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ecency-mobile/ios/Pods/boost-for-react-native/boost/math/cstdfloat/cstdfloat_cmath.hpp

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///////////////////////////////////////////////////////////////////////////////
// Copyright Christopher Kormanyos 2014.
// Copyright John Maddock 2014.
// Copyright Paul Bristow 2014.
// Distributed under the Boost Software License,
// Version 1.0. (See accompanying file LICENSE_1_0.txt
// or copy at http://www.boost.org/LICENSE_1_0.txt)
//
// Implement quadruple-precision <cmath> support.
#ifndef _BOOST_CSTDFLOAT_CMATH_2014_02_15_HPP_
#define _BOOST_CSTDFLOAT_CMATH_2014_02_15_HPP_
#include <boost/math/cstdfloat/cstdfloat_types.hpp>
#include <boost/math/cstdfloat/cstdfloat_limits.hpp>
#if defined(BOOST_CSTDFLOAT_HAS_INTERNAL_FLOAT128_T) && defined(BOOST_MATH_USE_FLOAT128) && !defined(BOOST_CSTDFLOAT_NO_LIBQUADMATH_SUPPORT)
#include <cmath>
#include <stdexcept>
#include <boost/cstdint.hpp>
#include <boost/static_assert.hpp>
#include <boost/throw_exception.hpp>
#if defined(_WIN32) && defined(__GNUC__)
// Several versions of Mingw and probably cygwin too have broken
// libquadmath implementations that segfault as soon as you call
// expq or any function that depends on it.
#define BOOST_CSTDFLOAT_BROKEN_FLOAT128_MATH_FUNCTIONS
#endif
// Here is a helper function used for raising the value of a given
// floating-point type to the power of n, where n has integral type.
namespace boost { namespace math { namespace cstdfloat { namespace detail {
template<class float_type, class integer_type>
inline float_type pown(const float_type& x, const integer_type p)
{
const bool isneg = (x < 0);
const bool isnan = (x != x);
const bool isinf = ((!isneg) ? bool(+x > (std::numeric_limits<float_type>::max)())
: bool(-x > (std::numeric_limits<float_type>::max)()));
if(isnan) { return x; }
if(isinf) { return std::numeric_limits<float_type>::quiet_NaN(); }
const bool x_is_neg = (x < 0);
const float_type abs_x = (x_is_neg ? -x : x);
if(p < static_cast<integer_type>(0))
{
if(abs_x < (std::numeric_limits<float_type>::min)())
{
return (x_is_neg ? -std::numeric_limits<float_type>::infinity()
: +std::numeric_limits<float_type>::infinity());
}
else
{
return float_type(1) / pown(x, static_cast<integer_type>(-p));
}
}
if(p == static_cast<integer_type>(0))
{
return float_type(1);
}
else
{
if(p == static_cast<integer_type>(1)) { return x; }
if(abs_x > (std::numeric_limits<float_type>::max)())
{
return (x_is_neg ? -std::numeric_limits<float_type>::infinity()
: +std::numeric_limits<float_type>::infinity());
}
if (p == static_cast<integer_type>(2)) { return (x * x); }
else if(p == static_cast<integer_type>(3)) { return ((x * x) * x); }
else if(p == static_cast<integer_type>(4)) { const float_type x2 = (x * x); return (x2 * x2); }
else
{
// The variable xn stores the binary powers of x.
float_type result(((p % integer_type(2)) != integer_type(0)) ? x : float_type(1));
float_type xn (x);
integer_type p2 = p;
while(integer_type(p2 /= 2) != integer_type(0))
{
// Square xn for each binary power.
xn *= xn;
const bool has_binary_power = (integer_type(p2 % integer_type(2)) != integer_type(0));
if(has_binary_power)
{
// Multiply the result with each binary power contained in the exponent.
result *= xn;
}
}
return result;
}
}
}
} } } } // boost::math::cstdfloat::detail
// We will now define preprocessor symbols representing quadruple-precision <cmath> functions.
#if defined(BOOST_INTEL)
#define BOOST_CSTDFLOAT_FLOAT128_LDEXP __ldexpq
#define BOOST_CSTDFLOAT_FLOAT128_FREXP __frexpq
#define BOOST_CSTDFLOAT_FLOAT128_FABS __fabsq
#define BOOST_CSTDFLOAT_FLOAT128_FLOOR __floorq
#define BOOST_CSTDFLOAT_FLOAT128_CEIL __ceilq
#if !defined(BOOST_CSTDFLOAT_FLOAT128_SQRT)
#define BOOST_CSTDFLOAT_FLOAT128_SQRT __sqrtq
#endif
#define BOOST_CSTDFLOAT_FLOAT128_TRUNC __truncq
#define BOOST_CSTDFLOAT_FLOAT128_EXP __expq
#define BOOST_CSTDFLOAT_FLOAT128_EXPM1 __expm1q
#define BOOST_CSTDFLOAT_FLOAT128_POW __powq
#define BOOST_CSTDFLOAT_FLOAT128_LOG __logq
#define BOOST_CSTDFLOAT_FLOAT128_LOG10 __log10q
#define BOOST_CSTDFLOAT_FLOAT128_SIN __sinq
#define BOOST_CSTDFLOAT_FLOAT128_COS __cosq
#define BOOST_CSTDFLOAT_FLOAT128_TAN __tanq
#define BOOST_CSTDFLOAT_FLOAT128_ASIN __asinq
#define BOOST_CSTDFLOAT_FLOAT128_ACOS __acosq
#define BOOST_CSTDFLOAT_FLOAT128_ATAN __atanq
#define BOOST_CSTDFLOAT_FLOAT128_SINH __sinhq
#define BOOST_CSTDFLOAT_FLOAT128_COSH __coshq
#define BOOST_CSTDFLOAT_FLOAT128_TANH __tanhq
#define BOOST_CSTDFLOAT_FLOAT128_ASINH __asinhq
#define BOOST_CSTDFLOAT_FLOAT128_ACOSH __acoshq
#define BOOST_CSTDFLOAT_FLOAT128_ATANH __atanhq
#define BOOST_CSTDFLOAT_FLOAT128_FMOD __fmodq
#define BOOST_CSTDFLOAT_FLOAT128_ATAN2 __atan2q
#define BOOST_CSTDFLOAT_FLOAT128_LGAMMA __lgammaq
#define BOOST_CSTDFLOAT_FLOAT128_TGAMMA __tgammaq
#elif defined(__GNUC__)
#define BOOST_CSTDFLOAT_FLOAT128_LDEXP ldexpq
#define BOOST_CSTDFLOAT_FLOAT128_FREXP frexpq
#define BOOST_CSTDFLOAT_FLOAT128_FABS fabsq
#define BOOST_CSTDFLOAT_FLOAT128_FLOOR floorq
#define BOOST_CSTDFLOAT_FLOAT128_CEIL ceilq
#if !defined(BOOST_CSTDFLOAT_FLOAT128_SQRT)
#define BOOST_CSTDFLOAT_FLOAT128_SQRT sqrtq
#endif
#define BOOST_CSTDFLOAT_FLOAT128_TRUNC truncq
#define BOOST_CSTDFLOAT_FLOAT128_POW powq
#define BOOST_CSTDFLOAT_FLOAT128_LOG logq
#define BOOST_CSTDFLOAT_FLOAT128_LOG10 log10q
#define BOOST_CSTDFLOAT_FLOAT128_SIN sinq
#define BOOST_CSTDFLOAT_FLOAT128_COS cosq
#define BOOST_CSTDFLOAT_FLOAT128_TAN tanq
#define BOOST_CSTDFLOAT_FLOAT128_ASIN asinq
#define BOOST_CSTDFLOAT_FLOAT128_ACOS acosq
#define BOOST_CSTDFLOAT_FLOAT128_ATAN atanq
#define BOOST_CSTDFLOAT_FLOAT128_FMOD fmodq
#define BOOST_CSTDFLOAT_FLOAT128_ATAN2 atan2q
#define BOOST_CSTDFLOAT_FLOAT128_LGAMMA lgammaq
#if !defined(BOOST_CSTDFLOAT_BROKEN_FLOAT128_MATH_FUNCTIONS)
#define BOOST_CSTDFLOAT_FLOAT128_EXP expq
#define BOOST_CSTDFLOAT_FLOAT128_EXPM1 expm1q_internal
#define BOOST_CSTDFLOAT_FLOAT128_SINH sinhq
#define BOOST_CSTDFLOAT_FLOAT128_COSH coshq
#define BOOST_CSTDFLOAT_FLOAT128_TANH tanhq
#define BOOST_CSTDFLOAT_FLOAT128_ASINH asinhq
#define BOOST_CSTDFLOAT_FLOAT128_ACOSH acoshq
#define BOOST_CSTDFLOAT_FLOAT128_ATANH atanhq
#define BOOST_CSTDFLOAT_FLOAT128_TGAMMA tgammaq
#else // BOOST_CSTDFLOAT_BROKEN_FLOAT128_MATH_FUNCTIONS
#define BOOST_CSTDFLOAT_FLOAT128_EXP expq_patch
#define BOOST_CSTDFLOAT_FLOAT128_SINH sinhq_patch
#define BOOST_CSTDFLOAT_FLOAT128_COSH coshq_patch
#define BOOST_CSTDFLOAT_FLOAT128_TANH tanhq_patch
#define BOOST_CSTDFLOAT_FLOAT128_ASINH asinhq_patch
#define BOOST_CSTDFLOAT_FLOAT128_ACOSH acoshq_patch
#define BOOST_CSTDFLOAT_FLOAT128_ATANH atanhq_patch
#define BOOST_CSTDFLOAT_FLOAT128_TGAMMA tgammaq_patch
#endif // BOOST_CSTDFLOAT_BROKEN_FLOAT128_MATH_FUNCTIONS
#endif
// Implement quadruple-precision <cmath> functions in the namespace
// boost::math::cstdfloat::detail. Subsequently inject these into the
// std namespace via *using* directive.
// Begin with some forward function declarations. Also implement patches
// for compilers that have broken float128 exponential functions.
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_LDEXP (boost::math::cstdfloat::detail::float_internal128_t, int) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_FREXP (boost::math::cstdfloat::detail::float_internal128_t, int*) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_FABS (boost::math::cstdfloat::detail::float_internal128_t) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_FLOOR (boost::math::cstdfloat::detail::float_internal128_t) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_CEIL (boost::math::cstdfloat::detail::float_internal128_t) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_SQRT (boost::math::cstdfloat::detail::float_internal128_t) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_TRUNC (boost::math::cstdfloat::detail::float_internal128_t) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_POW (boost::math::cstdfloat::detail::float_internal128_t, boost::math::cstdfloat::detail::float_internal128_t) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_LOG (boost::math::cstdfloat::detail::float_internal128_t) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_LOG10 (boost::math::cstdfloat::detail::float_internal128_t) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_SIN (boost::math::cstdfloat::detail::float_internal128_t) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_COS (boost::math::cstdfloat::detail::float_internal128_t) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_TAN (boost::math::cstdfloat::detail::float_internal128_t) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_ASIN (boost::math::cstdfloat::detail::float_internal128_t) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_ACOS (boost::math::cstdfloat::detail::float_internal128_t) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_ATAN (boost::math::cstdfloat::detail::float_internal128_t) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_FMOD (boost::math::cstdfloat::detail::float_internal128_t, boost::math::cstdfloat::detail::float_internal128_t) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_ATAN2 (boost::math::cstdfloat::detail::float_internal128_t, boost::math::cstdfloat::detail::float_internal128_t) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_LGAMMA(boost::math::cstdfloat::detail::float_internal128_t) throw();
#if !defined(BOOST_CSTDFLOAT_BROKEN_FLOAT128_MATH_FUNCTIONS)
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_EXP (boost::math::cstdfloat::detail::float_internal128_t x) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_SINH (boost::math::cstdfloat::detail::float_internal128_t x) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_COSH (boost::math::cstdfloat::detail::float_internal128_t x) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_TANH (boost::math::cstdfloat::detail::float_internal128_t x) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_ASINH (boost::math::cstdfloat::detail::float_internal128_t x) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_ACOSH (boost::math::cstdfloat::detail::float_internal128_t x) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_ATANH (boost::math::cstdfloat::detail::float_internal128_t x) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_TGAMMA(boost::math::cstdfloat::detail::float_internal128_t x) throw();
#else // BOOST_CSTDFLOAT_BROKEN_FLOAT128_MATH_FUNCTIONS
// Forward declaration of the patched exponent function, exp(x).
inline boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_EXP (boost::math::cstdfloat::detail::float_internal128_t x);
inline boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_EXPM1 (boost::math::cstdfloat::detail::float_internal128_t x)
{
// Compute exp(x) - 1 for x small.
// Use an order-36 polynomial approximation of the exponential function
// in the range of (-ln2 < x < ln2). Scale the argument to this range
// and subsequently multiply the result by 2^n accordingly.
// Derive the polynomial coefficients with Mathematica(R) by generating
// a table of high-precision values of exp(x) in the range (-ln2 < x < ln2)
// and subsequently applying the built-in *Fit* function.
// Table[{x, Exp[x] - 1}, {x, -Log[2], Log[2], 1/180}]
// N[%, 120]
// Fit[%, {x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^12,
// x^13, x^14, x^15, x^16, x^17, x^18, x^19, x^20, x^21, x^22,
// x^23, x^24, x^25, x^26, x^27, x^28, x^29, x^30, x^31, x^32,
// x^33, x^34, x^35, x^36}, x]
typedef boost::math::cstdfloat::detail::float_internal128_t float_type;
float_type sum;
if(x > BOOST_FLOAT128_C(0.693147180559945309417232121458176568075500134360255))
{
sum = ::BOOST_CSTDFLOAT_FLOAT128_EXP(x) - float_type(1);
}
else
{
// Compute the polynomial approximation of exp(alpha).
sum = (((((((((((((((((((((((((((((((((((( float_type(BOOST_FLOAT128_C(2.69291698127774166063293705964720493864630783729857438187365E-42)) * x
+ float_type(BOOST_FLOAT128_C(9.70937085471487654794114679403710456028986572118859594614033E-41))) * x
+ float_type(BOOST_FLOAT128_C(3.38715585158055097155585505318085512156885389014410753080500E-39))) * x
+ float_type(BOOST_FLOAT128_C(1.15162718532861050809222658798662695267019717760563645440433E-37))) * x
+ float_type(BOOST_FLOAT128_C(3.80039074689434663295873584133017767349635602413675471702393E-36))) * x
+ float_type(BOOST_FLOAT128_C(1.21612504934087520075905434734158045947460467096773246215239E-34))) * x
+ float_type(BOOST_FLOAT128_C(3.76998762883139753126119821241037824830069851253295480396224E-33))) * x
+ float_type(BOOST_FLOAT128_C(1.13099628863830344684998293828608215735777107850991029729440E-31))) * x
+ float_type(BOOST_FLOAT128_C(3.27988923706982293204067897468714277771890104022419696770352E-30))) * x
+ float_type(BOOST_FLOAT128_C(9.18368986379558482800593745627556950089950023355628325088207E-29))) * x
+ float_type(BOOST_FLOAT128_C(2.47959626322479746949155352659617642905315302382639380521497E-27))) * x
+ float_type(BOOST_FLOAT128_C(6.44695028438447337900255966737803112935639344283098705091949E-26))) * x
+ float_type(BOOST_FLOAT128_C(1.61173757109611834904452725462599961406036904573072897122957E-24))) * x
+ float_type(BOOST_FLOAT128_C(3.86817017063068403772269360016918092488847584660382953555804E-23))) * x
+ float_type(BOOST_FLOAT128_C(8.89679139245057328674891109315654704307721758924206107351744E-22))) * x
+ float_type(BOOST_FLOAT128_C(1.95729410633912612308475595397946731738088422488032228717097E-20))) * x
+ float_type(BOOST_FLOAT128_C(4.11031762331216485847799061511674191805055663711439605760231E-19))) * x
+ float_type(BOOST_FLOAT128_C(8.22063524662432971695598123977873600603370758794431071426640E-18))) * x
+ float_type(BOOST_FLOAT128_C(1.56192069685862264622163643500633782667263448653185159383285E-16))) * x
+ float_type(BOOST_FLOAT128_C(2.81145725434552076319894558300988749849555291507956994126835E-15))) * x
+ float_type(BOOST_FLOAT128_C(4.77947733238738529743820749111754320727153728139716409114011E-14))) * x
+ float_type(BOOST_FLOAT128_C(7.64716373181981647590113198578807092707697416852226691068627E-13))) * x
+ float_type(BOOST_FLOAT128_C(1.14707455977297247138516979786821056670509688396295740818677E-11))) * x
+ float_type(BOOST_FLOAT128_C(1.60590438368216145993923771701549479323291461578567184216302E-10))) * x
+ float_type(BOOST_FLOAT128_C(2.08767569878680989792100903212014323125428376052986408239620E-09))) * x
+ float_type(BOOST_FLOAT128_C(2.50521083854417187750521083854417187750523408006206780016659E-08))) * x
+ float_type(BOOST_FLOAT128_C(2.75573192239858906525573192239858906525573195144226062684604E-07))) * x
+ float_type(BOOST_FLOAT128_C(2.75573192239858906525573192239858906525573191310049321957902E-06))) * x
+ float_type(BOOST_FLOAT128_C(0.00002480158730158730158730158730158730158730158730149317774))) * x
+ float_type(BOOST_FLOAT128_C(0.00019841269841269841269841269841269841269841269841293575920))) * x
+ float_type(BOOST_FLOAT128_C(0.00138888888888888888888888888888888888888888888888889071045))) * x
+ float_type(BOOST_FLOAT128_C(0.00833333333333333333333333333333333333333333333333332986595))) * x
+ float_type(BOOST_FLOAT128_C(0.04166666666666666666666666666666666666666666666666666664876))) * x
+ float_type(BOOST_FLOAT128_C(0.16666666666666666666666666666666666666666666666666666669048))) * x
+ float_type(BOOST_FLOAT128_C(0.50000000000000000000000000000000000000000000000000000000006))) * x
+ float_type(BOOST_FLOAT128_C(0.99999999999999999999999999999999999999999999999999999999995))) * x);
}
return sum;
}
inline boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_EXP (boost::math::cstdfloat::detail::float_internal128_t x)
{
// Patch the expq() function for a subset of broken GCC compilers
// like GCC 4.7, 4.8 on MinGW.
// Use an order-36 polynomial approximation of the exponential function
// in the range of (-ln2 < x < ln2). Scale the argument to this range
// and subsequently multiply the result by 2^n accordingly.
// Derive the polynomial coefficients with Mathematica(R) by generating
// a table of high-precision values of exp(x) in the range (-ln2 < x < ln2)
// and subsequently applying the built-in *Fit* function.
// Table[{x, Exp[x] - 1}, {x, -Log[2], Log[2], 1/180}]
// N[%, 120]
// Fit[%, {x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^12,
// x^13, x^14, x^15, x^16, x^17, x^18, x^19, x^20, x^21, x^22,
// x^23, x^24, x^25, x^26, x^27, x^28, x^29, x^30, x^31, x^32,
// x^33, x^34, x^35, x^36}, x]
typedef boost::math::cstdfloat::detail::float_internal128_t float_type;
// Scale the argument x to the range (-ln2 < x < ln2).
BOOST_CONSTEXPR_OR_CONST float_type one_over_ln2 = float_type(BOOST_FLOAT128_C(1.44269504088896340735992468100189213742664595415299));
const float_type x_over_ln2 = x * one_over_ln2;
boost::int_fast32_t n;
if(x != x)
{
// The argument is NaN.
return std::numeric_limits<float_type>::quiet_NaN();
}
else if(::BOOST_CSTDFLOAT_FLOAT128_FABS(x) > BOOST_FLOAT128_C(+0.693147180559945309417232121458176568075500134360255))
{
// The absolute value of the argument exceeds ln2.
n = static_cast<boost::int_fast32_t>(::BOOST_CSTDFLOAT_FLOAT128_FLOOR(x_over_ln2));
}
else if(::BOOST_CSTDFLOAT_FLOAT128_FABS(x) < BOOST_FLOAT128_C(+0.693147180559945309417232121458176568075500134360255))
{
// The absolute value of the argument is less than ln2.
n = static_cast<boost::int_fast32_t>(0);
}
else
{
// The absolute value of the argument is exactly equal to ln2 (in the sense of floating-point equality).
return float_type(2);
}
// Check if the argument is very near an integer.
const float_type floor_of_x = ::BOOST_CSTDFLOAT_FLOAT128_FLOOR(x);
if(::BOOST_CSTDFLOAT_FLOAT128_FABS(x - floor_of_x) < float_type(BOOST_CSTDFLOAT_FLOAT128_EPS))
{
// Return e^n for arguments very near an integer.
return boost::math::cstdfloat::detail::pown(BOOST_FLOAT128_C(2.71828182845904523536028747135266249775724709369996), static_cast<boost::int_fast32_t>(floor_of_x));
}
// Compute the scaled argument alpha.
const float_type alpha = x - (n * BOOST_FLOAT128_C(0.693147180559945309417232121458176568075500134360255));
// Compute the polynomial approximation of expm1(alpha) and add to it
// in order to obtain the scaled result.
const float_type scaled_result = ::BOOST_CSTDFLOAT_FLOAT128_EXPM1(alpha) + float_type(1);
// Rescale the result and return it.
return scaled_result * boost::math::cstdfloat::detail::pown(float_type(2), n);
}
inline boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_SINH (boost::math::cstdfloat::detail::float_internal128_t x)
{
// Patch the sinhq() function for a subset of broken GCC compilers
// like GCC 4.7, 4.8 on MinGW.
typedef boost::math::cstdfloat::detail::float_internal128_t float_type;
// Here, we use the following:
// Set: ex = exp(x)
// Set: em1 = expm1(x)
// Then
// sinh(x) = (ex - 1/ex) / 2 ; for |x| >= 1
// sinh(x) = (2em1 + em1^2) / (2ex) ; for |x| < 1
const float_type ex = ::BOOST_CSTDFLOAT_FLOAT128_EXP(x);
if(::BOOST_CSTDFLOAT_FLOAT128_FABS(x) < float_type(+1))
{
const float_type em1 = ::BOOST_CSTDFLOAT_FLOAT128_EXPM1(x);
return ((em1 * 2) + (em1 * em1)) / (ex * 2);
}
else
{
return (ex - (float_type(1) / ex)) / 2;
}
}
inline boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_COSH (boost::math::cstdfloat::detail::float_internal128_t x)
{
// Patch the coshq() function for a subset of broken GCC compilers
// like GCC 4.7, 4.8 on MinGW.
typedef boost::math::cstdfloat::detail::float_internal128_t float_type;
const float_type ex = ::BOOST_CSTDFLOAT_FLOAT128_EXP(x);
return (ex + (float_type(1) / ex)) / 2;
}
inline boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_TANH (boost::math::cstdfloat::detail::float_internal128_t x)
{
// Patch the tanhq() function for a subset of broken GCC compilers
// like GCC 4.7, 4.8 on MinGW.
typedef boost::math::cstdfloat::detail::float_internal128_t float_type;
const float_type ex_plus = ::BOOST_CSTDFLOAT_FLOAT128_EXP(x);
const float_type ex_minus = (float_type(1) / ex_plus);
return (ex_plus - ex_minus) / (ex_plus + ex_minus);
}
inline boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_ASINH(boost::math::cstdfloat::detail::float_internal128_t x) throw()
{
// Patch the asinh() function since quadmath does not have it.
typedef boost::math::cstdfloat::detail::float_internal128_t float_type;
return ::BOOST_CSTDFLOAT_FLOAT128_LOG(x + ::BOOST_CSTDFLOAT_FLOAT128_SQRT((x * x) + float_type(1)));
}
inline boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_ACOSH(boost::math::cstdfloat::detail::float_internal128_t x) throw()
{
// Patch the acosh() function since quadmath does not have it.
typedef boost::math::cstdfloat::detail::float_internal128_t float_type;
const float_type zp(x + float_type(1));
const float_type zm(x - float_type(1));
return ::BOOST_CSTDFLOAT_FLOAT128_LOG(x + (zp * ::BOOST_CSTDFLOAT_FLOAT128_SQRT(zm / zp)));
}
inline boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_ATANH(boost::math::cstdfloat::detail::float_internal128_t x) throw()
{
// Patch the atanh() function since quadmath does not have it.
typedef boost::math::cstdfloat::detail::float_internal128_t float_type;
return ( ::BOOST_CSTDFLOAT_FLOAT128_LOG(float_type(1) + x)
- ::BOOST_CSTDFLOAT_FLOAT128_LOG(float_type(1) - x)) / 2;
}
inline boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_TGAMMA(boost::math::cstdfloat::detail::float_internal128_t x) throw()
{
// Patch the tgammaq() function for a subset of broken GCC compilers
// like GCC 4.7, 4.8 on MinGW.
typedef boost::math::cstdfloat::detail::float_internal128_t float_type;
if(x > float_type(0))
{
return ::BOOST_CSTDFLOAT_FLOAT128_EXP(::BOOST_CSTDFLOAT_FLOAT128_LGAMMA(x));
}
else if(x < float_type(0))
{
// For x < 0, compute tgamma(-x) and use the reflection formula.
const float_type positive_x = -x;
float_type gamma_value = ::BOOST_CSTDFLOAT_FLOAT128_TGAMMA(positive_x);
const float_type floor_of_positive_x = ::BOOST_CSTDFLOAT_FLOAT128_FLOOR (positive_x);
// Take the reflection checks (slightly adapted) from <boost/math/gamma.hpp>.
const bool floor_of_z_is_equal_to_z = (positive_x == ::BOOST_CSTDFLOAT_FLOAT128_FLOOR(positive_x));
BOOST_CONSTEXPR_OR_CONST float_type my_pi = BOOST_FLOAT128_C(3.14159265358979323846264338327950288419716939937511);
if(floor_of_z_is_equal_to_z)
{
const bool is_odd = ((boost::int32_t(floor_of_positive_x) % boost::int32_t(2)) != boost::int32_t(0));
return (is_odd ? -std::numeric_limits<float_type>::infinity()
: +std::numeric_limits<float_type>::infinity());
}
const float_type sinpx_value = x * ::BOOST_CSTDFLOAT_FLOAT128_SIN(my_pi * x);
gamma_value *= sinpx_value;
const bool result_is_too_large_to_represent = ( (::BOOST_CSTDFLOAT_FLOAT128_FABS(gamma_value) < float_type(1))
&& (((std::numeric_limits<float_type>::max)() * ::BOOST_CSTDFLOAT_FLOAT128_FABS(gamma_value)) < my_pi));
if(result_is_too_large_to_represent)
{
const bool is_odd = ((boost::int32_t(floor_of_positive_x) % boost::int32_t(2)) != boost::int32_t(0));
return (is_odd ? -std::numeric_limits<float_type>::infinity()
: +std::numeric_limits<float_type>::infinity());
}
gamma_value = -my_pi / gamma_value;
if((gamma_value > float_type(0)) || (gamma_value < float_type(0)))
{
return gamma_value;
}
else
{
// The value of gamma is too small to represent. Return 0.0 here.
return float_type(0);
}
}
else
{
// Gamma of zero is complex infinity. Return NaN here.
return std::numeric_limits<float_type>::quiet_NaN();
}
}
#endif // BOOST_CSTDFLOAT_BROKEN_FLOAT128_MATH_FUNCTIONS
// Define the quadruple-precision <cmath> functions in the namespace boost::math::cstdfloat::detail.
namespace boost { namespace math { namespace cstdfloat { namespace detail {
inline boost::math::cstdfloat::detail::float_internal128_t ldexp (boost::math::cstdfloat::detail::float_internal128_t x, int n) { return ::BOOST_CSTDFLOAT_FLOAT128_LDEXP (x, n); }
inline boost::math::cstdfloat::detail::float_internal128_t frexp (boost::math::cstdfloat::detail::float_internal128_t x, int* pn) { return ::BOOST_CSTDFLOAT_FLOAT128_FREXP (x, pn); }
inline boost::math::cstdfloat::detail::float_internal128_t fabs (boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_FABS (x); }
inline boost::math::cstdfloat::detail::float_internal128_t abs (boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_FABS (x); }
inline boost::math::cstdfloat::detail::float_internal128_t floor (boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_FLOOR (x); }
inline boost::math::cstdfloat::detail::float_internal128_t ceil (boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_CEIL (x); }
inline boost::math::cstdfloat::detail::float_internal128_t sqrt (boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_SQRT (x); }
inline boost::math::cstdfloat::detail::float_internal128_t trunc (boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_TRUNC (x); }
inline boost::math::cstdfloat::detail::float_internal128_t exp (boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_EXP (x); }
inline boost::math::cstdfloat::detail::float_internal128_t pow (boost::math::cstdfloat::detail::float_internal128_t x, boost::math::cstdfloat::detail::float_internal128_t a) { return ::BOOST_CSTDFLOAT_FLOAT128_POW (x, a); }
inline boost::math::cstdfloat::detail::float_internal128_t pow (boost::math::cstdfloat::detail::float_internal128_t x, int a) { return ::BOOST_CSTDFLOAT_FLOAT128_POW (x, boost::math::cstdfloat::detail::float_internal128_t(a)); }
inline boost::math::cstdfloat::detail::float_internal128_t log (boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_LOG (x); }
inline boost::math::cstdfloat::detail::float_internal128_t log10 (boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_LOG10 (x); }
inline boost::math::cstdfloat::detail::float_internal128_t sin (boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_SIN (x); }
inline boost::math::cstdfloat::detail::float_internal128_t cos (boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_COS (x); }
inline boost::math::cstdfloat::detail::float_internal128_t tan (boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_TAN (x); }
inline boost::math::cstdfloat::detail::float_internal128_t asin (boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_ASIN (x); }
inline boost::math::cstdfloat::detail::float_internal128_t acos (boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_ACOS (x); }
inline boost::math::cstdfloat::detail::float_internal128_t atan (boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_ATAN (x); }
inline boost::math::cstdfloat::detail::float_internal128_t sinh (boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_SINH (x); }
inline boost::math::cstdfloat::detail::float_internal128_t cosh (boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_COSH (x); }
inline boost::math::cstdfloat::detail::float_internal128_t tanh (boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_TANH (x); }
inline boost::math::cstdfloat::detail::float_internal128_t asinh (boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_ASINH (x); }
inline boost::math::cstdfloat::detail::float_internal128_t acosh (boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_ACOSH (x); }
inline boost::math::cstdfloat::detail::float_internal128_t atanh (boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_ATANH (x); }
inline boost::math::cstdfloat::detail::float_internal128_t fmod (boost::math::cstdfloat::detail::float_internal128_t a, boost::math::cstdfloat::detail::float_internal128_t b) { return ::BOOST_CSTDFLOAT_FLOAT128_FMOD (a, b); }
inline boost::math::cstdfloat::detail::float_internal128_t atan2 (boost::math::cstdfloat::detail::float_internal128_t y, boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_ATAN2 (y, x); }
inline boost::math::cstdfloat::detail::float_internal128_t lgamma(boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_LGAMMA(x); }
inline boost::math::cstdfloat::detail::float_internal128_t tgamma(boost::math::cstdfloat::detail::float_internal128_t x) { return ::BOOST_CSTDFLOAT_FLOAT128_TGAMMA(x); }
} } } } // boost::math::cstdfloat::detail
// We will now inject the quadruple-precision <cmath> functions
// into the std namespace. This is done via *using* directive.
namespace std
{
using boost::math::cstdfloat::detail::ldexp;
using boost::math::cstdfloat::detail::frexp;
using boost::math::cstdfloat::detail::fabs;
using boost::math::cstdfloat::detail::abs;
using boost::math::cstdfloat::detail::floor;
using boost::math::cstdfloat::detail::ceil;
using boost::math::cstdfloat::detail::sqrt;
using boost::math::cstdfloat::detail::trunc;
using boost::math::cstdfloat::detail::exp;
using boost::math::cstdfloat::detail::pow;
using boost::math::cstdfloat::detail::log;
using boost::math::cstdfloat::detail::log10;
using boost::math::cstdfloat::detail::sin;
using boost::math::cstdfloat::detail::cos;
using boost::math::cstdfloat::detail::tan;
using boost::math::cstdfloat::detail::asin;
using boost::math::cstdfloat::detail::acos;
using boost::math::cstdfloat::detail::atan;
using boost::math::cstdfloat::detail::sinh;
using boost::math::cstdfloat::detail::cosh;
using boost::math::cstdfloat::detail::tanh;
using boost::math::cstdfloat::detail::asinh;
using boost::math::cstdfloat::detail::acosh;
using boost::math::cstdfloat::detail::atanh;
using boost::math::cstdfloat::detail::fmod;
using boost::math::cstdfloat::detail::atan2;
using boost::math::cstdfloat::detail::lgamma;
using boost::math::cstdfloat::detail::tgamma;
} // namespace std
// We will now remove the preprocessor symbols representing quadruple-precision <cmath>
// functions from the preprocessor.
#undef BOOST_CSTDFLOAT_FLOAT128_LDEXP
#undef BOOST_CSTDFLOAT_FLOAT128_FREXP
#undef BOOST_CSTDFLOAT_FLOAT128_FABS
#undef BOOST_CSTDFLOAT_FLOAT128_FLOOR
#undef BOOST_CSTDFLOAT_FLOAT128_CEIL
#undef BOOST_CSTDFLOAT_FLOAT128_SQRT
#undef BOOST_CSTDFLOAT_FLOAT128_TRUNC
#undef BOOST_CSTDFLOAT_FLOAT128_EXP
#undef BOOST_CSTDFLOAT_FLOAT128_EXPM1
#undef BOOST_CSTDFLOAT_FLOAT128_POW
#undef BOOST_CSTDFLOAT_FLOAT128_LOG
#undef BOOST_CSTDFLOAT_FLOAT128_LOG10
#undef BOOST_CSTDFLOAT_FLOAT128_SIN
#undef BOOST_CSTDFLOAT_FLOAT128_COS
#undef BOOST_CSTDFLOAT_FLOAT128_TAN
#undef BOOST_CSTDFLOAT_FLOAT128_ASIN
#undef BOOST_CSTDFLOAT_FLOAT128_ACOS
#undef BOOST_CSTDFLOAT_FLOAT128_ATAN
#undef BOOST_CSTDFLOAT_FLOAT128_SINH
#undef BOOST_CSTDFLOAT_FLOAT128_COSH
#undef BOOST_CSTDFLOAT_FLOAT128_TANH
#undef BOOST_CSTDFLOAT_FLOAT128_ASINH
#undef BOOST_CSTDFLOAT_FLOAT128_ACOSH
#undef BOOST_CSTDFLOAT_FLOAT128_ATANH
#undef BOOST_CSTDFLOAT_FLOAT128_FMOD
#undef BOOST_CSTDFLOAT_FLOAT128_ATAN2
#undef BOOST_CSTDFLOAT_FLOAT128_LGAMMA
#undef BOOST_CSTDFLOAT_FLOAT128_TGAMMA
#endif // Not BOOST_CSTDFLOAT_NO_LIBQUADMATH_SUPPORT (i.e., the user would like to have libquadmath support)
#endif // _BOOST_CSTDFLOAT_CMATH_2014_02_15_HPP_
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