The-Forth-Scientific-Library

as found on https://www.taygeta.com/fsl/scilib.html

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) 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 (updated May 1999)
48. Gauss Jordan Elimination,V1.2.
49. Levenberg-Marquardt 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 Gauss-Legendre 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. One-dimensional Monte-Carlo 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
66. Logistic function and its first derivative.
67. Factorial function.
68. The Gamma, LogGamma and reciprocal Gamma functions (real args).
69. Parabolic Cylinder functions and related Confluent Hypergeometric functions.
70. Gauss probability function (ACM #209)
71. Regular spherical Bessel functions jn(x), n=0-9
72. Error functions
73. Medium accuracy error function
74. Complete and incomplete gamma and beta functions Special Integrals
75. Real Exponential Integral (ACM #20).
76. Complete Elliptic Integral (ACM #149).
77. Complete Elliptic Integrals of the first and second kinds (ACM #55 and #56), V1.1.
78. Complete Elliptic Integrals of the first and second kinds (ACM #165), V1.2. Interpolators
79. Aitken interpolation (ACM #70).
80. Hermite interpolation (ACM #211).
81. Lagrange interpolation (ACM #210).
82. Newton interpolation (ACM #168 & #169) (requires divided differences).
83. Polynomial and Rational function interpolation and extrapolation. Integrators
84. Adaptive Integration using Trapezoid rule, V1.1.
85. Gauss-Legendre Integration, V1.1.
86. Simpsons rule and Romberg algorithm Quadrature routines
87. Adaptive integration using trapezoidal rule with Richardson extrapolation
88. Adaptive integration using 3 point Gauss-Legendre with Richardson extrapolation
89. One-dimensional Monte-Carlo integration Polynomial/Power series algorithms
90. Polynomial evaluation by the Horner method.
91. Exponentiation of a series (ACM #158).
92. Polynomial and Rational function interpolation and extrapolation.
93. Special Polynomial (Chebyshev, Hermite, Laguerre, Generalized Laguerre, Legendre and Bessel) Evaluation.
94. Telescope 1 (reduction of degree of polynomial approximations) (ACM #37)
95. Telescope 2 (reduction of degree of polynomial approximations) (ACM #38)
96. shanks, Nonlinear transformation of series (ACM Algorithm #215)
97. Laguerre algorithm for polynomial roots
98. Roots of a real quadratic Transforms
99. Fast Hartley (Bracewell) Transform.
100. Direct Fourier Transforms (four methods)
101. Radix-2 Fast Fourier Transform routines (five methods)
102. Fast Walsh Transform Matrix algorithms
103. Finite segment of Hilbert Matrices, their inverses and determinants,V1.1.
104. LUFACT, LU Factorization of square matrices
105. Determinant of an LU factored matrix
106. Back-substitution solution for LU factored linear systems
107. Inverse of an LU factored matrix
108. Singular Value Decomposition
109. Gauss Jordan Elimination,V1.2.
110. Quaternions and rotation matrices Random numbers and related
111. R250 (also minimal standard) Pseudo-random number generator.
112. RAN4 Pseudo-random number generator, V1.1.
113. Random Number distributions
114. ISAAC Random Number generator
115. GGUBS floating point random number generator Miscellaneous algorithms
116. Cube root of real number by Newton's method.
117. Solution of cubic equations with real coefficients.
118. Regula Falsi root finder.
119. Forward and Backward divided differences.
120. Shell sort for floating point arrays.
121. Conversion between calendar date and Julian day (ACM #199).
122. FIND nth element of an unsorted array (ACM #65), V1.0.
123. 4th order and adaptive Runge-Kutta solvers for systems of ODEs, V1.2.
124. Amoeba -- Multidimensional Simplex minimization of a function
125. Sunday Quicksearch
126. 16-bit Cyclic Redundancy Checksums
127. Basic arithmetic and conversions for rational numbers
128. BIG -- Arithmetic on big signed magnitude numbers (updated May 1999)
129. Levenberg-Marquardt nonlinear fit
130. Permutations and combinations
131. Complex numbers and functions, V1.0.3