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AK: Add FixedPoint arithmetic helper

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Co-authored-by: Hendiadyoin1 <leon2002.la@gmail.com>
Co-authored-by: kleines Filmröllchen <malu.bertsch@gmail.com>
This commit is contained in:
Hediadyoin1 2021-08-20 17:35:03 +02:00 committed by Ali Mohammad Pur
parent beb8c48f26
commit fdef6e5f76
Notes: sideshowbarker 2024-07-18 05:02:25 +09:00 
Author: https://github.com/Hendiadyoin1
Commit: https://github.com/SerenityOS/serenity/commit/fdef6e5f76e
Pull-request: https://github.com/SerenityOS/serenity/pull/9638
Reviewed-by: https://github.com/alimpfard
Reviewed-by: https://github.com/kleinesfilmroellchen
3 changed files with 409 additions and 0 deletions
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334
AK/FixedPoint.h Normal file
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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/Math.h>
#include <AK/Types.h>
namespace AK {
// FIXME: this always uses round to nearest break-tie to even
template<size_t precision, Integral Underlying = i32>
class FixedPoint {
using This = FixedPoint<precision, Underlying>;
constexpr static Underlying radix_mask = (1 << precision) - 1;
public:
constexpr FixedPoint() = default;
template<Integral I>
constexpr FixedPoint(I value)
: m_value(value << precision)
{
}
template<FloatingPoint F>
constexpr FixedPoint(F value)
: m_value(static_cast<Underlying>(value * (1u << precision)))
{
}
template<FloatingPoint F>
explicit ALWAYS_INLINE operator F() const
{
return (F)m_value * pow<F>(0.5, precision);
}
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;
}
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 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);
}
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);
}
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;
}
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
{
if (m_value > 0)
return (m_value >> precision) > other || (m_value >> precision == other && (m_value & radix_mask));
if (other > 0)
return false;
return (m_value >> precision) > other || !(m_value >> precision == other && (m_value & radix_mask));
}
template<Integral I>
bool operator>=(I other) const
{
if (m_value > 0)
return (m_value >> precision) >= other || (m_value >> precision == other && (m_value & radix_mask));
if (other > 0)
return false;
return (m_value >> precision) >= other || !(m_value >> precision == other && (m_value & radix_mask));
}
template<Integral I>
bool operator<(I other) const
{
if (m_value > 0)
return (m_value >> precision) < other || !(m_value >> precision == other && (m_value & radix_mask));
if (other > 0)
return true;
return (m_value >> precision) < other || (m_value >> precision == other && (m_value & radix_mask));
}
template<Integral I>
bool operator<=(I other) const
{
if (m_value > 0)
return (m_value >> precision) <= other || !(m_value >> precision == other && (m_value & radix_mask));
if (other > 0)
return true;
return (m_value >> precision) <= other || (m_value >> precision == other && (m_value & radix_mask));
}
// 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; }
private:
static This create_raw(Underlying value)
{
This t {};
t.raw() = value;
return t;
}
Underlying m_value;
};
template<size_t precision, Integral Underlying>
struct Formatter<FixedPoint<precision, Underlying>> : StandardFormatter {
Formatter() = default;
explicit Formatter(StandardFormatter formatter)
: StandardFormatter(formatter)
{
}
void format(FormatBuilder& builder, FixedPoint<precision, Underlying> value)
{
Formatter<double> formatter { *this };
formatter.format(builder, (double)value);
}
};
}
using AK::FixedPoint;

1
Tests/AK/CMakeLists.txt
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@ -1,4 +1,5 @@
set(AK_TEST_SOURCES
TestFixedPoint.cpp
TestAllOf.cpp
TestAnyOf.cpp
TestArray.cpp

74
Tests/AK/TestFixedPoint.cpp Normal file
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/*
* Copyright (c) 2021, the SerenityOS developers.
*
* SPDX-License-Identifier: BSD-2-Clause
*/
#include <LibTest/TestCase.h>
#include <AK/FixedPoint.h>
using Type = FixedPoint<4>;
TEST_CASE(arithmetic)
{
EXPECT_EQ(
Type(0.5) + Type(0.5),
Type(1));
EXPECT_EQ(
Type(1) + Type(0.5),
Type(1.5));
EXPECT_EQ(
(float)(Type(1) + Type(0.5)),
1.5f);
// FIXME: Test for rounded multiply
EXPECT_EQ(
Type((int)1) * Type(0.5),
Type(0.5));
EXPECT_EQ(
Type((int)1) / Type(0.5),
Type(2));
}
TEST_CASE(rounding)
{
EXPECT_EQ(Type(0.5).round(), Type(0));
EXPECT_EQ(Type(0.5).floor(), Type(0));
EXPECT_EQ(Type(0.5).ceil(), Type(1));
EXPECT_EQ(Type(0.75).trunk(), Type(0));
EXPECT_EQ(Type(1.5).round(), Type(2));
EXPECT_EQ(Type(1.5).floor(), Type(1));
EXPECT_EQ(Type(1.5).ceil(), Type(2));
EXPECT_EQ(Type(1.25).trunk(), Type(1));
EXPECT_EQ(Type(-0.5).round(), Type(0));
EXPECT_EQ(Type(-0.5).floor(), Type(-1));
EXPECT_EQ(Type(-0.5).ceil(), Type(0));
EXPECT_EQ(Type(-0.75).trunk(), Type(0));
EXPECT_EQ(Type(-1.5).round(), Type(-2));
EXPECT_EQ(Type(-1.5).floor(), Type(-2));
EXPECT_EQ(Type(-1.5).ceil(), Type(-1));
EXPECT_EQ(Type(-1.25).trunk(), Type(-1));
EXPECT_EQ(Type(0.5).lround(), 0);
EXPECT_EQ(Type(0.5).lfloor(), 0);
EXPECT_EQ(Type(0.5).lceil(), 1);
EXPECT_EQ(Type(0.5).ltrunk(), 0);
EXPECT_EQ(Type(1.5).lround(), 2);
EXPECT_EQ(Type(1.5).lfloor(), 1);
EXPECT_EQ(Type(1.5).lceil(), 2);
EXPECT_EQ(Type(1.5).ltrunk(), 1);
EXPECT_EQ(Type(-0.5).lround(), 0);
EXPECT_EQ(Type(-0.5).lfloor(), -1);
EXPECT_EQ(Type(-0.5).lceil(), 0);
EXPECT_EQ(Type(-0.5).ltrunk(), 0);
EXPECT_EQ(Type(-1.5).lround(), -2);
EXPECT_EQ(Type(-1.5).lfloor(), -2);
EXPECT_EQ(Type(-1.5).lceil(), -1);
EXPECT_EQ(Type(-1.5).ltrunk(), -1);
}