Adding upstream version 110.0.1.upstream/110.0.1upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 648 insertions, 0 deletions

diff --git a/mfbt/FloatingPoint.h b/mfbt/FloatingPoint.h
new file mode 100644
index 0000000000..fcc62afaa2
--- /dev/null
+++ b/mfbt/FloatingPoint.h
@@ -0,0 +1,648 @@
+/* -*- 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/MemoryChecking.h"
+#include "mozilla/Types.h"
+
+#include <algorithm>
+#include <climits>
+#include <limits>
+#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.
+ */
+
+namespace detail {
+
+/*
+ * These implementations assume float/double are 32/64-bit single/double
+ * format number types compatible with the IEEE-754 standard.  C++ doesn't
+ * require this, but we required it in implementations of these algorithms that
+ * preceded this header, so we shouldn't break anything to continue doing so.
+ */
+template <typename T>
+struct FloatingPointTrait;
+
+template <>
+struct FloatingPointTrait<float> {
+ protected:
+  using Bits = uint32_t;
+
+  static constexpr unsigned kExponentWidth = 8;
+  static constexpr unsigned kSignificandWidth = 23;
+};
+
+template <>
+struct FloatingPointTrait<double> {
+ protected:
+  using Bits = uint64_t;
+
+  static constexpr unsigned kExponentWidth = 11;
+  static constexpr unsigned kSignificandWidth = 52;
+};
+
+}  // namespace detail
+
+/*
+ *  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 final : private detail::FloatingPointTrait<T> {
+ private:
+  using Base = detail::FloatingPointTrait<T>;
+
+ public:
+  /**
+   * An unsigned integral type suitable for accessing the bitwise representation
+   * of T.
+   */
+  using Bits = typename Base::Bits;
+
+  static_assert(sizeof(T) == sizeof(Bits), "Bits must be same size as T");
+
+  /** The bit-width of the exponent component of T. */
+  using Base::kExponentWidth;
+
+  /** The bit-width of the significand component of T. */
+  using Base::kSignificandWidth;
+
+  static_assert(1 + kExponentWidth + kSignificandWidth == CHAR_BIT * sizeof(T),
+                "sign bit plus bit widths should sum to overall bit width");
+
+  /**
+   * The exponent field in an IEEE-754 floating point number consists of bits
+   * encoding an unsigned number.  The *actual* represented exponent (for all
+   * values finite and not denormal) is that value, minus a bias |kExponentBias|
+   * so that a useful range of numbers is represented.
+   */
+  static constexpr unsigned kExponentBias = (1U << (kExponentWidth - 1)) - 1;
+
+  /**
+   * The amount by which the bits of the exponent-field in an IEEE-754 floating
+   * point number are shifted from the LSB of the floating point type.
+   */
+  static constexpr unsigned kExponentShift = kSignificandWidth;
+
+  /** The sign bit in the floating point representation. */
+  static constexpr Bits kSignBit = static_cast<Bits>(1)
+                                   << (CHAR_BIT * sizeof(Bits) - 1);
+
+  /** The exponent bits in the floating point representation. */
+  static constexpr Bits kExponentBits =
+      ((static_cast<Bits>(1) << kExponentWidth) - 1) << kSignificandWidth;
+
+  /** The significand bits in the floating point representation. */
+  static constexpr Bits kSignificandBits =
+      (static_cast<Bits>(1) << kSignificandWidth) - 1;
+
+  static_assert((kSignBit & kExponentBits) == 0,
+                "sign bit shouldn't overlap exponent bits");
+  static_assert((kSignBit & kSignificandBits) == 0,
+                "sign bit shouldn't overlap significand bits");
+  static_assert((kExponentBits & kSignificandBits) == 0,
+                "exponent bits shouldn't overlap significand bits");
+
+  static_assert((kSignBit | kExponentBits | kSignificandBits) == ~Bits(0),
+                "all bits accounted for");
+};
+
+/** 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 an infinity with the specified sign bit.
+ */
+template <typename T, int SignBit>
+struct InfinityBits {
+  using Traits = FloatingPoint<T>;
+
+  static_assert(SignBit == 0 || SignBit == 1, "bad sign bit");
+  static constexpr typename Traits::Bits value =
+      (SignBit * 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));
+}
+
+namespace detail {
+
+template <typename Float, typename SignedInteger>
+inline bool NumberEqualsSignedInteger(Float aValue, SignedInteger* aInteger) {
+  static_assert(std::is_same_v<Float, float> || std::is_same_v<Float, double>,
+                "Float must be an IEEE-754 floating point type");
+  static_assert(std::is_signed_v<SignedInteger>,
+                "this algorithm only works for signed types: a different one "
+                "will be required for unsigned types");
+  static_assert(sizeof(SignedInteger) >= sizeof(int),
+                "this function *might* require some finessing for signed types "
+                "subject to integral promotion before it can be used on them");
+
+  MOZ_MAKE_MEM_UNDEFINED(aInteger, sizeof(*aInteger));
+
+  // NaNs and infinities are not integers.
+  if (!IsFinite(aValue)) {
+    return false;
+  }
+
+  // Otherwise do direct comparisons against the minimum/maximum |SignedInteger|
+  // values that can be encoded in |Float|.
+
+  constexpr SignedInteger MaxIntValue =
+      std::numeric_limits<SignedInteger>::max();  // e.g. INT32_MAX
+  constexpr SignedInteger MinValue =
+      std::numeric_limits<SignedInteger>::min();  // e.g. INT32_MIN
+
+  static_assert(IsPowerOfTwo(Abs(MinValue)),
+                "MinValue should be is a small power of two, thus exactly "
+                "representable in float/double both");
+
+  constexpr unsigned SignedIntegerWidth = CHAR_BIT * sizeof(SignedInteger);
+  constexpr unsigned ExponentShift = FloatingPoint<Float>::kExponentShift;
+
+  // Careful!  |MaxIntValue| may not be the maximum |SignedInteger| value that
+  // can be encoded in |Float|.  Its |SignedIntegerWidth - 1| bits of precision
+  // may exceed |Float|'s |ExponentShift + 1| bits of precision.  If necessary,
+  // compute the maximum |SignedInteger| that fits in |Float| from IEEE-754
+  // first principles.  (|MinValue| doesn't have this problem because as a
+  // [relatively] small power of two it's always representable in |Float|.)
+
+  // Per C++11 [expr.const]p2, unevaluated subexpressions of logical AND/OR and
+  // conditional expressions *may* contain non-constant expressions, without
+  // making the enclosing expression not constexpr.  MSVC implements this -- but
+  // it sometimes warns about undefined behavior in unevaluated subexpressions.
+  // This bites us if we initialize |MaxValue| the obvious way including an
+  // |uint64_t(1) << (SignedIntegerWidth - 2 - ExponentShift)| subexpression.
+  // Pull that shift-amount out and give it a not-too-huge value when it's in an
+  // unevaluated subexpression.  🙄
+  constexpr unsigned PrecisionExceededShiftAmount =
+      ExponentShift > SignedIntegerWidth - 1
+          ? 0
+          : SignedIntegerWidth - 2 - ExponentShift;
+
+  constexpr SignedInteger MaxValue =
+      ExponentShift > SignedIntegerWidth - 1
+          ? MaxIntValue
+          : SignedInteger((uint64_t(1) << (SignedIntegerWidth - 1)) -
+                          (uint64_t(1) << PrecisionExceededShiftAmount));
+
+  if (static_cast<Float>(MinValue) <= aValue &&
+      aValue <= static_cast<Float>(MaxValue)) {
+    auto possible = static_cast<SignedInteger>(aValue);
+    if (static_cast<Float>(possible) == aValue) {
+      *aInteger = possible;
+      return true;
+    }
+  }
+
+  return false;
+}
+
+template <typename Float, typename SignedInteger>
+inline bool NumberIsSignedInteger(Float aValue, SignedInteger* aInteger) {
+  static_assert(std::is_same_v<Float, float> || std::is_same_v<Float, double>,
+                "Float must be an IEEE-754 floating point type");
+  static_assert(std::is_signed_v<SignedInteger>,
+                "this algorithm only works for signed types: a different one "
+                "will be required for unsigned types");
+  static_assert(sizeof(SignedInteger) >= sizeof(int),
+                "this function *might* require some finessing for signed types "
+                "subject to integral promotion before it can be used on them");
+
+  MOZ_MAKE_MEM_UNDEFINED(aInteger, sizeof(*aInteger));
+
+  if (IsNegativeZero(aValue)) {
+    return false;
+  }
+
+  return NumberEqualsSignedInteger(aValue, aInteger);
+}
+
+}  // namespace detail
+
+/**
+ * If |aValue| is identical to some |int32_t| value, set |*aInt32| to that value
+ * and return true.  Otherwise return false, leaving |*aInt32| in an
+ * indeterminate state.
+ *
+ * This method returns false for negative zero.  If you want to consider -0 to
+ * be 0, use NumberEqualsInt32 below.
+ */
+template <typename T>
+static MOZ_ALWAYS_INLINE bool NumberIsInt32(T aValue, int32_t* aInt32) {
+  return detail::NumberIsSignedInteger(aValue, aInt32);
+}
+
+/**
+ * If |aValue| is identical to some |int64_t| value, set |*aInt64| to that value
+ * and return true.  Otherwise return false, leaving |*aInt64| in an
+ * indeterminate state.
+ *
+ * This method returns false for negative zero.  If you want to consider -0 to
+ * be 0, use NumberEqualsInt64 below.
+ */
+template <typename T>
+static MOZ_ALWAYS_INLINE bool NumberIsInt64(T aValue, int64_t* aInt64) {
+  return detail::NumberIsSignedInteger(aValue, aInt64);
+}
+
+/**
+ * If |aValue| is equal to some int32_t value (where -0 and +0 are considered
+ * equal), set |*aInt32| to that value and return true.  Otherwise return false,
+ * leaving |*aInt32| in an indeterminate state.
+ *
+ * |NumberEqualsInt32(-0.0, ...)| will return true.  To test whether a value can
+ * be losslessly converted to |int32_t| and back, use NumberIsInt32 above.
+ */
+template <typename T>
+static MOZ_ALWAYS_INLINE bool NumberEqualsInt32(T aValue, int32_t* aInt32) {
+  return detail::NumberEqualsSignedInteger(aValue, aInt32);
+}
+
+/**
+ * If |aValue| is equal to some int64_t value (where -0 and +0 are considered
+ * equal), set |*aInt64| to that value and return true.  Otherwise return false,
+ * leaving |*aInt64| in an indeterminate state.
+ *
+ * |NumberEqualsInt64(-0.0, ...)| will return true.  To test whether a value can
+ * be losslessly converted to |int64_t| and back, use NumberIsInt64 above.
+ */
+template <typename T>
+static MOZ_ALWAYS_INLINE bool NumberEqualsInt64(T aValue, int64_t* aInt64) {
+  return detail::NumberEqualsSignedInteger(aValue, aInt64);
+}
+
+/**
+ * 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) {
+  using Bits = typename FloatingPoint<T>::Bits;
+  if (IsNaN(aValue1)) {
+    return IsNaN(aValue2);
+  }
+  return BitwiseCast<Bits>(aValue1) == BitwiseCast<Bits>(aValue2);
+}
+
+/**
+ * Compare two floating point values for bit-wise equality.
+ */
+template <typename T>
+static inline bool NumbersAreBitwiseIdentical(T aValue1, T aValue2) {
+  using Bits = typename FloatingPoint<T>::Bits;
+  return BitwiseCast<Bits>(aValue1) == BitwiseCast<Bits>(aValue2);
+}
+
+/**
+ * Return true iff |aValue| and |aValue2| are equal (ignoring sign if both are
+ * zero) or both NaN.
+ */
+template <typename T>
+static inline bool EqualOrBothNaN(T aValue1, T aValue2) {
+  if (IsNaN(aValue1)) {
+    return IsNaN(aValue2);
+  }
+  return aValue1 == aValue2;
+}
+
+/**
+ * Return NaN if either |aValue1| or |aValue2| is NaN, or the minimum of
+ * |aValue1| and |aValue2| otherwise.
+ */
+template <typename T>
+static inline T NaNSafeMin(T aValue1, T aValue2) {
+  if (IsNaN(aValue1) || IsNaN(aValue2)) {
+    return UnspecifiedNaN<T>();
+  }
+  return std::min(aValue1, aValue2);
+}
+
+/**
+ * Return NaN if either |aValue1| or |aValue2| is NaN, or the maximum of
+ * |aValue1| and |aValue2| otherwise.
+ */
+template <typename T>
+static inline T NaNSafeMax(T aValue1, T aValue2) {
+  if (IsNaN(aValue1) || IsNaN(aValue2)) {
+    return UnspecifiedNaN<T>();
+  }
+  return std::max(aValue1, 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(std::is_floating_point_v<T>, "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(std::is_floating_point_v<T>, "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 |aValue| can be losslessly represented as an IEEE-754 single
+ * precision number, false otherwise.  All NaN values are considered
+ * representable (even though the bit patterns of double precision NaNs can't
+ * all be exactly represented in single precision).
+ */
+[[nodiscard]] extern MFBT_API bool IsFloat32Representable(double aValue);
+
+} /* namespace mozilla */
+
+#endif /* mozilla_FloatingPoint_h */