The Forth Scientific Library
 The complete library and auxiliary files:
Gnuzipped TAR file.

In order of Algorithm number:
 1. Real
Exponential Integral (ACM #20), V1.1.
 2. Complete
Elliptic Integral (ACM #149), V1.2.
 3.
Polynomial evaluation by the Horner method, V1.5.
 4.
Logistic function and its first derivative, V1.2.
 5. Cube
root of real number by Newton's method, V1.2.
 6. Solution
of cubic equations with real coefficients, V 10/6/94.
 7.
Regula Falsi root finder, V1.0.
 8. Fast
Hartley (Bracewell) Transform, V1.3.
 9. Aitken
interpolation (ACM #70), V1.1.2.
 10.
Hermite interpolation (ACM #211), V1.2.
 11.
Lagrange interpolation (ACM #210), V1.2.
 12.
Forward and Backward divided differences, V1.3.
 13. Newton
interpolation (ACM #168 & #169), V1.4 (requires divided
differences).
 14.
Factorial function, V1.1.
 15.
Shell sort for floating point arrays, V1.3.
 16.
Exponentiation of a series (ACM #158), V1.3.
 17.
Polynomial and Rational function interpolation and
extrapolation, V1.2.
 18. The
Gamma, LogGamma and reciprocal Gamma functions (real args),
V1.2.
 19.
Adaptive Integration using Trapezoid rule, V1.1.
 20.
Parabolic Cylinder functions and related Confluent Hypergeometric
functions, V1.1.
 21. Special
Polynomial (Chebyshev, Hermite, Laguerre, Generalized Laguerre,
Legendre and Bessel) Evaluation, V1.1.
 22.
Conversion between calendar date and Julian day (ACM #199),
V1.2.
 23. R250
(also minimal standard) Pseudorandom number generator,
V1.5.
 24. RAN4
Pseudorandom number generator, V1.1.
 25.
Finite segment of Hilbert Matrices, their inverses and
determinants,V1.1.
 26. FIND nth
element of an unsorted array (ACM #65), V1.0.
 27.
GaussLegendre Integration, V1.1.
 28.
Complete Elliptic Integrals of the first and second kinds
(ACM #55 and #56), V1.1.
 29. 4th
order and adaptive RungeKutta solvers for systems of ODEs,
V1.2.
 30.
Complete Elliptic Integrals of the first and second kinds
(ACM #165), V1.2.
 31.
Telescope 1 (reduction of degree of polynomial
approximations) (ACM #37)
 32.
Telescope 2 (reduction of degree of polynomial
approximations) (ACM #38)
 33.
LUFACT, LU Factorization of square matrices
 34.
Determinant of an LU factored matrix
 35.
Backsubstitution solution for LU factored linear
systems
 36. Inverse
of an LU factored matrix
 37.
Direct Fourier Transforms (four methods)
 38.
Radix2 Fast Fourier Transform routines (five methods)
 39. Singular
Value Decomposition
 40. Amoeba
 Multidimensional Simplex minimization of a function
 41. Sunday
Quicksearch
 42. Gauss
probability function (ACM #209)
 43.
Regular spherical Bessel functions jn(x), n=09
 44. 16bit
Cyclic Redundancy Checksums
 45.
Simpsons rule and Romberg algorithm Quadrature
routines
 46. Basic
arithmetic and conversions for rational numbers
 47. BIG 
Arithmetic on big signed magnitude numbers (updated May
1999)
 48. Gauss
Jordan Elimination,V1.2.
 49.
LevenbergMarquardt nonlinear fit
 50. Fast
Walsh Transform
 51.
Random Number distributions
 52. ISAAC
Random Number generator
 53.
Adaptive integration using trapezoidal rule with Richardson
extrapolation
 54.
Adaptive integration using 3 point GaussLegendre with Richardson
extrapolation
 55.
shanks, Nonlinear transformation of series (ACM Algorithm
#215)
 56.
Quaternions and rotation matrices
 57.
GGUBS floating point random number generator
 58.
Onedimensional MonteCarlo integration
 59.
Permutations and combinations
 60.
Complex numbers and functions,V1.0.3
 61.
Laguerre algorithm for polynomial roots
 62.
Error functions
 63.
Roots of a real quadratic
 64.
Medium accuracy error function
 65.
Complete and incomplete gamma and beta functions
By Algorithm category:
Special Functions
 4.
Logistic function and its first derivative.
 14.
Factorial function.
 18. The
Gamma, LogGamma and reciprocal Gamma functions (real
args).
 20.
Parabolic Cylinder functions and related Confluent Hypergeometric
functions.
 42. Gauss
probability function (ACM #209)
 43.
Regular spherical Bessel functions jn(x), n=09
 62.
Error functions
 64.
Medium accuracy error function
 65.
Complete and incomplete gamma and beta functions
Special Integrals
 1. Real
Exponential Integral (ACM #20).
 2. Complete
Elliptic Integral (ACM #149).
 28.
Complete Elliptic Integrals of the first and second kinds
(ACM #55 and #56), V1.1.
 30.
Complete Elliptic Integrals of the first and second kinds
(ACM #165), V1.2.
Interpolators
 9. Aitken
interpolation (ACM #70).
 10.
Hermite interpolation (ACM #211).
 11.
Lagrange interpolation (ACM #210).
 13. Newton
interpolation (ACM #168 & #169) (requires divided
differences).
 17.
Polynomial and Rational function interpolation and
extrapolation.
Integrators
 19.
Adaptive Integration using Trapezoid rule, V1.1.
 27.
GaussLegendre Integration, V1.1.
 45.
Simpsons rule and Romberg algorithm Quadrature
routines
 53.
Adaptive integration using trapezoidal rule with Richardson
extrapolation
 54.
Adaptive integration using 3 point GaussLegendre with Richardson
extrapolation
 58.
Onedimensional MonteCarlo integration
Polynomial/Power series algorithms
 3.
Polynomial evaluation by the Horner method.
 16.
Exponentiation of a series (ACM #158).
 17.
Polynomial and Rational function interpolation and
extrapolation.
 21. Special
Polynomial (Chebyshev, Hermite, Laguerre, Generalized Laguerre,
Legendre and Bessel) Evaluation.
 31.
Telescope 1 (reduction of degree of polynomial
approximations) (ACM #37)
 32.
Telescope 2 (reduction of degree of polynomial
approximations) (ACM #38)
 55.
shanks, Nonlinear transformation of series (ACM Algorithm
#215)
 61.
Laguerre algorithm for polynomial roots
 63.
Roots of a real quadratic
Transforms
 8. Fast
Hartley (Bracewell) Transform.
 37.
Direct Fourier Transforms (four methods)
 38.
Radix2 Fast Fourier Transform routines (five methods)
 50. Fast
Walsh Transform
Matrix algorithms
 25.
Finite segment of Hilbert Matrices, their inverses and
determinants,V1.1.
 33.
LUFACT, LU Factorization of square matrices
 34.
Determinant of an LU factored matrix
 35.
Backsubstitution solution for LU factored linear
systems
 36. Inverse
of an LU factored matrix
 39. Singular
Value Decomposition
 48. Gauss
Jordan Elimination,V1.2.
 56.
Quaternions and rotation matrices
Random numbers and related
 23. R250
(also minimal standard) Pseudorandom number
generator.
 24. RAN4
Pseudorandom number generator, V1.1.
 51.
Random Number distributions
 52. ISAAC
Random Number generator
 57.
GGUBS floating point random number generator
Miscellaneous algorithms
 5. Cube
root of real number by Newton's method.
 6. Solution
of cubic equations with real coefficients.
 7.
Regula Falsi root finder.
 12.
Forward and Backward divided differences.
 15.
Shell sort for floating point arrays.
 22.
Conversion between calendar date and Julian day (ACM
#199).
 26. FIND nth
element of an unsorted array (ACM #65), V1.0.
 29. 4th
order and adaptive RungeKutta solvers for systems of ODEs,
V1.2.
 40. Amoeba
 Multidimensional Simplex minimization of a function
 41. Sunday
Quicksearch
 44. 16bit
Cyclic Redundancy Checksums
 46. Basic
arithmetic and conversions for rational numbers
 47. BIG 
Arithmetic on big signed magnitude numbers (updated May
1999)
 49.
LevenbergMarquardt nonlinear fit
 59.
Permutations and combinations
 60.
Complex numbers and functions, V1.0.3
Auxiliary code
Please note that the auxiliary files do not go through the
reviewing process used for the Library Algorithms. They have been
contributed by various authors in the hope they will be of use to
some Library users. In particular, some may have dependencies on
particular systems or implementations.
 FSL auxiliary code by Skip
Carter
 for FPC, ThisForth, or GFORTH
 FSL auxiliary code from Krishna Myneni suitable for either
 PFE or Gforth
 FSL auxiliary code by Pierre
Abbat, revised by Marcel Hendrix,
 for Win32For
 FSL
auxiliary code for Julian Noble's contributions.
 ttester
for the testing of Forth words, based on the Hayes suite
 and subsequently extended by several authors, and
 ttesterxf, a revision by David N. Williams
 with new relative error comparisons suggested by Krishna Myneni.
 Links to related utilities are included.
 Complex number
testing code for the words in Algorithm 60, V1.0.3.
 A set of syntactically equivalent complex number
implementations
 by Skip Carter, using
 the float stack
 a separate complex number
stack.
 data structures.
 data structures and a complex
number stack.
 Some complex
number operations by Skip Carter
 dynamic
memory package for arrays and structures.
 extra double
precision words (used by ThisForth).
 Supplemental Hartley Transform Utilities and
Tests.
 ASCII file
I/O utility words.
 Structures package.
 supplemental Quaternion code for
Win32Forth
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