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/*
* (C) Copyright 1996- ECMWF.
*
* This software is licensed under the terms of the Apache Licence Version 2.0
* which can be obtained at http://www.apache.org/licenses/LICENSE-2.0.
* In applying this licence, ECMWF does not waive the privileges and immunities
* granted to it by virtue of its status as an intergovernmental organisation nor
* does it submit to any jurisdiction.
*/
#include <cmath>
#include "eckit/types/FloatCompare.h"
#include "eckit/testing/Test.h"
using namespace std;
using namespace eckit;
using namespace eckit::testing;
namespace eckit::test {
namespace {
bool is_equal(float a, float b, float epsilon, int maxUlps) {
return eckit::types::is_approximately_equal(a, b, epsilon, maxUlps);
}
bool is_equal(float a, float b, float epsilon) {
return eckit::types::is_approximately_equal(a, b, epsilon);
}
bool is_equal(float a, float b) {
return eckit::types::is_approximately_equal(a, b, 0.00001f);
}
const float dEps = std::numeric_limits<float>::epsilon();
const float dInf = std::numeric_limits<float>::infinity();
const float sMin = std::numeric_limits<float>::denorm_min();
const float dMin = std::numeric_limits<float>::min();
const float dMax = std::numeric_limits<float>::max();
const float qNaN = std::numeric_limits<float>::quiet_NaN();
const float sNaN = std::numeric_limits<float>::signaling_NaN();
}; // namespace
//----------------------------------------------------------------------------------------------------------------------
CASE("test_large_numbers") {
Log::info() << "test_large_numbers" << std::endl;
EXPECT(is_equal(1000000, 1000000));
EXPECT(is_equal(1000000, 1000000.00001));
EXPECT(is_equal(1000000.00001, 1000000));
EXPECT(!is_equal(1000000.0, 1000001.0));
EXPECT(!is_equal(1000001.0, 1000000.0));
// -----------------------------------------------
EXPECT(is_equal(dMax, dMax));
EXPECT(is_equal(dMax, dMax, dEps));
EXPECT(is_equal(dMin, dMin));
EXPECT(is_equal(dMin, dMin, dEps));
}
CASE("test_negative_large_numbers") {
Log::info() << "test_negative_large_numbers " << dMin << std::endl;
EXPECT(is_equal(-1000000, -1000000));
EXPECT(is_equal(-1000000, -1000000.00001));
EXPECT(is_equal(-1000000.00001, -1000000));
EXPECT(!is_equal(-1000000.0, -1000001.0));
EXPECT(!is_equal(-1000001.0, -1000000.0));
// -----------------------------------------------
EXPECT(is_equal(-dMax, -dMax));
EXPECT(is_equal(-dMax, -dMax, dEps));
EXPECT(is_equal(-dMin, -dMin));
EXPECT(is_equal(-dMin, -dMin, dEps));
}
CASE("test_large_numbers_of_opposite_sign") {
EXPECT(!is_equal(-1000000, 1000000));
EXPECT(!is_equal(-1000000, 1000000.00001));
EXPECT(!is_equal(-1000000.00001, 1000000));
EXPECT(!is_equal(-1000000.0, 1000001.0));
EXPECT(!is_equal(-1000001.0, 1000000.0));
// Overflow occurs here in eckit::types::is_approximately_equal
EXPECT(!is_equal(-dMax, dMax));
EXPECT(!is_equal(-dMax, dMax, dEps));
}
CASE("test_ulp_around_one") {
Log::info() << "test_ulp_around_one" << std::endl;
// ULP distances up to 10 are equal
// Going right from 1 by eps increases distance by 1
// Going left from 1 by eps increases distance by 2
for (int i = 0; i <= 10; ++i) {
EXPECT(is_equal(1.0 + i * dEps, 1.0, dEps));
EXPECT(is_equal(1.0, 1.0 + i * dEps, dEps));
EXPECT(is_equal(1.0 - i * dEps / 2, 1.0, dEps));
EXPECT(is_equal(1.0, 1.0 - i * dEps / 2, dEps));
}
// ULP distances greater 10 are not equal
EXPECT(!is_equal(1.0 + 11 * dEps, 1.0, dEps));
EXPECT(!is_equal(1.0, 1.0 + 11 * dEps, dEps));
EXPECT(!is_equal(1.0 - 11 * dEps / 2, 1.0, dEps));
EXPECT(!is_equal(1.0, 1.0 - 11 * dEps / 2, dEps));
}
CASE("test_numbers_around_one") {
Log::info() << "test_numbers_around_one" << std::endl;
EXPECT(is_equal(1.0000001, 1.0000002));
EXPECT(is_equal(1.0000002, 1.0000001));
EXPECT(is_equal(1.123456, 1.123457));
EXPECT(is_equal(1.12345, 1.12344, 0.001));
EXPECT(!is_equal(1.0001, 1.0002));
EXPECT(!is_equal(1.0002, 1.0001));
}
CASE("test_numbers_around_negative_one") {
Log::info() << "test_numbers_around_negative_one" << std::endl;
EXPECT(is_equal(-1.0000001, -1.0000002));
EXPECT(is_equal(-1.0000002, -1.0000001));
EXPECT(!is_equal(-1.0001, -1.0002));
EXPECT(!is_equal(-1.0002, -1.0001));
}
CASE("test_numbers_between_one_and_zero") {
Log::info() << "test_numbers_between_one_and_zero" << std::endl;
EXPECT(is_equal(0.000000001000001, 0.000000001000002));
EXPECT(is_equal(0.000000001000002, 0.000000001000001));
EXPECT(!is_equal(0.0012, 0.0011));
EXPECT(!is_equal(0.0011, 0.0012));
}
CASE("test_numbers_between_minusone_and_zero") {
Log::info() << "test_numbers_between_minusone_and_zero" << std::endl;
EXPECT(is_equal(-0.000000001000001, -0.000000001000002));
EXPECT(is_equal(-0.000000001000002, -0.000000001000001));
EXPECT(!is_equal(-0.0012, -0.0011));
EXPECT(!is_equal(-0.0011, -0.0012));
}
CASE("test_comparisons_involving_zero") {
Log::info() << "test_comparisons_involving_zero" << std::endl;
EXPECT(is_equal(0.0, 0.0));
EXPECT(is_equal(0.0, -0.0));
EXPECT(is_equal(-0.0, -0.0));
EXPECT(!is_equal(0.0001, 0.0));
EXPECT(!is_equal(0.0, 0.0001));
EXPECT(!is_equal(-0.0001, 0.0));
EXPECT(!is_equal(0.0, -0.0001));
EXPECT(is_equal(0.0, 1e-30, 0.01));
EXPECT(is_equal(1e-30, 0.0, 0.01));
EXPECT(!is_equal(1e-30, 0.0, 1e-31));
EXPECT(!is_equal(0.0, 1e-30, 1e-31));
EXPECT(is_equal(0.0, -1e-30, 0.1));
EXPECT(is_equal(-1e-30, 0.0, 0.1));
EXPECT(!is_equal(-1e-30, 0.0, 1e-31));
EXPECT(!is_equal(0.0, -1e-30, 1e-31));
}
CASE("test_comparisons_involving_infinity") {
Log::info() << "test_comparisons_involving_infinity" << std::endl;
if (std::numeric_limits<float>::has_infinity) {
EXPECT(is_equal(dInf, dInf));
EXPECT(is_equal(-dInf, -dInf));
EXPECT(!is_equal(dInf, dMax));
EXPECT(!is_equal(dMax, dInf));
EXPECT(!is_equal(-dInf, -dMax));
EXPECT(!is_equal(-dMax, -dInf));
}
else {
Log::info() << "test_comparisons_involving_infinity NOT VALID on this platform" << std::endl;
}
}
CASE("test_comparisons_involving_nan") {
Log::info() << "test_comparisons_involving_nan" << std::endl;
// The value NaN (Not a Number) is used to represent a value that does not represent a real number.
// NaN's are represented by a bit pattern with an exponent of all 1s and a non-zero fraction. T
// there are two categories of NaN: QNaN (Quiet NaN) and SNaN (Signalling NaN).
//
// A QNaN is a NaN with the most significant fraction bit set.
// QNaN's propagate freely through most arithmetic operations.
// These values pop out of an operation when the result is not mathematically defined.
// An SNaN is a NaN with the most significant fraction bit clear.
// It is used to signal an exception when used in operations.
// SNaN's can be handy to assign to uninitialized variables to trap premature usage.
// Semantically, QNaN's denote indeterminate operations, while SNaN's denote invalid operations.
EXPECT(!is_equal(qNaN, qNaN));
EXPECT(!is_equal(qNaN, 0.0));
EXPECT(!is_equal(-0.0, qNaN));
EXPECT(!is_equal(qNaN, -0.0));
EXPECT(!is_equal(0.0, qNaN));
EXPECT(!is_equal(qNaN, dInf));
EXPECT(!is_equal(dInf, qNaN));
EXPECT(!is_equal(qNaN, dMax));
EXPECT(!is_equal(dMax, qNaN));
EXPECT(!is_equal(qNaN, -dMax));
EXPECT(!is_equal(-dMax, qNaN));
EXPECT(!is_equal(qNaN, dMin));
EXPECT(!is_equal(dMin, qNaN));
EXPECT(!is_equal(qNaN, -dMin));
EXPECT(!is_equal(-dMin, qNaN));
EXPECT(!is_equal(sNaN, sNaN));
EXPECT(!is_equal(sNaN, 0.0));
EXPECT(!is_equal(-0.0, sNaN));
EXPECT(!is_equal(sNaN, -0.0));
EXPECT(!is_equal(0.0, sNaN));
EXPECT(!is_equal(sNaN, dInf));
EXPECT(!is_equal(dInf, sNaN));
EXPECT(!is_equal(sNaN, dMax));
EXPECT(!is_equal(dMax, sNaN));
EXPECT(!is_equal(sNaN, -dMax));
EXPECT(!is_equal(-dMax, sNaN));
EXPECT(!is_equal(sNaN, dMin));
EXPECT(!is_equal(dMin, sNaN));
EXPECT(!is_equal(sNaN, -dMin));
EXPECT(!is_equal(-dMin, sNaN));
}
CASE("test_comparisons_opposite_side_of_zero") {
Log::info() << "test_comparisons_opposite_side_of_zero" << std::endl;
EXPECT(!is_equal(1.0000001, -1.0));
EXPECT(!is_equal(-1.0, 1.0000001));
EXPECT(!is_equal(-1.0000001, 1.0));
EXPECT(!is_equal(1.0, -1.0000001));
EXPECT(is_equal(10.0 * dMin, 10.0 * -dMin));
EXPECT(is_equal(10000 * dMin, 10000 * -dMin));
}
CASE("test_comparisons_very_close_to_zero") {
Log::info() << "test_comparisons_very_close_to_zero" << std::endl;
EXPECT(is_equal(dMin, -dMin, dEps));
EXPECT(is_equal(-dMin, dMin, dEps));
EXPECT(is_equal(dMin, 0, dEps));
EXPECT(is_equal(0, dMin, dEps));
EXPECT(is_equal(-dMin, 0, dEps));
EXPECT(is_equal(0, -dMin, dEps));
EXPECT(is_equal(0.000000001, -dMin));
EXPECT(is_equal(0.000000001, dMin));
EXPECT(is_equal(dMin, 0.000000001));
EXPECT(is_equal(-dMin, 0.000000001));
EXPECT(!is_equal(0.000000001, -dMin, 1e-10));
EXPECT(!is_equal(0.000000001, dMin, 1e-10));
EXPECT(!is_equal(dMin, 0.000000001, 1e-10));
EXPECT(!is_equal(-dMin, 0.000000001, 1e-10));
}
CASE("test_comparisons_with_denormal_numbers") {
Log::info() << "test_comparisons_with_denormal_numbers" << std::endl;
EXPECT(is_equal(sMin, -sMin, dEps));
EXPECT(is_equal(-sMin, sMin, dEps));
EXPECT(is_equal(sMin, 0, dEps));
EXPECT(is_equal(0, sMin, dEps));
EXPECT(is_equal(-sMin, 0, dEps));
EXPECT(is_equal(0, -sMin, dEps));
const float lMin = dMin - sMin; // largest denormal number
EXPECT(is_equal(lMin, -lMin, dEps));
EXPECT(is_equal(-lMin, lMin, dEps));
EXPECT(is_equal(lMin, 0, dEps));
EXPECT(is_equal(0, lMin, dEps));
EXPECT(is_equal(-lMin, 0, dEps));
EXPECT(is_equal(0, -lMin, dEps));
}
CASE("test_comparisons_ulps") {
Log::info() << "test_comparisons_ulps" << std::endl;
EXPECT(is_equal(dMin, -dMin, 0, 2));
EXPECT(is_equal(-dMin, dMin, 0, 2));
EXPECT(is_equal(dMin, 0, 0, 1));
EXPECT(is_equal(0, dMin, 0, 1));
EXPECT(is_equal(-dMin, 0, 0, 1));
EXPECT(is_equal(0, -dMin, 0, 1));
EXPECT(!is_equal(dMin, -dMin, 0, 1));
EXPECT(!is_equal(-dMin, dMin, 0, 1));
EXPECT(!is_equal(dMin, 0, 0, 0));
EXPECT(!is_equal(0, dMin, 0, 0));
EXPECT(!is_equal(-dMin, 0, 0, 0));
EXPECT(!is_equal(0, -dMin, 0, 0));
}
//----------------------------------------------------------------------------------------------------------------------
} // namespace eckit::test
//----------------------------------------------------------------------------------------------------------------------
#if defined(_CRAYC)
#include <fenv.h>
#else
static int fedisableexcept(int excepts) {
return 0;
}
static int FE_ALL_EXCEPT = 0;
#endif
int main(int argc, char** argv) {
fedisableexcept(FE_ALL_EXCEPT);
return run_tests(argc, argv);
}
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