/usr/include/GeographicLib/Constants.hpp is in libgeographiclib-dev 1.8-2.
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 Constants.hpp
* \brief Header for GeographicLib::Constants class
*
* Copyright (c) Charles Karney (2008, 2009, 2010, 2011) <charles@karney.com>
* and licensed under the LGPL. For more information, see
* http://geographiclib.sourceforge.net/
**********************************************************************/
#if !defined(GEOGRAPHICLIB_CONSTANTS_HPP)
#define GEOGRAPHICLIB_CONSTANTS_HPP "$Id: Constants.hpp 6967 2011-02-19 15:53:41Z karney $"
/**
* Are C++0X math functions available?
**********************************************************************/
#if !defined(GEOGRAPHICLIB_CPLUSPLUS0X_MATH)
#if defined(__GXX_EXPERIMENTAL_CXX0X__)
#define GEOGRAPHICLIB_CPLUSPLUS0X_MATH 1
#else
#define GEOGRAPHICLIB_CPLUSPLUS0X_MATH 0
#endif
#endif
/**
* A compile-time assert. Use C++0X static_assert, if available.
**********************************************************************/
#if !defined(STATIC_ASSERT)
#if defined(__GXX_EXPERIMENTAL_CXX0X__)
#define STATIC_ASSERT static_assert
#elif defined(_MSC_VER) && _MSC_VER >= 1600
#define STATIC_ASSERT static_assert
#else
#define STATIC_ASSERT(cond,reason) { enum{ STATIC_ASSERT_ENUM=1/int(cond) }; }
#endif
#endif
#if defined(__GNUC__)
// Suppress "defined but not used" warnings
#define RCSID_DECL(x) namespace \
{ char VAR_ ## x [] __attribute__((used)) = x; }
#else
/**
* Insertion of RCS Id strings into the object file.
**********************************************************************/
#define RCSID_DECL(x) namespace { char VAR_ ## x [] = x; }
#endif
RCSID_DECL(GEOGRAPHICLIB_CONSTANTS_HPP)
#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. Note that with Microsoft Visual Studio, long double is the
* same as double.
**********************************************************************/
#define GEOGRAPHICLIB_PREC 1
#endif
#if defined(__CYGWIN__) && defined(__GNUC__) && __GNUC__ < 4
// g++ 3.x under cygwin doesn't have long double
#define __NO_LONG_DOUBLE_MATH 1
#endif
#include <cmath>
#include <limits>
#include <algorithm>
#include <stdexcept>
/**
* \brief Namespace for %GeographicLib
*
* All of %GeographicLib is defined within the GeographicLib namespace. In
* addtion all the header files are included via %GeographicLib/filename. This
* minimizes the likelihood of conflicts with other packages.
**********************************************************************/
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.
**********************************************************************/
class Math {
private:
void dummy() {
STATIC_ASSERT((GEOGRAPHICLIB_PREC) >= 0 && (GEOGRAPHICLIB_PREC) <= 2,
"Bad value of precision");
}
Math(); // Disable constructor
public:
#if !defined(__NO_LONG_DOUBLE_MATH)
/**
* 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).
**********************************************************************/
typedef double real;
#elif GEOGRAPHICLIB_PREC == 0
typedef float real;
#elif GEOGRAPHICLIB_PREC == 2
typedef extended real;
#else
typedef double real;
#endif
/**
* @return \e pi
**********************************************************************/
template<typename T>
static inline T pi() throw()
// good for about 168-bit accuracy
{ return T(3.1415926535897932384626433832795028841971693993751L); }
/**
* A synonym for pi<real>().
**********************************************************************/
static inline real pi() throw() { return pi<real>(); }
/**
* <b>DEPRECATED</b> A synonym for pi<extened>().
**********************************************************************/
static inline extended epi() throw() { return pi<extended>(); }
/**
* @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>(); }
/**
* <b>DEPRECATED</b> A synonym for degree<extened>().
**********************************************************************/
static inline extended edegree() throw() { return degree<extended>(); }
#if defined(DOXYGEN)
/**
* The hypotenuse function avoiding underflow and overflow.
*
* @param[in] x
* @param[in] y
* @return sqrt(\e x<sup>2</sup> + \e y<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;
return a * std::sqrt(1 + b * b);
}
#elif GEOGRAPHICLIB_CPLUSPLUS0X_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); }
static inline float hypot(float x, float y) throw()
{ return _hypotf(x, y); }
#if !defined(__NO_LONG_DOUBLE_MATH)
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(__NO_LONG_DOUBLE_MATH)
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_CPLUSPLUS0X_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.
*
* @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_CPLUSPLUS0X_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(__NO_LONG_DOUBLE_MATH)
static inline long double expm1(long double x) throw()
{ return ::expm1l(x); }
#endif
#endif
#if defined(DOXYGEN) || (defined(_MSC_VER) && !GEOGRAPHICLIB_CPLUSPLUS0X_MATH)
/**
* log(\e x + 1) accurate near \e x = 0. This is taken See
* D. Goldberg,
* <a href="http://docs.sun.com/source/806-3568/ncg_goldberg.html"> 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.
*
* @param[in] x
* @return log(\e x + 1).
**********************************************************************/
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_CPLUSPLUS0X_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(__NO_LONG_DOUBLE_MATH)
static inline long double log1p(long double x) throw()
{ return ::log1pl(x); }
#endif
#endif
#if defined(DOXYGEN) || (defined(_MSC_VER) && !GEOGRAPHICLIB_CPLUSPLUS0X_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.
*
* @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_CPLUSPLUS0X_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(__NO_LONG_DOUBLE_MATH)
static inline long double asinh(long double x) throw()
{ return ::asinhl(x); }
#endif
#endif
#if defined(DOXYGEN) || (defined(_MSC_VER) && !GEOGRAPHICLIB_CPLUSPLUS0X_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.
*
* @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_CPLUSPLUS0X_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(__NO_LONG_DOUBLE_MATH)
static inline long double atanh(long double x) throw()
{ return ::atanhl(x); }
#endif
#endif
#if defined(DOXYGEN) || (defined(_MSC_VER) && !GEOGRAPHICLIB_CPLUSPLUS0X_MATH)
/**
* The cube root function.
*
* @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_CPLUSPLUS0X_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(__NO_LONG_DOUBLE_MATH)
static inline long double cbrt(long double x) throw() { return ::cbrtl(x); }
#endif
#endif
/**
* Test for finiteness.
*
* @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_CPLUSPLUS0X_MATH)
return _finite(x) != 0;
#else
return std::isfinite(x);
#endif
}
/**
* The NaN (not a number)
*
* @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.
*
* @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_CPLUSPLUS0X_MATH)
return x != x;
#else
return std::isnan(x);
#endif
}
/**
* Infinity
*
* @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>(); }
};
/**
* \brief %Constants needed by %GeographicLib
*
* Define constants specifying the WGS84 ellipsoid, the UTM and UPS
* projections, and various unit conversions.
**********************************************************************/
class Constants {
private:
typedef Math::real real;
Constants(); // Disable constructor
public:
/**
* <b>DEPRECATED</b> A synonym for Math::pi<real>().
**********************************************************************/
static inline Math::real pi() throw() { return Math::pi<real>(); }
/**
* A synonym for Math::degree<real>().
**********************************************************************/
static inline Math::real degree() throw() { return Math::degree<real>(); }
/**
* @return the number of radians in an arcminute.
**********************************************************************/
static inline Math::real arcminute() throw()
{ return Math::degree<real>() / 60; }
/**
* @return the number of radians in an arcsecond.
**********************************************************************/
static inline Math::real arcsecond() throw()
{ return Math::degree<real>() / 3600; }
/** \name Ellipsoid parameters
**********************************************************************/
///@{
/**
* @return the equatorial radius of WGS84 ellipsoid
**********************************************************************/
template<typename T>
static inline T WGS84_a() throw() { return T(6378137) * meter<T>(); }
/**
* A synonym for WGS84_a<real>().
**********************************************************************/
static inline Math::real WGS84_a() throw() { return WGS84_a<real>(); }
/**
* @return the reciprocal flattening of WGS84 ellipsoid
**********************************************************************/
template<typename T>
static inline T WGS84_r() throw() {
// 298.257223563 = 3393 * 87903691 / 1000000000
return (T(3393) * T(87903691)) / T(1000000000);
}
/**
* A synonym for WGS84_r<real>().
**********************************************************************/
static inline Math::real WGS84_r() throw() { return WGS84_r<real>(); }
/**
* @return the central scale factor for UTM
**********************************************************************/
template<typename T>
static inline T UTM_k0() throw() {return T(9996) / T(10000); } // 0.9996
/**
* A synonym for UTM_k0<real>().
**********************************************************************/
static inline Math::real UTM_k0() throw() { return UTM_k0<real>(); }
/**
* @return the central scale factor for UPS
**********************************************************************/
template<typename T>
static inline T UPS_k0() throw() { return T(994) / T(1000); } // 0.994
/**
* A synonym for UPS_k0<real>().
**********************************************************************/
static inline Math::real UPS_k0() throw() { return UPS_k0<real>(); }
///@}
/** \name SI units
**********************************************************************/
///@{
/**
* @return the number of meters in a meter.
*
* This is unity, but this lets the internal system of units be changed if
* necessary.
**********************************************************************/
template<typename T>
static inline T meter() throw() { return T(1); }
/**
* A synonym for meter<real>().
**********************************************************************/
static inline Math::real meter() throw() { return meter<real>(); }
/**
* @return the number of meters in a kilometer.
**********************************************************************/
static inline Math::real kilometer() throw()
{ return 1000 * meter<real>(); }
/**
* @return the number of meters in a nautical mile (approximately 1 arc
* minute)
**********************************************************************/
static inline Math::real nauticalmile() throw()
{ return 1852 * meter<real>(); }
///@}
/** \name Anachronistic British units
**********************************************************************/
///@{
/**
* @return the number of meters in an international foot.
**********************************************************************/
static inline Math::real foot() throw()
{ return real(0.0254L) * 12 * meter<real>(); }
/**
* @return the number of meters in a yard.
**********************************************************************/
static inline Math::real yard() throw() { return 3 * foot(); }
/**
* @return the number of meters in a fathom.
**********************************************************************/
static inline Math::real fathom() throw() { return 2 * yard(); }
/**
* @return the number of meters in a chain.
**********************************************************************/
static inline Math::real chain() throw() { return 22 * yard(); }
/**
* @return the number of meters in a furlong.
**********************************************************************/
static inline Math::real furlong() throw() { return 10 * chain(); }
/**
* @return the number of meters in a statute mile.
**********************************************************************/
static inline Math::real mile() throw() { return 8 * furlong(); }
///@}
/** \name Anachronistic US units
**********************************************************************/
///@{
/**
* @return the number of meters in a US survey foot.
**********************************************************************/
static inline Math::real surveyfoot() throw()
{ return real(1200) / real(3937) * meter<real>(); }
///@}
};
/**
* \brief %Exception handling for %GeographicLib
*
* A class to handle exceptions. It's derived off std::runtime_error so it
* can be caught by the usual catch clauses.
**********************************************************************/
class GeographicErr : public std::runtime_error {
public:
/**
* Constructor
*
* @param[in] msg a string message, which is accessible in the catch
* clause, via what().
**********************************************************************/
GeographicErr(const std::string& msg) : std::runtime_error(msg) {}
};
} // namespace GeographicLib
#endif
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