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gecko-dev/mfbt/tests/TestFloatingPoint.cpp

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/* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
/* vim: set ts=8 sts=2 et sw=2 tw=80: */
/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this file,
* You can obtain one at http://mozilla.org/MPL/2.0/. */
#include "mozilla/Assertions.h"
#include "mozilla/FloatingPoint.h"
#include <math.h>
using mozilla::ExponentComponent;
using mozilla::FloatingPoint;
using mozilla::FuzzyEqualsAdditive;
using mozilla::FuzzyEqualsMultiplicative;
using mozilla::IsFloat32Representable;
using mozilla::IsNegative;
using mozilla::IsNegativeZero;
using mozilla::IsPositiveZero;
using mozilla::NegativeInfinity;
using mozilla::NumberEqualsInt32;
using mozilla::NumberEqualsInt64;
using mozilla::NumberIsInt32;
using mozilla::NumberIsInt64;
using mozilla::NumbersAreIdentical;
using mozilla::PositiveInfinity;
using mozilla::SpecificNaN;
using mozilla::UnspecifiedNaN;
using std::exp2;
using std::exp2f;
#define A(a) MOZ_RELEASE_ASSERT(a)
template <typename T>
static void ShouldBeIdentical(T aD1, T aD2) {
A(NumbersAreIdentical(aD1, aD2));
A(NumbersAreIdentical(aD2, aD1));
}
template <typename T>
static void ShouldNotBeIdentical(T aD1, T aD2) {
A(!NumbersAreIdentical(aD1, aD2));
A(!NumbersAreIdentical(aD2, aD1));
}
static void TestDoublesAreIdentical() {
ShouldBeIdentical(+0.0, +0.0);
ShouldBeIdentical(-0.0, -0.0);
ShouldNotBeIdentical(+0.0, -0.0);
ShouldBeIdentical(1.0, 1.0);
ShouldNotBeIdentical(-1.0, 1.0);
ShouldBeIdentical(4294967295.0, 4294967295.0);
ShouldNotBeIdentical(-4294967295.0, 4294967295.0);
ShouldBeIdentical(4294967296.0, 4294967296.0);
ShouldBeIdentical(4294967297.0, 4294967297.0);
ShouldBeIdentical(1e300, 1e300);
ShouldBeIdentical(PositiveInfinity<double>(), PositiveInfinity<double>());
ShouldBeIdentical(NegativeInfinity<double>(), NegativeInfinity<double>());
ShouldNotBeIdentical(PositiveInfinity<double>(), NegativeInfinity<double>());
ShouldNotBeIdentical(-0.0, NegativeInfinity<double>());
ShouldNotBeIdentical(+0.0, NegativeInfinity<double>());
ShouldNotBeIdentical(1e300, NegativeInfinity<double>());
ShouldNotBeIdentical(3.141592654, NegativeInfinity<double>());
ShouldBeIdentical(UnspecifiedNaN<double>(), UnspecifiedNaN<double>());
ShouldBeIdentical(-UnspecifiedNaN<double>(), UnspecifiedNaN<double>());
ShouldBeIdentical(UnspecifiedNaN<double>(), -UnspecifiedNaN<double>());
ShouldBeIdentical(SpecificNaN<double>(0, 17), SpecificNaN<double>(0, 42));
ShouldBeIdentical(SpecificNaN<double>(1, 17), SpecificNaN<double>(1, 42));
ShouldBeIdentical(SpecificNaN<double>(0, 17), SpecificNaN<double>(1, 42));
ShouldBeIdentical(SpecificNaN<double>(1, 17), SpecificNaN<double>(0, 42));
const uint64_t Mask = 0xfffffffffffffULL;
for (unsigned i = 0; i < 52; i++) {
for (unsigned j = 0; j < 52; j++) {
for (unsigned sign = 0; i < 2; i++) {
ShouldBeIdentical(SpecificNaN<double>(0, 1ULL << i),
SpecificNaN<double>(sign, 1ULL << j));
ShouldBeIdentical(SpecificNaN<double>(1, 1ULL << i),
SpecificNaN<double>(sign, 1ULL << j));
ShouldBeIdentical(SpecificNaN<double>(0, Mask & ~(1ULL << i)),
SpecificNaN<double>(sign, Mask & ~(1ULL << j)));
ShouldBeIdentical(SpecificNaN<double>(1, Mask & ~(1ULL << i)),
SpecificNaN<double>(sign, Mask & ~(1ULL << j)));
}
}
}
ShouldBeIdentical(SpecificNaN<double>(0, 17),
SpecificNaN<double>(0, 0x8000000000000ULL));
ShouldBeIdentical(SpecificNaN<double>(0, 17),
SpecificNaN<double>(0, 0x4000000000000ULL));
ShouldBeIdentical(SpecificNaN<double>(0, 17),
SpecificNaN<double>(0, 0x2000000000000ULL));
ShouldBeIdentical(SpecificNaN<double>(0, 17),
SpecificNaN<double>(0, 0x1000000000000ULL));
ShouldBeIdentical(SpecificNaN<double>(0, 17),
SpecificNaN<double>(0, 0x0800000000000ULL));
ShouldBeIdentical(SpecificNaN<double>(0, 17),
SpecificNaN<double>(0, 0x0400000000000ULL));
ShouldBeIdentical(SpecificNaN<double>(0, 17),
SpecificNaN<double>(0, 0x0200000000000ULL));
ShouldBeIdentical(SpecificNaN<double>(0, 17),
SpecificNaN<double>(0, 0x0100000000000ULL));
ShouldBeIdentical(SpecificNaN<double>(0, 17),
SpecificNaN<double>(0, 0x0080000000000ULL));
ShouldBeIdentical(SpecificNaN<double>(0, 17),
SpecificNaN<double>(0, 0x0040000000000ULL));
ShouldBeIdentical(SpecificNaN<double>(0, 17),
SpecificNaN<double>(0, 0x0020000000000ULL));
ShouldBeIdentical(SpecificNaN<double>(0, 17),
SpecificNaN<double>(0, 0x0010000000000ULL));
ShouldBeIdentical(SpecificNaN<double>(1, 17),
SpecificNaN<double>(0, 0xff0ffffffffffULL));
ShouldBeIdentical(SpecificNaN<double>(1, 17),
SpecificNaN<double>(0, 0xfffffffffff0fULL));
ShouldNotBeIdentical(UnspecifiedNaN<double>(), +0.0);
ShouldNotBeIdentical(UnspecifiedNaN<double>(), -0.0);
ShouldNotBeIdentical(UnspecifiedNaN<double>(), 1.0);
ShouldNotBeIdentical(UnspecifiedNaN<double>(), -1.0);
ShouldNotBeIdentical(UnspecifiedNaN<double>(), PositiveInfinity<double>());
ShouldNotBeIdentical(UnspecifiedNaN<double>(), NegativeInfinity<double>());
}
static void TestFloatsAreIdentical() {
ShouldBeIdentical(+0.0f, +0.0f);
ShouldBeIdentical(-0.0f, -0.0f);
ShouldNotBeIdentical(+0.0f, -0.0f);
ShouldBeIdentical(1.0f, 1.0f);
ShouldNotBeIdentical(-1.0f, 1.0f);
ShouldBeIdentical(8388607.0f, 8388607.0f);
ShouldNotBeIdentical(-8388607.0f, 8388607.0f);
ShouldBeIdentical(8388608.0f, 8388608.0f);
ShouldBeIdentical(8388609.0f, 8388609.0f);
ShouldBeIdentical(1e36f, 1e36f);
ShouldBeIdentical(PositiveInfinity<float>(), PositiveInfinity<float>());
ShouldBeIdentical(NegativeInfinity<float>(), NegativeInfinity<float>());
ShouldNotBeIdentical(PositiveInfinity<float>(), NegativeInfinity<float>());
ShouldNotBeIdentical(-0.0f, NegativeInfinity<float>());
ShouldNotBeIdentical(+0.0f, NegativeInfinity<float>());
ShouldNotBeIdentical(1e36f, NegativeInfinity<float>());
ShouldNotBeIdentical(3.141592654f, NegativeInfinity<float>());
ShouldBeIdentical(UnspecifiedNaN<float>(), UnspecifiedNaN<float>());
ShouldBeIdentical(-UnspecifiedNaN<float>(), UnspecifiedNaN<float>());
ShouldBeIdentical(UnspecifiedNaN<float>(), -UnspecifiedNaN<float>());
ShouldBeIdentical(SpecificNaN<float>(0, 17), SpecificNaN<float>(0, 42));
ShouldBeIdentical(SpecificNaN<float>(1, 17), SpecificNaN<float>(1, 42));
ShouldBeIdentical(SpecificNaN<float>(0, 17), SpecificNaN<float>(1, 42));
ShouldBeIdentical(SpecificNaN<float>(1, 17), SpecificNaN<float>(0, 42));
const uint32_t Mask = 0x7fffffUL;
for (unsigned i = 0; i < 23; i++) {
for (unsigned j = 0; j < 23; j++) {
for (unsigned sign = 0; i < 2; i++) {
ShouldBeIdentical(SpecificNaN<float>(0, 1UL << i),
SpecificNaN<float>(sign, 1UL << j));
ShouldBeIdentical(SpecificNaN<float>(1, 1UL << i),
SpecificNaN<float>(sign, 1UL << j));
ShouldBeIdentical(SpecificNaN<float>(0, Mask & ~(1UL << i)),
SpecificNaN<float>(sign, Mask & ~(1UL << j)));
ShouldBeIdentical(SpecificNaN<float>(1, Mask & ~(1UL << i)),
SpecificNaN<float>(sign, Mask & ~(1UL << j)));
}
}
}
ShouldBeIdentical(SpecificNaN<float>(0, 17), SpecificNaN<float>(0, 0x700000));
ShouldBeIdentical(SpecificNaN<float>(0, 17), SpecificNaN<float>(0, 0x400000));
ShouldBeIdentical(SpecificNaN<float>(0, 17), SpecificNaN<float>(0, 0x200000));
ShouldBeIdentical(SpecificNaN<float>(0, 17), SpecificNaN<float>(0, 0x100000));
ShouldBeIdentical(SpecificNaN<float>(0, 17), SpecificNaN<float>(0, 0x080000));
ShouldBeIdentical(SpecificNaN<float>(0, 17), SpecificNaN<float>(0, 0x040000));
ShouldBeIdentical(SpecificNaN<float>(0, 17), SpecificNaN<float>(0, 0x020000));
ShouldBeIdentical(SpecificNaN<float>(0, 17), SpecificNaN<float>(0, 0x010000));
ShouldBeIdentical(SpecificNaN<float>(0, 17), SpecificNaN<float>(0, 0x008000));
ShouldBeIdentical(SpecificNaN<float>(0, 17), SpecificNaN<float>(0, 0x004000));
ShouldBeIdentical(SpecificNaN<float>(0, 17), SpecificNaN<float>(0, 0x002000));
ShouldBeIdentical(SpecificNaN<float>(0, 17), SpecificNaN<float>(0, 0x001000));
ShouldBeIdentical(SpecificNaN<float>(1, 17), SpecificNaN<float>(0, 0x7f0fff));
ShouldBeIdentical(SpecificNaN<float>(1, 17), SpecificNaN<float>(0, 0x7fff0f));
ShouldNotBeIdentical(UnspecifiedNaN<float>(), +0.0f);
ShouldNotBeIdentical(UnspecifiedNaN<float>(), -0.0f);
ShouldNotBeIdentical(UnspecifiedNaN<float>(), 1.0f);
ShouldNotBeIdentical(UnspecifiedNaN<float>(), -1.0f);
ShouldNotBeIdentical(UnspecifiedNaN<float>(), PositiveInfinity<float>());
ShouldNotBeIdentical(UnspecifiedNaN<float>(), NegativeInfinity<float>());
}
static void TestAreIdentical() {
TestDoublesAreIdentical();
TestFloatsAreIdentical();
}
static void TestDoubleExponentComponent() {
A(ExponentComponent(0.0) ==
-int_fast16_t(FloatingPoint<double>::kExponentBias));
A(ExponentComponent(-0.0) ==
-int_fast16_t(FloatingPoint<double>::kExponentBias));
A(ExponentComponent(0.125) == -3);
A(ExponentComponent(0.5) == -1);
A(ExponentComponent(1.0) == 0);
A(ExponentComponent(1.5) == 0);
A(ExponentComponent(2.0) == 1);
A(ExponentComponent(7.0) == 2);
A(ExponentComponent(PositiveInfinity<double>()) ==
FloatingPoint<double>::kExponentBias + 1);
A(ExponentComponent(NegativeInfinity<double>()) ==
FloatingPoint<double>::kExponentBias + 1);
A(ExponentComponent(UnspecifiedNaN<double>()) ==
FloatingPoint<double>::kExponentBias + 1);
}
static void TestFloatExponentComponent() {
A(ExponentComponent(0.0f) ==
-int_fast16_t(FloatingPoint<float>::kExponentBias));
A(ExponentComponent(-0.0f) ==
-int_fast16_t(FloatingPoint<float>::kExponentBias));
A(ExponentComponent(0.125f) == -3);
A(ExponentComponent(0.5f) == -1);
A(ExponentComponent(1.0f) == 0);
A(ExponentComponent(1.5f) == 0);
A(ExponentComponent(2.0f) == 1);
A(ExponentComponent(7.0f) == 2);
A(ExponentComponent(PositiveInfinity<float>()) ==
FloatingPoint<float>::kExponentBias + 1);
A(ExponentComponent(NegativeInfinity<float>()) ==
FloatingPoint<float>::kExponentBias + 1);
A(ExponentComponent(UnspecifiedNaN<float>()) ==
FloatingPoint<float>::kExponentBias + 1);
}
static void TestExponentComponent() {
TestDoubleExponentComponent();
TestFloatExponentComponent();
}
// Used to test Number{Is,Equals}{Int32,Int64} for -0.0, the only case where
// NumberEquals* and NumberIs* aren't equivalent.
template <typename T>
static void TestEqualsIsForNegativeZero() {
T negZero = T(-0.0);
int32_t i32;
A(!NumberIsInt32(negZero, &i32));
A(NumberEqualsInt32(negZero, &i32));
A(i32 == 0);
int64_t i64;
A(!NumberIsInt64(negZero, &i64));
A(NumberEqualsInt64(negZero, &i64));
A(i64 == 0);
}
// Used to test Number{Is,Equals}{Int32,Int64} for int32 values.
template <typename T>
static void TestEqualsIsForInt32(T aVal) {
int32_t i32;
A(NumberIsInt32(aVal, &i32));
MOZ_ASSERT(i32 == aVal);
A(NumberEqualsInt32(aVal, &i32));
MOZ_ASSERT(i32 == aVal);
int64_t i64;
A(NumberIsInt64(aVal, &i64));
MOZ_ASSERT(i64 == aVal);
A(NumberEqualsInt64(aVal, &i64));
MOZ_ASSERT(i64 == aVal);
};
// Used to test Number{Is,Equals}{Int32,Int64} for values that fit in int64 but
// not int32.
template <typename T>
static void TestEqualsIsForInt64(T aVal) {
int32_t i32;
A(!NumberIsInt32(aVal, &i32));
A(!NumberEqualsInt32(aVal, &i32));
int64_t i64;
A(NumberIsInt64(aVal, &i64));
MOZ_ASSERT(i64 == aVal);
A(NumberEqualsInt64(aVal, &i64));
MOZ_ASSERT(i64 == aVal);
};
// Used to test Number{Is,Equals}{Int32,Int64} for values that aren't equal to
// any int32 or int64.
template <typename T>
static void TestEqualsIsForNonInteger(T aVal) {
int32_t i32;
A(!NumberIsInt32(aVal, &i32));
A(!NumberEqualsInt32(aVal, &i32));
int64_t i64;
A(!NumberIsInt64(aVal, &i64));
A(!NumberEqualsInt64(aVal, &i64));
};
static void TestDoublesPredicates() {
A(std::isnan(UnspecifiedNaN<double>()));
A(std::isnan(SpecificNaN<double>(1, 17)));
;
A(std::isnan(SpecificNaN<double>(0, 0xfffffffffff0fULL)));
A(!std::isnan(PositiveInfinity<double>()));
A(!std::isnan(NegativeInfinity<double>()));
A(std::isinf(PositiveInfinity<double>()));
A(std::isinf(NegativeInfinity<double>()));
A(!std::isinf(UnspecifiedNaN<double>()));
A(!std::isfinite(PositiveInfinity<double>()));
A(!std::isfinite(NegativeInfinity<double>()));
A(!std::isfinite(UnspecifiedNaN<double>()));
A(!IsNegative(PositiveInfinity<double>()));
A(IsNegative(NegativeInfinity<double>()));
A(IsNegative(-0.0));
A(!IsNegative(0.0));
A(IsNegative(-1.0));
A(!IsNegative(1.0));
A(!IsNegativeZero(PositiveInfinity<double>()));
A(!IsNegativeZero(NegativeInfinity<double>()));
A(!IsNegativeZero(SpecificNaN<double>(1, 17)));
;
A(!IsNegativeZero(SpecificNaN<double>(1, 0xfffffffffff0fULL)));
A(!IsNegativeZero(SpecificNaN<double>(0, 17)));
;
A(!IsNegativeZero(SpecificNaN<double>(0, 0xfffffffffff0fULL)));
A(!IsNegativeZero(UnspecifiedNaN<double>()));
A(IsNegativeZero(-0.0));
A(!IsNegativeZero(0.0));
A(!IsNegativeZero(-1.0));
A(!IsNegativeZero(1.0));
// Edge case: negative zero.
TestEqualsIsForNegativeZero<double>();
// Int32 values.
auto testInt32 = TestEqualsIsForInt32<double>;
testInt32(0.0);
testInt32(1.0);
testInt32(INT32_MIN);
testInt32(INT32_MAX);
// Int64 values that don't fit in int32.
auto testInt64 = TestEqualsIsForInt64<double>;
testInt64(2147483648);
testInt64(2147483649);
testInt64(-2147483649);
testInt64(INT64_MIN);
// Note: INT64_MAX can't be represented exactly as double. Use a large double
// very close to it.
testInt64(9223372036854772000.0);
constexpr double MinSafeInteger = -9007199254740991.0;
constexpr double MaxSafeInteger = 9007199254740991.0;
testInt64(MinSafeInteger);
testInt64(MaxSafeInteger);
// Doubles that aren't equal to any int32 or int64.
auto testNonInteger = TestEqualsIsForNonInteger<double>;
testNonInteger(NegativeInfinity<double>());
testNonInteger(PositiveInfinity<double>());
testNonInteger(UnspecifiedNaN<double>());
testNonInteger(-double(1ULL << 52) + 0.5);
testNonInteger(double(1ULL << 52) - 0.5);
testNonInteger(double(INT32_MAX) + 0.1);
testNonInteger(double(INT32_MIN) - 0.1);
testNonInteger(0.5);
testNonInteger(-0.0001);
testNonInteger(-9223372036854778000.0);
testNonInteger(9223372036854776000.0);
// Sanity-check that the IEEE-754 double-precision-derived literals used in
// testing here work as we intend them to.
A(exp2(-1075.0) == 0.0);
A(exp2(-1074.0) != 0.0);
testNonInteger(exp2(-1074.0));
testNonInteger(2 * exp2(-1074.0));
A(1.0 - exp2(-54.0) == 1.0);
A(1.0 - exp2(-53.0) != 1.0);
testNonInteger(1.0 - exp2(-53.0));
testNonInteger(1.0 - exp2(-52.0));
A(1.0 + exp2(-53.0) == 1.0f);
A(1.0 + exp2(-52.0) != 1.0f);
testNonInteger(1.0 + exp2(-52.0));
}
static void TestFloatsPredicates() {
A(std::isnan(UnspecifiedNaN<float>()));
A(std::isnan(SpecificNaN<float>(1, 17)));
;
A(std::isnan(SpecificNaN<float>(0, 0x7fff0fUL)));
A(!std::isnan(PositiveInfinity<float>()));
A(!std::isnan(NegativeInfinity<float>()));
A(std::isinf(PositiveInfinity<float>()));
A(std::isinf(NegativeInfinity<float>()));
A(!std::isinf(UnspecifiedNaN<float>()));
A(!std::isfinite(PositiveInfinity<float>()));
A(!std::isfinite(NegativeInfinity<float>()));
A(!std::isfinite(UnspecifiedNaN<float>()));
A(!IsNegative(PositiveInfinity<float>()));
A(IsNegative(NegativeInfinity<float>()));
A(IsNegative(-0.0f));
A(!IsNegative(0.0f));
A(IsNegative(-1.0f));
A(!IsNegative(1.0f));
A(!IsNegativeZero(PositiveInfinity<float>()));
A(!IsNegativeZero(NegativeInfinity<float>()));
A(!IsNegativeZero(SpecificNaN<float>(1, 17)));
;
A(!IsNegativeZero(SpecificNaN<float>(1, 0x7fff0fUL)));
A(!IsNegativeZero(SpecificNaN<float>(0, 17)));
;
A(!IsNegativeZero(SpecificNaN<float>(0, 0x7fff0fUL)));
A(!IsNegativeZero(UnspecifiedNaN<float>()));
A(IsNegativeZero(-0.0f));
A(!IsNegativeZero(0.0f));
A(!IsNegativeZero(-1.0f));
A(!IsNegativeZero(1.0f));
A(!IsPositiveZero(PositiveInfinity<float>()));
A(!IsPositiveZero(NegativeInfinity<float>()));
A(!IsPositiveZero(SpecificNaN<float>(1, 17)));
;
A(!IsPositiveZero(SpecificNaN<float>(1, 0x7fff0fUL)));
A(!IsPositiveZero(SpecificNaN<float>(0, 17)));
;
A(!IsPositiveZero(SpecificNaN<float>(0, 0x7fff0fUL)));
A(!IsPositiveZero(UnspecifiedNaN<float>()));
A(IsPositiveZero(0.0f));
A(!IsPositiveZero(-0.0f));
A(!IsPositiveZero(-1.0f));
A(!IsPositiveZero(1.0f));
// Edge case: negative zero.
TestEqualsIsForNegativeZero<float>();
// Int32 values.
auto testInt32 = TestEqualsIsForInt32<float>;
testInt32(0.0f);
testInt32(1.0f);
testInt32(INT32_MIN);
testInt32(float(2147483648 - 128)); // max int32_t fitting in float
const int32_t BIG = 2097151;
testInt32(BIG);
// Int64 values that don't fit in int32.
auto testInt64 = TestEqualsIsForInt64<float>;
testInt64(INT64_MIN);
testInt64(9007199254740992.0f);
testInt64(-float(2147483648) - 256);
testInt64(float(2147483648));
testInt64(float(2147483648) + 256);
// Floats that aren't equal to any int32 or int64.
auto testNonInteger = TestEqualsIsForNonInteger<float>;
testNonInteger(NegativeInfinity<float>());
testNonInteger(PositiveInfinity<float>());
testNonInteger(UnspecifiedNaN<float>());
testNonInteger(0.5f);
testNonInteger(1.5f);
testNonInteger(-0.0001f);
testNonInteger(-19223373116872850000.0f);
testNonInteger(19223373116872850000.0f);
testNonInteger(float(BIG) + 0.1f);
A(powf(2.0f, -150.0f) == 0.0f);
A(powf(2.0f, -149.0f) != 0.0f);
testNonInteger(powf(2.0f, -149.0f));
testNonInteger(2 * powf(2.0f, -149.0f));
A(1.0f - powf(2.0f, -25.0f) == 1.0f);
A(1.0f - powf(2.0f, -24.0f) != 1.0f);
testNonInteger(1.0f - powf(2.0f, -24.0f));
testNonInteger(1.0f - powf(2.0f, -23.0f));
A(1.0f + powf(2.0f, -24.0f) == 1.0f);
A(1.0f + powf(2.0f, -23.0f) != 1.0f);
testNonInteger(1.0f + powf(2.0f, -23.0f));
}
static void TestPredicates() {
TestFloatsPredicates();
TestDoublesPredicates();
}
static void TestFloatsAreApproximatelyEqual() {
float epsilon = mozilla::detail::FuzzyEqualsEpsilon<float>::value();
float lessThanEpsilon = epsilon / 2.0f;
float moreThanEpsilon = epsilon * 2.0f;
// Additive tests using the default epsilon
// ... around 1.0
A(FuzzyEqualsAdditive(1.0f, 1.0f + lessThanEpsilon));
A(FuzzyEqualsAdditive(1.0f, 1.0f - lessThanEpsilon));
A(FuzzyEqualsAdditive(1.0f, 1.0f + epsilon));
A(FuzzyEqualsAdditive(1.0f, 1.0f - epsilon));
A(!FuzzyEqualsAdditive(1.0f, 1.0f + moreThanEpsilon));
A(!FuzzyEqualsAdditive(1.0f, 1.0f - moreThanEpsilon));
// ... around 1.0e2 (this is near the upper bound of the range where
// adding moreThanEpsilon will still be representable and return false)
A(FuzzyEqualsAdditive(1.0e2f, 1.0e2f + lessThanEpsilon));
A(FuzzyEqualsAdditive(1.0e2f, 1.0e2f + epsilon));
A(!FuzzyEqualsAdditive(1.0e2f, 1.0e2f + moreThanEpsilon));
// ... around 1.0e-10
A(FuzzyEqualsAdditive(1.0e-10f, 1.0e-10f + lessThanEpsilon));
A(FuzzyEqualsAdditive(1.0e-10f, 1.0e-10f + epsilon));
A(!FuzzyEqualsAdditive(1.0e-10f, 1.0e-10f + moreThanEpsilon));
// ... straddling 0
A(FuzzyEqualsAdditive(1.0e-6f, -1.0e-6f));
A(!FuzzyEqualsAdditive(1.0e-5f, -1.0e-5f));
// Using a small epsilon
A(FuzzyEqualsAdditive(1.0e-5f, 1.0e-5f + 1.0e-10f, 1.0e-9f));
A(!FuzzyEqualsAdditive(1.0e-5f, 1.0e-5f + 1.0e-10f, 1.0e-11f));
// Using a big epsilon
A(FuzzyEqualsAdditive(1.0e20f, 1.0e20f + 1.0e15f, 1.0e16f));
A(!FuzzyEqualsAdditive(1.0e20f, 1.0e20f + 1.0e15f, 1.0e14f));
// Multiplicative tests using the default epsilon
// ... around 1.0
A(FuzzyEqualsMultiplicative(1.0f, 1.0f + lessThanEpsilon));
A(FuzzyEqualsMultiplicative(1.0f, 1.0f - lessThanEpsilon));
A(FuzzyEqualsMultiplicative(1.0f, 1.0f + epsilon));
A(!FuzzyEqualsMultiplicative(1.0f, 1.0f - epsilon));
A(!FuzzyEqualsMultiplicative(1.0f, 1.0f + moreThanEpsilon));
A(!FuzzyEqualsMultiplicative(1.0f, 1.0f - moreThanEpsilon));
// ... around 1.0e10
A(FuzzyEqualsMultiplicative(1.0e10f, 1.0e10f + (lessThanEpsilon * 1.0e10f)));
A(!FuzzyEqualsMultiplicative(1.0e10f, 1.0e10f + (moreThanEpsilon * 1.0e10f)));
// ... around 1.0e-10
A(FuzzyEqualsMultiplicative(1.0e-10f,
1.0e-10f + (lessThanEpsilon * 1.0e-10f)));
A(!FuzzyEqualsMultiplicative(1.0e-10f,
1.0e-10f + (moreThanEpsilon * 1.0e-10f)));
// ... straddling 0
A(!FuzzyEqualsMultiplicative(1.0e-6f, -1.0e-6f));
A(FuzzyEqualsMultiplicative(1.0e-6f, -1.0e-6f, 1.0e2f));
// Using a small epsilon
A(FuzzyEqualsMultiplicative(1.0e-5f, 1.0e-5f + 1.0e-10f, 1.0e-4f));
A(!FuzzyEqualsMultiplicative(1.0e-5f, 1.0e-5f + 1.0e-10f, 1.0e-5f));
// Using a big epsilon
A(FuzzyEqualsMultiplicative(1.0f, 2.0f, 1.0f));
A(!FuzzyEqualsMultiplicative(1.0f, 2.0f, 0.1f));
// "real world case"
float oneThird = 10.0f / 3.0f;
A(FuzzyEqualsAdditive(10.0f, 3.0f * oneThird));
A(FuzzyEqualsMultiplicative(10.0f, 3.0f * oneThird));
// NaN check
A(!FuzzyEqualsAdditive(SpecificNaN<float>(1, 1), SpecificNaN<float>(1, 1)));
A(!FuzzyEqualsAdditive(SpecificNaN<float>(1, 2), SpecificNaN<float>(0, 8)));
A(!FuzzyEqualsMultiplicative(SpecificNaN<float>(1, 1),
SpecificNaN<float>(1, 1)));
A(!FuzzyEqualsMultiplicative(SpecificNaN<float>(1, 2),
SpecificNaN<float>(0, 200)));
}
static void TestDoublesAreApproximatelyEqual() {
double epsilon = mozilla::detail::FuzzyEqualsEpsilon<double>::value();
double lessThanEpsilon = epsilon / 2.0;
double moreThanEpsilon = epsilon * 2.0;
// Additive tests using the default epsilon
// ... around 1.0
A(FuzzyEqualsAdditive(1.0, 1.0 + lessThanEpsilon));
A(FuzzyEqualsAdditive(1.0, 1.0 - lessThanEpsilon));
A(FuzzyEqualsAdditive(1.0, 1.0 + epsilon));
A(FuzzyEqualsAdditive(1.0, 1.0 - epsilon));
A(!FuzzyEqualsAdditive(1.0, 1.0 + moreThanEpsilon));
A(!FuzzyEqualsAdditive(1.0, 1.0 - moreThanEpsilon));
// ... around 1.0e4 (this is near the upper bound of the range where
// adding moreThanEpsilon will still be representable and return false)
A(FuzzyEqualsAdditive(1.0e4, 1.0e4 + lessThanEpsilon));
A(FuzzyEqualsAdditive(1.0e4, 1.0e4 + epsilon));
A(!FuzzyEqualsAdditive(1.0e4, 1.0e4 + moreThanEpsilon));
// ... around 1.0e-25
A(FuzzyEqualsAdditive(1.0e-25, 1.0e-25 + lessThanEpsilon));
A(FuzzyEqualsAdditive(1.0e-25, 1.0e-25 + epsilon));
A(!FuzzyEqualsAdditive(1.0e-25, 1.0e-25 + moreThanEpsilon));
// ... straddling 0
A(FuzzyEqualsAdditive(1.0e-13, -1.0e-13));
A(!FuzzyEqualsAdditive(1.0e-12, -1.0e-12));
// Using a small epsilon
A(FuzzyEqualsAdditive(1.0e-15, 1.0e-15 + 1.0e-30, 1.0e-29));
A(!FuzzyEqualsAdditive(1.0e-15, 1.0e-15 + 1.0e-30, 1.0e-31));
// Using a big epsilon
A(FuzzyEqualsAdditive(1.0e40, 1.0e40 + 1.0e25, 1.0e26));
A(!FuzzyEqualsAdditive(1.0e40, 1.0e40 + 1.0e25, 1.0e24));
// Multiplicative tests using the default epsilon
// ... around 1.0
A(FuzzyEqualsMultiplicative(1.0, 1.0 + lessThanEpsilon));
A(FuzzyEqualsMultiplicative(1.0, 1.0 - lessThanEpsilon));
A(FuzzyEqualsMultiplicative(1.0, 1.0 + epsilon));
A(!FuzzyEqualsMultiplicative(1.0, 1.0 - epsilon));
A(!FuzzyEqualsMultiplicative(1.0, 1.0 + moreThanEpsilon));
A(!FuzzyEqualsMultiplicative(1.0, 1.0 - moreThanEpsilon));
// ... around 1.0e30
A(FuzzyEqualsMultiplicative(1.0e30, 1.0e30 + (lessThanEpsilon * 1.0e30)));
A(!FuzzyEqualsMultiplicative(1.0e30, 1.0e30 + (moreThanEpsilon * 1.0e30)));
// ... around 1.0e-30
A(FuzzyEqualsMultiplicative(1.0e-30, 1.0e-30 + (lessThanEpsilon * 1.0e-30)));
A(!FuzzyEqualsMultiplicative(1.0e-30, 1.0e-30 + (moreThanEpsilon * 1.0e-30)));
// ... straddling 0
A(!FuzzyEqualsMultiplicative(1.0e-6, -1.0e-6));
A(FuzzyEqualsMultiplicative(1.0e-6, -1.0e-6, 1.0e2));
// Using a small epsilon
A(FuzzyEqualsMultiplicative(1.0e-15, 1.0e-15 + 1.0e-30, 1.0e-15));
A(!FuzzyEqualsMultiplicative(1.0e-15, 1.0e-15 + 1.0e-30, 1.0e-16));
// Using a big epsilon
A(FuzzyEqualsMultiplicative(1.0e40, 2.0e40, 1.0));
A(!FuzzyEqualsMultiplicative(1.0e40, 2.0e40, 0.1));
// "real world case"
double oneThird = 10.0 / 3.0;
A(FuzzyEqualsAdditive(10.0, 3.0 * oneThird));
A(FuzzyEqualsMultiplicative(10.0, 3.0 * oneThird));
// NaN check
A(!FuzzyEqualsAdditive(SpecificNaN<double>(1, 1), SpecificNaN<double>(1, 1)));
A(!FuzzyEqualsAdditive(SpecificNaN<double>(1, 2), SpecificNaN<double>(0, 8)));
A(!FuzzyEqualsMultiplicative(SpecificNaN<double>(1, 1),
SpecificNaN<double>(1, 1)));
A(!FuzzyEqualsMultiplicative(SpecificNaN<double>(1, 2),
SpecificNaN<double>(0, 200)));
}
static void TestAreApproximatelyEqual() {
TestFloatsAreApproximatelyEqual();
TestDoublesAreApproximatelyEqual();
}
static void TestIsFloat32Representable() {
// Zeroes are representable.
A(IsFloat32Representable(+0.0));
A(IsFloat32Representable(-0.0));
// NaN and infinities are representable.
A(IsFloat32Representable(UnspecifiedNaN<double>()));
A(IsFloat32Representable(SpecificNaN<double>(0, 1)));
A(IsFloat32Representable(SpecificNaN<double>(0, 71389)));
A(IsFloat32Representable(SpecificNaN<double>(0, (uint64_t(1) << 52) - 2)));
A(IsFloat32Representable(SpecificNaN<double>(1, 1)));
A(IsFloat32Representable(SpecificNaN<double>(1, 71389)));
A(IsFloat32Representable(SpecificNaN<double>(1, (uint64_t(1) << 52) - 2)));
A(IsFloat32Representable(PositiveInfinity<double>()));
A(IsFloat32Representable(NegativeInfinity<double>()));
// Sanity-check that the IEEE-754 double-precision-derived literals used in
// testing here work as we intend them to.
A(exp2(-1075.0) == 0.0);
A(exp2(-1074.0) != 0.0);
for (double littleExp = -1074.0; littleExp < -149.0; littleExp++) {
// Powers of two representable as doubles but not as floats aren't
// representable.
A(!IsFloat32Representable(exp2(littleExp)));
}
// Sanity-check that the IEEE-754 single-precision-derived literals used in
// testing here work as we intend them to.
A(exp2f(-150.0f) == 0.0);
A(exp2f(-149.0f) != 0.0);
// Exact powers of two within the available range are representable.
for (double exponent = -149.0; exponent < 128.0; exponent++) {
A(IsFloat32Representable(exp2(exponent)));
}
// Powers of two above the available range aren't representable.
for (double bigExp = 128.0; bigExp < 1024.0; bigExp++) {
A(!IsFloat32Representable(exp2(bigExp)));
}
// Various denormal (i.e. super-small) doubles with MSB and LSB as far apart
// as possible are representable (but taken one bit further apart are not
// representable).
//
// Note that the final iteration tests non-denormal with exponent field
// containing (biased) 1, as |oneTooSmall| and |widestPossible| happen still
// to be correct for that exponent due to the extra bit of precision in the
// implicit-one bit.
double oneTooSmall = exp2(-150.0);
for (double denormExp = -149.0;
denormExp < 1 - double(FloatingPoint<double>::kExponentBias) + 1;
denormExp++) {
double baseDenorm = exp2(denormExp);
double tooWide = baseDenorm + oneTooSmall;
A(!IsFloat32Representable(tooWide));
double widestPossible = baseDenorm;
if (oneTooSmall * 2.0 != baseDenorm) {
widestPossible += oneTooSmall * 2.0;
}
A(IsFloat32Representable(widestPossible));
}
// Finally, check certain interesting/special values for basic sanity.
A(!IsFloat32Representable(2147483647.0));
A(!IsFloat32Representable(-2147483647.0));
}
#undef A
int main() {
TestAreIdentical();
TestExponentComponent();
TestPredicates();
TestAreApproximatelyEqual();
TestIsFloat32Representable();
return 0;
}
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