LEDAtools/partitions_permanents.hpp at master · LEDAcrypt/LEDAtools · GitHub

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#include <cstdint>
#include <iostream>

/*
 Permanent formulas for circulant matrices as obtained via Sage (macsyma)

+           +
| [m_0 m_1] |
| [m_1 m_0] | = (m_0 + m_1)^2 - 2*m_0*m_1


+               +
| [m_0 m_1 m_2] |
| [m_2 m_0 m_1] |
| [m_1 m_2 m_0] | = (m_0 + m_1 + m_2)^3 - 3*(m_0 + m_1)*(m_0 + m_2)*(m_1 + m_2) +
                  3*m_0*m_1*m_2

+                   +
| [m_0 m_1 m_2 m_3] |
| [m_3 m_0 m_1 m_2] |
| [m_2 m_3 m_0 m_1] |
| [m_1 m_2 m_3 m_0] | =  (m_0 + m_1 + m_2 + m_3)^4 -
                      4*(m_0 + m_1 + m_2)*(m_0 + m_1 + m_3)*(m_0 +m_2 + m_3)*
                      (m_1 + m_2 + m_3) +
                      2*(m_0 + m_2)^2*(m_1 + m_3)^2 + 4*(m_0 + m_1)*(m_0 + m_3)*
                      (m_1 + m_2)*(m_2 + m_3) - 4*m_0*m_1*m_2*m_3
*/

uint64_t ComputePermanent(int64_t mpartition[],
                          const uint64_t n_0){
            uint64_t permanent = 0;
switch(n_0){
    case 2:
        permanent =  (mpartition[0] + mpartition[1]) *
                     (mpartition[0] + mpartition[1]) -
                     2*mpartition[0]*mpartition[1];
        break;
    case 3:
        permanent =   (mpartition[0] + mpartition[1] + mpartition[2]) *
                      (mpartition[0] + mpartition[1] + mpartition[2]) *
                      (mpartition[0] + mpartition[1] + mpartition[2]) -
                    3*(mpartition[0] + mpartition[1]) *
                      (mpartition[0] + mpartition[2]) *
                      (mpartition[1] + mpartition[2]) +
                    3* mpartition[0] *
                       mpartition[1] *
                       mpartition[2];
        break;
    case 4:
        permanent =  (mpartition[0] + mpartition[1] + mpartition[2] + mpartition[3]) *
                     (mpartition[0] + mpartition[1] + mpartition[2] + mpartition[3]) *
                     (mpartition[0] + mpartition[1] + mpartition[2] + mpartition[3]) *
                     (mpartition[0] + mpartition[1] + mpartition[2] + mpartition[3]) -
                   4*(mpartition[0] + mpartition[1] + mpartition[2]) *
                     (mpartition[0] + mpartition[1] + mpartition[3]) *
                     (mpartition[0] + mpartition[2] + mpartition[3]) *
                     (mpartition[1] + mpartition[2] + mpartition[3]) +
                   2*((mpartition[0] + mpartition[2])*(mpartition[0] + mpartition[2])) *
                     ((mpartition[1] + mpartition[3])*(mpartition[1] + mpartition[3])) +
                   4*(mpartition[0] + mpartition[1]) *
                     (mpartition[0] + mpartition[3]) *
                     (mpartition[1] + mpartition[2]) *
                     (mpartition[2] + mpartition[3]) -
                   4* mpartition[0] *
                      mpartition[1] *
                      mpartition[2] *
                      mpartition[3];
        break;
    default: std::cout << "permanent not supported" << std::endl;
  }
  return permanent;
}

int FindmPartition(const uint64_t m,
                   uint64_t mpartition[],
                   const uint64_t n_0){
    // Enumerate partitions of m with length n_0,
    // according to TAOCP, Vol 4 Fascicle 3b, Algorithm H
    // PRE : m >= n_0 >= 2
    if ( (m < n_0) ||  (n_0 < 2) ){
        return 0;
    }

    int64_t mpartition_selected[n_0];
    int found_good_partition = 0;
    int64_t mpartition_tmp[n_0+1];
    mpartition_tmp[0] = m - (n_0 - 1);
    for(unsigned i = 1; i < n_0; i++){
        mpartition_tmp[i] = 1;
    }
    // theoretically, mpartition_tmp[n_0] = -1 according to knuth
    mpartition_tmp[n_0] = -1;
    do {
       // visit the partition
       if (ComputePermanent(mpartition_tmp,n_0) % 2 == 1U){
           for(unsigned i = 0; i < n_0; i++){
             mpartition_selected[i] = (uint64_t) mpartition_tmp[i];
           }
           found_good_partition = 1;
       }
       if (mpartition_tmp[1] < mpartition_tmp[0] - 1){
         // step H3: easy but very common case
           mpartition_tmp[0]--;
           mpartition_tmp[1]++;
       } else {
         // step H4
          int j = 2;
          int64_t s = mpartition_tmp[0] + mpartition_tmp[1] - 1;
          while (  mpartition_tmp[j] >= mpartition_tmp[0] - 1 ){
               s = s + mpartition_tmp[j];
               j++;
          }
          if( j >= (int)n_0 ){ // completed enumeration of partitions
             for(unsigned i = 0; i < n_0; i++){
                mpartition[i] = (uint64_t) mpartition_selected[i];
             }
             return found_good_partition;
          } else {
              uint64_t x = mpartition_tmp[j]+1;
              mpartition_tmp[j] = x;
              j--;
              while (j > 0) {
                 mpartition_tmp[j] = x;
                 s = s - x;
                 j--;
              }
              mpartition_tmp[0] = s;
          }
       }
    } while (1);
}