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// Author: Maxim Lifantsev
//
// Useful integer and floating point limits and type traits.
//
// This partially replaces/duplictes numeric_limits<> from <limits>.
// We get a Google-style class that we have a greater control over
// and thus can add new features to it or fix whatever happens to be broken in
// numeric_limits for the compilers we use.
//
#ifndef UTIL_MATH_MATHLIMITS_H__
#define UTIL_MATH_MATHLIMITS_H__
// <math.h> lacks a lot of prototypes. However, this file needs <math.h> to
// access old-fashioned isinf et al. Even worse more: this file must not
// include <cmath> because that breaks the definition of isinf with gcc 4.9.
//
// TODO(mec): after C++11 everywhere, use <cmath> and std::isinf in this file.
#include <math.h>
#include <string.h>
#include <cfloat>
// ========================================================================= //
// Useful integer and floating point limits and type traits.
// This is just for the documentation;
// real members are defined in our specializations below.
namespace google {
namespace protobuf {
template<typename T> struct MathLimits {
// Type name.
typedef T Type;
// Unsigned version of the Type with the same byte size.
// Same as Type for floating point and unsigned types.
typedef T UnsignedType;
// If the type supports negative values.
static const bool kIsSigned;
// If the type supports only integer values.
static const bool kIsInteger;
// Magnitude-wise smallest representable positive value.
static const Type kPosMin;
// Magnitude-wise largest representable positive value.
static const Type kPosMax;
// Smallest representable value.
static const Type kMin;
// Largest representable value.
static const Type kMax;
// Magnitude-wise smallest representable negative value.
// Present only if kIsSigned.
static const Type kNegMin;
// Magnitude-wise largest representable negative value.
// Present only if kIsSigned.
static const Type kNegMax;
// Smallest integer x such that 10^x is representable.
static const int kMin10Exp;
// Largest integer x such that 10^x is representable.
static const int kMax10Exp;
// Smallest positive value such that Type(1) + kEpsilon != Type(1)
static const Type kEpsilon;
// Typical rounding error that is enough to cover
// a few simple floating-point operations.
// Slightly larger than kEpsilon to account for a few rounding errors.
// Is zero if kIsInteger.
static const Type kStdError;
// Number of decimal digits of mantissa precision.
// Present only if !kIsInteger.
static const int kPrecisionDigits;
// Not a number, i.e. result of 0/0.
// Present only if !kIsInteger.
static const Type kNaN;
// Positive infinity, i.e. result of 1/0.
// Present only if !kIsInteger.
static const Type kPosInf;
// Negative infinity, i.e. result of -1/0.
// Present only if !kIsInteger.
static const Type kNegInf;
// NOTE: Special floating point values behave
// in a special (but mathematically-logical) way
// in terms of (in)equalty comparison and mathematical operations
// -- see out unittest for examples.
// Special floating point value testers.
// Present in integer types for convenience.
static bool IsFinite(const Type x);
static bool IsNaN(const Type x);
static bool IsInf(const Type x);
static bool IsPosInf(const Type x);
static bool IsNegInf(const Type x);
};
// ========================================================================= //
// All #define-s below are simply to refactor the declarations of
// MathLimits template specializations.
// They are all #undef-ined below.
// The hoop-jumping in *_INT_(MAX|MIN) below is so that the compiler does not
// get an overflow while computing the constants.
#define SIGNED_INT_MAX(Type) \
(((Type(1) << (sizeof(Type)*8 - 2)) - 1) + (Type(1) << (sizeof(Type)*8 - 2)))
#define SIGNED_INT_MIN(Type) \
(-(Type(1) << (sizeof(Type)*8 - 2)) - (Type(1) << (sizeof(Type)*8 - 2)))
#define UNSIGNED_INT_MAX(Type) \
(((Type(1) << (sizeof(Type)*8 - 1)) - 1) + (Type(1) << (sizeof(Type)*8 - 1)))
// Compile-time selected log10-related constants for integer types.
#define SIGNED_MAX_10_EXP(Type) \
(sizeof(Type) == 1 ? 2 : ( \
sizeof(Type) == 2 ? 4 : ( \
sizeof(Type) == 4 ? 9 : ( \
sizeof(Type) == 8 ? 18 : -1))))
#define UNSIGNED_MAX_10_EXP(Type) \
(sizeof(Type) == 1 ? 2 : ( \
sizeof(Type) == 2 ? 4 : ( \
sizeof(Type) == 4 ? 9 : ( \
sizeof(Type) == 8 ? 19 : -1))))
#define DECL_INT_LIMIT_FUNCS \
static bool IsFinite(const Type /*x*/) { return true; } \
static bool IsNaN(const Type /*x*/) { return false; } \
static bool IsInf(const Type /*x*/) { return false; } \
static bool IsPosInf(const Type /*x*/) { return false; } \
static bool IsNegInf(const Type /*x*/) { return false; }
#define DECL_SIGNED_INT_LIMITS(IntType, UnsignedIntType) \
template<> \
struct MathLimits<IntType> { \
typedef IntType Type; \
typedef UnsignedIntType UnsignedType; \
static const bool kIsSigned = true; \
static const bool kIsInteger = true; \
static const Type kPosMin = 1; \
static const Type kPosMax = SIGNED_INT_MAX(Type); \
static const Type kMin = SIGNED_INT_MIN(Type); \
static const Type kMax = kPosMax; \
static const Type kNegMin = -1; \
static const Type kNegMax = kMin; \
static const int kMin10Exp = 0; \
static const int kMax10Exp = SIGNED_MAX_10_EXP(Type); \
static const Type kEpsilon = 1; \
static const Type kStdError = 0; \
DECL_INT_LIMIT_FUNCS \
};
#define DECL_UNSIGNED_INT_LIMITS(IntType) \
template<> \
struct MathLimits<IntType> { \
typedef IntType Type; \
typedef IntType UnsignedType; \
static const bool kIsSigned = false; \
static const bool kIsInteger = true; \
static const Type kPosMin = 1; \
static const Type kPosMax = UNSIGNED_INT_MAX(Type); \
static const Type kMin = 0; \
static const Type kMax = kPosMax; \
static const int kMin10Exp = 0; \
static const int kMax10Exp = UNSIGNED_MAX_10_EXP(Type); \
static const Type kEpsilon = 1; \
static const Type kStdError = 0; \
DECL_INT_LIMIT_FUNCS \
};
DECL_SIGNED_INT_LIMITS(signed char, unsigned char)
DECL_SIGNED_INT_LIMITS(signed short int, unsigned short int)
DECL_SIGNED_INT_LIMITS(signed int, unsigned int)
DECL_SIGNED_INT_LIMITS(signed long int, unsigned long int)
DECL_SIGNED_INT_LIMITS(signed long long int, unsigned long long int)
DECL_UNSIGNED_INT_LIMITS(unsigned char)
DECL_UNSIGNED_INT_LIMITS(unsigned short int)
DECL_UNSIGNED_INT_LIMITS(unsigned int)
DECL_UNSIGNED_INT_LIMITS(unsigned long int)
DECL_UNSIGNED_INT_LIMITS(unsigned long long int)
#undef DECL_SIGNED_INT_LIMITS
#undef DECL_UNSIGNED_INT_LIMITS
#undef SIGNED_INT_MAX
#undef SIGNED_INT_MIN
#undef UNSIGNED_INT_MAX
#undef SIGNED_MAX_10_EXP
#undef UNSIGNED_MAX_10_EXP
#undef DECL_INT_LIMIT_FUNCS
// ========================================================================= //
#ifdef WIN32 // Lacks built-in isnan() and isinf()
#define DECL_FP_LIMIT_FUNCS \
static bool IsFinite(const Type x) { return _finite(x); } \
static bool IsNaN(const Type x) { return _isnan(x); } \
static bool IsInf(const Type x) { return (_fpclass(x) & (_FPCLASS_NINF | _FPCLASS_PINF)) != 0; } \
static bool IsPosInf(const Type x) { return _fpclass(x) == _FPCLASS_PINF; } \
static bool IsNegInf(const Type x) { return _fpclass(x) == _FPCLASS_NINF; }
#else
#define DECL_FP_LIMIT_FUNCS \
static bool IsFinite(const Type x) { return !isinf(x) && !isnan(x); } \
static bool IsNaN(const Type x) { return isnan(x); } \
static bool IsInf(const Type x) { return isinf(x); } \
static bool IsPosInf(const Type x) { return isinf(x) && x > 0; } \
static bool IsNegInf(const Type x) { return isinf(x) && x < 0; }
#endif
// We can't put floating-point constant values in the header here because
// such constants are not considered to be primitive-type constants by gcc.
// CAVEAT: Hence, they are going to be initialized only during
// the global objects construction time.
#define DECL_FP_LIMITS(FP_Type, PREFIX) \
template<> \
struct MathLimits<FP_Type> { \
typedef FP_Type Type; \
typedef FP_Type UnsignedType; \
static const bool kIsSigned = true; \
static const bool kIsInteger = false; \
static const Type kPosMin; \
static const Type kPosMax; \
static const Type kMin; \
static const Type kMax; \
static const Type kNegMin; \
static const Type kNegMax; \
static const int kMin10Exp = PREFIX##_MIN_10_EXP; \
static const int kMax10Exp = PREFIX##_MAX_10_EXP; \
static const Type kEpsilon; \
static const Type kStdError; \
static const int kPrecisionDigits = PREFIX##_DIG; \
static const Type kNaN; \
static const Type kPosInf; \
static const Type kNegInf; \
DECL_FP_LIMIT_FUNCS \
};
DECL_FP_LIMITS(float, FLT)
DECL_FP_LIMITS(double, DBL)
DECL_FP_LIMITS(long double, LDBL)
#undef DECL_FP_LIMITS
#undef DECL_FP_LIMIT_FUNCS
// ========================================================================= //
} // namespace protobuf
} // namespace google
#endif // UTIL_MATH_MATHLIMITS_H__
