external libraries: import boost.math.special_functions

Signed-off-by: Tim Blechmann <tim@klingt.org>

external_libraries/boost/boost/math/special_functions.hpp

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+//  Copyright John Maddock 2006, 2007.
+//  Copyright Paul A. Bristow 2006, 2007.
+
+//  Use, modification and distribution are subject to 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)
+
+// This file includes *all* the special functions.
+// this may be useful if many are used
+// - to avoid including each function individually.
+
+#ifndef BOOST_MATH_SPECIAL_FUNCTIONS_HPP
+#define BOOST_MATH_SPECIAL_FUNCTIONS_HPP
+
+#include <boost/math/special_functions/acosh.hpp>
+#include <boost/math/special_functions/asinh.hpp>
+#include <boost/math/special_functions/atanh.hpp>
+#include <boost/math/special_functions/bessel.hpp>
+#include <boost/math/special_functions/beta.hpp>
+#include <boost/math/special_functions/binomial.hpp>
+#include <boost/math/special_functions/cbrt.hpp>
+#include <boost/math/special_functions/cos_pi.hpp>
+#include <boost/math/special_functions/digamma.hpp>
+#include <boost/math/special_functions/ellint_1.hpp>
+#include <boost/math/special_functions/ellint_2.hpp>
+#include <boost/math/special_functions/ellint_3.hpp>
+#include <boost/math/special_functions/ellint_rc.hpp>
+#include <boost/math/special_functions/ellint_rd.hpp>
+#include <boost/math/special_functions/ellint_rf.hpp>
+#include <boost/math/special_functions/ellint_rj.hpp>
+#include <boost/math/special_functions/erf.hpp>
+#include <boost/math/special_functions/expint.hpp>
+#include <boost/math/special_functions/expm1.hpp>
+#include <boost/math/special_functions/factorials.hpp>
+#include <boost/math/special_functions/fpclassify.hpp>
+#include <boost/math/special_functions/gamma.hpp>
+#include <boost/math/special_functions/hermite.hpp>
+#include <boost/math/special_functions/hypot.hpp>
+#include <boost/math/special_functions/laguerre.hpp>
+#include <boost/math/special_functions/lanczos.hpp>
+#include <boost/math/special_functions/legendre.hpp>
+#include <boost/math/special_functions/log1p.hpp>
+#include <boost/math/special_functions/math_fwd.hpp>
+#include <boost/math/special_functions/next.hpp>
+#include <boost/math/special_functions/powm1.hpp>
+#include <boost/math/special_functions/sign.hpp>
+#include <boost/math/special_functions/sin_pi.hpp>
+#include <boost/math/special_functions/sinc.hpp>
+#include <boost/math/special_functions/sinhc.hpp>
+#include <boost/math/special_functions/spherical_harmonic.hpp>
+#include <boost/math/special_functions/sqrt1pm1.hpp>
+#include <boost/math/special_functions/zeta.hpp>
+#include <boost/math/special_functions/modf.hpp>
+#include <boost/math/special_functions/round.hpp>
+#include <boost/math/special_functions/trunc.hpp>
+#include <boost/math/special_functions/pow.hpp>
+#include <boost/math/special_functions/next.hpp>
+
+#endif // BOOST_MATH_SPECIAL_FUNCTIONS_HPP

external_libraries/boost/boost/math/special_functions/acosh.hpp

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+//    boost asinh.hpp header file
+
+//  (C) Copyright Eric Ford 2001 & Hubert Holin.
+//  (C) Copyright John Maddock 2008.
+//  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)
+
+// See http://www.boost.org for updates, documentation, and revision history.
+
+#ifndef BOOST_ACOSH_HPP
+#define BOOST_ACOSH_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/config/no_tr1/cmath.hpp>
+#include <boost/config.hpp>
+#include <boost/math/tools/precision.hpp>
+#include <boost/math/policies/error_handling.hpp>
+#include <boost/math/special_functions/math_fwd.hpp>
+#include <boost/math/special_functions/log1p.hpp>
+
+// This is the inverse of the hyperbolic cosine function.
+
+namespace boost
+{
+    namespace math
+    {
+       namespace detail
+       {
+#if defined(__GNUC__) && (__GNUC__ < 3)
+        // gcc 2.x ignores function scope using declarations,
+        // put them in the scope of the enclosing namespace instead:
+
+        using    ::std::abs;
+        using    ::std::sqrt;
+        using    ::std::log;
+
+        using    ::std::numeric_limits;
+#endif
+
+        template<typename T, typename Policy>
+        inline T    acosh_imp(const T x, const Policy& pol)
+        {
+            BOOST_MATH_STD_USING
+
+            if(x < 1)
+            {
+               return policies::raise_domain_error<T>(
+                  "boost::math::acosh<%1%>(%1%)",
+                  "acosh requires x >= 1, but got x = %1%.", x, pol);
+            }
+            else if    ((x - 1) >= tools::root_epsilon<T>())
+            {
+                if    (x > 1 / tools::root_epsilon<T>())
+                {
+                    // http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/06/01/0001/
+                    // approximation by laurent series in 1/x at 0+ order from -1 to 0
+                    return( log( x * 2) );
+                }
+                else if(x < 1.5f)
+                {
+                   // This is just a rearrangement of the standard form below
+                   // devised to minimse loss of precision when x ~ 1:
+                   T y = x - 1;
+                   return boost::math::log1p(y + sqrt(y * y + 2 * y), pol);
+                }
+                else
+                {
+                    // http://functions.wolfram.com/ElementaryFunctions/ArcCosh/02/
+                    return( log( x + sqrt(x * x - 1) ) );
+                }
+            }
+            else
+            {
+                // see http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/04/01/0001/
+                T y = x - 1;
+
+                // approximation by taylor series in y at 0 up to order 2
+                T result = sqrt(2 * y) * (1 - y /12 + 3 * y * y / 160);
+                return result;
+            }
+        }
+       }
+
+        template<typename T, typename Policy>
+        inline typename tools::promote_args<T>::type acosh(T x, const Policy&)
+        {
+            typedef typename tools::promote_args<T>::type result_type;
+            typedef typename policies::evaluation<result_type, Policy>::type value_type;
+            typedef typename policies::normalise<
+               Policy, 
+               policies::promote_float<false>, 
+               policies::promote_double<false>, 
+               policies::discrete_quantile<>,
+               policies::assert_undefined<> >::type forwarding_policy;
+           return policies::checked_narrowing_cast<result_type, forwarding_policy>(
+              detail::acosh_imp(static_cast<value_type>(x), forwarding_policy()),
+              "boost::math::acosh<%1%>(%1%)");
+        }
+        template<typename T>
+        inline typename tools::promote_args<T>::type acosh(T x)
+        {
+           return boost::math::acosh(x, policies::policy<>());
+        }
+
+    }
+}
+
+#endif /* BOOST_ACOSH_HPP */
+
+

external_libraries/boost/boost/math/special_functions/asinh.hpp

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+//    boost asinh.hpp header file
+
+//  (C) Copyright Eric Ford & Hubert Holin 2001.
+//  (C) Copyright John Maddock 2008.
+//  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)
+
+// See http://www.boost.org for updates, documentation, and revision history.
+
+#ifndef BOOST_ASINH_HPP
+#define BOOST_ASINH_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+
+#include <boost/config/no_tr1/cmath.hpp>
+#include <boost/config.hpp>
+#include <boost/math/tools/precision.hpp>
+#include <boost/math/special_functions/math_fwd.hpp>
+#include <boost/math/special_functions/sqrt1pm1.hpp>
+#include <boost/math/special_functions/log1p.hpp>
+
+// This is the inverse of the hyperbolic sine function.
+
+namespace boost
+{
+    namespace math
+    {
+       namespace detail{
+#if defined(__GNUC__) && (__GNUC__ < 3)
+        // gcc 2.x ignores function scope using declarations,
+        // put them in the scope of the enclosing namespace instead:
+
+        using    ::std::abs;
+        using    ::std::sqrt;
+        using    ::std::log;
+
+        using    ::std::numeric_limits;
+#endif
+
+        template<typename T, class Policy>
+        inline T    asinh_imp(const T x, const Policy& pol)
+        {
+            BOOST_MATH_STD_USING
+
+            if        (x >= tools::forth_root_epsilon<T>())
+            {
+               if        (x > 1 / tools::root_epsilon<T>())
+                {
+                    // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/06/01/0001/
+                    // approximation by laurent series in 1/x at 0+ order from -1 to 1
+                    return log(x * 2) + 1/ (4 * x * x);
+                }
+                else if(x < 0.5f)
+                {
+                   // As below, but rearranged to preserve digits:
+                   return boost::math::log1p(x + boost::math::sqrt1pm1(x * x, pol), pol);
+                }
+                else
+                {
+                    // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/02/
+                    return( log( x + sqrt(x*x+1) ) );
+                }
+            }
+            else if    (x <= -tools::forth_root_epsilon<T>())
+            {
+                return(-asinh(-x));
+            }
+            else
+            {
+                // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/03/01/0001/
+                // approximation by taylor series in x at 0 up to order 2
+                T    result = x;
+
+                if    (abs(x) >= tools::root_epsilon<T>())
+                {
+                    T    x3 = x*x*x;
+
+                    // approximation by taylor series in x at 0 up to order 4
+                    result -= x3/static_cast<T>(6);
+                }
+
+                return(result);
+            }
+        }
+       }
+
+        template<typename T>
+        inline typename tools::promote_args<T>::type asinh(T x)
+        {
+           return boost::math::asinh(x, policies::policy<>());
+        }
+        template<typename T, typename Policy>
+        inline typename tools::promote_args<T>::type asinh(T x, const Policy&)
+        {
+            typedef typename tools::promote_args<T>::type result_type;
+            typedef typename policies::evaluation<result_type, Policy>::type value_type;
+            typedef typename policies::normalise<
+               Policy, 
+               policies::promote_float<false>, 
+               policies::promote_double<false>, 
+               policies::discrete_quantile<>,
+               policies::assert_undefined<> >::type forwarding_policy;
+           return policies::checked_narrowing_cast<result_type, forwarding_policy>(
+              detail::asinh_imp(static_cast<value_type>(x), forwarding_policy()),
+              "boost::math::asinh<%1%>(%1%)");
+        }
+
+    }
+}
+
+#endif /* BOOST_ASINH_HPP */
+