'********************************************************
'*       Program to demonstrate arcsine recursion       *
'* ---------------------------------------------------- *
'*   Reference: BASIC Scientific Subroutines, Vol. II   *
'*   by F.R. Ruckdeschel, BYTE/McGRAWW-HILL, 1981 [1].  *
'*                                                      *
'* ---------------------------------------------------- *
'* SAMPLE RUN:                                          *
'*                                                      *
'*   X       ARCSIN(X)       STEPS        ERROR         *
'*  -----------------------------------------------     *
'*  0.00     0.0000000         0       0.0000000000     *
'*  0.05     0.0500209         7      -0.0000000013     *
'*  0.10     0.1001674         8      -0.0000000025     *
'*  0.15     0.1505683         9      -0.0000000021     *
'*  0.20     0.2013579        10      -0.0000000013     *
'*  0.25     0.2526803        10      -0.0000000025     *
'*  0.30     0.3046927        11      -0.0000000011     *
'*  0.35     0.3575711        11      -0.0000000017     *
'*  0.40     0.4115168        11      -0.0000000025     *
'*  0.45     0.4667653        12      -0.0000000009     *  
'*  0.50     0.5235988        12      -0.0000000012     *
'*  0.55     0.5823642        12      -0.0000000016     *
'*  0.60     0.6435011        12      -0.0000000021     *
'*  0.65     0.7075844        13      -0.0000000007     *
'*  0.70     0.7753975        13      -0.0000000008     *
'*  0.75     0.8480621        13      -0.0000000010     *
'*  0.80     0.9272952        13      -0.0000000012     *
'*  0.85     1.0159853        13      -0.0000000014     *
'*  0.90     1.1197695        14      -0.0000000004     *
'*  0.95     1.2532359        14      -0.0000000004     *
'*  1.00     1.5707963         0       0.0000000000     *
'*                                                      *
'********************************************************
'*********
defint i-n
defdbl a-h,o-z
cls
print
e=1e-8
print " X       ARCSIN(X)       STEPS        ERROR    "
print "-----------------------------------------------"
x=0
for i=1 to 21
  gosub 1000
  print using "#.##     #.#######        ##      ##.##########"; x; y; m; sin(y)-x
  x=x+0.05
next i
print
end

'************************************************
'*       Arcsin(x) recursion subroutine         *
'* Input is x (-1<x<1), output is y=arcsin(x),  *
'* convergence criteria is e.                   *
'* -------------------------------------------- *
'* Reference: Computational Analysis by Henrici *
'************************************************
1000 m=0 : pi=4#*ATN(1#)
  'Guard against failure
  if e<=0 then return
  if x<>0 then goto 1100
  y=0
  return
  'Check range
1100 if abs(x)>1 then goto 1300
  u0=x*sqr(1#-x*x)
  u1=x
1200 u2=u1*sqr(2#*u1/(u1+u0))
  y=u2
  m=m+1
  if abs(u2-u1)<e then return
  u0=u1:u1=u2
  goto 1200
1300 if abs(x-1) < 1e-10 then
    y=pi/2#
  end if
return

'End of file Arcsin.bas