gonzui

    1: /* k_rem_pio2f.c -- float version of k_rem_pio2.c
    2:  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
    3:  */
    4: 
    5: /*
    6:  * ====================================================
    7:  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
    8:  *
    9:  * Developed at SunPro, a Sun Microsystems, Inc. business.
   10:  * Permission to use, copy, modify, and distribute this
   11:  * software is freely granted, provided that this notice 
   12:  * is preserved.
   13:  * ====================================================
   14:  */
   15: 
   16: #include "math.h"
   17: #include "math_private.h"
   18: 
   19: /* In the float version, the input parameter x contains 8 bit
   20:    integers, not 24 bit integers.  113 bit precision is not supported.  */
   21: 
   22: static const int init_jk[] = {4,7,9}; /* initial value for jk */
   23: 
   24: static const float PIo2[] = {
   25:   1.5703125000e+00, /* 0x3fc90000 */
   26:   4.5776367188e-04, /* 0x39f00000 */
   27:   2.5987625122e-05, /* 0x37da0000 */
   28:   7.5437128544e-08, /* 0x33a20000 */
   29:   6.0026650317e-11, /* 0x2e840000 */
   30:   7.3896444519e-13, /* 0x2b500000 */
   31:   5.3845816694e-15, /* 0x27c20000 */
   32:   5.6378512969e-18, /* 0x22d00000 */
   33:   8.3009228831e-20, /* 0x1fc40000 */
   34:   3.2756352257e-22, /* 0x1bc60000 */
   35:   6.3331015649e-25, /* 0x17440000 */
   36: };
   37: 
   38: static const float                      
   39: zero   = 0.0,
   40: one    = 1.0,
   41: two8   =  2.5600000000e+02, /* 0x43800000 */
   42: twon8  =  3.9062500000e-03; /* 0x3b800000 */
   43: 
   44: int
   45: __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec,
   46:     const int32_t *ipio2) 
   47: {
   48:         int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
   49:         float z,fw,f[20],fq[20],q[20];
   50: 
   51:     /* initialize jk*/
   52:         jk = init_jk[prec];
   53:         jp = jk;
   54: 
   55:     /* determine jx,jv,q0, note that 3>q0 */
   56:         jx =  nx-1;
   57:         jv = (e0-3)/8; if(jv<0) jv=0;
   58:         q0 =  e0-8*(jv+1);
   59: 
   60:     /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
   61:         j = jv-jx; m = jx+jk;
   62:         for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
   63: 
   64:     /* compute q[0],q[1],...q[jk] */
   65:         for (i=0;i<=jk;i++) {
   66:             for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
   67:         }
   68: 
   69:         jz = jk;
   70: recompute:
   71:     /* distill q[] into iq[] reversingly */
   72:         for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
   73:             fw    =  (float)((int32_t)(twon8* z));
   74:             iq[i] =  (int32_t)(z-two8*fw);
   75:             z     =  q[j-1]+fw;
   76:         }
   77: 
   78:     /* compute n */
   79:         z  = scalbnf(z,q0);            /* actual value of z */
   80:         z -= (float)8.0*floorf(z*(float)0.125);        /* trim off integer >= 8 */
   81:         n  = (int32_t) z;
   82:         z -= (float)n;
   83:         ih = 0;
   84:         if(q0>0) {     /* need iq[jz-1] to determine n */
   85:             i  = (iq[jz-1]>>(8-q0)); n += i;
   86:             iq[jz-1] -= i<<(8-q0);
   87:             ih = iq[jz-1]>>(7-q0);
   88:         } 
   89:         else if(q0==0) ih = iq[jz-1]>>8;
   90:         else if(z>=(float)0.5) ih=2;
   91: 
   92:         if(ih>0) {     /* q > 0.5 */
   93:             n += 1; carry = 0;
   94:             for(i=0;i<jz ;i++) {       /* compute 1-q */
   95:                 j = iq[i];
   96:                 if(carry==0) {
   97:                     if(j!=0) {
   98:                         carry = 1; iq[i] = 0x100- j;
   99:                     }
  100:                 } else  iq[i] = 0xff - j;
  101:             }
  102:             if(q0>0) {         /* rare case: chance is 1 in 12 */
  103:                 switch(q0) {
  104:                 case 1:
  105:                   iq[jz-1] &= 0x7f; break;
  106:                case 2:
  107:                   iq[jz-1] &= 0x3f; break;
  108:                 }
  109:             }
  110:             if(ih==2) {
  111:                 z = one - z;
  112:                 if(carry!=0) z -= scalbnf(one,q0);
  113:             }
  114:         }
  115: 
  116:     /* check if recomputation is needed */
  117:         if(z==zero) {
  118:             j = 0;
  119:             for (i=jz-1;i>=jk;i--) j |= iq[i];
  120:             if(j==0) { /* need recomputation */
  121:                 for(k=1;iq[jk-k]==0;k++);   /* k = no. of terms needed */
  122: 
  123:                 for(i=jz+1;i<=jz+k;i++) {   /* add q[jz+1] to q[jz+k] */
  124:                     f[jx+i] = (float) ipio2[jv+i];
  125:                     for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
  126:                     q[i] = fw;
  127:                 }
  128:                 jz += k;
  129:                 goto recompute;
  130:             }
  131:         }
  132: 
  133:     /* chop off zero terms */
  134:         if(z==(float)0.0) {
  135:             jz -= 1; q0 -= 8;
  136:             while(iq[jz]==0) { jz--; q0-=8;}
  137:         } else { /* break z into 8-bit if necessary */
  138:             z = scalbnf(z,-q0);
  139:             if(z>=two8) { 
  140:                 fw = (float)((int32_t)(twon8*z));
  141:                 iq[jz] = (int32_t)(z-two8*fw);
  142:                 jz += 1; q0 += 8;
  143:                 iq[jz] = (int32_t) fw;
  144:             } else iq[jz] = (int32_t) z ;
  145:         }
  146: 
  147:     /* convert integer "bit" chunk to floating-point value */
  148:         fw = scalbnf(one,q0);
  149:         for(i=jz;i>=0;i--) {
  150:             q[i] = fw*(float)iq[i]; fw*=twon8;
  151:         }
  152: 
  153:     /* compute PIo2[0,...,jp]*q[jz,...,0] */
  154:         for(i=jz;i>=0;i--) {
  155:             for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
  156:             fq[jz-i] = fw;
  157:         }
  158: 
  159:     /* compress fq[] into y[] */
  160:         switch(prec) {
  161:             case 0:
  162:                 fw = 0.0;
  163:                 for (i=jz;i>=0;i--) fw += fq[i];
  164:                 y[0] = (ih==0)? fw: -fw; 
  165:                 break;
  166:             case 1:
  167:             case 2:
  168:                 fw = 0.0;
  169:                 for (i=jz;i>=0;i--) fw += fq[i]; 
  170:                 y[0] = (ih==0)? fw: -fw; 
  171:                 fw = fq[0]-fw;
  172:                 for (i=1;i<=jz;i++) fw += fq[i];
  173:                 y[1] = (ih==0)? fw: -fw; 
  174:                 break;
  175:             case 3:    /* painful */
  176:                 for (i=jz;i>0;i--) {
  177:                     fw      = fq[i-1]+fq[i]; 
  178:                     fq[i]  += fq[i-1]-fw;
  179:                     fq[i-1] = fw;
  180:                 }
  181:                 for (i=jz;i>1;i--) {
  182:                     fw      = fq[i-1]+fq[i]; 
  183:                     fq[i]  += fq[i-1]-fw;
  184:                     fq[i-1] = fw;
  185:                 }
  186:                 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; 
  187:                 if(ih==0) {
  188:                     y[0] =  fq[0]; y[1] =  fq[1]; y[2] =  fw;
  189:                 } else {
  190:                     y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
  191:                 }
  192:         }
  193:         return n&7;
  194: }