mirror of
https://github.com/SerenityOS/serenity
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8443d0a74d
This allows us to easily use an appropriate integer type when performing float bitfield operations. This change also adds a comment about the technically-incorrect 80-bit extended float mantissa field.
294 lines
10 KiB
C++
294 lines
10 KiB
C++
/*
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* Copyright (c) 2022, Jelle Raaijmakers <jelle@gmta.nl>
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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/BitCast.h>
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#include <AK/StdLibExtras.h>
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#include <AK/Types.h>
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namespace AK {
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template<typename T>
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union FloatExtractor;
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#ifdef AK_HAS_FLOAT_128
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template<>
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union FloatExtractor<f128> {
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using ComponentType = unsigned __int128;
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static constexpr int mantissa_bits = 112;
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static constexpr ComponentType mantissa_max = (((ComponentType)1) << 112) - 1;
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static constexpr int exponent_bias = 16383;
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static constexpr int exponent_bits = 15;
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static constexpr unsigned exponent_max = 32767;
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struct [[gnu::packed]] {
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ComponentType mantissa : 112;
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ComponentType exponent : 15;
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ComponentType sign : 1;
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};
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f128 d;
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};
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// Validate that f128 and the FloatExtractor union are 128 bits.
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static_assert(AssertSize<f128, 16>());
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static_assert(AssertSize<FloatExtractor<f128>, sizeof(f128)>());
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#endif
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#ifdef AK_HAS_FLOAT_80
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template<>
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union FloatExtractor<f80> {
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using ComponentType = unsigned long long;
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static constexpr int mantissa_bits = 64;
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static constexpr ComponentType mantissa_max = ~0ull;
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static constexpr int exponent_bias = 16383;
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static constexpr int exponent_bits = 15;
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static constexpr unsigned exponent_max = 32767;
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struct [[gnu::packed]] {
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// This is technically wrong: Extended floating point values really only have 63 bits of mantissa
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// and an "integer bit" that behaves in various strange, unintuitive and non-IEEE-754 ways.
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// However, since all bit-fiddling float code assumes IEEE floats, it cannot handle this properly.
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// If we pretend that 80-bit floats are IEEE floats with 64-bit mantissas, almost everything works correctly
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// and we just need a few special cases.
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ComponentType mantissa : 64;
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ComponentType exponent : 15;
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ComponentType sign : 1;
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};
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f80 d;
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};
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static_assert(AssertSize<FloatExtractor<f80>, sizeof(f80)>());
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#endif
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template<>
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union FloatExtractor<f64> {
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using ComponentType = unsigned long long;
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static constexpr int mantissa_bits = 52;
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static constexpr ComponentType mantissa_max = (1ull << 52) - 1;
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static constexpr int exponent_bias = 1023;
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static constexpr int exponent_bits = 11;
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static constexpr unsigned exponent_max = 2047;
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struct [[gnu::packed]] {
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// FIXME: These types have to all be the same, otherwise this struct
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// goes from being a bitfield describing the layout of an f64
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// into being a multibyte mess on windows.
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// Technically, '-mno-ms-bitfields' is supposed to disable this
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// very intuitive and portable behaviour on windows, but it doesn't
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// work with the msvc ABI.
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// See <https://github.com/llvm/llvm-project/issues/24757>
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ComponentType mantissa : 52;
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ComponentType exponent : 11;
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ComponentType sign : 1;
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};
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f64 d;
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};
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static_assert(AssertSize<FloatExtractor<f64>, sizeof(f64)>());
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template<>
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union FloatExtractor<f32> {
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using ComponentType = unsigned;
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static constexpr int mantissa_bits = 23;
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static constexpr ComponentType mantissa_max = (1 << 23) - 1;
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static constexpr int exponent_bias = 127;
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static constexpr int exponent_bits = 8;
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static constexpr ComponentType exponent_max = 255;
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struct [[gnu::packed]] {
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ComponentType mantissa : 23;
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ComponentType exponent : 8;
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ComponentType sign : 1;
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};
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f32 d;
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};
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static_assert(AssertSize<FloatExtractor<f32>, sizeof(f32)>());
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template<size_t S, size_t E, size_t M>
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requires(S <= 1 && E >= 1 && M >= 1 && (S + E + M) <= 64) class FloatingPointBits final {
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public:
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static size_t const signbit = S;
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static size_t const exponentbits = E;
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static size_t const mantissabits = M;
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template<typename T>
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requires(IsIntegral<T> && IsUnsigned<T> && sizeof(T) <= 8) constexpr FloatingPointBits(T bits)
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: m_bits(bits)
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{
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}
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constexpr FloatingPointBits(double value)
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: m_bits(bit_cast<u64>(value))
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{
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}
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constexpr FloatingPointBits(float value)
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: m_bits(bit_cast<u32>(value))
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{
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}
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double as_double() const
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requires(S == 1 && E == 11 && M == 52)
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{
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return bit_cast<double>(m_bits);
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}
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float as_float() const
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requires(S == 1 && E == 8 && M == 23)
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{
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return bit_cast<float>(static_cast<u32>(m_bits));
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}
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u64 bits() const { return m_bits; }
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private:
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u64 m_bits;
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};
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typedef FloatingPointBits<1, 8, 23> SingleFloatingPointBits;
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typedef FloatingPointBits<1, 11, 52> DoubleFloatingPointBits;
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/**
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* Convert between two IEEE 754 floating point types in any arrangement of sign, exponent and mantissa bits.
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*/
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template<typename To, typename From>
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constexpr To float_to_float(From const input)
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{
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constexpr u64 from_exponent_nonnumber = (1ull << From::exponentbits) - 1;
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constexpr u64 from_exponent_bias = (1ull << (From::exponentbits - 1)) - 1;
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constexpr u64 to_exponent_nonnumber = (1ull << To::exponentbits) - 1;
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constexpr u64 to_exponent_bias = (1ull << (To::exponentbits - 1)) - 1;
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constexpr u64 to_exponent_max = (1ull << To::exponentbits) - 2;
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// Deconstruct input bits to float components
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u64 from_sign = (input.bits() >> (From::exponentbits + From::mantissabits)) & From::signbit;
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u64 from_exponent = (input.bits() >> From::mantissabits) & ((1ull << From::exponentbits) - 1);
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u64 from_mantissa = input.bits() & ((1ull << From::mantissabits) - 1);
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u64 to_sign = from_sign & To::signbit;
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u64 to_exponent;
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u64 to_mantissa;
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auto target_value = [&to_sign, &to_exponent, &to_mantissa]() {
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return To((to_sign << (To::exponentbits + To::mantissabits)) | (to_exponent << To::mantissabits) | to_mantissa);
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};
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auto shift_mantissa = [](u64 mantissa) -> u64 {
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if constexpr (From::mantissabits < To::mantissabits)
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return mantissa << (To::mantissabits - From::mantissabits);
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else
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return mantissa >> (From::mantissabits - To::mantissabits);
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};
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// If target is unsigned and source is negative, clamp to 0 or keep NaN
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if constexpr (To::signbit == 0) {
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if (from_sign == 1) {
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if (from_exponent == from_exponent_nonnumber && from_mantissa > 0) {
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to_exponent = to_exponent_nonnumber;
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to_mantissa = 1;
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} else {
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to_exponent = 0;
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to_mantissa = 0;
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}
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return target_value();
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}
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}
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// If the source floating point is denormalized;
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if (from_exponent == 0) {
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// If the source mantissa is 0, the value is +/-0
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if (from_mantissa == 0) {
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to_exponent = 0;
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to_mantissa = 0;
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return target_value();
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}
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// If the source has more exponent bits than the target, then the largest possible
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// source mantissa still cannot be represented in the target denormalized value.
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if constexpr (From::exponentbits > To::exponentbits) {
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to_exponent = 0;
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to_mantissa = 0;
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return target_value();
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}
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// If the source and target have the same number of exponent bits, we only need to
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// shift the mantissa.
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if constexpr (From::exponentbits == To::exponentbits) {
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to_exponent = 0;
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to_mantissa = shift_mantissa(from_mantissa);
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return target_value();
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}
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// The target has more exponent bits, so our denormalized value can be represented
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// as a normalized value in the target floating point. Normalized values have an
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// implicit leading 1, so we shift the mantissa left until we find our explicit
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// leading 1 which is then dropped.
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int adjust_exponent = -1;
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to_mantissa = from_mantissa;
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do {
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++adjust_exponent;
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to_mantissa <<= 1;
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} while ((to_mantissa & (1ull << From::mantissabits)) == 0);
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to_exponent = to_exponent_bias - from_exponent_bias - adjust_exponent;
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// Drop the most significant bit from the mantissa
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to_mantissa &= (1ull << From::mantissabits) - 1;
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to_mantissa = shift_mantissa(to_mantissa);
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return target_value();
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}
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// If the source is NaN or +/-Inf, keep it that way
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if (from_exponent == from_exponent_nonnumber) {
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to_exponent = to_exponent_nonnumber;
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to_mantissa = (from_mantissa == 0) ? 0 : 1;
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return target_value();
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}
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// Determine the target exponent
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to_exponent = to_exponent_bias - from_exponent_bias + from_exponent;
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// If the calculated exponent exceeds the target's capacity, clamp both the exponent and the
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// mantissa to their maximum values.
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if (to_exponent > to_exponent_max) {
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to_exponent = to_exponent_max;
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to_mantissa = (1ull << To::mantissabits) - 1;
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return target_value();
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}
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// If the new exponent is less than 1, we can only represent this value as a denormalized number
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if (to_exponent < 1) {
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to_exponent = 0;
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// Add a leading 1 and shift the mantissa right
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int adjust_exponent = 1 - to_exponent_bias - from_exponent + from_exponent_bias;
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to_mantissa = ((1ull << From::mantissabits) | from_mantissa) >> adjust_exponent;
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to_mantissa = shift_mantissa(to_mantissa);
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return target_value();
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}
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// New exponent fits; shift the mantissa to fit as well
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to_mantissa = shift_mantissa(from_mantissa);
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return target_value();
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}
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template<typename O>
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constexpr O convert_from_native_double(double input) { return float_to_float<O>(DoubleFloatingPointBits(input)); }
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template<typename O>
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constexpr O convert_from_native_float(float input) { return float_to_float<O>(SingleFloatingPointBits(input)); }
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template<typename I>
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constexpr double convert_to_native_double(I input) { return float_to_float<DoubleFloatingPointBits>(input).as_double(); }
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template<typename I>
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constexpr float convert_to_native_float(I input) { return float_to_float<SingleFloatingPointBits>(input).as_float(); }
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}
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#if USING_AK_GLOBALLY
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using AK::DoubleFloatingPointBits;
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using AK::FloatExtractor;
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using AK::FloatingPointBits;
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using AK::SingleFloatingPointBits;
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using AK::convert_from_native_double;
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using AK::convert_from_native_float;
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using AK::convert_to_native_double;
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using AK::convert_to_native_float;
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using AK::float_to_float;
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#endif
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