Back to index

glibc  2.9
Functions | Variables
k_rem_pio2.c File Reference
#include "math.h"
#include "math_private.h"

Go to the source code of this file.

Functions

int __kernel_rem_pio2 (x, y, int e0, int nx, int prec, ipio2)

Variables

static int init_jk [] = {2,3,4,6}
static double PIo2 []
static double zero = 0.0
static double one = 1.0
static double two24 = 1.67772160000000000000e+07
static double twon24 = 5.96046447753906250000e-08

Function Documentation

int __kernel_rem_pio2 ( x  ,
y  ,
int  e0,
int  nx,
int  prec,
ipio2   
)

Definition at line 170 of file k_rem_pio2.c.

{
       int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
       double z,fw,f[20],fq[20],q[20];

    /* initialize jk*/
       jk = init_jk[prec];
       jp = jk;

    /* determine jx,jv,q0, note that 3>q0 */
       jx =  nx-1;
       jv = (e0-3)/24; if(jv<0) jv=0;
       q0 =  e0-24*(jv+1);

    /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
       j = jv-jx; m = jx+jk;
       for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j];

    /* compute q[0],q[1],...q[jk] */
       for (i=0;i<=jk;i++) {
           for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
       }

       jz = jk;
recompute:
    /* distill q[] into iq[] reversingly */
       for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
           fw    =  (double)((int32_t)(twon24* z));
           iq[i] =  (int32_t)(z-two24*fw);
           z     =  q[j-1]+fw;
       }

    /* compute n */
       z  = __scalbn(z,q0);        /* actual value of z */
       z -= 8.0*__floor(z*0.125);         /* trim off integer >= 8 */
       n  = (int32_t) z;
       z -= (double)n;
       ih = 0;
       if(q0>0) {    /* need iq[jz-1] to determine n */
           i  = (iq[jz-1]>>(24-q0)); n += i;
           iq[jz-1] -= i<<(24-q0);
           ih = iq[jz-1]>>(23-q0);
       }
       else if(q0==0) ih = iq[jz-1]>>23;
       else if(z>=0.5) ih=2;

       if(ih>0) {    /* q > 0.5 */
           n += 1; carry = 0;
           for(i=0;i<jz ;i++) {    /* compute 1-q */
              j = iq[i];
              if(carry==0) {
                  if(j!=0) {
                     carry = 1; iq[i] = 0x1000000- j;
                  }
              } else  iq[i] = 0xffffff - j;
           }
           if(q0>0) {              /* rare case: chance is 1 in 12 */
               switch(q0) {
               case 1:
                 iq[jz-1] &= 0x7fffff; break;
              case 2:
                 iq[jz-1] &= 0x3fffff; break;
               }
           }
           if(ih==2) {
              z = one - z;
              if(carry!=0) z -= __scalbn(one,q0);
           }
       }

    /* check if recomputation is needed */
       if(z==zero) {
           j = 0;
           for (i=jz-1;i>=jk;i--) j |= iq[i];
           if(j==0) { /* need recomputation */
              for(k=1;iq[jk-k]==0;k++);   /* k = no. of terms needed */

              for(i=jz+1;i<=jz+k;i++) {   /* add q[jz+1] to q[jz+k] */
                  f[jx+i] = (double) ipio2[jv+i];
                  for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
                  q[i] = fw;
              }
              jz += k;
              goto recompute;
           }
       }

    /* chop off zero terms */
       if(z==0.0) {
           jz -= 1; q0 -= 24;
           while(iq[jz]==0) { jz--; q0-=24;}
       } else { /* break z into 24-bit if necessary */
           z = __scalbn(z,-q0);
           if(z>=two24) {
              fw = (double)((int32_t)(twon24*z));
              iq[jz] = (int32_t)(z-two24*fw);
              jz += 1; q0 += 24;
              iq[jz] = (int32_t) fw;
           } else iq[jz] = (int32_t) z ;
       }

    /* convert integer "bit" chunk to floating-point value */
       fw = __scalbn(one,q0);
       for(i=jz;i>=0;i--) {
           q[i] = fw*(double)iq[i]; fw*=twon24;
       }

    /* compute PIo2[0,...,jp]*q[jz,...,0] */
       for(i=jz;i>=0;i--) {
           for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
           fq[jz-i] = fw;
       }

    /* compress fq[] into y[] */
       switch(prec) {
           case 0:
              fw = 0.0;
              for (i=jz;i>=0;i--) fw += fq[i];
              y[0] = (ih==0)? fw: -fw;
              break;
           case 1:
           case 2:
              fw = 0.0;
              for (i=jz;i>=0;i--) fw += fq[i];
              y[0] = (ih==0)? fw: -fw;
              fw = fq[0]-fw;
              for (i=1;i<=jz;i++) fw += fq[i];
              y[1] = (ih==0)? fw: -fw;
              break;
           case 3:   /* painful */
              for (i=jz;i>0;i--) {
                  fw      = fq[i-1]+fq[i];
                  fq[i]  += fq[i-1]-fw;
                  fq[i-1] = fw;
              }
              for (i=jz;i>1;i--) {
                  fw      = fq[i-1]+fq[i];
                  fq[i]  += fq[i-1]-fw;
                  fq[i-1] = fw;
              }
              for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
              if(ih==0) {
                  y[0] =  fq[0]; y[1] =  fq[1]; y[2] =  fw;
              } else {
                  y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
              }
       }
       return n&7;
}

Here is the call graph for this function:


Variable Documentation

int init_jk[] = {2,3,4,6} [static]

Definition at line 139 of file k_rem_pio2.c.

double one = 1.0 [static]

Definition at line 163 of file k_rem_pio2.c.

double PIo2[] [static]
Initial value:
 {

  1.57079625129699707031e+00, 
  7.54978941586159635335e-08, 
  5.39030252995776476554e-15, 
  3.28200341580791294123e-22, 
  1.27065575308067607349e-29, 
  1.22933308981111328932e-36, 
  2.73370053816464559624e-44, 
  2.16741683877804819444e-51, 
}

Definition at line 145 of file k_rem_pio2.c.

double two24 = 1.67772160000000000000e+07 [static]

Definition at line 164 of file k_rem_pio2.c.

double twon24 = 5.96046447753906250000e-08 [static]

Definition at line 165 of file k_rem_pio2.c.

double zero = 0.0 [static]

Definition at line 162 of file k_rem_pio2.c.