Continued fraction math library

Cfs is a FreeBasic library for computing with continued fractions.
Unpack to the base directory of your FreeBasic installation.

The Cf length (thus the maximum precision) is fixed at compile time,
also the number of mpz state registers (a b c d) / (e f g h).
Both are set in include file \modules\cfr_lib.bi
The same file laconically doubles as library documentation.

Contents of the Cfs packet

Makefiles are in the base directory

Windows

fbc_path.bat
make_cfr_dll.bat
1_make_cf_demos.bat
2_run_all_demos.bat

Linux

Requires GMP library libgmp10 and developers tools libgmp-dev to be installed.

make_cfr_so.sh
1_make_cf_demos.sh
2_installso.sh
3_run_all_demos.sh

A few additional scripts are in Cfs\library\more\

Cfs\library\

cfr_arith.bas
  R. W. Gosper's continued fraction arithmetic realized in FreeBasic

cfr_math.bas
  Generate algebraic and transcendental functions using cfr_arith

Cfs\modules\bin\

libgmp-32.dll
  GMP dynamic link library, 32-bit, build 6.2.1

libgmp-64.dll
  GMP dynamic link library, 64-bit, build 6.2.1

Cfs\modules\

cfr_lib.bi
  Include file for continued fraction arithmetic

gmp_short.bi
  Include file for the GMP functions called by cfr

cf_first.bas
  First steps: input conversion, convergents,
  building Cf power and cube root functions

cf_Gosper.bas
  Knuth exercises and Gosper's Appendix 2,
  Gosper's numbers in HAKMEM 239, items 97-101
 (Compare the code with the papers to get acquainted with the lib.)

cf_constants.bas
  Generate mathematical constants from continued fractions:
    sin(1 degree)
    i to the power i
    Omega (w * exp(w) = 1)
    Euler's constant
    ln(2)
    Gauss' constant
    Catalan's constant
    Apéry's constant zeta(3)
    gamma(1/4)

cf_ratarg.bas
  Applications with (Gaussian) rational arguments:
    sin((x + yi) / w)
    exp(pi * (x + yi) / w)
    principal value of Log(x + yi)
    complete elliptic integrals with rational parameter m
    Lambert's function: solve Cf_w * exp(Cf_w) = x / y
    demo run for functions with rational arguments

cf_trans.bas
  Demo run for functions with Cf arguments in cfr_math

cf_polroot
  Continued fraction expansion of real polynomial roots

cf_trees.bas
  P. J. Potts' expression trees for transcendental functions
  Iterating the logistic map

Cfs\workdir\

  Will hold logfiles

 

Copyright:

        (C) 2023 Djoser.j.Spacher, All rights reserved

License:

        GNU General Public License, GPL

      ______________________________________________

HAKMEM paper (Gosper on continued fractions)

His 'Appendix 2' on continued fraction arithmetic

Potts' PhD Thesis 'Exact Real Arithmetic...' (pdf)

The FreeBASIC compiler

Windows 32-bit and 64-bit ports of the GMP library