The Scientific Forth Library
  

The Forth Scientific Library

                    
The complete library: Gnu-zipped TAR file (142K).

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, V1.2.
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) Pseudo-random number generator, V1.5.
24. RAN4 Pseudo-random 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. Gauss-Legendre Integration, V1.1.
28. Complete Elliptic Integrals of the first and second kinds (ACM #55 and #56), V1.1.
29. 4th order and adaptive Runge-Kutta 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. Back-substitution solution for LU factored linear systems
36. Inverse of an LU factored matrix
37. Direct Fourier Transforms (four methods)
38. Radix-2 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=0-9
44. 16-bit 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

By Algorithm catagory:

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=0-9

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. Gauss-Legendre Integration, V1.1.
45. Simpsons rule and Romberg algorithm Quadrature routines

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)

Transforms

8. Fast Hartley (Bracewell) Transform.
37. Direct Fourier Transforms (four methods)
38. Radix-2 Fast Fourier Transform routines (five methods)

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. Back-substitution solution for LU factored linear systems
36. Inverse of an LU factored matrix
39. Singular Value Decomposition

Miscellanous 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).
23. R250 (also minimal standard) Pseudo-random number generator.
24. RAN4 Pseudo-random number generator, V1.1.
26. FIND nth element of an unsorted array (ACM #65), V1.0.
29. 4th order and adaptive Runge-Kutta solvers for systems of ODEs, V1.2.
40. Amoeba -- Multidimensional Simplex minimization of a function
41. Sunday Quicksearch
44. 16-bit Cyclic Redundancy Checksums
46. Basic arithmetic and conversions for rational numbers
47. BIG -- Arithmetic on big signed magnitude numbers

  

Auxiliary code

Syntactically equivalent Complex number implementations using,
the float stack
a separate complex number stack.
data structures.
data structures and a complex number stack.
FSL auxiliary code by Skip Carter
for F-PC, ThisForth or PFE
FSL auxiliary code for Julian Noble's contributions.
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.

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 Everett (Skip) Carter          Phone: 408-641-0645 FAX:  408-394-5561
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