williamr@2: //    boost asinh.hpp header file
williamr@2: 
williamr@2: //  (C) Copyright Eric Ford & Hubert Holin 2001.
williamr@2: //  Distributed under the Boost Software License, Version 1.0. (See
williamr@2: //  accompanying file LICENSE_1_0.txt or copy at
williamr@2: //  http://www.boost.org/LICENSE_1_0.txt)
williamr@2: 
williamr@2: // See http://www.boost.org for updates, documentation, and revision history.
williamr@2: 
williamr@2: #ifndef BOOST_ASINH_HPP
williamr@2: #define BOOST_ASINH_HPP
williamr@2: 
williamr@2: 
williamr@2: #include <cmath>
williamr@2: #include <limits>
williamr@2: #include <string>
williamr@2: #include <stdexcept>
williamr@2: 
williamr@2: 
williamr@2: #include <boost/config.hpp>
williamr@2: 
williamr@2: 
williamr@2: // This is the inverse of the hyperbolic sine function.
williamr@2: 
williamr@2: namespace boost
williamr@2: {
williamr@2:     namespace math
williamr@2:     {
williamr@2: #if defined(__GNUC__) && (__GNUC__ < 3)
williamr@2:         // gcc 2.x ignores function scope using declarations,
williamr@2:         // put them in the scope of the enclosing namespace instead:
williamr@2:         
williamr@2:         using    ::std::abs;
williamr@2:         using    ::std::sqrt;
williamr@2:         using    ::std::log;
williamr@2:         
williamr@2:         using    ::std::numeric_limits;
williamr@2: #endif
williamr@2:         
williamr@2:         template<typename T>
williamr@2:         inline T    asinh(const T x)
williamr@2:         {
williamr@2:             using    ::std::abs;
williamr@2:             using    ::std::sqrt;
williamr@2:             using    ::std::log;
williamr@2:             
williamr@2:             using    ::std::numeric_limits;
williamr@2:             
williamr@2:             
williamr@2:             T const            one = static_cast<T>(1);
williamr@2:             T const            two = static_cast<T>(2);
williamr@2:             
williamr@2:             static T const    taylor_2_bound = sqrt(numeric_limits<T>::epsilon());
williamr@2:             static T const    taylor_n_bound = sqrt(taylor_2_bound);
williamr@2:             static T const    upper_taylor_2_bound = one/taylor_2_bound;
williamr@2:             static T const    upper_taylor_n_bound = one/taylor_n_bound;
williamr@2:             
williamr@2:             if        (x >= +taylor_n_bound)
williamr@2:             {
williamr@2:                 if        (x > upper_taylor_n_bound)
williamr@2:                 {
williamr@2:                     if        (x > upper_taylor_2_bound)
williamr@2:                     {
williamr@2:                         // approximation by laurent series in 1/x at 0+ order from -1 to 0
williamr@2:                         return( log( x * two) );
williamr@2:                     }
williamr@2:                     else
williamr@2:                     {
williamr@2:                         // approximation by laurent series in 1/x at 0+ order from -1 to 1
williamr@2:                         return( log( x*two + (one/(x*two)) ) );
williamr@2:                     }
williamr@2:                 }
williamr@2:                 else
williamr@2:                 {
williamr@2:                     return( log( x + sqrt(x*x+one) ) );
williamr@2:                 }
williamr@2:             }
williamr@2:             else if    (x <= -taylor_n_bound)
williamr@2:             {
williamr@2:                 return(-asinh(-x));
williamr@2:             }
williamr@2:             else
williamr@2:             {
williamr@2:                 // approximation by taylor series in x at 0 up to order 2
williamr@2:                 T    result = x;
williamr@2:                 
williamr@2:                 if    (abs(x) >= taylor_2_bound)
williamr@2:                 {
williamr@2:                     T    x3 = x*x*x;
williamr@2:                     
williamr@2:                     // approximation by taylor series in x at 0 up to order 4
williamr@2:                     result -= x3/static_cast<T>(6);
williamr@2:                 }
williamr@2:                 
williamr@2:                 return(result);
williamr@2:             }
williamr@2:         }
williamr@2:     }
williamr@2: }
williamr@2: 
williamr@2: #endif /* BOOST_ASINH_HPP */