mathlimits.cc

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// All Rights Reserved.
//
// Author: Maxim Lifantsev
//
 
#include <google/protobuf/stubs/mathlimits.h>
 
#include <google/protobuf/stubs/common.h>
 
namespace google {
namespace protobuf {
 
// 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) \
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); \
const Type MathLimits<Type>::kNaN = HUGE_VAL - HUGE_VAL; \
const Type MathLimits<Type>::kPosInf = HUGE_VAL; \
const Type MathLimits<Type>::kNegInf = -HUGE_VAL;
 
DEF_FP_LIMITS(float, FLT)
DEF_FP_LIMITS(double, DBL)
DEF_FP_LIMITS(long double, LDBL);
 
#undef DEF_FP_LIMITS
}  // namespace protobuf
}  // namespace google