williamr@2: //    boost asinh.hpp header file
williamr@2: 
williamr@2: //  (C) Copyright Eric Ford 2001 & Hubert Holin.
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_ACOSH_HPP
williamr@2: #define BOOST_ACOSH_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 cosine 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: #if defined(BOOST_NO_TEMPLATE_PARTIAL_SPECIALIZATION)
williamr@2:         // This is the main fare
williamr@2:         
williamr@2:         template<typename T>
williamr@2:         inline T    acosh(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:             
williamr@2:             if        (x < one)
williamr@2:             {
williamr@2:                 if    (numeric_limits<T>::has_quiet_NaN)
williamr@2:                 {
williamr@2:                     return(numeric_limits<T>::quiet_NaN());
williamr@2:                 }
williamr@2:                 else
williamr@2:                 {
williamr@2:                     ::std::string        error_reporting("Argument to atanh is strictly greater than +1 or strictly smaller than -1!");
williamr@2:                     ::std::domain_error  bad_argument(error_reporting);
williamr@2:                     
williamr@2:                     throw(bad_argument);
williamr@2:                 }
williamr@2:             }
williamr@2:             else if    (x >= 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:                     return( log( x + sqrt(x*x-one) ) );
williamr@2:                 }
williamr@2:             }
williamr@2:             else
williamr@2:             {
williamr@2:                 T    y = sqrt(x-one);
williamr@2:                 
williamr@2:                 // approximation by taylor series in y at 0 up to order 2
williamr@2:                 T    result = y;
williamr@2:                 
williamr@2:                 if    (y >= taylor_2_bound)
williamr@2:                 {
williamr@2:                     T    y3 = y*y*y;
williamr@2:                     
williamr@2:                     // approximation by taylor series in y at 0 up to order 4
williamr@2:                     result -= y3/static_cast<T>(12);
williamr@2:                 }
williamr@2:                 
williamr@2:                 return(sqrt(static_cast<T>(2))*result);
williamr@2:             }
williamr@2:         }
williamr@2: #else
williamr@2:         // These are implementation details (for main fare see below)
williamr@2:         
williamr@2:         namespace detail
williamr@2:         {
williamr@2:             template    <
williamr@2:                             typename T,
williamr@2:                             bool QuietNanSupported
williamr@2:                         >
williamr@2:             struct    acosh_helper2_t
williamr@2:             {
williamr@2:                 static T    get_NaN()
williamr@2:                 {
williamr@2:                     return(::std::numeric_limits<T>::quiet_NaN());
williamr@2:                 }
williamr@2:             };  // boost::detail::acosh_helper2_t
williamr@2:             
williamr@2:             
williamr@2:             template<typename T>
williamr@2:             struct    acosh_helper2_t<T, false>
williamr@2:             {
williamr@2:                 static T    get_NaN()
williamr@2:                 {
williamr@2:                     ::std::string        error_reporting("Argument to acosh is greater than or equal to +1!");
williamr@2:                     ::std::domain_error  bad_argument(error_reporting);
williamr@2:                     
williamr@2:                     throw(bad_argument);
williamr@2:                 }
williamr@2:             };  // boost::detail::acosh_helper2_t
williamr@2:         
williamr@2:         }  // boost::detail
williamr@2:         
williamr@2:         
williamr@2:         // This is the main fare
williamr@2:         
williamr@2:         template<typename T>
williamr@2:         inline T    acosh(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:             typedef    detail::acosh_helper2_t<T, std::numeric_limits<T>::has_quiet_NaN>    helper2_type;
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:             
williamr@2:             if        (x < one)
williamr@2:             {
williamr@2:                 return(helper2_type::get_NaN());
williamr@2:             }
williamr@2:             else if    (x >= 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:                     return( log( x + sqrt(x*x-one) ) );
williamr@2:                 }
williamr@2:             }
williamr@2:             else
williamr@2:             {
williamr@2:                 T    y = sqrt(x-one);
williamr@2:                 
williamr@2:                 // approximation by taylor series in y at 0 up to order 2
williamr@2:                 T    result = y;
williamr@2:                 
williamr@2:                 if    (y >= taylor_2_bound)
williamr@2:                 {
williamr@2:                     T    y3 = y*y*y;
williamr@2:                     
williamr@2:                     // approximation by taylor series in y at 0 up to order 4
williamr@2:                     result -= y3/static_cast<T>(12);
williamr@2:                 }
williamr@2:                 
williamr@2:                 return(sqrt(static_cast<T>(2))*result);
williamr@2:             }
williamr@2:         }
williamr@2: #endif /* defined(BOOST_NO_TEMPLATE_PARTIAL_SPECIALIZATION) */
williamr@2:     }
williamr@2: }
williamr@2: 
williamr@2: #endif /* BOOST_ACOSH_HPP */
williamr@2: 
williamr@2: