/*
uint128_t.h
An unsigned 128 bit integer type for C++

Copyright (c) 2013 - 2017 Jason Lee @ calccrypto at gmail.com

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.

With much help from Auston Sterling

Thanks to Stefan Deigmüller for finding
a bug in operator*.

Thanks to François Dessenne for convincing me
to do a general rewrite of this class.
*/

#ifndef __UINT128_T__
#define __UINT128_T__

#include <algorithm>
#include <cctype>
#include <sstream>

#include <cstdint>
#include <ostream>
#include <stdexcept>
#include <string>
#include <type_traits>
#include <utility>
#include <vector>

#include "endianness.h"

class uint128_t
{
  private:
#ifdef __BIG_ENDIAN__
        uint64_t UPPER, LOWER;
#endif
#ifdef __LITTLE_ENDIAN__
        uint64_t LOWER, UPPER;
#endif
  public:
    // Constructors
    constexpr uint128_t() : LOWER{0}, UPPER{0} {}
    constexpr uint128_t(const uint128_t & rhs) = default;
    constexpr uint128_t(uint128_t && rhs) = default;

    // do not use prefixes (0x, 0b, etc.)
    // if the input string is too long, only right most characters are read
    uint128_t(const std::string & s, uint8_t base)
     : LOWER{}, UPPER{}
    {
        init(s.c_str(), s.size(), base);
    }

    uint128_t(const char *s, const std::size_t len, uint8_t base)
     : LOWER{}, UPPER{}
    {
        init(s, len, base);
    }

    constexpr uint128_t(const bool & b)
        : uint128_t((uint8_t) b)
    {}

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr uint128_t(const T & rhs)
#ifdef __BIG_ENDIAN__
        : UPPER(0), LOWER(rhs)
#endif
#ifdef __LITTLE_ENDIAN__
        : LOWER(rhs), UPPER(0)
#endif
    {
        if (std::is_signed<T>::value) {
            if (rhs < 0) {
                UPPER = -1;
            }
        }
    }

    template <typename S, typename T, typename = typename std::enable_if <std::is_integral<S>::value && std::is_integral<T>::value, void>::type>
    constexpr uint128_t(const S & upper_rhs, const T & lower_rhs)
#ifdef __BIG_ENDIAN__
        : UPPER(upper_rhs), LOWER(lower_rhs)
#endif
#ifdef __LITTLE_ENDIAN__
        : LOWER(lower_rhs), UPPER(upper_rhs)
#endif
    {}

    // Assignment Operator
    constexpr uint128_t & operator=(const uint128_t & rhs) = default;
    constexpr uint128_t & operator=(uint128_t && rhs) = default;

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr uint128_t & operator=(const T & rhs)
    {
        UPPER = 0;

        if (std::is_signed<T>::value) {
            if (rhs < 0) {
                UPPER = -1;
            }
        }

        LOWER = rhs;
        return *this;
    }

    constexpr uint128_t & operator=(const bool & rhs)
    {
        UPPER = 0;
        LOWER = rhs;
        return *this;
    }

    // Typecast Operators
    constexpr operator bool() const
    {
        return static_cast<bool>(UPPER | LOWER);
    }

    constexpr operator uint8_t() const
    {
        return static_cast<uint8_t>(LOWER);
    }

    constexpr operator uint16_t() const
    {
        return static_cast<uint16_t>(LOWER);
    }

    constexpr operator uint32_t() const
    {
        return static_cast<uint32_t>(LOWER);
    }

    constexpr operator uint64_t() const
    {
        return static_cast<uint64_t>(LOWER);
    }

    // Bitwise Operators
    constexpr uint128_t operator&(const uint128_t & rhs) const
    {
        return uint128_t(UPPER & rhs.UPPER, LOWER & rhs.LOWER);
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr uint128_t operator&(const T & rhs) const
    {
        return uint128_t(0, LOWER & (uint64_t) rhs);
    }

    constexpr uint128_t & operator&=(const uint128_t & rhs)
    {
        UPPER &= rhs.UPPER;
        LOWER &= rhs.LOWER;
        return *this;
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr uint128_t & operator&=(const T & rhs){
        UPPER = 0;
        LOWER &= rhs;
        return *this;
    }

    constexpr uint128_t operator|(const uint128_t & rhs) const
    {
        return uint128_t(UPPER | rhs.UPPER, LOWER | rhs.LOWER);
    }


    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr uint128_t operator|(const T & rhs) const
    {
        return uint128_t(UPPER, LOWER | (uint64_t) rhs);
    }

    constexpr uint128_t & operator|=(const uint128_t & rhs)
    {
        UPPER |= rhs.UPPER;
        LOWER |= rhs.LOWER;
        return *this;
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr uint128_t & operator|=(const T & rhs)
    {
        LOWER |= (uint64_t) rhs;
        return *this;
    }

    constexpr uint128_t operator^(const uint128_t & rhs) const
    {
        return uint128_t(UPPER ^ rhs.UPPER, LOWER ^ rhs.LOWER);
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr uint128_t operator^(const T & rhs) const
    {
        return uint128_t(UPPER, LOWER ^ (uint64_t) rhs);
    }

    constexpr uint128_t & operator^=(const uint128_t & rhs)
    {
        UPPER ^= rhs.UPPER;
        LOWER ^= rhs.LOWER;
        return *this;
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr uint128_t & operator^=(const T & rhs)
    {
        LOWER ^= (uint64_t) rhs;
        return *this;
    }

    constexpr uint128_t operator~() const
    {
        return uint128_t(~UPPER, ~LOWER);
    }

    // Bit Shift Operators
    constexpr uint128_t operator<<(const uint128_t & rhs) const
    {
        const uint64_t shift = rhs.LOWER;
        if (static_cast<bool>(rhs.UPPER) || (shift >= 128))
        {
            return uint128_t{0};
        }
        else if (shift == 64)
        {
            return uint128_t(LOWER, 0);
        }
        else if (shift == 0)
        {
            return *this;
        }
        else if (shift < 64)
        {
            return uint128_t((UPPER << shift) + (LOWER >> (64 - shift)), LOWER << shift);
        }
        else if ((128 > shift) && (shift > 64))
        {
            return uint128_t(LOWER << (shift - 64), 0);
        }
        else{
            return uint128_t{0};
        }
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr uint128_t operator<<(const T & rhs) const
    {
        return *this << uint128_t(rhs);
    }

    constexpr uint128_t & operator<<=(const uint128_t & rhs)
    {
        *this = *this << rhs;
        return *this;
    }

    constexpr uint128_t operator>>(const uint128_t & rhs) const
    {
        const uint64_t shift = rhs.LOWER;
        if (static_cast<bool>(rhs.UPPER) || (shift >= 128))
        {
            return uint128_t{0};
        }
        else if (shift == 64)
        {
            return uint128_t(0, UPPER);
        }
        else if (shift == 0)
        {
            return *this;
        }
        else if (shift < 64)
        {
            return uint128_t(UPPER >> shift, (UPPER << (64 - shift)) + (LOWER >> shift));
        }
        else if ((128 > shift) && (shift > 64))
        {
            return uint128_t(0, (UPPER >> (shift - 64)));
        }
        else{
            return uint128_t{0};
        }
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr uint128_t operator>>(const T & rhs) const
    {
        return *this >> uint128_t(rhs);
    }

    constexpr uint128_t & operator>>=(const uint128_t & rhs)
    {
        *this = *this >> rhs;
        return *this;
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr uint128_t & operator>>=(const T & rhs)
    {
        *this = *this >> uint128_t(rhs);
        return *this;
    }

    // Logical Operators
    constexpr bool operator!() const
    {
        return !static_cast<bool>(UPPER | LOWER);
    }

    constexpr bool operator&&(const uint128_t & rhs) const
    {
        return static_cast<bool>(*this && rhs);
    }

    constexpr bool operator||(const uint128_t & rhs) const
    {
        return static_cast<bool>(*this || rhs);
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr bool operator&&(const T & rhs) const
    {
        return static_cast<bool>(*this && rhs);
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr bool operator||(const T & rhs) const
    {
        return static_cast<bool>(*this || rhs);
    }

    constexpr bool operator==(const uint128_t & rhs) const
    {
        return ((UPPER == rhs.UPPER) && (LOWER == rhs.LOWER));
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr bool operator==(const T & rhs) const
    {
        return (!UPPER && (LOWER == (uint64_t) rhs));
    }

    constexpr bool operator!=(const uint128_t & rhs) const
    {
        return ((UPPER != rhs.UPPER) | (LOWER != rhs.LOWER));
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr bool operator!=(const T & rhs) const
    {
        return (UPPER | (LOWER != (uint64_t) rhs));
    }

    constexpr bool operator>(const uint128_t & rhs) const
    {
        if (UPPER == rhs.UPPER)
        {
            return (LOWER > rhs.LOWER);
        }
        return (UPPER > rhs.UPPER);
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr bool operator>(const T & rhs) const
    {
        return (UPPER || (LOWER > (uint64_t) rhs));
    }

    constexpr bool operator<(const uint128_t & rhs) const
    {
        if (UPPER == rhs.UPPER)
        {
            return (LOWER < rhs.LOWER);
        }
        return (UPPER < rhs.UPPER);
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr bool operator<(const T & rhs) const
    {
        return (!UPPER)?(LOWER < (uint64_t) rhs):false;
    }

    constexpr bool operator>=(const uint128_t & rhs) const
    {
        return ((*this > rhs) | (*this == rhs));
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr bool operator>=(const T & rhs) const
    {
        return ((*this > rhs) | (*this == rhs));
    }

    constexpr bool operator<=(const uint128_t & rhs) const
    {
        return ((*this < rhs) | (*this == rhs));
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr bool operator<=(const T & rhs) const
    {
        return ((*this < rhs) | (*this == rhs));
    }

    // Arithmetic Operators
    constexpr uint128_t operator+(const uint128_t & rhs) const
    {
        return uint128_t(UPPER + rhs.UPPER + ((LOWER + rhs.LOWER) < LOWER), LOWER + rhs.LOWER);
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr uint128_t operator+(const T & rhs) const
    {
        return uint128_t(UPPER + ((LOWER + (uint64_t) rhs) < LOWER), LOWER + (uint64_t) rhs);
    }

    constexpr uint128_t & operator+=(const uint128_t & rhs)
    {
        UPPER += rhs.UPPER + ((LOWER + rhs.LOWER) < LOWER);
        LOWER += rhs.LOWER;
        return *this;
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr uint128_t & operator+=(const T & rhs)
    {
        return *this += uint128_t(rhs);
    }

    constexpr uint128_t operator-(const uint128_t & rhs) const
    {
        return uint128_t(UPPER - rhs.UPPER - ((LOWER - rhs.LOWER) > LOWER), LOWER - rhs.LOWER);
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr uint128_t operator-(const T & rhs) const
    {
        return uint128_t((uint64_t) (UPPER - ((LOWER - rhs) > LOWER)), (uint64_t) (LOWER - rhs));
    }

    constexpr uint128_t & operator-=(const uint128_t & rhs)
    {
        *this = *this - rhs;
        return *this;
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr uint128_t & operator-=(const T & rhs)
    {
        return *this = *this - uint128_t(rhs);
    }

    constexpr uint128_t operator*(const uint128_t & rhs) const
    {
        // split values into 4 32-bit parts
        uint64_t top[4] = {UPPER >> 32, UPPER & 0xffffffff, LOWER >> 32, LOWER & 0xffffffff};
        uint64_t bottom[4] = {rhs.UPPER >> 32, rhs.UPPER & 0xffffffff, rhs.LOWER >> 32, rhs.LOWER & 0xffffffff};
        uint64_t products[4][4]{};

        // multiply each component of the values
        for (int y = 3; y > -1; y--)
        {
            for (int x = 3; x > -1; x--)
            {
                products[3 - x][y] = top[x] * bottom[y];
            }
        }

        // first row
        uint64_t fourth32 = (products[0][3] & 0xffffffff);
        uint64_t third32  = (products[0][2] & 0xffffffff) + (products[0][3] >> 32);
        uint64_t second32 = (products[0][1] & 0xffffffff) + (products[0][2] >> 32);
        uint64_t first32  = (products[0][0] & 0xffffffff) + (products[0][1] >> 32);

        // second row
        third32  += (products[1][3] & 0xffffffff);
        second32 += (products[1][2] & 0xffffffff) + (products[1][3] >> 32);
        first32  += (products[1][1] & 0xffffffff) + (products[1][2] >> 32);

        // third row
        second32 += (products[2][3] & 0xffffffff);
        first32  += (products[2][2] & 0xffffffff) + (products[2][3] >> 32);

        // fourth row
        first32  += (products[3][3] & 0xffffffff);

        // move carry to next digit
        third32  += fourth32 >> 32;
        second32 += third32  >> 32;
        first32  += second32 >> 32;

        // remove carry from current digit
        fourth32 &= 0xffffffff;
        third32  &= 0xffffffff;
        second32 &= 0xffffffff;
        first32  &= 0xffffffff;

        // combine components
        return uint128_t((first32 << 32) | second32, (third32 << 32) | fourth32);
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr uint128_t operator*(const T & rhs) const
    {
        return *this * uint128_t(rhs);
    }

    constexpr uint128_t & operator*=(const uint128_t & rhs)
    {
        *this = *this * rhs;
        return *this;
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr uint128_t & operator*=(const T & rhs)
    {
        return *this = *this * uint128_t(rhs);
    }

    void export_bits(std::vector<uint8_t> & ret) const
    {
        ConvertToVector(ret, const_cast<const uint64_t&>(UPPER));
        ConvertToVector(ret, const_cast<const uint64_t&>(LOWER));
    }

private:
    constexpr std::pair<uint128_t, uint128_t> divmod(const uint128_t & lhs, const uint128_t & rhs) const
    {
        // Save some calculations /////////////////////
        if (rhs == uint128_t{0})
        {
            throw std::domain_error("Error: division or modulus by 0");
        }
        else if (rhs == uint128_t{1})
        {
            return std::pair <uint128_t, uint128_t> (lhs, uint128_t{0});
        }
        else if (lhs == rhs)
        {
            return std::pair <uint128_t, uint128_t> (uint128_t{1}, uint128_t{0});
        }
        else if ((lhs == uint128_t{0}) || (lhs < rhs))
        {
            return std::pair <uint128_t, uint128_t> (uint128_t{0}, lhs);
        }

        std::pair<uint128_t, uint128_t> qr(uint128_t{0}, uint128_t{0});
        for (uint8_t x = lhs.bits(); x > 0; x--)
        {
            qr.first  <<= uint128_t{1};
            qr.second <<= uint128_t{1};

            if ((lhs >> (x - 1U)) & 1)
            {
                ++qr.second;
            }

            if (qr.second >= rhs)
            {
                qr.second -= rhs;
                ++qr.first;
            }
        }
        return qr;
    }
    void ConvertToVector(std::vector<uint8_t> & ret, const uint64_t & val) const
    {
        ret.push_back(static_cast<uint8_t>(val >> 56));
        ret.push_back(static_cast<uint8_t>(val >> 48));
        ret.push_back(static_cast<uint8_t>(val >> 40));
        ret.push_back(static_cast<uint8_t>(val >> 32));
        ret.push_back(static_cast<uint8_t>(val >> 24));
        ret.push_back(static_cast<uint8_t>(val >> 16));
        ret.push_back(static_cast<uint8_t>(val >> 8));
        ret.push_back(static_cast<uint8_t>(val));
    }

    // do not use prefixes (0x, 0b, etc.)
    // if the input string is too long, only right most characters are read
    void init(const char *s, std::size_t len, uint8_t base)
    {
        if ((s == NULL) || !len || (s[0] == '\x00'))
        {
            LOWER = UPPER = 0;
            return;
        }

        while (*s && len && std::isspace(*s))
        {
            ++s;
            len--;
        }

        // no prefixes
        switch (base)
        {
            case 16:
                _init_hex(s, len);
                break;
            case 10:
                _init_dec(s, len);
                break;
            case 8:
                _init_oct(s, len);
                break;
            case 2:
                _init_bin(s, len);
                break;
            default:
                // should probably throw error here
                break;
        }
    }

    void _init_hex(const char *s, std::size_t len)
    {
        // 2**128 = 0x100000000000000000000000000000000.
        static const std::size_t MAX_LEN = 32;

        LOWER = UPPER = 0;
        if (!s || !len)
        {
            return;
        }

        const std::size_t max_len = std::min(len, MAX_LEN);
        const std::size_t starting_index = (MAX_LEN < len)?(len - MAX_LEN):0;
        const std::size_t double_lower = sizeof(LOWER) * 2;
        const std::size_t lower_len = (max_len >= double_lower)?double_lower:max_len;
        const std::size_t upper_len = (max_len >= double_lower)?(max_len - double_lower):0;

        std::stringstream lower_s, upper_s;
        upper_s << std::hex << std::string(s + starting_index, upper_len);
        lower_s << std::hex << std::string(s + starting_index + upper_len, lower_len);

        // should check for errors
        upper_s >> UPPER;
        lower_s >> LOWER;
    }

    void _init_dec(const char *s, std::size_t len)
    {
        // 2**128 = 340282366920938463463374607431768211456.
        static const std::size_t MAX_LEN = 39;

        LOWER = UPPER = 0;
        if (!s || !len)
        {
            return;
        }

        const std::size_t max_len = std::min(len, MAX_LEN);
        const std::size_t starting_index = (MAX_LEN < len)?(len - MAX_LEN):0;
        s += starting_index;

        for (std::size_t i = 0; *s && ('0' <= *s) && (*s <= '9') && (i < max_len); ++s, ++i)
        {
            *this *= 10;
            *this += *s - '0';
        }
    }

    void _init_oct(const char *s, std::size_t len)
    {
        // 2**128 = 0o4000000000000000000000000000000000000000000.
        static const std::size_t MAX_LEN = 43;

        LOWER = UPPER = 0;
        if (!s || !len)
        {
            return;
        }

        const std::size_t max_len = std::min(len, MAX_LEN);
        const std::size_t starting_index = (MAX_LEN < len)?(len - MAX_LEN):0;
        s += starting_index;

        for (std::size_t i = 0; *s && ('0' <= *s) && (*s <= '7') && (i < max_len); ++s, ++i)
        {
            *this *= 8;
            *this += *s - '0';
        }
    }

    void _init_bin(const char *s, std::size_t len)
    {
        // 2**128 = 0x100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.
        static const std::size_t MAX_LEN = 128;

        LOWER = UPPER = 0;
        if (!s || !len)
        {
            return;
        }

        const std::size_t max_len = std::min(len, MAX_LEN);
        const std::size_t starting_index = (MAX_LEN < len)?(len - MAX_LEN):0;
        const std::size_t eight_lower = sizeof(LOWER) * 8;
        const std::size_t lower_len = (max_len >= eight_lower)?eight_lower:max_len;
        const std::size_t upper_len = (max_len >= eight_lower)?(max_len - eight_lower):0;
        s += starting_index;

        for (std::size_t i = 0; *s && ('0' <= *s) && (*s <= '1') && (i < upper_len); ++s, ++i)
        {
            UPPER <<= 1;
            UPPER |= *s - '0';
        }

        for (std::size_t i = 0; *s && ('0' <= *s) && (*s <= '1') && (i < lower_len); ++s, ++i)
        {
            LOWER <<= 1;
            LOWER |= *s - '0';
        }
    }

  public:
    constexpr uint128_t operator/(const uint128_t & rhs) const
    {
        return divmod(*this, rhs).first;
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr uint128_t operator/(const T & rhs) const
    {
        return *this / uint128_t(rhs);
    }

    constexpr uint128_t & operator/=(const uint128_t & rhs)
    {
        *this = *this / rhs;
        return *this;
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr uint128_t & operator/=(const T & rhs)
    {
        return *this = *this / uint128_t(rhs);
    }

    constexpr uint128_t operator%(const uint128_t & rhs) const
    {
        return divmod(*this, rhs).second;
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr uint128_t operator%(const T & rhs) const
    {
        return *this % uint128_t(rhs);
    }

    constexpr uint128_t & operator%=(const uint128_t & rhs)
    {
        *this = *this % rhs;
        return *this;
    }

    template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
    constexpr uint128_t & operator%=(const T & rhs)
    {
        return *this = *this % uint128_t(rhs);
    }

    // Increment Operator
    constexpr uint128_t & operator++()
    {
        return *this += uint128_t{1};
    }

    constexpr uint128_t operator++(int)
    {
        uint128_t temp(*this);
        ++*this;
        return temp;
    }

    // Decrement Operator
    constexpr uint128_t & operator--()
    {
        return *this -= uint128_t{1};
    }

    constexpr uint128_t operator--(int)
    {
        uint128_t temp(*this);
        --*this;
        return temp;
    }

    // Nothing done since promotion doesn't work here
    constexpr uint128_t operator+() const
    {
        return *this;
    }

    // two's complement
    constexpr uint128_t operator-() const
    {
        return ~*this + uint128_t{1};
    }

    // Get private values
    constexpr const uint64_t & upper() const
    {
        return UPPER;
    }

    constexpr const uint64_t & lower() const
    {
        return LOWER;
    }

    // Get bitsize of value
    constexpr uint8_t bits() const
    {
        uint8_t out = 0;
        if (UPPER)
        {
            out = 64;
            uint64_t up = UPPER;
            while (up)
            {
                up >>= 1;
                out++;
            }
        }
        else{
            uint64_t low = LOWER;
            while (low)
            {
                low >>= 1;
                out++;
            }
        }
        return out;
    }

    // Get string representation of value
    std::string str(uint8_t base = 10, const unsigned int & len = 0) const
    {
        if ((base < 2) || (base > 16))
        {
            throw std::invalid_argument("Base must be in the range [2, 16]");
        }
        std::string out = "";
        if (!(*this))
        {
            out = "0";
        }
        else{
            std::pair <uint128_t, uint128_t> qr(*this, uint128_t{0});
            do{
                qr = divmod(qr.first, base);
                out = "0123456789abcdef"[(uint8_t) qr.second] + out;
            } while (qr.first);
        }
        if (out.size() < len)
        {
            out = std::string(len - out.size(), '0') + out;
        }
        return out;
    }
};  // class uint256_t

// lhs type T as first arguemnt
// If the output is not a bool, casts to type T

// Bitwise Operators
template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr uint128_t operator&(const T &lhs, const uint128_t & rhs)
{
    return rhs & lhs;
}

template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr T & operator&=(T &lhs, const uint128_t & rhs)
{
    return lhs = static_cast <T> (rhs & lhs);
}

template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr uint128_t operator|(const T &lhs, const uint128_t & rhs)
{
    return rhs | lhs;
}

template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr T & operator|=(T &lhs, const uint128_t & rhs)
{
    return lhs = static_cast <T> (rhs | lhs);
}

template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr uint128_t operator^(const T &lhs, const uint128_t & rhs)
{
    return rhs ^ lhs;
}

template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr T & operator^=(T &lhs, const uint128_t & rhs)
{
    return lhs = static_cast <T> (rhs ^ lhs);
}

constexpr uint128_t operator<<(const bool & lhs, const uint128_t & rhs)
{
    return uint128_t(lhs) << rhs;
}

constexpr uint128_t operator<<(const uint8_t & lhs, const uint128_t & rhs)
{
    return uint128_t(lhs) << rhs;
}

constexpr uint128_t operator<<(const uint16_t & lhs, const uint128_t & rhs)
{
    return uint128_t(lhs) << rhs;
}

constexpr uint128_t operator<<(const uint32_t & lhs, const uint128_t & rhs)
{
    return uint128_t(lhs) << rhs;
}

constexpr uint128_t operator<<(const uint64_t & lhs, const uint128_t & rhs)
{
    return uint128_t(lhs) << rhs;
}

constexpr uint128_t operator<<(const int8_t & lhs, const uint128_t & rhs)
{
    return uint128_t(lhs) << rhs;
}

constexpr uint128_t operator<<(const int16_t & lhs, const uint128_t & rhs)
{
    return uint128_t(lhs) << rhs;
}

constexpr uint128_t operator<<(const int32_t & lhs, const uint128_t & rhs)
{
    return uint128_t(lhs) << rhs;
}

constexpr uint128_t operator<<(const int64_t & lhs, const uint128_t & rhs)
{
    return uint128_t(lhs) << rhs;
}

template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr T & operator<<=(T &lhs, const uint128_t & rhs)
{
    return lhs = static_cast <T> (uint128_t(lhs) << rhs);
}

constexpr uint128_t operator>>(const bool & lhs, const uint128_t & rhs)
{
    return uint128_t(lhs) >> rhs;
}

constexpr uint128_t operator>>(const uint8_t & lhs, const uint128_t & rhs)
{
    return uint128_t(lhs) >> rhs;
}

constexpr uint128_t operator>>(const uint16_t & lhs, const uint128_t & rhs)
{
    return uint128_t(lhs) >> rhs;
}

constexpr uint128_t operator>>(const uint32_t & lhs, const uint128_t & rhs)
{
    return uint128_t(lhs) >> rhs;
}

constexpr uint128_t operator>>(const uint64_t & lhs, const uint128_t & rhs)
{
    return uint128_t(lhs) >> rhs;
}

constexpr uint128_t operator>>(const int8_t & lhs, const uint128_t & rhs)
{
    return uint128_t(lhs) >> rhs;
}

constexpr uint128_t operator>>(const int16_t & lhs, const uint128_t & rhs)
{
    return uint128_t(lhs) >> rhs;
}

constexpr uint128_t operator>>(const int32_t & lhs, const uint128_t & rhs)
{
    return uint128_t(lhs) >> rhs;
}

constexpr uint128_t operator>>(const int64_t & lhs, const uint128_t & rhs)
{
    return uint128_t(lhs) >> rhs;
}

template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr T & operator>>=(T &lhs, const uint128_t & rhs)
{
    return lhs = static_cast <T> (uint128_t(lhs) >> rhs);
}

// Comparison Operators
template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr bool operator==(const T &lhs, const uint128_t & rhs)
{
    return (!rhs.upper() && ((uint64_t) lhs == rhs.lower()));
}

template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr bool operator!=(const T &lhs, const uint128_t & rhs)
{
    return (rhs.upper() | ((uint64_t) lhs != rhs.lower()));
}

template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr bool operator>(const T &lhs, const uint128_t & rhs)
{
    return (!rhs.upper()) && ((uint64_t) lhs > rhs.lower());
}

template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr bool operator<(const T &lhs, const uint128_t & rhs)
{
    if (rhs.upper())
    {
        return true;
    }
    return ((uint64_t) lhs < rhs.lower());
}

template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr bool operator>=(const T &lhs, const uint128_t & rhs)
{
    if (rhs.upper())
    {
        return false;
    }
    return ((uint64_t) lhs >= rhs.lower());
}

template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr bool operator<=(const T &lhs, const uint128_t & rhs)
{
    if (rhs.upper())
    {
        return true;
    }
    return ((uint64_t) lhs <= rhs.lower());
}

// Arithmetic Operators
template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr uint128_t operator+(const T &lhs, const uint128_t & rhs)
{
    return rhs + lhs;
}

template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr T & operator+=(T &lhs, const uint128_t & rhs)
{
    return lhs = static_cast <T> (rhs + lhs);
}

template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr uint128_t operator-(const T &lhs, const uint128_t & rhs)
{
    return -(rhs - lhs);
}

template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr T & operator-=(T &lhs, const uint128_t & rhs)
{
    return lhs = static_cast <T> (-(rhs - lhs));
}

template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr uint128_t operator*(const T &lhs, const uint128_t & rhs)
{
    return rhs * lhs;
}

template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr T & operator*=(T &lhs, const uint128_t & rhs)
{
    return lhs = static_cast <T> (rhs * lhs);
}

template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr uint128_t operator/(const T &lhs, const uint128_t & rhs)
{
    return uint128_t(lhs) / rhs;
}

template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr T & operator/=(T &lhs, const uint128_t & rhs)
{
    return lhs = static_cast <T> (uint128_t(lhs) / rhs);
}

template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr uint128_t operator%(const T &lhs, const uint128_t & rhs)
{
    return uint128_t(lhs) % rhs;
}

template <typename T, typename = typename std::enable_if<std::is_integral<T>::value, T>::type >
constexpr T & operator%=(T &lhs, const uint128_t & rhs)
{
    return lhs = static_cast <T> (uint128_t(lhs) % rhs);
}

std::ostream & operator<<(std::ostream & stream, const uint128_t & rhs)
{
    if (stream.flags() & stream.oct)
    {
        stream << rhs.str(8);
    }
    else if (stream.flags() & stream.dec)
    {
        stream << rhs.str(10);
    }
    else if (stream.flags() & stream.hex)
    {
        stream << rhs.str(16);
    }
    return stream;
}

#endif