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[/] [or1k/] [trunk/] [newlib/] [newlib/] [libm/] [math/] [kf_rem_pio2.c] - Blame information for rev 1775

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1 39 lampret 
/* kf_rem_pio2.c -- float version of k_rem_pio2.c
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 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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 */
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/*
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 * ====================================================
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 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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 *
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 * Developed at SunPro, a Sun Microsystems, Inc. business.
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 * Permission to use, copy, modify, and distribute this
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 * software is freely granted, provided that this notice
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 * is preserved.
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 * ====================================================
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 */
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#include "fdlibm.h"
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/* In the float version, the input parameter x contains 8 bit
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   integers, not 24 bit integers.  113 bit precision is not supported.  */
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#ifdef __STDC__
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static const int init_jk[] = {4,7,9}; /* initial value for jk */
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#else
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static int init_jk[] = {4,7,9};
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#endif
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#ifdef __STDC__
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static const float PIo2[] = {
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#else
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static float PIo2[] = {
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#endif
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  1.5703125000e+00, /* 0x3fc90000 */
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  4.5776367188e-04, /* 0x39f00000 */
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  2.5987625122e-05, /* 0x37da0000 */
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  7.5437128544e-08, /* 0x33a20000 */
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  6.0026650317e-11, /* 0x2e840000 */
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  7.3896444519e-13, /* 0x2b500000 */
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  5.3845816694e-15, /* 0x27c20000 */
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  5.6378512969e-18, /* 0x22d00000 */
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  8.3009228831e-20, /* 0x1fc40000 */
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  3.2756352257e-22, /* 0x1bc60000 */
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  6.3331015649e-25, /* 0x17440000 */
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};
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#ifdef __STDC__
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static const float
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#else
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static float
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#endif
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zero   = 0.0,
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one    = 1.0,
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two8   =  2.5600000000e+02, /* 0x43800000 */
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twon8  =  3.9062500000e-03; /* 0x3b800000 */
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#ifdef __STDC__
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        int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const __int32_t *ipio2)
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#else
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        int __kernel_rem_pio2f(x,y,e0,nx,prec,ipio2)
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        float x[], y[]; int e0,nx,prec; __int32_t ipio2[];
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#endif
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{
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        __int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
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        float z,fw,f[20],fq[20],q[20];
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    /* initialize jk*/
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        jk = init_jk[prec];
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        jp = jk;
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    /* determine jx,jv,q0, note that 3>q0 */
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        jx =  nx-1;
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        jv = (e0-3)/8; if(jv<0) jv=0;
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        q0 =  e0-8*(jv+1);
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    /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
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        j = jv-jx; m = jx+jk;
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        for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
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    /* compute q[0],q[1],...q[jk] */
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        for (i=0;i<=jk;i++) {
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            for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
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        }
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        jz = jk;
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recompute:
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    /* distill q[] into iq[] reversingly */
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        for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
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            fw    =  (float)((__int32_t)(twon8* z));
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            iq[i] =  (__int32_t)(z-two8*fw);
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            z     =  q[j-1]+fw;
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        }
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    /* compute n */
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        z  = scalbnf(z,(int)q0);        /* actual value of z */
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        z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */
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        n  = (__int32_t) z;
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        z -= (float)n;
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        ih = 0;
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        if(q0>0) {       /* need iq[jz-1] to determine n */
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            i  = (iq[jz-1]>>(8-q0)); n += i;
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            iq[jz-1] -= i<<(8-q0);
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            ih = iq[jz-1]>>(7-q0);
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        }
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        else if(q0==0) ih = iq[jz-1]>>8;
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        else if(z>=(float)0.5) ih=2;
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        if(ih>0) {       /* q > 0.5 */
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            n += 1; carry = 0;
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            for(i=0;i<jz ;i++) { /* compute 1-q */
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                j = iq[i];
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                if(carry==0) {
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                    if(j!=0) {
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                        carry = 1; iq[i] = 0x100- j;
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                    }
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                } else  iq[i] = 0xff - j;
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            }
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            if(q0>0) {           /* rare case: chance is 1 in 12 */
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                switch(q0) {
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                case 1:
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                   iq[jz-1] &= 0x7f; break;
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                case 2:
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                   iq[jz-1] &= 0x3f; break;
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                }
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            }
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            if(ih==2) {
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                z = one - z;
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                if(carry!=0) z -= scalbnf(one,(int)q0);
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            }
128 
        }
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    /* check if recomputation is needed */
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        if(z==zero) {
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            j = 0;
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            for (i=jz-1;i>=jk;i--) j |= iq[i];
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            if(j==0) { /* need recomputation */
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                for(k=1;iq[jk-k]==0;k++);   /* k = no. of terms needed */
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                for(i=jz+1;i<=jz+k;i++) {   /* add q[jz+1] to q[jz+k] */
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                    f[jx+i] = (float) ipio2[jv+i];
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                    for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
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                    q[i] = fw;
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                }
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                jz += k;
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                goto recompute;
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            }
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        }
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    /* chop off zero terms */
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        if(z==(float)0.0) {
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            jz -= 1; q0 -= 8;
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            while(iq[jz]==0) { jz--; q0-=8;}
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        } else { /* break z into 8-bit if necessary */
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            z = scalbnf(z,-(int)q0);
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            if(z>=two8) {
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                fw = (float)((__int32_t)(twon8*z));
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                iq[jz] = (__int32_t)(z-two8*fw);
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                jz += 1; q0 += 8;
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                iq[jz] = (__int32_t) fw;
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            } else iq[jz] = (__int32_t) z ;
159 
        }
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    /* convert integer "bit" chunk to floating-point value */
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        fw = scalbnf(one,(int)q0);
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        for(i=jz;i>=0;i--) {
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            q[i] = fw*(float)iq[i]; fw*=twon8;
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        }
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167 
    /* compute PIo2[0,...,jp]*q[jz,...,0] */
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        for(i=jz;i>=0;i--) {
169 
            for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
170 
            fq[jz-i] = fw;
171 
        }
172 
 
173 
    /* compress fq[] into y[] */
174 
        switch(prec) {
175 
            case 0:
176 
                fw = 0.0;
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                for (i=jz;i>=0;i--) fw += fq[i];
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                y[0] = (ih==0)? fw: -fw;
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                break;
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            case 1:
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            case 2:
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                fw = 0.0;
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                for (i=jz;i>=0;i--) fw += fq[i];
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                y[0] = (ih==0)? fw: -fw;
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                fw = fq[0]-fw;
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                for (i=1;i<=jz;i++) fw += fq[i];
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                y[1] = (ih==0)? fw: -fw;
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                break;
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            case 3:     /* painful */
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                for (i=jz;i>0;i--) {
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                    fw      = fq[i-1]+fq[i];
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                    fq[i]  += fq[i-1]-fw;
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                    fq[i-1] = fw;
194 
                }
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                for (i=jz;i>1;i--) {
196 
                    fw      = fq[i-1]+fq[i];
197 
                    fq[i]  += fq[i-1]-fw;
198 
                    fq[i-1] = fw;
199 
                }
200 
                for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
201 
                if(ih==0) {
202 
                    y[0] =  fq[0]; y[1] =  fq[1]; y[2] =  fw;
203 
                } else {
204 
                    y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
205 
                }
206 
        }
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        return n&7;
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}

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