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The Math::Cephes module provides a perl interface to over
150 functions of the cephes math library of Stephen Moshier.
Please read the INSTALL file for instructions on installation.
The functions available are grouped as
- trigonometric: sin, cos, etc., and their inverses; also
included are versions of sin, cos, tan, and cot which accept
angles in degrees, as well as a degree to radian converter.
- hyperbolic: sinh, cosh, tanh, and their inverses.
- exponential and logarithmic: exp and log functions,
with versions in base e (2.718282...), base 10, and base 2.
- Bessel functions: various Bessel functions (J, Y, I, K)
of different orders.
- Gamma functions: the gamma function, the incomplete gamma
integral and its inverse, and the digamma function (psi).
- Beta functions: the beta function and the incomplete
beta integral and its inverse.
- elliptic integrals: complete, incomplete, and Jacobian
elliptic integrals.
- hypergeometric functions: 2F0, 2F1, 1F2, 3F0, and the
confluent hypergeometric function.
- distributions: binomial, beta, chi-square, F, gamma, normal,
Poisson, and Student's t distribution, as well as their inverses.
- miscellaneous: Airy function, Dawson's integral, exponential
integrals, error functions, sin/cos and sinh/cosh integrals,
Fresnel integral, dilogarithm (Spence integral), the Struve
function, Riemann zeta functions, polylogarithms, the Planck
distribution, finding the angle between two vectors, and Simpson's
rule for estimating an integral.
- utilities: square and cube roots, ceiling, floor, round, pseudo random
number generators, the power function, the factorial function, and
some others.
Some common constants, such as PI and SQRT2, are also available.
As well, there is support for arithmetic operations for fractions
(adding, subtracting, dividing, multiplying) and also for various
functions of complex numbers (arithmetic, trigonometric, hyperbolic,
exponential, logarithm, powers). Interfaces to these are available
in the included Math::Cephes::Fraction and Math::Cephes::Complex
modules. There is also support for some common operations for
polynomials of a real variable (adding, subtracting, multiplying,
dividing, evaluating, root finding) in the included module
Math::Cephes::Polynomial, the coefficients of which can be real,
fractional, or (for some operations) complex. Finally, routines for
square matrices (adding, subtracting, multiplying, dividing,
inverting) are available in the included module Math::Cephes::Matrix,
which also includes routines for solving simultaneous equations and
for finding the eigenvalues and eigenvectors of a real symmetric matrix.
A description of these functions and their usage may be read
either as a man page (eg, man Math::Cephes) or through perldoc
(eg, perldoc Math::Cephes), for the relevant module.
A simple "calculator" script (pmath) is included which provides
a command line interface to this module; help on the various functions
is also available within this script. The script will use the
Term::ReadLine module if available. Help on its usage is available
either though the man page (man pmath) or perldoc (perldoc pmath).
This module has been built and tested on a Linux and on a WinXP machine
running ActivePerl (build 6xx); to build on different systems will
probably require editing of the file libmd/mconf.h, which
among other things defines the type of computer arithmetic
used. If you need to edit this file for your system, please
let me know of the changes needed, so they can be automatically
set in a future release.
If you are running ActiveState's Win32 perl (build version 6xx), a
ppm package is available at
http://theoryx5.uwinnipeg.ca/ppmpackages/
To install, within the ppm shell set the repository to
http://theoryx5.uwinnipeg.ca/cgi-bin/ppmserver?urn:/PPMServer
and then
ppm> install Math-Cephes
For Win32 ActivePerl 8xx, the corresponding repository is
http://theoryx5.uwinnipeg.ca/ppms/
with the repository location within the ppm shell as
http://theoryx5.uwinnipeg.ca/cgi-bin/ppmserver?urn:/PPMServer58
The C code for the Cephes Math Library is Copyright 1984, 1987,
1989, 2002 by Stephen L. Moshier, and is available at
http://www.netlib.org/cephes/. The perl interface is Copyright 2000, 2002
by Randy Kobes , and may be
distributed under the same terms as Perl itself.