987cc904c2
This patch makes tgamma use an approximation that is more accurate with regards to floating point arithmetic, and fixes some issues when tgamma was called with positive integer values. It also makes lgamma set signgam to the correct value, and makes its return value be more inline with what the C standard defines.
1367 lines
29 KiB
C++
1367 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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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions are met:
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*
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* 1. Redistributions of source code must retain the above copyright notice, this
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* list of conditions and the following disclaimer.
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*
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* 2. Redistributions in binary form must reproduce the above copyright notice,
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* this list of conditions and the following disclaimer in the documentation
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* and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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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 -= 1.0;
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else
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extractor.d += 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 / x) * powl(x / M_E, 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 + 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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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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return ampsin(angle) / ampsin(M_PI_2 + angle);
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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"
|
|
: "=t"(res)
|
|
: "0"(x));
|
|
return res;
|
|
}
|
|
|
|
long double sinhl(long double x) NOEXCEPT
|
|
{
|
|
long double exponentiated = expl(x);
|
|
if (x > 0)
|
|
return (exponentiated * exponentiated - 1) / 2 / exponentiated;
|
|
return (exponentiated - 1 / exponentiated) / 2;
|
|
}
|
|
|
|
double sinh(double x) NOEXCEPT
|
|
{
|
|
return (double)sinhl(x);
|
|
}
|
|
|
|
float sinhf(float x) NOEXCEPT
|
|
{
|
|
return (float)sinhl(x);
|
|
}
|
|
|
|
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 - trunc(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)
|
|
return atanl(y / x);
|
|
if (x == 0) {
|
|
if (y > 0)
|
|
return M_PI_2;
|
|
if (y < 0)
|
|
return -M_PI_2;
|
|
return 0;
|
|
}
|
|
if (y >= 0)
|
|
return atanl(y / x) + M_PI;
|
|
return atanl(y / x) - M_PI;
|
|
}
|
|
|
|
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 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 == 1.0 || value == 2.0)
|
|
return 0.0;
|
|
if (isinf(value) || value == 0.0)
|
|
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);
|
|
}
|
|
}
|