5d180d1f99
(...and ASSERT_NOT_REACHED => VERIFY_NOT_REACHED) Since all of these checks are done in release builds as well, let's rename them to VERIFY to prevent confusion, as everyone is used to assertions being compiled out in release. We can introduce a new ASSERT macro that is specifically for debug checks, but I'm doing this wholesale conversion first since we've accumulated thousands of these already, and it's not immediately obvious which ones are suitable for ASSERT.
745 lines
17 KiB
C++
745 lines
17 KiB
C++
/*
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* Copyright (c) 2018-2020, Andreas Kling <kling@serenityos.org>
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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 <LibC/assert.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,
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Up,
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Down,
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ToEven
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};
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template<typename T>
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union FloatExtractor;
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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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extern "C" {
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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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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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// 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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double pow(double x, 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 == (double)y_as_int) {
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double result = x;
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for (int i = 0; i < fabs(y) - 1; ++i)
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result *= x;
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if (y < 0)
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result = 1.0 / result;
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return result;
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}
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return exp2(y * log2(x));
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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)pow(x, y);
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}
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double ldexp(double x, int exp) NOEXCEPT
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{
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return x * exp2(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 x * exp2f(exp);
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}
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double tanh(double x) NOEXCEPT
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{
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if (x > 0) {
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double exponentiated = exp(2 * x);
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return (exponentiated - 1) / (exponentiated + 1);
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}
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double plusX = exp(x);
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double minusX = 1 / plusX;
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return (plusX - minusX) / (plusX + minusX);
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}
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static double ampsin(double angle) NOEXCEPT
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{
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double looped_angle = fmod(M_PI + angle, M_TAU) - M_PI;
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double looped_angle_squared = looped_angle * looped_angle;
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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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double linear_term = M_PI * looped_angle;
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return quadratic_term + linear_term;
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}
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double tan(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 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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double sinh(double x) NOEXCEPT
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{
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double exponentiated = exp(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 log10(double x) NOEXCEPT
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{
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double ret = 0.0;
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__asm__(
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"fldlg2\n"
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"fld %%st(1)\n"
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"fyl2x\n"
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"fstp %%st(1)"
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: "=t"(ret)
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: "0"(x));
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return ret;
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}
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double log(double x) NOEXCEPT
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{
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double ret = 0.0;
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__asm__(
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"fldln2\n"
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"fld %%st(1)\n"
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"fyl2x\n"
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"fstp %%st(1)"
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: "=t"(ret)
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: "0"(x));
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return ret;
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}
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float logf(float x) NOEXCEPT
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{
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return (float)log(x);
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}
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double fmod(double index, double period) NOEXCEPT
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{
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return index - trunc(index / period) * period;
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}
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float fmodf(float index, float period) NOEXCEPT
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{
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return index - trunc(index / period) * period;
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}
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double exp(double exponent) NOEXCEPT
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{
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double res = 0;
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__asm__("fldl2e\n"
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"fmulp\n"
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"fld1\n"
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"fld %%st(1)\n"
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"fprem\n"
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"f2xm1\n"
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"faddp\n"
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"fscale\n"
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"fstp %%st(1)"
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: "=t"(res)
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: "0"(exponent));
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return res;
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}
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float expf(float exponent) NOEXCEPT
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{
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return (float)exp(exponent);
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}
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double exp2(double exponent) NOEXCEPT
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{
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double res = 0;
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__asm__("fld1\n"
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"fld %%st(1)\n"
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"fprem\n"
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"f2xm1\n"
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"faddp\n"
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"fscale\n"
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"fstp %%st(1)"
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: "=t"(res)
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: "0"(exponent));
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return res;
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}
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float exp2f(float exponent) NOEXCEPT
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{
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return (float)exp2(exponent);
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}
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double cosh(double x) NOEXCEPT
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{
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double exponentiated = exp(-x);
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if (x < 0)
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return (1 + exponentiated * exponentiated) / 2 / exponentiated;
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return (1 / exponentiated + exponentiated) / 2;
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}
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double atan2(double y, double x) NOEXCEPT
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{
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if (x > 0)
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return atan(y / x);
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if (x == 0) {
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if (y > 0)
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return M_PI_2;
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if (y < 0)
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return -M_PI_2;
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return 0;
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}
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if (y >= 0)
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return atan(y / x) + M_PI;
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return atan(y / x) - M_PI;
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}
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float atan2f(float y, float x) NOEXCEPT
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{
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return (float)atan2(y, x);
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}
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double atan(double x) NOEXCEPT
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{
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if (x < 0)
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return -atan(-x);
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if (x > 1)
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return M_PI_2 - atan(1 / x);
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double squared = x * x;
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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)))))));
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}
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double asin(double x) NOEXCEPT
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{
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if (x > 1 || x < -1)
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return NAN;
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if (x > 0.5 || x < -0.5)
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return 2 * atan(x / (1 + sqrt(1 - x * x)));
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double squared = x * x;
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double value = x;
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double i = x * squared;
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value += i * product_odd<1>() / product_even<2>() / 3;
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i *= squared;
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value += i * product_odd<3>() / product_even<4>() / 5;
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i *= squared;
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value += i * product_odd<5>() / product_even<6>() / 7;
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i *= squared;
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value += i * product_odd<7>() / product_even<8>() / 9;
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i *= squared;
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value += i * product_odd<9>() / product_even<10>() / 11;
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i *= squared;
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value += i * product_odd<11>() / product_even<12>() / 13;
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return value;
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}
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float asinf(float x) NOEXCEPT
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{
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return (float)asin(x);
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}
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double acos(double x) NOEXCEPT
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{
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return M_PI_2 - asin(x);
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}
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float acosf(float x) NOEXCEPT
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{
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return M_PI_2 - asinf(x);
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}
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double fabs(double value) NOEXCEPT
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{
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return value < 0 ? -value : value;
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}
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double log2(double x) NOEXCEPT
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{
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double ret = 0.0;
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__asm__(
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"fld1\n"
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"fld %%st(1)\n"
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"fyl2x\n"
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"fstp %%st(1)"
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: "=t"(ret)
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: "0"(x));
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return ret;
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}
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float log2f(float x) NOEXCEPT
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{
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return log2(x);
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}
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long double log2l(long double x) NOEXCEPT
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{
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return log2(x);
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}
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double frexp(double, int*) NOEXCEPT
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{
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VERIFY_NOT_REACHED();
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return 0;
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}
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float frexpf(float, int*) NOEXCEPT
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{
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VERIFY_NOT_REACHED();
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return 0;
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}
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long double frexpl(long double, int*) NOEXCEPT
|
|
{
|
|
VERIFY_NOT_REACHED();
|
|
return 0;
|
|
}
|
|
|
|
double round(double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::ToEven);
|
|
}
|
|
|
|
float roundf(float 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);
|
|
}
|
|
|
|
double rint(double value) NOEXCEPT
|
|
{
|
|
// This should be the current rounding mode
|
|
return internal_to_integer(value, RoundingMode::ToEven);
|
|
}
|
|
|
|
float ceilf(float value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::Up);
|
|
}
|
|
|
|
double ceil(double value) NOEXCEPT
|
|
{
|
|
return internal_to_integer(value, RoundingMode::Up);
|
|
}
|
|
|
|
double modf(double x, double* intpart) NOEXCEPT
|
|
{
|
|
double integer_part = internal_to_integer(x, RoundingMode::ToZero);
|
|
*intpart = integer_part;
|
|
auto fraction = x - integer_part;
|
|
if (signbit(fraction) != signbit(x))
|
|
fraction = -fraction;
|
|
return fraction;
|
|
}
|
|
|
|
double gamma(double x) NOEXCEPT
|
|
{
|
|
// Stirling approximation
|
|
return sqrt(2.0 * M_PI / x) * pow(x / M_E, x);
|
|
}
|
|
|
|
double expm1(double x) NOEXCEPT
|
|
{
|
|
return exp(x) - 1;
|
|
}
|
|
|
|
double cbrt(double x) NOEXCEPT
|
|
{
|
|
if (isinf(x) || x == 0)
|
|
return x;
|
|
if (x < 0)
|
|
return -cbrt(-x);
|
|
|
|
double r = x;
|
|
double ex = 0;
|
|
|
|
while (r < 0.125) {
|
|
r *= 8;
|
|
ex--;
|
|
}
|
|
while (r > 1.0) {
|
|
r *= 0.125;
|
|
ex++;
|
|
}
|
|
|
|
r = (-0.46946116 * r + 1.072302) * r + 0.3812513;
|
|
|
|
while (ex < 0) {
|
|
r *= 0.5;
|
|
ex++;
|
|
}
|
|
while (ex > 0) {
|
|
r *= 2;
|
|
ex--;
|
|
}
|
|
|
|
r = (2.0 / 3.0) * r + (1.0 / 3.0) * x / (r * r);
|
|
r = (2.0 / 3.0) * r + (1.0 / 3.0) * x / (r * r);
|
|
r = (2.0 / 3.0) * r + (1.0 / 3.0) * x / (r * r);
|
|
r = (2.0 / 3.0) * r + (1.0 / 3.0) * x / (r * r);
|
|
|
|
return r;
|
|
}
|
|
|
|
double log1p(double x) NOEXCEPT
|
|
{
|
|
return log(1 + x);
|
|
}
|
|
|
|
double acosh(double x) NOEXCEPT
|
|
{
|
|
return log(x + sqrt(x * x - 1));
|
|
}
|
|
|
|
double asinh(double x) NOEXCEPT
|
|
{
|
|
return log(x + sqrt(x * x + 1));
|
|
}
|
|
|
|
double atanh(double x) NOEXCEPT
|
|
{
|
|
return log((1 + x) / (1 - x)) / 2.0;
|
|
}
|
|
|
|
double hypot(double x, double y) NOEXCEPT
|
|
{
|
|
return sqrt(x * x + y * y);
|
|
}
|
|
|
|
double erf(double x) NOEXCEPT
|
|
{
|
|
// algorithm taken from Abramowitz and Stegun (no. 26.2.17)
|
|
double t = 1 / (1 + 0.47047 * fabs(x));
|
|
double poly = t * (0.3480242 + t * (-0.958798 + t * 0.7478556));
|
|
double answer = 1 - poly * exp(-x * x);
|
|
if (x < 0)
|
|
return -answer;
|
|
|
|
return answer;
|
|
}
|
|
|
|
double erfc(double x) NOEXCEPT
|
|
{
|
|
return 1 - erf(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, long double) NOEXCEPT
|
|
{
|
|
TODO();
|
|
}
|
|
|
|
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, long double) NOEXCEPT
|
|
{
|
|
TODO();
|
|
}
|
|
}
|