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396 lines
10 KiB
C++
396 lines
10 KiB
C++
/*
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* Copyright (c) 2021, Leon Albrecht <leon2002.la@gmail.com>
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*
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* SPDX-License-Identifier: BSD-2-Clause
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*/
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#pragma once
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#include <AK/Concepts.h>
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#include <AK/Format.h>
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#include <AK/IntegralMath.h>
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#include <AK/NumericLimits.h>
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#include <AK/Types.h>
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#ifndef KERNEL
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# include <AK/Math.h>
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#endif
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namespace AK {
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// FIXME: this always uses round to nearest break-tie to even
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// FIXME: use the Integral concept to constrain Underlying
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template<size_t precision, typename Underlying>
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class FixedPoint {
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using This = FixedPoint<precision, Underlying>;
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constexpr static Underlying radix_mask = (static_cast<Underlying>(1) << precision) - 1;
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template<size_t P, typename U>
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friend class FixedPoint;
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public:
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constexpr FixedPoint() = default;
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template<Integral I>
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constexpr FixedPoint(I value)
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: m_value(static_cast<Underlying>(value) << precision)
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{
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}
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template<FloatingPoint F>
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constexpr FixedPoint(F value)
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: m_value(static_cast<Underlying>(value * (static_cast<Underlying>(1) << precision)))
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{
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}
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template<size_t P, typename U>
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explicit constexpr FixedPoint(FixedPoint<P, U> const& other)
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: m_value(other.template cast_to<precision, Underlying>().m_value)
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{
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}
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#ifndef KERNEL
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template<FloatingPoint F>
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explicit ALWAYS_INLINE operator F() const
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{
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return (F)m_value * pow<F>(0.5, precision);
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}
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#endif
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template<Integral I>
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explicit constexpr operator I() const
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{
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I value = m_value >> precision;
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// fract(m_value) >= .5?
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if (m_value & (1u << (precision - 1))) {
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// fract(m_value) > .5?
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if (m_value & (radix_mask >> 2u)) {
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// yes: round "up";
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value += (m_value > 0 ? 1 : -1);
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} else {
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// no: round to even;
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value += value & 1;
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}
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}
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return value;
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}
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constexpr Underlying raw() const
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{
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return m_value;
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}
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constexpr Underlying& raw()
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{
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return m_value;
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}
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constexpr This fract() const
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{
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return create_raw(m_value & radix_mask);
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}
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constexpr This round() const
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{
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return This { static_cast<Underlying>(*this) };
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}
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constexpr This floor() const
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{
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return create_raw(m_value & ~radix_mask);
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}
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constexpr This ceil() const
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{
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return create_raw((m_value & ~radix_mask)
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+ (m_value & radix_mask ? 1 << precision : 0));
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}
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constexpr This trunk() const
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{
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return create_raw((m_value & ~radix_mask)
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+ ((m_value & radix_mask)
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? (m_value > 0 ? 0 : (1 << precision))
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: 0));
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}
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constexpr Underlying lround() const { return static_cast<Underlying>(*this); }
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constexpr Underlying lfloor() const { return m_value >> precision; }
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constexpr Underlying lceil() const
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{
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return (m_value >> precision)
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+ (m_value & radix_mask ? 1 : 0);
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}
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constexpr Underlying ltrunk() const
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{
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return (m_value >> precision)
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+ ((m_value & radix_mask)
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? m_value > 0 ? 0 : 1
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: 0);
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}
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// http://www.claysturner.com/dsp/BinaryLogarithm.pdf
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constexpr This log2() const
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{
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// 0.5
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This b = create_raw(1 << (precision - 1));
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This y = 0;
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This x = *this;
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// FIXME: There's no negative infinity.
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if (x.raw() <= 0)
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return create_raw(NumericLimits<Underlying>::min());
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if (x != 1) {
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i32 shift_amount = AK::log2<Underlying>(x.raw()) - precision;
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if (shift_amount > 0)
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x >>= shift_amount;
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else
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x <<= -shift_amount;
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y += shift_amount;
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}
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for (size_t i = 0; i < precision; ++i) {
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x *= x;
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if (x >= 2) {
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x >>= 1;
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y += b;
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}
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b >>= 1;
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}
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return y;
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}
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constexpr bool signbit() const
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requires(IsSigned<Underlying>)
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{
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return m_value >> (sizeof(Underlying) * 8 - 1);
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}
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constexpr This operator-() const
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requires(IsSigned<Underlying>)
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{
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return create_raw(-m_value);
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}
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constexpr This operator+(This const& other) const
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{
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return create_raw(m_value + other.m_value);
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}
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constexpr This operator-(This const& other) const
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{
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return create_raw(m_value - other.m_value);
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}
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constexpr This operator*(This const& other) const
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{
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// FIXME: Potential Overflow, although result could be represented accurately
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Underlying value = m_value * other.raw();
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This ret {};
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ret.raw() = value >> precision;
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// fract(value) >= .5?
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if (value & (1u << (precision - 1))) {
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// fract(value) > .5?
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if (value & (radix_mask >> 2u)) {
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// yes: round up;
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ret.raw() += (value > 0 ? 1 : -1);
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} else {
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// no: round to even (aka unset last sigificant bit);
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ret.raw() += m_value & 1;
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}
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}
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return ret;
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}
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constexpr This operator/(This const& other) const
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{
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// FIXME: Better rounding?
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return create_raw((m_value / other.m_value) << (precision));
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}
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template<Integral I>
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constexpr This operator+(I other) const
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{
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return create_raw(m_value + (other << precision));
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}
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template<Integral I>
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constexpr This operator-(I other) const
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{
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return create_raw(m_value - (other << precision));
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}
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template<Integral I>
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constexpr This operator*(I other) const
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{
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return create_raw(m_value * other);
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}
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template<Integral I>
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constexpr This operator/(I other) const
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{
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return create_raw(m_value / other);
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}
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template<Integral I>
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constexpr This operator>>(I other) const
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{
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return create_raw(m_value >> other);
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}
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template<Integral I>
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constexpr This operator<<(I other) const
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{
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return create_raw(m_value << other);
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}
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This& operator+=(This const& other)
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{
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m_value += other.raw();
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return *this;
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}
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This& operator-=(This const& other)
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{
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m_value -= other.raw();
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return *this;
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}
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This& operator*=(This const& other)
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{
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Underlying value = m_value * other.raw();
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m_value = value >> precision;
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// fract(value) >= .5?
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if (value & (1u << (precision - 1))) {
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// fract(value) > .5?
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if (value & (radix_mask >> 2u)) {
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// yes: round up;
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m_value += (value > 0 ? 1 : -1);
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} else {
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// no: round to even (aka unset last sigificant bit);
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m_value += m_value & 1;
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}
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}
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return *this;
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}
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This& operator/=(This const& other)
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{
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// FIXME: See above
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m_value /= other.raw();
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m_value <<= precision;
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return *this;
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}
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template<Integral I>
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This& operator+=(I other)
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{
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m_value += other << precision;
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return *this;
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}
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template<Integral I>
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This& operator-=(I other)
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{
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m_value -= other << precision;
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return *this;
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}
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template<Integral I>
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This& operator*=(I other)
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{
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m_value *= other;
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return *this;
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}
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template<Integral I>
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This& operator/=(I other)
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{
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m_value /= other;
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return *this;
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}
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template<Integral I>
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This& operator>>=(I other)
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{
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m_value >>= other;
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return *this;
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}
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template<Integral I>
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This& operator<<=(I other)
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{
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m_value <<= other;
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return *this;
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}
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bool operator==(This const& other) const { return raw() == other.raw(); }
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bool operator!=(This const& other) const { return raw() != other.raw(); }
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bool operator>(This const& other) const { return raw() > other.raw(); }
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bool operator>=(This const& other) const { return raw() >= other.raw(); }
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bool operator<(This const& other) const { return raw() < other.raw(); }
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bool operator<=(This const& other) const { return raw() <= other.raw(); }
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// FIXE: There are probably better ways to do these
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template<Integral I>
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bool operator==(I other) const
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{
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return m_value >> precision == other && !(m_value & radix_mask);
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}
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template<Integral I>
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bool operator!=(I other) const
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{
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return (m_value >> precision) != other || m_value & radix_mask;
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}
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template<Integral I>
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bool operator>(I other) const
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{
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return !(*this <= other);
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}
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template<Integral I>
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bool operator>=(I other) const
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{
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return !(*this < other);
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}
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template<Integral I>
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bool operator<(I other) const
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{
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return (m_value >> precision) < other || m_value < (other << precision);
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}
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template<Integral I>
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bool operator<=(I other) const
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{
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return *this < other || *this == other;
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}
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// Casting from a float should be faster than casting to a float
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template<FloatingPoint F>
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bool operator==(F other) const { return *this == (This)other; }
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template<FloatingPoint F>
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bool operator!=(F other) const { return *this != (This)other; }
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template<FloatingPoint F>
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bool operator>(F other) const { return *this > (This)other; }
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template<FloatingPoint F>
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bool operator>=(F other) const { return *this >= (This)other; }
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template<FloatingPoint F>
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bool operator<(F other) const { return *this < (This)other; }
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template<FloatingPoint F>
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bool operator<=(F other) const { return *this <= (This)other; }
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template<size_t P, typename U>
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operator FixedPoint<P, U>() const
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{
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return cast_to<P, U>();
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}
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private:
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template<size_t P, typename U>
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constexpr FixedPoint<P, U> cast_to() const
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{
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U raw_value = static_cast<U>(m_value >> precision) << P;
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if constexpr (precision > P)
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raw_value |= (m_value & radix_mask) >> (precision - P);
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else if constexpr (precision < P)
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raw_value |= static_cast<U>(m_value & radix_mask) << (P - precision);
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else
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raw_value |= m_value & radix_mask;
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return FixedPoint<P, U>::create_raw(raw_value);
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}
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static This create_raw(Underlying value)
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{
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This t {};
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t.raw() = value;
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return t;
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}
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Underlying m_value;
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};
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}
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#if USING_AK_GLOBALLY
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using AK::FixedPoint;
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#endif
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