Use a combination of polynomial approximation and Newton-Raphson
iterations in 64-bit and 128-bit integers to improve the performance of
sqrtf128. The correct rounding is provided by squaring the result and
comparing it with the argument.
Performance improvement using the newly added perf test:
- My function = the improved implementation from this PR
- Other function = current implementation using
`libc/src/__support/FPUtil/generic/sqrt.h`
```
Performance tests with inputs in denormal range:
-- My function --
Total time : 1260765265 ns
Average runtime : 125.951 ns/op
Ops per second : 7939623 op/s
-- Other function --
Total time : 7160726518 ns
Average runtime : 715.357 ns/op
Ops per second : 1397902 op/s
-- Average runtime ratio --
Mine / Other's : 0.176067
Performance tests with inputs in normal range:
-- My function --
Total time : 373003808 ns
Average runtime : 37.2631 ns/op
Ops per second : 26836189 op/s
-- Other function --
Total time : 7353398916 ns
Average runtime : 734.605 ns/op
Ops per second : 1361275 op/s
-- Average runtime ratio --
Mine / Other's : 0.0507254
```
---------
Co-authored-by: Alexei Sibidanov <sibid@uvic.ca>
455 lines
22 KiB
C++
455 lines
22 KiB
C++
//===-- FPMatchers.h --------------------------------------------*- C++ -*-===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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#ifndef LLVM_LIBC_TEST_UNITTEST_FPMATCHER_H
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#define LLVM_LIBC_TEST_UNITTEST_FPMATCHER_H
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#include "src/__support/CPP/array.h"
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#include "src/__support/CPP/type_traits.h"
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#include "src/__support/FPUtil/FEnvImpl.h"
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#include "src/__support/FPUtil/FPBits.h"
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#include "src/__support/FPUtil/fpbits_str.h"
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#include "src/__support/macros/config.h"
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#include "src/__support/macros/properties/architectures.h"
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#include "test/UnitTest/RoundingModeUtils.h"
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#include "test/UnitTest/StringUtils.h"
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#include "test/UnitTest/Test.h"
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#include "hdr/math_macros.h"
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using LIBC_NAMESPACE::Sign;
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namespace LIBC_NAMESPACE_DECL {
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namespace testing {
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template <typename T, TestCond Condition> class FPMatcher : public Matcher<T> {
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static_assert(cpp::is_floating_point_v<T>,
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"FPMatcher can only be used with floating point values.");
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static_assert(Condition == TestCond::EQ || Condition == TestCond::NE,
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"Unsupported FPMatcher test condition.");
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T expected;
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T actual;
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public:
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FPMatcher(T expectedValue) : expected(expectedValue) {}
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bool match(T actualValue) {
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actual = actualValue;
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fputil::FPBits<T> actualBits(actual), expectedBits(expected);
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if (Condition == TestCond::EQ)
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return (actualBits.is_nan() && expectedBits.is_nan()) ||
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(actualBits.uintval() == expectedBits.uintval());
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// If condition == TestCond::NE.
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if (actualBits.is_nan())
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return !expectedBits.is_nan();
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return expectedBits.is_nan() ||
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(actualBits.uintval() != expectedBits.uintval());
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}
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void explainError() override {
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tlog << "Expected floating point value: "
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<< str(fputil::FPBits<T>(expected)) << '\n';
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tlog << "Actual floating point value: " << str(fputil::FPBits<T>(actual))
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<< '\n';
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}
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};
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template <typename T, TestCond Condition> class CFPMatcher : public Matcher<T> {
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static_assert(
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cpp::is_complex_v<T>,
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"CFPMatcher can only be used with complex floating point values.");
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static_assert(Condition == TestCond::EQ || Condition == TestCond::NE,
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"Unsupported CFPMatcher test condition.");
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T expected;
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T actual;
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public:
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CFPMatcher(T expectedValue) : expected(expectedValue) {}
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template <typename CFT> bool matchComplex() {
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CFT *actualCmplxPtr = reinterpret_cast<CFT *>(&actual);
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CFT *expectedCmplxPtr = reinterpret_cast<CFT *>(&expected);
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CFT actualReal = actualCmplxPtr[0];
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CFT actualImag = actualCmplxPtr[1];
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CFT expectedReal = expectedCmplxPtr[0];
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CFT expectedImag = expectedCmplxPtr[1];
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fputil::FPBits<CFT> actualRealBits(actualReal),
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expectedRealBits(expectedReal);
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fputil::FPBits<CFT> actualImagBits(actualImag),
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expectedImagBits(expectedImag);
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if (Condition == TestCond::EQ)
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return ((actualRealBits.is_nan() && expectedRealBits.is_nan()) ||
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(actualRealBits.uintval() == expectedRealBits.uintval())) &&
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((actualImagBits.is_nan() && expectedImagBits.is_nan()) ||
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(actualImagBits.uintval() == expectedImagBits.uintval()));
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// If condition == TestCond::NE.
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if (actualRealBits.is_nan() && expectedRealBits.is_nan())
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return !expectedRealBits.is_nan() && !expectedImagBits.is_nan();
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if (actualRealBits.is_nan())
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return !expectedRealBits.is_nan();
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if (actualImagBits.is_nan())
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return !expectedImagBits.is_nan();
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return (expectedRealBits.is_nan() ||
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actualRealBits.uintval() != expectedRealBits.uintval()) &&
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(expectedImagBits.is_nan() ||
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actualImagBits.uintval() != expectedImagBits.uintval());
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}
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template <typename CFT> void explainErrorComplex() {
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CFT *actualCmplxPtr = reinterpret_cast<CFT *>(&actual);
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CFT *expectedCmplxPtr = reinterpret_cast<CFT *>(&expected);
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CFT actualReal = actualCmplxPtr[0];
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CFT actualImag = actualCmplxPtr[1];
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CFT expectedReal = expectedCmplxPtr[0];
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CFT expectedImag = expectedCmplxPtr[1];
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tlog << "Expected complex floating point value: "
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<< str(fputil::FPBits<CFT>(expectedReal)) + " + " +
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str(fputil::FPBits<CFT>(expectedImag)) + "i"
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<< '\n';
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tlog << "Actual complex floating point value: "
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<< str(fputil::FPBits<CFT>(actualReal)) + " + " +
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str(fputil::FPBits<CFT>(actualImag)) + "i"
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<< '\n';
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}
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bool match(T actualValue) {
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actual = actualValue;
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if constexpr (cpp::is_complex_type_same<T, _Complex float>())
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return matchComplex<float>();
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else if constexpr (cpp::is_complex_type_same<T, _Complex double>())
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return matchComplex<double>();
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else if constexpr (cpp::is_complex_type_same<T, _Complex long double>())
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return matchComplex<long double>();
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#ifdef LIBC_TYPES_HAS_CFLOAT16
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else if constexpr (cpp::is_complex_type_same<T, cfloat16>())
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return matchComplex<float16>();
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#endif
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#ifdef LIBC_TYPES_HAS_CFLOAT128
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else if constexpr (cpp::is_complex_type_same<T, cfloat128>())
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return matchComplex<float128>();
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#endif
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}
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void explainError() override {
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if constexpr (cpp::is_complex_type_same<T, _Complex float>())
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return explainErrorComplex<float>();
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else if constexpr (cpp::is_complex_type_same<T, _Complex double>())
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return explainErrorComplex<double>();
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else if constexpr (cpp::is_complex_type_same<T, _Complex long double>())
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return explainErrorComplex<long double>();
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#ifdef LIBC_TYPES_HAS_CFLOAT16
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else if constexpr (cpp::is_complex_type_same<T, cfloat16>())
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return explainErrorComplex<float16>();
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#endif
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#ifdef LIBC_TYPES_HAS_CFLOAT128
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else if constexpr (cpp::is_complex_type_same<T, cfloat128>())
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return explainErrorComplex<float128>();
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#endif
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}
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};
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template <TestCond C, typename T> FPMatcher<T, C> getMatcher(T expectedValue) {
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return FPMatcher<T, C>(expectedValue);
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}
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template <TestCond C, typename T>
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CFPMatcher<T, C> getMatcherComplex(T expectedValue) {
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return CFPMatcher<T, C>(expectedValue);
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}
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template <typename T> struct FPTest : public Test {
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using FPBits = LIBC_NAMESPACE::fputil::FPBits<T>;
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using StorageType = typename FPBits::StorageType;
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static constexpr StorageType STORAGE_MAX =
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LIBC_NAMESPACE::cpp::numeric_limits<StorageType>::max();
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static constexpr T zero = FPBits::zero(Sign::POS).get_val();
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static constexpr T neg_zero = FPBits::zero(Sign::NEG).get_val();
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static constexpr T aNaN = FPBits::quiet_nan(Sign::POS).get_val();
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static constexpr T neg_aNaN = FPBits::quiet_nan(Sign::NEG).get_val();
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static constexpr T sNaN = FPBits::signaling_nan().get_val();
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static constexpr T inf = FPBits::inf(Sign::POS).get_val();
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static constexpr T neg_inf = FPBits::inf(Sign::NEG).get_val();
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static constexpr T min_normal = FPBits::min_normal().get_val();
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static constexpr T max_normal = FPBits::max_normal(Sign::POS).get_val();
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static constexpr T neg_max_normal = FPBits::max_normal(Sign::NEG).get_val();
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static constexpr T min_denormal = FPBits::min_subnormal().get_val();
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static constexpr T max_denormal = FPBits::max_subnormal().get_val();
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static constexpr int N_ROUNDING_MODES = 4;
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static constexpr fputil::testing::RoundingMode ROUNDING_MODES[4] = {
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fputil::testing::RoundingMode::Nearest,
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fputil::testing::RoundingMode::Upward,
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fputil::testing::RoundingMode::Downward,
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fputil::testing::RoundingMode::TowardZero,
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};
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};
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// Add facility to test Flush-Denormal-To-Zero (FTZ) and Denormal-As-Zero (DAZ)
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// modes.
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// These tests to ensure that our implementations will not crash under these
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// modes.
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#if defined(LIBC_TARGET_ARCH_IS_X86_64) && __has_builtin(__builtin_ia32_stmxcsr)
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#define LIBC_TEST_FTZ_DAZ
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static constexpr unsigned FTZ = 0x8000; // Flush denormal to zero
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static constexpr unsigned DAZ = 0x0040; // Denormal as zero
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struct ModifyMXCSR {
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ModifyMXCSR(unsigned flags) {
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old_mxcsr = __builtin_ia32_stmxcsr();
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__builtin_ia32_ldmxcsr(old_mxcsr | flags);
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}
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~ModifyMXCSR() { __builtin_ia32_ldmxcsr(old_mxcsr); }
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private:
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unsigned old_mxcsr;
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};
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#endif
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} // namespace testing
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} // namespace LIBC_NAMESPACE_DECL
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#define DECLARE_SPECIAL_CONSTANTS(T) \
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using FPBits = LIBC_NAMESPACE::fputil::FPBits<T>; \
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using StorageType = typename FPBits::StorageType; \
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\
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static constexpr StorageType STORAGE_MAX = \
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LIBC_NAMESPACE::cpp::numeric_limits<StorageType>::max(); \
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const T zero = FPBits::zero(Sign::POS).get_val(); \
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const T neg_zero = FPBits::zero(Sign::NEG).get_val(); \
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const T aNaN = FPBits::quiet_nan(Sign::POS).get_val(); \
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const T neg_aNaN = FPBits::quiet_nan(Sign::NEG).get_val(); \
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const T sNaN = FPBits::signaling_nan(Sign::POS).get_val(); \
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const T neg_sNaN = FPBits::signaling_nan(Sign::NEG).get_val(); \
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const T inf = FPBits::inf(Sign::POS).get_val(); \
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const T neg_inf = FPBits::inf(Sign::NEG).get_val(); \
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const T min_normal = FPBits::min_normal().get_val(); \
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const T max_normal = FPBits::max_normal(Sign::POS).get_val(); \
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const T neg_max_normal = FPBits::max_normal(Sign::NEG).get_val(); \
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const T min_denormal = FPBits::min_subnormal(Sign::POS).get_val(); \
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const T neg_min_denormal = FPBits::min_subnormal(Sign::NEG).get_val(); \
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const T max_denormal = FPBits::max_subnormal().get_val(); \
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static constexpr int UNKNOWN_MATH_ROUNDING_DIRECTION = 99; \
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static constexpr LIBC_NAMESPACE::cpp::array<int, 6> \
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MATH_ROUNDING_DIRECTIONS_INCLUDING_UNKNOWN = { \
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FP_INT_UPWARD, FP_INT_DOWNWARD, \
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FP_INT_TOWARDZERO, FP_INT_TONEARESTFROMZERO, \
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FP_INT_TONEAREST, UNKNOWN_MATH_ROUNDING_DIRECTION, \
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};
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#define EXPECT_FP_EQ(expected, actual) \
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EXPECT_THAT(actual, LIBC_NAMESPACE::testing::getMatcher< \
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LIBC_NAMESPACE::testing::TestCond::EQ>(expected))
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#define EXPECT_CFP_EQ(expected, actual) \
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EXPECT_THAT(actual, LIBC_NAMESPACE::testing::getMatcherComplex< \
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LIBC_NAMESPACE::testing::TestCond::EQ>(expected))
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#define TEST_FP_EQ(expected, actual) \
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LIBC_NAMESPACE::testing::getMatcher<LIBC_NAMESPACE::testing::TestCond::EQ>( \
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expected) \
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.match(actual)
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#define EXPECT_FP_IS_NAN(actual) EXPECT_TRUE((actual) != (actual))
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#define ASSERT_FP_EQ(expected, actual) \
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ASSERT_THAT(actual, LIBC_NAMESPACE::testing::getMatcher< \
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LIBC_NAMESPACE::testing::TestCond::EQ>(expected))
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#define EXPECT_FP_NE(expected, actual) \
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EXPECT_THAT(actual, LIBC_NAMESPACE::testing::getMatcher< \
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LIBC_NAMESPACE::testing::TestCond::NE>(expected))
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#define ASSERT_FP_NE(expected, actual) \
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ASSERT_THAT(actual, LIBC_NAMESPACE::testing::getMatcher< \
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LIBC_NAMESPACE::testing::TestCond::NE>(expected))
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#define EXPECT_MATH_ERRNO(expected) \
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do { \
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if (math_errhandling & MATH_ERRNO) { \
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int actual = LIBC_NAMESPACE::libc_errno; \
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LIBC_NAMESPACE::libc_errno = 0; \
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EXPECT_EQ(actual, expected); \
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} \
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} while (0)
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#define ASSERT_MATH_ERRNO(expected) \
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do { \
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if (math_errhandling & MATH_ERRNO) { \
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int actual = LIBC_NAMESPACE::libc_errno; \
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LIBC_NAMESPACE::libc_errno = 0; \
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ASSERT_EQ(actual, expected); \
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} \
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} while (0)
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#define EXPECT_FP_EXCEPTION(expected) \
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do { \
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if (math_errhandling & MATH_ERREXCEPT) { \
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EXPECT_EQ( \
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LIBC_NAMESPACE::fputil::test_except( \
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static_cast<int>(FE_ALL_EXCEPT)) & \
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((expected) ? (expected) : static_cast<int>(FE_ALL_EXCEPT)), \
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(expected)); \
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} \
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} while (0)
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#define ASSERT_FP_EXCEPTION(expected) \
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do { \
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if (math_errhandling & MATH_ERREXCEPT) { \
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ASSERT_EQ( \
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LIBC_NAMESPACE::fputil::test_except( \
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static_cast<int>(FE_ALL_EXCEPT)) & \
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((expected) ? (expected) : static_cast<int>(FE_ALL_EXCEPT)), \
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(expected)); \
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} \
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} while (0)
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#define EXPECT_FP_EQ_WITH_EXCEPTION(expected_val, actual_val, expected_except) \
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do { \
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LIBC_NAMESPACE::fputil::clear_except(static_cast<int>(FE_ALL_EXCEPT)); \
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EXPECT_FP_EQ(expected_val, actual_val); \
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EXPECT_FP_EXCEPTION(expected_except); \
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} while (0)
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#define EXPECT_FP_IS_NAN_WITH_EXCEPTION(actual_val, expected_except) \
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do { \
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LIBC_NAMESPACE::fputil::clear_except(static_cast<int>(FE_ALL_EXCEPT)); \
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EXPECT_FP_IS_NAN(actual_val); \
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EXPECT_FP_EXCEPTION(expected_except); \
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} while (0)
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#define EXPECT_FP_EQ_ROUNDING_MODE(expected, actual, rounding_mode) \
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do { \
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using namespace LIBC_NAMESPACE::fputil::testing; \
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ForceRoundingMode __r((rounding_mode)); \
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if (__r.success) { \
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EXPECT_FP_EQ((expected), (actual)); \
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} \
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} while (0)
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#define EXPECT_FP_EQ_ROUNDING_NEAREST(expected, actual) \
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EXPECT_FP_EQ_ROUNDING_MODE((expected), (actual), RoundingMode::Nearest)
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#define EXPECT_FP_EQ_ROUNDING_UPWARD(expected, actual) \
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EXPECT_FP_EQ_ROUNDING_MODE((expected), (actual), RoundingMode::Upward)
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#define EXPECT_FP_EQ_ROUNDING_DOWNWARD(expected, actual) \
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EXPECT_FP_EQ_ROUNDING_MODE((expected), (actual), RoundingMode::Downward)
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#define EXPECT_FP_EQ_ROUNDING_TOWARD_ZERO(expected, actual) \
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EXPECT_FP_EQ_ROUNDING_MODE((expected), (actual), RoundingMode::TowardZero)
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#define EXPECT_FP_EQ_ALL_ROUNDING_1(expected, actual) \
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do { \
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EXPECT_FP_EQ_ROUNDING_NEAREST((expected), (actual)); \
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EXPECT_FP_EQ_ROUNDING_UPWARD((expected), (actual)); \
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EXPECT_FP_EQ_ROUNDING_DOWNWARD((expected), (actual)); \
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EXPECT_FP_EQ_ROUNDING_TOWARD_ZERO((expected), (actual)); \
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} while (0)
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#define EXPECT_FP_EQ_ALL_ROUNDING_4(expected_nearest, expected_upward, \
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expected_downward, expected_toward_zero, \
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actual) \
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do { \
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EXPECT_FP_EQ_ROUNDING_NEAREST((expected_nearest), (actual)); \
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EXPECT_FP_EQ_ROUNDING_UPWARD((expected_upward), (actual)); \
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EXPECT_FP_EQ_ROUNDING_DOWNWARD((expected_downward), (actual)); \
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EXPECT_FP_EQ_ROUNDING_TOWARD_ZERO((expected_toward_zero), (actual)); \
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} while (0)
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#define EXPECT_FP_EQ_ALL_ROUNDING_UNSUPPORTED(...) \
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static_assert(false, "Unsupported number of arguments")
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#define EXPECT_FP_EQ_ALL_ROUNDING_GET_6TH_ARG(ARG1, ARG2, ARG3, ARG4, ARG5, \
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ARG6, ...) \
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ARG6
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#define EXPECT_FP_EQ_ALL_ROUNDING_SELECTION(...) \
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EXPECT_FP_EQ_ALL_ROUNDING_GET_6TH_ARG( \
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__VA_ARGS__, EXPECT_FP_EQ_ALL_ROUNDING_4, \
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EXPECT_FP_EQ_ALL_ROUNDING_UNSUPPORTED, \
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EXPECT_FP_EQ_ALL_ROUNDING_UNSUPPORTED, EXPECT_FP_EQ_ALL_ROUNDING_1)
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#define EXPECT_FP_EQ_ALL_ROUNDING(...) \
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EXPECT_FP_EQ_ALL_ROUNDING_SELECTION(__VA_ARGS__)(__VA_ARGS__)
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#define ASSERT_FP_EQ_ROUNDING_MODE(expected, actual, rounding_mode) \
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do { \
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using namespace LIBC_NAMESPACE::fputil::testing; \
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ForceRoundingMode __r((rounding_mode)); \
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if (__r.success) { \
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ASSERT_FP_EQ((expected), (actual)); \
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} \
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} while (0)
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#define ASSERT_FP_EQ_ROUNDING_NEAREST(expected, actual) \
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ASSERT_FP_EQ_ROUNDING_MODE((expected), (actual), RoundingMode::Nearest)
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#define ASSERT_FP_EQ_ROUNDING_UPWARD(expected, actual) \
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ASSERT_FP_EQ_ROUNDING_MODE((expected), (actual), RoundingMode::Upward)
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#define ASSERT_FP_EQ_ROUNDING_DOWNWARD(expected, actual) \
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ASSERT_FP_EQ_ROUNDING_MODE((expected), (actual), RoundingMode::Downward)
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#define ASSERT_FP_EQ_ROUNDING_TOWARD_ZERO(expected, actual) \
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ASSERT_FP_EQ_ROUNDING_MODE((expected), (actual), RoundingMode::TowardZero)
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#define EXPECT_FP_EQ_WITH_EXCEPTION_ROUNDING_MODE( \
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expected, actual, expected_except, rounding_mode) \
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do { \
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using namespace LIBC_NAMESPACE::fputil::testing; \
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ForceRoundingMode __r((rounding_mode)); \
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if (__r.success) { \
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LIBC_NAMESPACE::fputil::clear_except(static_cast<int>(FE_ALL_EXCEPT)); \
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EXPECT_FP_EQ((expected), (actual)); \
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EXPECT_FP_EXCEPTION(expected_except); \
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} \
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} while (0)
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#define EXPECT_FP_EQ_WITH_EXCEPTION_ROUNDING_NEAREST(expected, actual, \
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expected_except) \
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EXPECT_FP_EQ_WITH_EXCEPTION_ROUNDING_MODE( \
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(expected), (actual), (expected_except), RoundingMode::Nearest)
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|
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#define EXPECT_FP_EQ_WITH_EXCEPTION_ROUNDING_UPWARD(expected, actual, \
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|
expected_except) \
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EXPECT_FP_EQ_WITH_EXCEPTION_ROUNDING_MODE( \
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|
(expected), (actual), (expected_except), RoundingMode::Upward)
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|
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#define EXPECT_FP_EQ_WITH_EXCEPTION_ROUNDING_DOWNWARD(expected, actual, \
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|
expected_except) \
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EXPECT_FP_EQ_WITH_EXCEPTION_ROUNDING_MODE( \
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|
(expected), (actual), (expected_except), RoundingMode::Downward)
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|
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#define EXPECT_FP_EQ_WITH_EXCEPTION_ROUNDING_TOWARD_ZERO(expected, actual, \
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|
expected_except) \
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EXPECT_FP_EQ_WITH_EXCEPTION_ROUNDING_MODE( \
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|
(expected), (actual), (expected_except), RoundingMode::TowardZero)
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|
|
|
#define EXPECT_FP_EQ_WITH_EXCEPTION_ALL_ROUNDING(expected, actual, \
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|
expected_except) \
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|
do { \
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EXPECT_FP_EQ_WITH_EXCEPTION_ROUNDING_NEAREST((expected), (actual), \
|
|
(expected_except)); \
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|
EXPECT_FP_EQ_WITH_EXCEPTION_ROUNDING_UPWARD((expected), (actual), \
|
|
(expected_except)); \
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EXPECT_FP_EQ_WITH_EXCEPTION_ROUNDING_DOWNWARD((expected), (actual), \
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|
(expected_except)); \
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EXPECT_FP_EQ_WITH_EXCEPTION_ROUNDING_TOWARD_ZERO((expected), (actual), \
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|
(expected_except)); \
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} while (0)
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#endif // LLVM_LIBC_TEST_UNITTEST_FPMATCHER_H
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