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diff --git a/src/google/protobuf/stubs/mathutil.h b/src/google/protobuf/stubs/mathutil.h
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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 <float.h>
+#include <math.h>
+
+#include <google/protobuf/stubs/common.h>
+#include <google/protobuf/stubs/logging.h>
+#include <google/protobuf/stubs/mathlimits.h>
+
+namespace google {
+namespace protobuf {
+namespace internal {
+template<typename T>
+bool IsNan(T value) {
+ return false;
+}
+template<>
+inline bool IsNan(float value) {
+#ifdef _MSC_VER
+ return _isnan(value);
+#else
+ return isnan(value);
+#endif
+}
+template<>
+inline bool IsNan(double value) {
+#ifdef _MSC_VER
+ return _isnan(value);
+#else
+ return isnan(value);
+#endif
+}
+
+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) || ::google::protobuf::internal::IsNan<T>(value)) {
+ return value;
+ }
+ return value > T(0) ? value : -value;
+ }
+
+ template<typename T>
+ static bool AlmostEquals(T a, T b) {
+ return ::google::protobuf::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 MathLimits<T>::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 MathLimits<T>::UnsignedType AbsDiff(const T x, const T y) {
+ // Carries out arithmetic as unsigned to avoid overflow.
+ typedef typename MathLimits<T>::UnsignedType 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 (MathLimits<T>::kIsInteger) {
+ return x == y;
+ } else {
+ // IsFinite checks are to make kPosInf and kNegInf not within fraction
+ if (!MathLimits<T>::IsFinite(x) && !MathLimits<T>::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_