boost/math
2
0
Fork 0
mirror of https://github.com/boostorg/math.git synced 2026-01-19 04:22:09 +00:00
Code Issues Projects Releases Wiki Activity

Special functions, octonions, quaternions by Hubert Holin

Browse Source 
[SVN r10404]
This commit is contained in:
Jens Maurer
2001-06-23 08:02:37 +00:00
commit f483d1189b
6 changed files with 5757 additions and 0 deletions
Download Patch File Download Diff File Expand all files Collapse all files

96
.gitattributes vendored Normal file
View File

@@ -0,0 +1,96 @@
* text=auto !eol svneol=native#text/plain
*.gitattributes text svneol=native#text/plain
# Scriptish formats
*.bat text svneol=native#text/plain
*.bsh text svneol=native#text/x-beanshell
*.cgi text svneol=native#text/plain
*.cmd text svneol=native#text/plain
*.js text svneol=native#text/javascript
*.php text svneol=native#text/x-php
*.pl text svneol=native#text/x-perl
*.pm text svneol=native#text/x-perl
*.py text svneol=native#text/x-python
*.sh eol=lf svneol=LF#text/x-sh
configure eol=lf svneol=LF#text/x-sh
# Image formats
*.bmp binary svneol=unset#image/bmp
*.gif binary svneol=unset#image/gif
*.ico binary svneol=unset#image/ico
*.jpeg binary svneol=unset#image/jpeg
*.jpg binary svneol=unset#image/jpeg
*.png binary svneol=unset#image/png
*.tif binary svneol=unset#image/tiff
*.tiff binary svneol=unset#image/tiff
*.svg text svneol=native#image/svg%2Bxml
# Data formats
*.pdf binary svneol=unset#application/pdf
*.avi binary svneol=unset#video/avi
*.doc binary svneol=unset#application/msword
*.dsp text svneol=crlf#text/plain
*.dsw text svneol=crlf#text/plain
*.eps binary svneol=unset#application/postscript
*.gz binary svneol=unset#application/gzip
*.mov binary svneol=unset#video/quicktime
*.mp3 binary svneol=unset#audio/mpeg
*.ppt binary svneol=unset#application/vnd.ms-powerpoint
*.ps binary svneol=unset#application/postscript
*.psd binary svneol=unset#application/photoshop
*.rdf binary svneol=unset#text/rdf
*.rss text svneol=unset#text/xml
*.rtf binary svneol=unset#text/rtf
*.sln text svneol=native#text/plain
*.swf binary svneol=unset#application/x-shockwave-flash
*.tgz binary svneol=unset#application/gzip
*.vcproj text svneol=native#text/xml
*.vcxproj text svneol=native#text/xml
*.vsprops text svneol=native#text/xml
*.wav binary svneol=unset#audio/wav
*.xls binary svneol=unset#application/vnd.ms-excel
*.zip binary svneol=unset#application/zip
# Text formats
.htaccess text svneol=native#text/plain
*.bbk text svneol=native#text/xml
*.cmake text svneol=native#text/plain
*.css text svneol=native#text/css
*.dtd text svneol=native#text/xml
*.htm text svneol=native#text/html
*.html text svneol=native#text/html
*.ini text svneol=native#text/plain
*.log text svneol=native#text/plain
*.mak text svneol=native#text/plain
*.qbk text svneol=native#text/plain
*.rst text svneol=native#text/plain
*.sql text svneol=native#text/x-sql
*.txt text svneol=native#text/plain
*.xhtml text svneol=native#text/xhtml%2Bxml
*.xml text svneol=native#text/xml
*.xsd text svneol=native#text/xml
*.xsl text svneol=native#text/xml
*.xslt text svneol=native#text/xml
*.xul text svneol=native#text/xul
*.yml text svneol=native#text/plain
boost-no-inspect text svneol=native#text/plain
CHANGES text svneol=native#text/plain
COPYING text svneol=native#text/plain
INSTALL text svneol=native#text/plain
Jamfile text svneol=native#text/plain
Jamroot text svneol=native#text/plain
Jamfile.v2 text svneol=native#text/plain
Jamrules text svneol=native#text/plain
Makefile* text svneol=native#text/plain
README text svneol=native#text/plain
TODO text svneol=native#text/plain
# Code formats
*.c text svneol=native#text/plain
*.cpp text svneol=native#text/plain
*.h text svneol=native#text/plain
*.hpp text svneol=native#text/plain
*.ipp text svneol=native#text/plain
*.tpp text svneol=native#text/plain
*.jam text svneol=native#text/plain
*.java text svneol=native#text/plain

3696
include/boost/math/octonion.hpp Normal file
View File

File diff suppressed because it is too large Load Diff

1606
include/boost/math/quaternion.hpp Normal file
View File

File diff suppressed because it is too large Load Diff

155
include/boost/math/special_functions/atanh.hpp Normal file
View File

@@ -0,0 +1,155 @@
// boost atanh.hpp header file
// (C) Copyright Hubert Holin 2001. Permission to copy, use, modify, sell and
// distribute this software is granted provided this copyright notice appears
// in all copies. This software is provided "as is" without express or implied
// warranty, and with no claim as to its suitability for any purpose.
// See http://www.boost.org for updates, documentation, and revision history.
#ifndef BOOST_ATANH_HPP
#define BOOST_ATANH_HPP
#include <cmath>
#include <limits>
#include <string>
#include <stdexcept>
// This is the inverse of the hyperbolic tangent function.
namespace boost
{
// These are implementation details (for main fare see below)
namespace detail
{
template <
typename T,
bool InfinitySupported
>
struct atanh_helper1_t
{
static T get_pos_infinity()
{
return(+std::numeric_limits<T>::infinity());
}
static T get_neg_infinity()
{
return(-std::numeric_limits<T>::infinity());
}
}; // boost::detail::atanh_helper1_t
template<typename T>
struct atanh_helper1_t<T, false>
{
static T get_pos_infinity()
{
::std::string error_reporting("Argument to atanh is +1 (result: +Infinity)!");
::std::out_of_range bad_argument(error_reporting);
throw(bad_argument);
}
static T get_neg_infinity()
{
::std::string error_reporting("Argument to atanh is -1 (result: -Infinity)!");
::std::out_of_range bad_argument(error_reporting);
throw(bad_argument);
}
}; // boost::detail::atanh_helper1_t
template <
typename T,
bool QuietNanSupported
>
struct atanh_helper2_t
{
static T get_pos_NaN()
{
return(+std::numeric_limits<T>::quiet_NaN());
}
static T get_neg_NaN()
{
return(-std::numeric_limits<T>::quiet_NaN());
}
}; // boost::detail::atanh_helper2_t
template<typename T>
struct atanh_helper2_t<T, false>
{
static T get_pos_NaN()
{
::std::string error_reporting("Argument to atanh is strictly greater than +1!");
::std::domain_error bad_argument(error_reporting);
throw(bad_argument);
}
static T get_neg_NaN()
{
::std::string error_reporting("Argument to atanh is strictly smaller than -1!");
::std::domain_error bad_argument(error_reporting);
throw(bad_argument);
}
}; // boost::detail::atanh_helper2_t
} // boost::detail
// This is the main fare
template<typename T>
inline T atanh(const T x)
{
using ::std::abs;
using ::std::sqrt;
using ::std::numeric_limits;
typedef detail::atanh_helper1_t<T, std::numeric_limits<T>::has_infinity> helper1_type;
typedef detail::atanh_helper2_t<T, std::numeric_limits<T>::has_quiet_NaN> helper2_type;
static T const e0 = sqrt(numeric_limits<T>::epsilon());
T const one = static_cast<T>(1);
T const two = static_cast<T>(2);
if (x < -one)
{
return(helper2_type::get_neg_NaN());
}
else if (x == -one)
{
return(helper1_type::get_neg_infinity());
}
else if (x == +one)
{
return(helper1_type::get_pos_infinity());
}
else if (x > +one)
{
return(helper2_type::get_pos_NaN());
}
else if (abs(x) < e0)
{
return(x);
}
else // -one < x <= -e0 or +e0 <= x < +one
{
using ::std::log;
return(log( (one + x) / (one - x) ) / two);
}
}
}
#endif /* BOOST_ATANH_HPP */

102
include/boost/math/special_functions/sinc.hpp Normal file
View File

@@ -0,0 +1,102 @@
// boost sinc.hpp header file
// (C) Copyright Hubert Holin 2001. Permission to copy, use, modify, sell and
// distribute this software is granted provided this copyright notice appears
// in all copies. This software is provided "as is" without express or implied
// warranty, and with no claim as to its suitability for any purpose.
// See http://www.boost.org for updates, documentation, and revision history.
#ifndef BOOST_SINC_HPP
#define BOOST_SINC_HPP
#include <cmath>
#include <limits>
#include <string>
#include <stdexcept>
// These are the the "Sinus Cardinal" functions.
namespace boost
{
// This is the "Sinus Cardinal" of index Pi.
template<typename T>
inline T sinc_pi(const T x)
{
using ::std::abs;
using ::std::sin;
using ::std::sqrt;
using ::std::numeric_limits;
static T const e1 = numeric_limits<T>::epsilon();
static T const e2 = sqrt(e1);
static T const e3 = sqrt(e2);
if (abs(x) > e3)
{
return(sin(x)/x);
}
else
{
T result = static_cast<T>(1);
if (abs(x) > e1)
{
T x2 = x*x;
result -= x2/static_cast<T>(6);
if (abs(x) > e2)
{
result += (x2*x2)/static_cast<T>(120);
}
}
return(result);
}
}
template<typename T, template<typename> class U>
inline U<T> sinc_pi(const U<T> x)
{
using ::std::abs;
using ::std::sin;
using ::std::sqrt;
using ::std::numeric_limits;
static T const e1 = numeric_limits<T>::epsilon();
static T const e2 = sqrt(e1);
static T const e3 = sqrt(e2);
if (abs(x) > e3)
{
return(sin(x)/x);
}
else
{
U<T> result = static_cast< U<T> >(1);
if (abs(x) > e1)
{
U<T> x2 = x*x;
result -= x2/static_cast<T>(6);
if (abs(x) > e2)
{
result += (x2*x2)/static_cast<T>(120);
}
}
return(result);
}
}
}
#endif /* BOOST_SINC_HPP */

102
include/boost/math/special_functions/sinhc.hpp Normal file
View File

@@ -0,0 +1,102 @@
// boost sinhc.hpp header file
// (C) Copyright Hubert Holin 2001. Permission to copy, use, modify, sell and
// distribute this software is granted provided this copyright notice appears
// in all copies. This software is provided "as is" without express or implied
// warranty, and with no claim as to its suitability for any purpose.
// See http://www.boost.org for updates, documentation, and revision history.
#ifndef BOOST_SINHC_HPP
#define BOOST_SINHC_HPP
#include <cmath>
#include <limits>
#include <string>
#include <stdexcept>
// These are the the "Hyperbolic Sinus Cardinal" functions.
namespace boost
{
// This is the "Hyperbolic Sinus Cardinal" of index Pi.
template<typename T>
inline T sinhc_pi(const T x)
{
using ::std::abs;
using ::std::sinh;
using ::std::sqrt;
using ::std::numeric_limits;
static T const e1 = numeric_limits<T>::epsilon();
static T const e2 = sqrt(e1);
static T const e3 = sqrt(e2);
if (abs(x) > e3)
{
return(sinh(x)/x);
}
else
{
T result = static_cast<T>(1);
if (abs(x) > e1)
{
T x2 = x*x;
result += x2/static_cast<T>(6);
if (abs(x) > e2)
{
result += (x2*x2)/static_cast<T>(120);
}
}
return(result);
}
}
template<typename T, template<typename> class U>
inline U<T> sinhc_pi(const U<T> x)
{
using ::std::abs;
using ::std::sinh;
using ::std::sqrt;
using ::std::numeric_limits;
static T const e1 = numeric_limits<T>::epsilon();
static T const e2 = sqrt(e1);
static T const e3 = sqrt(e2);
if (abs(x) > e3)
{
return(sinh(x)/x);
}
else
{
U<T> result = static_cast< U<T> >(1);
if (abs(x) > e1)
{
U<T> x2 = x*x;
result += x2/static_cast<T>(6);
if (abs(x) > e2)
{
result += (x2*x2)/static_cast<T>(120);
}
}
return(result);
}
}
}
#endif /* BOOST_SINHC_HPP */