fixed-point.hh

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/*
 
MIT License
 
Copyright (c) 2023 PCSX-Redux authors
 
Permission is hereby granted, free of charge, to any person obtaining a copy
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*/
 
#pragma once
 
#include <EASTL/functional.h>
#include <stdint.h>
 
#include <compare>
#include <concepts>
#include <type_traits>
 
namespace psyqo {
 
namespace FixedPointInternals {
 
void printInt(uint32_t value, const eastl::function<void(char)>&, unsigned scale);
 
constexpr uint32_t iDiv(uint64_t rem, uint32_t base, unsigned scale) {
    rem *= scale;
    uint64_t b = base;
    uint64_t res, d = 1;
    uint32_t high = rem >> 32;
 
    res = 0;
    if (high >= base) {
        high /= base;
        res = static_cast<uint64_t>(high) << 32;
        rem -= static_cast<uint64_t>(high * base) << 32;
    }
 
    while (static_cast<int64_t>(b) > 0 && b < rem) {
        b = b + b;
        d = d + d;
    }
 
    do {
        if (rem >= b) {
            rem -= b;
            res += d;
        }
        b >>= 1;
        d >>= 1;
    } while (d);
 
    return res;
}
 
constexpr int32_t dDiv(int32_t a, int32_t b, unsigned scale) {
    int s = 1;
    if (a < 0) {
        a = -a;
        s = -1;
    }
    if (b < 0) {
        b = -b;
        s = -s;
    }
    return iDiv(a, b, scale) * s;
}
 
}  // namespace FixedPointInternals
 
template <unsigned precisionBits = 12, std::integral T = int32_t, unsigned Scale = 1 << precisionBits>
    requires((precisionBits > 0) && (precisionBits < 32) && ((sizeof(T) == 4) || (sizeof(T) == 2) || sizeof(T) == 1))
class FixedPoint {
    using signedUpType = std::conditional<sizeof(T) == 4, int64_t, int32_t>::type;
    using unsignedUpType = std::conditional<sizeof(T) == 4, uint64_t, uint32_t>::type;
    using upType = std::conditional<std::is_signed<T>::value, signedUpType, unsignedUpType>::type;
 
  public:
    T value;
    T raw() const { return value; }
 
    static constexpr unsigned scale = Scale;
 
    explicit constexpr FixedPoint(T integer, T fraction) : value(integer * scale + fraction) {
        static_assert(sizeof(FixedPoint) == sizeof(T));
    }
 
    consteval FixedPoint(long double ld) {
        bool negative = ld < 0;
        T integer = negative ? -ld : ld;
        T fraction = ld * scale - integer * scale + (negative ? -0.5 : 0.5);
        value = integer * scale + fraction;
    }
 
    constexpr FixedPoint() : value(0) {}
    constexpr FixedPoint(const FixedPoint&) = default;
    constexpr FixedPoint(FixedPoint&&) = default;
    constexpr FixedPoint& operator=(const FixedPoint&) = default;
 
    enum Raw { RAW };
    constexpr FixedPoint(T raw, Raw) : value(raw) {}
 
    template <unsigned otherPrecisionBits = 12, std::integral U = int32_t>
    explicit FixedPoint(FixedPoint<otherPrecisionBits, U> other) {
        if constexpr (precisionBits == otherPrecisionBits) {
            value = T(other.value);
        } else if constexpr (precisionBits > otherPrecisionBits) {
            value = T(other.value << (precisionBits - otherPrecisionBits));
        } else if constexpr (precisionBits < otherPrecisionBits) {
            value = T(other.value >> (otherPrecisionBits - precisionBits));
        }
    }
 
    template <size_t factor = 1>
    constexpr T integer() const {
        if constexpr (std::is_signed<T>::value) {
            if (value < 0) {
                return T(value - scale / (2 * factor)) / T(scale / factor);
            }
        }
        return T(value + scale / (2 * factor)) / T(scale / factor);
    }
 
    template <std::integral U>
    constexpr U integer() const {
        if constexpr (std::is_signed<T>::value) {
            if (value < 0) {
                return U((value - scale / 2) / scale);
            }
        }
        return U((value + scale / 2) / scale);
    }
 
    template <std::integral U = T>
    constexpr U floor() const {
        if constexpr (std::is_signed<T>::value) {
            if (value < 0) {
                return U(value - scale + 1) / U(scale);
            }
        }
        return U(value) / U(scale);
    }
 
    template <std::integral U = T>
    constexpr U ceil() const {
        if constexpr (std::is_signed<T>::value) {
            if (value < 0) {
                return U(value) / U(scale);
            }
        }
        return U(value + scale - 1) / U(scale);
    }
 
    void print(const eastl::function<void(char)>& charPrinter) const {
        T copy = value;
        if constexpr (std::is_signed<T>::value) {
            if (copy < 0) {
                charPrinter('-');
                copy = -copy;
            }
        }
        FixedPointInternals::printInt(copy, charPrinter, scale);
    }
 
    constexpr FixedPoint abs() const {
        FixedPoint ret = *this;
        if constexpr (std::is_signed<T>::value) {
            if (ret.value < 0) {
                ret.value = -ret.value;
            }
        }
        return ret;
    }
 
    constexpr FixedPoint operator+(FixedPoint other) const {
        FixedPoint ret = *this;
        ret.value += other.value;
        return ret;
    }
 
    template <std::integral U>
    constexpr FixedPoint operator+(U other) const {
        FixedPoint ret = *this;
        ret.value += other * scale;
        return ret;
    }
 
    constexpr FixedPoint operator-(FixedPoint other) const {
        FixedPoint ret = *this;
        ret.value -= other.value;
        return ret;
    }
 
    template <std::integral U>
    constexpr FixedPoint operator-(U other) const {
        FixedPoint ret = *this;
        ret.value -= other * scale;
        return ret;
    }
 
    constexpr FixedPoint operator*(FixedPoint other) const {
        upType t = value;
        t *= other.value;
        t /= scale;
        FixedPoint ret;
        ret.value = t;
        return ret;
    }
 
    template <std::integral U>
    constexpr FixedPoint operator*(U other) const {
        FixedPoint ret = *this;
        ret.value *= other;
        return ret;
    }
 
    constexpr FixedPoint operator/(FixedPoint other) const {
        FixedPoint ret;
        if constexpr (sizeof(T) == 4) {
            if constexpr (std::is_signed<T>::value) {
                ret.value = FixedPointInternals::dDiv(value, other.value, scale);
            } else if constexpr (!std::is_signed<T>::value) {
                ret.value = FixedPointInternals::iDiv(value, other.value, scale);
            }
        } else if constexpr (sizeof(T) < 4) {
            upType t = value;
            t *= scale;
            t /= other.value;
            ret.value = t;
        }
        return ret;
    }
 
    template <std::integral U>
    constexpr FixedPoint operator/(U other) const {
        FixedPoint ret = *this;
        ret.value /= other;
        return ret;
    }
 
    constexpr FixedPoint operator-() const {
        FixedPoint ret = *this;
        ret.value = -ret.value;
        return ret;
    }
 
    constexpr FixedPoint& operator+=(FixedPoint other) {
        value += other.value;
        return *this;
    }
 
    template <std::integral U>
    constexpr FixedPoint& operator+=(U other) {
        value += other * scale;
        return *this;
    }
 
    constexpr FixedPoint& operator-=(FixedPoint other) {
        value -= other.value;
        return *this;
    }
 
    template <std::integral U>
    constexpr FixedPoint& operator-=(U other) {
        value -= other * scale;
        return *this;
    }
 
    constexpr FixedPoint& operator*=(FixedPoint other) {
        upType t = value;
        t *= other.value;
        t /= scale;
        value = t;
        return *this;
    }
 
    template <std::integral U>
    constexpr FixedPoint& operator*=(U other) {
        value *= other;
        return *this;
    }
 
    constexpr FixedPoint& operator/=(FixedPoint other) {
        if constexpr (sizeof(T) == 4) {
            if constexpr (std::is_signed<T>::value) {
                value = FixedPointInternals::dDiv(value, other.value, scale);
            } else if constexpr (!std::is_signed<T>::value) {
                value = FixedPointInternals::iDiv(value, other.value, scale);
            }
        } else if constexpr (sizeof(T) == 2) {
            upType t = value;
            t *= scale;
            t /= other.value;
            value = t;
        }
        return *this;
    }
 
    template <std::integral U>
    constexpr FixedPoint& operator/=(U other) {
        value /= other;
        return *this;
    }
 
    auto operator<=>(const FixedPoint& other) const = default;
 
    constexpr FixedPoint operator<<(unsigned shift) const {
        FixedPoint ret = *this;
        ret.value <<= shift;
        return ret;
    }
 
    constexpr FixedPoint operator>>(unsigned shift) const {
        FixedPoint ret = *this;
        ret.value >>= shift;
        return ret;
    }
 
    constexpr FixedPoint& operator<<=(unsigned shift) {
        value <<= shift;
        return *this;
    }
 
    constexpr FixedPoint& operator>>=(unsigned shift) {
        value >>= shift;
        return *this;
    }
 
    constexpr FixedPoint operator++() {
        value += scale;
        return *this;
    }
 
    constexpr FixedPoint operator++(int) {
        FixedPoint ret = *this;
        value += scale;
        return ret;
    }
 
    constexpr FixedPoint operator--() {
        value -= scale;
        return *this;
    }
 
    constexpr FixedPoint operator--(int) {
        FixedPoint ret = *this;
        value -= scale;
        return ret;
    }
 
    constexpr bool operator!() const { return value == 0; }
};
 
template <unsigned precisionBits = 12, std::integral T = int32_t, unsigned scale = 1 << precisionBits,
          std::integral U = int32_t>
constexpr FixedPoint<precisionBits, T, scale> operator+(U a, FixedPoint<precisionBits, T, scale> b) {
    return b + a;
}
 
template <unsigned precisionBits = 12, std::integral T = int32_t, unsigned scale = 1 << precisionBits,
          std::integral U = int32_t>
constexpr FixedPoint<precisionBits, T, scale> operator-(U a, FixedPoint<precisionBits, T, scale> b) {
    return -b + a;
}
 
template <unsigned precisionBits = 12, std::integral T = int32_t, unsigned scale = 1 << precisionBits,
          std::integral U = int32_t>
constexpr FixedPoint<precisionBits, T, scale> operator*(U a, FixedPoint<precisionBits, T, scale> b) {
    return b * a;
}
 
template <unsigned precisionBits = 12, std::integral T = int32_t, unsigned scale = 1 << precisionBits,
          std::integral U = int32_t>
constexpr FixedPoint<precisionBits, T, scale> operator/(U a, FixedPoint<precisionBits, T, scale> b) {
    FixedPoint<precisionBits, T, scale> ret;
    if constexpr (sizeof(T) == 4) {
        if constexpr (std::is_signed<T>::value || std::is_signed<U>::value) {
            ret.value = FixedPointInternals::dDiv(a * FixedPoint<precisionBits, T>::scale, b.raw(), scale);
        } else if constexpr (!std::is_signed<T>::value && !std::is_signed<U>::value) {
            ret.value = FixedPointInternals::iDiv(a * FixedPoint<precisionBits, T>::scale, b.raw(), scale);
        }
    } else if constexpr (sizeof(T) == 2) {
        ret.value = a * FixedPoint<precisionBits, T>::scale / b.raw();
    }
    return ret;
}
 
namespace fixed_point_literals {
 
consteval FixedPoint<> operator""_fp(long double value) { return value; }
 
}  // namespace fixed_point_literals
 
}  // namespace psyqo