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1129 lines (815 loc) · 35.7 KB
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////////////////////////////////////////////////////////////////////////////////////////////////////
//
// Simple Long Integer Math for C++
// version 2.0
//
////////////////////////////////////////////////////////////////////////////////////////////////////
//
// Licensed under the MIT License <http://opensource.org/licenses/MIT>.
// SPDX-License-Identifier: MIT
//
// Copyright (c) 2020-2026 Yury Kalmykov <y_kalmykov@mail.ru>.
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
//
////////////////////////////////////////////////////////////////////////////////////////////////////
#pragma once
#include "long_math_array.h"
#include <functional>
namespace slim
{
////////////////////////////////////////////////////////////////////////////////////////////////////
// type definitions
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
class long_uint_t;
template<typename type_t, uint_t size>
class long_int_t;
} // namespace slim
namespace std
{
////////////////////////////////////////////////////////////////////////////////////////////////////
// class numeric_limits<slim::long_uint_t<type_t, size>>
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, size_t size>
struct numeric_limits<slim::long_uint_t<type_t, size>> {
public:
using long_uint_t = slim::long_uint_t<type_t, size>;
static constexpr bool is_specialized = true;
static constexpr bool is_signed = false;
static constexpr bool is_integer = true;
static constexpr bool is_exact = true;
static constexpr bool has_infinity = false;
static constexpr bool has_quiet_NaN = false;
static constexpr bool has_signaling_NaN = false;
static constexpr float_denorm_style has_denorm = denorm_absent;
static constexpr bool has_denorm_loss = false;
static constexpr float_round_style round_style = round_toward_zero;
static constexpr bool is_iec559 = false;
static constexpr bool is_bounded = true;
static constexpr bool is_modulo = true;
static constexpr int digits = static_cast<int>(slim::bit_count_v<long_uint_t>);
static constexpr int digits10 = digits * 301 / 1000;
static constexpr int radix = 2;
static constexpr int min_exponent = 0;
static constexpr int min_exponent10 = 0;
static constexpr int max_exponent = 0;
static constexpr int max_exponent10 = 0;
static constexpr bool traps = false;
static constexpr bool tinyness_before = false;
static constexpr long_uint_t min() noexcept
{
return long_uint_t(0);
}
static constexpr long_uint_t lowest() noexcept
{
return long_uint_t(0);
}
static constexpr long_uint_t max() noexcept
{
return long_uint_t(-1);
}
static constexpr long_uint_t epsilon() noexcept
{
return long_uint_t(0);
}
static constexpr long_uint_t round_error() noexcept
{
return long_uint_t(0);
}
static constexpr long_uint_t infinity() noexcept
{
return long_uint_t(0);
}
static constexpr long_uint_t quiet_NaN() noexcept
{
return long_uint_t(0);
}
static constexpr long_uint_t signaling_NaN() noexcept
{
return long_uint_t(0);
}
static constexpr long_uint_t denorm_min() noexcept
{
return long_uint_t(0);
}
};
////////////////////////////////////////////////////////////////////////////////////////////////////
// class numeric_limits<slim::long_int_t<type_t, size>>
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, size_t size>
struct numeric_limits<slim::long_int_t<type_t, size>> {
public:
using long_int_t = slim::long_int_t<type_t, size>;
static constexpr bool is_specialized = true;
static constexpr bool is_signed = true;
static constexpr bool is_integer = true;
static constexpr bool is_exact = true;
static constexpr bool has_infinity = false;
static constexpr bool has_quiet_NaN = false;
static constexpr bool has_signaling_NaN = false;
static constexpr float_denorm_style has_denorm = denorm_absent;
static constexpr bool has_denorm_loss = false;
static constexpr float_round_style round_style = round_toward_zero;
static constexpr bool is_iec559 = false;
static constexpr bool is_bounded = true;
static constexpr bool is_modulo = true;
static constexpr int digits = static_cast<int>(slim::bit_count_v<long_int_t> - 1);
static constexpr int digits10 = digits * 301 / 1000;
static constexpr int radix = 2;
static constexpr int min_exponent = 0;
static constexpr int min_exponent10 = 0;
static constexpr int max_exponent = 0;
static constexpr int max_exponent10 = 0;
static constexpr bool traps = false;
static constexpr bool tinyness_before = false;
static constexpr long_int_t min() noexcept
{
return slim::long_uint_t<type_t, size>(1) << (slim::bit_count_v<long_int_t> - 1);
}
static constexpr long_int_t lowest() noexcept
{
return min();
}
static constexpr long_int_t max() noexcept
{
return ~slim::long_uint_t<type_t, size>(min());
}
static constexpr long_int_t epsilon() noexcept
{
return long_int_t(0);
}
static constexpr long_int_t round_error() noexcept
{
return long_int_t(0);
}
static constexpr long_int_t infinity() noexcept
{
return long_int_t(0);
}
static constexpr long_int_t quiet_NaN() noexcept
{
return long_int_t(0);
}
static constexpr long_int_t signaling_NaN() noexcept
{
return long_int_t(0);
}
static constexpr long_int_t denorm_min() noexcept
{
return long_int_t(0);
}
};
////////////////////////////////////////////////////////////////////////////////////////////////////
// class hash<slim::long_uint_t<type_t, size>>
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, size_t size>
struct hash<slim::long_uint_t<type_t, size>> {
public:
using long_uint_t = slim::long_uint_t<type_t, size>;
static constexpr size_t combine_hash(size_t value1, size_t value2) noexcept
{
return value1 ^ (value2 + size_t(0x9e3779b9) + (value1 << 6) + (value1 >> 2));
}
static constexpr size_t hash_word(type_t value) noexcept
{
if constexpr (sizeof(type_t) <= sizeof(size_t))
return static_cast<size_t>(value);
else
return combine_hash(static_cast<size_t>(slim::half_lo(value)), static_cast<size_t>(slim::half_hi(value)));
}
constexpr size_t operator()(const long_uint_t& value) const noexcept
{
size_t result = hash_word(value.digits[0]);
for (slim::uint_t n = 1; n < size; ++n)
result = combine_hash(result, hash_word(value.digits[n]));
return result;
}
};
////////////////////////////////////////////////////////////////////////////////////////////////////
// class hash<slim::long_int_t<type_t, size>>
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, size_t size>
struct hash<slim::long_int_t<type_t, size>> {
public:
using long_uint_t = slim::long_uint_t<type_t, size>;
using long_int_t = slim::long_int_t<type_t, size>;
constexpr size_t operator()(const long_int_t& value) const noexcept
{
return hash<long_uint_t>()(static_cast<const long_uint_t&>(value));
}
};
} // namespace std
namespace slim
{
////////////////////////////////////////////////////////////////////////////////////////////////////
// make_unsigned_t
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename native_t, uint_t size>
struct make_unsigned<long_uint_t<native_t, size>> {
using type = long_uint_t<native_t, size>;
};
template<typename native_t, uint_t size>
struct make_unsigned<long_int_t<native_t, size>> {
using type = long_uint_t<native_t, size>;
};
////////////////////////////////////////////////////////////////////////////////////////////////////
// make_signed_t
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename native_t, uint_t size>
struct make_signed<long_uint_t<native_t, size>> {
using type = long_int_t<native_t, size>;
};
template<typename native_t, uint_t size>
struct make_signed<long_int_t<native_t, size>> {
using type = long_int_t<native_t, size>;
};
////////////////////////////////////////////////////////////////////////////////////////////////////
// half_t
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
struct half_type<long_uint_t<type_t, size>> {
using type = long_uint_t<type_t, size / 2>;
};
template<typename type_t>
struct half_type<long_uint_t<type_t, 2>> {
using type = type_t;
};
////////////////////////////////////////////////////////////////////////////////////////////////////
// standalone routines
////////////////////////////////////////////////////////////////////////////////////////////////////
// extract low half of unsigned integer
template<typename type_t, uint_t size>
constexpr long_uint_t<type_t, size / 2> half_lo(const long_uint_t<type_t, size>& value) noexcept;
template<typename type_t>
constexpr type_t half_lo(const long_uint_t<type_t, 2>& value) noexcept;
// extract high half of unsigned integer
template<typename type_t, uint_t size>
constexpr long_uint_t<type_t, size / 2> half_hi(const long_uint_t<type_t, size>& value) noexcept;
template<typename type_t>
constexpr type_t half_hi(const long_uint_t<type_t, 2>& value) noexcept;
// make unsigned integer from low and high
template<typename type_t, uint_t size>
constexpr long_uint_t<type_t, size * 2> half_make(const long_uint_t<type_t, size>& high, const long_uint_t<type_t, size>& low) noexcept;
template<typename type_t>
constexpr long_uint_t<type_t, 2> half_make(const type_t& high, const type_t& low) noexcept;
// move low half to high
template<typename type_t, uint_t size>
constexpr long_uint_t<type_t, size> half_make_hi(const long_uint_t<type_t, size>& value) noexcept;
// return most significant bit
template<typename type_t, uint_t size>
constexpr bool sign(const long_uint_t<type_t, size>& value) noexcept;
template<typename type_t, uint_t size>
constexpr bool sign(const long_int_t<type_t, size>& value) noexcept;
// calculate leading zero bits
template<typename type_t, uint_t size>
constexpr uint_t nlz(const long_uint_t<type_t, size>& value) noexcept;
template<typename type_t, uint_t size>
constexpr bool half_hi_zero(const long_uint_t<type_t, size>& value) noexcept;
// bit operations
template<typename type_t, uint_t size>
constexpr void bit_not(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2) noexcept;
template<typename type_t, uint_t size>
constexpr void bit_and(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2) noexcept;
template<typename type_t, uint_t size>
constexpr void bit_or(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2) noexcept;
template<typename type_t, uint_t size>
constexpr void bit_xor(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2) noexcept;
// shift bits to the left
template<typename type_t, uint_t size>
constexpr long_uint_t<type_t, size> shl2(const long_uint_t<type_t, size>& value_hi, const long_uint_t<type_t, size>& value_lo, uint_t shift) noexcept;
template<typename type_t, uint_t size>
constexpr long_uint_t<type_t, size> shr2(const long_uint_t<type_t, size>& value_hi, const long_uint_t<type_t, size>& value_lo, uint_t shift) noexcept;
// add with carry
template<typename type_t, uint_t size>
constexpr bool add(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2) noexcept;
template<typename type_t, uint_t size>
constexpr bool addc(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2, bool carry) noexcept;
// subtract with borrow
template<typename type_t, uint_t size>
constexpr bool sub(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2) noexcept;
template<typename type_t, uint_t size>
constexpr bool subb(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2, bool borrow) noexcept;
// compare values
template<typename type_t, uint_t size>
constexpr bool cmp_equal(const long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2) noexcept;
template<typename type_t, uint_t size>
constexpr bool cmp_less(const long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2) noexcept;
// multiply with carry
template<typename type_t, uint_t size>
constexpr long_uint_t<type_t, size> mul(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2) noexcept;
template<typename type_t, uint_t size>
constexpr long_uint_t<type_t, size> mulc(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2, const long_uint_t<type_t, size>& carry) noexcept;
// divide
template<typename type_t, uint_t size>
constexpr void div(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2) noexcept;
template<typename type_t, uint_t size>
constexpr long_uint_t<type_t, size> divr(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2) noexcept;
template<typename type_t, uint_t size>
constexpr void div2(long_uint_t<type_t, size> value1_hi, long_uint_t<type_t, size>& value1_lo, long_uint_t<type_t, size> value2) noexcept;
template<typename type_t, uint_t size>
constexpr long_uint_t<type_t, size> divr2(long_uint_t<type_t, size> value1_hi, long_uint_t<type_t, size>& value1_lo, long_uint_t<type_t, size> value2) noexcept;
template<typename type_t, uint_t size>
constexpr void mod(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2) noexcept;
template<typename type_t, uint_t size>
constexpr void mod2(long_uint_t<type_t, size> value1_hi, long_uint_t<type_t, size>& value1_lo, long_uint_t<type_t, size> value2) noexcept;
////////////////////////////////////////////////////////////////////////////////////////////////////
// standalone routines
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr long_uint_t<type_t, size / 2> half_lo(const long_uint_t<type_t, size>& value) noexcept
{
constexpr uint_t half_size = size / 2;
long_uint_t<type_t, half_size> result;
for (uint_t n = 0; n < half_size; ++n)
result.digits[n] = value.digits[n];
return result;
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t>
constexpr type_t half_lo(const long_uint_t<type_t, 2>& value) noexcept
{
return value.digits[0];
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr long_uint_t<type_t, size / 2> half_hi(const long_uint_t<type_t, size>& value) noexcept
{
constexpr uint_t half_size = size / 2;
long_uint_t<type_t, half_size> result;
for (uint_t n = 0; n < half_size; ++n)
result.digits[n] = value.digits[n + half_size];
return result;
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t>
constexpr type_t half_hi(const long_uint_t<type_t, 2>& value) noexcept
{
return value.digits[1];
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr long_uint_t<type_t, size * 2> half_make(const long_uint_t<type_t, size>& value_hi, const long_uint_t<type_t, size>& value_lo) noexcept
{
constexpr uint_t double_size = size * 2;
long_uint_t<type_t, double_size> result;
for (uint_t n = 0; n < size; ++n)
result.digits[n] = value_lo.digits[n];
for (uint_t n = size; n < double_size; ++n)
result.digits[n] = value_hi.digits[n - size];
return result;
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t>
constexpr long_uint_t<type_t, 2> half_make(const type_t& value_hi, const type_t& value_lo) noexcept
{
return long_uint_t<type_t, 2>({ value_lo, value_hi });
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr long_uint_t<type_t, size> half_make_hi(const long_uint_t<type_t, size>& value) noexcept
{
using long_uint_t = long_uint_t<type_t, size>;
constexpr uint_t half_size = size / 2;
long_uint_t result;
for (uint_t n = 0; n < half_size; ++n)
result.digits[n] = 0;
for (uint_t n = half_size; n < size; ++n)
result.digits[n] = value.digits[n - half_size];
return result;
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr bool sign(const long_uint_t<type_t, size>& value) noexcept
{
using long_uint_t = long_uint_t<type_t, size>;
return make_signed_t<type_t>(value.digits[long_uint_t::hi]) < 0;
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr bool sign(const long_int_t<type_t, size>& value) noexcept
{
return value.sign();
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr uint_t nlz(const long_uint_t<type_t, size>& value) noexcept
{
using long_uint_t = long_uint_t<type_t, size>;
uint_t count = 0;
for (uint_t n = std::size(value.digits); n-- > 0;) {
const uint_t scount = nlz(value.digits[n]);
count += scount;
if (scount < bit_count_v<type_t>)
break;
}
return count;
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr bool half_hi_zero(const long_uint_t<type_t, size>& value) noexcept
{
for (uint_t n = size / 2; n < size; ++n) {
if (value.digits[n] != 0)
return false;
}
return true;
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr void bit_not(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2) noexcept
{
array::bit_not(std::span(value1.digits), std::span(value2.digits));
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr void bit_and(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2) noexcept
{
array::bit_and(std::span(value1.digits), std::span(value2.digits));
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr void bit_or(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2) noexcept
{
array::bit_or(std::span(value1.digits), std::span(value2.digits));
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr void bit_xor(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2) noexcept
{
array::bit_xor(std::span(value1.digits), std::span(value2.digits));
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr long_uint_t<type_t, size> shl2(const long_uint_t<type_t, size>& value_hi, const long_uint_t<type_t, size>& value_lo, uint_t shift) noexcept
{
using long_uint_t = long_uint_t<type_t, size>;
if (shift == 0 || shift >= bit_count_v<long_uint_t> * 2)
return value_hi;
if (shift < bit_count_v<long_uint_t>) {
long_uint_t result = value_hi;
long_uint_t carry = value_lo;
array::shl(std::span(result.digits), shift);
array::shr(std::span(carry.digits), bit_count_v<long_uint_t> - shift);
bit_or(result, carry);
return result;
}
long_uint_t result = value_lo;
array::shl(std::span(result.digits), shift - bit_count_v<long_uint_t>);
return result;
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr long_uint_t<type_t, size> shr2(const long_uint_t<type_t, size>& value_hi, const long_uint_t<type_t, size>& value_lo, uint_t shift) noexcept
{
using long_uint_t = long_uint_t<type_t, size>;
if (shift == 0 || shift >= bit_count_v<long_uint_t> * 2)
return value_lo;
if (shift < bit_count_v<long_uint_t>) {
long_uint_t result = value_lo;
long_uint_t carry = value_hi;
array::shr(std::span(result.digits), shift);
array::shl(std::span(carry.digits), bit_count_v<long_uint_t> - shift);
bit_or(result, carry);
return result;
}
long_uint_t result = value_hi;
array::shr(std::span(result.digits), shift - bit_count_v<long_uint_t>);
return result;
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr bool add(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2) noexcept
{
return array::add(std::span(value1.digits), std::span(value2.digits));
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr bool addc(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2, bool carry) noexcept
{
return array::addc(std::span(value1.digits), std::span(value2.digits), carry);
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr bool sub(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2) noexcept
{
return array::sub(std::span(value1.digits), std::span(value2.digits));
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr bool subb(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2, bool borrow) noexcept
{
return array::subb(std::span(value1.digits), std::span(value2.digits), borrow);
}
template<typename type_t, uint_t size>
constexpr bool cmp_equal(const long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2) noexcept
{
return array::cmp_equal(std::span(value1.digits), std::span(value2.digits));
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr bool cmp_less(const long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2) noexcept
{
return array::cmp_less(std::span(value1.digits), std::span(value2.digits));
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr long_uint_t<type_t, size> mul(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2) noexcept
{
using long_uint_t = long_uint_t<type_t, size>;
long_uint_t carry;
array::mul(std::span(value1.digits), std::span(value2.digits), std::span(carry.digits));
return carry;
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr long_uint_t<type_t, size> mulc(long_uint_t<type_t, size>& value1, const long_uint_t<type_t, size>& value2, const long_uint_t<type_t, size>& carry) noexcept
{
using long_uint_t = long_uint_t<type_t, size>;
long_uint_t carry_hi;
array::mul(std::span(value1.digits), std::span(value2.digits), std::span(carry_hi.digits));
const bool add_carry = array::add(std::span(value1.digits), std::span(carry.digits));
bool carry_digit = add_carry;
for (uint_t n = 0; carry_digit && n < size; ++n)
carry_digit = add(carry_hi.digits[n], type_t(1));
return carry_hi;
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr void div2(long_uint_t<type_t, size> value1_hi, long_uint_t<type_t, size>& value1_lo, long_uint_t<type_t, size> value2) noexcept
{
using long_uint_t = long_uint_t<type_t, size>;
if (value2 != 0 && value1_hi >= value2) {
value1_lo = ~long_uint_t(0);
return;
}
const uint_t shift = nlz(value2);
long_uint_t svalue2 = value2;
array::shl(std::span(svalue2.digits), shift);
const long_uint_t nvalue2_hi = half_hi(svalue2);
const long_uint_t nvalue2_lo = half_lo(svalue2);
const long_uint_t nvalue1_32 = shl2(value1_hi, value1_lo, shift);
long_uint_t nvalue1_10 = value1_lo;
array::shl(std::span(nvalue1_10.digits), shift);
const long_uint_t nvalue1_hi = half_hi(nvalue1_10);
const long_uint_t nvalue1_lo = half_lo(nvalue1_10);
long_uint_t quotient_hi = nvalue1_32;
const long_uint_t remainder_hi = divr(quotient_hi, nvalue2_hi);
long_uint_t t1 = quotient_hi;
mul(t1, nvalue2_lo);
long_uint_t t2 = half_make_hi(remainder_hi);
bit_or(t2, nvalue1_hi);
if (cmp_less(t2, t1)) {
--quotient_hi;
long_uint_t delta = t1;
sub(delta, t2);
if (cmp_less(svalue2, delta))
--quotient_hi;
}
long_uint_t nvalue1_21 = half_make_hi(nvalue1_32);
add(nvalue1_21, nvalue1_hi);
long_uint_t product_hi = quotient_hi;
mul(product_hi, svalue2);
sub(nvalue1_21, product_hi);
long_uint_t quotient_lo = nvalue1_21;
const long_uint_t remainder_lo = divr(quotient_lo, nvalue2_hi);
long_uint_t t3 = quotient_lo;
mul(t3, nvalue2_lo);
long_uint_t t4 = half_make_hi(remainder_lo);
bit_or(t4, nvalue1_lo);
if (cmp_less(t4, t3)) {
--quotient_lo;
long_uint_t delta = t3;
sub(delta, t4);
if (cmp_less(svalue2, delta))
--quotient_lo;
}
value1_lo = half_make_hi(quotient_hi);
bit_or(value1_lo, quotient_lo);
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr long_uint_t<type_t, size> divr2(long_uint_t<type_t, size> value1_hi, long_uint_t<type_t, size>& value1_lo, long_uint_t<type_t, size> value2) noexcept
{
using long_uint_t = long_uint_t<type_t, size>;
if (value2 != 0 && value1_hi >= value2) {
value1_lo = ~long_uint_t(0);
return value1_lo;
}
const uint_t shift = nlz(value2);
long_uint_t svalue2 = value2;
array::shl(std::span(svalue2.digits), shift);
const long_uint_t nvalue2_hi = half_hi(svalue2);
const long_uint_t nvalue2_lo = half_lo(svalue2);
const long_uint_t nvalue1_32 = shl2(value1_hi, value1_lo, shift);
long_uint_t nvalue1_10 = value1_lo;
array::shl(std::span(nvalue1_10.digits), shift);
const long_uint_t nvalue1_hi = half_hi(nvalue1_10);
const long_uint_t nvalue1_lo = half_lo(nvalue1_10);
long_uint_t quotient_hi = nvalue1_32;
const long_uint_t remainder_hi = divr(quotient_hi, nvalue2_hi);
long_uint_t t1 = quotient_hi;
mul(t1, nvalue2_lo);
long_uint_t t2 = half_make_hi(remainder_hi);
bit_or(t2, nvalue1_hi);
if (cmp_less(t2, t1)) {
--quotient_hi;
long_uint_t delta = t1;
sub(delta, t2);
if (cmp_less(svalue2, delta))
--quotient_hi;
}
long_uint_t nvalue1_21 = half_make_hi(nvalue1_32);
add(nvalue1_21, nvalue1_hi);
long_uint_t product_hi = quotient_hi;
mul(product_hi, svalue2);
sub(nvalue1_21, product_hi);
long_uint_t quotient_lo = nvalue1_21;
const long_uint_t remainder_lo = divr(quotient_lo, nvalue2_hi);
long_uint_t t3 = quotient_lo;
mul(t3, nvalue2_lo);
long_uint_t t4 = half_make_hi(remainder_lo);
bit_or(t4, nvalue1_lo);
if (cmp_less(t4, t3)) {
--quotient_lo;
long_uint_t delta = t3;
sub(delta, t4);
if (cmp_less(svalue2, delta))
--quotient_lo;
}
value1_lo = half_make_hi(quotient_hi);
bit_or(value1_lo, quotient_lo);
long_uint_t result = half_make_hi(nvalue1_21);
add(result, nvalue1_lo);
long_uint_t product_lo = quotient_lo;
mul(product_lo, svalue2);
sub(result, product_lo);
array::shr(std::span(result.digits), shift);
return result;
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename type_t, uint_t size>
constexpr void mod2(long_uint_t<type_t, size> value1_hi, long_uint_t<type_t, size>& value1_lo, long_uint_t<type_t, size> value2) noexcept
{
using long_uint_t = long_uint_t<type_t, size>;
if (value2 != 0 && value1_hi >= value2) {
value1_lo = ~long_uint_t(0);
return;
}
const uint_t shift = nlz(value2);
long_uint_t svalue2 = value2;
array::shl(std::span(svalue2.digits), shift);
const long_uint_t nvalue2_hi = half_hi(svalue2);
const long_uint_t nvalue2_lo = half_lo(svalue2);
const long_uint_t nvalue1_32 = shl2(value1_hi, value1_lo, shift);
long_uint_t nvalue1_10 = value1_lo;
array::shl(std::span(nvalue1_10.digits), shift);
const long_uint_t nvalue1_hi = half_hi(nvalue1_10);
const long_uint_t nvalue1_lo = half_lo(nvalue1_10);
long_uint_t quotient_hi = nvalue1_32;
const long_uint_t remainder_hi = divr(quotient_hi, nvalue2_hi);
long_uint_t t1 = quotient_hi;
mul(t1, nvalue2_lo);
long_uint_t t2 = half_make_hi(remainder_hi);
bit_or(t2, nvalue1_hi);
if (cmp_less(t2, t1)) {
--quotient_hi;
long_uint_t delta = t1;
sub(delta, t2);
if (cmp_less(svalue2, delta))
--quotient_hi;
}
long_uint_t nvalue1_21 = half_make_hi(nvalue1_32);
add(nvalue1_21, nvalue1_hi);
long_uint_t product_hi = quotient_hi;
mul(product_hi, svalue2);
sub(nvalue1_21, product_hi);
long_uint_t quotient_lo = nvalue1_21;
const long_uint_t remainder_lo = divr(quotient_lo, nvalue2_hi);
long_uint_t t3 = quotient_lo;
mul(t3, nvalue2_lo);
long_uint_t t4 = half_make_hi(remainder_lo);
bit_or(t4, nvalue1_lo);
if (cmp_less(t4, t3)) {
--quotient_lo;
long_uint_t delta = t3;
sub(delta, t4);
if (cmp_less(svalue2, delta))
--quotient_lo;
}
long_uint_t result = half_make_hi(nvalue1_21);
add(result, nvalue1_lo);
long_uint_t product_lo = quotient_lo;
mul(product_lo, svalue2);
sub(result, product_lo);
array::shr(std::span(result.digits), shift);
value1_lo = result;
}
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