gecko/mfbt/FloatingPoint.h

/* -*- Mode: C++; tab-width: 2; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
/* 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/StandardInteger.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.
 */
MOZ_STATIC_ASSERT(sizeof(double) == sizeof(uint64_t), "double must be 64 bits");

const unsigned DoubleExponentBias = 1023;
const unsigned DoubleExponentShift = 52;

namespace detail {

const uint64_t DoubleSignBit         = 0x8000000000000000ULL;
const uint64_t DoubleExponentBits    = 0x7ff0000000000000ULL;
const uint64_t DoubleSignificandBits = 0x000fffffffffffffULL;

MOZ_STATIC_ASSERT((DoubleSignBit & DoubleExponentBits) == 0,
                  "sign bit doesn't overlap exponent bits");
MOZ_STATIC_ASSERT((DoubleSignBit & DoubleSignificandBits) == 0,
                  "sign bit doesn't overlap significand bits");
MOZ_STATIC_ASSERT((DoubleExponentBits & DoubleSignificandBits) == 0,
                  "exponent bits don't overlap significand bits");

MOZ_STATIC_ASSERT((DoubleSignBit | DoubleExponentBits | DoubleSignificandBits) ==
                  ~uint64_t(0),
                  "all bits accounted for");

union DoublePun
{
    /*
     * Every way to pun the bits of a double introduces an additional layer of
     * complexity, across a multitude of platforms, architectures, and ABIs.
     * Use *only* uint64_t to reduce complexity.  Don't add new punning here
     * without discussion!
     */
    uint64_t u;
    double d;
};

} /* namespace detail */

/** Determines whether a double is NaN. */
static MOZ_ALWAYS_INLINE bool
IsNaN(double d)
{
  union detail::DoublePun pun;
  pun.d = d;

  /*
   * A double is NaN if all exponent bits are 1 and the significand contains at
   * least one non-zero bit.
   */
  return (pun.u & detail::DoubleExponentBits) == detail::DoubleExponentBits &&
         (pun.u & detail::DoubleSignificandBits) != 0;
}

/** Determines whether a double is +Infinity or -Infinity. */
static MOZ_ALWAYS_INLINE bool
IsInfinite(double d)
{
  union detail::DoublePun pun;
  pun.d = d;

  /* Infinities have all exponent bits set to 1 and an all-0 significand. */
  return (pun.u & ~detail::DoubleSignBit) == detail::DoubleExponentBits;
}

/** Determines whether a double is not NaN or infinite. */
static MOZ_ALWAYS_INLINE bool
IsFinite(double d)
{
  union detail::DoublePun pun;
  pun.d = d;

  /*
   * NaN and Infinities are the only non-finite doubles, and both have all
   * exponent bits set to 1.
   */
  return (pun.u & detail::DoubleExponentBits) != detail::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");

  union detail::DoublePun pun;
  pun.d = d;

  /* The sign bit is set if the double is negative. */
  return (pun.u & detail::DoubleSignBit) != 0;
}

/** Determines whether a double represents -0. */
static MOZ_ALWAYS_INLINE bool
IsNegativeZero(double d)
{
  union detail::DoublePun pun;
  pun.d = d;

  /* Only the sign bit is set if the double is -0. */
  return pun.u == detail::DoubleSignBit;
}

/** Returns the exponent portion of the double. */
static MOZ_ALWAYS_INLINE int_fast16_t
ExponentComponent(double d)
{
  union detail::DoublePun pun;
  pun.d = d;

  /*
   * The exponent component of a double is an unsigned number, biased from its
   * actual value.  Subtract the bias to retrieve the actual exponent.
   */
  return int_fast16_t((pun.u & detail::DoubleExponentBits) >> DoubleExponentShift) -
         int_fast16_t(DoubleExponentBias);
}

/** Returns +Infinity. */
static MOZ_ALWAYS_INLINE double
PositiveInfinity()
{
  union detail::DoublePun pun;

  /*
   * Positive infinity has all exponent bits set, sign bit set to 0, and no
   * significand.
   */
  pun.u = detail::DoubleExponentBits;
  return pun.d;
}

/** Returns -Infinity. */
static MOZ_ALWAYS_INLINE double
NegativeInfinity()
{
  union detail::DoublePun pun;

  /*
   * Negative infinity has all exponent bits set, sign bit set to 1, and no
   * significand.
   */
  pun.u = detail::DoubleSignBit | detail::DoubleExponentBits;
  return pun.d;
}

/** 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 & ~detail::DoubleSignificandBits) == 0);
  MOZ_ASSERT(significand & detail::DoubleSignificandBits);

  union detail::DoublePun pun;
  pun.u = (signbit ? detail::DoubleSignBit : 0) |
          detail::DoubleExponentBits |
          significand;
  MOZ_ASSERT(IsNaN(pun.d));
  return pun.d;
}

/** Computes the smallest non-zero positive double value. */
static MOZ_ALWAYS_INLINE double
MinDoubleValue()
{
  union detail::DoublePun pun;
  pun.u = 1;
  return pun.d;
}

static MOZ_ALWAYS_INLINE bool
DoubleIsInt32(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 !IsNegativeZero(d) && d == (*i = int32_t(d));
}

/**
 * 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()
{
  return mozilla::SpecificNaN(0, 0xfffffffffffffULL);
}

} /* namespace mozilla */

#endif  /* mozilla_FloatingPoint_h_ */