mirror of
https://github.com/RGBCube/serenity
synced 2025-05-27 23:45:07 +00:00
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.
250 lines
13 KiB
C++
250 lines
13 KiB
C++
/*
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* Copyright (c) 2018-2021, 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 <AK/TestSuite.h>
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#include <float.h>
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#include <math.h>
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TEST_CASE(trig)
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{
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EXPECT_APPROXIMATE(sin(1234), 0.601927);
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EXPECT_APPROXIMATE(cos(1234), -0.798550);
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EXPECT_APPROXIMATE(tan(1234), -0.753775);
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EXPECT_APPROXIMATE(sqrt(1234), 35.128336);
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EXPECT_APPROXIMATE(sin(-1), -0.8414709848078965);
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EXPECT_APPROXIMATE(cos(-1), 0.5403023058681398);
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EXPECT_APPROXIMATE(tan(-1), -1.5574077246549023);
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EXPECT(isnan(sqrt(-1)));
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EXPECT(isnan(asin(1.1)));
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EXPECT(isnan(asin(-1.1)));
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EXPECT_APPROXIMATE(asin(0), 0.0);
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EXPECT_APPROXIMATE(asin(0.01), 0.01);
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EXPECT_APPROXIMATE(asin(0.1), 0.100167);
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EXPECT_APPROXIMATE(asin(0.3), 0.304693);
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EXPECT_APPROXIMATE(asin(0.499), 0.522444);
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EXPECT_APPROXIMATE(asin(0.5), 0.523599);
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EXPECT_APPROXIMATE(asin(0.501), 0.524754);
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EXPECT_APPROXIMATE(asin(0.9), 1.119770);
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EXPECT_APPROXIMATE(asin(0.99), 1.429245);
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EXPECT_APPROXIMATE(asin(1.0), 1.570750);
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EXPECT_APPROXIMATE(atan(0), 0.0);
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EXPECT_APPROXIMATE(atan(0.5), 0.463648);
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EXPECT_APPROXIMATE(atan(-0.5), -0.463648);
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EXPECT_APPROXIMATE(atan(5.5), 1.390943);
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EXPECT_APPROXIMATE(atan(-5.5), -1.390943);
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EXPECT_APPROXIMATE(atan(555.5), 1.568996);
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}
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TEST_CASE(other)
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{
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EXPECT_EQ(trunc(9999999999999.5), 9999999999999.0);
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EXPECT_EQ(trunc(-9999999999999.5), -9999999999999.0);
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}
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TEST_CASE(exponents)
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{
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struct values {
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double x;
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double exp;
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double sinh;
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double cosh;
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double tanh;
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};
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values values[8] {
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{ 1.500000, 4.481626, 2.129246, 2.352379, 0.905148 },
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{ 20.990000, 1304956710.432035, 652478355.216017, 652478355.216017, 1.000000 },
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{ 20.010000, 490041186.687082, 245020593.343541, 245020593.343541, 1.000000 },
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{ 0.000000, 1.000000, 0.000000, 1.000000, 0.000000 },
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{ 0.010000, 1.010050, 0.010000, 1.000050, 0.010000 },
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{ -0.010000, 0.990050, -0.010000, 1.000050, -0.010000 },
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{ -1.000000, 0.367879, -1.175201, 1.543081, -0.761594 },
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{ -17.000000, 0.000000, -12077476.376788, 12077476.376788, -1.000000 },
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};
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for (auto& v : values) {
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EXPECT_APPROXIMATE(exp(v.x), v.exp);
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EXPECT_APPROXIMATE(sinh(v.x), v.sinh);
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EXPECT_APPROXIMATE(cosh(v.x), v.cosh);
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EXPECT_APPROXIMATE(tanh(v.x), v.tanh);
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}
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EXPECT_EQ(exp(1000), __builtin_huge_val());
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}
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TEST_CASE(logarithms)
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{
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EXPECT(isnan(log(-1)));
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EXPECT(log(0) < -1000000);
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EXPECT_APPROXIMATE(log(0.5), -0.693233);
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EXPECT_APPROXIMATE(log(1.1), 0.095310);
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EXPECT_APPROXIMATE(log(5), 1.609480);
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EXPECT_APPROXIMATE(log(5.5), 1.704842);
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EXPECT_APPROXIMATE(log(500), 6.214104);
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EXPECT_APPROXIMATE(log2(5), 2.321989);
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EXPECT_APPROXIMATE(log10(5), 0.698988);
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}
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union Extractor {
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explicit Extractor(double d)
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: d(d)
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{
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}
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Extractor(unsigned sign, unsigned exponent, unsigned long long mantissa)
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: mantissa(mantissa)
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, exponent(exponent)
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, sign(sign)
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{
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}
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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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bool operator==(const Extractor& other) const
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{
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return other.sign == sign && other.exponent == exponent && other.mantissa == mantissa;
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}
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};
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namespace AK {
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template<>
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struct Formatter<Extractor> : StandardFormatter {
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void format(FormatBuilder& builder, const Extractor& value)
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{
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builder.put_literal("{");
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builder.put_u64(value.sign);
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builder.put_literal(", ");
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builder.put_u64(value.exponent, 16, true);
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builder.put_literal(", ");
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builder.put_u64(value.mantissa, 16, true);
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builder.put_literal("}");
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}
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};
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}
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static Extractor nextafter_translator(Extractor x, Extractor target)
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{
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return Extractor(nextafter(x.d, target.d));
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}
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TEST_CASE(nextafter)
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{
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x1, 0x0), Extractor(0x0, 0x412, 0xe848000000000)), Extractor(0x0, 0x1, 0x1));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x3ff, 0x0), Extractor(0x0, 0x412, 0xe848200000000)), Extractor(0x0, 0x3ff, 0x1));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x0), Extractor(0x0, 0x412, 0xe848000000000)), Extractor(0x0, 0x0, 0x1));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x0), Extractor(0x0, 0x412, 0xe848000000000)), Extractor(0x0, 0x0, 0x1));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x3ff, 0x0), Extractor(0x0, 0x412, 0xe847e00000000)), Extractor(0x1, 0x3fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x1), Extractor(0x0, 0x412, 0xe848000000000)), Extractor(0x0, 0x0, 0x2));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe848000000000), Extractor(0x0, 0x1, 0x0)), Extractor(0x0, 0x412, 0xe847fffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe848200000000), Extractor(0x0, 0x3ff, 0x0)), Extractor(0x0, 0x412, 0xe8481ffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe848000000000), Extractor(0x1, 0x0, 0x0)), Extractor(0x0, 0x412, 0xe847fffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe848000000000), Extractor(0x0, 0x0, 0x0)), Extractor(0x0, 0x412, 0xe847fffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe847e00000000), Extractor(0x1, 0x3ff, 0x0)), Extractor(0x0, 0x412, 0xe847dffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe848000000000), Extractor(0x0, 0x0, 0x1)), Extractor(0x0, 0x412, 0xe847fffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x1, 0x0), Extractor(0x0, 0x1, 0x0)), Extractor(0x0, 0x1, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x3ff, 0x0), Extractor(0x0, 0x3ff, 0x0)), Extractor(0x0, 0x3ff, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x0), Extractor(0x1, 0x0, 0x0)), Extractor(0x1, 0x0, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x0), Extractor(0x0, 0x0, 0x0)), Extractor(0x0, 0x0, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x3ff, 0x0), Extractor(0x1, 0x3ff, 0x0)), Extractor(0x1, 0x3ff, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x1), Extractor(0x0, 0x0, 0x1)), Extractor(0x0, 0x0, 0x1));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x1, 0x7fe, 0xffffffffffffe));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x1, 0x0), Extractor(0x0, 0x1, 0x0)), Extractor(0x1, 0x0, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x3ff, 0x0), Extractor(0x0, 0x3ff, 0x0)), Extractor(0x1, 0x3fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x0), Extractor(0x1, 0x0, 0x0)), Extractor(0x1, 0x0, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x0), Extractor(0x0, 0x0, 0x0)), Extractor(0x0, 0x0, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x3ff, 0x0), Extractor(0x1, 0x3ff, 0x0)), Extractor(0x0, 0x3fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x1), Extractor(0x0, 0x0, 0x1)), Extractor(0x1, 0x0, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x1, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xffffffffffffe));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x1, 0x0), Extractor(0x1, 0x1, 0x0)), Extractor(0x0, 0x0, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x3ff, 0x0), Extractor(0x1, 0x3ff, 0x0)), Extractor(0x0, 0x3fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x0), Extractor(0x0, 0x0, 0x0)), Extractor(0x0, 0x0, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x0), Extractor(0x1, 0x0, 0x0)), Extractor(0x1, 0x0, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x3ff, 0x0), Extractor(0x0, 0x3ff, 0x0)), Extractor(0x1, 0x3fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x1), Extractor(0x1, 0x0, 0x1)), Extractor(0x0, 0x0, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x1, 0x0), Extractor(0x1, 0x419, 0x7d78400000000)), Extractor(0x0, 0x0, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x3ff, 0x0), Extractor(0x1, 0x419, 0x7d783fc000000)), Extractor(0x0, 0x3fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x0), Extractor(0x1, 0x419, 0x7d78400000000)), Extractor(0x1, 0x0, 0x1));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x0), Extractor(0x1, 0x419, 0x7d78400000000)), Extractor(0x1, 0x0, 0x1));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x3ff, 0x0), Extractor(0x1, 0x419, 0x7d78404000000)), Extractor(0x1, 0x3ff, 0x1));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x1), Extractor(0x1, 0x419, 0x7d78400000000)), Extractor(0x0, 0x0, 0x0));
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EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xfffffffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d78400000000), Extractor(0x0, 0x1, 0x0)), Extractor(0x1, 0x419, 0x7d783ffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d783fc000000), Extractor(0x0, 0x3ff, 0x0)), Extractor(0x1, 0x419, 0x7d783fbffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d78400000000), Extractor(0x1, 0x0, 0x0)), Extractor(0x1, 0x419, 0x7d783ffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d78400000000), Extractor(0x0, 0x0, 0x0)), Extractor(0x1, 0x419, 0x7d783ffffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d78404000000), Extractor(0x1, 0x3ff, 0x0)), Extractor(0x1, 0x419, 0x7d78403ffffff));
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EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d78400000000), Extractor(0x0, 0x0, 0x1)), Extractor(0x1, 0x419, 0x7d783ffffffff));
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}
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TEST_CASE(scalbn)
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{
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EXPECT(isnan(scalbn(NAN, 3)));
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EXPECT(!isfinite(scalbn(INFINITY, 5)));
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EXPECT_EQ(scalbn(0, 3), 0);
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EXPECT_EQ(scalbn(15.3, 0), 15.3);
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EXPECT_EQ(scalbn(0x0.0000000000008p-1022, 16), 0x0.0000000000008p-1006);
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static constexpr auto biggest_subnormal = DBL_MIN - DBL_TRUE_MIN;
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auto smallest_normal = scalbn(biggest_subnormal, 1);
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Extractor ex(smallest_normal);
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EXPECT(ex.exponent != 0);
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EXPECT_EQ(scalbn(2.0, 4), 32.0);
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}
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TEST_CASE(gamma)
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{
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EXPECT(isinf(tgamma(+0.0)) && !signbit(tgamma(+0.0)));
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EXPECT(isinf(tgamma(-0.0)) && signbit(tgamma(-0.0)));
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EXPECT(isinf(tgamma(INFINITY)) && !signbit(tgamma(INFINITY)));
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EXPECT(isnan(tgamma(NAN)));
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EXPECT(isnan(tgamma(-INFINITY)));
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EXPECT(isnan(tgamma(-5)));
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EXPECT_APPROXIMATE(tgamma(0.5), sqrt(M_PI));
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EXPECT_EQ(tgammal(21.0l), 2'432'902'008'176'640'000.0l);
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EXPECT_EQ(tgamma(19.0), 6'402'373'705'728'000.0);
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EXPECT_EQ(tgammaf(11.0f), 3628800.0f);
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EXPECT_EQ(tgamma(4.0), 6);
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EXPECT_EQ(lgamma(1.0), 0.0);
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EXPECT_EQ(lgamma(2.0), 0.0);
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EXPECT(isinf(lgamma(0.0)));
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EXPECT(!signbit(lgamma(-0.0)));
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EXPECT(isnan(lgamma(NAN)));
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EXPECT(isinf(lgamma(INFINITY)));
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EXPECT(isinf(lgamma(-INFINITY)));
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EXPECT_EQ(signgam, 1);
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lgamma(-2.5);
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EXPECT_EQ(signgam, -1);
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}
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TEST_MAIN(Math)
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