gecko-dev/mfbt/FloatingPoint.h

373 lines
12 KiB
C++

/* -*- 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/. */
/* Various predicates and operations on IEEE-754 floating point types. */
#ifndef mozilla_FloatingPoint_h
#define mozilla_FloatingPoint_h
#include "mozilla/Assertions.h"
#include "mozilla/Attributes.h"
#include "mozilla/Casting.h"
#include "mozilla/MathAlgorithms.h"
#include "mozilla/Types.h"
#include <stdint.h>
namespace mozilla {
/*
* It's reasonable to ask why we have this header at all. Don't isnan,
* copysign, the built-in comparison operators, and the like solve these
* problems? Unfortunately, they don't. We've found that various compilers
* (MSVC, MSVC when compiling with PGO, and GCC on OS X, at least) miscompile
* the standard methods in various situations, so we can't use them. Some of
* these compilers even have problems compiling seemingly reasonable bitwise
* algorithms! But with some care we've found algorithms that seem to not
* trigger those compiler bugs.
*
* For the aforementioned reasons, be very wary of making changes to any of
* these algorithms. If you must make changes, keep a careful eye out for
* compiler bustage, particularly PGO-specific bustage.
*/
/*
* These implementations all assume |double| is a 64-bit double format number
* type, compatible with the IEEE-754 standard. C/C++ don't require this to be
* the case. But we required this in implementations of these algorithms that
* preceded this header, so we shouldn't break anything if we continue doing so.
*/
static_assert(sizeof(double) == sizeof(uint64_t), "double must be 64 bits");
const unsigned DoubleExponentBias = 1023;
const unsigned DoubleExponentShift = 52;
const uint64_t DoubleSignBit = 0x8000000000000000ULL;
const uint64_t DoubleExponentBits = 0x7ff0000000000000ULL;
const uint64_t DoubleSignificandBits = 0x000fffffffffffffULL;
static_assert((DoubleSignBit & DoubleExponentBits) == 0,
"sign bit doesn't overlap exponent bits");
static_assert((DoubleSignBit & DoubleSignificandBits) == 0,
"sign bit doesn't overlap significand bits");
static_assert((DoubleExponentBits & DoubleSignificandBits) == 0,
"exponent bits don't overlap significand bits");
static_assert((DoubleSignBit | DoubleExponentBits | DoubleSignificandBits) ==
~uint64_t(0),
"all bits accounted for");
/*
* Ditto for |float| that must be a 32-bit double format number type, compatible
* with the IEEE-754 standard.
*/
static_assert(sizeof(float) == sizeof(uint32_t), "float must be 32bits");
const unsigned FloatExponentBias = 127;
const unsigned FloatExponentShift = 23;
const uint32_t FloatSignBit = 0x80000000UL;
const uint32_t FloatExponentBits = 0x7F800000UL;
const uint32_t FloatSignificandBits = 0x007FFFFFUL;
static_assert((FloatSignBit & FloatExponentBits) == 0,
"sign bit doesn't overlap exponent bits");
static_assert((FloatSignBit & FloatSignificandBits) == 0,
"sign bit doesn't overlap significand bits");
static_assert((FloatExponentBits & FloatSignificandBits) == 0,
"exponent bits don't overlap significand bits");
static_assert((FloatSignBit | FloatExponentBits | FloatSignificandBits) ==
~uint32_t(0),
"all bits accounted for");
/** Determines whether a double is NaN. */
static MOZ_ALWAYS_INLINE bool
IsNaN(double d)
{
/*
* A double is NaN if all exponent bits are 1 and the significand contains at
* least one non-zero bit.
*/
uint64_t bits = BitwiseCast<uint64_t>(d);
return (bits & DoubleExponentBits) == DoubleExponentBits &&
(bits & DoubleSignificandBits) != 0;
}
/** Determines whether a double is +Infinity or -Infinity. */
static MOZ_ALWAYS_INLINE bool
IsInfinite(double d)
{
/* Infinities have all exponent bits set to 1 and an all-0 significand. */
uint64_t bits = BitwiseCast<uint64_t>(d);
return (bits & ~DoubleSignBit) == DoubleExponentBits;
}
/** Determines whether a double is not NaN or infinite. */
static MOZ_ALWAYS_INLINE bool
IsFinite(double d)
{
/*
* NaN and Infinities are the only non-finite doubles, and both have all
* exponent bits set to 1.
*/
uint64_t bits = BitwiseCast<uint64_t>(d);
return (bits & DoubleExponentBits) != DoubleExponentBits;
}
/**
* Determines whether a double is negative. It is an error to call this method
* on a double which is NaN.
*/
static MOZ_ALWAYS_INLINE bool
IsNegative(double d)
{
MOZ_ASSERT(!IsNaN(d), "NaN does not have a sign");
/* The sign bit is set if the double is negative. */
uint64_t bits = BitwiseCast<uint64_t>(d);
return (bits & DoubleSignBit) != 0;
}
/** Determines whether a double represents -0. */
static MOZ_ALWAYS_INLINE bool
IsNegativeZero(double d)
{
/* Only the sign bit is set if the double is -0. */
uint64_t bits = BitwiseCast<uint64_t>(d);
return bits == DoubleSignBit;
}
/**
* Returns the exponent portion of the double.
*
* Zero is not special-cased, so ExponentComponent(0.0) is
* -int_fast16_t(DoubleExponentBias).
*/
static MOZ_ALWAYS_INLINE int_fast16_t
ExponentComponent(double d)
{
/*
* The exponent component of a double is an unsigned number, biased from its
* actual value. Subtract the bias to retrieve the actual exponent.
*/
uint64_t bits = BitwiseCast<uint64_t>(d);
return int_fast16_t((bits & DoubleExponentBits) >> DoubleExponentShift) -
int_fast16_t(DoubleExponentBias);
}
/** Returns +Infinity. */
static MOZ_ALWAYS_INLINE double
PositiveInfinity()
{
/*
* Positive infinity has all exponent bits set, sign bit set to 0, and no
* significand.
*/
return BitwiseCast<double>(DoubleExponentBits);
}
/** Returns -Infinity. */
static MOZ_ALWAYS_INLINE double
NegativeInfinity()
{
/*
* Negative infinity has all exponent bits set, sign bit set to 1, and no
* significand.
*/
return BitwiseCast<double>(DoubleSignBit | DoubleExponentBits);
}
/** Constructs a NaN value with the specified sign bit and significand bits. */
static MOZ_ALWAYS_INLINE double
SpecificNaN(int signbit, uint64_t significand)
{
MOZ_ASSERT(signbit == 0 || signbit == 1);
MOZ_ASSERT((significand & ~DoubleSignificandBits) == 0);
MOZ_ASSERT(significand & DoubleSignificandBits);
double d = BitwiseCast<double>((signbit ? DoubleSignBit : 0) |
DoubleExponentBits |
significand);
MOZ_ASSERT(IsNaN(d));
return d;
}
/** Computes the smallest non-zero positive double value. */
static MOZ_ALWAYS_INLINE double
MinDoubleValue()
{
return BitwiseCast<double>(uint64_t(1));
}
/**
* If d is equal to some int32_t value, set *i to that value and return true;
* otherwise return false.
*
* Note that negative zero is "equal" to zero here. To test whether a value can
* be losslessly converted to int32_t and back, use DoubleIsInt32 instead.
*/
static MOZ_ALWAYS_INLINE bool
DoubleEqualsInt32(double d, int32_t* i)
{
/*
* XXX Casting a double that doesn't truncate to int32_t, to int32_t, induces
* undefined behavior. We should definitely fix this (bug 744965), but as
* apparently it "works" in practice, it's not a pressing concern now.
*/
return d == (*i = int32_t(d));
}
/**
* If d can be converted to int32_t and back to an identical double value,
* set *i to that value and return true; otherwise return false.
*
* The difference between this and DoubleEqualsInt32 is that this method returns
* false for negative zero.
*/
static MOZ_ALWAYS_INLINE bool
DoubleIsInt32(double d, int32_t* i)
{
return !IsNegativeZero(d) && DoubleEqualsInt32(d, i);
}
/**
* Computes a NaN value. Do not use this method if you depend upon a particular
* NaN value being returned.
*/
static MOZ_ALWAYS_INLINE double
UnspecifiedNaN()
{
/*
* If we can use any quiet NaN, we might as well use the all-ones NaN,
* since it's cheap to materialize on common platforms (such as x64, where
* this value can be represented in a 32-bit signed immediate field, allowing
* it to be stored to memory in a single instruction).
*/
return SpecificNaN(1, 0xfffffffffffffULL);
}
/**
* Compare two doubles for equality, *without* equating -0 to +0, and equating
* any NaN value to any other NaN value. (The normal equality operators equate
* -0 with +0, and they equate NaN to no other value.)
*/
static inline bool
DoublesAreIdentical(double d1, double d2)
{
if (IsNaN(d1))
return IsNaN(d2);
return BitwiseCast<uint64_t>(d1) == BitwiseCast<uint64_t>(d2);
}
/** Determines whether a float is NaN. */
static MOZ_ALWAYS_INLINE bool
IsFloatNaN(float f)
{
/*
* A float is NaN if all exponent bits are 1 and the significand contains at
* least one non-zero bit.
*/
uint32_t bits = BitwiseCast<uint32_t>(f);
return (bits & FloatExponentBits) == FloatExponentBits &&
(bits & FloatSignificandBits) != 0;
}
/** Constructs a NaN value with the specified sign bit and significand bits. */
static MOZ_ALWAYS_INLINE float
SpecificFloatNaN(int signbit, uint32_t significand)
{
MOZ_ASSERT(signbit == 0 || signbit == 1);
MOZ_ASSERT((significand & ~FloatSignificandBits) == 0);
MOZ_ASSERT(significand & FloatSignificandBits);
float f = BitwiseCast<float>((signbit ? FloatSignBit : 0) |
FloatExponentBits |
significand);
MOZ_ASSERT(IsFloatNaN(f));
return f;
}
namespace detail {
template<typename T>
struct FuzzyEqualsEpsilon;
template<>
struct FuzzyEqualsEpsilon<float>
{
// A number near 1e-5 that is exactly representable in
// floating point
static const float value() { return 1.0f / (1 << 17); }
};
template<>
struct FuzzyEqualsEpsilon<double>
{
// A number near 1e-12 that is exactly representable in
// a double
static const double value() { return 1.0 / (1LL << 40); }
};
} // namespace detail
/**
* Compare two floating point values for equality, modulo rounding error. That
* is, the two values are considered equal if they are both not NaN and if they
* are less than or equal to epsilon apart. The default value of epsilon is near
* 1e-5.
*
* For most scenarios you will want to use FuzzyEqualsMultiplicative instead,
* as it is more reasonable over the entire range of floating point numbers.
* This additive version should only be used if you know the range of the numbers
* you are dealing with is bounded and stays around the same order of magnitude.
*/
template<typename T>
static MOZ_ALWAYS_INLINE bool
FuzzyEqualsAdditive(T val1, T val2, T epsilon = detail::FuzzyEqualsEpsilon<T>::value())
{
static_assert(IsFloatingPoint<T>::value, "floating point type required");
return Abs(val1 - val2) <= epsilon;
}
/**
* Compare two floating point values for equality, allowing for rounding error
* relative to the magnitude of the values. That is, the two values are
* considered equal if they are both not NaN and they are less than or equal to
* some epsilon apart, where the epsilon is scaled by the smaller of the two
* argument values.
*
* In most cases you will want to use this rather than FuzzyEqualsAdditive, as
* this function effectively masks out differences in the bottom few bits of
* the floating point numbers being compared, regardless of what order of magnitude
* those numbers are at.
*/
template<typename T>
static MOZ_ALWAYS_INLINE bool
FuzzyEqualsMultiplicative(T val1, T val2, T epsilon = detail::FuzzyEqualsEpsilon<T>::value())
{
static_assert(IsFloatingPoint<T>::value, "floating point type required");
// can't use std::min because of bug 965340
T smaller = Abs(val1) < Abs(val2) ? Abs(val1) : Abs(val2);
return Abs(val1 - val2) <= epsilon * smaller;
}
/**
* Returns true if the given value can be losslessly represented as an IEEE-754
* single format number, false otherwise. All NaN values are considered
* representable (notwithstanding that the exact bit pattern of a double format
* NaN value can't be exactly represented in single format).
*
* This function isn't inlined to avoid buggy optimizations by MSVC.
*/
MOZ_WARN_UNUSED_RESULT
extern MFBT_API bool
IsFloat32Representable(double x);
} /* namespace mozilla */
#endif /* mozilla_FloatingPoint_h */