ladybird/AK/FloatingPoint.h
Ben Wiederhake f07847e099 Everywhere: Remove unused includes of AK/Concepts.h
These instances were detected by searching for files that include
AK/Concepts.h, but don't match the regex:

\\b(AnyString|Arithmetic|ArrayLike|DerivedFrom|Enum|FallibleFunction|Flo
atingPoint|Fundamental|HashCompatible|Indexable|Integral|IterableContain
er|IteratorFunction|IteratorPairWith|OneOf|OneOfIgnoringCV|SameAs|Signed
|SpecializationOf|Unsigned|VoidFunction)\\b

(Without the linebreaks.)

This regex is pessimistic, so there might be more files that don't
actually use any concepts.

In theory, one might use LibCPP to detect things like this
automatically, but let's do this one step after another.
2023-01-02 20:27:20 -05:00

274 lines
8.9 KiB
C++

/*
* Copyright (c) 2022, Jelle Raaijmakers <jelle@gmta.nl>
*
* SPDX-License-Identifier: BSD-2-Clause
*/
#pragma once
#include <AK/BitCast.h>
#include <AK/Types.h>
namespace AK {
template<typename T>
union FloatExtractor;
#ifdef AK_HAS_FLOAT_128
template<>
union FloatExtractor<f128> {
static constexpr int mantissa_bits = 112;
static constexpr unsigned __int128 mantissa_max = (((unsigned __int128)1) << 112) - 1;
static constexpr int exponent_bias = 16383;
static constexpr int exponent_bits = 15;
static constexpr unsigned exponent_max = 32767;
struct {
unsigned __int128 mantissa : 112;
unsigned exponent : 15;
unsigned sign : 1;
};
f128 d;
};
// Validate that f128 and the FloatExtractor union are 128 bits.
static_assert(sizeof(f128) == 16);
static_assert(sizeof(FloatExtractor<f128>) == 16);
#endif
#ifdef AK_HAS_FLOAT_80
template<>
union FloatExtractor<f80> {
static constexpr int mantissa_bits = 64;
static constexpr unsigned long long mantissa_max = ~0u;
static constexpr int exponent_bias = 16383;
static constexpr int exponent_bits = 15;
static constexpr unsigned exponent_max = 32767;
struct {
unsigned long long mantissa;
unsigned exponent : 15;
unsigned sign : 1;
};
f80 d;
};
#endif
template<>
union FloatExtractor<f64> {
static constexpr int mantissa_bits = 52;
static constexpr unsigned long long mantissa_max = (1ull << 52) - 1;
static constexpr int exponent_bias = 1023;
static constexpr int exponent_bits = 11;
static constexpr unsigned exponent_max = 2047;
struct {
unsigned long long mantissa : 52;
unsigned exponent : 11;
unsigned sign : 1;
};
f64 d;
};
template<>
union FloatExtractor<f32> {
static constexpr int mantissa_bits = 23;
static constexpr unsigned mantissa_max = (1 << 23) - 1;
static constexpr int exponent_bias = 127;
static constexpr int exponent_bits = 8;
static constexpr unsigned exponent_max = 255;
struct {
unsigned long long mantissa : 23;
unsigned exponent : 8;
unsigned sign : 1;
};
f32 d;
};
template<size_t S, size_t E, size_t M>
requires(S <= 1 && E >= 1 && M >= 1 && (S + E + M) <= 64) class FloatingPointBits final {
public:
static const size_t signbit = S;
static const size_t exponentbits = E;
static const size_t mantissabits = M;
template<typename T>
requires(IsIntegral<T> && IsUnsigned<T> && sizeof(T) <= 8) constexpr FloatingPointBits(T bits)
: m_bits(bits)
{
}
constexpr FloatingPointBits(double value)
: m_bits(bit_cast<u64>(value))
{
}
constexpr FloatingPointBits(float value)
: m_bits(bit_cast<u32>(value))
{
}
double as_double() const
requires(S == 1 && E == 11 && M == 52)
{
return bit_cast<double>(m_bits);
}
float as_float() const
requires(S == 1 && E == 8 && M == 23)
{
return bit_cast<float>(static_cast<u32>(m_bits));
}
u64 bits() const { return m_bits; }
private:
u64 m_bits;
};
typedef FloatingPointBits<1, 8, 23> SingleFloatingPointBits;
typedef FloatingPointBits<1, 11, 52> DoubleFloatingPointBits;
/**
* Convert between two IEEE 754 floating point types in any arrangement of sign, exponent and mantissa bits.
*/
template<typename To, typename From>
constexpr To float_to_float(From const input)
{
constexpr u64 from_exponent_nonnumber = (1ull << From::exponentbits) - 1;
constexpr u64 from_exponent_bias = (1ull << (From::exponentbits - 1)) - 1;
constexpr u64 to_exponent_nonnumber = (1ull << To::exponentbits) - 1;
constexpr u64 to_exponent_bias = (1ull << (To::exponentbits - 1)) - 1;
constexpr u64 to_exponent_max = (1ull << To::exponentbits) - 2;
// Deconstruct input bits to float components
u64 from_sign = (input.bits() >> (From::exponentbits + From::mantissabits)) & From::signbit;
u64 from_exponent = (input.bits() >> From::mantissabits) & ((1ull << From::exponentbits) - 1);
u64 from_mantissa = input.bits() & ((1ull << From::mantissabits) - 1);
u64 to_sign = from_sign & To::signbit;
u64 to_exponent;
u64 to_mantissa;
auto target_value = [&to_sign, &to_exponent, &to_mantissa]() {
return To((to_sign << (To::exponentbits + To::mantissabits)) | (to_exponent << To::mantissabits) | to_mantissa);
};
auto shift_mantissa = [](u64 mantissa) -> u64 {
if constexpr (From::mantissabits < To::mantissabits)
return mantissa << (To::mantissabits - From::mantissabits);
else
return mantissa >> (From::mantissabits - To::mantissabits);
};
// If target is unsigned and source is negative, clamp to 0 or keep NaN
if constexpr (To::signbit == 0) {
if (from_sign == 1) {
if (from_exponent == from_exponent_nonnumber && from_mantissa > 0) {
to_exponent = to_exponent_nonnumber;
to_mantissa = 1;
} else {
to_exponent = 0;
to_mantissa = 0;
}
return target_value();
}
}
// If the source floating point is denormalized;
if (from_exponent == 0) {
// If the source mantissa is 0, the value is +/-0
if (from_mantissa == 0) {
to_exponent = 0;
to_mantissa = 0;
return target_value();
}
// If the source has more exponent bits than the target, then the largest possible
// source mantissa still cannot be represented in the target denormalized value.
if constexpr (From::exponentbits > To::exponentbits) {
to_exponent = 0;
to_mantissa = 0;
return target_value();
}
// If the source and target have the same number of exponent bits, we only need to
// shift the mantissa.
if constexpr (From::exponentbits == To::exponentbits) {
to_exponent = 0;
to_mantissa = shift_mantissa(from_mantissa);
return target_value();
}
// The target has more exponent bits, so our denormalized value can be represented
// as a normalized value in the target floating point. Normalized values have an
// implicit leading 1, so we shift the mantissa left until we find our explicit
// leading 1 which is then dropped.
int adjust_exponent = -1;
to_mantissa = from_mantissa;
do {
++adjust_exponent;
to_mantissa <<= 1;
} while ((to_mantissa & (1ull << From::mantissabits)) == 0);
to_exponent = to_exponent_bias - from_exponent_bias - adjust_exponent;
// Drop the most significant bit from the mantissa
to_mantissa &= (1ull << From::mantissabits) - 1;
to_mantissa = shift_mantissa(to_mantissa);
return target_value();
}
// If the source is NaN or +/-Inf, keep it that way
if (from_exponent == from_exponent_nonnumber) {
to_exponent = to_exponent_nonnumber;
to_mantissa = (from_mantissa == 0) ? 0 : 1;
return target_value();
}
// Determine the target exponent
to_exponent = to_exponent_bias - from_exponent_bias + from_exponent;
// If the calculated exponent exceeds the target's capacity, clamp both the exponent and the
// mantissa to their maximum values.
if (to_exponent > to_exponent_max) {
to_exponent = to_exponent_max;
to_mantissa = (1ull << To::mantissabits) - 1;
return target_value();
}
// If the new exponent is less than 1, we can only represent this value as a denormalized number
if (to_exponent < 1) {
to_exponent = 0;
// Add a leading 1 and shift the mantissa right
int adjust_exponent = 1 - to_exponent_bias - from_exponent + from_exponent_bias;
to_mantissa = ((1ull << From::mantissabits) | from_mantissa) >> adjust_exponent;
to_mantissa = shift_mantissa(to_mantissa);
return target_value();
}
// New exponent fits; shift the mantissa to fit as well
to_mantissa = shift_mantissa(from_mantissa);
return target_value();
}
template<typename O>
constexpr O convert_from_native_double(double input) { return float_to_float<O>(DoubleFloatingPointBits(input)); }
template<typename O>
constexpr O convert_from_native_float(float input) { return float_to_float<O>(SingleFloatingPointBits(input)); }
template<typename I>
constexpr double convert_to_native_double(I input) { return float_to_float<DoubleFloatingPointBits>(input).as_double(); }
template<typename I>
constexpr float convert_to_native_float(I input) { return float_to_float<SingleFloatingPointBits>(input).as_float(); }
}
#if USING_AK_GLOBALLY
using AK::DoubleFloatingPointBits;
using AK::FloatExtractor;
using AK::FloatingPointBits;
using AK::SingleFloatingPointBits;
using AK::convert_from_native_double;
using AK::convert_from_native_float;
using AK::convert_to_native_double;
using AK::convert_to_native_float;
using AK::float_to_float;
#endif