Updated boost to v1.55.0

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

diff --git a/boost/math/special_functions/sinc.hpp b/boost/math/special_functions/sinc.hpp
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+++ b/boost/math/special_functions/sinc.hpp
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+//  boost sinc.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_SINC_HPP
+#define BOOST_SINC_HPP
+
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/math/tools/config.hpp>
+#include <boost/math/tools/precision.hpp>
+#include <boost/math/policies/policy.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 "Sinus Cardinal" functions.
+
+namespace boost
+{
+    namespace math
+    {
+       namespace detail
+       {
+        // This is the "Sinus Cardinal" of index Pi.
+
+        template<typename T>
+        inline T    sinc_pi_imp(const T x)
+        {
+            BOOST_MATH_STD_USING
+
+            T const    taylor_0_bound = tools::epsilon<T>();
+            T const    taylor_2_bound = tools::root_epsilon<T>();
+            T const    taylor_n_bound = tools::forth_root_epsilon<T>();
+
+            if    (abs(x) >= taylor_n_bound)
+            {
+                return(sin(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 sinc_pi(T x)
+       {
+          typedef typename tools::promote_args<T>::type result_type;
+          return detail::sinc_pi_imp(static_cast<result_type>(x));
+       }
+
+       template <class T, class Policy>
+       inline typename tools::promote_args<T>::type sinc_pi(T x, const Policy&)
+       {
+          typedef typename tools::promote_args<T>::type result_type;
+          return detail::sinc_pi_imp(static_cast<result_type>(x));
+       }
+
+#ifndef    BOOST_NO_TEMPLATE_TEMPLATES
+        template<typename T, template<typename> class U>
+        inline U<T>    sinc_pi(const U<T> x)
+        {
+            BOOST_MATH_STD_USING
+            using    ::std::numeric_limits;
+
+            T const    taylor_0_bound = tools::epsilon<T>();
+            T const    taylor_2_bound = tools::root_epsilon<T>();
+            T const    taylor_n_bound = tools::forth_root_epsilon<T>();
+
+            if    (abs(x) >= taylor_n_bound)
+            {
+                return(sin(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);
+            }
+        }
+
+        template<typename T, template<typename> class U, class Policy>
+        inline U<T>    sinc_pi(const U<T> x, const Policy&)
+        {
+           return sinc_pi(x);
+        }
+#endif    /* BOOST_NO_TEMPLATE_TEMPLATES */
+    }
+}
+
+#endif /* BOOST_SINC_HPP */
+