From c4ec0fca9b8aac5e58b3edf59430a6b02038b71f Mon Sep 17 00:00:00 2001 From: Bhargav Annem Date: Fri, 4 Jul 2025 14:43:33 +0900 Subject: [PATCH 1/2] feat: gf2 implementaiton and tests --- algebra/ff/gf2.py | 23 ++ tests/test_gf2.py | 32 ++ uv.lock | 783 +--------------------------------------------- 3 files changed, 56 insertions(+), 782 deletions(-) create mode 100644 algebra/ff/gf2.py create mode 100644 tests/test_gf2.py diff --git a/algebra/ff/gf2.py b/algebra/ff/gf2.py new file mode 100644 index 0000000..82cbcf0 --- /dev/null +++ b/algebra/ff/gf2.py @@ -0,0 +1,23 @@ +class GF2: + def __init__(self, x): + self.value = int(x) & 1 + + def __add__(self, other): + return GF2(self.value ^ other.value) + + def __mul__(self, other): + return GF2(self.value & other.value) + + def __repr__(self): + return str(self.value) + + def __int__(self): + return self.value + + def __eq__(self, other): + if isinstance(other, GF2): + return self.value == other.value + return self.value == (int(other) & 1) + + __radd__ = __add__ + __rmul__ = __mul__ \ No newline at end of file diff --git a/tests/test_gf2.py b/tests/test_gf2.py new file mode 100644 index 0000000..3ea86b2 --- /dev/null +++ b/tests/test_gf2.py @@ -0,0 +1,32 @@ +from algebra.ff.gf2 import GF2 + +def test_basic_ops(): + assert GF2(0) + GF2(0) == GF2(0) + assert GF2(0) + GF2(1) == GF2(1) + assert GF2(1) + GF2(0) == GF2(1) + assert GF2(1) + GF2(1) == GF2(0) + + assert GF2(0) * GF2(0) == GF2(0) + assert GF2(0) * GF2(1) == GF2(0) + assert GF2(1) * GF2(0) == GF2(0) + assert GF2(1) * GF2(1) == GF2(1) + +def test_polynomials(): + p_coeffs = [GF2(1), GF2(1)] # 1 + x + q_coeffs = [GF2(0), GF2(1)] # x + + max_len = max(len(p_coeffs), len(q_coeffs)) + p_padded = p_coeffs + [GF2(0)] * (max_len - len(p_coeffs)) + q_padded = q_coeffs + [GF2(0)] * (max_len - len(q_coeffs)) + + result = [p_padded[i] + q_padded[i] for i in range(max_len)] + expected = [GF2(1), GF2(0)] # 1 + 0x = 1 + assert result == expected + + p_mul_q = [GF2(0), GF2(1), GF2(1)] # 0 + 1x + 1x^2 = x + x^2 + + c0 = p_coeffs[0] * q_coeffs[0] # 1 * 0 = 0 + c1 = p_coeffs[0] * q_coeffs[1] + p_coeffs[1] * q_coeffs[0] # 1*1 + 1*0 = 1 + c2 = p_coeffs[1] * q_coeffs[1] # 1 * 1 = 1 + + assert [c0, c1, c2] == p_mul_q \ No newline at end of file diff --git a/uv.lock b/uv.lock index dd814c0..45591c2 100644 --- a/uv.lock +++ b/uv.lock @@ -6,18 +6,9 @@ resolution-markers = [ "python_full_version < '3.11'", ] -[[package]] -name = "alabaster" -version = "1.0.0" -source = { registry = "https://pypi.org/simple" } -sdist = { url = "https://files.pythonhosted.org/packages/a6/f8/d9c74d0daf3f742840fd818d69cfae176fa332022fd44e3469487d5a9420/alabaster-1.0.0.tar.gz", hash = "sha256:c00dca57bca26fa62a6d7d0a9fcce65f3e026e9bfe33e9c538fd3fbb2144fd9e", size = 24210, upload-time = "2024-07-26T18:15:03.762Z" } -wheels = [ - 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1) + for i in range(len(self.coeffs)): + for j in range(len(other.coeffs)): + result[i + j] += self.coeffs[i] * other.coeffs[j] + + return type(self)(self._reduce(result)) + + def _reduce(self, coeffs): + while len(coeffs) > self.degree and coeffs[-1] == GF2(1): + for i, coeff in enumerate(self.irreducible_poly): + idx = len(coeffs) - len(self.irreducible_poly) + i + if idx >= 0: + coeffs[idx] += coeff + coeffs.pop() + + return coeffs[:self.degree] + [GF2(0)] * (self.degree - len(coeffs)) + + +class GF4(GF2n): + degree = 2 + irreducible_poly = [GF2(1), GF2(1), GF2(1)] + + +class GF8(GF2n): + degree = 3 + irreducible_poly = [GF2(1), GF2(1), GF2(0), GF2(1)] \ No newline at end of file diff --git a/algebra/ff/bigint_field.py b/algebra/ff/bigint_field.py index bcc24b6..0d75ed8 100644 --- a/algebra/ff/bigint_field.py +++ b/algebra/ff/bigint_field.py @@ -1,11 +1,12 @@ """BigInt-based prime field implementation that avoids tinygrad tensor operations with large constants""" from algebra.bigint.bigint import BigInt +from algebra.ff.prime_field import PrimeField from tinygrad.tensor import Tensor from tinygrad import dtypes -class BigIntPrimeField: +class BigIntPrimeField(PrimeField): """Prime field implementation using BigInt for all arithmetic""" P: int = None diff --git a/algebra/ff/gf2.py b/algebra/ff/gf2.py index 82cbcf0..4027f0c 100644 --- a/algebra/ff/gf2.py +++ b/algebra/ff/gf2.py @@ -1,23 +1,16 @@ -class GF2: +from algebra.ff.prime_field import PrimeField + +class GF2(PrimeField): + P = 2 + def __init__(self, x): - self.value = int(x) & 1 + self.value = self.t32(int(x) & 1) def __add__(self, other): - return GF2(self.value ^ other.value) + return GF2(self.value.item() ^ GF2(other).value.item()) def __mul__(self, other): - return GF2(self.value & other.value) - - def __repr__(self): - return str(self.value) - - def __int__(self): - return self.value - - def __eq__(self, other): - if isinstance(other, GF2): - return self.value == other.value - return self.value == (int(other) & 1) + return GF2(self.value.item() & GF2(other).value.item()) __radd__ = __add__ __rmul__ = __mul__ \ No newline at end of file diff --git a/tests/test_extensions.py b/tests/test_extensions.py new file mode 100644 index 0000000..5abf8d5 --- /dev/null +++ b/tests/test_extensions.py @@ -0,0 +1,34 @@ +from algebra.extensions.gf2n import GF4, GF8 +from algebra.ff.gf2 import GF2 + + +def test_gf4(): + # Test elements in GF(4) + a = GF4([GF2(1), GF2(0)]) # 1 + b = GF4([GF2(0), GF2(1)]) # x + c = GF4([GF2(1), GF2(1)]) # 1 + x + + # Test addition (XOR) + assert a + b == c + assert b + b == GF4([GF2(0), GF2(0)]) # x + x = 0 + + # Test multiplication + # x * x = x^2, but x^2 = x + 1 in GF(4) with irreducible x^2 + x + 1 + result = b * b + expected = GF4([GF2(1), GF2(1)]) # x + 1 + assert result == expected + + +def test_gf8(): + # Test elements in GF(8) + a = GF8([GF2(1), GF2(0), GF2(0)]) # 1 + b = GF8([GF2(0), GF2(1), GF2(0)]) # x + + # Test addition + result = a + b + expected = GF8([GF2(1), GF2(1), GF2(0)]) # 1 + x + assert result == expected + + # Test that x + x = 0 + assert b + b == GF8([GF2(0), GF2(0), GF2(0)]) +