epoc32/include/stdapis/boost/math/complex/asinh.hpp
branchSymbian2
changeset 3 e1b950c65cb4
parent 2 2fe1408b6811
child 4 837f303aceeb
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/epoc32/include/stdapis/boost/math/complex/asinh.hpp	Wed Mar 31 12:27:01 2010 +0100
@@ -0,0 +1,101 @@
+//    boost asinh.hpp header file
+
+//  (C) Copyright Eric Ford & 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_ASINH_HPP
+#define BOOST_ASINH_HPP
+
+
+#include <cmath>
+#include <limits>
+#include <string>
+#include <stdexcept>
+
+
+#include <boost/config.hpp>
+
+
+// This is the inverse of the hyperbolic sine function.
+
+namespace boost
+{
+    namespace math
+    {
+#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>
+        inline T    asinh(const T x)
+        {
+            using    ::std::abs;
+            using    ::std::sqrt;
+            using    ::std::log;
+            
+            using    ::std::numeric_limits;
+            
+            
+            T const            one = static_cast<T>(1);
+            T const            two = static_cast<T>(2);
+            
+            static T const    taylor_2_bound = sqrt(numeric_limits<T>::epsilon());
+            static T const    taylor_n_bound = sqrt(taylor_2_bound);
+            static T const    upper_taylor_2_bound = one/taylor_2_bound;
+            static T const    upper_taylor_n_bound = one/taylor_n_bound;
+            
+            if        (x >= +taylor_n_bound)
+            {
+                if        (x > upper_taylor_n_bound)
+                {
+                    if        (x > upper_taylor_2_bound)
+                    {
+                        // approximation by laurent series in 1/x at 0+ order from -1 to 0
+                        return( log( x * two) );
+                    }
+                    else
+                    {
+                        // approximation by laurent series in 1/x at 0+ order from -1 to 1
+                        return( log( x*two + (one/(x*two)) ) );
+                    }
+                }
+                else
+                {
+                    return( log( x + sqrt(x*x+one) ) );
+                }
+            }
+            else if    (x <= -taylor_n_bound)
+            {
+                return(-asinh(-x));
+            }
+            else
+            {
+                // approximation by taylor series in x at 0 up to order 2
+                T    result = x;
+                
+                if    (abs(x) >= taylor_2_bound)
+                {
+                    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);
+            }
+        }
+    }
+}
+
+#endif /* BOOST_ASINH_HPP */