Mirror of roytam1's UXP fork just in case Moonchild and Tobin decide to go after him
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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/. */
/* 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.
*/
struct FloatTypeTraits
{
typedef uint32_t Bits;
static const unsigned kExponentBias = 127;
static const unsigned kExponentShift = 23;
static const Bits kSignBit = 0x80000000UL;
static const Bits kExponentBits = 0x7F800000UL;
static const Bits kSignificandBits = 0x007FFFFFUL;
};
struct DoubleTypeTraits
{
typedef uint64_t Bits;
static const unsigned kExponentBias = 1023;
static const unsigned kExponentShift = 52;
static const Bits kSignBit = 0x8000000000000000ULL;
static const Bits kExponentBits = 0x7ff0000000000000ULL;
static const Bits kSignificandBits = 0x000fffffffffffffULL;
};
template<typename T> struct SelectTrait;
template<> struct SelectTrait<float> : public FloatTypeTraits {};
template<> struct SelectTrait<double> : public DoubleTypeTraits {};
/*
* This struct contains details regarding the encoding of floating-point
* numbers that can be useful for direct bit manipulation. As of now, the
* template parameter has to be float or double.
*
* The nested typedef |Bits| is the unsigned integral type with the same size
* as T: uint32_t for float and uint64_t for double (static assertions
* double-check these assumptions).
*
* kExponentBias is the offset that is subtracted from the exponent when
* computing the value, i.e. one plus the opposite of the mininum possible
* exponent.
* kExponentShift is the shift that one needs to apply to retrieve the
* exponent component of the value.
*
* kSignBit contains a bits mask. Bit-and-ing with this mask will result in
* obtaining the sign bit.
* kExponentBits contains the mask needed for obtaining the exponent bits and
* kSignificandBits contains the mask needed for obtaining the significand
* bits.
*
* Full details of how floating point number formats are encoded are beyond
* the scope of this comment. For more information, see
* http://en.wikipedia.org/wiki/IEEE_floating_point
* http://en.wikipedia.org/wiki/Floating_point#IEEE_754:_floating_point_in_modern_computers
*/
template<typename T>
struct FloatingPoint : public SelectTrait<T>
{
typedef SelectTrait<T> Base;
typedef typename Base::Bits Bits;
static_assert((Base::kSignBit & Base::kExponentBits) == 0,
"sign bit shouldn't overlap exponent bits");
static_assert((Base::kSignBit & Base::kSignificandBits) == 0,
"sign bit shouldn't overlap significand bits");
static_assert((Base::kExponentBits & Base::kSignificandBits) == 0,
"exponent bits shouldn't overlap significand bits");
static_assert((Base::kSignBit | Base::kExponentBits | Base::kSignificandBits) ==
~Bits(0),
"all bits accounted for");
/*
* These implementations assume float/double are 32/64-bit single/double
* format number types compatible with the IEEE-754 standard. 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 keep doing so.
*/
static_assert(sizeof(T) == sizeof(Bits), "Bits must be same size as T");
};
/** Determines whether a float/double is NaN. */
template<typename T>
static MOZ_ALWAYS_INLINE bool
IsNaN(T aValue)
{
/*
* A float/double is NaN if all exponent bits are 1 and the significand
* contains at least one non-zero bit.
*/
typedef FloatingPoint<T> Traits;
typedef typename Traits::Bits Bits;
return (BitwiseCast<Bits>(aValue) & Traits::kExponentBits) == Traits::kExponentBits &&
(BitwiseCast<Bits>(aValue) & Traits::kSignificandBits) != 0;
}
/** Determines whether a float/double is +Infinity or -Infinity. */
template<typename T>
static MOZ_ALWAYS_INLINE bool
IsInfinite(T aValue)
{
/* Infinities have all exponent bits set to 1 and an all-0 significand. */
typedef FloatingPoint<T> Traits;
typedef typename Traits::Bits Bits;
Bits bits = BitwiseCast<Bits>(aValue);
return (bits & ~Traits::kSignBit) == Traits::kExponentBits;
}
/** Determines whether a float/double is not NaN or infinite. */
template<typename T>
static MOZ_ALWAYS_INLINE bool
IsFinite(T aValue)
{
/*
* NaN and Infinities are the only non-finite floats/doubles, and both have
* all exponent bits set to 1.
*/
typedef FloatingPoint<T> Traits;
typedef typename Traits::Bits Bits;
Bits bits = BitwiseCast<Bits>(aValue);
return (bits & Traits::kExponentBits) != Traits::kExponentBits;
}
/**
* Determines whether a float/double is negative or -0. It is an error
* to call this method on a float/double which is NaN.
*/
template<typename T>
static MOZ_ALWAYS_INLINE bool
IsNegative(T aValue)
{
MOZ_ASSERT(!IsNaN(aValue), "NaN does not have a sign");
/* The sign bit is set if the double is negative. */
typedef FloatingPoint<T> Traits;
typedef typename Traits::Bits Bits;
Bits bits = BitwiseCast<Bits>(aValue);
return (bits & Traits::kSignBit) != 0;
}
/** Determines whether a float/double represents -0. */
template<typename T>
static MOZ_ALWAYS_INLINE bool
IsNegativeZero(T aValue)
{
/* Only the sign bit is set if the value is -0. */
typedef FloatingPoint<T> Traits;
typedef typename Traits::Bits Bits;
Bits bits = BitwiseCast<Bits>(aValue);
return bits == Traits::kSignBit;
}
/** Determines wether a float/double represents +0. */
template<typename T>
static MOZ_ALWAYS_INLINE bool
IsPositiveZero(T aValue)
{
/* All bits are zero if the value is +0. */
typedef FloatingPoint<T> Traits;
typedef typename Traits::Bits Bits;
Bits bits = BitwiseCast<Bits>(aValue);
return bits == 0;
}
/**
* Returns 0 if a float/double is NaN or infinite;
* otherwise, the float/double is returned.
*/
template<typename T>
static MOZ_ALWAYS_INLINE T
ToZeroIfNonfinite(T aValue)
{
return IsFinite(aValue) ? aValue : 0;
}
/**
* Returns the exponent portion of the float/double.
*
* Zero is not special-cased, so ExponentComponent(0.0) is
* -int_fast16_t(Traits::kExponentBias).
*/
template<typename T>
static MOZ_ALWAYS_INLINE int_fast16_t
ExponentComponent(T aValue)
{
/*
* The exponent component of a float/double is an unsigned number, biased
* from its actual value. Subtract the bias to retrieve the actual exponent.
*/
typedef FloatingPoint<T> Traits;
typedef typename Traits::Bits Bits;
Bits bits = BitwiseCast<Bits>(aValue);
return int_fast16_t((bits & Traits::kExponentBits) >> Traits::kExponentShift) -
int_fast16_t(Traits::kExponentBias);
}
/** Returns +Infinity. */
template<typename T>
static MOZ_ALWAYS_INLINE T
PositiveInfinity()
{
/*
* Positive infinity has all exponent bits set, sign bit set to 0, and no
* significand.
*/
typedef FloatingPoint<T> Traits;
return BitwiseCast<T>(Traits::kExponentBits);
}
/** Returns -Infinity. */
template<typename T>
static MOZ_ALWAYS_INLINE T
NegativeInfinity()
{
/*
* Negative infinity has all exponent bits set, sign bit set to 1, and no
* significand.
*/
typedef FloatingPoint<T> Traits;
return BitwiseCast<T>(Traits::kSignBit | Traits::kExponentBits);
}
/**
* Computes the bit pattern for a NaN with the specified sign bit and
* significand bits.
*/
template<typename T,
int SignBit,
typename FloatingPoint<T>::Bits Significand>
struct SpecificNaNBits
{
using Traits = FloatingPoint<T>;
static_assert(SignBit == 0 || SignBit == 1, "bad sign bit");
static_assert((Significand & ~Traits::kSignificandBits) == 0,
"significand must only have significand bits set");
static_assert(Significand & Traits::kSignificandBits,
"significand must be nonzero");
static constexpr typename Traits::Bits value =
(SignBit * Traits::kSignBit) | Traits::kExponentBits | Significand;
};
/**
* Constructs a NaN value with the specified sign bit and significand bits.
*
* There is also a variant that returns the value directly. In most cases, the
* two variants should be identical. However, in the specific case of x86
* chips, the behavior differs: returning floating-point values directly is done
* through the x87 stack, and x87 loads and stores turn signaling NaNs into
* quiet NaNs... silently. Returning floating-point values via outparam,
* however, is done entirely within the SSE registers when SSE2 floating-point
* is enabled in the compiler, which has semantics-preserving behavior you would
* expect.
*
* If preserving the distinction between signaling NaNs and quiet NaNs is
* important to you, you should use the outparam version. In all other cases,
* you should use the direct return version.
*/
template<typename T>
static MOZ_ALWAYS_INLINE void
SpecificNaN(int signbit, typename FloatingPoint<T>::Bits significand, T* result)
{
typedef FloatingPoint<T> Traits;
MOZ_ASSERT(signbit == 0 || signbit == 1);
MOZ_ASSERT((significand & ~Traits::kSignificandBits) == 0);
MOZ_ASSERT(significand & Traits::kSignificandBits);
BitwiseCast<T>((signbit ? Traits::kSignBit : 0) |
Traits::kExponentBits |
significand,
result);
MOZ_ASSERT(IsNaN(*result));
}
template<typename T>
static MOZ_ALWAYS_INLINE T
SpecificNaN(int signbit, typename FloatingPoint<T>::Bits significand)
{
T t;
SpecificNaN(signbit, significand, &t);
return t;
}
/** Computes the smallest non-zero positive float/double value. */
template<typename T>
static MOZ_ALWAYS_INLINE T
MinNumberValue()
{
typedef FloatingPoint<T> Traits;
typedef typename Traits::Bits Bits;
return BitwiseCast<T>(Bits(1));
}
/**
* If aValue is equal to some int32_t value, set *aInt32 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 NumberIsInt32 instead.
*/
template<typename T>
static MOZ_ALWAYS_INLINE bool
NumberEqualsInt32(T aValue, int32_t* aInt32)
{
/*
* XXX Casting a floating-point value 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 aValue == (*aInt32 = int32_t(aValue));
}
/**
* If d can be converted to int32_t and back to an identical double value,
* set *aInt32 to that value and return true; otherwise return false.
*
* The difference between this and NumberEqualsInt32 is that this method returns
* false for negative zero.
*/
template<typename T>
static MOZ_ALWAYS_INLINE bool
NumberIsInt32(T aValue, int32_t* aInt32)
{
return !IsNegativeZero(aValue) && NumberEqualsInt32(aValue, aInt32);
}
/**
* Computes a NaN value. Do not use this method if you depend upon a particular
* NaN value being returned.
*/
template<typename T>
static MOZ_ALWAYS_INLINE T
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).
*/
typedef FloatingPoint<T> Traits;
return SpecificNaN<T>(1, Traits::kSignificandBits);
}
/**
* 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.)
*/
template<typename T>
static inline bool
NumbersAreIdentical(T aValue1, T aValue2)
{
typedef FloatingPoint<T> Traits;
typedef typename Traits::Bits Bits;
if (IsNaN(aValue1)) {
return IsNaN(aValue2);
}
return BitwiseCast<Bits>(aValue1) == BitwiseCast<Bits>(aValue2);
}
namespace detail {
template<typename T>
struct FuzzyEqualsEpsilon;
template<>
struct FuzzyEqualsEpsilon<float>
{
// A number near 1e-5 that is exactly representable in a float.
static float value() { return 1.0f / (1 << 17); }
};
template<>
struct FuzzyEqualsEpsilon<double>
{
// A number near 1e-12 that is exactly representable in a double.
static 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 aEpsilon apart. The default value of aEpsilon 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 aValue1, T aValue2,
T aEpsilon = detail::FuzzyEqualsEpsilon<T>::value())
{
static_assert(IsFloatingPoint<T>::value, "floating point type required");
return Abs(aValue1 - aValue2) <= aEpsilon;
}
/**
* 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 aEpsilon apart, where the aEpsilon 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 aValue1, T aValue2,
T aEpsilon = 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(aValue1) < Abs(aValue2) ? Abs(aValue1) : Abs(aValue2);
return Abs(aValue1 - aValue2) <= aEpsilon * 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_MUST_USE
extern MFBT_API bool
IsFloat32Representable(double aFloat32);
} /* namespace mozilla */
#endif /* mozilla_FloatingPoint_h */