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ladybird/AK/FixedPoint.h

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/*
* Copyright (c) 2021, Leon Albrecht <leon2002.la@gmail.com>
*
* SPDX-License-Identifier: BSD-2-Clause
*/
#pragma once
#include <AK/Concepts.h>
#include <AK/Format.h>
#include <AK/IntegralMath.h>
#include <AK/NumericLimits.h>
#include <AK/Types.h>
#ifndef KERNEL
# include <AK/Math.h>
#endif
// Solaris' definition of signbit in math_c99.h conflicts with our implementation.
#ifdef AK_OS_SOLARIS
# undef signbit
#endif
namespace AK {
// FIXME: this always uses round to nearest break-tie to even
// FIXME: use the Integral concept to constrain Underlying
template<size_t precision, typename Underlying>
class FixedPoint {
using This = FixedPoint<precision, Underlying>;
constexpr static Underlying radix_mask = (static_cast<Underlying>(1) << precision) - 1;
template<size_t P, typename U>
friend class FixedPoint;
public:
constexpr FixedPoint() = default;
template<Integral I>
constexpr FixedPoint(I value)
: m_value(static_cast<Underlying>(value) << precision)
{
}
#ifndef KERNEL
template<FloatingPoint F>
FixedPoint(F value)
: m_value(round_to<Underlying>(value * (static_cast<Underlying>(1) << precision)))
{
}
#endif
template<size_t P, typename U>
explicit constexpr FixedPoint(FixedPoint<P, U> const& other)
: m_value(other.template cast_to<precision, Underlying>().m_value)
{
}
#ifndef KERNEL
template<FloatingPoint F>
explicit ALWAYS_INLINE operator F() const
{
return (F)m_value * pow<F>(0.5, precision);
}
#endif
template<Integral I>
explicit constexpr operator I() const
{
I value = m_value >> precision;
// fract(m_value) >= .5?
if (m_value & (1u << (precision - 1))) {
// fract(m_value) > .5?
if (m_value & (radix_mask >> 2u)) {
// yes: round "up";
value += (m_value > 0 ? 1 : -1);
} else {
// no: round to even;
value += value & 1;
}
}
return value;
}
static constexpr This create_raw(Underlying value)
{
This t {};
t.raw() = value;
return t;
}
constexpr Underlying raw() const
{
return m_value;
}
constexpr Underlying& raw()
{
return m_value;
}
constexpr This fract() const
{
return create_raw(m_value & radix_mask);
}
constexpr This clamp(This minimum, This maximum) const
{
if (*this < minimum)
return minimum;
if (*this > maximum)
return maximum;
return *this;
}
constexpr This round() const
{
return This { static_cast<Underlying>(*this) };
}
constexpr This floor() const
{
return create_raw(m_value & ~radix_mask);
}
constexpr This ceil() const
{
return create_raw((m_value & ~radix_mask)
+ (m_value & radix_mask ? 1 << precision : 0));
}
constexpr This trunk() const
{
return create_raw((m_value & ~radix_mask)
+ ((m_value & radix_mask)
? (m_value > 0 ? 0 : (1 << precision))
: 0));
}
constexpr Underlying lround() const { return static_cast<Underlying>(*this); }
constexpr Underlying lfloor() const { return m_value >> precision; }
constexpr Underlying lceil() const
{
return (m_value >> precision)
+ (m_value & radix_mask ? 1 : 0);
}
constexpr Underlying ltrunk() const
{
return (m_value >> precision)
+ ((m_value & radix_mask)
? m_value > 0 ? 0 : 1
: 0);
}
// http://www.claysturner.com/dsp/BinaryLogarithm.pdf
constexpr This log2() const
{
// 0.5
This b = create_raw(1 << (precision - 1));
This y = 0;
This x = *this;
// FIXME: There's no negative infinity.
if (x.raw() <= 0)
return create_raw(NumericLimits<Underlying>::min());
if (x != 1) {
i32 shift_amount = AK::log2<Underlying>(x.raw()) - precision;
if (shift_amount > 0)
x >>= shift_amount;
else
x <<= -shift_amount;
y += shift_amount;
}
for (size_t i = 0; i < precision; ++i) {
x *= x;
if (x >= 2) {
x >>= 1;
y += b;
}
b >>= 1;
}
return y;
}
constexpr bool signbit() const
requires(IsSigned<Underlying>)
{
return m_value >> (sizeof(Underlying) * 8 - 1);
}
constexpr This operator-() const
requires(IsSigned<Underlying>)
{
return create_raw(-m_value);
}
constexpr This operator+(This const& other) const
{
return create_raw(m_value + other.m_value);
}
constexpr This operator-(This const& other) const
{
return create_raw(m_value - other.m_value);
}
constexpr This operator*(This const& other) const
{
// FIXME: Potential Overflow, although result could be represented accurately
Underlying value = m_value * other.raw();
This ret {};
ret.raw() = value >> precision;
// fract(value) >= .5?
if (value & (1u << (precision - 1))) {
// fract(value) > .5?
if (value & (radix_mask >> 2u)) {
// yes: round up;
ret.raw() += (value > 0 ? 1 : -1);
} else {
// no: round to even (aka unset last sigificant bit);
ret.raw() += m_value & 1;
}
}
return ret;
}
constexpr This operator/(This const& other) const
{
// FIXME: Better rounding?
return create_raw((m_value / other.m_value) << (precision));
}
template<Integral I>
constexpr This operator+(I other) const
{
return create_raw(m_value + (other << precision));
}
template<Integral I>
constexpr This operator-(I other) const
{
return create_raw(m_value - (other << precision));
}
template<Integral I>
constexpr This operator*(I other) const
{
return create_raw(m_value * other);
}
template<Integral I>
constexpr This operator/(I other) const
{
return create_raw(m_value / other);
}
template<Integral I>
constexpr This operator>>(I other) const
{
return create_raw(m_value >> other);
}
template<Integral I>
constexpr This operator<<(I other) const
{
return create_raw(m_value << other);
}
This& operator+=(This const& other)
{
m_value += other.raw();
return *this;
}
This& operator-=(This const& other)
{
m_value -= other.raw();
return *this;
}
This& operator*=(This const& other)
{
Underlying value = m_value * other.raw();
m_value = value >> precision;
// fract(value) >= .5?
if (value & (1u << (precision - 1))) {
// fract(value) > .5?
if (value & (radix_mask >> 2u)) {
// yes: round up;
m_value += (value > 0 ? 1 : -1);
} else {
// no: round to even (aka unset last sigificant bit);
m_value += m_value & 1;
}
}
return *this;
}
This& operator/=(This const& other)
{
// FIXME: See above
m_value /= other.raw();
m_value <<= precision;
return *this;
}
template<Integral I>
This& operator+=(I other)
{
m_value += other << precision;
return *this;
}
template<Integral I>
This& operator-=(I other)
{
m_value -= other << precision;
return *this;
}
template<Integral I>
This& operator*=(I other)
{
m_value *= other;
return *this;
}
template<Integral I>
This& operator/=(I other)
{
m_value /= other;
return *this;
}
template<Integral I>
This& operator>>=(I other)
{
m_value >>= other;
return *this;
}
template<Integral I>
This& operator<<=(I other)
{
m_value <<= other;
return *this;
}
bool operator==(This const& other) const { return raw() == other.raw(); }
bool operator!=(This const& other) const { return raw() != other.raw(); }
bool operator>(This const& other) const { return raw() > other.raw(); }
bool operator>=(This const& other) const { return raw() >= other.raw(); }
bool operator<(This const& other) const { return raw() < other.raw(); }
bool operator<=(This const& other) const { return raw() <= other.raw(); }
// FIXE: There are probably better ways to do these
template<Integral I>
bool operator==(I other) const
{
return m_value >> precision == other && !(m_value & radix_mask);
}
template<Integral I>
bool operator!=(I other) const
{
return (m_value >> precision) != other || m_value & radix_mask;
}
template<Integral I>
bool operator>(I other) const
{
return !(*this <= other);
}
template<Integral I>
bool operator>=(I other) const
{
return !(*this < other);
}
template<Integral I>
bool operator<(I other) const
{
return (m_value >> precision) < other || m_value < (other << precision);
}
template<Integral I>
bool operator<=(I other) const
{
return *this < other || *this == other;
}
// Casting from a float should be faster than casting to a float
template<FloatingPoint F>
bool operator==(F other) const { return *this == (This)other; }
template<FloatingPoint F>
bool operator!=(F other) const { return *this != (This)other; }
template<FloatingPoint F>
bool operator>(F other) const { return *this > (This)other; }
template<FloatingPoint F>
bool operator>=(F other) const { return *this >= (This)other; }
template<FloatingPoint F>
bool operator<(F other) const { return *this < (This)other; }
template<FloatingPoint F>
bool operator<=(F other) const { return *this <= (This)other; }
template<size_t P, typename U>
operator FixedPoint<P, U>() const
{
return cast_to<P, U>();
}
private:
template<size_t P, typename U>
constexpr FixedPoint<P, U> cast_to() const
{
U raw_value = static_cast<U>(m_value >> precision) << P;
if constexpr (precision > P)
raw_value |= (m_value & radix_mask) >> (precision - P);
else if constexpr (precision < P)
raw_value |= static_cast<U>(m_value & radix_mask) << (P - precision);
else
raw_value |= m_value & radix_mask;
return FixedPoint<P, U>::create_raw(raw_value);
}
Underlying m_value;
};
template<size_t precision, typename Underlying>
struct Formatter<FixedPoint<precision, Underlying>> : StandardFormatter {
Formatter() = default;
explicit Formatter(StandardFormatter formatter)
: StandardFormatter(formatter)
{
}
ErrorOr<void> format(FormatBuilder& builder, FixedPoint<precision, Underlying> value)
{
u8 base;
bool upper_case;
FormatBuilder::RealNumberDisplayMode real_number_display_mode = FormatBuilder::RealNumberDisplayMode::General;
if (m_mode == Mode::Default || m_mode == Mode::FixedPoint) {
base = 10;
upper_case = false;
if (m_mode == Mode::FixedPoint)
real_number_display_mode = FormatBuilder::RealNumberDisplayMode::FixedPoint;
} else if (m_mode == Mode::Hexfloat) {
base = 16;
upper_case = false;
} else if (m_mode == Mode::HexfloatUppercase) {
base = 16;
upper_case = true;
} else {
VERIFY_NOT_REACHED();
}
m_width = m_width.value_or(0);
m_precision = m_precision.value_or(6);
bool is_negative = false;
if constexpr (IsSigned<Underlying>)
is_negative = value < 0;
i64 integer = value.ltrunk();
constexpr u64 one = static_cast<Underlying>(1) << precision;
u64 fraction_raw = value.raw() & (one - 1);
return builder.put_fixed_point(is_negative, integer, fraction_raw, one, base, upper_case, m_zero_pad, m_align, m_width.value(), m_precision.value(), m_fill, m_sign_mode, real_number_display_mode);
}
};
}
#if USING_AK_GLOBALLY
using AK::FixedPoint;
#endif
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