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Diffstat (limited to 'boost/math/cstdfloat/cstdfloat_cmath.hpp')
| -rw-r--r-- | boost/math/cstdfloat/cstdfloat_cmath.hpp | 600 |
1 files changed, 600 insertions, 0 deletions
diff --git a/boost/math/cstdfloat/cstdfloat_cmath.hpp b/boost/math/cstdfloat/cstdfloat_cmath.hpp new file mode 100644 index 0000000000..3043d90567 --- /dev/null +++ b/boost/math/cstdfloat/cstdfloat_cmath.hpp @@ -0,0 +1,600 @@ +/////////////////////////////////////////////////////////////////////////////// +// 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_ |