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306 | #pragma once
#include <utility>
#include <limits><--- Include file: not found. Please note: Cppcheck does not need standard library headers to get proper results.
#include <type_traits><--- Include file: not found. Please note: Cppcheck does not need standard library headers to get proper results.
#include "template/debug.hpp"
#include "snippet/aliases.hpp"
#include "internal/types.hpp"
#include "internal/concepts.hpp"
#include "numeric/bit.hpp"
#include "numeric/arithmetic.hpp"
namespace uni {
namespace internal {
template<std::unsigned_integral Value, std::unsigned_integral Large>
requires has_double_digits_of<Large, Value>
struct montgomery_reduction {
using value_type = Value;
using large_type = Large;
private:
value_type _mod = 0, _r2, _mp;
constexpr value_type _inv() const noexcept(NO_EXCEPT) {
value_type res = this->_mod;
while(this->_mod * res != 1) res *= value_type{ 2 } - this->_mod * res;
return res;
}
public:
static constexpr int digits = std::numeric_limits<value_type>::digits - 2;
static constexpr value_type max() noexcept { return (value_type{ 1 } << montgomery_reduction::digits) - 1; }
inline constexpr value_type mod() const noexcept(NO_EXCEPT) { return this->_mod; }
value_type zero = 0;
value_type one;
constexpr montgomery_reduction() noexcept = default;
constexpr montgomery_reduction(const value_type mod) noexcept(NO_EXCEPT)<--- Struct 'montgomery_reduction' has a constructor with 1 argument that is not explicit. [+]Struct 'montgomery_reduction' has a constructor with 1 argument that is not explicit. Such, so called "Converting constructors", should in general be explicit for type safety reasons as that prevents unintended implicit conversions.
: _mod(mod), _r2(static_cast<value_type>(-static_cast<large_type>(mod) % mod)),
_mp(-this->_inv()), one(this->reduce(this->_r2))
{
assert((mod & 1) == 1);
assert(mod <= montgomery_reduction::max());
}
constexpr value_type reduce(const large_type v) const noexcept(NO_EXCEPT) {
return
static_cast<value_type>(
(
v + static_cast<large_type>(static_cast<value_type>(v) * this->_mp) * this->_mod
) >> std::numeric_limits<value_type>::digits
);
}
inline constexpr value_type add(value_type x, const value_type y) const noexcept(NO_EXCEPT) {
x += y;
if(x >= (this->_mod << 1)) x -= (this->_mod << 1);
return x;
}
inline constexpr value_type subtract(value_type x, const value_type y) const noexcept(NO_EXCEPT) {
if(x < y) x += (this->_mod << 1);
x -= y;
return x;
}
inline constexpr value_type multiply(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return this->reduce(static_cast<large_type>(x) * static_cast<large_type>(y));
}
template<std::integral K>
inline constexpr value_type pow(const large_type v, const K p) const noexcept(NO_EXCEPT) {
if constexpr(std::signed_integral<K>) assert(p >= 0);
if(this->_mod == 1) return 0;
return uni::pow(
v, p,
[&](const value_type x, const value_type y) noexcept(NO_EXCEPT) { return this->multiply(x, y); },
static_cast<large_type>(this->one)
);
}
inline constexpr value_type normalize(const value_type v) const noexcept(NO_EXCEPT) {
assert(0 <= v && v < (this->_mod << 1));
if(v < this->_mod) return v;
return v - this->_mod;
}
inline constexpr auto compare(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return this->normalize(x) <=> this->normalize(y);
}
inline constexpr value_type convert_raw(const value_type v) const noexcept(NO_EXCEPT) {
if(v == 1) return this->one;
return this->multiply(v, this->_r2);
}
template<std::integral T>
constexpr value_type convert(T v) const noexcept(NO_EXCEPT) {
if(v == 1) return this->one;
using common_type = std::common_type_t<T, value_type>;
const common_type mod2 = static_cast<common_type>(this->_mod << 1);
if(v > 0 && static_cast<common_type>(v) >= mod2) {
v %= mod2;
}
if constexpr(std::is_signed_v<T>) {
if(v < 0 && static_cast<common_type>(-v) >= mod2) {
v %= mod2;
if(v != 0) v += mod2;
}
}
return this->multiply(v, this->_r2);
}
constexpr value_type revert(const value_type v) const noexcept(NO_EXCEPT) {
return this->normalize(this->reduce(v));
}
};
// Thanks to: https://www.mathenachia.blog/even-mod-montgomery-impl/
template<std::unsigned_integral Value, std::unsigned_integral Large>
requires has_double_digits_of<Large, Value>
struct arbitrary_montgomery_reduction {
using value_type = Value;
using large_type = Large;
private:
using context = arbitrary_montgomery_reduction;
static constexpr int width = std::numeric_limits<value_type>::digits;
value_type _mod = 0;
int _tz;
value_type _m0;
large_type _m0i, _mask;
value_type _r2;
constexpr large_type _inv() const noexcept(NO_EXCEPT) {
large_type res = this->_m0;
while(((this->_m0 * res) & this->_mask) != 1) res *= large_type{ 2 } - this->_m0 * res;
return res & this->_mask;
}
constexpr value_type _m0ip() const noexcept(NO_EXCEPT) {
if(this->_tz == 0) return 0;
value_type res = this->_m0;
const value_type mask = (value_type{ 1 } << this->_tz) - 1;
while(((this->_m0 * res) & mask) != 1) res *= value_type{ 2 } - this->_m0 * res;
return res & mask;
}
public:
static constexpr int digits = std::numeric_limits<value_type>::digits - 2;
static constexpr value_type max() noexcept { return (value_type{ 1 } << context::digits) - 1; }
inline constexpr value_type mod() const noexcept(NO_EXCEPT) { return this->_mod; }
value_type one;
constexpr arbitrary_montgomery_reduction() noexcept = default;<--- Member variable 'arbitrary_montgomery_reduction::_tz' is not initialized in the constructor. [+]Member variable 'arbitrary_montgomery_reduction::_tz' is not initialized in the constructor. Member variables of native types, pointers, or references are left uninitialized when the class is instantiated. That may cause bugs or undefined behavior.
constexpr arbitrary_montgomery_reduction(value_type m) noexcept(NO_EXCEPT) {<--- Struct 'arbitrary_montgomery_reduction' has a constructor with 1 argument that is not explicit. [+]Struct 'arbitrary_montgomery_reduction' has a constructor with 1 argument that is not explicit. Such, so called "Converting constructors", should in general be explicit for type safety reasons as that prevents unintended implicit conversions.
assert(0 < m);
if(this->_mod == m) return;
this->_mod = m;
this->_tz = std::countr_zero(m);
this->_m0 = m >> this->_tz;
assert(this->_mod < context::max());
this->_mask = (large_type{ 1 } << (context::width + this->_tz)) - 1;
this->_m0i = this->_inv();
{
const value_type x = (std::numeric_limits<large_type>::max() % this->_m0) + 1;
const value_type mask = (value_type{ 1 } << this->_tz) - 1;
this->_r2 = (x + ((((large_type{ 1 } - x) * this->_m0ip()) & mask) * this->_m0));
}
this->one = this->reduce(this->_r2);
}
constexpr value_type reduce(const large_type v) const noexcept(NO_EXCEPT) {
const value_type res =
static_cast<value_type>(
(
v +
this->_m0 *
((((v << std::numeric_limits<value_type>::digits) - v) * this->_m0i) & this->_mask)
) >> std::numeric_limits<value_type>::digits
);
return res;
}
inline constexpr value_type add(value_type x, const value_type y) const noexcept(NO_EXCEPT) {
x += y;
if(x >= (this->_mod << 1)) x -= (this->_mod << 1);
return x;
}
inline constexpr value_type subtract(value_type x, const value_type y) const noexcept(NO_EXCEPT) {
if(x < y) x += (this->_mod << 1);
x -= y;
return x;
}
inline constexpr value_type multiply(const value_type x, const value_type y) const noexcept(NO_EXCEPT) {
return this->reduce(static_cast<large_type>(x) * static_cast<large_type>(y));
}
template<std::integral K>
inline constexpr value_type pow(const large_type v, K p) const noexcept(NO_EXCEPT) {
if constexpr(std::signed_integral<K>) assert(p >= 0);
if(this->_mod == 1) return 0;
return uni::pow(
v, p,
[&](const value_type x, const value_type y) noexcept(NO_EXCEPT) { return this->multiply(x, y); },
static_cast<large_type>(this->one)
);
}
inline constexpr value_type normalize(const value_type v) const noexcept(NO_EXCEPT) {
assert(0 <= v && v < (this->_mod << 1));
if(v < this->_mod) return v;
return v - this->_mod;
}
inline constexpr auto compare(const large_type x, const large_type y) const noexcept(NO_EXCEPT) {
return this->normalize(x) <=> this->normalize(y);
}
inline constexpr value_type convert_raw(const value_type v) const noexcept(NO_EXCEPT) {
if(v == 1) return this->one;
return this->multiply(v, this->_r2);
}
template<std::integral T>
constexpr value_type convert(T v) const noexcept(NO_EXCEPT) {
if(v == 1) return this->one;
using common_type = std::common_type_t<T, value_type>;
const common_type mod2 = static_cast<common_type>(this->_mod << 1);
if(v > 0 && static_cast<common_type>(v) >= mod2) {
v %= mod2;
}
if constexpr(std::signed_integral<T>) {
if(v < 0) {
if(static_cast<common_type>(-v) >= mod2) v %= mod2;
if(v < 0) v += mod2;
}
}
return this->multiply(v, this->_r2);
}
constexpr value_type revert(const value_type v) const noexcept(NO_EXCEPT) {
return this->normalize(this->reduce(v));
}
};
} // namespace internal
using montgomery_reduction_32bit = internal::montgomery_reduction<u32, u64>;
using montgomery_reduction_64bit = internal::montgomery_reduction<u64, u128>;
using arbitrary_montgomery_reduction_32bit = internal::arbitrary_montgomery_reduction<u32, u64>;
using arbitrary_montgomery_reduction_64bit = internal::arbitrary_montgomery_reduction<u64, u128>;
} // namespace uni
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