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https://github.com/LadybirdBrowser/ladybird.git
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352480338e
The main change is the simplification of the expression
`(10^precision * fraction) / 2^precision` to `5^precision * fraction`.
Those expressions overflow or not depends on the value of `precision`
and `fraction`. For the maximum value of `fraction`, the following table
shows for which value of `precision` overflow will occur.
Old New
u32 08 10
u64 15 20
u128 30 39
As of now `u64` type is used to calculate the result of the expression.
Meaning that before, only FixedPoints with `precision` less than 15
could be accurately rendered (for every value of fraction) in decimal.
Now, this limit gets increased to 20.
This refactor also fixes, broken decimal render for explicitly specified
precision width in format string, and broken hexadecimal render.
454 lines
12 KiB
C++
454 lines
12 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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// Solaris' definition of signbit in math_c99.h conflicts with our implementation.
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#ifdef AK_OS_SOLARIS
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# undef signbit
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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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#ifndef KERNEL
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template<FloatingPoint F>
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FixedPoint(F value)
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: m_value(round_to<Underlying>(value * (static_cast<Underlying>(1) << precision)))
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{
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}
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#endif
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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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return trunc().raw() >> precision;
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}
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static constexpr 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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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 clamp(This minimum, This maximum) const
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{
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if (*this < minimum)
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return minimum;
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if (*this > maximum)
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return maximum;
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return *this;
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}
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constexpr This rint() const
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{
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// Note: Round fair, break tie to even
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Underlying value = m_value >> precision;
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// Note: For negative numbers the ordering are reversed,
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// and they were already decremented by the shift, so we need to
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// add 1 when we see a fract values behind the `.5`s place set,
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// because that means they are smaller than .5
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// fract(m_value) >= .5?
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if (m_value & (static_cast<Underlying>(1) << (precision - 1))) {
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// fract(m_value) > .5?
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if (m_value & (radix_mask >> 1)) {
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// yes: round "up";
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value += 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 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 ? static_cast<Underlying>(1) << precision : 0));
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}
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constexpr This trunc() 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 : (static_cast<Underlying>(1) << precision))
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: 0));
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}
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constexpr Underlying lrint() const { return rint().raw() >> precision; }
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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 ltrunc() 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(static_cast<Underlying>(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: Figure out a way to use more narrow types and avoid __int128
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using MulRes = Conditional<sizeof(Underlying) < sizeof(i64), i64, __int128>;
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MulRes value = raw();
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value *= other.raw();
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This ret = create_raw(value >> precision);
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// Rounding:
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// If last bit cut off is 1:
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if (value & (static_cast<Underlying>(1) << (precision - 1))) {
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// If the bit after is 1 as well
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if (value & (radix_mask >> 1)) {
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// We round away from 0
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ret.raw() += 1;
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} else {
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// Otherwise we round to the next even value
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// Which means we add the least significant bit of the raw return value
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ret.raw() += ret.raw() & 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: Figure out a way to use more narrow types and avoid __int128
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using DivRes = Conditional<sizeof(Underlying) < sizeof(i64), i64, __int128>;
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DivRes value = raw();
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value <<= precision;
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value /= other.raw();
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return create_raw(value);
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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 + (static_cast<Underlying>(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 - (static_cast<Underlying>(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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*this = *this * other;
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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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*this = *this / 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 += static_cast<Underlying>(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 -= static_cast<Underlying>(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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// FIXME: 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 < (static_cast<Underlying>(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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Underlying m_value;
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};
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template<size_t precision, typename Underlying>
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struct Formatter<FixedPoint<precision, Underlying>> : StandardFormatter {
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Formatter() = default;
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explicit Formatter(StandardFormatter formatter)
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: StandardFormatter(formatter)
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{
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}
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ErrorOr<void> format(FormatBuilder& builder, FixedPoint<precision, Underlying> value)
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{
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u8 base;
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bool upper_case;
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if (m_mode == Mode::Default || m_mode == Mode::FixedPoint) {
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base = 10;
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upper_case = false;
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} else if (m_mode == Mode::Hexfloat) {
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base = 16;
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upper_case = false;
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} else if (m_mode == Mode::HexfloatUppercase) {
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base = 16;
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upper_case = true;
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} else {
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VERIFY_NOT_REACHED();
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}
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m_width = m_width.value_or(0);
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m_precision = m_precision.value_or(6);
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bool is_negative = false;
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if constexpr (IsSigned<Underlying>)
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is_negative = value < 0;
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i64 integer = value.ltrunc();
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constexpr u64 one = static_cast<Underlying>(1) << precision;
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u64 fraction_raw = value.raw() & (one - 1);
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return builder.put_fixed_point(is_negative, integer, fraction_raw, one, precision, base, upper_case, m_zero_pad, m_use_separator, m_align, m_width.value(), m_precision.value(), m_fill, m_sign_mode);
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}
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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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