.\" -*- mode: troff; coding: utf-8 -*-
.\" Automatically generated by Pod::Man 5.01 (Pod::Simple 3.43)
.\"
.\" Standard preamble:
.\" ========================================================================
.de Sp \" Vertical space (when we can't use .PP)
.if t .sp .5v
.if n .sp
..
.de Vb \" Begin verbatim text
.ft CW
.nf
.ne \\$1
..
.de Ve \" End verbatim text
.ft R
.fi
..
.\" \*(C` and \*(C' are quotes in nroff, nothing in troff, for use with C<>.
.ie n \{\
.    ds C` ""
.    ds C' ""
'br\}
.el\{\
.    ds C`
.    ds C'
'br\}
.\"
.\" Escape single quotes in literal strings from groff's Unicode transform.
.ie \n(.g .ds Aq \(aq
.el       .ds Aq '
.\"
.\" If the F register is >0, we'll generate index entries on stderr for
.\" titles (.TH), headers (.SH), subsections (.SS), items (.Ip), and index
.\" entries marked with X<> in POD.  Of course, you'll have to process the
.\" output yourself in some meaningful fashion.
.\"
.\" Avoid warning from groff about undefined register 'F'.
.de IX
..
.nr rF 0
.if \n(.g .if rF .nr rF 1
.if (\n(rF:(\n(.g==0)) \{\
.    if \nF \{\
.        de IX
.        tm Index:\\$1\t\\n%\t"\\$2"
..
.        if !\nF==2 \{\
.            nr % 0
.            nr F 2
.        \}
.    \}
.\}
.rr rF
.\" ========================================================================
.\"
.IX Title "Math::GSL::Sys 3pm"
.TH Math::GSL::Sys 3pm 2024-03-07 "perl v5.38.2" "User Contributed Perl Documentation"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
.if n .ad l
.nh
.SH NAME
Math::GSL::Sys \- Misc Math Functions
.SH SYNOPSIS
.IX Header "SYNOPSIS"
.Vb 1
\&    use Math::GSL::Sys qw/:all/;
.Ve
.SH DESCRIPTION
.IX Header "DESCRIPTION"
This module contains various useful math functions that are not usually
provided by standard libraries.
.IP \(bu 4
\&\f(CWgsl_log1p($x)\fR
.Sp
This function computes the value of \elog(1+$x) in a way that is accurate for
small \f(CW$x\fR. It provides an alternative to the BSD math function log1p(x).
.IP \(bu 4
\&\f(CWgsl_expm1($x)\fR
.Sp
This function computes the value of \eexp($x)\-1 in a way that is accurate for
small \f(CW$x\fR. It provides an alternative to the BSD math function expm1(x).
.IP \(bu 4
\&\f(CW\*(C`gsl_hypot($x, $y)\*(C'\fR
.Sp
This function computes the value of \esqrt{$x^2 + \f(CW$y\fR^2} in a way that avoids
overflow. It provides an alternative to the BSD math function hypot($x,$y).
.IP \(bu 4
\&\f(CW\*(C`gsl_hypot3($x, $y, $z)\*(C'\fR
.Sp
This function computes the value of \esqrt{$x^2 + \f(CW$y\fR^2 + \f(CW$z\fR^2} in a way that
avoids overflow.
.IP \(bu 4
\&\f(CWgsl_acosh($x)\fR
.Sp
This function computes the value of \earccosh($x). It provides an alternative to
the standard math function acosh($x).
.IP \(bu 4
\&\f(CWgsl_asinh($x)\fR
.Sp
This function computes the value of \earcsinh($x). It provides an alternative to
the standard math function asinh($x).
.IP \(bu 4
\&\f(CWgsl_atanh($x)\fR
.Sp
This function computes the value of \earctanh($x). It provides an alternative to
the standard math function atanh($x).
.IP \(bu 4
\&\f(CWgsl_isnan($x)\fR
.Sp
This function returns 1 if \f(CW$x\fR is not-a-number.
.IP \(bu 4
\&\f(CWgsl_isinf($x)\fR
.Sp
This function returns +1 if \f(CW$x\fR is positive infinity, \-1 if \f(CW$x\fR is negative
infinity and 0 otherwise.
.IP \(bu 4
\&\f(CWgsl_finite($x)\fR
.Sp
This function returns 1 if \f(CW$x\fR is a real number, and 0 if it is infinite or not-a-number.
.IP \(bu 4
\&\f(CW\*(C`gsl_posinf \*(C'\fR
.IP \(bu 4
\&\f(CW\*(C`gsl_neginf \*(C'\fR
.IP \(bu 4
\&\f(CW\*(C`gsl_fdiv \*(C'\fR
.IP \(bu 4
\&\f(CW\*(C`gsl_coerce_double \*(C'\fR
.IP \(bu 4
\&\f(CW\*(C`gsl_coerce_float \*(C'\fR
.IP \(bu 4
\&\f(CW\*(C`gsl_coerce_long_double \*(C'\fR
.IP \(bu 4
\&\f(CW\*(C`gsl_ldexp($x, $e)\*(C'\fR
.Sp
This function computes the value of \f(CW$x\fR * 2**$e. It provides an alternative to
the standard math function ldexp($x,$e).
.IP \(bu 4
\&\f(CWgsl_frexp($x)\fR
.Sp
This function splits the number \f(CW$x\fR into its normalized fraction f and exponent
e, such that \f(CW$x\fR = f * 2^e and 0.5 <= f < 1. The function returns f and then the
exponent in e. If \f(CW$x\fR is zero, both f and e are set to zero. This function
provides an alternative to the standard math function frexp(x, e).
.IP \(bu 4
\&\f(CW\*(C`gsl_fcmp($x, $y, $epsilon)\*(C'\fR
.Sp
This function determines whether \f(CW$x\fR and \f(CW$y\fR are approximately equal to a
relative accuracy \f(CW$epsilon\fR. The relative accuracy is measured using an interval
of size 2 \edelta, where \edelta = 2^k \eepsilon and k is the maximum base\-2
exponent of \f(CW$x\fR and \f(CW$y\fR as computed by the function frexp. If \f(CW$x\fR and \f(CW$y\fR lie
within this interval, they are considered approximately equal and the function
returns 0. Otherwise if \f(CW$x\fR < \f(CW$y\fR, the function returns \-1, or if \f(CW$x\fR > \f(CW$y\fR, the
function returns +1. Note that \f(CW$x\fR and \f(CW$y\fR are compared to relative accuracy, so
this function is not suitable for testing whether a value is approximately
zero. The implementation is based on the package fcmp by T.C. Belding.
.PP
For more information on the functions, we refer you to the GSL official
documentation: <http://www.gnu.org/software/gsl/manual/html_node/>
.SH AUTHORS
.IX Header "AUTHORS"
Jonathan "Duke" Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>
.SH "COPYRIGHT AND LICENSE"
.IX Header "COPYRIGHT AND LICENSE"
Copyright (C) 2008\-2023 Jonathan "Duke" Leto and Thierry Moisan
.PP
This program is free software; you can redistribute it and/or modify it
under the same terms as Perl itself.