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+// Protocol Buffers - Google's data interchange format
+// Copyright 2008 Google Inc.  All rights reserved.
+// https://developers.google.com/protocol-buffers/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//     * Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+//     * Redistributions in binary form must reproduce the above
+// copyright notice, this list of conditions and the following disclaimer
+// in the documentation and/or other materials provided with the
+// distribution.
+//     * Neither the name of Google Inc. nor the names of its
+// contributors may be used to endorse or promote products derived from
+// this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+#ifndef GOOGLE_PROTOBUF_STUBS_MATHUTIL_H_
+#define GOOGLE_PROTOBUF_STUBS_MATHUTIL_H_
+
+#include <cmath>
+#include <float.h>
+#include <limits>
+
+#include <stubs/common.h>
+#include <stubs/logging.h>
+
+namespace google {
+namespace protobuf {
+namespace internal {
+
+// Like std::make_unsigned_t except floating point types map to themselves.
+template <typename T>
+using MakeUnsignedT =
+    typename std::conditional<std::is_integral<T>::value, std::make_unsigned<T>,
+                              std::common_type<T>>::type::type;
+
+// Like std::isnan() except a template function that is defined for all numeric
+// types.
+template <typename T,
+          typename std::enable_if<std::is_integral<T>::value, int>::type = 0>
+bool IsNan(T /*val*/) {
+  return false;
+}
+
+template <typename T, typename std::enable_if<std::is_floating_point<T>::value,
+                                              int>::type = 0>
+bool IsNan(T val) {
+  return std::isnan(val);
+}
+
+template<typename T>
+bool AlmostEquals(T a, T b) {
+  return a == b;
+}
+template<>
+inline bool AlmostEquals(float a, float b) {
+  return fabs(a - b) < 32 * FLT_EPSILON;
+}
+
+template<>
+inline bool AlmostEquals(double a, double b) {
+  return fabs(a - b) < 32 * DBL_EPSILON;
+}
+
+}  // namespace internal
+
+class MathUtil {
+ public:
+  template <typename T>
+  static T Sign(T value) {
+    if (value == T(0) || internal::IsNan(value)) {
+      return value;
+    }
+    return value > T(0) ? 1 : -1;
+  }
+
+  template <typename T>
+  static bool AlmostEquals(T a, T b) {
+    return internal::AlmostEquals(a, b);
+  }
+
+  // Largest of two values.
+  // Works correctly for special floating point values.
+  // Note: 0.0 and -0.0 are not differentiated by Max (Max(0.0, -0.0) is -0.0),
+  // which should be OK because, although they (can) have different
+  // bit representation, they are observably the same when examined
+  // with arithmetic and (in)equality operators.
+  template <typename T>
+  static T Max(const T x, const T y) {
+    return internal::IsNan(x) || x > y ? x : y;
+  }
+
+  // Absolute value of x
+  // Works correctly for unsigned types and
+  // for special floating point values.
+  // Note: 0.0 and -0.0 are not differentiated by Abs (Abs(0.0) is -0.0),
+  // which should be OK: see the comment for Max above.
+  template<typename T>
+  static T Abs(const T x) {
+    return x > T(0) ? x : -x;
+  }
+
+  // Absolute value of the difference between two numbers.
+  // Works correctly for signed types and special floating point values.
+  template <typename T>
+  static typename internal::MakeUnsignedT<T> AbsDiff(const T x, const T y) {
+    // Carries out arithmetic as unsigned to avoid overflow.
+    typedef typename internal::MakeUnsignedT<T> R;
+    return x > y ? R(x) - R(y) : R(y) - R(x);
+  }
+
+  // If two (usually floating point) numbers are within a certain
+  // fraction of their magnitude or within a certain absolute margin of error.
+  // This is the same as the following but faster:
+  //   WithinFraction(x, y, fraction)  ||  WithinMargin(x, y, margin)
+  // E.g. WithinFraction(0.0, 1e-10, 1e-5) is false but
+  //      WithinFractionOrMargin(0.0, 1e-10, 1e-5, 1e-5) is true.
+  template<typename T>
+  static bool WithinFractionOrMargin(const T x, const T y,
+                                     const T fraction, const T margin);
+};
+
+template<typename T>
+bool MathUtil::WithinFractionOrMargin(const T x, const T y,
+                                      const T fraction, const T margin) {
+  // Not just "0 <= fraction" to fool the compiler for unsigned types.
+  GOOGLE_DCHECK((T(0) < fraction || T(0) == fraction) &&
+         fraction < T(1) &&
+         margin >= T(0));
+
+  // Template specialization will convert the if() condition to a constant,
+  // which will cause the compiler to generate code for either the "if" part
+  // or the "then" part.  In this way we avoid a compiler warning
+  // about a potential integer overflow in crosstool v12 (gcc 4.3.1).
+  if (std::numeric_limits<T>::is_integer) {
+    return x == y;
+  } else {
+    if (!std::isfinite(x) || !std::isfinite(y)) {
+      return false;
+    }
+    T relative_margin = static_cast<T>(fraction * Max(Abs(x), Abs(y)));
+    return AbsDiff(x, y) <= Max(margin, relative_margin);
+  }
+}
+
+}  // namespace protobuf
+}  // namespace google
+
+#endif  // GOOGLE_PROTOBUF_STUBS_MATHUTIL_H_