Type.ComplexFloat : Rt.dtype(),
+      out._impl->storage() = Storage(Rt._impl->storage().size(),
+                                     Type.type_promote(Type.ComplexFloat, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(), Type.type_promote(Type.ComplexFloat, Rt.dtype()),
       // Rt.device());
 
       if (Rt.device() == Device.cpu) {
@@ -152,9 +151,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.ComplexFloat][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        linalg_internal::cuMul_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Mul] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -170,10 +169,9 @@ namespace cytnx {
       Cnst.at<cytnx_double>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Rt._impl->storage().size(), Type.Double < Rt.dtype() ? Type.Double : Rt.dtype(),
-                Rt.device());
-      // Tensor out(Rt.shape(), Type.Double < Rt.dtype() ? Type.Double : Rt.dtype(), Rt.device());
+      out._impl->storage() = Storage(Rt._impl->storage().size(),
+                                     Type.type_promote(Type.Double, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(), Type.type_promote(Type.Double, Rt.dtype()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -187,9 +185,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Double][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        linalg_internal::cuMul_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Mul] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -205,9 +203,9 @@ namespace cytnx {
       Cnst.at<cytnx_float>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Rt._impl->storage().size(), Type.Float < Rt.dtype() ? Type.Float : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(), Type.Float < Rt.dtype() ? Type.Float : Rt.dtype(), Rt.device());
+      out._impl->storage() =
+        Storage(Rt._impl->storage().size(), Type.type_promote(Type.Float, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(), Type.type_promote(Type.Float, Rt.dtype()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -221,9 +219,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Float][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        linalg_internal::cuMul_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Mul] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -239,9 +237,9 @@ namespace cytnx {
       Cnst.at<cytnx_int64>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Rt._impl->storage().size(), Type.Int64 < Rt.dtype() ? Type.Int64 : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(), Type.Int64 < Rt.dtype() ? Type.Int64 : Rt.dtype(), Rt.device());
+      out._impl->storage() =
+        Storage(Rt._impl->storage().size(), Type.type_promote(Type.Int64, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(), Type.type_promote(Type.Int64, Rt.dtype()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -255,9 +253,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Int64][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        linalg_internal::cuMul_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Mul] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -273,10 +271,9 @@ namespace cytnx {
       Cnst.at<cytnx_uint64>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Rt._impl->storage().size(), Type.Uint64 < Rt.dtype() ? Type.Uint64 : Rt.dtype(),
-                Rt.device());
-      // Tensor out(Rt.shape(), Type.Uint64 < Rt.dtype() ? Type.Uint64 : Rt.dtype(), Rt.device());
+      out._impl->storage() = Storage(Rt._impl->storage().size(),
+                                     Type.type_promote(Type.Uint64, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(), Type.type_promote(Type.Uint64, Rt.dtype()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -290,9 +287,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Uint64][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        linalg_internal::cuMul_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Mul] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -308,9 +305,9 @@ namespace cytnx {
       Cnst.at<cytnx_int32>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Rt._impl->storage().size(), Type.Int32 < Rt.dtype() ? Type.Int32 : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(), Type.Int32 < Rt.dtype() ? Type.Int32 : Rt.dtype(), Rt.device());
+      out._impl->storage() =
+        Storage(Rt._impl->storage().size(), Type.type_promote(Type.Int32, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(), Type.type_promote(Type.Int32, Rt.dtype()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -324,9 +321,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Int32][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        linalg_internal::cuMul_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Mul] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -342,10 +339,9 @@ namespace cytnx {
       Cnst.at<cytnx_uint32>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Rt._impl->storage().size(), Type.Uint32 < Rt.dtype() ? Type.Uint32 : Rt.dtype(),
-                Rt.device());
-      // Tensor out(Rt.shape(), Type.Uint32 < Rt.dtype() ? Type.Uint32 : Rt.dtype(), Rt.device());
+      out._impl->storage() = Storage(Rt._impl->storage().size(),
+                                     Type.type_promote(Type.Uint32, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(), Type.type_promote(Type.Uint32, Rt.dtype()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -359,9 +355,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Uint32][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        linalg_internal::cuMul_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Mul] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -377,9 +373,9 @@ namespace cytnx {
       Cnst.at<cytnx_int16>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Rt._impl->storage().size(), Type.Int16 < Rt.dtype() ? Type.Int16 : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(), Type.Int16 < Rt.dtype() ? Type.Int16 : Rt.dtype(), Rt.device());
+      out._impl->storage() =
+        Storage(Rt._impl->storage().size(), Type.type_promote(Type.Int16, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(), Type.type_promote(Type.Int16, Rt.dtype()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -393,9 +389,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Int16][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        linalg_internal::cuMul_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Mul] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -411,10 +407,9 @@ namespace cytnx {
       Cnst.at<cytnx_uint16>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Rt._impl->storage().size(), Type.Uint16 < Rt.dtype() ? Type.Uint16 : Rt.dtype(),
-                Rt.device());
-      // Tensor out(Rt.shape(), Type.Uint16 < Rt.dtype() ? Type.Uint16 : Rt.dtype(), Rt.device());
+      out._impl->storage() = Storage(Rt._impl->storage().size(),
+                                     Type.type_promote(Type.Uint16, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(), Type.type_promote(Type.Uint16, Rt.dtype()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -428,9 +423,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Uint16][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        linalg_internal::cuMul_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Mul] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -446,9 +441,9 @@ namespace cytnx {
       Cnst.at<cytnx_bool>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(Rt._impl->storage().size(),
-                                     Type.Bool < Rt.dtype() ? Type.Bool : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(), Type.Bool < Rt.dtype() ? Type.Bool : Rt.dtype(), Rt.device());
+      out._impl->storage() =
+        Storage(Rt._impl->storage().size(), Type.type_promote(Type.Bool, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(), Type.type_promote(Type.Bool, Rt.dtype()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -462,9 +457,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Bool][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        linalg_internal::cuMul_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Mul] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -481,8 +476,8 @@ namespace cytnx {
 
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Rt._impl->storage().size(), lc.dtype() < Rt.dtype() ? lc.dtype() : Rt.dtype(), Rt.device());
+      out._impl->storage() =
+        Storage(Rt._impl->storage().size(), Type.type_promote(lc.dtype(), Rt.dtype()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -501,9 +496,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        linalg_internal::lii.cuAri_ii[lc.dtype()][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 1);
+        linalg_internal::cuMul_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Mul] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
diff --git a/src/linalg/Sub.cpp b/src/linalg/Sub.cpp
index 0947733b6..807aab17f 100644
--- a/src/linalg/Sub.cpp
+++ b/src/linalg/Sub.cpp
@@ -16,20 +16,20 @@ namespace cytnx {
       bool icnst = false;
       if (Lt.shape().size() == 1 && Lt.shape()[0] == 1) {
         out._impl = Rt._impl->_clone_meta_only();
-        out._impl->storage() = Storage(
-          Rt.storage().size(), Lt.dtype() < Rt.dtype() ? Lt.dtype() : Rt.dtype(), Rt.device());
-        // out.Init(Rt.shape(),Lt.dtype() < Rt.dtype()?Lt.dtype():Rt.dtype(),Lt.device());
+        out._impl->storage() =
+          Storage(Rt.storage().size(), Type.type_promote(Lt.dtype(), Rt.dtype()), Rt.device());
+        // out.Init(Rt.shape(),Type.type_promote(Lt.dtype(), Rt.dtype()),Lt.device());
         icnst = true;
       } else if (Rt.shape().size() == 1 && Rt.shape()[0] == 1) {
         out._impl = Lt._impl->_clone_meta_only();
-        out._impl->storage() = Storage(
-          Lt.storage().size(), Lt.dtype() < Rt.dtype() ? Lt.dtype() : Rt.dtype(), Lt.device());
-        // out.Init(Lt.shape(),Lt.dtype() < Rt.dtype()?Lt.dtype():Rt.dtype(),Lt.device());
+        out._impl->storage() =
+          Storage(Lt.storage().size(), Type.type_promote(Lt.dtype(), Rt.dtype()), Lt.device());
+        // out.Init(Lt.shape(),Type.type_promote(Lt.dtype(), Rt.dtype()),Lt.device());
         icnst = true;
       } else {
         cytnx_error_msg(Lt.shape() != Rt.shape(),
                         "[Sub] The two tensors do not have the same shape.%s", "\n");
-        out.Init(Lt.shape(), Lt.dtype() < Rt.dtype() ? Lt.dtype() : Rt.dtype(), Lt.device());
+        out.Init(Lt.shape(), Type.type_promote(Lt.dtype(), Rt.dtype()), Lt.device());
       }
 
       if ((Lt.is_contiguous() && Rt.is_contiguous()) || icnst) {
@@ -51,9 +51,9 @@ namespace cytnx {
         } else {
   #ifdef UNI_GPU
           checkCudaErrors(cudaSetDevice(Rt.device()));
-          cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Rt.dtype()](
-            out._impl->storage()._impl, Lt._impl->storage()._impl, Rt._impl->storage()._impl,
-            out._impl->storage()._impl->size(), {}, {}, {}, 2);
+          linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                          Rt._impl->storage()._impl,
+                                          out._impl->storage()._impl->size(), {}, {}, {});
   #else
           cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                           "\n");
@@ -79,10 +79,10 @@ namespace cytnx {
         } else {
   #ifdef UNI_GPU
           checkCudaErrors(cudaSetDevice(Rt.device()));
-          cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Rt.dtype()](
-            out._impl->storage()._impl, Lt._impl->storage()._impl, Rt._impl->storage()._impl,
-            out._impl->storage()._impl->size(), Lt._impl->shape(), Lt._impl->invmapper(),
-            Rt._impl->invmapper(), 2);
+          linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                          Rt._impl->storage()._impl,
+                                          out._impl->storage()._impl->size(), Lt._impl->shape(),
+                                          Lt._impl->invmapper(), Rt._impl->invmapper());
   #else
           cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                           "\n");
@@ -114,9 +114,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.ComplexDouble][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -132,10 +132,9 @@ namespace cytnx {
       Cnst.at<cytnx_complex64>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Rt._impl->storage().size(),
-                Type.ComplexFloat < Rt.dtype() ? Type.ComplexFloat : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(), Type.ComplexFloat < Rt.dtype() ? Type.ComplexFloat : Rt.dtype(),
+      out._impl->storage() = Storage(Rt._impl->storage().size(),
+                                     Type.type_promote(Type.ComplexFloat, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(), Type.type_promote(Type.ComplexFloat, Rt.dtype()),
       // Rt.device());
 
       if (Rt.device() == Device.cpu) {
@@ -150,9 +149,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.ComplexFloat][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -168,10 +167,9 @@ namespace cytnx {
       Cnst.at<cytnx_double>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Rt._impl->storage().size(), Type.Double < Rt.dtype() ? Type.Double : Rt.dtype(),
-                Rt.device());
-      // Tensor out(Rt.shape(), Type.Double < Rt.dtype() ? Type.Double : Rt.dtype(), Rt.device());
+      out._impl->storage() = Storage(Rt._impl->storage().size(),
+                                     Type.type_promote(Type.Double, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(), Type.type_promote(Type.Double, Rt.dtype()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -185,9 +183,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Double][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -203,9 +201,9 @@ namespace cytnx {
       Cnst.at<cytnx_float>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Rt._impl->storage().size(), Type.Float < Rt.dtype() ? Type.Float : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(), Type.Float < Rt.dtype() ? Type.Float : Rt.dtype(), Rt.device());
+      out._impl->storage() =
+        Storage(Rt._impl->storage().size(), Type.type_promote(Type.Float, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(), Type.type_promote(Type.Float, Rt.dtype()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -219,9 +217,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Float][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -237,9 +235,9 @@ namespace cytnx {
       Cnst.at<cytnx_int64>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Rt._impl->storage().size(), Type.Int64 < Rt.dtype() ? Type.Int64 : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(), Type.Int64 < Rt.dtype() ? Type.Int64 : Rt.dtype(), Rt.device());
+      out._impl->storage() =
+        Storage(Rt._impl->storage().size(), Type.type_promote(Type.Int64, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(), Type.type_promote(Type.Int64, Rt.dtype()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -253,9 +251,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Int64][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -271,10 +269,9 @@ namespace cytnx {
       Cnst.at<cytnx_uint64>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Rt._impl->storage().size(), Type.Uint64 < Rt.dtype() ? Type.Uint64 : Rt.dtype(),
-                Rt.device());
-      // Tensor out(Rt.shape(), Type.Uint64 < Rt.dtype() ? Type.Uint64 : Rt.dtype(), Rt.device());
+      out._impl->storage() = Storage(Rt._impl->storage().size(),
+                                     Type.type_promote(Type.Uint64, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(), Type.type_promote(Type.Uint64, Rt.dtype()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -288,9 +285,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Uint64][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -306,9 +303,9 @@ namespace cytnx {
       Cnst.at<cytnx_int32>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Rt._impl->storage().size(), Type.Int32 < Rt.dtype() ? Type.Int32 : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(), Type.Int32 < Rt.dtype() ? Type.Int32 : Rt.dtype(), Rt.device());
+      out._impl->storage() =
+        Storage(Rt._impl->storage().size(), Type.type_promote(Type.Int32, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(), Type.type_promote(Type.Int32, Rt.dtype()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -322,9 +319,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Int32][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -340,10 +337,9 @@ namespace cytnx {
       Cnst.at<cytnx_uint32>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Rt._impl->storage().size(), Type.Uint32 < Rt.dtype() ? Type.Uint32 : Rt.dtype(),
-                Rt.device());
-      // Tensor out(Rt.shape(), Type.Uint32 < Rt.dtype() ? Type.Uint32 : Rt.dtype(), Rt.device());
+      out._impl->storage() = Storage(Rt._impl->storage().size(),
+                                     Type.type_promote(Type.Uint32, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(), Type.type_promote(Type.Uint32, Rt.dtype()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -357,9 +353,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Uint32][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -375,9 +371,9 @@ namespace cytnx {
       Cnst.at<cytnx_int16>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Rt._impl->storage().size(), Type.Int16 < Rt.dtype() ? Type.Int16 : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(), Type.Int16 < Rt.dtype() ? Type.Int16 : Rt.dtype(), Rt.device());
+      out._impl->storage() =
+        Storage(Rt._impl->storage().size(), Type.type_promote(Type.Int16, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(), Type.type_promote(Type.Int16, Rt.dtype()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -391,9 +387,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Int16][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -409,10 +405,9 @@ namespace cytnx {
       Cnst.at<cytnx_uint16>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Rt._impl->storage().size(), Type.Uint16 < Rt.dtype() ? Type.Uint16 : Rt.dtype(),
-                Rt.device());
-      // Tensor out(Rt.shape(), Type.Uint16 < Rt.dtype() ? Type.Uint16 : Rt.dtype(), Rt.device());
+      out._impl->storage() = Storage(Rt._impl->storage().size(),
+                                     Type.type_promote(Type.Uint16, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(), Type.type_promote(Type.Uint16, Rt.dtype()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -426,9 +421,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Uint16][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -444,9 +439,9 @@ namespace cytnx {
       Cnst.at<cytnx_bool>(0) = lc;
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(Rt._impl->storage().size(),
-                                     Type.Bool < Rt.dtype() ? Type.Bool : Rt.dtype(), Rt.device());
-      // Tensor out(Rt.shape(), Type.Bool < Rt.dtype() ? Type.Bool : Rt.dtype(), Rt.device());
+      out._impl->storage() =
+        Storage(Rt._impl->storage().size(), Type.type_promote(Type.Bool, Rt.dtype()), Rt.device());
+      // Tensor out(Rt.shape(), Type.type_promote(Type.Bool, Rt.dtype()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -460,9 +455,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Type.Bool][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -479,8 +474,8 @@ namespace cytnx {
 
       Tensor out;
       out._impl = Rt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Rt._impl->storage().size(), lc.dtype() < Rt.dtype() ? lc.dtype() : Rt.dtype(), Rt.device());
+      out._impl->storage() =
+        Storage(Rt._impl->storage().size(), Type.type_promote(lc.dtype(), Rt.dtype()), Rt.device());
 
       if (Rt.device() == Device.cpu) {
         std::visit(
@@ -499,9 +494,9 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Rt.device()));
-        linalg_internal::lii.cuAri_ii[lc.dtype()][Rt.dtype()](
-          out._impl->storage()._impl, Cnst._impl, Rt._impl->storage()._impl,
-          Rt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Cnst._impl,
+                                        Rt._impl->storage()._impl,
+                                        Rt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -533,9 +528,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.ComplexDouble](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -551,10 +545,9 @@ namespace cytnx {
       Cnst.at<cytnx_complex64>(0) = rc;
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Lt._impl->storage().size(),
-                Type.ComplexFloat < Lt.dtype() ? Type.ComplexFloat : Lt.dtype(), Lt.device());
-      // Tensor out(Lt.shape(), Type.ComplexFloat < Lt.dtype() ? Type.ComplexFloat : Lt.dtype(),
+      out._impl->storage() = Storage(Lt._impl->storage().size(),
+                                     Type.type_promote(Type.ComplexFloat, Lt.dtype()), Lt.device());
+      // Tensor out(Lt.shape(), Type.type_promote(Type.ComplexFloat, Lt.dtype()),
       // Lt.device());
 
       if (Lt.device() == Device.cpu) {
@@ -569,9 +562,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.ComplexFloat](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -587,10 +579,9 @@ namespace cytnx {
       Cnst.at<cytnx_double>(0) = rc;
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Lt._impl->storage().size(), Type.Double < Lt.dtype() ? Type.Double : Lt.dtype(),
-                Lt.device());
-      // Tensor out(Lt.shape(), Type.Double < Lt.dtype() ? Type.Double : Lt.dtype(), Lt.device());
+      out._impl->storage() = Storage(Lt._impl->storage().size(),
+                                     Type.type_promote(Type.Double, Lt.dtype()), Lt.device());
+      // Tensor out(Lt.shape(), Type.type_promote(Type.Double, Lt.dtype()), Lt.device());
 
       if (Lt.device() == Device.cpu) {
         std::visit(
@@ -604,9 +595,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.Double](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -622,9 +612,9 @@ namespace cytnx {
       Cnst.at<cytnx_float>(0) = rc;
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Lt._impl->storage().size(), Type.Float < Lt.dtype() ? Type.Float : Lt.dtype(), Lt.device());
-      // Tensor out(Lt.shape(), Type.Float < Lt.dtype() ? Type.Float : Lt.dtype(), Lt.device());
+      out._impl->storage() =
+        Storage(Lt._impl->storage().size(), Type.type_promote(Type.Float, Lt.dtype()), Lt.device());
+      // Tensor out(Lt.shape(), Type.type_promote(Type.Float, Lt.dtype()), Lt.device());
 
       if (Lt.device() == Device.cpu) {
         std::visit(
@@ -638,9 +628,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.Float](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -656,9 +645,9 @@ namespace cytnx {
       Cnst.at<cytnx_int64>(0) = rc;
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Lt._impl->storage().size(), Type.Int64 < Lt.dtype() ? Type.Int64 : Lt.dtype(), Lt.device());
-      // Tensor out(Lt.shape(), Type.Int64 < Lt.dtype() ? Type.Int64 : Lt.dtype(), Lt.device());
+      out._impl->storage() =
+        Storage(Lt._impl->storage().size(), Type.type_promote(Type.Int64, Lt.dtype()), Lt.device());
+      // Tensor out(Lt.shape(), Type.type_promote(Type.Int64, Lt.dtype()), Lt.device());
 
       if (Lt.device() == Device.cpu) {
         std::visit(
@@ -672,9 +661,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.Int64](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -690,10 +678,9 @@ namespace cytnx {
       Cnst.at<cytnx_uint64>(0) = rc;
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Lt._impl->storage().size(), Type.Uint64 < Lt.dtype() ? Type.Uint64 : Lt.dtype(),
-                Lt.device());
-      // Tensor out(Lt.shape(), Type.Uint64 < Lt.dtype() ? Type.Uint64 : Lt.dtype(), Lt.device());
+      out._impl->storage() = Storage(Lt._impl->storage().size(),
+                                     Type.type_promote(Type.Uint64, Lt.dtype()), Lt.device());
+      // Tensor out(Lt.shape(), Type.type_promote(Type.Uint64, Lt.dtype()), Lt.device());
 
       if (Lt.device() == Device.cpu) {
         std::visit(
@@ -707,9 +694,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.Uint64](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -725,9 +711,9 @@ namespace cytnx {
       Cnst.at<cytnx_int32>(0) = rc;
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Lt._impl->storage().size(), Type.Int32 < Lt.dtype() ? Type.Int32 : Lt.dtype(), Lt.device());
-      // Tensor out(Lt.shape(), Type.Int32 < Lt.dtype() ? Type.Int32 : Lt.dtype(), Lt.device());
+      out._impl->storage() =
+        Storage(Lt._impl->storage().size(), Type.type_promote(Type.Int32, Lt.dtype()), Lt.device());
+      // Tensor out(Lt.shape(), Type.type_promote(Type.Int32, Lt.dtype()), Lt.device());
 
       if (Lt.device() == Device.cpu) {
         std::visit(
@@ -741,9 +727,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.Int32](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -759,10 +744,9 @@ namespace cytnx {
       Cnst.at<cytnx_uint32>(0) = rc;
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Lt._impl->storage().size(), Type.Uint32 < Lt.dtype() ? Type.Uint32 : Lt.dtype(),
-                Lt.device());
-      // Tensor out(Lt.shape(), Type.Uint32 < Lt.dtype() ? Type.Uint32 : Lt.dtype(), Lt.device());
+      out._impl->storage() = Storage(Lt._impl->storage().size(),
+                                     Type.type_promote(Type.Uint32, Lt.dtype()), Lt.device());
+      // Tensor out(Lt.shape(), Type.type_promote(Type.Uint32, Lt.dtype()), Lt.device());
 
       if (Lt.device() == Device.cpu) {
         std::visit(
@@ -776,9 +760,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.Uint32](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -794,9 +777,9 @@ namespace cytnx {
       Cnst.at<cytnx_int16>(0) = rc;
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Lt._impl->storage().size(), Type.Int16 < Lt.dtype() ? Type.Int16 : Lt.dtype(), Lt.device());
-      // Tensor out(Lt.shape(), Type.Int16 < Lt.dtype() ? Type.Int16 : Lt.dtype(), Lt.device());
+      out._impl->storage() =
+        Storage(Lt._impl->storage().size(), Type.type_promote(Type.Int16, Lt.dtype()), Lt.device());
+      // Tensor out(Lt.shape(), Type.type_promote(Type.Int16, Lt.dtype()), Lt.device());
 
       if (Lt.device() == Device.cpu) {
         std::visit(
@@ -810,9 +793,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.Int16](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -828,10 +810,9 @@ namespace cytnx {
       Cnst.at<cytnx_uint16>(0) = rc;
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();
-      out._impl->storage() =
-        Storage(Lt._impl->storage().size(), Type.Uint16 < Lt.dtype() ? Type.Uint16 : Lt.dtype(),
-                Lt.device());
-      // Tensor out(Lt.shape(), Type.Uint16 < Lt.dtype() ? Type.Uint16 : Lt.dtype(), Lt.device());
+      out._impl->storage() = Storage(Lt._impl->storage().size(),
+                                     Type.type_promote(Type.Uint16, Lt.dtype()), Lt.device());
+      // Tensor out(Lt.shape(), Type.type_promote(Type.Uint16, Lt.dtype()), Lt.device());
 
       if (Lt.device() == Device.cpu) {
         std::visit(
@@ -845,9 +826,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.Uint16](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -863,9 +843,9 @@ namespace cytnx {
       Cnst.at<cytnx_bool>(0) = rc;
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(Lt._impl->storage().size(),
-                                     Type.Bool < Lt.dtype() ? Type.Bool : Lt.dtype(), Lt.device());
-      // Tensor out(Lt.shape(), Type.Bool < Lt.dtype() ? Type.Bool : Lt.dtype(), Lt.device());
+      out._impl->storage() =
+        Storage(Lt._impl->storage().size(), Type.type_promote(Type.Bool, Lt.dtype()), Lt.device());
+      // Tensor out(Lt.shape(), Type.type_promote(Type.Bool, Lt.dtype()), Lt.device());
 
       if (Lt.device() == Device.cpu) {
         std::visit(
@@ -879,9 +859,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        cytnx::linalg_internal::lii.cuAri_ii[Lt.dtype()][Type.Bool](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
@@ -898,8 +877,8 @@ namespace cytnx {
 
       Tensor out;
       out._impl = Lt._impl->_clone_meta_only();
-      out._impl->storage() = Storage(
-        Lt._impl->storage().size(), Lt.dtype() < rc.dtype() ? Lt.dtype() : rc.dtype(), Lt.device());
+      out._impl->storage() =
+        Storage(Lt._impl->storage().size(), Type.type_promote(Lt.dtype(), rc.dtype()), Lt.device());
 
       if (Lt.device() == Device.cpu) {
         std::visit(
@@ -918,9 +897,8 @@ namespace cytnx {
       } else {
   #ifdef UNI_GPU
         checkCudaErrors(cudaSetDevice(Lt.device()));
-        linalg_internal::lii.cuAri_ii[Lt.dtype()][rc.dtype()](
-          out._impl->storage()._impl, Lt._impl->storage()._impl, Cnst._impl,
-          Lt._impl->storage()._impl->size(), {}, {}, {}, 2);
+        linalg_internal::cuSub_dispatch(out._impl->storage()._impl, Lt._impl->storage()._impl,
+                                        Cnst._impl, Lt._impl->storage()._impl->size(), {}, {}, {});
   #else
         cytnx_error_msg(true, "[Sub] fatal error, the tensor is on GPU without CUDA support.%s",
                         "\n");
diff --git a/tests/gpu/linalg_test/Div_test.cpp b/tests/gpu/linalg_test/Div_test.cpp
index 7e712a0b2..9f73063b4 100644
--- a/tests/gpu/linalg_test/Div_test.cpp
+++ b/tests/gpu/linalg_test/Div_test.cpp
@@ -199,6 +199,44 @@ namespace DivTest {
     }
   }
 
+  TEST(DivMixedDtypeTest, gpu_tensor_div_tensor_mixed_unsigned_signed_type_promote) {
+    cytnx::Tensor lhs = cytnx::arange(1, 7, 1, cytnx::Type.Uint32).reshape({2, 3});
+    cytnx::Tensor rhs = cytnx::arange(1, 7, 1, cytnx::Type.Int16).reshape({2, 3});
+    lhs = lhs.to(cytnx::Device.cuda);
+    rhs = rhs.to(cytnx::Device.cuda);
+
+    cytnx::Tensor gpu_result = cytnx::linalg::Div(lhs, rhs);
+    cytnx::Tensor expected_cpu =
+      cytnx::linalg::Div(lhs.to(cytnx::Device.cpu), rhs.to(cytnx::Device.cpu));
+    cytnx::Tensor gpu_result_cpu = gpu_result.to(cytnx::Device.cpu);
+
+    EXPECT_EQ(gpu_result.dtype(), expected_cpu.dtype());
+    EXPECT_TRUE(cytnx::TestTools::AreNearlyEqTensor(gpu_result_cpu, expected_cpu,
+                                                    GetTolerance(gpu_result.dtype())));
+  }
+
+  TEST(DivMixedDtypeTest, gpu_scalar_div_tensor_mixed_unsigned_signed_type_promote) {
+    const cytnx::cytnx_uint32 scalar = 12;
+    cytnx::Tensor rhs =
+      cytnx::arange(1, 7, 1, cytnx::Type.Int16).reshape({2, 3}).to(cytnx::Device.cuda);
+
+    cytnx::Tensor gpu_result_l = cytnx::linalg::Div(scalar, rhs);
+    cytnx::Tensor gpu_result_r = cytnx::linalg::Div(rhs, scalar);
+
+    cytnx::Tensor rhs_cpu = rhs.to(cytnx::Device.cpu);
+    cytnx::Tensor expected_l = cytnx::linalg::Div(scalar, rhs_cpu);
+    cytnx::Tensor expected_r = cytnx::linalg::Div(rhs_cpu, scalar);
+    cytnx::Tensor gpu_result_l_cpu = gpu_result_l.to(cytnx::Device.cpu);
+    cytnx::Tensor gpu_result_r_cpu = gpu_result_r.to(cytnx::Device.cpu);
+
+    EXPECT_EQ(gpu_result_l.dtype(), expected_l.dtype());
+    EXPECT_EQ(gpu_result_r.dtype(), expected_r.dtype());
+    EXPECT_TRUE(cytnx::TestTools::AreNearlyEqTensor(gpu_result_l_cpu, expected_l,
+                                                    GetTolerance(gpu_result_l.dtype())));
+    EXPECT_TRUE(cytnx::TestTools::AreNearlyEqTensor(gpu_result_r_cpu, expected_r,
+                                                    GetTolerance(gpu_result_r.dtype())));
+  }
+
   INSTANTIATE_TEST_SUITE_P(DivTests, DivTestAllShapes, ::testing::ValuesIn(GetTestShapes()));
 
 }  // namespace DivTest
diff --git a/tests/gpu/linalg_test/Mul_test.cpp b/tests/gpu/linalg_test/Mul_test.cpp
index be7e75a35..e8207dbc4 100644
--- a/tests/gpu/linalg_test/Mul_test.cpp
+++ b/tests/gpu/linalg_test/Mul_test.cpp
@@ -128,6 +128,41 @@ namespace MulTest {
     }
   }
 
+  TEST(MulMixedDtypeTest, gpu_tensor_mul_tensor_mixed_unsigned_signed_type_promote) {
+    cytnx::Tensor lhs = cytnx::arange(0, 6, 1, cytnx::Type.Uint32).reshape({2, 3});
+    cytnx::Tensor rhs = cytnx::arange(0, 6, 1, cytnx::Type.Int16).reshape({2, 3});
+    lhs = lhs.to(cytnx::Device.cuda);
+    rhs = rhs.to(cytnx::Device.cuda);
+
+    cytnx::Tensor gpu_result = cytnx::linalg::Mul(lhs, rhs);
+    cytnx::Tensor expected_cpu =
+      cytnx::linalg::Mul(lhs.to(cytnx::Device.cpu), rhs.to(cytnx::Device.cpu));
+    cytnx::Tensor gpu_result_cpu = gpu_result.to(cytnx::Device.cpu);
+
+    EXPECT_EQ(gpu_result.dtype(), expected_cpu.dtype());
+    EXPECT_TRUE(cytnx::TestTools::AreNearlyEqTensor(gpu_result_cpu, expected_cpu, 1e-6));
+  }
+
+  TEST(MulMixedDtypeTest, gpu_scalar_mul_tensor_mixed_unsigned_signed_type_promote) {
+    const cytnx::cytnx_uint32 scalar = 5;
+    cytnx::Tensor rhs =
+      cytnx::arange(0, 6, 1, cytnx::Type.Int16).reshape({2, 3}).to(cytnx::Device.cuda);
+
+    cytnx::Tensor gpu_result_l = cytnx::linalg::Mul(scalar, rhs);
+    cytnx::Tensor gpu_result_r = cytnx::linalg::Mul(rhs, scalar);
+
+    cytnx::Tensor rhs_cpu = rhs.to(cytnx::Device.cpu);
+    cytnx::Tensor expected_l = cytnx::linalg::Mul(scalar, rhs_cpu);
+    cytnx::Tensor expected_r = cytnx::linalg::Mul(rhs_cpu, scalar);
+    cytnx::Tensor gpu_result_l_cpu = gpu_result_l.to(cytnx::Device.cpu);
+    cytnx::Tensor gpu_result_r_cpu = gpu_result_r.to(cytnx::Device.cpu);
+
+    EXPECT_EQ(gpu_result_l.dtype(), expected_l.dtype());
+    EXPECT_EQ(gpu_result_r.dtype(), expected_r.dtype());
+    EXPECT_TRUE(cytnx::TestTools::AreNearlyEqTensor(gpu_result_l_cpu, expected_l, 1e-6));
+    EXPECT_TRUE(cytnx::TestTools::AreNearlyEqTensor(gpu_result_r_cpu, expected_r, 1e-6));
+  }
+
   INSTANTIATE_TEST_SUITE_P(MulTests, MulTestAllShapes, ::testing::ValuesIn(GetTestShapes()));
 
   ::testing::AssertionResult CheckMulResult(const cytnx::Tensor& gpu_result,
diff --git a/tests/gpu/linalg_test/Sub_test.cpp b/tests/gpu/linalg_test/Sub_test.cpp
index a1a97261a..3e7ad3d61 100644
--- a/tests/gpu/linalg_test/Sub_test.cpp
+++ b/tests/gpu/linalg_test/Sub_test.cpp
@@ -128,6 +128,41 @@ namespace SubTest {
     }
   }
 
+  TEST(SubMixedDtypeTest, gpu_tensor_sub_tensor_mixed_unsigned_signed_type_promote) {
+    cytnx::Tensor lhs = cytnx::arange(0, 6, 1, cytnx::Type.Uint32).reshape({2, 3});
+    cytnx::Tensor rhs = cytnx::arange(0, 6, 1, cytnx::Type.Int16).reshape({2, 3});
+    lhs = lhs.to(cytnx::Device.cuda);
+    rhs = rhs.to(cytnx::Device.cuda);
+
+    cytnx::Tensor gpu_result = cytnx::linalg::Sub(lhs, rhs);
+    cytnx::Tensor expected_cpu =
+      cytnx::linalg::Sub(lhs.to(cytnx::Device.cpu), rhs.to(cytnx::Device.cpu));
+    cytnx::Tensor gpu_result_cpu = gpu_result.to(cytnx::Device.cpu);
+
+    EXPECT_EQ(gpu_result.dtype(), expected_cpu.dtype());
+    EXPECT_TRUE(cytnx::TestTools::AreNearlyEqTensor(gpu_result_cpu, expected_cpu, 1e-6));
+  }
+
+  TEST(SubMixedDtypeTest, gpu_scalar_sub_tensor_mixed_unsigned_signed_type_promote) {
+    const cytnx::cytnx_uint32 scalar = 5;
+    cytnx::Tensor rhs =
+      cytnx::arange(0, 6, 1, cytnx::Type.Int16).reshape({2, 3}).to(cytnx::Device.cuda);
+
+    cytnx::Tensor gpu_result_l = cytnx::linalg::Sub(scalar, rhs);
+    cytnx::Tensor gpu_result_r = cytnx::linalg::Sub(rhs, scalar);
+
+    cytnx::Tensor rhs_cpu = rhs.to(cytnx::Device.cpu);
+    cytnx::Tensor expected_l = cytnx::linalg::Sub(scalar, rhs_cpu);
+    cytnx::Tensor expected_r = cytnx::linalg::Sub(rhs_cpu, scalar);
+    cytnx::Tensor gpu_result_l_cpu = gpu_result_l.to(cytnx::Device.cpu);
+    cytnx::Tensor gpu_result_r_cpu = gpu_result_r.to(cytnx::Device.cpu);
+
+    EXPECT_EQ(gpu_result_l.dtype(), expected_l.dtype());
+    EXPECT_EQ(gpu_result_r.dtype(), expected_r.dtype());
+    EXPECT_TRUE(cytnx::TestTools::AreNearlyEqTensor(gpu_result_l_cpu, expected_l, 1e-6));
+    EXPECT_TRUE(cytnx::TestTools::AreNearlyEqTensor(gpu_result_r_cpu, expected_r, 1e-6));
+  }
+
   INSTANTIATE_TEST_SUITE_P(SubTests, SubTestAllShapes, ::testing::ValuesIn(GetTestShapes()));
 
   ::testing::AssertionResult CheckSubResult(const cytnx::Tensor& gpu_result,