bigint.hpp

// Copyright Take Vos 2019-2020.
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt)
 
#pragma once
 
#include "strings.hpp"
#include "math.hpp"
#include "int_carry.hpp"
#include "codec/base_n.hpp"
#include <format>
#include <type_traits>
#include <ostream>
#include <concepts>
 
namespace hi::inline v1 {
 
template<std::unsigned_integral DigitType, std::size_t NumDigits, bool IsSigned>
struct bigint {
    using digit_type = DigitType;
    using signed_digit_type = std::make_signed_t<digit_type>;
    static constexpr auto num_digits = NumDigits;
    static constexpr auto is_signed = IsSigned;
    static constexpr auto bits_per_digit = sizeof(digit_type) * CHAR_BIT;
 
    static constexpr digit_type zero_digit = 0;
    static constexpr digit_type min1_digit = static_cast<digit_type>(signed_digit_type{-1});
 
    digit_type digits[num_digits];
 
    constexpr bigint() noexcept
    {
        for (std::size_t i = 0; i != num_digits; ++i) {
            digits[i] = zero_digit;
        }
    }
 
    constexpr bigint(bigint const &) noexcept = default;
    constexpr bigint &operator=(bigint const &) noexcept = default;
    constexpr bigint(bigint &&) noexcept = default;
    constexpr bigint &operator=(bigint &&) noexcept = default;
 
    template<std::size_t N, bool S>
    constexpr bigint(bigint<digit_type, N, S> const &rhs) noexcept requires(N < num_digits)
    {
        std::size_t i = 0;
 
        // Copy the data from a smaller bigint.
        for (; i != N; ++i) {
            digits[i] = rhs.digits[i];
        }
 
        // Sign extent the most-siginificant-digit.
        hilet sign = rhs.is_negative() ? min1_digit : zero_digit;
        for (; i != num_digits; ++i) {
            digits[i] = sign;
        }
    }
 
    template<std::size_t N, bool S>
    constexpr bigint &operator=(bigint<digit_type, N, S> const &rhs) noexcept requires(N < num_digits)
    {
        std::size_t i = 0;
 
        // Copy the data from a smaller bigint.
        for (; i != N; ++i) {
            digits[i] = rhs.digits[i];
        }
 
        // Sign extent the most-siginificant-digit.
        hilet sign = rhs.is_negative() ? min1_digit : zero_digit;
        for (; i != num_digits; ++i) {
            digits[i] = sign;
        }
        return *this;
    }
 
    constexpr bigint(std::integral auto value) noexcept
    {
        static_assert(sizeof(value) <= sizeof(digit_type));
        static_assert(num_digits > 0);
 
        if constexpr (std::is_signed_v<decltype(value)>) {
            // Sign extent the value to the size of the first digit.
            digits[0] = static_cast<digit_type>(static_cast<signed_digit_type>(value));
        } else {
            digits[0] = static_cast<digit_type>(value);
        }
 
        // Sign extent to the rest of the digits.
        hilet sign = value < 0 ? min1_digit : zero_digit;
        for (std::size_t i = 1; i != num_digits; ++i) {
            digits[i] = sign;
        }
    }
 
    constexpr bigint &operator=(std::integral auto value) noexcept
    {
        static_assert(sizeof(value) <= sizeof(digit_type));
        static_assert(num_digits > 0);
 
        if constexpr (std::is_signed_v<decltype(value)>) {
            // Sign extent the value to the size of the first digit.
            digits[0] = static_cast<digit_type>(static_cast<signed_digit_type>(value));
        } else {
            digits[0] = static_cast<digit_type>(value);
        }
 
        // Sign extent to the rest of the digits.
        hilet sign = value < 0 ? min1_digit : zero_digit;
        for (std::size_t i = 1; i != num_digits; ++i) {
            digits[i] = sign;
        }
        return *this;
    }
 
    constexpr explicit bigint(std::string_view str, int base = 10) noexcept : bigint()
    {
        std::size_t i = 0;
        for (; i < str.size(); ++i) {
            (*this) *= base;
            (*this) += base16::int_from_char<int>(str[i]);
        }
    }
 
    constexpr explicit operator unsigned long long() const noexcept
    {
        return static_cast<unsigned long long>(digits[0]);
    }
    constexpr explicit operator signed long long() const noexcept
    {
        return static_cast<signed long long>(digits[0]);
    }
    constexpr explicit operator unsigned long() const noexcept
    {
        return static_cast<unsigned long>(digits[0]);
    }
    constexpr explicit operator signed long() const noexcept
    {
        return static_cast<signed long>(digits[0]);
    }
    constexpr explicit operator unsigned int() const noexcept
    {
        return static_cast<unsigned int>(digits[0]);
    }
    constexpr explicit operator signed int() const noexcept
    {
        return static_cast<signed int>(digits[0]);
    }
    constexpr explicit operator unsigned short() const noexcept
    {
        return static_cast<unsigned short>(digits[0]);
    }
    constexpr explicit operator signed short() const noexcept
    {
        return static_cast<signed short>(digits[0]);
    }
    constexpr explicit operator unsigned char() const noexcept
    {
        return static_cast<unsigned char>(digits[0]);
    }
    constexpr explicit operator signed char() const noexcept
    {
        return static_cast<signed char>(digits[0]);
    }
 
    constexpr explicit operator bool() const noexcept
    {
        for (std::size_t i = 0; i != num_digits; ++i) {
            if (digits[i] != 0) {
                return true;
            }
        }
        return false;
    }
 
    [[nodiscard]] constexpr bool is_negative() const noexcept
    {
        if constexpr (is_signed and num_digits > 0) {
            return static_cast<signed_digit_type>(digits[num_digits - 1]) < 0;
        } else {
            return false;
        }
    }
 
    template<std::size_t N, bool S>
    constexpr explicit operator bigint<digit_type, N, S>() const noexcept
    {
        auto r = bigint<digit_type, N, S>{};
 
        hilet sign = is_negative() ? min1_digit : zero_digit;
        for (auto i = 0; i != N; ++i) {
            r.digits[i] = i < num_digits ? digits[i] : sign;
        }
        return r;
    }
 
    std::string string() const noexcept
    {
        constexpr auto oneOver10 = reciprocal(bigint<digit_type, num_digits * 2, is_signed>{10});
 
        auto tmp = *this;
 
        std::string r;
 
        if (tmp == 0) {
            r = "0";
        } else {
            while (tmp > 0) {
                bigint remainder;
                std::tie(tmp, remainder) = div(tmp, bigint{10}, oneOver10);
                r += (static_cast<unsigned char>(remainder) + '0');
            }
        }
 
        std::reverse(r.begin(), r.end());
        return r;
    }
 
    std::string uuid_string() const noexcept
    {
        static_assert(
            std::is_same_v<digit_type, uint64_t> && num_digits == 2,
            "uuid_string should only be called on a uuid compatible type");
        return std::format(
            "{:08x}-{:04x}-{:04x}-{:04x}-{:012x}",
            static_cast<uint32_t>(digits[1] >> 32),
            static_cast<uint16_t>(digits[1] >> 16),
            static_cast<uint16_t>(digits[1]),
            static_cast<uint16_t>(digits[0] >> 48),
            digits[0] & 0x0000ffff'ffffffffULL);
    }
 
    [[nodiscard]] constexpr bigint operator-() const noexcept
    {
        bigint r;
        neg_carry_chain(r.digits, digits, num_digits);
        return r;
    }
 
    constexpr bigint &operator<<=(std::size_t rhs) noexcept
    {
        sll_carry_chain(digits, digits, rhs, num_digits);
        return *this;
    }
 
    constexpr bigint &operator>>=(std::size_t rhs) noexcept
    {
        if constexpr (is_signed) {
            sra_carry_chain(digits, digits, rhs, num_digits);
        } else {
            srl_carry_chain(digits, digits, rhs, num_digits);
        }
        return *this;
    }
 
    constexpr bigint &operator*=(bigint const &rhs) noexcept
    {
        auto r = bigint{0};
        mul_carry_chain(r.digits, digits, rhs.digits, num_digits);
        *this = r;
        return *this;
    }
 
    constexpr bigint &operator+=(bigint const &rhs) noexcept
    {
        add_carry_chain(digits, digits, rhs.digits, num_digits);
        return *this;
    }
 
    constexpr bigint &operator-=(bigint const &rhs) noexcept
    {
        sub_carry_chain(digits, digits, rhs.digits, num_digits);
        return *this;
    }
 
    constexpr bigint &operator&=(bigint const &rhs) noexcept
    {
        and_carry_chain(digits, digits, rhs.digits, num_digits);
        return *this;
    }
 
    constexpr bigint &operator|=(bigint const &rhs) noexcept
    {
        or_carry_chain(digits, digits, rhs.digits, num_digits);
        return *this;
    }
 
    constexpr bigint &operator^=(bigint const &rhs) noexcept
    {
        xor_carry_chain(digits, digits, rhs.digits, num_digits);
        return *this;
    }
 
    static bigint from_big_endian(uint8_t const *data) noexcept
    {
        auto r = bigint{};
        for (ssize_t i = static_cast<ssize_t>(num_digits) - 1; i >= 0; i--) {
            digit_type d = 0;
            for (std::size_t j = 0; j < sizeof(digit_type); j++) {
                d <<= 8;
                d |= *(data++);
            }
            r.digits[i] = d;
        }
        return r;
    }
 
    static bigint from_little_endian(uint8_t const *data) noexcept
    {
        auto r = bigint{};
        for (int i = 0; i < num_digits; ++i) {
            digit_type d = 0;
            for (std::size_t j = 0; j < sizeof(digit_type); j++) {
                d |= static_cast<digit_type>(*(data++)) << (j * 8);
            }
            r.digits[i] = d;
        }
        return r;
    }
 
    static bigint from_big_endian(void const *data) noexcept
    {
        return from_big_endian(static_cast<uint8_t const *>(data));
    }
 
    static bigint from_little_endian(void const *data) noexcept
    {
        return from_little_endian(static_cast<uint8_t const *>(data));
    }
 
    [[nodiscard]] constexpr friend bigint crc(bigint const &lhs, bigint const &rhs) noexcept requires(not is_signed)
    {
        hilet polynomialOrder = bsr_carry_chain(rhs.digits, rhs.num_digits);
        hi_assert(polynomialOrder >= 0);
 
        auto tmp = static_cast<bigint<digit_type, 2 * num_digits, is_signed>>(lhs) << polynomialOrder;
        auto rhs_ = static_cast<bigint<digit_type, 2 * num_digits, is_signed>>(rhs);
 
        auto tmp_highest_bit = bsr_carry_chain(tmp.digits, tmp.num_digits);
        while (tmp_highest_bit >= polynomialOrder) {
            hilet divident = rhs_ << (tmp_highest_bit - polynomialOrder);
 
            tmp ^= divident;
            tmp_highest_bit = bsr_carry_chain(tmp.digits, tmp.num_digits);
        }
 
        return static_cast<bigint>(tmp);
    }
 
    [[nodiscard]] constexpr friend bigint reciprocal(bigint const &rhs)
    {
        auto r = bigint<digit_type, num_digits + 1, is_signed>(0);
        r.digits[num_digits] = 1;
        return static_cast<bigint>(r / rhs);
    }
 
    [[nodiscard]] constexpr friend bool operator==(bigint const &lhs, bigint const &rhs) noexcept
    {
        return eq_carry_chain(lhs.digits, rhs.digits, lhs.num_digits);
    }
 
    [[nodiscard]] constexpr friend std::strong_ordering operator<=>(bigint const &lhs, bigint const &rhs) noexcept
    {
        if constexpr (lhs.is_signed or rhs.is_signed) {
            return cmp_signed_carry_chain(lhs.digits, rhs.digits, lhs.num_digits);
        } else {
            return cmp_unsigned_carry_chain(lhs.digits, rhs.digits, lhs.num_digits);
        }
    }
 
    [[nodiscard]] constexpr friend bigint operator<<(bigint const &lhs, std::size_t rhs) noexcept
    {
        auto r = bigint{};
        sll_carry_chain(r.digits, lhs.digits, rhs, lhs.num_digits);
        return r;
    }
 
    [[nodiscard]] constexpr friend bigint operator>>(bigint const &lhs, std::size_t rhs) noexcept
    {
        auto r = bigint{};
        if constexpr (lhs.is_signed) {
            sra_carry_chain(r.digits, lhs.digits, rhs, lhs.num_digits);
        } else {
            srl_carry_chain(r.digits, lhs.digits, rhs, lhs.num_digits);
        }
        return r;
    }
 
    [[nodiscard]] constexpr friend bigint operator*(bigint const &lhs, bigint const &rhs) noexcept
    {
        auto r = bigint{};
        mul_carry_chain(r.digits, lhs.digits, rhs.digits, lhs.num_digits);
        return r;
    }
 
    [[nodiscard]] constexpr friend bigint operator+(bigint const &lhs, bigint const &rhs) noexcept
    {
        auto r = bigint{};
        add_carry_chain(r.digits, lhs.digits, rhs.digits, lhs.num_digits);
        return r;
    }
 
    [[nodiscard]] constexpr friend bigint operator-(bigint const &lhs, bigint const &rhs) noexcept
    {
        auto r = bigint{};
        sub_carry_chain(r.digits, lhs.digits, rhs.digits, lhs.num_digits);
        return r;
    }
 
    [[nodiscard]] constexpr friend bigint operator~(bigint const &rhs) noexcept
    {
        auto r = bigint{};
        invert_carry_chain(r.digits, rhs.digits, rhs.num_digits);
        return r;
    }
 
    [[nodiscard]] constexpr friend bigint operator|(bigint const &lhs, bigint const &rhs) noexcept
    {
        auto r = bigint{};
        or_carry_chain(r.digits, lhs.digits, rhs.digits, lhs.num_digits);
        return r;
    }
 
    [[nodiscard]] constexpr friend bigint operator&(bigint const &lhs, bigint const &rhs) noexcept
    {
        auto r = bigint{};
        and_carry_chain(r.digits, lhs.digits, rhs.digits, lhs.num_digits);
        return r;
    }
 
    [[nodiscard]] constexpr friend bigint operator^(bigint const &lhs, bigint const &rhs) noexcept
    {
        auto r = bigint{};
        xor_carry_chain(r.digits, lhs.digits, rhs.digits, lhs.num_digits);
        return r;
    }
 
    [[nodiscard]] constexpr friend std::pair<bigint, bigint> div(bigint const &lhs, bigint const &rhs) noexcept
    {
        auto quotient = bigint{};
        auto remainder = bigint{};
 
        if constexpr (is_signed) {
            signed_div_carry_chain(quotient.digits, remainder.digits, lhs.digits, rhs.digits, lhs.num_digits);
        } else {
            div_carry_chain(quotient.digits, remainder.digits, lhs.digits, rhs.digits, lhs.num_digits);
        }
        return std::pair{quotient, remainder};
    }
 
    [[nodiscard]] constexpr friend std::pair<bigint, bigint>
    div(bigint const &lhs, bigint const &rhs, bigint<digit_type, 2 * num_digits, is_signed> const &rhs_reciprocal) noexcept
        requires(not is_signed)
    {
        constexpr auto nr_bits = num_digits * bits_per_digit;
 
        using bigint_x3_type = bigint<digit_type, 3 * num_digits, is_signed>;
 
        auto quotient = bigint_x3_type{lhs} * bigint_x3_type{rhs_reciprocal};
        quotient >>= (2 * nr_bits);
 
        auto product = bigint_x3_type{quotient} * bigint_x3_type{rhs};
 
        hi_axiom(product <= lhs);
        auto remainder = lhs - product;
 
        int retry = 0;
        while (remainder >= rhs) {
            if (retry++ > 3) {
                return div(lhs, rhs);
            }
 
            remainder -= rhs;
            quotient += 1;
        }
        return std::pair{static_cast<bigint>(quotient), static_cast<bigint>(remainder)};
    }
 
    [[nodiscard]] constexpr friend bigint operator/(bigint const &lhs, bigint const &rhs) noexcept
    {
        auto quotient = bigint{};
        auto remainder = bigint{};
 
        if constexpr (is_signed) {
            signed_div_carry_chain(quotient.digits, remainder.digits, lhs.digits, rhs.digits, lhs.num_digits);
        } else {
            div_carry_chain(quotient.digits, remainder.digits, lhs.digits, rhs.digits, lhs.num_digits);
        }
        return quotient;
    }
 
    [[nodiscard]] constexpr friend bigint operator%(bigint const &lhs, bigint const &rhs) noexcept
    {
        auto quotient = bigint{};
        auto remainder = bigint{};
 
        if constexpr (is_signed) {
            signed_div_carry_chain(quotient.digits, remainder.digits, lhs.digits, rhs.digits, lhs.num_digits);
        } else {
            div_carry_chain(quotient.digits, remainder.digits, lhs.digits, rhs.digits, lhs.num_digits);
        }
        return remainder;
    }
 
    friend std::ostream &operator<<(std::ostream &lhs, bigint const &rhs)
    {
        return lhs << rhs.string();
    }
};
 
template<std::unsigned_integral T, std::size_t N>
struct is_numeric_unsigned_integral<bigint<T, N, false>> : std::true_type {
};
 
template<std::unsigned_integral T, std::size_t N>
struct is_numeric_signed_integral<bigint<T, N, true>> : std::true_type {
};
 
template<std::unsigned_integral T, std::size_t N, bool S>
struct is_numeric_integral<bigint<T, N, S>> : std::true_type {
};
 
using ubig128 = bigint<uint64_t, 2, false>;
using big128 = bigint<uint64_t, 2, true>;
using uuid = bigint<uint64_t, 2, false>;
 
} // namespace hi::inline v1
 
 
template<std::unsigned_integral DigitType, std::size_t NumDigits, bool IsSigned>
struct std::numeric_limits<hi::bigint<DigitType, NumDigits, IsSigned>> {
    using value_type = hi::bigint<DigitType, NumDigits, IsSigned>;
 
    static constexpr bool is_specialized = true;
    static constexpr bool is_signed = IsSigned;
    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 = std::denorm_absent;
    static constexpr bool has_denorm_loss = false;
    static constexpr float_round_style round_style = std::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 = std::numeric_limits<DigitType>::digits * NumDigits;
    static constexpr int digits10 = std::numeric_limits<DigitType>::digits10 * NumDigits;
    static constexpr int max_digits10 = 0;
    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 = std::numeric_limits<DigitType>::traps;
    static constexpr bool tinyness_before = false;
 
    static constexpr value_type min() noexcept
    {
        auto r = value_type{};
        constexpr auto smin = std::numeric_limits<typename value_type::signed_digit_type>::min();
        constexpr auto umin = std::numeric_limits<typename value_type::digit_type>::min();
 
        for (std::size_t i = 0; i != value_type::num_digits; ++i) {
            r.digits[i] = umin;
        }
 
        if constexpr (value_type::is_signed and value_type::num_digits > 0) {
            r.digits[value_type::num_digits - 1] = static_cast<hi_typename value_type::digit_type>(smin);
        }
 
        return r;
    }
 
    static constexpr value_type lowest() noexcept
    {
        return min();
    }
 
    static constexpr value_type max() noexcept
    {
        auto r = value_type{};
        constexpr auto smax = std::numeric_limits<typename value_type::signed_digit_type>::max();
        constexpr auto umax = std::numeric_limits<typename value_type::digit_type>::max();
 
        for (std::size_t i = 0; i != value_type::num_digits; ++i) {
            r.digits[i] = umax;
        }
 
        if constexpr (value_type::is_signed and value_type::num_digits > 0) {
            r.digits[value_type::num_digits - 1] = smax;
        }
 
        return r;
    }
 
    static constexpr value_type epsilon() noexcept
    {
        return value_type{0};
    }
 
    static constexpr value_type round_error() noexcept
    {
        return value_type{0};
    }
 
    static constexpr value_type infinity() noexcept
    {
        return value_type{0};
    }
 
    static constexpr value_type quiet_NaN() noexcept
    {
        return value_type{0};
    }
 
    static constexpr value_type signaling_NaN() noexcept
    {
        return value_type{0};
    }
 
    static constexpr value_type denorm_min() noexcept
    {
        return value_type{0};
    }
};