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added reference implementation and exhaustive testing

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Ahmet Inan 2023-04-19 13:44:01 +02:00
commit 9774948cd3
2 changed files with 111 additions and 0 deletions
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87
galois_field.hh
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@ -318,4 +318,91 @@ private:
GF::Tables<M, POLY, TYPE> Tables;
};
template <int M, int64_t POLY, typename TYPE>
struct GaloisFieldReference
{
static const int64_t Q = int64_t(1) << M;
static const TYPE N = Q - 1;
static_assert(M <= 8 * sizeof(TYPE), "TYPE not wide enough");
static_assert(Q == (POLY & ~(Q - 1)), "POLY not of degree Q");
static const TYPE P = POLY;
TYPE v;
GaloisFieldReference() = default;
explicit GaloisFieldReference(TYPE v) : v(v)
{
assert(v <= N);
}
GaloisFieldReference<M, POLY, TYPE> operator *= (GaloisFieldReference<M, POLY, TYPE> a)
{
return *this = *this * a;
}
GaloisFieldReference<M, POLY, TYPE> operator += (GaloisFieldReference<M, POLY, TYPE> a)
{
return *this = *this + a;
}
};
template <int M, int64_t POLY, typename TYPE>
bool operator == (GaloisFieldReference<M, POLY, TYPE> a, GaloisFieldReference<M, POLY, TYPE> b)
{
return a.v == b.v;
}
template <int M, int64_t POLY, typename TYPE>
bool operator != (GaloisFieldReference<M, POLY, TYPE> a, GaloisFieldReference<M, POLY, TYPE> b)
{
return a.v != b.v;
}
template <int M, int64_t POLY, typename TYPE>
GaloisFieldReference<M, POLY, TYPE> operator + (GaloisFieldReference<M, POLY, TYPE> a, GaloisFieldReference<M, POLY, TYPE> b)
{
return GaloisFieldReference<M, POLY, TYPE>(a.v ^ b.v);
}
template <int M, int64_t POLY, typename TYPE>
GaloisFieldReference<M, POLY, TYPE> operator - (GaloisFieldReference<M, POLY, TYPE> a, GaloisFieldReference<M, POLY, TYPE> b)
{
return a + b;
}
template <int M, int64_t POLY, typename TYPE>
GaloisFieldReference<M, POLY, TYPE> operator - (GaloisFieldReference<M, POLY, TYPE> a)
{
return a;
}
template <int M, int64_t POLY, typename TYPE>
GaloisFieldReference<M, POLY, TYPE> operator * (GaloisFieldReference<M, POLY, TYPE> a, GaloisFieldReference<M, POLY, TYPE> b)
{
GaloisFieldReference<M, POLY, TYPE> p(0);
for (int i = 0; i < M; ++i) {
if (b.v & 1)
p.v ^= a.v;
if (a.v & (TYPE(1) << (M - 1)))
a.v = (a.v << 1) ^ a.P;
else
a.v <<= 1;
b.v >>= 1;
}
return p;
}
template <int M, int64_t POLY, typename TYPE>
GaloisFieldReference<M, POLY, TYPE> rcp(GaloisFieldReference<M, POLY, TYPE> a)
{
assert(a.v);
GaloisFieldReference<M, POLY, TYPE> t(a *= a);
for (int i = 0; i < M - 2; ++i)
t *= a *= a;
return t;
}
template <int M, int64_t POLY, typename TYPE>
GaloisFieldReference<M, POLY, TYPE> operator / (GaloisFieldReference<M, POLY, TYPE> a, GaloisFieldReference<M, POLY, TYPE> b)
{
assert(b.v);
return a * rcp(b);
}
}

24
tests/gf_test.cc
View file

@ -8,36 +8,60 @@ Copyright 2018 Ahmet Inan <inan@aicodix.de>
#include <iostream>
#include "galois_field.hh"
template <typename GF, typename GFR>
void exhaustive_test()
{
for (int j = 0; j < GF::Q; ++j) {
typename GF::ValueType a(j);
for (int i = 0; i < GF::Q; ++i) {
typename GF::ValueType b(i);
assert((a * b).v == (GFR(j) * GFR(i)).v);
}
}
for (int i = 1; i < GF::Q; ++i) {
typename GF::ValueType a(i);
assert(rcp(a).v == rcp(GFR(i)).v);
}
}
int main()
{
if (1) {
// BBC WHP031 RS(15, 11) T=2
typedef CODE::GaloisField<4, 0b10011, uint8_t> GF;
typedef CODE::GaloisFieldReference<4, 0b10011, uint8_t> GFR;
GF instance;
GF::ValueType a(3), b(7), c(15), d(6);
assert(a * b + c == d);
exhaustive_test<GF, GFR>();
}
if (1) {
// DVB-T RS(255, 239) T=8
typedef CODE::GaloisField<8, 0b100011101, uint8_t> GF;
typedef CODE::GaloisFieldReference<8, 0b100011101, uint8_t> GFR;
GF instance;
GF::ValueType a(154), b(83), c(144), d(63);
assert(fma(a, b, c) == d);
exhaustive_test<GF, GFR>();
}
if (1) {
// FUN RS(65535, 65471) T=32
typedef CODE::GaloisField<16, 0b10001000000001011, uint16_t> GF;
typedef CODE::GaloisFieldReference<16, 0b10001000000001011, uint16_t> GFR;
GF *instance = new GF();
GF::ValueType a(42145), b(13346), c(40958), d(35941);
assert(a / b + c == d);
exhaustive_test<GF, GFR>();
delete instance;
}
if (1) {
// DVB-S2 FULL BCH(65535, 65343) T=12
typedef CODE::GaloisField<16, 0b10000000000101101, uint16_t> GF;
typedef CODE::GaloisFieldReference<16, 0b10000000000101101, uint16_t> GFR;
GF *instance = new GF();
GF::ValueType a(38532), b(7932), c(34283), d(22281);
assert(a / (rcp(b) + c) == d);
exhaustive_test<GF, GFR>();
delete instance;
}
std::cerr << "Galois field arithmetic test passed!" << std::endl;