cvw/pipelined/srt/stine/srt4div.c

#include "disp.h"
#include <math.h>

// QSLC is for division by recuerrence for
// r=4 using a CPA - See Table 5.9 EL
int qslc (double prem, double d) {

  int q;

  // For Debugging
  printf("d  --> %lg\n", d);
  printf("rw --> %lg\n", prem);
  
  if ((d>=8.0)&&(d<9.0)) {
    if (prem>=6.0)
       q = 2;
    else if (prem>=2.0)
      q = 1;
    else if (prem>=-2.0)
      q = 0;
    else if (prem >= -6)
      q = -1;
    else 
      q = -2;
    return q;
  }

  if ((d>=9.0)&&(d<10.0)) {
    if (prem>=7)
       q = 2;
    else if (prem>=2.0)
      q = 1;
    else if (prem>=-2.0)
      q = 0;
    else if (prem >= 7.0)
      q = -1;
    else 
      q = -2;
    return q;
  }

  if ((d>=10.0)&&(d<11.0)) {
    if (prem>=8.0)
       q = 2;
    else if (prem>=2.0)
      q = 1;
    else if (prem>=-2.0)
      q = 0;
    else if (prem >= -8.0)
      q = -1;
    else 
      q = -2;
    return q;
  }

  if ((d>=11.0)&&(d<12.0)) {
    if (prem>=8.0)
       q = 2;
    else if (prem>=2.0)
      q = 1;
    else if (prem>=-2.0)
      q = 0;
    else if (prem >= -8.0)
      q = -1;
    else 
      q = -2;
    return q;
  }

  if ((d>=12.0)&&(d<13.0)) {
    if (prem>=10.0)
       q = 2;
    else if (prem>=4.0)
      q = 1;
    else if (prem>=-4.0)
      q = 0;
    else if (prem >= -10.0)
      q = -1;
    else 
      q = -2;
    return q;
  }

  if ((d>=13.0)&&(d<14.0)) {
    if (prem>=10.0)
       q = 2;
    else if (prem>=4.0)
      q = 1;
    else if (prem>=-4.0)
      q = 0;
    else if (prem >= -10.0)
      q = -1;
    else 
      q = -2;
    return q;
  }

  if ((d>=14.0)&&(d<15.0)) {
    if (prem>=10.0)
       q = 2;
    else if (prem>=4.0)
      q = 1;
    else if (prem>=-4.0)
      q = 0;
    else if (prem >= -10.0)
      q = -1;
    else 
      q = -2;
    return q;
  }

  if ((d>=15.0)&&(d<16.0)) {
    if (prem>=12.0)
       q = 2;
    else if (prem>=4.0)
      q = 1;
    else if (prem>=-4.0)
      q = 0;
    else if (prem >= -12.0)
      q = -1;
    else 
      q = -2;
    return q;
  }

}


/*
 This routine performs a radix-4 SRT division 
 algorithm.  The user inputs the numerator, the denominator, 
 and the number of iterations. It assumes that 0.5 <= D < 1.
        
*/

int main(int argc, char* argv[]) {

   double P, N, D, Q, RQ, RD, RREM, scale;   
   int q;
   int num_iter, i;
   int prec;
   int radix = 4;
   
   if (argc < 5) {
      fprintf(stderr,
	      "Usage: %s numerator denominator num_iterations prec\n", 
	      argv[0]);
      exit(1);
   }
   sscanf(argv[1],"%lg", &N);
   sscanf(argv[2],"%lg", &D);
   sscanf(argv[3],"%d", &num_iter);
   sscanf(argv[4],"%d", &prec);
   // Round to precision
   N = rne(N, prec);
   D = rne(D, prec);
   printf("N = ");
   disp_bin(N, 3, prec, stdout);
   printf("\n");
   printf("D = ");
   disp_bin(D, 3, prec, stdout);
   printf("\n");

   Q = 0;
   P = N * pow(2.0, -log2(radix));
   printf("N = %lg, D = %lg, N/D = %lg, num_iter = %d \n\n", 
	  N, D, N/D, num_iter); 
   for (scale = 1, i = 0; i < num_iter; i++) {
     // Shift by r
     scale = scale * pow(2.0, -log2(radix));
     // (4*P)*8 because of footnote in Table 5.9, page 296 EL
     // i.e., real value = shown value / 8
     // D*16 since we use 4 bits of D (1 bit known)
     q = qslc(flr((radix * P) * 8, 3), D*16);
     printf("4*W[n] = ");
     disp_bin(radix*P, 3, prec, stdout);
     printf("\n");
     printf("q*D = ");      
     disp_bin(q*D, 3, prec, stdout);
     printf("\n");
     printf("W[n+1] = ");            
     disp_bin(P ,3, prec, stdout);
     printf("\n");
     // Recurrence
     P = radix * P - q * D;
     // OTFC
     Q = Q + q * scale;
     printf("i = %d, q = %d, Q = %1.18lf, W = %1.18lf\n", i, q, Q, P); 
     printf("i = %d, q = %d", i, q);
     printf(", Q = ");
     disp_bin(Q, 3, prec, stdout);
     printf(", W = ");
     disp_bin(P, 3, prec, stdout);
     printf("\n\n");
   }
   // Is shifted partial remainder negative?
   if (P < 0) {
     Q = Q - pow(2.0, -prec);
     P = P + D;
     printf("\nCorrecting Negative Remainder\n"); 
     printf("Q = %1.18lf, W = %1.18lf\n", Q, P); 
     printf("Q = ");
     disp_bin(Q, 3, prec, stdout);
     printf(", W = ");
     disp_bin(P, 3, prec, stdout);
     printf("\n");
   }

   // Output Results
   RQ = flr(N/D, prec);
   // Since q_{computed} = q / radix, multiply by radix
   RD = Q * radix;
   printf("true = %1.18lf, computed = %1.18lf, \n", RQ, RD);
   printf("true = ");
   disp_bin(RQ, 3, prec, stdout);
   printf(", computed = ");
   disp_bin(RD, 3, prec, stdout);
   printf("\n\n");
   printf("REM = %1.18lf \n", P);
   printf("REM = ");
   disp_bin(P, 3, prec, stdout);
   printf("\n\n");

   return 0;

}