Number.h

#ifndef XRPL_BASICS_NUMBER_H_INCLUDED
#define XRPL_BASICS_NUMBER_H_INCLUDED
 
#include <cstdint>
#include <limits>
#include <ostream>
#include <string>
 
namespace xrpl {
 
class Number;
 
std::string
to_string(Number const& amount);
 
template <typename T>
constexpr bool
isPowerOfTen(T value)
{
    while (value >= 10 && value % 10 == 0)
        value /= 10;
    return value == 1;
}
 
class Number
{
    using rep = std::int64_t;
    rep mantissa_{0};
    int exponent_{std::numeric_limits<int>::lowest()};
 
public:
    // The range for the mantissa when normalized
    constexpr static std::int64_t minMantissa = 1'000'000'000'000'000LL;
    static_assert(isPowerOfTen(minMantissa));
    constexpr static std::int64_t maxMantissa = minMantissa * 10 - 1;
    static_assert(maxMantissa == 9'999'999'999'999'999LL);
 
    // The range for the exponent when normalized
    constexpr static int minExponent = -32768;
    constexpr static int maxExponent = 32768;
 
    struct unchecked
    {
        explicit unchecked() = default;
    };
 
    explicit constexpr Number() = default;
 
    Number(rep mantissa);
    explicit Number(rep mantissa, int exponent);
    explicit constexpr Number(rep mantissa, int exponent, unchecked) noexcept;
 
    constexpr rep
    mantissa() const noexcept;
    constexpr int
    exponent() const noexcept;
 
    constexpr Number
    operator+() const noexcept;
    constexpr Number
    operator-() const noexcept;
    Number&
    operator++();
    Number
    operator++(int);
    Number&
    operator--();
    Number
    operator--(int);
 
    Number&
    operator+=(Number const& x);
    Number&
    operator-=(Number const& x);
 
    Number&
    operator*=(Number const& x);
    Number&
    operator/=(Number const& x);
 
    static constexpr Number
    min() noexcept;
    static constexpr Number
    max() noexcept;
    static constexpr Number
    lowest() noexcept;
 
    explicit
    operator rep() const;  // round to nearest, even on tie
 
    friend constexpr bool
    operator==(Number const& x, Number const& y) noexcept
    {
        return x.mantissa_ == y.mantissa_ && x.exponent_ == y.exponent_;
    }
 
    friend constexpr bool
    operator!=(Number const& x, Number const& y) noexcept
    {
        return !(x == y);
    }
 
    friend constexpr bool
    operator<(Number const& x, Number const& y) noexcept
    {
        // If the two amounts have different signs (zero is treated as positive)
        // then the comparison is true iff the left is negative.
        bool const lneg = x.mantissa_ < 0;
        bool const rneg = y.mantissa_ < 0;
 
        if (lneg != rneg)
            return lneg;
 
        // Both have same sign and the left is zero: the right must be
        // greater than 0.
        if (x.mantissa_ == 0)
            return y.mantissa_ > 0;
 
        // Both have same sign, the right is zero and the left is non-zero.
        if (y.mantissa_ == 0)
            return false;
 
        // Both have the same sign, compare by exponents:
        if (x.exponent_ > y.exponent_)
            return lneg;
        if (x.exponent_ < y.exponent_)
            return !lneg;
 
        // If equal exponents, compare mantissas
        return x.mantissa_ < y.mantissa_;
    }
 
    constexpr int
    signum() const noexcept
    {
        return (mantissa_ < 0) ? -1 : (mantissa_ ? 1 : 0);
    }
 
    Number
    truncate() const noexcept;
 
    friend constexpr bool
    operator>(Number const& x, Number const& y) noexcept
    {
        return y < x;
    }
 
    friend constexpr bool
    operator<=(Number const& x, Number const& y) noexcept
    {
        return !(y < x);
    }
 
    friend constexpr bool
    operator>=(Number const& x, Number const& y) noexcept
    {
        return !(x < y);
    }
 
    friend std::ostream&
    operator<<(std::ostream& os, Number const& x)
    {
        return os << to_string(x);
    }
 
    // Thread local rounding control.  Default is to_nearest
    enum rounding_mode { to_nearest, towards_zero, downward, upward };
    static rounding_mode
    getround();
    // Returns previously set mode
    static rounding_mode
    setround(rounding_mode mode);
 
private:
    static thread_local rounding_mode mode_;
 
    void
    normalize();
    constexpr bool
    isnormal() const noexcept;
 
    class Guard;
};
 
constexpr static Number numZero{};
 
inline constexpr Number::Number(rep mantissa, int exponent, unchecked) noexcept
    : mantissa_{mantissa}, exponent_{exponent}
{
}
 
inline Number::Number(rep mantissa, int exponent)
    : mantissa_{mantissa}, exponent_{exponent}
{
    normalize();
}
 
inline Number::Number(rep mantissa) : Number{mantissa, 0}
{
}
 
inline constexpr Number::rep
Number::mantissa() const noexcept
{
    return mantissa_;
}
 
inline constexpr int
Number::exponent() const noexcept
{
    return exponent_;
}
 
inline constexpr Number
Number::operator+() const noexcept
{
    return *this;
}
 
inline constexpr Number
Number::operator-() const noexcept
{
    auto x = *this;
    x.mantissa_ = -x.mantissa_;
    return x;
}
 
inline Number&
Number::operator++()
{
    *this += Number{1000000000000000, -15, unchecked{}};
    return *this;
}
 
inline Number
Number::operator++(int)
{
    auto x = *this;
    ++(*this);
    return x;
}
 
inline Number&
Number::operator--()
{
    *this -= Number{1000000000000000, -15, unchecked{}};
    return *this;
}
 
inline Number
Number::operator--(int)
{
    auto x = *this;
    --(*this);
    return x;
}
 
inline Number&
Number::operator-=(Number const& x)
{
    return *this += -x;
}
 
inline Number
operator+(Number const& x, Number const& y)
{
    auto z = x;
    z += y;
    return z;
}
 
inline Number
operator-(Number const& x, Number const& y)
{
    auto z = x;
    z -= y;
    return z;
}
 
inline Number
operator*(Number const& x, Number const& y)
{
    auto z = x;
    z *= y;
    return z;
}
 
inline Number
operator/(Number const& x, Number const& y)
{
    auto z = x;
    z /= y;
    return z;
}
 
inline constexpr Number
Number::min() noexcept
{
    return Number{minMantissa, minExponent, unchecked{}};
}
 
inline constexpr Number
Number::max() noexcept
{
    return Number{maxMantissa, maxExponent, unchecked{}};
}
 
inline constexpr Number
Number::lowest() noexcept
{
    return -Number{maxMantissa, maxExponent, unchecked{}};
}
 
inline constexpr bool
Number::isnormal() const noexcept
{
    auto const abs_m = mantissa_ < 0 ? -mantissa_ : mantissa_;
    return minMantissa <= abs_m && abs_m <= maxMantissa &&
        minExponent <= exponent_ && exponent_ <= maxExponent;
}
 
inline constexpr Number
abs(Number x) noexcept
{
    if (x < Number{})
        x = -x;
    return x;
}
 
// Returns f^n
// Uses a log_2(n) number of multiplications
 
Number
power(Number const& f, unsigned n);
 
// Returns f^(1/d)
// Uses Newton–Raphson iterations until the result stops changing
// to find the root of the polynomial g(x) = x^d - f
 
Number
root(Number f, unsigned d);
 
Number
root2(Number f);
 
// Returns f^(n/d)
 
Number
power(Number const& f, unsigned n, unsigned d);
 
// Return 0 if abs(x) < limit, else returns x
 
inline constexpr Number
squelch(Number const& x, Number const& limit) noexcept
{
    if (abs(x) < limit)
        return Number{};
    return x;
}
 
class saveNumberRoundMode
{
    Number::rounding_mode mode_;
 
public:
    ~saveNumberRoundMode()
    {
        Number::setround(mode_);
    }
    explicit saveNumberRoundMode(Number::rounding_mode mode) noexcept
        : mode_{mode}
    {
    }
    saveNumberRoundMode(saveNumberRoundMode const&) = delete;
    saveNumberRoundMode&
    operator=(saveNumberRoundMode const&) = delete;
};
 
// saveNumberRoundMode doesn't do quite enough for us.  What we want is a
// Number::RoundModeGuard that sets the new mode and restores the old mode
// when it leaves scope.  Since Number doesn't have that facility, we'll
// build it here.
class NumberRoundModeGuard
{
    saveNumberRoundMode saved_;
 
public:
    explicit NumberRoundModeGuard(Number::rounding_mode mode) noexcept
        : saved_{Number::setround(mode)}
    {
    }
 
    NumberRoundModeGuard(NumberRoundModeGuard const&) = delete;
 
    NumberRoundModeGuard&
    operator=(NumberRoundModeGuard const&) = delete;
};
 
}  // namespace xrpl
 
#endif  // XRPL_BASICS_NUMBER_H_INCLUDED