compiler/mlib/k_rem_pio2f.c

   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 #ifndef lint
  17 static char rcsid[] = "$FreeBSD: src/lib/msun/src/k_rem_pio2f.c,v 1.8 2005/10/11 07:56:05 bde Exp $";
  18 #endif
  19
  20 #include "math.h"
  21 #include "math_private.h"
  22
  23 /* In the float version, the input parameter x contains 8 bit
  24    integers, not 24 bit integers.  113 bit precision is not supported.  */
  25
  26 static const int init_jk[] = {4,7,9}; /* initial value for jk */
  27
  28 static const float PIo2[] = {
  29   1.5703125000e+00, /* 0x3fc90000 */
  30   4.5776367188e-04, /* 0x39f00000 */
  31   2.5987625122e-05, /* 0x37da0000 */
  32   7.5437128544e-08, /* 0x33a20000 */
  33   6.0026650317e-11, /* 0x2e840000 */
  34   7.3896444519e-13, /* 0x2b500000 */
  35   5.3845816694e-15, /* 0x27c20000 */
  36   5.6378512969e-18, /* 0x22d00000 */
  37   8.3009228831e-20, /* 0x1fc40000 */
  38   3.2756352257e-22, /* 0x1bc60000 */
  39   6.3331015649e-25, /* 0x17440000 */
  40 };
  41
  42 static const float
  43 zero   = 0.0,
  44 one    = 1.0,
  45 two8   =  2.5600000000e+02, /* 0x43800000 */
  46 twon8  =  3.9062500000e-03; /* 0x3b800000 */
  47
  48         int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2)
  49 {
  50         int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
  51         float z,fw,f[20],fq[20],q[20];
  52
  53     /* initialize jk*/
  54         jk = init_jk[prec];
  55         jp = jk;
  56
  57     /* determine jx,jv,q0, note that 3>q0 */
  58         jx =  nx-1;
  59         jv = (e0-3)/8; if(jv<0) jv=0;
  60         q0 =  e0-8*(jv+1);
  61
  62     /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
  63         j = jv-jx; m = jx+jk;
  64         for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
  65
  66     /* compute q[0],q[1],...q[jk] */
  67         for (i=0;i<=jk;i++) {
  68             for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
  69         }
  70
  71         jz = jk;
  72 recompute:
  73     /* distill q[] into iq[] reversingly */
  74         for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
  75             fw    =  (float)((int32_t)(twon8* z));
  76             iq[i] =  (int32_t)(z-two8*fw);
  77             z     =  q[j-1]+fw;
  78         }
  79
  80     /* compute n */
  81         z  = scalbnf(z,q0);             /* actual value of z */
  82         z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */
  83         n  = (int32_t) z;
  84         z -= (float)n;
  85         ih = 0;
  86         if(q0>0) {      /* need iq[jz-1] to determine n */
  87             i  = (iq[jz-1]>>(8-q0)); n += i;
  88             iq[jz-1] -= i<<(8-q0);
  89             ih = iq[jz-1]>>(7-q0);
  90         }
  91         else if(q0==0) ih = iq[jz-1]>>7;
  92         else if(z>=(float)0.5) ih=2;
  93
  94         if(ih>0) {      /* q > 0.5 */
  95             n += 1; carry = 0;
  96             for(i=0;i<jz ;i++) {        /* compute 1-q */
  97                 j = iq[i];
  98                 if(carry==0) {
  99                     if(j!=0) {
 100                         carry = 1; iq[i] = 0x100- j;
 101                     }
 102                 } else  iq[i] = 0xff - j;
 103             }
 104             if(q0>0) {          /* rare case: chance is 1 in 12 */
 105                 switch(q0) {
 106                 case 1:
 107                    iq[jz-1] &= 0x7f; break;
 108                 case 2:
 109                    iq[jz-1] &= 0x3f; break;
 110                 }
 111             }
 112             if(ih==2) {
 113                 z = one - z;
 114                 if(carry!=0) z -= scalbnf(one,q0);
 115             }
 116         }
 117
 118     /* check if recomputation is needed */
 119         if(z==zero) {
 120             j = 0;
 121             for (i=jz-1;i>=jk;i--) j |= iq[i];
 122             if(j==0) { /* need recomputation */
 123                 for(k=1;iq[jk-k]==0;k++);   /* k = no. of terms needed */
 124
 125                 for(i=jz+1;i<=jz+k;i++) {   /* add q[jz+1] to q[jz+k] */
 126                     f[jx+i] = (float) ipio2[jv+i];
 127                     for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
 128                     q[i] = fw;
 129                 }
 130                 jz += k;
 131                 goto recompute;
 132             }
 133         }
 134
 135     /* chop off zero terms */
 136         if(z==(float)0.0) {
 137             jz -= 1; q0 -= 8;
 138             while(iq[jz]==0) { jz--; q0-=8;}
 139         } else { /* break z into 8-bit if necessary */
 140             z = scalbnf(z,-q0);
 141             if(z>=two8) {
 142                 fw = (float)((int32_t)(twon8*z));
 143                 iq[jz] = (int32_t)(z-two8*fw);
 144                 jz += 1; q0 += 8;
 145                 iq[jz] = (int32_t) fw;
 146             } else iq[jz] = (int32_t) z ;
 147         }
 148
 149     /* convert integer "bit" chunk to floating-point value */
 150         fw = scalbnf(one,q0);
 151         for(i=jz;i>=0;i--) {
 152             q[i] = fw*(float)iq[i]; fw*=twon8;
 153         }
 154
 155     /* compute PIo2[0,...,jp]*q[jz,...,0] */
 156         for(i=jz;i>=0;i--) {
 157             for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
 158             fq[jz-i] = fw;
 159         }
 160
 161     /* compress fq[] into y[] */
 162         switch(prec) {
 163             case 0:
 164                 fw = 0.0;
 165                 for (i=jz;i>=0;i--) fw += fq[i];
 166                 y[0] = (ih==0)? fw: -fw;
 167                 break;
 168             case 1:
 169             case 2:
 170                 fw = 0.0;
 171                 for (i=jz;i>=0;i--) fw += fq[i];
 172                 fw = *(volatile float *)&fw;    /* clip any extra precision */
 173                 y[0] = (ih==0)? fw: -fw;
 174                 fw = fq[0]-fw;
 175                 for (i=1;i<=jz;i++) fw += fq[i];
 176                 y[1] = (ih==0)? fw: -fw;
 177                 break;
 178             case 3:     /* painful */
 179                 for (i=jz;i>0;i--) {
 180                     fw      = fq[i-1]+fq[i];
 181                     fq[i]  += fq[i-1]-fw;
 182                     fq[i-1] = fw;
 183                 }
 184                 for (i=jz;i>1;i--) {
 185                     fw      = fq[i-1]+fq[i];
 186                     fq[i]  += fq[i-1]-fw;
 187                     fq[i-1] = fw;
 188                 }
 189                 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
 190                 if(ih==0) {
 191                     y[0] =  fq[0]; y[1] =  fq[1]; y[2] =  fw;
 192                 } else {
 193                     y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
 194                 }
 195         }
 196         return n&7;
 197 }