text: // 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
  