lib/libm/src/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 #include <sys/cdefs.h>
  17 #if defined(LIBM_SCCS) && !defined(lint)
  18 __RCSID("$NetBSD: k_rem_pio2f.c,v 1.6 1999/07/02 15:37:41 simonb Exp $");
  19 #endif
  20
  21 #include "math.h"
  22 #include "math_private.h"
  23
  24 /* In the float version, the input parameter x contains 8 bit
  25    integers, not 24 bit integers.  113 bit precision is not supported.  */
  26
  27 static const int init_jk[] = {4,7,9}; /* initial value for jk */
  28
  29 static const float PIo2[] = {
  30   1.5703125000e+00, /* 0x3fc90000 */
  31   4.5776367188e-04, /* 0x39f00000 */
  32   2.5987625122e-05, /* 0x37da0000 */
  33   7.5437128544e-08, /* 0x33a20000 */
  34   6.0026650317e-11, /* 0x2e840000 */
  35   7.3896444519e-13, /* 0x2b500000 */
  36   5.3845816694e-15, /* 0x27c20000 */
  37   5.6378512969e-18, /* 0x22d00000 */
  38   8.3009228831e-20, /* 0x1fc40000 */
  39   3.2756352257e-22, /* 0x1bc60000 */
  40   6.3331015649e-25, /* 0x17440000 */
  41 };
  42
  43 static const float
  44 zero   = 0.0,
  45 one    = 1.0,
  46 two8   =  2.5600000000e+02, /* 0x43800000 */
  47 twon8  =  3.9062500000e-03; /* 0x3b800000 */
  48
  49 int
  50 __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2)
  51 {
  52         int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
  53         float z,fw,f[20],fq[20],q[20];
  54
  55     /* initialize jk*/
  56         jk = init_jk[prec];
  57         jp = jk;
  58
  59     /* determine jx,jv,q0, note that 3>q0 */
  60         jx =  nx-1;
  61         jv = (e0-3)/8; if(jv<0) jv=0;
  62         q0 =  e0-8*(jv+1);
  63
  64     /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
  65         j = jv-jx; m = jx+jk;
  66         for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
  67
  68     /* compute q[0],q[1],...q[jk] */
  69         for (i=0;i<=jk;i++) {
  70             for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
  71         }
  72
  73         jz = jk;
  74 recompute:
  75     /* distill q[] into iq[] reversingly */
  76         for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
  77             fw    =  (float)((int32_t)(twon8* z));
  78             iq[i] =  (int32_t)(z-two8*fw);
  79             z     =  q[j-1]+fw;
  80         }
  81
  82     /* compute n */
  83         z  = scalbnf(z,q0);             /* actual value of z */
  84         z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */
  85         n  = (int32_t) z;
  86         z -= (float)n;
  87         ih = 0;
  88         if(q0>0) {      /* need iq[jz-1] to determine n */
  89             i  = (iq[jz-1]>>(8-q0)); n += i;
  90             iq[jz-1] -= i<<(8-q0);
  91             ih = iq[jz-1]>>(7-q0);
  92         }
  93         else if(q0==0) ih = iq[jz-1]>>8;
  94         else if(z>=(float)0.5) ih=2;
  95
  96         if(ih>0) {      /* q > 0.5 */
  97             n += 1; carry = 0;
  98             for(i=0;i<jz ;i++) {        /* compute 1-q */
  99                 j = iq[i];
 100                 if(carry==0) {
 101                     if(j!=0) {
 102                         carry = 1; iq[i] = 0x100- j;
 103                     }
 104                 } else  iq[i] = 0xff - j;
 105             }
 106             if(q0>0) {          /* rare case: chance is 1 in 12 */
 107                 switch(q0) {
 108                 case 1:
 109                    iq[jz-1] &= 0x7f; break;
 110                 case 2:
 111                    iq[jz-1] &= 0x3f; break;
 112                 }
 113             }
 114             if(ih==2) {
 115                 z = one - z;
 116                 if(carry!=0) z -= scalbnf(one,q0);
 117             }
 118         }
 119
 120     /* check if recomputation is needed */
 121         if(z==zero) {
 122             j = 0;
 123             for (i=jz-1;i>=jk;i--) j |= iq[i];
 124             if(j==0) { /* need recomputation */
 125                 for(k=1;iq[jk-k]==0;k++);   /* k = no. of terms needed */
 126
 127                 for(i=jz+1;i<=jz+k;i++) {   /* add q[jz+1] to q[jz+k] */
 128                     f[jx+i] = (float) ipio2[jv+i];
 129                     for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
 130                     q[i] = fw;
 131                 }
 132                 jz += k;
 133                 goto recompute;
 134             }
 135         }
 136
 137     /* chop off zero terms */
 138         if(z==(float)0.0) {
 139             jz -= 1; q0 -= 8;
 140             while(iq[jz]==0) { jz--; q0-=8;}
 141         } else { /* break z into 8-bit if necessary */
 142             z = scalbnf(z,-q0);
 143             if(z>=two8) {
 144                 fw = (float)((int32_t)(twon8*z));
 145                 iq[jz] = (int32_t)(z-two8*fw);
 146                 jz += 1; q0 += 8;
 147                 iq[jz] = (int32_t) fw;
 148             } else iq[jz] = (int32_t) z ;
 149         }
 150
 151     /* convert integer "bit" chunk to floating-point value */
 152         fw = scalbnf(one,q0);
 153         for(i=jz;i>=0;i--) {
 154             q[i] = fw*(float)iq[i]; fw*=twon8;
 155         }
 156
 157     /* compute PIo2[0,...,jp]*q[jz,...,0] */
 158         for(i=jz;i>=0;i--) {
 159             for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
 160             fq[jz-i] = fw;
 161         }
 162
 163     /* compress fq[] into y[] */
 164         switch(prec) {
 165             case 0:
 166                 fw = 0.0;
 167                 for (i=jz;i>=0;i--) fw += fq[i];
 168                 y[0] = (ih==0)? fw: -fw;
 169                 break;
 170             case 1:
 171             case 2:
 172                 fw = 0.0;
 173                 for (i=jz;i>=0;i--) fw += fq[i];
 174                 y[0] = (ih==0)? fw: -fw;
 175                 fw = fq[0]-fw;
 176                 for (i=1;i<=jz;i++) fw += fq[i];
 177                 y[1] = (ih==0)? fw: -fw;
 178                 break;
 179             case 3:     /* painful */
 180                 for (i=jz;i>0;i--) {
 181                     fw      = fq[i-1]+fq[i];
 182                     fq[i]  += fq[i-1]-fw;
 183                     fq[i-1] = fw;
 184                 }
 185                 for (i=jz;i>1;i--) {
 186                     fw      = fq[i-1]+fq[i];
 187                     fq[i]  += fq[i-1]-fw;
 188                     fq[i-1] = fw;
 189                 }
 190                 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
 191                 if(ih==0) {
 192                     y[0] =  fq[0]; y[1] =  fq[1]; y[2] =  fw;
 193                 } else {
 194                     y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
 195                 }
 196         }
 197         return n&7;
 198 }