fixed-point.hh

/*

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Copyright (c) 2023 PCSX-Redux authors

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*/

#pragma once

#include <EASTL/functional.h>
#include <stdint.h>

#include <compare>
#include <concepts>
#include <type_traits>

namespace psyqo {

namespace FixedPointInternals {

uint32_t iDiv(uint64_t rem, uint32_t base, unsigned scale);
int32_t dDiv(int32_t a, int32_t b, unsigned scale);
void printInt(uint32_t value, const eastl::function<void(char)>&, unsigned scale);

}  // namespace FixedPointInternals

/**
 * @brief Fixed point number type.
 *
 * @details This is a fixed point number type with a configurable number
 * of fractional bits. The default is 12 fractional bits, which is
 * suitable for representing 3D coordinates in the PSX's 20.12 fixed
 * point format. The number of fractional bits can be changed by
 * specifying a different value for the template parameter
 * `precisionBits`. The underlying integer type can also be changed
 * by specifying a different type for the template parameter `T`.
 * The default is `int32_t`, but `int16_t`, `int8_t`, `uint32_t`,
 * `uint16_t`, and `uint8_t` are also supported. The template
 * behaves as a value type, and supports most of the usual arithmetic
 * operators. Its size is the same as the underlying integer type.
 *
 * @tparam precisionBits The number of fractional bits to use.
 * @tparam T The underlying integer type to use.
 * @tparam Scale The scale of the fixed point number. The default is
 * 2 raised to the power of `precisionBits`, but this can be changed
 * to produce fixed point numbers with a different range. A scale
 * which is not a power of 2 will produce slower codegen. This is
 * used for the external representation of the fixed point number.
 */
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:
    /**
     * @brief The raw value of the fixed point number.
     *
     * @details This is the raw value of the fixed point number, and
     * can be used to access the underlying integer type directly, which
     * can be useful for some operations.
     */
    T value;
    T raw() const { return value; }

    /**
     * @brief The scale of the fixed point number.
     *
     */
    static constexpr unsigned scale = Scale;

    /**
     * @brief Constructs a fixed point number from an integer and a
     * fraction. Specifying a fraction different from 0 when the
     * scale is not a power of 2 is undefined behavior.
     */
    explicit constexpr FixedPoint(T integer, T fraction) : value(integer * scale + fraction) {
        static_assert(sizeof(FixedPoint) == sizeof(T));
    }

    /**
     * @brief Constructs a fixed point number from a floating point
     * number.
     *
     * @details Note that this is a `consteval` function, so it can
     * only be used with compile-time constants. This is intentional,
     * as the conversion from floating point to fixed point is
     * basically impossible to do at runtime without using floating
     * point arithmetic, which is not available on the PSX.
     */
    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) {}

    /**
     * @brief Construct a new Fixed Point number from a different
     * fixed point number.
     */
    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));
        }
    }

    /**
     * @brief Returns the integer part of the fixed point number.
     *
     * @details This returns the integer part of the fixed point,
     * rounded to the nearest integer. Note that this is not the same
     * as truncating the fixed point number, as it rounds to the
     * nearest integer, rather than towards zero.
     *
     * @tparam factor The factor to scale the integer part by. This
     * defaults to 1, which means that the integer part is returned
     * as-is. It can be used to return the integer part scaled by
     * some factor, which can be useful for some operations.
     * The codegen for this will be bad if the factor is not a
     * power of 2.
     * @return constexpr T The integer part of the fixed point number.
     */
    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) / U(scale);
    }

    /**
     * @brief Returns the floor of the fixed point number.
     *
     * @details This returns the largest integer less than or equal
     * to the fixed point number. For example, floor of 3.7 is 3,
     * floor of -3.7 is -4.
     *
     * @tparam U The type to return the floor value in. Defaults to
     * the underlying type T.
     * @return constexpr U The floor value of the fixed point number.
     */
    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);
    }

    /**
     * @brief Returns the ceiling of the fixed point number.
     *
     * @details This returns the smallest integer greater than or
     * equal to the fixed point number. For example, ceil of 3.2
     * is 4, ceil of -3.2 is -3.
     *
     * @tparam U The type to return the ceiling value in. Defaults
     * to the underlying type T.
     * @return constexpr U The ceiling value of the fixed point number.
     */
    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);
    }

    /**
     * @brief Prints out the fixed point number.
     *
     * @details This prints out the fixed point number using the provided
     * function for emitting characters out. Note that the formatting is
     * pretty basic for now, and only supports printing out the number in
     * decimal format, with no padding or precision setting. Maximum
     * displayed precision is 5 decimal places.
     *
     * @param charPrinter A function that prints a single character, to
     * be used to print the fixed point number.
     */
    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 {

/**
 * @brief User-defined literal for constructing a 20.12 fixed point number.
 *
 * @param value The value to construct the fixed point number from.
 * @return consteval FixedPoint<> The constructed fixed point number.
 */
consteval FixedPoint<> operator""_fp(long double value) { return value; }

}  // namespace fixed_point_literals

}  // namespace psyqo