/usr/include/GeographicLib/Math.hpp is in libgeographiclib-dev 1.21-1ubuntu1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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* \file Math.hpp
* \brief Header for GeographicLib::Math class
*
* Copyright (c) Charles Karney (2008-2011) <charles@karney.com> and licensed
* under the MIT/X11 License. For more information, see
* http://geographiclib.sourceforge.net/
**********************************************************************/
// Constants.hpp includes Math.hpp. Place this include outside Math.hpp's
// include guard to enforce this ordering.
#include <GeographicLib/Constants.hpp>
#if !defined(GEOGRAPHICLIB_MATH_HPP)
#define GEOGRAPHICLIB_MATH_HPP "$Id: edd244e4c5c74e696096c2b6d598728957a0d36d $"
/**
* Are C++11 math functions available?
**********************************************************************/
#if !defined(GEOGRAPHICLIB_CPLUSPLUS11_MATH)
# if defined(__GXX_EXPERIMENTAL_CXX0X__)
# define GEOGRAPHICLIB_CPLUSPLUS11_MATH 1
# else
# define GEOGRAPHICLIB_CPLUSPLUS11_MATH 0
# endif
#endif
#if !defined(WORDS_BIGENDIAN)
# define WORDS_BIGENDIAN 0
#endif
#if !defined(GEOGRAPHICLIB_PREC)
/**
* The precision of floating point numbers used in %GeographicLib. 0 means
* float; 1 (default) means double; 2 means long double. Nearly all the
* testing has been carried out with doubles and that's the recommended
* configuration. In order for long double to be used, HAVE_LONG_DOUBLE needs
* to be defined. Note that with Microsoft Visual Studio, long double is the
* same as double.
**********************************************************************/
#define GEOGRAPHICLIB_PREC 1
#endif
#include <cmath>
#include <limits>
#include <algorithm>
#include <vector>
namespace GeographicLib {
/**
* \brief Mathematical functions needed by %GeographicLib
*
* Define mathematical functions in order to localize system dependencies and
* to provide generic versions of the functions. In addition define a real
* type to be used by %GeographicLib.
*
* Example of use:
* \include example-Math.cpp
**********************************************************************/
class GEOGRAPHIC_EXPORT Math {
private:
void dummy() {
STATIC_ASSERT(GEOGRAPHICLIB_PREC >= 0 && GEOGRAPHICLIB_PREC <= 2,
"Bad value of precision");
}
Math(); // Disable constructor
public:
#if defined(HAVE_LONG_DOUBLE)
/**
* The extended precision type for real numbers, used for some testing.
* This is long double on computers with this type; otherwise it is double.
**********************************************************************/
typedef long double extended;
#else
typedef double extended;
#endif
#if GEOGRAPHICLIB_PREC == 1
/**
* The real type for %GeographicLib. Nearly all the testing has been done
* with \e real = double. However, the algorithms should also work with
* float and long double (where available). (<b>CAUTION</b>: reasonable
* accuracy typically cannot be obtained using floats.)
**********************************************************************/
typedef double real;
#elif GEOGRAPHICLIB_PREC == 0
typedef float real;
#elif GEOGRAPHICLIB_PREC == 2
typedef extended real;
#else
typedef double real;
#endif
/**
* true if the machine is big-endian
**********************************************************************/
static const bool bigendian = WORDS_BIGENDIAN;
/**
* @tparam T the type of the returned value.
* @return \e pi.
**********************************************************************/
template<typename T> static inline T pi() throw()
{ return std::atan2(T(0), -T(1)); }
/**
* A synonym for pi<real>().
**********************************************************************/
static inline real pi() throw() { return pi<real>(); }
/**
* @tparam T the type of the returned value.
* @return the number of radians in a degree.
**********************************************************************/
template<typename T> static inline T degree() throw()
{ return pi<T>() / T(180); }
/**
* A synonym for degree<real>().
**********************************************************************/
static inline real degree() throw() { return degree<real>(); }
/**
* Square a number.
* @tparam T the type of the argument and the returned value.
* @param[in] x
* @return <i>x</i><sup>2</sup>.
**********************************************************************/
template<typename T> static inline T sq(T x) throw()
{ return x * x; }
#if defined(DOXYGEN)
/**
* The hypotenuse function avoiding underflow and overflow.
*
* @tparam T the type of the arguments and the returned value.
* @param[in] x
* @param[in] y
* @return sqrt(<i>x</i><sup>2</sup> + <i>y</i><sup>2</sup>).
**********************************************************************/
template<typename T> static inline T hypot(T x, T y) throw() {
x = std::abs(x);
y = std::abs(y);
T a = (std::max)(x, y),
b = (std::min)(x, y) / (a ? a : 1);
return a * std::sqrt(1 + b * b);
}
#elif GEOGRAPHICLIB_CPLUSPLUS11_MATH
template<typename T> static inline T hypot(T x, T y) throw()
{ return std::hypot(x, y); }
#elif defined(_MSC_VER)
static inline double hypot(double x, double y) throw()
{ return _hypot(x, y); }
#if _MSC_VER < 1400
// Visual C++ 7.1/VS .NET 2003 does not have _hypotf()
static inline float hypot(float x, float y) throw()
{ return float(_hypot(x, y)); }
#else
static inline float hypot(float x, float y) throw()
{ return _hypotf(x, y); }
#endif
#if defined(HAVE_LONG_DOUBLE)
static inline long double hypot(long double x, long double y) throw()
{ return _hypot(x, y); }
#endif
#else
// Use overloading to define generic versions
static inline double hypot(double x, double y) throw()
{ return ::hypot(x, y); }
static inline float hypot(float x, float y) throw()
{ return ::hypotf(x, y); }
#if defined(HAVE_LONG_DOUBLE)
static inline long double hypot(long double x, long double y) throw()
{ return ::hypotl(x, y); }
#endif
#endif
#if defined(DOXYGEN) || (defined(_MSC_VER) && !GEOGRAPHICLIB_CPLUSPLUS11_MATH)
/**
* exp(\e x) - 1 accurate near \e x = 0. This is taken from
* N. J. Higham, Accuracy and Stability of Numerical Algorithms, 2nd
* Edition (SIAM, 2002), Sec 1.14.1, p 19.
*
* @tparam T the type of the argument and the returned value.
* @param[in] x
* @return exp(\e x) - 1.
**********************************************************************/
template<typename T> static inline T expm1(T x) throw() {
volatile T
y = std::exp(x),
z = y - 1;
// The reasoning here is similar to that for log1p. The expression
// mathematically reduces to exp(x) - 1, and the factor z/log(y) = (y -
// 1)/log(y) is a slowly varying quantity near y = 1 and is accurately
// computed.
return std::abs(x) > 1 ? z : (z == 0 ? x : x * z / std::log(y));
}
#elif GEOGRAPHICLIB_CPLUSPLUS11_MATH
template<typename T> static inline T expm1(T x) throw()
{ return std::expm1(x); }
#else
static inline double expm1(double x) throw() { return ::expm1(x); }
static inline float expm1(float x) throw() { return ::expm1f(x); }
#if defined(HAVE_LONG_DOUBLE)
static inline long double expm1(long double x) throw()
{ return ::expm1l(x); }
#endif
#endif
#if defined(DOXYGEN) || (defined(_MSC_VER) && !GEOGRAPHICLIB_CPLUSPLUS11_MATH)
/**
* log(1 + \e x) accurate near \e x = 0.
*
* This is taken from D. Goldberg,
* <a href="http://dx.doi.org/10.1145/103162.103163">What every computer
* scientist should know about floating-point arithmetic</a> (1991),
* Theorem 4. See also, Higham (op. cit.), Answer to Problem 1.5, p 528.
*
* @tparam T the type of the argument and the returned value.
* @param[in] x
* @return log(1 + \e x).
**********************************************************************/
template<typename T> static inline T log1p(T x) throw() {
volatile T
y = 1 + x,
z = y - 1;
// Here's the explanation for this magic: y = 1 + z, exactly, and z
// approx x, thus log(y)/z (which is nearly constant near z = 0) returns
// a good approximation to the true log(1 + x)/x. The multiplication x *
// (log(y)/z) introduces little additional error.
return z == 0 ? x : x * std::log(y) / z;
}
#elif GEOGRAPHICLIB_CPLUSPLUS11_MATH
template<typename T> static inline T log1p(T x) throw()
{ return std::log1p(x); }
#else
static inline double log1p(double x) throw() { return ::log1p(x); }
static inline float log1p(float x) throw() { return ::log1pf(x); }
#if defined(HAVE_LONG_DOUBLE)
static inline long double log1p(long double x) throw()
{ return ::log1pl(x); }
#endif
#endif
#if defined(DOXYGEN) || (defined(_MSC_VER) && !GEOGRAPHICLIB_CPLUSPLUS11_MATH)
/**
* The inverse hyperbolic sine function. This is defined in terms of
* Math::log1p(\e x) in order to maintain accuracy near \e x = 0. In
* addition, the odd parity of the function is enforced.
*
* @tparam T the type of the argument and the returned value.
* @param[in] x
* @return asinh(\e x).
**********************************************************************/
template<typename T> static inline T asinh(T x) throw() {
T y = std::abs(x); // Enforce odd parity
y = log1p(y * (1 + y/(hypot(T(1), y) + 1)));
return x < 0 ? -y : y;
}
#elif GEOGRAPHICLIB_CPLUSPLUS11_MATH
template<typename T> static inline T asinh(T x) throw()
{ return std::asinh(x); }
#else
static inline double asinh(double x) throw() { return ::asinh(x); }
static inline float asinh(float x) throw() { return ::asinhf(x); }
#if defined(HAVE_LONG_DOUBLE)
static inline long double asinh(long double x) throw()
{ return ::asinhl(x); }
#endif
#endif
#if defined(DOXYGEN) || (defined(_MSC_VER) && !GEOGRAPHICLIB_CPLUSPLUS11_MATH)
/**
* The inverse hyperbolic tangent function. This is defined in terms of
* Math::log1p(\e x) in order to maintain accuracy near \e x = 0. In
* addition, the odd parity of the function is enforced.
*
* @tparam T the type of the argument and the returned value.
* @param[in] x
* @return atanh(\e x).
**********************************************************************/
template<typename T> static inline T atanh(T x) throw() {
T y = std::abs(x); // Enforce odd parity
y = log1p(2 * y/(1 - y))/2;
return x < 0 ? -y : y;
}
#elif GEOGRAPHICLIB_CPLUSPLUS11_MATH
template<typename T> static inline T atanh(T x) throw()
{ return std::atanh(x); }
#else
static inline double atanh(double x) throw() { return ::atanh(x); }
static inline float atanh(float x) throw() { return ::atanhf(x); }
#if defined(HAVE_LONG_DOUBLE)
static inline long double atanh(long double x) throw()
{ return ::atanhl(x); }
#endif
#endif
#if defined(DOXYGEN) || (defined(_MSC_VER) && !GEOGRAPHICLIB_CPLUSPLUS11_MATH)
/**
* The cube root function.
*
* @tparam T the type of the argument and the returned value.
* @param[in] x
* @return the real cube root of \e x.
**********************************************************************/
template<typename T> static inline T cbrt(T x) throw() {
T y = std::pow(std::abs(x), 1/T(3)); // Return the real cube root
return x < 0 ? -y : y;
}
#elif GEOGRAPHICLIB_CPLUSPLUS11_MATH
template<typename T> static inline T cbrt(T x) throw()
{ return std::cbrt(x); }
#else
static inline double cbrt(double x) throw() { return ::cbrt(x); }
static inline float cbrt(float x) throw() { return ::cbrtf(x); }
#if defined(HAVE_LONG_DOUBLE)
static inline long double cbrt(long double x) throw() { return ::cbrtl(x); }
#endif
#endif
/**
* Test for finiteness.
*
* @tparam T the type of the argument.
* @param[in] x
* @return true if number is finite, false if NaN or infinite.
**********************************************************************/
template<typename T> static inline bool isfinite(T x) throw() {
#if defined(DOXYGEN)
return std::abs(x) <= (std::numeric_limits<T>::max)();
#elif (defined(_MSC_VER) && !GEOGRAPHICLIB_CPLUSPLUS11_MATH)
return _finite(x) != 0;
#else
return std::isfinite(x);
#endif
}
/**
* The NaN (not a number)
*
* @tparam T the type of the returned value.
* @return NaN if available, otherwise return the max real.
**********************************************************************/
template<typename T> static inline T NaN() throw() {
return std::numeric_limits<T>::has_quiet_NaN ?
std::numeric_limits<T>::quiet_NaN() :
(std::numeric_limits<T>::max)();
}
/**
* A synonym for NaN<real>().
**********************************************************************/
static inline real NaN() throw() { return NaN<real>(); }
/**
* Test for NaN.
*
* @tparam T the type of the argument.
* @param[in] x
* @return true if argument is a NaN.
**********************************************************************/
template<typename T> static inline bool isnan(T x) throw() {
#if defined(DOXYGEN) || (defined(_MSC_VER) && !GEOGRAPHICLIB_CPLUSPLUS11_MATH)
return x != x;
#else
return std::isnan(x);
#endif
}
/**
* Infinity
*
* @tparam T the type of the returned value.
* @return infinity if available, otherwise return the max real.
**********************************************************************/
template<typename T> static inline T infinity() throw() {
return std::numeric_limits<T>::has_infinity ?
std::numeric_limits<T>::infinity() :
(std::numeric_limits<T>::max)();
}
/**
* A synonym for infinity<real>().
**********************************************************************/
static inline real infinity() throw() { return infinity<real>(); }
/**
* Swap the bytes of a quantity
*
* @tparam T the type of the argument and the returned value.
* @param[in] x
* @return x with its bytes swapped.
**********************************************************************/
template<typename T> static inline T swab(T x) {
union {
T r;
unsigned char c[sizeof(T)];
} b;
b.r = x;
for (int i = sizeof(T)/2; i--; )
std::swap(b.c[i], b.c[sizeof(T) - 1 - i]);
return b.r;
}
};
} // namespace GeographicLib
#endif // GEOGRAPHICLIB_MATH_HPP
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