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// Protocol Buffers - Google's data interchange format
// Copyright 2008 Google Inc. All rights reserved.
// https://developers.google.com/protocol-buffers/
//
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// modification, are permitted provided that the following conditions are
// met:
//
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#ifndef GOOGLE_PROTOBUF_STUBS_MATHUTIL_H_
#define GOOGLE_PROTOBUF_STUBS_MATHUTIL_H_
#include <cmath>
#include <float.h>
#include <limits>
#include <google/protobuf/stubs/common.h>
#include <google/protobuf/stubs/logging.h>
namespace google {
namespace protobuf {
namespace internal {
// Like std::make_unsigned_t except floating point types map to themselves.
template <typename T>
using MakeUnsignedT =
typename std::conditional<std::is_integral<T>::value, std::make_unsigned<T>,
std::common_type<T>>::type::type;
// Like std::isnan() except a template function that is defined for all numeric
// types.
template <typename T,
typename std::enable_if<std::is_integral<T>::value, int>::type = 0>
bool IsNan(T val) {
return false;
}
template <typename T, typename std::enable_if<std::is_floating_point<T>::value,
int>::type = 0>
bool IsNan(T val) {
return std::isnan(val);
}
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) || internal::IsNan(value)) {
return value;
}
return value > T(0) ? 1 : -1;
}
template <typename T>
static bool AlmostEquals(T a, T b) {
return 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 internal::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 internal::MakeUnsignedT<T> AbsDiff(const T x, const T y) {
// Carries out arithmetic as unsigned to avoid overflow.
typedef typename internal::MakeUnsignedT<T> 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 (std::numeric_limits<T>::is_integer) {
return x == y;
} else {
if (!std::isfinite(x) || !std::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_
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