**CMU Artificial Intelligence Repository**

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## CLMath: Common Lisp library of mathematical functions.

lang/lisp/code/math/clmath/

CLMath is a Lisp library of mathematical functions that calculate
hyperbolic and inverse hyperbolic functions, Bessel functions,
elliptic integrals, the gamma and beta functions, and the incomplete
gamma and beta functions. There are probability density functions,
cumulative distributions, and random number generators for the normal,
Poisson, chi-square, Student's T, and Snedecor's F functions. Discrete
Fourier Transforms. Multiple linear regression, Fletcher-Powell
unconstrained minimization, numerical integration, root finding,
and convergence. Code to factor numbers and to do the
Solovay-Strassen probabilistic prime test is included.
Origin:
ftp.ai.mit.edu:pub/clmath.tar

Version: 1989
Copying: Noncommercial use, distribution, and modification.
CD-ROM: Prime Time Freeware for AI, Issue 1-1
Author(s): Gerald Roylance
Keywords:
Authors!Roylance, Bessel, Beta Function, CLMath,
Elliptic Integrals,
Fletcher-Powell Unconstrained Minimization,
Fourier Transforms, Gamma Function, Hyperbolic,
Integer Factorization, Linear Regression, Lisp!Math, Math,
Matrix Routines, Numerical Integration, Prime Numbers,
Probability, Random Number Generators, Root Finding,
Solovay-Strassen Primality Testing
References:
Gerald Roylance, "Some Scientific Subroutines in LISP", MIT AI Lab
Memo 774, September 1984. [Documentation of the CLMath package.]
M. Abramowitz and I. Stegun, editors, "Handbook of Mathematical
Functions", National Bureau of Standards, 1964. [For Bessel,
Beta, Gamma, elliptic, error, and extended functions. Also
numerical integration, probability, and statistics.]
Philip R. Bevington, "Data Reduction and Error Analysis for the
Physical Sciences", McGraw-Hill, New York, 1969. [For Fletcher
Power functional minimization, Marquardt algorithm, and multiple
linear regression.]
Digital Equipment Corporation, "PDP-11 Paper Tape Software
Programming Handbook", DEC-11-GGPA-D, Section 7.7. [For error and
extended functions.]
R. W. Hamming, "Numerical Methods for Scientist and Engineers",
McGraw-Hill, 1973. [For various integration methods.]
Cecil Hastings, Jr., "Approximations for Digital Computers",
Princeton University Press, Princeton, NJ, 1955. [For error and
extended functions.]
A. J. Kinderman & J. F. Monahan, "Computer Generation of Random
Variables Using the Ratio of Uniform Deviates", ACM Transactions on
Mathematical Software 3(3):257-260, September 1977. [For
probability and statistics.]
D. Knuth, "The Art of Computer Programming", Addison Wesley, 1981.
[For factoring, Totient, probability, and statistics.]
James Kuester and Joe Mize, "Optimization Techniques with
Fortran", McGraw-Hill, New York, 1973. [For Fletcher Power
functional minimization and Marquardt algorithm.]
David G. Luenberger, "Introduction to Linear and Nonlinear Programming",
Addison Wesley, Reading, MA, 1965. [For matrix routines and Fletcher
Power functional minimization.]
Alan Oppenheim and Ronald Schafer, "Digital Signal Processing",
Prentice Hall, 1975. [For DFT code.]
William H. Press, Brian P. Flannery, Saul A. Teukolsky and William T.
Vetterling, "Numerical Recipes in C, The Art of Scientific Computing",
Cambridge University Press, 1988. [Page 178, for Beta and Gamma
functions and combinatorial algorithms.]
R. L. Rivest, A. Shamir, and L Adleman, "A Method for Obtaining
Digital Signatures and Public-Key Cryptosystems", CACM 21(2):120-126,
February 1978. [For modular arithmetic.]
Robert Solovay and Volker Strassen, "A Fast Monte-Carlo Test for Primality",
SIAM Journal on Computing, 1977, pp 84-85. [For modular arithmetic.]

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