k_rem_pio2f.c

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/* k_rem_pio2f.c -- float version of k_rem_pio2.c
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

#include "math.h"
#include "math_private.h"

/* In the float version, the input parameter x contains 8 bit
   integers, not 24 bit integers.  113 bit precision is not supported.  */

static const int init_jk[] = {4,7,9}; /* initial value for jk */

static const float PIo2[] = {
  1.5703125000e+00, /* 0x3fc90000 */
  4.5776367188e-04, /* 0x39f00000 */
  2.5987625122e-05, /* 0x37da0000 */
  7.5437128544e-08, /* 0x33a20000 */
  6.0026650317e-11, /* 0x2e840000 */
  7.3896444519e-13, /* 0x2b500000 */
  5.3845816694e-15, /* 0x27c20000 */
  5.6378512969e-18, /* 0x22d00000 */
  8.3009228831e-20, /* 0x1fc40000 */
  3.2756352257e-22, /* 0x1bc60000 */
  6.3331015649e-25, /* 0x17440000 */
};

static const float          
zero   = 0.0,
one    = 1.0,
two8   =  2.5600000000e+02, /* 0x43800000 */
twon8  =  3.9062500000e-03; /* 0x3b800000 */

int
__kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec,
    const int32_t *ipio2) 
{
    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;
}