/home/jaouen/pok_official/pok/trunk/libpok/libm/k_rem_pio2f.c

/*
 *                               POK header
 * 
 * The following file is a part of the POK project. Any modification should
 * made according to the POK licence. You CANNOT use this file or a part of
 * this file is this part of a file for your own project
 *
 * For more information on the POK licence, please see our LICENCE FILE
 *
 * Please follow the coding guidelines described in doc/CODING_GUIDELINES
 *
 *                                      Copyright (c) 2007-2009 POK team 
 *
 * Created by julien on Sat Jan 31 20:12:07 2009 
 */

/* 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.
 * ====================================================
 */

#ifdef POK_NEEDS_LIBMATH

#include <libm.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 int *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;
}

#endif