mirror of
https://github.com/SerenityOS/serenity
synced 2024-07-09 04:44:24 +00:00
0c1ad05f50
Whenever the floating-point values are in integer range, we can use the various FCVT functions with static rounding mode to perform fast rounding. I took this opportunity to clean up the architecture differentiation for these functions, which allows us to use the software rounding implementation for all extreme and unimplemented cases, including AArch64. Also adds more round & trunc tests.
343 lines
16 KiB
C++
343 lines
16 KiB
C++
/*
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* Copyright (c) 2018-2021, Andreas Kling <kling@serenityos.org>
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*
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* SPDX-License-Identifier: BSD-2-Clause
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*/
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#include <AK/Platform.h>
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#if defined(AK_COMPILER_CLANG)
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# pragma clang optimize off
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#else
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# pragma GCC optimize("O0")
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#endif
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#include <LibTest/TestCase.h>
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#include <float.h>
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#include <math.h>
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TEST_CASE(atan2)
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{
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EXPECT_APPROXIMATE(atan2(-1, -0.0e0), -M_PI_2);
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EXPECT_APPROXIMATE(atan2(-0.0e0, -1), -M_PI);
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EXPECT_APPROXIMATE(atan2(0.0e0, -1), M_PI);
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EXPECT_APPROXIMATE(atan2(-0.0e0, 1), -0.0e0);
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EXPECT_APPROXIMATE(atan2(0.0e0, 1), 0.0e0);
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}
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TEST_CASE(trig)
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{
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EXPECT_APPROXIMATE(sin(1234), 0.601928);
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EXPECT_APPROXIMATE(cos(1234), -0.798551);
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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), 1.429257);
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EXPECT_APPROXIMATE(asin(1.0), 1.570796);
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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(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, 4.481689, 2.129279, 2.352410, 0.905148 },
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{ 20.990000, 1305693298.670892, 652846649.335446, 652846649.335446, 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), -0.693147);
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EXPECT_APPROXIMATE(log(1.1), 0.095310);
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EXPECT_APPROXIMATE(log(5), 1.609438);
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EXPECT_APPROXIMATE(log(5.5), 1.704748);
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EXPECT_APPROXIMATE(log(500), 6.214608);
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EXPECT_APPROXIMATE(log2(5), 2.321928);
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EXPECT_APPROXIMATE(log10(5), 0.698970);
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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==(Extractor const& 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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ErrorOr<void> format(FormatBuilder& builder, Extractor const& value)
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{
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TRY(builder.put_literal("{"sv));
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TRY(builder.put_u64(value.sign));
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TRY(builder.put_literal(", "sv));
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TRY(builder.put_u64(value.exponent, 16, true));
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TRY(builder.put_literal(", "sv));
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TRY(builder.put_u64(value.mantissa, 16, true));
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TRY(builder.put_literal("}"sv));
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return {};
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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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// TODO: implement denormal handling in fallback scalbn
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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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// TODO: investigate Stirling approximation implementation of gamma function
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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_CASE(fmax_and_fmin)
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{
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EXPECT(fmax(-INFINITY, 0) == 0);
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EXPECT(fmax(NAN, 12) == 12);
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EXPECT(fmax(5, NAN) == 5);
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EXPECT(isnan(fmax(NAN, NAN)));
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EXPECT(isinf(fmax(1'000'000, INFINITY)));
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EXPECT(isinf(fmin(-INFINITY, 0)));
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EXPECT(fmin(0, INFINITY) == 0);
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EXPECT(fmin(NAN, 5) == 5);
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EXPECT(fmin(0, NAN) == 0);
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EXPECT(isnan(fmin(NAN, NAN)));
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}
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TEST_CASE(acos)
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{
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EXPECT_APPROXIMATE(acos(-1), M_PI);
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EXPECT_APPROXIMATE(acos(0), 0.5 * M_PI);
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EXPECT_APPROXIMATE(acos(1), 0);
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EXPECT(isnan(acos(1.1)));
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}
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TEST_CASE(floor)
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{
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// NOTE: We run tests for all three float types since architecture-specific code may vary significantly between types.
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#define TEST_FLOOR_FOR(suffix) \
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EXPECT_EQ(floor##suffix(0.125f), 0.f); \
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EXPECT_EQ(floor##suffix(-0.125f), -1.0f); \
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EXPECT_EQ(floor##suffix(0.5f), 0.f); \
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EXPECT_EQ(floor##suffix(-0.5f), -1.0f); \
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EXPECT_EQ(floor##suffix(0.25f), 0.f); \
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EXPECT_EQ(floor##suffix(-0.25f), -1.0f); \
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EXPECT_EQ(floor##suffix(-3.0f / 2.0f), -2.0f);
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TEST_FLOOR_FOR();
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TEST_FLOOR_FOR(f);
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TEST_FLOOR_FOR(l);
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EXPECT_EQ(floor(-9999999999999.5), -10000000000000.0);
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EXPECT_EQ(floor(9999999999999.5), 9999999999999.0);
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}
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TEST_CASE(ceil)
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{
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#define TEST_CEIL_FOR(suffix) \
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EXPECT_EQ(ceil##suffix(0.125##suffix), 1.0##suffix); \
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EXPECT_EQ(ceil##suffix(-0.125##suffix), 0.##suffix); \
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EXPECT_EQ(ceil##suffix(0.5##suffix), 1.0##suffix); \
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EXPECT_EQ(ceil##suffix(-0.5##suffix), 0.##suffix); \
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EXPECT_EQ(ceil##suffix(0.25##suffix), 1.0##suffix); \
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EXPECT_EQ(ceil##suffix(-0.25##suffix), 0.##suffix); \
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|
EXPECT_EQ(ceil##suffix(-3.0##suffix / 2.0##suffix), -1.0##suffix);
|
|
|
|
TEST_CEIL_FOR();
|
|
TEST_CEIL_FOR(f);
|
|
TEST_CEIL_FOR(l);
|
|
|
|
EXPECT_EQ(ceil(9999999999999.5), 10000000000000.0);
|
|
EXPECT_EQ(ceil(-9999999999999.5), -9999999999999.0);
|
|
}
|
|
|
|
TEST_CASE(trunc)
|
|
{
|
|
#define TEST_TRUNC_FOR(suffix) \
|
|
EXPECT_EQ(trunc##suffix(0.125##suffix), 0.##suffix); \
|
|
EXPECT_EQ(trunc##suffix(-0.125##suffix), 0.##suffix); \
|
|
EXPECT_EQ(trunc##suffix(0.5##suffix), 0.##suffix); \
|
|
EXPECT_EQ(trunc##suffix(-0.5##suffix), 0.##suffix); \
|
|
EXPECT_EQ(trunc##suffix(0.25##suffix), 0.##suffix); \
|
|
EXPECT_EQ(trunc##suffix(-0.25##suffix), 0.##suffix); \
|
|
EXPECT_EQ(trunc##suffix(-3.0##suffix / 2.0##suffix), -1.0##suffix);
|
|
|
|
TEST_TRUNC_FOR();
|
|
TEST_TRUNC_FOR(f);
|
|
TEST_TRUNC_FOR(l);
|
|
|
|
EXPECT_EQ(trunc(9999999999999.5), 9999999999999.0);
|
|
EXPECT_EQ(trunc(-9999999999999.5), -9999999999999.0);
|
|
}
|
|
|
|
TEST_CASE(round)
|
|
{
|
|
#define TEST_ROUND_FOR(suffix) \
|
|
EXPECT_EQ(round##suffix(0.125##suffix), 0.##suffix); \
|
|
EXPECT_EQ(round##suffix(-0.125##suffix), 0.##suffix); \
|
|
EXPECT_EQ(round##suffix(0.5##suffix), 1.0##suffix); \
|
|
EXPECT_EQ(round##suffix(-0.5##suffix), -1.0##suffix); \
|
|
EXPECT_EQ(round##suffix(0.25##suffix), 0.##suffix); \
|
|
EXPECT_EQ(round##suffix(-0.25##suffix), 0.##suffix); \
|
|
EXPECT_EQ(round##suffix(-3.0##suffix / 2.0##suffix), -2.0##suffix);
|
|
|
|
TEST_ROUND_FOR();
|
|
TEST_ROUND_FOR(f);
|
|
TEST_ROUND_FOR(l);
|
|
|
|
EXPECT_EQ(round(9999999999999.5), 10000000000000.0);
|
|
EXPECT_EQ(round(-9999999999999.5), -10000000000000.0);
|
|
}
|