/*******************************************************
*       Program to demonstrate arcsine recursion       *
* ---------------------------------------------------- *
*   Reference: BASIC Scientific Subroutines, Vol. II   *
*   By F.R. Ruckdeschel, BYTE/McGRAWW-HILL, 1981 [1].  *
*                                                      *
*                C++ Version by J.-P. Moreau, Paris.   *
* ---------------------------------------------------- *
* 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     *
*                                                      *
*******************************************************/
#include <stdio.h>
#include <math.h>

double  e,x,y;
int     i, m;


/************************************************
*       Arcsin(x) recursion subroutine          *
* --------------------------------------------- *
* Input is x (-1<x<1), output is y=arcsin(x),   *
* convergence criteria is e.                    *
* --------------------------------------------- *
* Reference: Computational Analysis by Henrici. *
************************************************/
void Arcsin()  {
// Labels used: e100, e200, e300, fin
  double pi,u0,u1,u2;
  m=0; pi = 4*atan(1);
  // Guard against failure
  if (e <= 0) goto fin;
  if (x != 0) goto e100;
  y=0.0;
  goto fin;
  // Check range
e100: if (fabs(x)>1) goto e300;
  u0=x*sqrt(1.0-x*x);
  u1=x;
e200: u2=u1*sqrt(2.0*u1/(u1+u0));
  y=u2;
  m=m+1;
  if (fabs(u2-u1)<e) goto fin;
  u0=u1; u1=u2;
  goto e200;
e300: if (fabs(x-1) < 1e-10) y=pi/2.0;
fin: ; }


void main()  {
  e=1e-8;
  printf(" X       ARCSIN(X)       STEPS        ERROR    \n");
  printf("-----------------------------------------------\n");
  x=0.0;
  for (i=1; i<22; i++) {
    Arcsin();
    printf("%4.2f     %9.7f        %2d      %13.10f\n",x,y,m,sin(y)-x);
    x += 0.05;
  }
}


// End of file Arcsin.cpp