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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.
+
+// All Rights Reserved.
+//
+// Author: Maxim Lifantsev
+//
+
+#include <google/protobuf/stubs/mathlimits.h>
+
+#include <google/protobuf/stubs/common.h>
+
+namespace google {
+namespace protobuf {
+
+// MSVC++ 2005 and older compilers think the header declaration was a
+// definition, and erroneously flag these as a duplicate definition.
+#if defined(COMPILER_MSVC) || __cpluscplus < 201103L
+
+#define DEF_COMMON_LIMITS(Type)
+#define DEF_UNSIGNED_INT_LIMITS(Type)
+#define DEF_SIGNED_INT_LIMITS(Type)
+#define DEF_PRECISION_LIMITS(Type)
+
+#else
+
+#define DEF_COMMON_LIMITS(Type) \
+const bool MathLimits<Type>::kIsSigned; \
+const bool MathLimits<Type>::kIsInteger; \
+const int MathLimits<Type>::kMin10Exp; \
+const int MathLimits<Type>::kMax10Exp;
+
+#define DEF_UNSIGNED_INT_LIMITS(Type) \
+DEF_COMMON_LIMITS(Type) \
+const Type MathLimits<Type>::kPosMin; \
+const Type MathLimits<Type>::kPosMax; \
+const Type MathLimits<Type>::kMin; \
+const Type MathLimits<Type>::kMax; \
+const Type MathLimits<Type>::kEpsilon; \
+const Type MathLimits<Type>::kStdError;
+
+#define DEF_SIGNED_INT_LIMITS(Type) \
+DEF_UNSIGNED_INT_LIMITS(Type) \
+const Type MathLimits<Type>::kNegMin; \
+const Type MathLimits<Type>::kNegMax;
+
+#define DEF_PRECISION_LIMITS(Type) \
+const int MathLimits<Type>::kPrecisionDigits;
+
+#endif // not COMPILER_MSVC
+
+// http://en.wikipedia.org/wiki/Quadruple_precision_floating-point_format#Double-double_arithmetic
+// With some compilers (gcc 4.6.x) on some platforms (powerpc64),
+// "long double" is implemented as a pair of double: "double double" format.
+// This causes a problem with epsilon (eps).
+// eps is the smallest positive number such that 1.0 + eps > 1.0
+//
+// Normal format: 1.0 + e = 1.0...01 // N-1 zeros for N fraction bits
+// D-D format: 1.0 + e = 1.000...0001 // epsilon can be very small
+//
+// In the normal format, 1.0 + e has to fit in one stretch of bits.
+// The maximum rounding error is half of eps.
+//
+// In the double-double format, 1.0 + e splits across two doubles:
+// 1.0 in the high double, e in the low double, and they do not have to
+// be contiguous. The maximum rounding error on a value close to 1.0 is
+// much larger than eps.
+//
+// Some code checks for errors by comparing a computed value to a golden
+// value +/- some multiple of the maximum rounding error. The maximum
+// rounding error is not available so we use eps as an approximation
+// instead. That fails when long double is in the double-double format.
+// Therefore, we define kStdError as a multiple of
+// max(DBL_EPSILON * DBL_EPSILON, kEpsilon) rather than a multiple of kEpsilon.
+
+#define DEF_FP_LIMITS(Type, PREFIX) \
+DEF_COMMON_LIMITS(Type) \
+const Type MathLimits<Type>::kPosMin = PREFIX##_MIN; \
+const Type MathLimits<Type>::kPosMax = PREFIX##_MAX; \
+const Type MathLimits<Type>::kMin = -MathLimits<Type>::kPosMax; \
+const Type MathLimits<Type>::kMax = MathLimits<Type>::kPosMax; \
+const Type MathLimits<Type>::kNegMin = -MathLimits<Type>::kPosMin; \
+const Type MathLimits<Type>::kNegMax = -MathLimits<Type>::kPosMax; \
+const Type MathLimits<Type>::kEpsilon = PREFIX##_EPSILON; \
+/* 32 is 5 bits of mantissa error; should be adequate for common errors */ \
+const Type MathLimits<Type>::kStdError = \
+ 32 * (DBL_EPSILON * DBL_EPSILON > MathLimits<Type>::kEpsilon \
+ ? DBL_EPSILON * DBL_EPSILON : MathLimits<Type>::kEpsilon); \
+DEF_PRECISION_LIMITS(Type) \
+const Type MathLimits<Type>::kNaN = HUGE_VAL - HUGE_VAL; \
+const Type MathLimits<Type>::kPosInf = HUGE_VAL; \
+const Type MathLimits<Type>::kNegInf = -HUGE_VAL;
+
+// The following are *not* casts!
+DEF_SIGNED_INT_LIMITS(int8)
+DEF_SIGNED_INT_LIMITS(int16) // NOLINT(readability/casting)
+DEF_SIGNED_INT_LIMITS(int32) // NOLINT(readability/casting)
+DEF_SIGNED_INT_LIMITS(int64) // NOLINT(readability/casting)
+DEF_UNSIGNED_INT_LIMITS(uint8)
+DEF_UNSIGNED_INT_LIMITS(uint16) // NOLINT(readability/casting)
+DEF_UNSIGNED_INT_LIMITS(uint32) // NOLINT(readability/casting)
+DEF_UNSIGNED_INT_LIMITS(uint64) // NOLINT(readability/casting)
+
+DEF_SIGNED_INT_LIMITS(long int)
+DEF_UNSIGNED_INT_LIMITS(unsigned long int)
+
+DEF_FP_LIMITS(float, FLT)
+DEF_FP_LIMITS(double, DBL)
+DEF_FP_LIMITS(long double, LDBL);
+
+#undef DEF_COMMON_LIMITS
+#undef DEF_SIGNED_INT_LIMITS
+#undef DEF_UNSIGNED_INT_LIMITS
+#undef DEF_FP_LIMITS
+#undef DEF_PRECISION_LIMITS
+} // namespace protobuf
+} // namespace google