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159 lines
3.4 KiB
C++
159 lines
3.4 KiB
C++
/*
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Prime field arithmetic
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Copyright 2024 Ahmet Inan <inan@aicodix.de>
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*/
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#pragma once
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#include <cassert>
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namespace CODE {
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template <typename TYPE, TYPE PRIME>
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struct PrimeField
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{
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static_assert(std::is_unsigned<TYPE>::value, "TYPE must be unsigned");
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static_assert(std::numeric_limits<TYPE>::max() / (PRIME-1) >= (PRIME-1), "Type not wide enough");
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static constexpr TYPE P = PRIME;
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TYPE v;
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PrimeField() = default;
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explicit PrimeField(TYPE v) : v(v)
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{
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}
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PrimeField<TYPE, PRIME> operator *= (PrimeField<TYPE, PRIME> a)
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{
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return *this = *this * a;
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}
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PrimeField<TYPE, PRIME> operator /= (PrimeField<TYPE, PRIME> a)
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{
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return *this = *this / a;
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}
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PrimeField<TYPE, PRIME> operator += (PrimeField<TYPE, PRIME> a)
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{
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return *this = *this + a;
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}
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PrimeField<TYPE, PRIME> operator -= (PrimeField<TYPE, PRIME> a)
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{
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return *this = *this - a;
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}
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TYPE operator () ()
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{
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return v;
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}
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};
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template <typename TYPE, TYPE PRIME>
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PrimeField<TYPE, PRIME> reduce(PrimeField<TYPE, PRIME> a)
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{
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return PrimeField<TYPE, PRIME>(a.v % a.P);
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}
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template <typename TYPE, TYPE PRIME>
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bool operator == (PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
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{
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return a.v == b.v;
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}
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template <typename TYPE, TYPE PRIME>
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bool operator != (PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
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{
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return a.v != b.v;
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}
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template <typename TYPE, TYPE PRIME>
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PrimeField<TYPE, PRIME> add(PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
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{
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return PrimeField<TYPE, PRIME>(a.v + b.v);
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}
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template <typename TYPE, TYPE PRIME>
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PrimeField<TYPE, PRIME> operator + (PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
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{
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return reduce(add(a, b));
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}
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template <typename TYPE, TYPE PRIME>
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PrimeField<TYPE, PRIME> sub(PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
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{
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return PrimeField<TYPE, PRIME>(a.v - b.v + a.P);
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}
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template <typename TYPE, TYPE PRIME>
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PrimeField<TYPE, PRIME> operator - (PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
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{
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return reduce(sub(a, b));
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}
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template <typename TYPE, TYPE PRIME>
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PrimeField<TYPE, PRIME> neg(PrimeField<TYPE, PRIME> a)
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{
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return PrimeField<TYPE, PRIME>(a.P - a.v);
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}
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template <typename TYPE, TYPE PRIME>
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PrimeField<TYPE, PRIME> operator - (PrimeField<TYPE, PRIME> a)
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{
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return reduce(neg(a));
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}
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template <typename TYPE, TYPE PRIME>
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PrimeField<TYPE, PRIME> mul(PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
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{
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return PrimeField<TYPE, PRIME>(a.v * b.v);
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}
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template <typename TYPE, TYPE PRIME>
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PrimeField<TYPE, PRIME> operator * (PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
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{
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return reduce(mul(a, b));
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}
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template <typename TYPE, TYPE PRIME>
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PrimeField<TYPE, PRIME> pow(PrimeField<TYPE, PRIME> a, TYPE m)
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{
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PrimeField<TYPE, PRIME> t(1);
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for (;m; m >>= 1, a *= a)
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if (m & 1)
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t *= a;
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return t;
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}
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template <typename TYPE, TYPE PRIME>
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PrimeField<TYPE, PRIME> rcp(PrimeField<TYPE, PRIME> a)
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{
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assert(a.v);
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#if 1
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return pow(a, a.P - 2);
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#else
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if (a.v == 1)
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return a;
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TYPE t = 0, newt = 1;
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TYPE r = a.P, newr = a.v;
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while (newr) {
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TYPE quotient = r / newr;
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t -= quotient * newt;
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r -= quotient * newr;
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std::swap(newt, t);
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std::swap(newr, r);
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}
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assert(r == 1);
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if (t >= a.P)
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t += a.P;
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return PrimeField<TYPE, PRIME>(t);
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#endif
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}
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template <typename TYPE, TYPE PRIME>
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PrimeField<TYPE, PRIME> div(PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
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{
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return mul(a, rcp(b));
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}
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template <typename TYPE, TYPE PRIME>
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PrimeField<TYPE, PRIME> operator / (PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
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{
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return reduce(div(a, b));
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}
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}
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