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stabilize build system: depends, installer, boost/bdb fixes, cross targets groundwork

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Nathan Slaven
2026-02-24 18:38:47 +00:00
parent da8c28aaeb
commit 65cb2619a7
13106 changed files with 2484322 additions and 1804 deletions
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depends/x86_64-pc-linux-gnu/include/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_
depends/x86_64-pc-linux-gnu/include/boost/math/cstdfloat/cstdfloat_complex.hpp
+38
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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 (and extended) support for <complex>.
#ifndef _BOOST_CSTDFLOAT_COMPLEX_2014_02_15_HPP_
#define _BOOST_CSTDFLOAT_COMPLEX_2014_02_15_HPP_
#include <boost/math/cstdfloat/cstdfloat_types.hpp>
#include <boost/math/cstdfloat/cstdfloat_limits.hpp>
#include <boost/math/cstdfloat/cstdfloat_cmath.hpp>
#include <boost/math/cstdfloat/cstdfloat_iostream.hpp>
#if defined(BOOST_CSTDFLOAT_NO_LIBQUADMATH_LIMITS)
#error You can not use <boost/math/cstdfloat/cstdfloat_complex.hpp> with BOOST_CSTDFLOAT_NO_LIBQUADMATH_LIMITS defined.
#endif
#if defined(BOOST_CSTDFLOAT_NO_LIBQUADMATH_CMATH)
#error You can not use <boost/math/cstdfloat/cstdfloat_complex.hpp> with BOOST_CSTDFLOAT_NO_LIBQUADMATH_CMATH defined.
#endif
#if defined(BOOST_CSTDFLOAT_NO_LIBQUADMATH_IOSTREAM)
#error You can not use <boost/math/cstdfloat/cstdfloat_complex.hpp> with BOOST_CSTDFLOAT_NO_LIBQUADMATH_IOSTREAM defined.
#endif
#if defined(BOOST_CSTDFLOAT_HAS_INTERNAL_FLOAT128_T) && defined(BOOST_MATH_USE_FLOAT128) && !defined(BOOST_CSTDFLOAT_NO_LIBQUADMATH_SUPPORT)
#define BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE boost::math::cstdfloat::detail::float_internal128_t
#include <boost/math/cstdfloat/cstdfloat_complex_std.hpp>
#undef BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE
#endif // Not BOOST_CSTDFLOAT_NO_LIBQUADMATH_SUPPORT (i.e., the user would like to have libquadmath support)
#endif // _BOOST_CSTDFLOAT_COMPLEX_2014_02_15_HPP_
depends/x86_64-pc-linux-gnu/include/boost/math/cstdfloat/cstdfloat_complex_std.hpp
+641
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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 a specialization of std::complex<> for *anything* that
// is defined as BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE.
#ifndef _BOOST_CSTDFLOAT_COMPLEX_STD_2014_02_15_HPP_
#define _BOOST_CSTDFLOAT_COMPLEX_STD_2014_02_15_HPP_
#if defined(__GNUC__)
#pragma GCC system_header
#endif
#include <complex>
#include <boost/math/constants/constants.hpp>
namespace std
{
// Forward declarations.
template<class float_type>
class complex;
template<>
class complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>;
inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE real(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE imag(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE abs (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE arg (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE norm(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> conj (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> proj (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> polar(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE&,
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& = 0);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> sqrt (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> sin (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> cos (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> tan (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> asin (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> acos (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> atan (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> exp (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> log (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> log10(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&,
int);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&,
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE&);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&,
const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow (const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE&,
const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> sinh (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> cosh (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> tanh (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> asinh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> acosh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> atanh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
template<class char_type, class traits_type>
inline std::basic_ostream<char_type, traits_type>& operator<<(std::basic_ostream<char_type, traits_type>&, const std::complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
template<class char_type, class traits_type>
inline std::basic_istream<char_type, traits_type>& operator>>(std::basic_istream<char_type, traits_type>&, std::complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>&);
// Template specialization of the complex class.
template<>
class complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>
{
public:
typedef BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE value_type;
explicit complex(const complex<float>&);
explicit complex(const complex<double>&);
explicit complex(const complex<long double>&);
#if defined(BOOST_NO_CXX11_CONSTEXPR)
complex(const value_type& r = value_type(),
const value_type& i = value_type()) : re(r),
im(i) { }
template<typename X>
complex(const complex<X>& x) : re(x.real()),
im(x.imag()) { }
const value_type& real() const { return re; }
const value_type& imag() const { return im; }
value_type& real() { return re; }
value_type& imag() { return im; }
#else
BOOST_CONSTEXPR complex(const value_type& r = value_type(),
const value_type& i = value_type()) : re(r),
im(i) { }
template<typename X>
BOOST_CONSTEXPR complex(const complex<X>& x) : re(x.real()),
im(x.imag()) { }
value_type real() const { return re; }
value_type imag() const { return im; }
#endif
void real(value_type r) { re = r; }
void imag(value_type i) { im = i; }
complex<value_type>& operator=(const value_type& v)
{
re = v;
im = value_type(0);
return *this;
}
complex<value_type>& operator+=(const value_type& v)
{
re += v;
return *this;
}
complex<value_type>& operator-=(const value_type& v)
{
re -= v;
return *this;
}
complex<value_type>& operator*=(const value_type& v)
{
re *= v;
im *= v;
return *this;
}
complex<value_type>& operator/=(const value_type& v)
{
re /= v;
im /= v;
return *this;
}
template<typename X>
complex<value_type>& operator=(const complex<X>& x)
{
re = x.real();
im = x.imag();
return *this;
}
template<typename X>
complex<value_type>& operator+=(const complex<X>& x)
{
re += x.real();
im += x.imag();
return *this;
}
template<typename X>
complex<value_type>& operator-=(const complex<X>& x)
{
re -= x.real();
im -= x.imag();
return *this;
}
template<typename X>
complex<value_type>& operator*=(const complex<X>& x)
{
const value_type tmp_real = (re * x.real()) - (im * x.imag());
im = (re * x.imag()) + (im * x.real());
re = tmp_real;
return *this;
}
template<typename X>
complex<value_type>& operator/=(const complex<X>& x)
{
const value_type tmp_real = (re * x.real()) + (im * x.imag());
const value_type the_norm = std::norm(x);
im = ((im * x.real()) - (re * x.imag())) / the_norm;
re = tmp_real / the_norm;
return *this;
}
private:
value_type re;
value_type im;
};
// Constructors from built-in complex representation of floating-point types.
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::complex(const complex<float>& f) : re(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE( f.real())), im(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE( f.imag())) { }
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::complex(const complex<double>& d) : re(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE( d.real())), im(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE( d.imag())) { }
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::complex(const complex<long double>& ld) : re(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(ld.real())), im(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(ld.imag())) { }
} // namespace std
namespace boost { namespace math { namespace cstdfloat { namespace detail {
template<class float_type> inline std::complex<float_type> multiply_by_i(const std::complex<float_type>& x)
{
// Multiply x (in C) by I (the imaginary component), and return the result.
return std::complex<float_type>(-x.imag(), x.real());
}
} } } } // boost::math::cstdfloat::detail
namespace std
{
// ISO/IEC 14882:2011, Section 26.4.7, specific values.
inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE real(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { return x.real(); }
inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE imag(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { return x.imag(); }
inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE abs (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { using std::sqrt; return sqrt ((real(x) * real(x)) + (imag(x) * imag(x))); }
inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE arg (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { using std::atan2; return atan2(x.imag(), x.real()); }
inline BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE norm(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { return (real(x) * real(x)) + (imag(x) * imag(x)); }
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> conj (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(x.real(), -x.imag()); }
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> proj (const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x)
{
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE m = (std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::max)();
if ((x.real() > m)
|| (x.real() < -m)
|| (x.imag() > m)
|| (x.imag() < -m))
{
// We have an infinity, return a normalized infinity, respecting the sign of the imaginary part:
return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::infinity(), x.imag() < 0 ? -0 : 0);
}
return x;
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> polar(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& rho,
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& theta)
{
using std::sin;
using std::cos;
return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(rho * cos(theta), rho * sin(theta));
}
// Global add, sub, mul, div.
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator+(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& u, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& v) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(u.real() + v.real(), u.imag() + v.imag()); }
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator-(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& u, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& v) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(u.real() - v.real(), u.imag() - v.imag()); }
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator*(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& u, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& v)
{
return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>((u.real() * v.real()) - (u.imag() * v.imag()),
(u.real() * v.imag()) + (u.imag() * v.real()));
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator/(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& u, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& v)
{
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE the_norm = std::norm(v);
return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(((u.real() * v.real()) + (u.imag() * v.imag())) / the_norm,
((u.imag() * v.real()) - (u.real() * v.imag())) / the_norm);
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator+(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& u, const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& v) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(u.real() + v, u.imag()); }
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator-(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& u, const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& v) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(u.real() - v, u.imag()); }
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator*(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& u, const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& v) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(u.real() * v, u.imag() * v); }
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator/(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& u, const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& v) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(u.real() / v, u.imag() / v); }
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator+(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& u, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& v) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(u + v.real(), v.imag()); }
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator-(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& u, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& v) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(u - v.real(), -v.imag()); }
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator*(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& u, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& v) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(u * v.real(), u * v.imag()); }
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator/(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& u, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& v) { const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE v_norm = norm(v); return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>((u * v.real()) / v_norm, (-u * v.imag()) / v_norm); }
// Unary plus / minus.
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator+(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& u) { return u; }
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> operator-(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& u) { return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(-u.real(), -u.imag()); }
// Equality and inequality.
inline bool operator==(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& y) { return ((x.real() == y.real()) && (x.imag() == y.imag())); }
inline bool operator==(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x, const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& y) { return ((x.real() == y) && (x.imag() == BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(0))); }
inline bool operator==(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& x, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& y) { return ((x == y.real()) && (y.imag() == BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(0))); }
inline bool operator!=(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& y) { return ((x.real() != y.real()) || (x.imag() != y.imag())); }
inline bool operator!=(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x, const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& y) { return ((x.real() != y) || (x.imag() != BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(0))); }
inline bool operator!=(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& x, const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& y) { return ((x != y.real()) || (y.imag() != BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(0))); }
// ISO/IEC 14882:2011, Section 26.4.8, transcendentals.
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> sqrt(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x)
{
using std::fabs;
using std::sqrt;
// Compute sqrt(x) for x in C:
// sqrt(x) = (s , xi / 2s) : for xr > 0,
// (|xi| / 2s, +-s) : for xr < 0,
// (sqrt(xi), sqrt(xi) : for xr = 0,
// where s = sqrt{ [ |xr| + sqrt(xr^2 + xi^2) ] / 2 },
// and the +- sign is the same as the sign of xi.
if(x.real() > 0)
{
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE s = sqrt((fabs(x.real()) + std::abs(x)) / 2);
return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(s, x.imag() / (s * 2));
}
else if(x.real() < 0)
{
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE s = sqrt((fabs(x.real()) + std::abs(x)) / 2);
const bool imag_is_neg = (x.imag() < 0);
return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(fabs(x.imag()) / (s * 2), (imag_is_neg ? -s : s));
}
else
{
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sqrt_xi_half = sqrt(x.imag() / 2);
return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(sqrt_xi_half, sqrt_xi_half);
}
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> sin(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x)
{
using std::sin;
using std::cos;
using std::exp;
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sin_x = sin (x.real());
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cos_x = cos (x.real());
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_yp = exp (x.imag());
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_ym = BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) / exp_yp;
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sinh_y = (exp_yp - exp_ym) / 2;
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cosh_y = (exp_yp + exp_ym) / 2;
return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(sin_x * cosh_y, cos_x * sinh_y);
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> cos(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x)
{
using std::sin;
using std::cos;
using std::exp;
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sin_x = sin (x.real());
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cos_x = cos (x.real());
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_yp = exp (x.imag());
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_ym = BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) / exp_yp;
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sinh_y = (exp_yp - exp_ym) / 2;
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cosh_y = (exp_yp + exp_ym) / 2;
return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(cos_x * cosh_y, -(sin_x * sinh_y));
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> tan(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x)
{
using std::sin;
using std::cos;
using std::exp;
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sin_x = sin (x.real());
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cos_x = cos (x.real());
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_yp = exp (x.imag());
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_ym = BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) / exp_yp;
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sinh_y = (exp_yp - exp_ym) / 2;
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cosh_y = (exp_yp + exp_ym) / 2;
return ( complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(sin_x * cosh_y, cos_x * sinh_y)
/ complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(cos_x * cosh_y, -sin_x * sinh_y));
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> asin(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x)
{
return -boost::math::cstdfloat::detail::multiply_by_i(std::log(boost::math::cstdfloat::detail::multiply_by_i(x) + std::sqrt(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) - (x * x))));
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> acos(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x)
{
return boost::math::constants::half_pi<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>() - std::asin(x);
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> atan(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x)
{
const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> izz = boost::math::cstdfloat::detail::multiply_by_i(x);
return boost::math::cstdfloat::detail::multiply_by_i(std::log(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) - izz) - std::log(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) + izz)) / 2;
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> exp(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x)
{
using std::exp;
return std::polar(exp(x.real()), x.imag());
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> log(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x)
{
using std::atan2;
using std::log;
return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(log(std::norm(x)) / 2, atan2(x.imag(), x.real()));
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> log10(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x)
{
return std::log(x) / boost::math::constants::ln_ten<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>();
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x,
int p)
{
const bool re_isneg = (x.real() < 0);
const bool re_isnan = (x.real() != x.real());
const bool re_isinf = ((!re_isneg) ? bool(+x.real() > (std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::max)())
: bool(-x.real() > (std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::max)()));
const bool im_isneg = (x.imag() < 0);
const bool im_isnan = (x.imag() != x.imag());
const bool im_isinf = ((!im_isneg) ? bool(+x.imag() > (std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::max)())
: bool(-x.imag() > (std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::max)()));
if(re_isnan || im_isnan) { return x; }
if(re_isinf || im_isinf)
{
return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::quiet_NaN(),
std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::quiet_NaN());
}
if(p < 0)
{
if(std::abs(x) < (std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::min)())
{
return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::infinity(),
std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::infinity());
}
else
{
return BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) / std::pow(x, -p);
}
}
if(p == 0)
{
return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1));
}
else
{
if(p == 1) { return x; }
if(std::abs(x) > (std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::max)())
{
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE re = (re_isneg ? -std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::infinity()
: +std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::infinity());
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE im = (im_isneg ? -std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::infinity()
: +std::numeric_limits<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>::infinity());
return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(re, im);
}
if (p == 2) { return (x * x); }
else if(p == 3) { return ((x * x) * x); }
else if(p == 4) { const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> x2 = (x * x); return (x2 * x2); }
else
{
// The variable xn stores the binary powers of x.
complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> result(((p % 2) != 0) ? x : complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1)));
complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> xn (x);
int p2 = p;
while((p2 /= 2) != 0)
{
// Square xn for each binary power.
xn *= xn;
const bool has_binary_power = ((p2 % 2) != 0);
if(has_binary_power)
{
// Multiply the result with each binary power contained in the exponent.
result *= xn;
}
}
return result;
}
}
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x,
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& a)
{
return std::exp(a * std::log(x));
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x,
const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& a)
{
return std::exp(a * std::log(x));
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> pow(const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE& x,
const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& a)
{
return std::exp(a * std::log(x));
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> sinh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x)
{
using std::sin;
using std::cos;
using std::exp;
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sin_y = sin (x.imag());
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cos_y = cos (x.imag());
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_xp = exp (x.real());
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_xm = BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) / exp_xp;
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sinh_x = (exp_xp - exp_xm) / 2;
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cosh_x = (exp_xp + exp_xm) / 2;
return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(cos_y * sinh_x, cosh_x * sin_y);
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> cosh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x)
{
using std::sin;
using std::cos;
using std::exp;
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sin_y = sin (x.imag());
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cos_y = cos (x.imag());
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_xp = exp (x.real());
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE exp_xm = BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) / exp_xp;
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE sinh_x = (exp_xp - exp_xm) / 2;
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE cosh_x = (exp_xp + exp_xm) / 2;
return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(cos_y * cosh_x, sin_y * sinh_x);
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> tanh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x)
{
const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> ex_plus = std::exp(x);
const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> ex_minus = BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) / ex_plus;
return (ex_plus - ex_minus) / (ex_plus + ex_minus);
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> asinh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x)
{
return std::log(x + std::sqrt((x * x) + BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1)));
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> acosh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x)
{
const BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE my_one(1);
const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> zp(x.real() + my_one, x.imag());
const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> zm(x.real() - my_one, x.imag());
return std::log(x + (zp * std::sqrt(zm / zp)));
}
inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> atanh(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x)
{
return (std::log(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) + x) - std::log(BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE(1) - x)) / 2.0;
}
template<class char_type, class traits_type>
inline std::basic_ostream<char_type, traits_type>& operator<<(std::basic_ostream<char_type, traits_type>& os, const std::complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x)
{
std::basic_ostringstream<char_type, traits_type> ostr;
ostr.flags(os.flags());
ostr.imbue(os.getloc());
ostr.precision(os.precision());
ostr << char_type('(')
<< x.real()
<< char_type(',')
<< x.imag()
<< char_type(')');
return (os << ostr.str());
}
template<class char_type, class traits_type>
inline std::basic_istream<char_type, traits_type>& operator>>(std::basic_istream<char_type, traits_type>& is, std::complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x)
{
BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE rx;
BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE ix;
char_type the_char;
static_cast<void>(is >> the_char);
if(the_char == static_cast<char_type>('('))
{
static_cast<void>(is >> rx >> the_char);
if(the_char == static_cast<char_type>(','))
{
static_cast<void>(is >> ix >> the_char);
if(the_char == static_cast<char_type>(')'))
{
x = complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>(rx, ix);
}
else
{
is.setstate(ios_base::failbit);
}
}
else if(the_char == static_cast<char_type>(')'))
{
x = rx;
}
else
{
is.setstate(ios_base::failbit);
}
}
else
{
static_cast<void>(is.putback(the_char));
static_cast<void>(is >> rx);
x = rx;
}
return is;
}
} // namespace std
#endif // _BOOST_CSTDFLOAT_COMPLEX_STD_2014_02_15_HPP_
depends/x86_64-pc-linux-gnu/include/boost/math/cstdfloat/cstdfloat_iostream.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 I/O stream operations.
#ifndef _BOOST_CSTDFLOAT_IOSTREAM_2014_02_15_HPP_
#define _BOOST_CSTDFLOAT_IOSTREAM_2014_02_15_HPP_
#include <boost/math/cstdfloat/cstdfloat_types.hpp>
#include <boost/math/cstdfloat/cstdfloat_limits.hpp>
#include <boost/math/cstdfloat/cstdfloat_cmath.hpp>
#if defined(BOOST_CSTDFLOAT_NO_LIBQUADMATH_CMATH)
#error You can not use <boost/math/cstdfloat/cstdfloat_iostream.hpp> with BOOST_CSTDFLOAT_NO_LIBQUADMATH_CMATH defined.
#endif
#if defined(BOOST_CSTDFLOAT_HAS_INTERNAL_FLOAT128_T) && defined(BOOST_MATH_USE_FLOAT128) && !defined(BOOST_CSTDFLOAT_NO_LIBQUADMATH_SUPPORT)
#include <cstddef>
#include <istream>
#include <ostream>
#include <sstream>
#include <stdexcept>
#include <string>
#include <boost/static_assert.hpp>
#include <boost/throw_exception.hpp>
// #if (0)
#if defined(__GNUC__)
// Forward declarations of quadruple-precision string functions.
extern "C" int quadmath_snprintf(char *str, size_t size, const char *format, ...) throw();
extern "C" boost::math::cstdfloat::detail::float_internal128_t strtoflt128(const char*, char **) throw();
namespace std
{
template<typename char_type, class traits_type>
inline std::basic_ostream<char_type, traits_type>& operator<<(std::basic_ostream<char_type, traits_type>& os, const boost::math::cstdfloat::detail::float_internal128_t& x)
{
std::basic_ostringstream<char_type, traits_type> ostr;
ostr.flags(os.flags());
ostr.imbue(os.getloc());
ostr.precision(os.precision());
char my_buffer[64U];
const int my_prec = static_cast<int>(os.precision());
const int my_digits = ((my_prec == 0) ? 36 : my_prec);
const std::ios_base::fmtflags my_flags = os.flags();
char my_format_string[8U];
std::size_t my_format_string_index = 0U;
my_format_string[my_format_string_index] = '%';
++my_format_string_index;
if(my_flags & std::ios_base::showpos) { my_format_string[my_format_string_index] = '+'; ++my_format_string_index; }
if(my_flags & std::ios_base::showpoint) { my_format_string[my_format_string_index] = '#'; ++my_format_string_index; }
my_format_string[my_format_string_index + 0U] = '.';
my_format_string[my_format_string_index + 1U] = '*';
my_format_string[my_format_string_index + 2U] = 'Q';
my_format_string_index += 3U;
char the_notation_char;
if (my_flags & std::ios_base::scientific) { the_notation_char = 'e'; }
else if(my_flags & std::ios_base::fixed) { the_notation_char = 'f'; }
else { the_notation_char = 'g'; }
my_format_string[my_format_string_index + 0U] = the_notation_char;
my_format_string[my_format_string_index + 1U] = 0;
const int v = ::quadmath_snprintf(my_buffer,
static_cast<int>(sizeof(my_buffer)),
my_format_string,
my_digits,
x);
if(v < 0) { BOOST_THROW_EXCEPTION(std::runtime_error("Formatting of boost::float128_t failed internally in quadmath_snprintf().")); }
if(v >= static_cast<int>(sizeof(my_buffer) - 1U))
{
// Evidently there is a really long floating-point string here,
// such as a small decimal representation in non-scientific notation.
// So we have to use dynamic memory allocation for the output
// string buffer.
char* my_buffer2 = static_cast<char*>(0U);
#ifndef BOOST_NO_EXCEPTIONS
try
{
#endif
my_buffer2 = new char[v + 3];
#ifndef BOOST_NO_EXCEPTIONS
}
catch(const std::bad_alloc&)
{
BOOST_THROW_EXCEPTION(std::runtime_error("Formatting of boost::float128_t failed while allocating memory."));
}
#endif
const int v2 = ::quadmath_snprintf(my_buffer2,
v + 3,
my_format_string,
my_digits,
x);
if(v2 >= v + 3)
{
BOOST_THROW_EXCEPTION(std::runtime_error("Formatting of boost::float128_t failed."));
}
static_cast<void>(ostr << my_buffer2);
delete [] my_buffer2;
}
else
{
static_cast<void>(ostr << my_buffer);
}
return (os << ostr.str());
}
template<typename char_type, class traits_type>
inline std::basic_istream<char_type, traits_type>& operator>>(std::basic_istream<char_type, traits_type>& is, boost::math::cstdfloat::detail::float_internal128_t& x)
{
std::string str;
static_cast<void>(is >> str);
char* p_end;
x = strtoflt128(str.c_str(), &p_end);
if(static_cast<std::ptrdiff_t>(p_end - str.c_str()) != static_cast<std::ptrdiff_t>(str.length()))
{
for(std::string::const_reverse_iterator it = str.rbegin(); it != str.rend(); ++it)
{
static_cast<void>(is.putback(*it));
}
is.setstate(ios_base::failbit);
BOOST_THROW_EXCEPTION(std::runtime_error("Unable to interpret input string as a boost::float128_t"));
}
return is;
}
}
// #elif defined(__GNUC__)
#elif defined(BOOST_INTEL)
// The section for I/O stream support for the ICC compiler is particularly
// long, because these functions must be painstakingly synthesized from
// manually-written routines (ICC does not support I/O stream operations
// for its _Quad type).
// The following string-extraction routines are based on the methodology
// used in Boost.Multiprecision by John Maddock and Christopher Kormanyos.
// This methodology has been slightly modified here for boost::float128_t.
#include <cstring>
#include <cctype>
#include <boost/lexical_cast.hpp>
namespace boost { namespace math { namespace cstdfloat { namespace detail {
template<class string_type>
void format_float_string(string_type& str,
int my_exp,
int digits,
const std::ios_base::fmtflags f,
const bool iszero)
{
typedef typename string_type::size_type size_type;
const bool scientific = ((f & std::ios_base::scientific) == std::ios_base::scientific);
const bool fixed = ((f & std::ios_base::fixed) == std::ios_base::fixed);
const bool showpoint = ((f & std::ios_base::showpoint) == std::ios_base::showpoint);
const bool showpos = ((f & std::ios_base::showpos) == std::ios_base::showpos);
const bool b_neg = ((str.size() != 0U) && (str[0] == '-'));
if(b_neg)
{
str.erase(0, 1);
}
if(digits == 0)
{
digits = static_cast<int>((std::max)(str.size(), size_type(16)));
}
if(iszero || str.empty() || (str.find_first_not_of('0') == string_type::npos))
{
// We will be printing zero, even though the value might not
// actually be zero (it just may have been rounded to zero).
str = "0";
if(scientific || fixed)
{
str.append(1, '.');
str.append(size_type(digits), '0');
if(scientific)
{
str.append("e+00");
}
}
else
{
if(showpoint)
{
str.append(1, '.');
if(digits > 1)
{
str.append(size_type(digits - 1), '0');
}
}
}
if(b_neg)
{
str.insert(0U, 1U, '-');
}
else if(showpos)
{
str.insert(0U, 1U, '+');
}
return;
}
if(!fixed && !scientific && !showpoint)
{
// Suppress trailing zeros.
typename string_type::iterator pos = str.end();
while(pos != str.begin() && *--pos == '0') { ; }
if(pos != str.end())
{
++pos;
}
str.erase(pos, str.end());
if(str.empty())
{
str = '0';
}
}
else if(!fixed || (my_exp >= 0))
{
// Pad out the end with zero's if we need to.
int chars = static_cast<int>(str.size());
chars = digits - chars;
if(scientific)
{
++chars;
}
if(chars > 0)
{
str.append(static_cast<size_type>(chars), '0');
}
}
if(fixed || (!scientific && (my_exp >= -4) && (my_exp < digits)))
{
if((1 + my_exp) > static_cast<int>(str.size()))
{
// Just pad out the end with zeros.
str.append(static_cast<size_type>((1 + my_exp) - static_cast<int>(str.size())), '0');
if(showpoint || fixed)
{
str.append(".");
}
}
else if(my_exp + 1 < static_cast<int>(str.size()))
{
if(my_exp < 0)
{
str.insert(0U, static_cast<size_type>(-1 - my_exp), '0');
str.insert(0U, "0.");
}
else
{
// Insert the decimal point:
str.insert(static_cast<size_type>(my_exp + 1), 1, '.');
}
}
else if(showpoint || fixed) // we have exactly the digits we require to left of the point
{
str += ".";
}
if(fixed)
{
// We may need to add trailing zeros.
int l = static_cast<int>(str.find('.') + 1U);
l = digits - (static_cast<int>(str.size()) - l);
if(l > 0)
{
str.append(size_type(l), '0');
}
}
}
else
{
// Scientific format:
if(showpoint || (str.size() > 1))
{
str.insert(1U, 1U, '.');
}
str.append(1U, 'e');
string_type e = boost::lexical_cast<string_type>(std::abs(my_exp));
if(e.size() < 2U)
{
e.insert(0U, 2U - e.size(), '0');
}
if(my_exp < 0)
{
e.insert(0U, 1U, '-');
}
else
{
e.insert(0U, 1U, '+');
}
str.append(e);
}
if(b_neg)
{
str.insert(0U, 1U, '-');
}
else if(showpos)
{
str.insert(0U, 1U, '+');
}
}
template<class float_type, class type_a> inline void eval_convert_to(type_a* pa, const float_type& cb) { *pa = static_cast<type_a>(cb); }
template<class float_type, class type_a> inline void eval_add (float_type& b, const type_a& a) { b += a; }
template<class float_type, class type_a> inline void eval_subtract (float_type& b, const type_a& a) { b -= a; }
template<class float_type, class type_a> inline void eval_multiply (float_type& b, const type_a& a) { b *= a; }
template<class float_type> inline void eval_multiply (float_type& b, const float_type& cb, const float_type& cb2) { b = (cb * cb2); }
template<class float_type, class type_a> inline void eval_divide (float_type& b, const type_a& a) { b /= a; }
template<class float_type> inline void eval_log10 (float_type& b, const float_type& cb) { b = std::log10(cb); }
template<class float_type> inline void eval_floor (float_type& b, const float_type& cb) { b = std::floor(cb); }
inline void round_string_up_at(std::string& s, int pos, int& expon)
{
// This subroutine rounds up a string representation of a
// number at the given position pos.
if(pos < 0)
{
s.insert(0U, 1U, '1');
s.erase(s.size() - 1U);
++expon;
}
else if(s[pos] == '9')
{
s[pos] = '0';
round_string_up_at(s, pos - 1, expon);
}
else
{
if((pos == 0) && (s[pos] == '0') && (s.size() == 1))
{
++expon;
}
++s[pos];
}
}
template<class float_type>
std::string convert_to_string(float_type& x,
std::streamsize digits,
const std::ios_base::fmtflags f)
{
const bool isneg = (x < 0);
const bool iszero = ((!isneg) ? bool(+x < (std::numeric_limits<float_type>::min)())
: bool(-x < (std::numeric_limits<float_type>::min)()));
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)()));
int expon = 0;
if(digits <= 0) { digits = std::numeric_limits<float_type>::max_digits10; }
const int org_digits = static_cast<int>(digits);
std::string result;
if(iszero)
{
result = "0";
}
else if(isinf)
{
if(x < 0)
{
return "-inf";
}
else
{
return ((f & std::ios_base::showpos) == std::ios_base::showpos) ? "+inf" : "inf";
}
}
else if(isnan)
{
return "nan";
}
else
{
// Start by figuring out the base-10 exponent.
if(isneg) { x = -x; }
float_type t;
float_type ten = 10;
eval_log10(t, x);
eval_floor(t, t);
eval_convert_to(&expon, t);
if(-expon > std::numeric_limits<float_type>::max_exponent10 - 3)
{
int e = -expon / 2;
const float_type t2 = boost::math::cstdfloat::detail::pown(ten, e);
eval_multiply(t, t2, x);
eval_multiply(t, t2);
if((expon & 1) != 0)
{
eval_multiply(t, ten);
}
}
else
{
t = boost::math::cstdfloat::detail::pown(ten, -expon);
eval_multiply(t, x);
}
// Make sure that the value lies between [1, 10), and adjust if not.
if(t < 1)
{
eval_multiply(t, 10);
--expon;
}
else if(t >= 10)
{
eval_divide(t, 10);
++expon;
}
float_type digit;
int cdigit;
// Adjust the number of digits required based on formatting options.
if(((f & std::ios_base::fixed) == std::ios_base::fixed) && (expon != -1))
{
digits += (expon + 1);
}
if((f & std::ios_base::scientific) == std::ios_base::scientific)
{
++digits;
}
// Extract the base-10 digits one at a time.
for(int i = 0; i < digits; ++i)
{
eval_floor(digit, t);
eval_convert_to(&cdigit, digit);
result += static_cast<char>('0' + cdigit);
eval_subtract(t, digit);
eval_multiply(t, ten);
}
// Possibly round the result.
if(digits >= 0)
{
eval_floor(digit, t);
eval_convert_to(&cdigit, digit);
eval_subtract(t, digit);
if((cdigit == 5) && (t == 0))
{
// Use simple bankers rounding.
if((static_cast<int>(*result.rbegin() - '0') & 1) != 0)
{
round_string_up_at(result, static_cast<int>(result.size() - 1U), expon);
}
}
else if(cdigit >= 5)
{
round_string_up_at(result, static_cast<int>(result.size() - 1), expon);
}
}
}
while((result.size() > static_cast<std::string::size_type>(digits)) && result.size())
{
// We may get here as a result of rounding.
if(result.size() > 1U)
{
result.erase(result.size() - 1U);
}
else
{
if(expon > 0)
{
--expon; // so we put less padding in the result.
}
else
{
++expon;
}
++digits;
}
}
if(isneg)
{
result.insert(0U, 1U, '-');
}
format_float_string(result, expon, org_digits, f, iszero);
return result;
}
template <class float_type>
bool convert_from_string(float_type& value, const char* p)
{
value = 0;
if((p == static_cast<const char*>(0U)) || (*p == static_cast<char>(0)))
{
return;
}
bool is_neg = false;
bool is_neg_expon = false;
BOOST_CONSTEXPR_OR_CONST int ten = 10;
int expon = 0;
int digits_seen = 0;
BOOST_CONSTEXPR_OR_CONST int max_digits = std::numeric_limits<float_type>::max_digits10 + 1;
if(*p == static_cast<char>('+'))
{
++p;
}
else if(*p == static_cast<char>('-'))
{
is_neg = true;
++p;
}
const bool isnan = ((std::strcmp(p, "nan") == 0) || (std::strcmp(p, "NaN") == 0) || (std::strcmp(p, "NAN") == 0));
if(isnan)
{
eval_divide(value, 0);
if(is_neg)
{
value = -value;
}
return true;
}
const bool isinf = ((std::strcmp(p, "inf") == 0) || (std::strcmp(p, "Inf") == 0) || (std::strcmp(p, "INF") == 0));
if(isinf)
{
value = 1;
eval_divide(value, 0);
if(is_neg)
{
value = -value;
}
return true;
}
// Grab all the leading digits before the decimal point.
while(std::isdigit(*p))
{
eval_multiply(value, ten);
eval_add(value, static_cast<int>(*p - '0'));
++p;
++digits_seen;
}
if(*p == static_cast<char>('.'))
{
// Grab everything after the point, stop when we've seen
// enough digits, even if there are actually more available.
++p;
while(std::isdigit(*p))
{
eval_multiply(value, ten);
eval_add(value, static_cast<int>(*p - '0'));
++p;
--expon;
if(++digits_seen > max_digits)
{
break;
}
}
while(std::isdigit(*p))
{
++p;
}
}
// Parse the exponent.
if((*p == static_cast<char>('e')) || (*p == static_cast<char>('E')))
{
++p;
if(*p == static_cast<char>('+'))
{
++p;
}
else if(*p == static_cast<char>('-'))
{
is_neg_expon = true;
++p;
}
int e2 = 0;
while(std::isdigit(*p))
{
e2 *= 10;
e2 += (*p - '0');
++p;
}
if(is_neg_expon)
{
e2 = -e2;
}
expon += e2;
}
if(expon)
{
// Scale by 10^expon. Note that 10^expon can be outside the range
// of our number type, even though the result is within range.
// If that looks likely, then split the calculation in two parts.
float_type t;
t = ten;
if(expon > (std::numeric_limits<float_type>::min_exponent10 + 2))
{
t = boost::math::cstdfloat::detail::pown(t, expon);
eval_multiply(value, t);
}
else
{
t = boost::math::cstdfloat::detail::pown(t, (expon + digits_seen + 1));
eval_multiply(value, t);
t = ten;
t = boost::math::cstdfloat::detail::pown(t, (-digits_seen - 1));
eval_multiply(value, t);
}
}
if(is_neg)
{
value = -value;
}
return (*p == static_cast<char>(0));
}
} } } } // boost::math::cstdfloat::detail
namespace std
{
template<typename char_type, class traits_type>
inline std::basic_ostream<char_type, traits_type>& operator<<(std::basic_ostream<char_type, traits_type>& os, const boost::math::cstdfloat::detail::float_internal128_t& x)
{
boost::math::cstdfloat::detail::float_internal128_t non_const_x = x;
const std::string str = boost::math::cstdfloat::detail::convert_to_string(non_const_x,
os.precision(),
os.flags());
std::basic_ostringstream<char_type, traits_type> ostr;
ostr.flags(os.flags());
ostr.imbue(os.getloc());
ostr.precision(os.precision());
static_cast<void>(ostr << str);
return (os << ostr.str());
}
template<typename char_type, class traits_type>
inline std::basic_istream<char_type, traits_type>& operator>>(std::basic_istream<char_type, traits_type>& is, boost::math::cstdfloat::detail::float_internal128_t& x)
{
std::string str;
static_cast<void>(is >> str);
const bool conversion_is_ok = boost::math::cstdfloat::detail::convert_from_string(x, str.c_str());
if(false == conversion_is_ok)
{
for(std::string::const_reverse_iterator it = str.rbegin(); it != str.rend(); ++it)
{
static_cast<void>(is.putback(*it));
}
is.setstate(ios_base::failbit);
BOOST_THROW_EXCEPTION(std::runtime_error("Unable to interpret input string as a boost::float128_t"));
}
return is;
}
}
#endif // Use __GNUC__ or BOOST_INTEL libquadmath
#endif // Not BOOST_CSTDFLOAT_NO_LIBQUADMATH_SUPPORT (i.e., the user would like to have libquadmath support)
#endif // _BOOST_CSTDFLOAT_IOSTREAM_2014_02_15_HPP_
depends/x86_64-pc-linux-gnu/include/boost/math/cstdfloat/cstdfloat_limits.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 std::numeric_limits<> support.
#ifndef _BOOST_CSTDFLOAT_LIMITS_2014_01_09_HPP_
#define _BOOST_CSTDFLOAT_LIMITS_2014_01_09_HPP_
#include <boost/math/cstdfloat/cstdfloat_types.hpp>
#if defined(BOOST_CSTDFLOAT_HAS_INTERNAL_FLOAT128_T) && defined(BOOST_MATH_USE_FLOAT128) && !defined(BOOST_CSTDFLOAT_NO_LIBQUADMATH_SUPPORT)
#include <limits>
// Define the name of the global quadruple-precision function to be used for
// calculating quiet_NaN() in the specialization of std::numeric_limits<>.
#if defined(BOOST_INTEL)
#define BOOST_CSTDFLOAT_FLOAT128_SQRT __sqrtq
#elif defined(__GNUC__)
#define BOOST_CSTDFLOAT_FLOAT128_SQRT sqrtq
#endif
// Forward declaration of the quadruple-precision square root function.
extern "C" boost::math::cstdfloat::detail::float_internal128_t BOOST_CSTDFLOAT_FLOAT128_SQRT(boost::math::cstdfloat::detail::float_internal128_t) throw();
namespace std
{
template<>
class numeric_limits<boost::math::cstdfloat::detail::float_internal128_t>
{
public:
BOOST_STATIC_CONSTEXPR bool is_specialized = true;
static boost::math::cstdfloat::detail::float_internal128_t (min) () BOOST_NOEXCEPT { return BOOST_CSTDFLOAT_FLOAT128_MIN; }
static boost::math::cstdfloat::detail::float_internal128_t (max) () BOOST_NOEXCEPT { return BOOST_CSTDFLOAT_FLOAT128_MAX; }
static boost::math::cstdfloat::detail::float_internal128_t lowest() BOOST_NOEXCEPT { return -(max)(); }
BOOST_STATIC_CONSTEXPR int digits = 113;
BOOST_STATIC_CONSTEXPR int digits10 = 33;
BOOST_STATIC_CONSTEXPR int max_digits10 = 36;
BOOST_STATIC_CONSTEXPR bool is_signed = true;
BOOST_STATIC_CONSTEXPR bool is_integer = false;
BOOST_STATIC_CONSTEXPR bool is_exact = false;
BOOST_STATIC_CONSTEXPR int radix = 2;
static boost::math::cstdfloat::detail::float_internal128_t epsilon () { return BOOST_CSTDFLOAT_FLOAT128_EPS; }
static boost::math::cstdfloat::detail::float_internal128_t round_error() { return BOOST_FLOAT128_C(0.5); }
BOOST_STATIC_CONSTEXPR int min_exponent = -16381;
BOOST_STATIC_CONSTEXPR int min_exponent10 = static_cast<int>((min_exponent * 301L) / 1000L);
BOOST_STATIC_CONSTEXPR int max_exponent = +16384;
BOOST_STATIC_CONSTEXPR int max_exponent10 = static_cast<int>((max_exponent * 301L) / 1000L);
BOOST_STATIC_CONSTEXPR bool has_infinity = true;
BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = true;
BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false;
BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_absent;
BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false;
static boost::math::cstdfloat::detail::float_internal128_t infinity () { return BOOST_FLOAT128_C(1.0) / BOOST_FLOAT128_C(0.0); }
static boost::math::cstdfloat::detail::float_internal128_t quiet_NaN () { return ::BOOST_CSTDFLOAT_FLOAT128_SQRT(BOOST_FLOAT128_C(-1.0)); }
static boost::math::cstdfloat::detail::float_internal128_t signaling_NaN() { return BOOST_FLOAT128_C(0.0); }
static boost::math::cstdfloat::detail::float_internal128_t denorm_min () { return BOOST_FLOAT128_C(0.0); }
BOOST_STATIC_CONSTEXPR bool is_iec559 = true;
BOOST_STATIC_CONSTEXPR bool is_bounded = false;
BOOST_STATIC_CONSTEXPR bool is_modulo = false;
BOOST_STATIC_CONSTEXPR bool traps = false;
BOOST_STATIC_CONSTEXPR bool tinyness_before = false;
BOOST_STATIC_CONSTEXPR float_round_style round_style = round_to_nearest;
};
} // namespace std
#endif // Not BOOST_CSTDFLOAT_NO_LIBQUADMATH_SUPPORT (i.e., the user would like to have libquadmath support)
#endif // _BOOST_CSTDFLOAT_LIMITS_2014_01_09_HPP_
depends/x86_64-pc-linux-gnu/include/boost/math/cstdfloat/cstdfloat_types.hpp
+440
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@@ -0,0 +1,440 @@
///////////////////////////////////////////////////////////////////////////////
// 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 the types for floating-point typedefs having specified widths.
#ifndef _BOOST_CSTDFLOAT_TYPES_2014_01_09_HPP_
#define _BOOST_CSTDFLOAT_TYPES_2014_01_09_HPP_
#include <float.h>
#include <limits>
#include <boost/static_assert.hpp>
#include <boost/math/tools/config.hpp>
// This is the beginning of the preamble.
// In this preamble, the preprocessor is used to query certain
// preprocessor definitions from <float.h>. Based on the results
// of these queries, an attempt is made to automatically detect
// the presence of built-in floating-point types having specified
// widths. These are *thought* to be conformant with IEEE-754,
// whereby an unequivocal test based on std::numeric_limits<>
// follows below.
// In addition, various macros that are used for initializing
// floating-point literal values having specified widths and
// some basic min/max values are defined.
// First, we will pre-load certain preprocessor definitions
// with a dummy value.
#define BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH 0
#define BOOST_CSTDFLOAT_HAS_FLOAT16_NATIVE_TYPE 0
#define BOOST_CSTDFLOAT_HAS_FLOAT32_NATIVE_TYPE 0
#define BOOST_CSTDFLOAT_HAS_FLOAT64_NATIVE_TYPE 0
#define BOOST_CSTDFLOAT_HAS_FLOAT80_NATIVE_TYPE 0
#define BOOST_CSTDFLOAT_HAS_FLOAT128_NATIVE_TYPE 0
// Ensure that the compiler has a radix-2 floating-point representation.
#if (!defined(FLT_RADIX) || ((defined(FLT_RADIX) && (FLT_RADIX != 2))))
#error The compiler does not support any radix-2 floating-point types required for <boost/cstdfloat.hpp>.
#endif
// Check if built-in float is equivalent to float16_t, float32_t, float64_t, float80_t, or float128_t.
#if(defined(FLT_MANT_DIG) && defined(FLT_MAX_EXP))
#if ((FLT_MANT_DIG == 11) && (FLT_MAX_EXP == 16) && (BOOST_CSTDFLOAT_HAS_FLOAT16_NATIVE_TYPE == 0))
#define BOOST_CSTDFLOAT_FLOAT16_NATIVE_TYPE float
#undef BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH
#define BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH 16
#undef BOOST_CSTDFLOAT_HAS_FLOAT16_NATIVE_TYPE
#define BOOST_CSTDFLOAT_HAS_FLOAT16_NATIVE_TYPE 1
#define BOOST_FLOAT16_C(x) (x ## F)
#define BOOST_CSTDFLOAT_FLOAT_16_MIN FLT_MIN
#define BOOST_CSTDFLOAT_FLOAT_16_MAX FLT_MAX
#elif((FLT_MANT_DIG == 24) && (FLT_MAX_EXP == 128) && (BOOST_CSTDFLOAT_HAS_FLOAT32_NATIVE_TYPE == 0))
#define BOOST_CSTDFLOAT_FLOAT32_NATIVE_TYPE float
#undef BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH
#define BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH 32
#undef BOOST_CSTDFLOAT_HAS_FLOAT32_NATIVE_TYPE
#define BOOST_CSTDFLOAT_HAS_FLOAT32_NATIVE_TYPE 1
#define BOOST_FLOAT32_C(x) (x ## F)
#define BOOST_CSTDFLOAT_FLOAT_32_MIN FLT_MIN
#define BOOST_CSTDFLOAT_FLOAT_32_MAX FLT_MAX
#elif((FLT_MANT_DIG == 53) && (FLT_MAX_EXP == 1024) && (BOOST_CSTDFLOAT_HAS_FLOAT64_NATIVE_TYPE == 0))
#define BOOST_CSTDFLOAT_FLOAT64_NATIVE_TYPE float
#undef BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH
#define BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH 64
#undef BOOST_CSTDFLOAT_HAS_FLOAT64_NATIVE_TYPE
#define BOOST_CSTDFLOAT_HAS_FLOAT64_NATIVE_TYPE 1
#define BOOST_FLOAT64_C(x) (x ## F)
#define BOOST_CSTDFLOAT_FLOAT_64_MIN FLT_MIN
#define BOOST_CSTDFLOAT_FLOAT_64_MAX FLT_MAX
#elif((FLT_MANT_DIG == 64) && (FLT_MAX_EXP == 16384) && (BOOST_CSTDFLOAT_HAS_FLOAT80_NATIVE_TYPE == 0))
#define BOOST_CSTDFLOAT_FLOAT80_NATIVE_TYPE float
#undef BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH
#define BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH 80
#undef BOOST_CSTDFLOAT_HAS_FLOAT80_NATIVE_TYPE
#define BOOST_CSTDFLOAT_HAS_FLOAT80_NATIVE_TYPE 1
#define BOOST_FLOAT80_C(x) (x ## F)
#define BOOST_CSTDFLOAT_FLOAT_80_MIN FLT_MIN
#define BOOST_CSTDFLOAT_FLOAT_80_MAX FLT_MAX
#elif((FLT_MANT_DIG == 113) && (FLT_MAX_EXP == 16384) && (BOOST_CSTDFLOAT_HAS_FLOAT128_NATIVE_TYPE == 0))
#define BOOST_CSTDFLOAT_FLOAT128_NATIVE_TYPE float
#undef BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH
#define BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH 128
#undef BOOST_CSTDFLOAT_HAS_FLOAT128_NATIVE_TYPE
#define BOOST_CSTDFLOAT_HAS_FLOAT128_NATIVE_TYPE 1
#define BOOST_FLOAT128_C(x) (x ## F)
#define BOOST_CSTDFLOAT_FLOAT_128_MIN FLT_MIN
#define BOOST_CSTDFLOAT_FLOAT_128_MAX FLT_MAX
#endif
#endif
// Check if built-in double is equivalent to float16_t, float32_t, float64_t, float80_t, or float128_t.
#if(defined(DBL_MANT_DIG) && defined(DBL_MAX_EXP))
#if ((DBL_MANT_DIG == 11) && (DBL_MAX_EXP == 16) && (BOOST_CSTDFLOAT_HAS_FLOAT16_NATIVE_TYPE == 0))
#define BOOST_CSTDFLOAT_FLOAT16_NATIVE_TYPE double
#undef BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH
#define BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH 16
#undef BOOST_CSTDFLOAT_HAS_FLOAT16_NATIVE_TYPE
#define BOOST_CSTDFLOAT_HAS_FLOAT16_NATIVE_TYPE 1
#define BOOST_FLOAT16_C(x) (x)
#define BOOST_CSTDFLOAT_FLOAT_16_MIN DBL_MIN
#define BOOST_CSTDFLOAT_FLOAT_16_MAX DBL_MAX
#elif((DBL_MANT_DIG == 24) && (DBL_MAX_EXP == 128) && (BOOST_CSTDFLOAT_HAS_FLOAT32_NATIVE_TYPE == 0))
#define BOOST_CSTDFLOAT_FLOAT32_NATIVE_TYPE double
#undef BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH
#define BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH 32
#undef BOOST_CSTDFLOAT_HAS_FLOAT32_NATIVE_TYPE
#define BOOST_CSTDFLOAT_HAS_FLOAT32_NATIVE_TYPE 1
#define BOOST_FLOAT32_C(x) (x)
#define BOOST_CSTDFLOAT_FLOAT_32_MIN DBL_MIN
#define BOOST_CSTDFLOAT_FLOAT_32_MAX DBL_MAX
#elif((DBL_MANT_DIG == 53) && (DBL_MAX_EXP == 1024) && (BOOST_CSTDFLOAT_HAS_FLOAT64_NATIVE_TYPE == 0))
#define BOOST_CSTDFLOAT_FLOAT64_NATIVE_TYPE double
#undef BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH
#define BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH 64
#undef BOOST_CSTDFLOAT_HAS_FLOAT64_NATIVE_TYPE
#define BOOST_CSTDFLOAT_HAS_FLOAT64_NATIVE_TYPE 1
#define BOOST_FLOAT64_C(x) (x)
#define BOOST_CSTDFLOAT_FLOAT_64_MIN DBL_MIN
#define BOOST_CSTDFLOAT_FLOAT_64_MAX DBL_MAX
#elif((DBL_MANT_DIG == 64) && (DBL_MAX_EXP == 16384) && (BOOST_CSTDFLOAT_HAS_FLOAT80_NATIVE_TYPE == 0))
#define BOOST_CSTDFLOAT_FLOAT80_NATIVE_TYPE double
#undef BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH
#define BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH 80
#undef BOOST_CSTDFLOAT_HAS_FLOAT80_NATIVE_TYPE
#define BOOST_CSTDFLOAT_HAS_FLOAT80_NATIVE_TYPE 1
#define BOOST_FLOAT80_C(x) (x)
#define BOOST_CSTDFLOAT_FLOAT_80_MIN DBL_MIN
#define BOOST_CSTDFLOAT_FLOAT_80_MAX DBL_MAX
#elif((DBL_MANT_DIG == 113) && (DBL_MAX_EXP == 16384) && (BOOST_CSTDFLOAT_HAS_FLOAT128_NATIVE_TYPE == 0))
#define BOOST_CSTDFLOAT_FLOAT128_NATIVE_TYPE double
#undef BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH
#define BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH 128
#undef BOOST_CSTDFLOAT_HAS_FLOAT128_NATIVE_TYPE
#define BOOST_CSTDFLOAT_HAS_FLOAT128_NATIVE_TYPE 1
#define BOOST_FLOAT128_C(x) (x)
#define BOOST_CSTDFLOAT_FLOAT_128_MIN DBL_MIN
#define BOOST_CSTDFLOAT_FLOAT_128_MAX DBL_MAX
#endif
#endif
// Disable check long double capability even if supported by compiler since some math runtime
// implementations are broken for long double.
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
// Check if built-in long double is equivalent to float16_t, float32_t, float64_t, float80_t, or float128_t.
#if(defined(LDBL_MANT_DIG) && defined(LDBL_MAX_EXP))
#if ((LDBL_MANT_DIG == 11) && (LDBL_MAX_EXP == 16) && (BOOST_CSTDFLOAT_HAS_FLOAT16_NATIVE_TYPE == 0))
#define BOOST_CSTDFLOAT_FLOAT16_NATIVE_TYPE long double
#undef BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH
#define BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH 16
#undef BOOST_CSTDFLOAT_HAS_FLOAT16_NATIVE_TYPE
#define BOOST_CSTDFLOAT_HAS_FLOAT16_NATIVE_TYPE 1
#define BOOST_FLOAT16_C(x) (x ## L)
#define BOOST_CSTDFLOAT_FLOAT_16_MIN LDBL_MIN
#define BOOST_CSTDFLOAT_FLOAT_16_MAX LDBL_MAX
#elif((LDBL_MANT_DIG == 24) && (LDBL_MAX_EXP == 128) && (BOOST_CSTDFLOAT_HAS_FLOAT32_NATIVE_TYPE == 0))
#define BOOST_CSTDFLOAT_FLOAT32_NATIVE_TYPE long double
#undef BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH
#define BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH 32
#undef BOOST_CSTDFLOAT_HAS_FLOAT32_NATIVE_TYPE
#define BOOST_CSTDFLOAT_HAS_FLOAT32_NATIVE_TYPE 1
#define BOOST_FLOAT32_C(x) (x ## L)
#define BOOST_CSTDFLOAT_FLOAT_32_MIN LDBL_MIN
#define BOOST_CSTDFLOAT_FLOAT_32_MAX LDBL_MAX
#elif((LDBL_MANT_DIG == 53) && (LDBL_MAX_EXP == 1024) && (BOOST_CSTDFLOAT_HAS_FLOAT64_NATIVE_TYPE == 0))
#define BOOST_CSTDFLOAT_FLOAT64_NATIVE_TYPE long double
#undef BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH
#define BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH 64
#undef BOOST_CSTDFLOAT_HAS_FLOAT64_NATIVE_TYPE
#define BOOST_CSTDFLOAT_HAS_FLOAT64_NATIVE_TYPE 1
#define BOOST_FLOAT64_C(x) (x ## L)
#define BOOST_CSTDFLOAT_FLOAT_64_MIN LDBL_MIN
#define BOOST_CSTDFLOAT_FLOAT_64_MAX LDBL_MAX
#elif((LDBL_MANT_DIG == 64) && (LDBL_MAX_EXP == 16384) && (BOOST_CSTDFLOAT_HAS_FLOAT80_NATIVE_TYPE == 0))
#define BOOST_CSTDFLOAT_FLOAT80_NATIVE_TYPE long double
#undef BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH
#define BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH 80
#undef BOOST_CSTDFLOAT_HAS_FLOAT80_NATIVE_TYPE
#define BOOST_CSTDFLOAT_HAS_FLOAT80_NATIVE_TYPE 1
#define BOOST_FLOAT80_C(x) (x ## L)
#define BOOST_CSTDFLOAT_FLOAT_80_MIN LDBL_MIN
#define BOOST_CSTDFLOAT_FLOAT_80_MAX LDBL_MAX
#elif((LDBL_MANT_DIG == 113) && (LDBL_MAX_EXP == 16384) && (BOOST_CSTDFLOAT_HAS_FLOAT128_NATIVE_TYPE == 0))
#define BOOST_CSTDFLOAT_FLOAT128_NATIVE_TYPE long double
#undef BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH
#define BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH 128
#undef BOOST_CSTDFLOAT_HAS_FLOAT128_NATIVE_TYPE
#define BOOST_CSTDFLOAT_HAS_FLOAT128_NATIVE_TYPE 1
#define BOOST_FLOAT128_C(x) (x ## L)
#define BOOST_CSTDFLOAT_FLOAT_128_MIN LDBL_MIN
#define BOOST_CSTDFLOAT_FLOAT_128_MAX LDBL_MAX
#endif
#endif
#endif
// Check if quadruple-precision is supported. Here, we are checking
// for the presence of __float128 from GCC's quadmath.h or _Quad
// from ICC's /Qlong-double flag). To query these, we use the
// BOOST_MATH_USE_FLOAT128 pre-processor definition from
// <boost/math/tools/config.hpp>.
#if (BOOST_CSTDFLOAT_HAS_FLOAT128_NATIVE_TYPE == 0) && defined(BOOST_MATH_USE_FLOAT128) && !defined(BOOST_CSTDFLOAT_NO_LIBQUADMATH_SUPPORT)
// Specify the underlying name of the internal 128-bit floating-point type definition.
namespace boost { namespace math { namespace cstdfloat { namespace detail {
#if defined(__GNUC__)
typedef __float128 float_internal128_t;
#elif defined(BOOST_INTEL)
typedef _Quad float_internal128_t;
#else
#error "Sorry, the compiler is neither GCC, nor Intel, I don't know how to configure <boost/cstdfloat.hpp>."
#endif
} } } } // boost::math::cstdfloat::detail
#define BOOST_CSTDFLOAT_FLOAT128_NATIVE_TYPE boost::math::cstdfloat::detail::float_internal128_t
#undef BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH
#define BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH 128
#undef BOOST_CSTDFLOAT_HAS_FLOAT128_NATIVE_TYPE
#define BOOST_CSTDFLOAT_HAS_FLOAT128_NATIVE_TYPE 1
#define BOOST_FLOAT128_C(x) (x ## Q)
#define BOOST_CSTDFLOAT_FLOAT128_MIN 3.36210314311209350626267781732175260e-4932Q
#define BOOST_CSTDFLOAT_FLOAT128_MAX 1.18973149535723176508575932662800702e+4932Q
#define BOOST_CSTDFLOAT_FLOAT128_EPS 1.92592994438723585305597794258492732e-0034Q
#endif // Not BOOST_CSTDFLOAT_NO_LIBQUADMATH_SUPPORT (i.e., the user would like to have libquadmath support)
// This is the end of the preamble, and also the end of the
// sections providing support for the C++ standard library
// for quadruple-precision.
// Now we use the results of the queries that have been obtained
// in the preamble (far above) for the final type definitions in
// the namespace boost.
// Make sure that the compiler has any floating-point type(s) whatsoever.
#if ( (BOOST_CSTDFLOAT_HAS_FLOAT16_NATIVE_TYPE == 0) \
&& (BOOST_CSTDFLOAT_HAS_FLOAT32_NATIVE_TYPE == 0) \
&& (BOOST_CSTDFLOAT_HAS_FLOAT64_NATIVE_TYPE == 0) \
&& (BOOST_CSTDFLOAT_HAS_FLOAT80_NATIVE_TYPE == 0) \
&& (BOOST_CSTDFLOAT_HAS_FLOAT128_NATIVE_TYPE == 0))
#error The compiler does not support any of the floating-point types required for <boost/cstdfloat.hpp>.
#endif
// The following section contains the various min/max macros
// for the *leastN and *fastN types.
#if(BOOST_CSTDFLOAT_HAS_FLOAT16_NATIVE_TYPE == 1)
#define BOOST_FLOAT_FAST16_MIN BOOST_CSTDFLOAT_FLOAT_16_MIN
#define BOOST_FLOAT_LEAST16_MIN BOOST_CSTDFLOAT_FLOAT_16_MIN
#define BOOST_FLOAT_FAST16_MAX BOOST_CSTDFLOAT_FLOAT_16_MAX
#define BOOST_FLOAT_LEAST16_MAX BOOST_CSTDFLOAT_FLOAT_16_MAX
#endif
#if(BOOST_CSTDFLOAT_HAS_FLOAT32_NATIVE_TYPE == 1)
#define BOOST_FLOAT_FAST32_MIN BOOST_CSTDFLOAT_FLOAT_32_MIN
#define BOOST_FLOAT_LEAST32_MIN BOOST_CSTDFLOAT_FLOAT_32_MIN
#define BOOST_FLOAT_FAST32_MAX BOOST_CSTDFLOAT_FLOAT_32_MAX
#define BOOST_FLOAT_LEAST32_MAX BOOST_CSTDFLOAT_FLOAT_32_MAX
#endif
#if(BOOST_CSTDFLOAT_HAS_FLOAT64_NATIVE_TYPE == 1)
#define BOOST_FLOAT_FAST64_MIN BOOST_CSTDFLOAT_FLOAT_64_MIN
#define BOOST_FLOAT_LEAST64_MIN BOOST_CSTDFLOAT_FLOAT_64_MIN
#define BOOST_FLOAT_FAST64_MAX BOOST_CSTDFLOAT_FLOAT_64_MAX
#define BOOST_FLOAT_LEAST64_MAX BOOST_CSTDFLOAT_FLOAT_64_MAX
#endif
#if(BOOST_CSTDFLOAT_HAS_FLOAT80_NATIVE_TYPE == 1)
#define BOOST_FLOAT_FAST80_MIN BOOST_CSTDFLOAT_FLOAT_80_MIN
#define BOOST_FLOAT_LEAST80_MIN BOOST_CSTDFLOAT_FLOAT_80_MIN
#define BOOST_FLOAT_FAST80_MAX BOOST_CSTDFLOAT_FLOAT_80_MAX
#define BOOST_FLOAT_LEAST80_MAX BOOST_CSTDFLOAT_FLOAT_80_MAX
#endif
#if(BOOST_CSTDFLOAT_HAS_FLOAT128_NATIVE_TYPE == 1)
#define BOOST_CSTDFLOAT_HAS_INTERNAL_FLOAT128_T
#define BOOST_FLOAT_FAST128_MIN BOOST_CSTDFLOAT_FLOAT_128_MIN
#define BOOST_FLOAT_LEAST128_MIN BOOST_CSTDFLOAT_FLOAT_128_MIN
#define BOOST_FLOAT_FAST128_MAX BOOST_CSTDFLOAT_FLOAT_128_MAX
#define BOOST_FLOAT_LEAST128_MAX BOOST_CSTDFLOAT_FLOAT_128_MAX
#endif
// The following section contains the various min/max macros
// for the *floatmax types.
#if (BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH == 16)
#define BOOST_FLOATMAX_C(x) BOOST_FLOAT16_C(x)
#define BOOST_FLOATMAX_MIN BOOST_CSTDFLOAT_FLOAT_16_MIN
#define BOOST_FLOATMAX_MAX BOOST_CSTDFLOAT_FLOAT_16_MAX
#elif(BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH == 32)
#define BOOST_FLOATMAX_C(x) BOOST_FLOAT32_C(x)
#define BOOST_FLOATMAX_MIN BOOST_CSTDFLOAT_FLOAT_32_MIN
#define BOOST_FLOATMAX_MAX BOOST_CSTDFLOAT_FLOAT_32_MAX
#elif(BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH == 64)
#define BOOST_FLOATMAX_C(x) BOOST_FLOAT64_C(x)
#define BOOST_FLOATMAX_MIN BOOST_CSTDFLOAT_FLOAT_64_MIN
#define BOOST_FLOATMAX_MAX BOOST_CSTDFLOAT_FLOAT_64_MAX
#elif(BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH == 80)
#define BOOST_FLOATMAX_C(x) BOOST_FLOAT80_C(x)
#define BOOST_FLOATMAX_MIN BOOST_CSTDFLOAT_FLOAT_80_MIN
#define BOOST_FLOATMAX_MAX BOOST_CSTDFLOAT_FLOAT_80_MAX
#elif(BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH == 128)
#define BOOST_FLOATMAX_C(x) BOOST_FLOAT128_C(x)
#define BOOST_FLOATMAX_MIN BOOST_CSTDFLOAT_FLOAT_128_MIN
#define BOOST_FLOATMAX_MAX BOOST_CSTDFLOAT_FLOAT_128_MAX
#else
#error The maximum available floating-point width for <boost/cstdfloat.hpp> is undefined.
#endif
// And finally..., we define the floating-point typedefs having
// specified widths. The types are defined in the namespace boost.
// For simplicity, the least and fast types are type defined identically
// as the corresponding fixed-width type. This behavior may, however,
// be modified when being optimized for a given compiler implementation.
// In addition, a clear assessment of IEEE-754 comformance is carried out
// using compile-time assertion.
namespace boost
{
#if(BOOST_CSTDFLOAT_HAS_FLOAT16_NATIVE_TYPE == 1)
typedef BOOST_CSTDFLOAT_FLOAT16_NATIVE_TYPE float16_t;
typedef boost::float16_t float_fast16_t;
typedef boost::float16_t float_least16_t;
BOOST_STATIC_ASSERT_MSG(std::numeric_limits<boost::float16_t>::is_iec559 == true, "boost::float16_t has been detected in <boost/cstdfloat>, but verification with std::numeric_limits fails");
BOOST_STATIC_ASSERT_MSG(std::numeric_limits<boost::float16_t>::radix == 2, "boost::float16_t has been detected in <boost/cstdfloat>, but verification with std::numeric_limits fails");
BOOST_STATIC_ASSERT_MSG(std::numeric_limits<boost::float16_t>::digits == 11, "boost::float16_t has been detected in <boost/cstdfloat>, but verification with std::numeric_limits fails");
BOOST_STATIC_ASSERT_MSG(std::numeric_limits<boost::float16_t>::max_exponent == 16, "boost::float16_t has been detected in <boost/cstdfloat>, but verification with std::numeric_limits fails");
#undef BOOST_CSTDFLOAT_FLOAT_16_MIN
#undef BOOST_CSTDFLOAT_FLOAT_16_MAX
#endif
#if(BOOST_CSTDFLOAT_HAS_FLOAT32_NATIVE_TYPE == 1)
typedef BOOST_CSTDFLOAT_FLOAT32_NATIVE_TYPE float32_t;
typedef boost::float32_t float_fast32_t;
typedef boost::float32_t float_least32_t;
BOOST_STATIC_ASSERT_MSG(std::numeric_limits<boost::float32_t>::is_iec559 == true, "boost::float32_t has been detected in <boost/cstdfloat>, but verification with std::numeric_limits fails");
BOOST_STATIC_ASSERT_MSG(std::numeric_limits<boost::float32_t>::radix == 2, "boost::float32_t has been detected in <boost/cstdfloat>, but verification with std::numeric_limits fails");
BOOST_STATIC_ASSERT_MSG(std::numeric_limits<boost::float32_t>::digits == 24, "boost::float32_t has been detected in <boost/cstdfloat>, but verification with std::numeric_limits fails");
BOOST_STATIC_ASSERT_MSG(std::numeric_limits<boost::float32_t>::max_exponent == 128, "boost::float32_t has been detected in <boost/cstdfloat>, but verification with std::numeric_limits fails");
#undef BOOST_CSTDFLOAT_FLOAT_32_MIN
#undef BOOST_CSTDFLOAT_FLOAT_32_MAX
#endif
#if (defined(__SGI_STL_PORT) || defined(_STLPORT_VERSION)) && defined(__SUNPRO_CC)
#undef BOOST_CSTDFLOAT_HAS_FLOAT80_NATIVE_TYPE
#define BOOST_CSTDFLOAT_HAS_FLOAT80_NATIVE_TYPE 0
#undef BOOST_CSTDFLOAT_HAS_FLOAT128_NATIVE_TYPE
#define BOOST_CSTDFLOAT_HAS_FLOAT128_NATIVE_TYPE 0
#undef BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH
#define BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH 64
#endif
#if(BOOST_CSTDFLOAT_HAS_FLOAT64_NATIVE_TYPE == 1)
typedef BOOST_CSTDFLOAT_FLOAT64_NATIVE_TYPE float64_t;
typedef boost::float64_t float_fast64_t;
typedef boost::float64_t float_least64_t;
BOOST_STATIC_ASSERT_MSG(std::numeric_limits<boost::float64_t>::is_iec559 == true, "boost::float64_t has been detected in <boost/cstdfloat>, but verification with std::numeric_limits fails");
BOOST_STATIC_ASSERT_MSG(std::numeric_limits<boost::float64_t>::radix == 2, "boost::float64_t has been detected in <boost/cstdfloat>, but verification with std::numeric_limits fails");
BOOST_STATIC_ASSERT_MSG(std::numeric_limits<boost::float64_t>::digits == 53, "boost::float64_t has been detected in <boost/cstdfloat>, but verification with std::numeric_limits fails");
BOOST_STATIC_ASSERT_MSG(std::numeric_limits<boost::float64_t>::max_exponent == 1024, "boost::float64_t has been detected in <boost/cstdfloat>, but verification with std::numeric_limits fails");
#undef BOOST_CSTDFLOAT_FLOAT_64_MIN
#undef BOOST_CSTDFLOAT_FLOAT_64_MAX
#endif
#if(BOOST_CSTDFLOAT_HAS_FLOAT80_NATIVE_TYPE == 1)
typedef BOOST_CSTDFLOAT_FLOAT80_NATIVE_TYPE float80_t;
typedef boost::float80_t float_fast80_t;
typedef boost::float80_t float_least80_t;
BOOST_STATIC_ASSERT_MSG(std::numeric_limits<boost::float80_t>::is_iec559 == true, "boost::float80_t has been detected in <boost/cstdfloat>, but verification with std::numeric_limits fails");
BOOST_STATIC_ASSERT_MSG(std::numeric_limits<boost::float80_t>::radix == 2, "boost::float80_t has been detected in <boost/cstdfloat>, but verification with std::numeric_limits fails");
BOOST_STATIC_ASSERT_MSG(std::numeric_limits<boost::float80_t>::digits == 64, "boost::float80_t has been detected in <boost/cstdfloat>, but verification with std::numeric_limits fails");
BOOST_STATIC_ASSERT_MSG(std::numeric_limits<boost::float80_t>::max_exponent == 16384, "boost::float80_t has been detected in <boost/cstdfloat>, but verification with std::numeric_limits fails");
#undef BOOST_CSTDFLOAT_FLOAT_80_MIN
#undef BOOST_CSTDFLOAT_FLOAT_80_MAX
#endif
#if(BOOST_CSTDFLOAT_HAS_FLOAT128_NATIVE_TYPE == 1)
typedef BOOST_CSTDFLOAT_FLOAT128_NATIVE_TYPE float128_t;
typedef boost::float128_t float_fast128_t;
typedef boost::float128_t float_least128_t;
#if defined(BOOST_CSTDFLOAT_HAS_INTERNAL_FLOAT128_T) && defined(BOOST_MATH_USE_FLOAT128) && !defined(BOOST_CSTDFLOAT_NO_LIBQUADMATH_SUPPORT)
// This configuration does not *yet* support std::numeric_limits<boost::float128_t>.
// Support for std::numeric_limits<boost::float128_t> is added in the detail
// file <boost/math/cstdfloat/cstdfloat_limits.hpp>.
#else
BOOST_STATIC_ASSERT_MSG(std::numeric_limits<boost::float128_t>::is_iec559 == true, "boost::float128_t has been detected in <boost/cstdfloat>, but verification with std::numeric_limits fails");
BOOST_STATIC_ASSERT_MSG(std::numeric_limits<boost::float128_t>::radix == 2, "boost::float128_t has been detected in <boost/cstdfloat>, but verification with std::numeric_limits fails");
BOOST_STATIC_ASSERT_MSG(std::numeric_limits<boost::float128_t>::digits == 113, "boost::float128_t has been detected in <boost/cstdfloat>, but verification with std::numeric_limits fails");
BOOST_STATIC_ASSERT_MSG(std::numeric_limits<boost::float128_t>::max_exponent == 16384, "boost::float128_t has been detected in <boost/cstdfloat>, but verification with std::numeric_limits fails");
#endif
#undef BOOST_CSTDFLOAT_FLOAT_128_MIN
#undef BOOST_CSTDFLOAT_FLOAT_128_MAX
#endif
#if (BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH == 16)
typedef boost::float16_t floatmax_t;
#elif(BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH == 32)
typedef boost::float32_t floatmax_t;
#elif(BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH == 64)
typedef boost::float64_t floatmax_t;
#elif(BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH == 80)
typedef boost::float80_t floatmax_t;
#elif(BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH == 128)
typedef boost::float128_t floatmax_t;
#else
#error The maximum available floating-point width for <boost/cstdfloat.hpp> is undefined.
#endif
#undef BOOST_CSTDFLOAT_HAS_FLOAT16_NATIVE_TYPE
#undef BOOST_CSTDFLOAT_HAS_FLOAT32_NATIVE_TYPE
#undef BOOST_CSTDFLOAT_HAS_FLOAT64_NATIVE_TYPE
#undef BOOST_CSTDFLOAT_HAS_FLOAT80_NATIVE_TYPE
#undef BOOST_CSTDFLOAT_HAS_FLOAT128_NATIVE_TYPE
#undef BOOST_CSTDFLOAT_MAXIMUM_AVAILABLE_WIDTH
}
// namespace boost
#endif // _BOOST_CSTDFLOAT_BASE_TYPES_2014_01_09_HPP_