mirror of
https://github.com/LadybirdBrowser/ladybird.git
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1417 lines
29 KiB
C++
1417 lines
29 KiB
C++
/*
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* Copyright (c) 2018-2020, Andreas Kling <kling@serenityos.org>
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* Copyright (c) 2021, Mițca Dumitru <dumitru0mitca@gmail.com>
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*
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* SPDX-License-Identifier: BSD-2-Clause
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*/
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#include <AK/ExtraMathConstants.h>
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#include <AK/Platform.h>
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#include <AK/StdLibExtras.h>
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#include <LibC/assert.h>
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#include <fenv.h>
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#include <math.h>
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#include <stdint.h>
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#include <stdlib.h>
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template<size_t>
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constexpr double e_to_power();
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template<>
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constexpr double e_to_power<0>() { return 1; }
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template<size_t exponent>
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constexpr double e_to_power() { return M_E * e_to_power<exponent - 1>(); }
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template<size_t>
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constexpr size_t factorial();
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template<>
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constexpr size_t factorial<0>() { return 1; }
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template<size_t value>
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constexpr size_t factorial() { return value * factorial<value - 1>(); }
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template<size_t>
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constexpr size_t product_even();
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template<>
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constexpr size_t product_even<2>() { return 2; }
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template<size_t value>
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constexpr size_t product_even() { return value * product_even<value - 2>(); }
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template<size_t>
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constexpr size_t product_odd();
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template<>
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constexpr size_t product_odd<1>() { return 1; }
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template<size_t value>
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constexpr size_t product_odd() { return value * product_odd<value - 2>(); }
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enum class RoundingMode {
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ToZero = FE_TOWARDZERO,
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Up = FE_UPWARD,
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Down = FE_DOWNWARD,
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ToEven = FE_TONEAREST
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};
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template<typename T>
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union FloatExtractor;
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#if ARCH(I386) || ARCH(X86_64)
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// This assumes long double is 80 bits, which is true with GCC on Intel platforms
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template<>
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union FloatExtractor<long double> {
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static const int mantissa_bits = 64;
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static const unsigned long long mantissa_max = ~0u;
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static const int exponent_bias = 16383;
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static const int exponent_bits = 15;
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static const unsigned exponent_max = 32767;
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struct {
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unsigned long long mantissa;
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unsigned exponent : 15;
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unsigned sign : 1;
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};
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long double d;
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};
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#endif
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template<>
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union FloatExtractor<double> {
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static const int mantissa_bits = 52;
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static const unsigned long long mantissa_max = (1ull << 52) - 1;
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static const int exponent_bias = 1023;
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static const int exponent_bits = 11;
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static const unsigned exponent_max = 2047;
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struct {
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unsigned long long mantissa : 52;
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unsigned exponent : 11;
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unsigned sign : 1;
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};
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double d;
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};
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template<>
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union FloatExtractor<float> {
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static const int mantissa_bits = 23;
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static const unsigned mantissa_max = (1 << 23) - 1;
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static const int exponent_bias = 127;
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static const int exponent_bits = 8;
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static const unsigned exponent_max = 255;
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struct {
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unsigned long long mantissa : 23;
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unsigned exponent : 8;
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unsigned sign : 1;
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};
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float d;
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};
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// This is much branchier than it really needs to be
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template<typename FloatType>
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static FloatType internal_to_integer(FloatType x, RoundingMode rounding_mode)
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{
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if (!isfinite(x))
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return x;
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using Extractor = FloatExtractor<decltype(x)>;
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Extractor extractor;
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extractor.d = x;
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auto unbiased_exponent = extractor.exponent - Extractor::exponent_bias;
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bool round = false;
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bool guard = false;
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if (unbiased_exponent < 0) {
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// it was easier to special case [0..1) as it saves us from
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// handling subnormals, underflows, etc
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if (unbiased_exponent == -1) {
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round = true;
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}
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guard = extractor.mantissa != 0;
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extractor.mantissa = 0;
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extractor.exponent = 0;
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} else {
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if (unbiased_exponent >= Extractor::mantissa_bits)
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return x;
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auto dead_bitcount = Extractor::mantissa_bits - unbiased_exponent;
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auto dead_mask = (1ull << dead_bitcount) - 1;
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auto dead_bits = extractor.mantissa & dead_mask;
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extractor.mantissa &= ~dead_mask;
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auto guard_mask = dead_mask >> 1;
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guard = (dead_bits & guard_mask) != 0;
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round = (dead_bits & ~guard_mask) != 0;
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}
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bool should_round = false;
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switch (rounding_mode) {
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case RoundingMode::ToEven:
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should_round = round;
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break;
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case RoundingMode::Up:
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if (!extractor.sign)
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should_round = guard || round;
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break;
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case RoundingMode::Down:
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if (extractor.sign)
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should_round = guard || round;
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break;
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case RoundingMode::ToZero:
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break;
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}
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if (should_round) {
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// We could do this ourselves, but this saves us from manually
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// handling overflow.
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if (extractor.sign)
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extractor.d -= static_cast<FloatType>(1.0);
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else
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extractor.d += static_cast<FloatType>(1.0);
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}
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return extractor.d;
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}
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// This is much branchier than it really needs to be
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template<typename FloatType>
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static FloatType internal_nextafter(FloatType x, bool up)
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{
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if (!isfinite(x))
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return x;
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using Extractor = FloatExtractor<decltype(x)>;
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Extractor extractor;
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extractor.d = x;
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if (x == 0) {
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if (!extractor.sign) {
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extractor.mantissa = 1;
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extractor.sign = !up;
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return extractor.d;
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}
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if (up) {
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extractor.sign = false;
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extractor.mantissa = 1;
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return extractor.d;
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}
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extractor.mantissa = 1;
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extractor.sign = up != extractor.sign;
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return extractor.d;
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}
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if (up != extractor.sign) {
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extractor.mantissa++;
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if (!extractor.mantissa) {
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// no need to normalize the mantissa as we just hit a power
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// of two.
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extractor.exponent++;
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if (extractor.exponent == Extractor::exponent_max) {
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extractor.exponent = Extractor::exponent_max - 1;
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extractor.mantissa = Extractor::mantissa_max;
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}
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}
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return extractor.d;
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}
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if (!extractor.mantissa) {
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if (extractor.exponent) {
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extractor.exponent--;
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extractor.mantissa = Extractor::mantissa_max;
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} else {
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extractor.d = 0;
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}
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return extractor.d;
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}
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extractor.mantissa--;
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if (extractor.mantissa != Extractor::mantissa_max)
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return extractor.d;
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if (extractor.exponent) {
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extractor.exponent--;
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// normalize
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extractor.mantissa <<= 1;
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} else {
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if (extractor.sign) {
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// Negative infinity
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extractor.mantissa = 0;
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extractor.exponent = Extractor::exponent_max;
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}
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}
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return extractor.d;
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}
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template<typename FloatT>
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static int internal_ilogb(FloatT x) NOEXCEPT
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{
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if (x == 0)
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return FP_ILOGB0;
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if (isnan(x))
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return FP_ILOGNAN;
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if (!isfinite(x))
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return INT_MAX;
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using Extractor = FloatExtractor<FloatT>;
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Extractor extractor;
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extractor.d = x;
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return (int)extractor.exponent - Extractor::exponent_bias;
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}
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template<typename FloatT>
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static FloatT internal_modf(FloatT x, FloatT* intpart) NOEXCEPT
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{
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FloatT integer_part = internal_to_integer(x, RoundingMode::ToZero);
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*intpart = integer_part;
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auto fraction = x - integer_part;
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if (signbit(fraction) != signbit(x))
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fraction = -fraction;
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return fraction;
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}
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template<typename FloatT>
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static FloatT internal_scalbn(FloatT x, int exponent) NOEXCEPT
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{
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if (x == 0 || !isfinite(x) || isnan(x) || exponent == 0)
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return x;
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using Extractor = FloatExtractor<FloatT>;
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Extractor extractor;
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extractor.d = x;
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if (extractor.exponent != 0) {
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extractor.exponent = clamp((int)extractor.exponent + exponent, 0, (int)Extractor::exponent_max);
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return extractor.d;
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}
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unsigned leading_mantissa_zeroes = extractor.mantissa == 0 ? 32 : __builtin_clz(extractor.mantissa);
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int shift = min((int)leading_mantissa_zeroes, exponent);
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exponent = max(exponent - shift, 0);
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extractor.exponent <<= shift;
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extractor.exponent = exponent + 1;
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return extractor.d;
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}
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template<typename FloatT>
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static FloatT internal_copysign(FloatT x, FloatT y) NOEXCEPT
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{
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using Extractor = FloatExtractor<FloatT>;
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Extractor ex, ey;
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ex.d = x;
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ey.d = y;
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ex.sign = ey.sign;
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return ex.d;
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}
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template<typename FloatT>
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static FloatT internal_gamma(FloatT x) NOEXCEPT
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{
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if (isnan(x))
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return (FloatT)NAN;
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if (x == (FloatT)0.0)
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return signbit(x) ? (FloatT)-INFINITY : (FloatT)INFINITY;
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if (x < (FloatT)0 && (rintl(x) == x || isinf(x)))
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return (FloatT)NAN;
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if (isinf(x))
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return (FloatT)INFINITY;
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using Extractor = FloatExtractor<FloatT>;
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// These constants were obtained through use of WolframAlpha
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constexpr long long max_integer_whose_factorial_fits = (Extractor::mantissa_bits == FloatExtractor<long double>::mantissa_bits ? 20 : (Extractor::mantissa_bits == FloatExtractor<double>::mantissa_bits ? 18 : (Extractor::mantissa_bits == FloatExtractor<float>::mantissa_bits ? 10 : 0)));
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static_assert(max_integer_whose_factorial_fits != 0, "internal_gamma needs to be aware of the integer factorial that fits in this floating point type.");
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if (rintl(x) == (long double)x && x <= max_integer_whose_factorial_fits) {
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long long result = 1;
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for (long long cursor = 1; cursor <= min(max_integer_whose_factorial_fits, (long long)x); cursor++)
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result *= cursor;
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return (FloatT)result;
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}
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// Stirling approximation
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return sqrtl(2.0 * M_PI / static_cast<long double>(x)) * powl(static_cast<long double>(x) / M_E, static_cast<long double>(x));
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}
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extern "C" {
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float nanf(const char* s) NOEXCEPT
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{
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return __builtin_nanf(s);
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}
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double nan(const char* s) NOEXCEPT
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{
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return __builtin_nan(s);
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}
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long double nanl(const char* s) NOEXCEPT
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{
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return __builtin_nanl(s);
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}
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double trunc(double x) NOEXCEPT
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{
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return internal_to_integer(x, RoundingMode::ToZero);
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}
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float truncf(float x) NOEXCEPT
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{
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return internal_to_integer(x, RoundingMode::ToZero);
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}
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long double truncl(long double x) NOEXCEPT
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{
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return internal_to_integer(x, RoundingMode::ToZero);
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}
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long double cosl(long double angle) NOEXCEPT
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{
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return sinl(angle + M_PI_2);
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}
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double cos(double angle) NOEXCEPT
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{
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return sin(angle + M_PI_2);
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}
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float cosf(float angle) NOEXCEPT
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{
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return sinf(angle + static_cast<float>(M_PI_2));
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}
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long double sinl(long double angle) NOEXCEPT
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{
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long double ret = 0.0;
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__asm__(
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"fsin"
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: "=t"(ret)
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: "0"(angle));
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return ret;
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}
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// This can also be done with a taylor expansion, but for
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// now this works pretty well (and doesn't mess anything up
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// in quake in particular, which is very Floating-Point precision
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// heavy)
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double sin(double angle) NOEXCEPT
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{
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double ret = 0.0;
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__asm__(
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"fsin"
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: "=t"(ret)
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: "0"(angle));
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return ret;
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}
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float sinf(float angle) NOEXCEPT
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{
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float ret = 0.0f;
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__asm__(
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"fsin"
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: "=t"(ret)
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: "0"(angle));
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return ret;
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}
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long double powl(long double x, long double y) NOEXCEPT
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{
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// FIXME: Please fix me. I am naive.
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if (isnan(y))
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return y;
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if (y == 0)
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return 1;
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if (x == 0)
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return 0;
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if (y == 1)
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return x;
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int y_as_int = (int)y;
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if (y == (long double)y_as_int) {
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long double result = x;
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for (int i = 0; i < fabsl(y) - 1; ++i)
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result *= x;
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if (y < 0)
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result = 1.0l / result;
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return result;
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}
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return exp2l(y * log2l(x));
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}
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double pow(double x, double y) NOEXCEPT
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{
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return (double)powl(x, y);
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}
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float powf(float x, float y) NOEXCEPT
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{
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return (float)powl(x, y);
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}
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// On systems where FLT_RADIX == 2, ldexp is equivalent to scalbn
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long double ldexpl(long double x, int exp) NOEXCEPT
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{
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return internal_scalbn(x, exp);
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}
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double ldexp(double x, int exp) NOEXCEPT
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{
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return internal_scalbn(x, exp);
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}
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float ldexpf(float x, int exp) NOEXCEPT
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{
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return internal_scalbn(x, exp);
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}
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long double tanhl(long double x) NOEXCEPT
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{
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if (x > 0) {
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long double exponentiated = expl(2 * x);
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return (exponentiated - 1) / (exponentiated + 1);
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}
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long double plusX = expl(x);
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long double minusX = 1 / plusX;
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return (plusX - minusX) / (plusX + minusX);
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}
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double tanh(double x) NOEXCEPT
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{
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return (double)tanhl(x);
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}
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float tanhf(float x) NOEXCEPT
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{
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return (float)tanhl(x);
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}
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[[maybe_unused]] static long double ampsin(long double angle) NOEXCEPT
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{
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long double looped_angle = fmodl(M_PI + angle, M_TAU) - M_PI;
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long double looped_angle_squared = looped_angle * looped_angle;
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long double quadratic_term;
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if (looped_angle > 0) {
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quadratic_term = -looped_angle_squared;
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} else {
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quadratic_term = looped_angle_squared;
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}
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long double linear_term = M_PI * looped_angle;
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return quadratic_term + linear_term;
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}
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long double tanl(long double angle) NOEXCEPT
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{
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long double ret = 0.0, one;
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__asm__(
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"fptan"
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: "=t"(one), "=u"(ret)
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: "0"(angle));
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return ret;
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}
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double tan(double angle) NOEXCEPT
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{
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return (double)tanl(angle);
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}
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float tanf(float angle) NOEXCEPT
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{
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return (float)tanl(angle);
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}
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long double sqrtl(long double x) NOEXCEPT
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{
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long double res;
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asm("fsqrt"
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: "=t"(res)
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: "0"(x));
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return res;
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}
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double sqrt(double x) NOEXCEPT
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{
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double res;
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__asm__("fsqrt"
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: "=t"(res)
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: "0"(x));
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return res;
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}
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float sqrtf(float x) NOEXCEPT
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{
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float res;
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__asm__("fsqrt"
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: "=t"(res)
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: "0"(x));
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return res;
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}
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long double sinhl(long double x) NOEXCEPT
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{
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long double exponentiated = expl(x);
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if (x > 0)
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return (exponentiated * exponentiated - 1) / 2 / exponentiated;
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return (exponentiated - 1 / exponentiated) / 2;
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}
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double sinh(double x) NOEXCEPT
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{
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return (double)sinhl(x);
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}
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float sinhf(float x) NOEXCEPT
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{
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return (float)sinhl(x);
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}
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|
long double log10l(long double x) NOEXCEPT
|
|
{
|
|
long double ret = 0.0l;
|
|
__asm__(
|
|
"fldlg2\n"
|
|
"fld %%st(1)\n"
|
|
"fyl2x\n"
|
|
"fstp %%st(1)"
|
|
: "=t"(ret)
|
|
: "0"(x));
|
|
return ret;
|
|
}
|
|
|
|
double log10(double x) NOEXCEPT
|
|
{
|
|
return (double)log10l(x);
|
|
}
|
|
|
|
float log10f(float x) NOEXCEPT
|
|
{
|
|
return (float)log10l(x);
|
|
}
|
|
|
|
long double logl(long double x) NOEXCEPT
|
|
{
|
|
long double ret = 0.0l;
|
|
asm(
|
|
"fldln2\n"
|
|
"fld %%st(1)\n"
|
|
"fyl2x\n"
|
|
"fstp %%st(1)"
|
|
: "=t"(ret)
|
|
: "0"(x));
|
|
return ret;
|
|
}
|
|
|
|
double log(double x) NOEXCEPT
|
|
{
|
|
return (double)logl(x);
|
|
}
|
|
|
|
float logf(float x) NOEXCEPT
|
|
{
|
|
return (float)logl(x);
|
|
}
|
|
|
|
long double fmodl(long double index, long double period) NOEXCEPT
|
|
{
|
|
return index - truncl(index / period) * period;
|
|
}
|
|
|
|
double fmod(double index, double period) NOEXCEPT
|
|
{
|
|
return index - trunc(index / period) * period;
|
|
}
|
|
|
|
float fmodf(float index, float period) NOEXCEPT
|
|
{
|
|
return index - truncf(index / period) * period;
|
|
}
|
|
|
|
// FIXME: These aren't exactly like fmod, but these definitions are probably good enough for now
|
|
long double remainderl(long double x, long double y) NOEXCEPT
|
|
{
|
|
return fmodl(x, y);
|
|
}
|
|
|
|
double remainder(double x, double y) NOEXCEPT
|
|
{
|
|
return fmod(x, y);
|
|
}
|
|
|
|
float remainderf(float x, float y) NOEXCEPT
|
|
{
|
|
return fmodf(x, y);
|
|
}
|
|
|
|
long double expl(long double exponent) NOEXCEPT
|
|
{
|
|
long double res = 0;
|
|
asm("fldl2e\n"
|
|
"fmulp\n"
|
|
"fld1\n"
|
|
"fld %%st(1)\n"
|
|
"fprem\n"
|
|
"f2xm1\n"
|
|
"faddp\n"
|
|
"fscale\n"
|
|
"fstp %%st(1)"
|
|
: "=t"(res)
|
|
: "0"(exponent));
|
|
return res;
|
|
}
|
|
|
|
double exp(double exponent) NOEXCEPT
|
|
{
|
|
return (double)expl(exponent);
|
|
}
|
|
|
|
float expf(float exponent) NOEXCEPT
|
|
{
|
|
return (float)expl(exponent);
|
|
}
|
|
|
|
long double exp2l(long double exponent) NOEXCEPT
|
|
{
|
|
long double res = 0;
|
|
asm("fld1\n"
|
|
"fld %%st(1)\n"
|
|
"fprem\n"
|
|
"f2xm1\n"
|
|
"faddp\n"
|
|
"fscale\n"
|
|
"fstp %%st(1)"
|
|
: "=t"(res)
|
|
: "0"(exponent));
|
|
return res;
|
|
}
|
|
|
|
double exp2(double exponent) NOEXCEPT
|
|
{
|
|
return (double)exp2l(exponent);
|
|
}
|
|
|
|
float exp2f(float exponent) NOEXCEPT
|
|
{
|
|
return (float)exp2l(exponent);
|
|
}
|
|
|
|
long double coshl(long double x) NOEXCEPT
|
|
{
|
|
long double exponentiated = expl(-x);
|
|
if (x < 0)
|
|
return (1 + exponentiated * exponentiated) / 2 / exponentiated;
|
|
return (1 / exponentiated + exponentiated) / 2;
|
|
}
|
|
|
|
double cosh(double x) NOEXCEPT
|
|
{
|
|
return (double)coshl(x);
|
|
}
|
|
|
|
float coshf(float x) NOEXCEPT
|
|
{
|
|
return (float)coshl(x);
|
|
}
|
|
|
|
long double atan2l(long double y, long double x) NOEXCEPT
|
|
{
|
|
if (x == 0) {
|
|
if (y > 0)
|
|
return M_PI_2;
|
|
if (y < 0)
|
|
return -M_PI_2;
|
|
return 0;
|
|
}
|
|
|
|
long double result = 0; //atanl(y / x);
|
|
__asm__("fpatan"
|
|
: "=t"(result)
|
|
: "0"(x), "u"(y)
|
|
: "st(1)");
|
|
return result;
|
|
}
|
|
|
|
double atan2(double y, double x) NOEXCEPT
|
|
{
|
|
return (double)atan2l(y, x);
|
|
}
|
|
|
|
float atan2f(float y, float x) NOEXCEPT
|
|
{
|
|
return (float)atan2l(y, x);
|
|
}
|
|
|
|
long double atanl(long double x) NOEXCEPT
|
|
{
|
|
if (x < 0)
|
|
return -atanl(-x);
|
|
if (x > 1)
|
|
return M_PI_2 - atanl(1 / x);
|
|
long double squared = x * x;
|
|
return x / (1 + 1 * 1 * squared / (3 + 2 * 2 * squared / (5 + 3 * 3 * squared / (7 + 4 * 4 * squared / (9 + 5 * 5 * squared / (11 + 6 * 6 * squared / (13 + 7 * 7 * squared)))))));
|
|
}
|
|
|
|
double atan(double x) NOEXCEPT
|
|
{
|
|
return (double)atanl(x);
|
|
}
|
|
|
|
float atanf(float x) NOEXCEPT
|
|
{
|
|
return (float)atanl(x);
|
|
}
|
|
|
|
long double asinl(long double x) NOEXCEPT
|
|
{
|
|
if (x > 1 || x < -1)
|
|
return NAN;
|
|
if (x > 0.5 || x < -0.5)
|
|
return 2 * atanl(x / (1 + sqrtl(1 - x * x)));
|
|
long double squared = x * x;
|
|
long double value = x;
|
|
long double i = x * squared;
|
|
value += i * product_odd<1>() / product_even<2>() / 3;
|
|
i *= squared;
|
|
value += i * product_odd<3>() / product_even<4>() / 5;
|
|
i *= squared;
|
|
value += i * product_odd<5>() / product_even<6>() / 7;
|
|
i *= squared;
|
|
value += i * product_odd<7>() / product_even<8>() / 9;
|
|
i *= squared;
|
|
value += i * product_odd<9>() / product_even<10>() / 11;
|
|
i *= squared;
|
|
value += i * product_odd<11>() / product_even<12>() / 13;
|
|
return value;
|
|
}
|
|
|
|
double asin(double x) NOEXCEPT
|
|
{
|
|
return (double)asinl(x);
|
|
}
|
|
|
|
float asinf(float x) NOEXCEPT
|
|
{
|
|
return (float)asinl(x);
|
|
}
|
|
|
|
long double acosl(long double x) NOEXCEPT
|
|
{
|
|
return M_PI_2 - asinl(x);
|
|
}
|
|
|
|
double acos(double x) NOEXCEPT
|
|
{
|
|
return M_PI_2 - asin(x);
|
|
}
|
|
|
|
float acosf(float x) NOEXCEPT
|
|
{
|
|
return static_cast<float>(M_PI_2) - asinf(x);
|
|
}
|
|
|
|
long double fabsl(long double value) NOEXCEPT
|
|
{
|
|
return value < 0 ? -value : value;
|
|
}
|
|
|
|
double fabs(double value) NOEXCEPT
|
|
{
|
|
return value < 0 ? -value : value;
|
|
}
|
|
|
|
float fabsf(float value) NOEXCEPT
|
|
{
|
|
return value < 0 ? -value : value;
|
|
}
|
|
|
|
int ilogbl(long double x) NOEXCEPT
|
|
{
|
|
return internal_ilogb(x);
|
|
}
|
|
|
|
int ilogb(double x) NOEXCEPT
|
|
{
|
|
return internal_ilogb(x);
|
|
}
|
|
|
|
int ilogbf(float x) NOEXCEPT
|
|
{
|
|
return internal_ilogb(x);
|
|
}
|
|
|
|
long double logbl(long double x) NOEXCEPT
|
|
{
|
|
return ilogbl(x);
|
|
}
|
|
|
|
double logb(double x) NOEXCEPT
|
|
{
|
|
return ilogb(x);
|
|
}
|
|
|
|
float logbf(float x) NOEXCEPT
|
|
{
|
|
return ilogbf(x);
|
|
}
|
|
|
|
long double log2l(long double x) NOEXCEPT
|
|
{
|
|
long double ret = 0.0;
|
|
asm(
|
|
"fld1\n"
|
|
"fld %%st(1)\n"
|
|
"fyl2x\n"
|
|
"fstp %%st(1)"
|
|
: "=t"(ret)
|
|
: "0"(x));
|
|
return ret;
|
|
}
|
|
|
|
double log2(double x) NOEXCEPT
|
|
{
|
|
return (double)log2l(x);
|
|
}
|
|
|
|
float log2f(float x) NOEXCEPT
|
|
{
|
|
return (float)log2l(x);
|
|
}
|
|
|
|
double frexp(double x, int* exp) NOEXCEPT
|
|
{
|
|
*exp = (x == 0) ? 0 : (1 + ilogb(x));
|
|
return scalbn(x, -(*exp));
|
|
}
|
|
|
|
float frexpf(float x, int* exp) NOEXCEPT
|
|
{
|
|
*exp = (x == 0) ? 0 : (1 + ilogbf(x));
|
|
return scalbnf(x, -(*exp));
|
|
}
|
|
|
|
long double frexpl(long double x, int* exp) NOEXCEPT
|
|
{
|
|
*exp = (x == 0) ? 0 : (1 + ilogbl(x));
|
|
return scalbnl(x, -(*exp));
|
|
}
|
|
|
|
double round(double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::ToEven);
|
|
}
|
|
|
|
float roundf(float value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::ToEven);
|
|
}
|
|
|
|
long double roundl(long double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::ToEven);
|
|
}
|
|
|
|
long lroundf(float value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::ToEven);
|
|
}
|
|
|
|
long lround(double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::ToEven);
|
|
}
|
|
|
|
long lroundl(long double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::ToEven);
|
|
}
|
|
|
|
long long llroundf(float value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::ToEven);
|
|
}
|
|
|
|
long long llround(double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::ToEven);
|
|
}
|
|
|
|
long long llroundd(long double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::ToEven);
|
|
}
|
|
|
|
float floorf(float value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::Down);
|
|
}
|
|
|
|
double floor(double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::Down);
|
|
}
|
|
|
|
long double floorl(long double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::Down);
|
|
}
|
|
|
|
long double rintl(long double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode { fegetround() });
|
|
}
|
|
|
|
double rint(double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode { fegetround() });
|
|
}
|
|
|
|
float rintf(float value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode { fegetround() });
|
|
}
|
|
|
|
long lrintl(long double value) NOEXCEPT
|
|
{
|
|
return (long)internal_to_integer(value, RoundingMode { fegetround() });
|
|
}
|
|
|
|
long lrint(double value) NOEXCEPT
|
|
{
|
|
return (long)internal_to_integer(value, RoundingMode { fegetround() });
|
|
}
|
|
|
|
long lrintf(float value) NOEXCEPT
|
|
{
|
|
return (long)internal_to_integer(value, RoundingMode { fegetround() });
|
|
}
|
|
|
|
long long llrintl(long double value) NOEXCEPT
|
|
{
|
|
return (long long)internal_to_integer(value, RoundingMode { fegetround() });
|
|
}
|
|
|
|
long long llrint(double value) NOEXCEPT
|
|
{
|
|
return (long long)internal_to_integer(value, RoundingMode { fegetround() });
|
|
}
|
|
|
|
long long llrintf(float value) NOEXCEPT
|
|
{
|
|
return (long long)internal_to_integer(value, RoundingMode { fegetround() });
|
|
}
|
|
|
|
float ceilf(float value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::Up);
|
|
}
|
|
|
|
double ceil(double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::Up);
|
|
}
|
|
|
|
long double ceill(long double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::Up);
|
|
}
|
|
|
|
long double modfl(long double x, long double* intpart) NOEXCEPT
|
|
{
|
|
return internal_modf(x, intpart);
|
|
}
|
|
|
|
double modf(double x, double* intpart) NOEXCEPT
|
|
{
|
|
return internal_modf(x, intpart);
|
|
}
|
|
|
|
float modff(float x, float* intpart) NOEXCEPT
|
|
{
|
|
return internal_modf(x, intpart);
|
|
}
|
|
|
|
double gamma(double x) NOEXCEPT
|
|
{
|
|
// Stirling approximation
|
|
return sqrt(2.0 * M_PI / x) * pow(x / M_E, x);
|
|
}
|
|
|
|
long double tgammal(long double value) NOEXCEPT
|
|
{
|
|
return internal_gamma(value);
|
|
}
|
|
|
|
double tgamma(double value) NOEXCEPT
|
|
{
|
|
return internal_gamma(value);
|
|
}
|
|
|
|
float tgammaf(float value) NOEXCEPT
|
|
{
|
|
return internal_gamma(value);
|
|
}
|
|
|
|
int signgam = 0;
|
|
|
|
long double lgammal(long double value) NOEXCEPT
|
|
{
|
|
return lgammal_r(value, &signgam);
|
|
}
|
|
|
|
double lgamma(double value) NOEXCEPT
|
|
{
|
|
return lgamma_r(value, &signgam);
|
|
}
|
|
|
|
float lgammaf(float value) NOEXCEPT
|
|
{
|
|
return lgammaf_r(value, &signgam);
|
|
}
|
|
|
|
long double lgammal_r(long double value, int* sign) NOEXCEPT
|
|
{
|
|
if (value == 1.0 || value == 2.0)
|
|
return 0.0;
|
|
if (isinf(value) || value == 0.0)
|
|
return INFINITY;
|
|
long double result = logl(internal_gamma(value));
|
|
*sign = signbit(result) ? -1 : 1;
|
|
return result;
|
|
}
|
|
|
|
double lgamma_r(double value, int* sign) NOEXCEPT
|
|
{
|
|
if (value == 1.0 || value == 2.0)
|
|
return 0.0;
|
|
if (isinf(value) || value == 0.0)
|
|
return INFINITY;
|
|
double result = log(internal_gamma(value));
|
|
*sign = signbit(result) ? -1 : 1;
|
|
return result;
|
|
}
|
|
|
|
float lgammaf_r(float value, int* sign) NOEXCEPT
|
|
{
|
|
if (value == 1.0f || value == 2.0f)
|
|
return 0.0;
|
|
if (isinf(value) || value == 0.0f)
|
|
return INFINITY;
|
|
float result = logf(internal_gamma(value));
|
|
*sign = signbit(result) ? -1 : 1;
|
|
return result;
|
|
}
|
|
|
|
long double expm1l(long double x) NOEXCEPT
|
|
{
|
|
return expl(x) - 1;
|
|
}
|
|
|
|
double expm1(double x) NOEXCEPT
|
|
{
|
|
return exp(x) - 1;
|
|
}
|
|
|
|
float expm1f(float x) NOEXCEPT
|
|
{
|
|
return expf(x) - 1;
|
|
}
|
|
|
|
long double cbrtl(long double x) NOEXCEPT
|
|
{
|
|
if (isinf(x) || x == 0)
|
|
return x;
|
|
if (x < 0)
|
|
return -cbrtl(-x);
|
|
|
|
long double r = x;
|
|
long double ex = 0;
|
|
|
|
while (r < 0.125l) {
|
|
r *= 8;
|
|
ex--;
|
|
}
|
|
while (r > 1.0l) {
|
|
r *= 0.125l;
|
|
ex++;
|
|
}
|
|
|
|
r = (-0.46946116l * r + 1.072302l) * r + 0.3812513l;
|
|
|
|
while (ex < 0) {
|
|
r *= 0.5l;
|
|
ex++;
|
|
}
|
|
while (ex > 0) {
|
|
r *= 2.0l;
|
|
ex--;
|
|
}
|
|
|
|
r = (2.0l / 3.0l) * r + (1.0l / 3.0l) * x / (r * r);
|
|
r = (2.0l / 3.0l) * r + (1.0l / 3.0l) * x / (r * r);
|
|
r = (2.0l / 3.0l) * r + (1.0l / 3.0l) * x / (r * r);
|
|
r = (2.0l / 3.0l) * r + (1.0l / 3.0l) * x / (r * r);
|
|
|
|
return r;
|
|
}
|
|
|
|
double cbrt(double x) NOEXCEPT
|
|
{
|
|
return (double)cbrtl(x);
|
|
}
|
|
|
|
float cbrtf(float x) NOEXCEPT
|
|
{
|
|
return (float)cbrtl(x);
|
|
}
|
|
|
|
long double log1pl(long double x) NOEXCEPT
|
|
{
|
|
return logl(1 + x);
|
|
}
|
|
|
|
double log1p(double x) NOEXCEPT
|
|
{
|
|
return log(1 + x);
|
|
}
|
|
|
|
float log1pf(float x) NOEXCEPT
|
|
{
|
|
return logf(1 + x);
|
|
}
|
|
|
|
long double acoshl(long double x) NOEXCEPT
|
|
{
|
|
return logl(x + sqrtl(x * x - 1));
|
|
}
|
|
|
|
double acosh(double x) NOEXCEPT
|
|
{
|
|
return log(x + sqrt(x * x - 1));
|
|
}
|
|
|
|
float acoshf(float x) NOEXCEPT
|
|
{
|
|
return logf(x + sqrtf(x * x - 1));
|
|
}
|
|
|
|
long double asinhl(long double x) NOEXCEPT
|
|
{
|
|
return logl(x + sqrtl(x * x + 1));
|
|
}
|
|
|
|
double asinh(double x) NOEXCEPT
|
|
{
|
|
return log(x + sqrt(x * x + 1));
|
|
}
|
|
|
|
float asinhf(float x) NOEXCEPT
|
|
{
|
|
return logf(x + sqrtf(x * x + 1));
|
|
}
|
|
|
|
long double atanhl(long double x) NOEXCEPT
|
|
{
|
|
return logl((1 + x) / (1 - x)) / 2.0l;
|
|
}
|
|
|
|
double atanh(double x) NOEXCEPT
|
|
{
|
|
return log((1 + x) / (1 - x)) / 2.0;
|
|
}
|
|
|
|
float atanhf(float x) NOEXCEPT
|
|
{
|
|
return logf((1 + x) / (1 - x)) / 2.0f;
|
|
}
|
|
|
|
long double hypotl(long double x, long double y) NOEXCEPT
|
|
{
|
|
return sqrtl(x * x + y * y);
|
|
}
|
|
|
|
double hypot(double x, double y) NOEXCEPT
|
|
{
|
|
return sqrt(x * x + y * y);
|
|
}
|
|
|
|
float hypotf(float x, float y) NOEXCEPT
|
|
{
|
|
return sqrtf(x * x + y * y);
|
|
}
|
|
|
|
long double erfl(long double x) NOEXCEPT
|
|
{
|
|
// algorithm taken from Abramowitz and Stegun (no. 26.2.17)
|
|
long double t = 1 / (1 + 0.47047l * fabsl(x));
|
|
long double poly = t * (0.3480242l + t * (-0.958798l + t * 0.7478556l));
|
|
long double answer = 1 - poly * expl(-x * x);
|
|
if (x < 0)
|
|
return -answer;
|
|
|
|
return answer;
|
|
}
|
|
|
|
double erf(double x) NOEXCEPT
|
|
{
|
|
return (double)erfl(x);
|
|
}
|
|
|
|
float erff(float x) NOEXCEPT
|
|
{
|
|
return (float)erf(x);
|
|
}
|
|
|
|
long double erfcl(long double x) NOEXCEPT
|
|
{
|
|
return 1 - erfl(x);
|
|
}
|
|
|
|
double erfc(double x) NOEXCEPT
|
|
{
|
|
return 1 - erf(x);
|
|
}
|
|
|
|
float erfcf(float x) NOEXCEPT
|
|
{
|
|
return 1 - erff(x);
|
|
}
|
|
|
|
double nextafter(double x, double target) NOEXCEPT
|
|
{
|
|
if (x == target)
|
|
return target;
|
|
return internal_nextafter(x, target >= x);
|
|
}
|
|
|
|
float nextafterf(float x, float target) NOEXCEPT
|
|
{
|
|
if (x == target)
|
|
return target;
|
|
return internal_nextafter(x, target >= x);
|
|
}
|
|
|
|
long double nextafterl(long double x, long double target) NOEXCEPT
|
|
{
|
|
return internal_nextafter(x, target >= x);
|
|
}
|
|
|
|
double nexttoward(double x, long double target) NOEXCEPT
|
|
{
|
|
if (x == target)
|
|
return target;
|
|
return internal_nextafter(x, target >= x);
|
|
}
|
|
|
|
float nexttowardf(float x, long double target) NOEXCEPT
|
|
{
|
|
if (x == target)
|
|
return target;
|
|
return internal_nextafter(x, target >= x);
|
|
}
|
|
|
|
long double nexttowardl(long double x, long double target) NOEXCEPT
|
|
{
|
|
if (x == target)
|
|
return target;
|
|
return internal_nextafter(x, target >= x);
|
|
}
|
|
|
|
float copysignf(float x, float y) NOEXCEPT
|
|
{
|
|
return internal_copysign(x, y);
|
|
}
|
|
|
|
double copysign(double x, double y) NOEXCEPT
|
|
{
|
|
return internal_copysign(x, y);
|
|
}
|
|
|
|
long double copysignl(long double x, long double y) NOEXCEPT
|
|
{
|
|
return internal_copysign(x, y);
|
|
}
|
|
|
|
float scalbnf(float x, int exponent) NOEXCEPT
|
|
{
|
|
return internal_scalbn(x, exponent);
|
|
}
|
|
|
|
double scalbn(double x, int exponent) NOEXCEPT
|
|
{
|
|
return internal_scalbn(x, exponent);
|
|
}
|
|
|
|
long double scalbnl(long double x, int exponent) NOEXCEPT
|
|
{
|
|
return internal_scalbn(x, exponent);
|
|
}
|
|
|
|
float scalbnlf(float x, long exponent) NOEXCEPT
|
|
{
|
|
return internal_scalbn(x, exponent);
|
|
}
|
|
|
|
double scalbln(double x, long exponent) NOEXCEPT
|
|
{
|
|
return internal_scalbn(x, exponent);
|
|
}
|
|
|
|
long double scalblnl(long double x, long exponent) NOEXCEPT
|
|
{
|
|
return internal_scalbn(x, exponent);
|
|
}
|
|
|
|
long double fmaxl(long double x, long double y) NOEXCEPT
|
|
{
|
|
if (isnan(x))
|
|
return y;
|
|
if (isnan(y))
|
|
return x;
|
|
|
|
return x > y ? x : y;
|
|
}
|
|
|
|
double fmax(double x, double y) NOEXCEPT
|
|
{
|
|
if (isnan(x))
|
|
return y;
|
|
if (isnan(y))
|
|
return x;
|
|
|
|
return x > y ? x : y;
|
|
}
|
|
|
|
float fmaxf(float x, float y) NOEXCEPT
|
|
{
|
|
if (isnan(x))
|
|
return y;
|
|
if (isnan(y))
|
|
return x;
|
|
|
|
return x > y ? x : y;
|
|
}
|
|
|
|
long double fminl(long double x, long double y) NOEXCEPT
|
|
{
|
|
if (isnan(x))
|
|
return y;
|
|
if (isnan(y))
|
|
return x;
|
|
|
|
return x < y ? x : y;
|
|
}
|
|
|
|
double fmin(double x, double y) NOEXCEPT
|
|
{
|
|
if (isnan(x))
|
|
return y;
|
|
if (isnan(y))
|
|
return x;
|
|
|
|
return x < y ? x : y;
|
|
}
|
|
|
|
float fminf(float x, float y) NOEXCEPT
|
|
{
|
|
if (isnan(x))
|
|
return y;
|
|
if (isnan(y))
|
|
return x;
|
|
|
|
return x < y ? x : y;
|
|
}
|
|
}
|