author | William Roberts <williamr@symbian.org> |
Wed, 31 Mar 2010 12:27:01 +0100 | |
branch | Symbian2 |
changeset 3 | e1b950c65cb4 |
parent 2 | epoc32/include/stdapis/boost/math/special_functions/acosh.hpp@2fe1408b6811 |
child 4 | 837f303aceeb |
permissions | -rw-r--r-- |
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// boost asinh.hpp header file |
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// (C) Copyright Eric Ford 2001 & Hubert Holin. |
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// Distributed under the Boost Software License, Version 1.0. (See |
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// accompanying file LICENSE_1_0.txt or copy at |
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// http://www.boost.org/LICENSE_1_0.txt) |
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|
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// See http://www.boost.org for updates, documentation, and revision history. |
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#ifndef BOOST_ACOSH_HPP |
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#define BOOST_ACOSH_HPP |
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#include <cmath> |
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#include <limits> |
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#include <string> |
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#include <stdexcept> |
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#include <boost/config.hpp> |
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// This is the inverse of the hyperbolic cosine function. |
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namespace boost |
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{ |
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namespace math |
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{ |
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#if defined(__GNUC__) && (__GNUC__ < 3) |
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// gcc 2.x ignores function scope using declarations, |
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// put them in the scope of the enclosing namespace instead: |
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|
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using ::std::abs; |
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using ::std::sqrt; |
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using ::std::log; |
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using ::std::numeric_limits; |
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#endif |
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#if defined(BOOST_NO_TEMPLATE_PARTIAL_SPECIALIZATION) |
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// This is the main fare |
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|
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template<typename T> |
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inline T acosh(const T x) |
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{ |
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using ::std::abs; |
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using ::std::sqrt; |
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using ::std::log; |
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|
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using ::std::numeric_limits; |
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T const one = static_cast<T>(1); |
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T const two = static_cast<T>(2); |
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|
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static T const taylor_2_bound = sqrt(numeric_limits<T>::epsilon()); |
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static T const taylor_n_bound = sqrt(taylor_2_bound); |
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static T const upper_taylor_2_bound = one/taylor_2_bound; |
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|
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if (x < one) |
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{ |
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if (numeric_limits<T>::has_quiet_NaN) |
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{ |
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return(numeric_limits<T>::quiet_NaN()); |
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} |
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else |
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{ |
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::std::string error_reporting("Argument to atanh is strictly greater than +1 or strictly smaller than -1!"); |
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::std::domain_error bad_argument(error_reporting); |
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throw(bad_argument); |
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} |
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} |
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else if (x >= taylor_n_bound) |
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{ |
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if (x > upper_taylor_2_bound) |
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{ |
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// approximation by laurent series in 1/x at 0+ order from -1 to 0 |
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return( log( x*two) ); |
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} |
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else |
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{ |
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return( log( x + sqrt(x*x-one) ) ); |
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} |
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} |
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else |
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{ |
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T y = sqrt(x-one); |
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|
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// approximation by taylor series in y at 0 up to order 2 |
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T result = y; |
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|
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if (y >= taylor_2_bound) |
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{ |
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T y3 = y*y*y; |
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|
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// approximation by taylor series in y at 0 up to order 4 |
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result -= y3/static_cast<T>(12); |
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} |
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return(sqrt(static_cast<T>(2))*result); |
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} |
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} |
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#else |
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// These are implementation details (for main fare see below) |
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|
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namespace detail |
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{ |
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template < |
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typename T, |
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bool QuietNanSupported |
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> |
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struct acosh_helper2_t |
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{ |
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static T get_NaN() |
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{ |
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return(::std::numeric_limits<T>::quiet_NaN()); |
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} |
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}; // boost::detail::acosh_helper2_t |
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template<typename T> |
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struct acosh_helper2_t<T, false> |
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{ |
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static T get_NaN() |
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{ |
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::std::string error_reporting("Argument to acosh is greater than or equal to +1!"); |
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::std::domain_error bad_argument(error_reporting); |
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|
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throw(bad_argument); |
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} |
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}; // boost::detail::acosh_helper2_t |
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} // boost::detail |
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// This is the main fare |
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template<typename T> |
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inline T acosh(const T x) |
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{ |
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using ::std::abs; |
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using ::std::sqrt; |
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using ::std::log; |
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|
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using ::std::numeric_limits; |
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typedef detail::acosh_helper2_t<T, std::numeric_limits<T>::has_quiet_NaN> helper2_type; |
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T const one = static_cast<T>(1); |
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T const two = static_cast<T>(2); |
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|
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static T const taylor_2_bound = sqrt(numeric_limits<T>::epsilon()); |
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static T const taylor_n_bound = sqrt(taylor_2_bound); |
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static T const upper_taylor_2_bound = one/taylor_2_bound; |
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|
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if (x < one) |
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{ |
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return(helper2_type::get_NaN()); |
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} |
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else if (x >= taylor_n_bound) |
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{ |
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if (x > upper_taylor_2_bound) |
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{ |
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// approximation by laurent series in 1/x at 0+ order from -1 to 0 |
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return( log( x*two) ); |
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} |
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else |
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{ |
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return( log( x + sqrt(x*x-one) ) ); |
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} |
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} |
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else |
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{ |
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T y = sqrt(x-one); |
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|
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// approximation by taylor series in y at 0 up to order 2 |
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T result = y; |
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|
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if (y >= taylor_2_bound) |
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{ |
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T y3 = y*y*y; |
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|
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// approximation by taylor series in y at 0 up to order 4 |
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result -= y3/static_cast<T>(12); |
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} |
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return(sqrt(static_cast<T>(2))*result); |
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} |
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} |
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#endif /* defined(BOOST_NO_TEMPLATE_PARTIAL_SPECIALIZATION) */ |
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} |
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} |
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#endif /* BOOST_ACOSH_HPP */ |
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