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glibc  2.9
Functions | Variables
k_rem_pio2f.c File Reference
#include "math.h"
#include "math_private.h"

Go to the source code of this file.

Functions

int __kernel_rem_pio2f (x, y, int e0, int nx, int prec, ipio2)

Variables

static int init_jk [] = {4,7,9}
static float PIo2 []
static float zero = 0.0
static float one = 1.0
static float two8 = 2.5600000000e+02
static float twon8 = 3.9062500000e-03

Function Documentation

int __kernel_rem_pio2f ( x  ,
y  ,
int  e0,
int  nx,
int  prec,
ipio2   
)

Definition at line 63 of file k_rem_pio2f.c.

{
       int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
       float 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)/8; if(jv<0) jv=0;
       q0 =  e0-8*(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 : (float) 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    =  (float)((int32_t)(twon8* z));
           iq[i] =  (int32_t)(z-two8*fw);
           z     =  q[j-1]+fw;
       }

    /* compute n */
       z  = __scalbnf(z,q0);              /* actual value of z */
       z -= (float)8.0*__floorf(z*(float)0.125); /* trim off integer >= 8 */
       n  = (int32_t) z;
       z -= (float)n;
       ih = 0;
       if(q0>0) {    /* need iq[jz-1] to determine n */
           i  = (iq[jz-1]>>(8-q0)); n += i;
           iq[jz-1] -= i<<(8-q0);
           ih = iq[jz-1]>>(7-q0);
       } 
       else if(q0==0) ih = iq[jz-1]>>8;
       else if(z>=(float)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] = 0x100- j;
                  }
              } else  iq[i] = 0xff - j;
           }
           if(q0>0) {              /* rare case: chance is 1 in 12 */
               switch(q0) {
               case 1:
                 iq[jz-1] &= 0x7f; break;
              case 2:
                 iq[jz-1] &= 0x3f; break;
               }
           }
           if(ih==2) {
              z = one - z;
              if(carry!=0) z -= __scalbnf(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] = (float) 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==(float)0.0) {
           jz -= 1; q0 -= 8;
           while(iq[jz]==0) { jz--; q0-=8;}
       } else { /* break z into 8-bit if necessary */
           z = __scalbnf(z,-q0);
           if(z>=two8) { 
              fw = (float)((int32_t)(twon8*z));
              iq[jz] = (int32_t)(z-two8*fw);
              jz += 1; q0 += 8;
              iq[jz] = (int32_t) fw;
           } else iq[jz] = (int32_t) z ;
       }

    /* convert integer "bit" chunk to floating-point value */
       fw = __scalbnf(one,q0);
       for(i=jz;i>=0;i--) {
           q[i] = fw*(float)iq[i]; fw*=twon8;
       }

    /* 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;
}

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Variable Documentation

int init_jk[] = {4,7,9} [static]

Definition at line 29 of file k_rem_pio2f.c.

float one = 1.0 [static]

Definition at line 56 of file k_rem_pio2f.c.

float PIo2[] [static]
Initial value:
 {

  1.5703125000e+00, 
  4.5776367188e-04, 
  2.5987625122e-05, 
  7.5437128544e-08, 
  6.0026650317e-11, 
  7.3896444519e-13, 
  5.3845816694e-15, 
  5.6378512969e-18, 
  8.3009228831e-20, 
  3.2756352257e-22, 
  6.3331015649e-25, 
}

Definition at line 35 of file k_rem_pio2f.c.

float two8 = 2.5600000000e+02 [static]

Definition at line 57 of file k_rem_pio2f.c.

float twon8 = 3.9062500000e-03 [static]

Definition at line 58 of file k_rem_pio2f.c.

float zero = 0.0 [static]

Definition at line 55 of file k_rem_pio2f.c.