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prime_field.hh
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prime_field.hh
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/*
Prime field arithmetic
Copyright 2024 Ahmet Inan <inan@aicodix.de>
*/
#pragma once
namespace CODE {
template <typename TYPE, TYPE PRIME>
struct PrimeField
{
static constexpr TYPE P = PRIME;
TYPE v;
PrimeField() = default;
explicit PrimeField(TYPE v) : v(v)
{
}
PrimeField<TYPE, PRIME> operator *= (PrimeField<TYPE, PRIME> a)
{
return *this = *this * a;
}
PrimeField<TYPE, PRIME> operator /= (PrimeField<TYPE, PRIME> a)
{
return *this = *this / a;
}
PrimeField<TYPE, PRIME> operator += (PrimeField<TYPE, PRIME> a)
{
return *this = *this + a;
}
PrimeField<TYPE, PRIME> operator -= (PrimeField<TYPE, PRIME> a)
{
return *this = *this - a;
}
TYPE operator () ()
{
return v;
}
};
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> reduce(PrimeField<TYPE, PRIME> a)
{
return PrimeField<TYPE, PRIME>(a.v % a.P);
}
template <typename TYPE, TYPE PRIME>
bool operator == (PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
{
return a.v == b.v;
}
template <typename TYPE, TYPE PRIME>
bool operator != (PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
{
return a.v != b.v;
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> add(PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
{
return PrimeField<TYPE, PRIME>(a.v + b.v);
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> operator + (PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
{
return reduce(add(a, b));
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> sub(PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
{
return PrimeField<TYPE, PRIME>(a.v - b.v + (a.v < b.v ? a.P : 0));
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> operator - (PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
{
return reduce(sub(a, b));
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> neg(PrimeField<TYPE, PRIME> a)
{
return PrimeField<TYPE, PRIME>(a.P - a.v);
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> operator - (PrimeField<TYPE, PRIME> a)
{
return reduce(neg(a));
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> mul(PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
{
return PrimeField<TYPE, PRIME>(a.v * b.v);
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> operator * (PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
{
return reduce(mul(a, b));
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> pow(PrimeField<TYPE, PRIME> a, TYPE m)
{
PrimeField<TYPE, PRIME> t(1);
for (;m; m >>= 1, a *= a)
if (m & 1)
t *= a;
return t;
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> rcp(PrimeField<TYPE, PRIME> a)
{
return pow(a, a.P - 2);
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> div(PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
{
return mul(a, rcp(b));
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> operator / (PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
{
return reduce(div(a, b));
}
}