/*  txchser.c    CCMATH mathematics library source code.
 *
 *  Copyright (C)  2000   Daniel A. Atkinson    All rights reserved.
 *  This code may be redistributed under the terms of the GNU library
 *  public license (LGPL). ( See the lgpl.license file for details.)
 * ------------------------------------------------------------------------
 */
/*
    Test:  xchcof  xevtch

    Uses:  xdiv  xmul  xadd  inttox  xpr2  xtodub  prxpr
           xsin  xsqrt  xex

    Input parameter:  m -> integer: maximum degree of
                                    Tchebycheff polynominal
*/
#define XMATH 1
#include "ccmath.h"
#include <math.h>
struct xpr c[20];
struct xpr isin();
void main(int na,char **av)
{ struct xpr z,dz,u,h; int j,m;
  struct xpr xevtch(); double y;
  if(na!=2){ printf("para: ncof\n"); exit(-1);}
  printf("     Test of Tchebycheff Expansion\n");
  m=atoi(*++av);

/* compute Tchebycheff expansion coefficients */
  xchcof(c,m,isin);

  printf(" series coefficients\n");
  for(j=0; j<=m ;){
    printf(" %2d  ",j); prxpr(c[j++],30); }
  c[0]=xpr2(c[0],-1);
  z=zero; dz=xdiv(one,inttox(10));
  printf("     z          sin(z)             Tchebycheff series\n");
  for(j=0; j<16 ;++j,z=xadd(z,dz,0)){

/* scale expansion variables */
    h=xdiv(z,pi2); u=xadd(xpr2(xmul(h,h),1),one,1);

/* evaluate Tchebycheff series for sin(x) */
    u=xmul(h,xevtch(u,c,m));

    y=xtodub(z);
    printf(" %6.2f %17.15f  ",y,sin(y)); prxpr(u,25);
   }
}

/* evaluate sin((pi/2)*y)/y with y=sqrt((1+z)/2) */
struct xpr isin(z)
struct xpr z;
{ z=xsqrt(xpr2(xadd(z,one,0),-1));
  if(xex(&z)== -16383) return pi2;
  else return xdiv(xsin(xmul(pi2,z)),z);
}
/*  Test output

     Test of Tchebycheff Expansion
 series coefficients
  0    2.552557924804531760415273944172e+0
  1   -2.852615691810360095702940903036e-1
  2    9.118016006651802497767922609504e-3
  3   -1.365875135419666724364765329542e-4
  4    1.184961857661690108290062477114e-6
  5   -6.702791603827441236048376155605e-9
  6    2.667278599019659364897350084318e-11
  7   -7.872922121718594384361661445215e-14
  8    1.792294735924872741814445918645e-16
  9   -3.242712736631485672296795646963e-19
 10    4.774743247331700352283058230130e-22
 11   -5.833273589373253665487745391160e-25
 12    6.008135424889910153613249185946e-28
     z          sin(z)             Tchebycheff series
   0.00 0.000000000000000    0.0000000000000000000000000e+0
   0.10 0.099833416646828    9.9833416646828152306814198e-2
   0.20 0.198669330795061    1.9866933079506121545941263e-1
   0.30 0.295520206661340    2.9552020666133957510532075e-1
   0.40 0.389418342308650    3.8941834230865049166631176e-1
   0.50 0.479425538604203    4.7942553860420300027328794e-1
   0.60 0.564642473395035    5.6464247339503535720094545e-1
   0.70 0.644217687237691    6.4421768723769105367261435e-1
   0.80 0.717356090899523    7.1735609089952276162717461e-1
   0.90 0.783326909627483    7.8332690962748338846138232e-1
   1.00 0.841470984807896    8.4147098480789650665250232e-1
   1.10 0.891207360061435    8.9120736006143533995180258e-1
   1.20 0.932039085967226    9.3203908596722634967013444e-1
   1.30 0.963558185417193    9.6355818541719296470134863e-1
   1.40 0.985449729988460    9.8544972998846018065947458e-1
   1.50 0.997494986604054    9.9749498660405443094172337e-1
*/