//------------------------------------------------------------------------------
/*
    This file is part of rippled: https://github.com/ripple/rippled
    Copyright (c) 2022 Ripple Labs Inc.

    Permission to use, copy, modify, and/or distribute this software for any
    purpose  with  or without fee is hereby granted, provided that the above
    copyright notice and this permission notice appear in all copies.

    THE  SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
    WITH  REGARD  TO  THIS  SOFTWARE  INCLUDING  ALL  IMPLIED  WARRANTIES  OF
    MERCHANTABILITY  AND  FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
    ANY  SPECIAL ,  DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
    WHATSOEVER  RESULTING  FROM  LOSS  OF USE, DATA OR PROFITS, WHETHER IN AN
    ACTION  OF  CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
    OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*/
//==============================================================================

#include <ripple/basics/Number.h>
#include <algorithm>
#include <cassert>
#include <numeric>
#include <stdexcept>
#include <type_traits>

#ifdef _MSVC_LANG
#include <boost/multiprecision/cpp_int.hpp>
using uint128_t = boost::multiprecision::uint128_t;
#else   // !defined(_MSVC_LANG)
using uint128_t = __uint128_t;
#endif  // !defined(_MSVC_LANG)

namespace ripple {

// guard

class Number::guard
{
    std::uint64_t digits_;
    std::uint8_t xbit_ : 1;
    std::uint8_t sbit_ : 1;  // TODO :  get rid of

public:
    explicit guard() : digits_{0}, xbit_{0}, sbit_{0}
    {
    }

    void
    set_positive() noexcept;
    void
    set_negative() noexcept;
    bool
    is_negative() const noexcept;
    void
    push(unsigned d) noexcept;
    unsigned
    pop() noexcept;
    int
    round() noexcept;
};

inline void
Number::guard::set_positive() noexcept
{
    sbit_ = 0;
}

inline void
Number::guard::set_negative() noexcept
{
    sbit_ = 1;
}

inline bool
Number::guard::is_negative() const noexcept
{
    return sbit_ == 1;
}

inline void
Number::guard::push(unsigned d) noexcept
{
    xbit_ = xbit_ || (digits_ & 0x0000'0000'0000'000F) != 0;
    digits_ >>= 4;
    digits_ |= (d & 0x0000'0000'0000'000FULL) << 60;
}

inline unsigned
Number::guard::pop() noexcept
{
    unsigned d = (digits_ & 0xF000'0000'0000'0000) >> 60;
    digits_ <<= 4;
    return d;
}

int
Number::guard::round() noexcept
{
    if (digits_ > 0x5000'0000'0000'0000)
        return 1;
    if (digits_ < 0x5000'0000'0000'0000)
        return -1;
    if (xbit_)
        return 1;
    return 0;
}

// Number

constexpr Number one{1000000000000000, -15, Number::unchecked{}};

void
Number::normalize()
{
    if (mantissa_ == 0)
    {
        *this = Number{};
        return;
    }
    bool const negative = (mantissa_ < 0);
    if (negative)
        mantissa_ = -mantissa_;
    auto m = static_cast<std::make_unsigned_t<rep>>(mantissa_);
    while ((m < minMantissa) && (exponent_ > minExponent))
    {
        m *= 10;
        --exponent_;
    }
    while (m > maxMantissa)
    {
        if (exponent_ >= maxExponent)
            throw std::overflow_error("Number::normalize 1");
        m /= 10;
        ++exponent_;
    }
    mantissa_ = m;
    if ((exponent_ < minExponent) || (mantissa_ < minMantissa))
    {
        *this = Number{};
        return;
    }

    if (exponent_ > maxExponent)
        throw std::overflow_error("Number::normalize 2");

    if (negative)
        mantissa_ = -mantissa_;
}

Number&
Number::operator+=(Number const& y)
{
    if (y == Number{})
        return *this;
    if (*this == Number{})
    {
        *this = y;
        return *this;
    }
    if (*this == -y)
    {
        *this = Number{};
        return *this;
    }
    assert(isnormal() && y.isnormal());
    auto xm = mantissa();
    auto xe = exponent();
    int xn = 1;
    if (xm < 0)
    {
        xm = -xm;
        xn = -1;
    }
    auto ym = y.mantissa();
    auto ye = y.exponent();
    int yn = 1;
    if (ym < 0)
    {
        ym = -ym;
        yn = -1;
    }
    guard g;
    if (xe < ye)
    {
        if (xn == -1)
            g.set_negative();
        do
        {
            g.push(xm % 10);
            xm /= 10;
            ++xe;
        } while (xe < ye);
    }
    else if (xe > ye)
    {
        if (yn == -1)
            g.set_negative();
        do
        {
            g.push(ym % 10);
            ym /= 10;
            ++ye;
        } while (xe > ye);
    }
    if (xn == yn)
    {
        xm += ym;
        if (xm > maxMantissa)
        {
            g.push(xm % 10);
            xm /= 10;
            ++xe;
        }
        auto r = g.round();
        if (r == 1 || (r == 0 && (xm & 1) == 1))
        {
            ++xm;
            if (xm > maxMantissa)
            {
                xm /= 10;
                ++xe;
            }
        }
        if (xe > maxExponent)
            throw std::overflow_error("Number::addition overflow");
    }
    else
    {
        if (xm > ym)
        {
            xm = xm - ym;
        }
        else
        {
            xm = ym - xm;
            xe = ye;
            xn = yn;
        }
        while (xm < minMantissa)
        {
            xm *= 10;
            xm -= g.pop();
            --xe;
        }
        auto r = g.round();
        if (r == 1 || (r == 0 && (xm & 1) == 1))
        {
            --xm;
            if (xm < minMantissa)
            {
                xm *= 10;
                --xe;
            }
        }
        if (xe < minExponent)
        {
            xm = 0;
            xe = Number{}.exponent_;
        }
    }
    mantissa_ = xm * xn;
    exponent_ = xe;
    assert(isnormal());
    return *this;
}

Number&
Number::operator*=(Number const& y)
{
    if (*this == Number{})
        return *this;
    if (y == Number{})
    {
        *this = y;
        return *this;
    }
    assert(isnormal() && y.isnormal());
    auto xm = mantissa();
    auto xe = exponent();
    int xn = 1;
    if (xm < 0)
    {
        xm = -xm;
        xn = -1;
    }
    auto ym = y.mantissa();
    auto ye = y.exponent();
    int yn = 1;
    if (ym < 0)
    {
        ym = -ym;
        yn = -1;
    }
    auto zm = uint128_t(xm) * uint128_t(ym);
    auto ze = xe + ye;
    auto zn = xn * yn;
    guard g;
    while (zm > maxMantissa)
    {
        g.push(static_cast<unsigned>(zm % 10));
        zm /= 10;
        ++ze;
    }
    xm = static_cast<rep>(zm);
    xe = ze;
    auto r = g.round();
    if (r == 1 || (r == 0 && (xm & 1) == 1))
    {
        ++xm;
        if (xm > maxMantissa)
        {
            xm /= 10;
            ++xe;
        }
    }
    if (xe < minExponent)
    {
        xm = 0;
        xe = Number{}.exponent_;
    }
    if (xe > maxExponent)
        throw std::overflow_error(
            "Number::multiplication overflow : exponent is " +
            std::to_string(xe));
    mantissa_ = xm * zn;
    exponent_ = xe;
    assert(isnormal());
    return *this;
}

Number&
Number::operator/=(Number const& y)
{
    if (y == Number{})
        throw std::overflow_error("Number: divide by 0");
    int np = 1;
    auto nm = mantissa();
    if (nm < 0)
    {
        nm = -nm;
        np = -1;
    }
    int dp = 1;
    auto dm = y.mantissa();
    if (dm < 0)
    {
        dm = -dm;
        dp = -1;
    }
    // Divide numerator and denominator such that the
    //     denominator is in the range [1, 10).
    const int offset = -15 - y.exponent();
    Number n{nm * (np * dp), exponent() + offset};
    Number d{dm, y.exponent() + offset};
    // Quadratic least squares fit to 1/x in the range [1, 10]
    constexpr Number a0{9178756872006464, -16, unchecked{}};
    constexpr Number a1{-2149215784206187, -16, unchecked{}};
    constexpr Number a2{1405502114116773, -17, unchecked{}};
    static_assert(a0.isnormal());
    static_assert(a1.isnormal());
    static_assert(a2.isnormal());
    Number rm2{};
    Number rm1{};
    Number r = a2;
    r = (a2 * d + a1) * d + a0;
    do
    {
        rm2 = rm1;
        rm1 = r;
        r = r + r * (one - d * r);
    } while (r != rm1 && r != rm2);
    *this = n * r;
    return *this;
}

std::string
to_string(Number const& amount)
{
    // keep full internal accuracy, but make more human friendly if possible
    if (amount == Number{})
        return "0";

    auto const exponent = amount.exponent();
    auto mantissa = amount.mantissa();

    // Use scientific notation for exponents that are too small or too large
    if (((exponent != 0) && ((exponent < -25) || (exponent > -5))))
    {
        std::string ret = std::to_string(mantissa);
        ret.append(1, 'e');
        ret.append(std::to_string(exponent));
        return ret;
    }

    bool negative = false;

    if (mantissa < 0)
    {
        mantissa = -mantissa;
        negative = true;
    }

    assert(exponent + 43 > 0);

    size_t const pad_prefix = 27;
    size_t const pad_suffix = 23;

    std::string const raw_value(std::to_string(mantissa));
    std::string val;

    val.reserve(raw_value.length() + pad_prefix + pad_suffix);
    val.append(pad_prefix, '0');
    val.append(raw_value);
    val.append(pad_suffix, '0');

    size_t const offset(exponent + 43);

    auto pre_from(val.begin());
    auto const pre_to(val.begin() + offset);

    auto const post_from(val.begin() + offset);
    auto post_to(val.end());

    // Crop leading zeroes. Take advantage of the fact that there's always a
    // fixed amount of leading zeroes and skip them.
    if (std::distance(pre_from, pre_to) > pad_prefix)
        pre_from += pad_prefix;

    assert(post_to >= post_from);

    pre_from = std::find_if(pre_from, pre_to, [](char c) { return c != '0'; });

    // Crop trailing zeroes. Take advantage of the fact that there's always a
    // fixed amount of trailing zeroes and skip them.
    if (std::distance(post_from, post_to) > pad_suffix)
        post_to -= pad_suffix;

    assert(post_to >= post_from);

    post_to = std::find_if(
                  std::make_reverse_iterator(post_to),
                  std::make_reverse_iterator(post_from),
                  [](char c) { return c != '0'; })
                  .base();

    std::string ret;

    if (negative)
        ret.append(1, '-');

    // Assemble the output:
    if (pre_from == pre_to)
        ret.append(1, '0');
    else
        ret.append(pre_from, pre_to);

    if (post_to != post_from)
    {
        ret.append(1, '.');
        ret.append(post_from, post_to);
    }

    return ret;
}

// Returns f^n
// Uses a log_2(n) number of mulitiplications

Number
power(Number f, unsigned n)
{
    if (n == 0)
        return one;
    if (n == 1)
        return f;
    auto r = power(f, n / 2);
    r *= r;
    if (n % 2 != 0)
        r *= f;
    return r;
}

// Returns f^(1/d)
// Uses Newton–Raphson iterations until the result stops changing
// to find the non-negative root of the polynomial g(x) = x^d - f

Number
root(Number f, unsigned d)
{
    if (f == one || d == 1)
        return f;
    if (d == 0)
    {
        if (f == -one)
            return one;
        if (abs(f) < one)
            return Number{};
        throw std::overflow_error("Number::root infinity");
    }
    if (f < Number{} && d % 2 == 0)
        throw std::overflow_error("Number::root nan");
    if (f == Number{})
        return f;

    // Scale f into the range (0, 1) such that f's exponent is a multiple of d
    auto e = f.exponent() + 16;
    auto const di = static_cast<int>(d);
    auto ex = [e = e, di = di]()  // Euclidean remainder of e/d
    {
        int k = (e >= 0 ? e : e - (di - 1)) / di;
        int k2 = e - k * di;
        if (k2 == 0)
            return 0;
        return di - k2;
    }();
    e += ex;
    f = Number{f.mantissa(), f.exponent() - e};  // f /= 10^e;
    bool neg = false;
    if (f < Number{})
    {
        neg = true;
        f = -f;
    }

    // Quadratic least squares curve fit of f^(1/d) in the range [0, 1]
    auto const D = ((6 * di + 11) * di + 6) * di + 1;
    auto const a0 = 3 * di * ((2 * di - 3) * di + 1);
    auto const a1 = 24 * di * (2 * di - 1);
    auto const a2 = -30 * (di - 1) * di;
    Number r = ((Number{a2} * f + Number{a1}) * f + Number{a0}) / Number{D};
    if (neg)
    {
        f = -f;
        r = -r;
    }

    //  Newton–Raphson iteration of f^(1/d) with initial guess r
    //  halt when r stops changing, checking for bouncing on the last iteration
    Number rm1{};
    Number rm2{};
    do
    {
        rm2 = rm1;
        rm1 = r;
        r = (Number(d - 1) * r + f / power(r, d - 1)) / Number(d);
    } while (r != rm1 && r != rm2);

    //  return r * 10^(e/d) to reverse scaling
    return Number{r.mantissa(), r.exponent() + e / di};
}

// Returns f^(n/d)

Number
power(Number f, unsigned n, unsigned d)
{
    if (f == one)
        return f;
    auto g = std::gcd(n, d);
    if (g == 0)
        throw std::overflow_error("Number::power nan");
    if (d == 0)
    {
        if (f == -one)
            return one;
        if (abs(f) < one)
            return Number{};
        if (abs(f) > one)
            throw std::overflow_error("Number::power infinity");
        throw std::overflow_error("Number::power nan");
    }
    if (n == 0)
        return one;
    n /= g;
    d /= g;
    if ((n % 2) == 1 && (d % 2) == 0 && f < Number{})
        throw std::overflow_error("Number::power nan");
    return root(power(f, n), d);
}

}  // namespace ripple