diff -r 000000000000 -r 6474c204b198 mfbt/FloatingPoint.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/mfbt/FloatingPoint.h	Wed Dec 31 06:09:35 2014 +0100
@@ -0,0 +1,409 @@
+/* -*- 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 ExponentBias = 127;
+    static const unsigned ExponentShift = 23;
+
+    static const Bits SignBit         = 0x80000000UL;
+    static const Bits ExponentBits    = 0x7F800000UL;
+    static const Bits SignificandBits = 0x007FFFFFUL;
+};
+
+struct DoubleTypeTraits
+{
+    typedef uint64_t Bits;
+
+    static const unsigned ExponentBias = 1023;
+    static const unsigned ExponentShift = 52;
+
+    static const Bits SignBit         = 0x8000000000000000ULL;
+    static const Bits ExponentBits    = 0x7ff0000000000000ULL;
+    static const Bits SignificandBits = 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).
+ *
+ *  ExponentBias is the offset that is subtracted from the exponent when
+ *  computing the value, i.e. one plus the opposite of the mininum possible
+ *  exponent.
+ *  ExponentShift is the shift that one needs to apply to retrieve the exponent
+ *  component of the value.
+ *
+ *  SignBit contains a bits mask. Bit-and-ing with this mask will result in
+ *  obtaining the sign bit.
+ *  ExponentBits contains the mask needed for obtaining the exponent bits and
+ *  SignificandBits 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::SignBit & Base::ExponentBits) == 0,
+                  "sign bit shouldn't overlap exponent bits");
+    static_assert((Base::SignBit & Base::SignificandBits) == 0,
+                  "sign bit shouldn't overlap significand bits");
+    static_assert((Base::ExponentBits & Base::SignificandBits) == 0,
+                  "exponent bits shouldn't overlap significand bits");
+
+    static_assert((Base::SignBit | Base::ExponentBits | Base::SignificandBits) ==
+                  ~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 double is NaN. */
+template<typename T>
+static MOZ_ALWAYS_INLINE bool
+IsNaN(T t)
+{
+  /*
+   * 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;
+  Bits bits = BitwiseCast<Bits>(t);
+  return (bits & Traits::ExponentBits) == Traits::ExponentBits &&
+         (bits & Traits::SignificandBits) != 0;
+}
+
+/** Determines whether a float/double is +Infinity or -Infinity. */
+template<typename T>
+static MOZ_ALWAYS_INLINE bool
+IsInfinite(T t)
+{
+  /* 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>(t);
+  return (bits & ~Traits::SignBit) == Traits::ExponentBits;
+}
+
+/** Determines whether a float/double is not NaN or infinite. */
+template<typename T>
+static MOZ_ALWAYS_INLINE bool
+IsFinite(T t)
+{
+  /*
+   * 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>(t);
+  return (bits & Traits::ExponentBits) != Traits::ExponentBits;
+}
+
+/**
+ * Determines whether a float/double is negative.  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 t)
+{
+  MOZ_ASSERT(!IsNaN(t), "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>(t);
+  return (bits & Traits::SignBit) != 0;
+}
+
+/** Determines whether a float/double represents -0. */
+template<typename T>
+static MOZ_ALWAYS_INLINE bool
+IsNegativeZero(T t)
+{
+  /* Only the sign bit is set if the value is -0. */
+  typedef FloatingPoint<T> Traits;
+  typedef typename Traits::Bits Bits;
+  Bits bits = BitwiseCast<Bits>(t);
+  return bits == Traits::SignBit;
+}
+
+/**
+ * Returns the exponent portion of the float/double.
+ *
+ * Zero is not special-cased, so ExponentComponent(0.0) is
+ * -int_fast16_t(Traits::ExponentBias).
+ */
+template<typename T>
+static MOZ_ALWAYS_INLINE int_fast16_t
+ExponentComponent(T t)
+{
+  /*
+   * 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>(t);
+  return int_fast16_t((bits & Traits::ExponentBits) >> Traits::ExponentShift) -
+         int_fast16_t(Traits::ExponentBias);
+}
+
+/** 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::ExponentBits);
+}
+
+/** 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::SignBit | Traits::ExponentBits);
+}
+
+
+/** Constructs a NaN value with the specified sign bit and significand bits. */
+template<typename T>
+static MOZ_ALWAYS_INLINE T
+SpecificNaN(int signbit, typename FloatingPoint<T>::Bits significand)
+{
+  typedef FloatingPoint<T> Traits;
+  MOZ_ASSERT(signbit == 0 || signbit == 1);
+  MOZ_ASSERT((significand & ~Traits::SignificandBits) == 0);
+  MOZ_ASSERT(significand & Traits::SignificandBits);
+
+  T t = BitwiseCast<T>((signbit ? Traits::SignBit : 0) |
+                       Traits::ExponentBits |
+                       significand);
+  MOZ_ASSERT(IsNaN(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 t 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 NumberIsInt32 instead.
+ */
+template<typename T>
+static MOZ_ALWAYS_INLINE bool
+NumberEqualsInt32(T t, int32_t* i)
+{
+  /*
+   * 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 t == (*i = int32_t(t));
+}
+
+/**
+ * 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 NumberEqualsInt32 is that this method returns
+ * false for negative zero.
+ */
+template<typename T>
+static MOZ_ALWAYS_INLINE bool
+NumberIsInt32(T t, int32_t* i)
+{
+  return !IsNegativeZero(t) && NumberEqualsInt32(t, i);
+}
+
+/**
+ * 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::SignificandBits);
+}
+
+/**
+ * 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 t1, T t2)
+{
+  typedef FloatingPoint<T> Traits;
+  typedef typename Traits::Bits Bits;
+  if (IsNaN(t1))
+    return IsNaN(t2);
+  return BitwiseCast<Bits>(t1) == BitwiseCast<Bits>(t2);
+}
+
+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 */