Status of the Forth Scientific Library Project 28 January 2011 Code contributions: Reviewed and accepted: (reviewed code is available via WWW at http://www.taygeta.com/fsl/scilib.html) 1. Real Exponential Integral (ACM #20) Skip Carter 2. Complete Elliptic Integral (ACM #149) Skip Carter 3. Polynomial evaluation by the Horner method Skip Carter 4. Logistic function and its first derivative Skip Carter 5. Cube root of real number by Newton's method Julian Noble 6. Solution of cubic equations with real coefficients Julian Noble 7. Regula Falsi root finder Julian Noble 8. Fast Hartley (Bracewell) Transform Skip Carter (with supplemental utilities and tests by Marcel Hendrix) 9. Aitken Interpolation (ACM #70) Skip Carter 10. Hermite Interpolation (ACM #211) Skip Carter 11. Lagrange Interpolation (ACM #210) Skip Carter 12. Forward and Backward divided differences Skip Carter 13. Newton Interpolation with Divided differences (ACM 168 & 169) Skip Carter 14. Factorial Skip Carter 15. Shell sort for floating point arrays Charles Montgomery 16. Exponentiation of a series (ACM # 158) Skip Carter 17. Polynomial and Rational function interpolation and extrapolation Marcel Hendrix 18. The Gamma, LogGamma and reciprocal Gamma functions Skip Carter 19. Adaptive Integration using Trapezoid rule Julian Noble 20. Parabolic Cylinder functions and related Confluent Hypergeometric functions Skip Carter 21. Special Polynomial (Chebyshev, Hermite, Laguerre, Generalized Laguerre, Legendre and Bessel) Evaluation Skip Carter 22. Conversion between calendar date and Julian day (ACM 199) Skip Carter 23. R250 (also minimal standard) Pseudo-random number generator Skip Carter 24. RAN4 Pseudo-random number generator Gordon Charlton 25. Finite segment of Hilbert Matrices, their inverses and determinants Skip Carter 26. FIND nth element of an unsorted array (ACM #65) Skip Carter 27. Gauss-Legendre Integration Skip Carter 28. Complete Elliptic Integral of the first kind and second kind (ACM #55 and #56) Skip Carter 29. 4th order and adaptive Runge-Kutta solvers for systems of ODEs Skip Carter 30. Complete Elliptic Integrals of 1st and 2nd kinds (ACM #165) Skip Carter 31. Telescope 1 (ACM 37) (reduction of degree of polynomial approximations) Skip Carter 32. Telescope 2 (ACM 38) Skip Carter 33. LUFACT, LU Factorization of square matrices Skip Carter 34. Determinant of an LU factored matrix Skip Carter 35. Back-substitution solution for LU factored linear systems Skip Carter 36. Inverse of an LU factored matrix Skip Carter 37. Four methods for Direct Fourier Transforms Skip Carter 38. Radix-2 Fast Fourier Transform routines Skip Carter (5 versions one, two, and three butterflies, tabular, non-tabular) 39. Singular Value Decomposition Marcel Hendrix 40. Amoeba -- Multidimensional Simplex minimization of a function Marcel Hendrix 41. Sunday Quicksearch Leonard Morgenstern 42. Gauss probability function (ACM #209) Skip Carter 43. Regular spherical Bessel functions jn(x), n=0-9 Julian Noble 44. 16-bit Cyclic Redundancy Checksums Gordon Charlton 45. Simpsons rule and Romberg algorithm Quadrature routines Marcel Hendrix 46. Basic arithmetic and conversions for rational numbers Gordon Charlton 47. BIG -- Arithmetic on big signed magnitude numbers Len Zettel 48. Gauss-Jordan Elimination Marcel Hendrix 49. Levenberg-Marquardt nonlinear fit Marcel Hendrix 50. Fast Walsh Transform Skip Carter 51. Generation of Random number distributions Pierre Abbat 52. ISAAC Random number generator Pierre Abbat 53. Adaptive Integration using trapezoidal rule with Julian Noble Richardson extrapolation 54. Adaptive integration using 3 point Gauss-Legendre Julian Noble with Richardson extrapolation 55. Nonlinear transformation of series (SHANKS) (ACM #215) Skip Carter 56. Quarternions and matrices of rotation Pierre Abbat 57. GGUBS floating point random number generator Julian Noble 58. One-dimensional Monte-Carlo integration Julian Noble 59. Permutations and combinations Gordon Charlton 60. Complex numbers and functions J.Noble & D.N.Williams 61. Laguerre algorithm for polynomial roots Julian Noble 62. Error function Krishna Myneni 63. Roots of real quadratic Krishna Myneni Contributed but not yet reviewed: Faddeeva function Krishna Myneni Under review: System floating point parameters David N. Williams New code contributions and offers to help with reviewing would be welcomed. mailto: Charles Montgomery