bsnes/nall/galois-field.hpp

71 lines
2.0 KiB
C++

#pragma once
//table-driven galois field modulo 2
//do not use with GF(2^17) or larger
namespace nall {
template<typename field, uint Elements, uint Polynomial>
struct GaloisField {
using type = GaloisField;
GaloisField(uint x = 0) : x(x) {}
operator field() const { return x; }
auto operator^(field y) const -> type { return x ^ y; }
auto operator+(field y) const -> type { return x ^ y; }
auto operator-(field y) const -> type { return x ^ y; }
auto operator*(field y) const -> type { return x && y ? exp(log(x) + log(y)) : 0; }
auto operator/(field y) const -> type { return x && y ? exp(log(x) + Elements - log(y)) : 0; }
auto& operator =(field y) { return x = y, *this; }
auto& operator^=(field y) { return x = operator^(y), *this; }
auto& operator+=(field y) { return x = operator^(y), *this; }
auto& operator-=(field y) { return x = operator^(y), *this; }
auto& operator*=(field y) { return x = operator*(y), *this; }
auto& operator/=(field y) { return x = operator/(y), *this; }
auto pow(field y) const -> type { return exp(log(x) * y); }
auto inv() const -> type { return exp(Elements - log(x)); } // 1/x
static auto log(uint x) -> uint {
enum : uint { Size = bit::round(Elements), Mask = Size - 1 };
static array<field[Size]> log = [] {
uint shift = 0, polynomial = Polynomial;
while(polynomial >>= 1) shift++;
shift--;
array<field[Size]> log;
field x = 1;
for(uint n : range(Elements)) {
log[x] = n;
x = x << 1 ^ (x >> shift ? Polynomial : 0);
}
log[0] = 0; //-inf (undefined)
return log;
}();
return log[x & Mask];
}
static auto exp(uint x) -> uint {
static array<field[Elements]> exp = [] {
uint shift = 0, polynomial = Polynomial;
while(polynomial >>= 1) shift++;
shift--;
array<field[Elements]> exp;
field x = 1;
for(uint n : range(Elements)) {
exp[n] = x;
x = x << 1 ^ (x >> shift ? Polynomial : 0);
}
return exp;
}();
return exp[x % Elements];
}
field x;
};
}