Updated boost to v1.55.0

[rsem.git] / boost / math / special_functions / sinhc.hpp

diff --git a/boost/math/special_functions/sinhc.hpp b/boost/math/special_functions/sinhc.hpp
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+//  boost sinhc.hpp header file
+
+//  (C) Copyright Hubert Holin 2001.
+//  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_SINHC_HPP
+#define BOOST_SINHC_HPP
+
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/math/tools/config.hpp>
+#include <boost/math/tools/precision.hpp>
+#include <boost/math/special_functions/math_fwd.hpp>
+#include <boost/config/no_tr1/cmath.hpp>
+#include <boost/limits.hpp>
+#include <string>
+#include <stdexcept>
+
+#include <boost/config.hpp>
+
+
+// These are the the "Hyperbolic Sinus Cardinal" functions.
+
+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::sinh;
+
+        using    ::std::numeric_limits;
+#endif    /* defined(__GNUC__) && (__GNUC__ < 3) */
+
+        // This is the "Hyperbolic Sinus Cardinal" of index Pi.
+
+        template<typename T>
+        inline T    sinhc_pi_imp(const T x)
+        {
+#if defined(BOOST_NO_STDC_NAMESPACE) && !defined(__SUNPRO_CC)
+            using    ::abs;
+            using    ::sinh;
+            using    ::sqrt;
+#else    /* BOOST_NO_STDC_NAMESPACE */
+            using    ::std::abs;
+            using    ::std::sinh;
+            using    ::std::sqrt;
+#endif    /* BOOST_NO_STDC_NAMESPACE */
+
+            static T const    taylor_0_bound = tools::epsilon<T>();
+            static T const    taylor_2_bound = sqrt(taylor_0_bound);
+            static T const    taylor_n_bound = sqrt(taylor_2_bound);
+
+            if    (abs(x) >= taylor_n_bound)
+            {
+                return(sinh(x)/x);
+            }
+            else
+            {
+                // approximation by taylor series in x at 0 up to order 0
+                T    result = static_cast<T>(1);
+
+                if    (abs(x) >= taylor_0_bound)
+                {
+                    T    x2 = x*x;
+
+                    // approximation by taylor series in x at 0 up to order 2
+                    result += x2/static_cast<T>(6);
+
+                    if    (abs(x) >= taylor_2_bound)
+                    {
+                        // approximation by taylor series in x at 0 up to order 4
+                        result += (x2*x2)/static_cast<T>(120);
+                    }
+                }
+
+                return(result);
+            }
+        }
+
+       } // namespace detail
+
+       template <class T>
+       inline typename tools::promote_args<T>::type sinhc_pi(T x)
+       {
+          typedef typename tools::promote_args<T>::type result_type;
+          return detail::sinhc_pi_imp(static_cast<result_type>(x));
+       }
+
+       template <class T, class Policy>
+       inline typename tools::promote_args<T>::type sinhc_pi(T x, const Policy&)
+       {
+          return boost::math::sinhc_pi(x);
+       }
+
+#ifdef    BOOST_NO_TEMPLATE_TEMPLATES
+#else    /* BOOST_NO_TEMPLATE_TEMPLATES */
+        template<typename T, template<typename> class U>
+        inline U<T>    sinhc_pi(const U<T> x)
+        {
+#if defined(BOOST_FUNCTION_SCOPE_USING_DECLARATION_BREAKS_ADL) || defined(__GNUC__)
+            using namespace std;
+#elif    defined(BOOST_NO_STDC_NAMESPACE) && !defined(__SUNPRO_CC)
+            using    ::abs;
+            using    ::sinh;
+            using    ::sqrt;
+#else    /* BOOST_NO_STDC_NAMESPACE */
+            using    ::std::abs;
+            using    ::std::sinh;
+            using    ::std::sqrt;
+#endif    /* BOOST_NO_STDC_NAMESPACE */
+
+            using    ::std::numeric_limits;
+
+            static T const    taylor_0_bound = tools::epsilon<T>();
+            static T const    taylor_2_bound = sqrt(taylor_0_bound);
+            static T const    taylor_n_bound = sqrt(taylor_2_bound);
+
+            if    (abs(x) >= taylor_n_bound)
+            {
+                return(sinh(x)/x);
+            }
+            else
+            {
+                // approximation by taylor series in x at 0 up to order 0
+#ifdef __MWERKS__
+                U<T>    result = static_cast<U<T> >(1);
+#else
+                U<T>    result = U<T>(1);
+#endif
+
+                if    (abs(x) >= taylor_0_bound)
+                {
+                    U<T>    x2 = x*x;
+
+                    // approximation by taylor series in x at 0 up to order 2
+                    result += x2/static_cast<T>(6);
+
+                    if    (abs(x) >= taylor_2_bound)
+                    {
+                        // approximation by taylor series in x at 0 up to order 4
+                        result += (x2*x2)/static_cast<T>(120);
+                    }
+                }
+
+                return(result);
+            }
+        }
+#endif    /* BOOST_NO_TEMPLATE_TEMPLATES */
+    }
+}
+
+#endif /* BOOST_SINHC_HPP */
+