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 1.8 2010/04/23 19:17:07 drochner Exp $");
  19 #endif
  20
  21 #include "namespace.h"
  22 #include "math.h"
  23 #include "math_private.h"
  24
  25 /* In the float version, the input parameter x contains 8 bit
  26    integers, not 24 bit integers.  113 bit precision is not supported.  */
  27
  28 static const int init_jk[] = {4,7,9}; /* initial value for jk */
  29
  30 static const float PIo2[] = {
  31   1.5703125000e+00, /* 0x3fc90000 */
  32   4.5776367188e-04, /* 0x39f00000 */
  33   2.5987625122e-05, /* 0x37da0000 */
  34   7.5437128544e-08, /* 0x33a20000 */
  35   6.0026650317e-11, /* 0x2e840000 */
  36   7.3896444519e-13, /* 0x2b500000 */
  37   5.3845816694e-15, /* 0x27c20000 */
  38   5.6378512969e-18, /* 0x22d00000 */
  39   8.3009228831e-20, /* 0x1fc40000 */
  40   3.2756352257e-22, /* 0x1bc60000 */
  41   6.3331015649e-25, /* 0x17440000 */
  42 };
  43
  44 static const float
  45 zero   = 0.0,
  46 one    = 1.0,
  47 two8   =  2.5600000000e+02, /* 0x43800000 */
  48 twon8  =  3.9062500000e-03; /* 0x3b800000 */
  49
  50 int
  51 __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2)
  52 {
  53         int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
  54         float z,fw,f[20],fq[20],q[20];
  55
  56     /* initialize jk*/
  57         jk = init_jk[prec];
  58         jp = jk;
  59
  60     /* determine jx,jv,q0, note that 3>q0 */
  61         jx =  nx-1;
  62         jv = (e0-3)/8; if(jv<0) jv=0;
  63         q0 =  e0-8*(jv+1);
  64
  65     /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
  66         j = jv-jx; m = jx+jk;
  67         for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
  68
  69     /* compute q[0],q[1],...q[jk] */
  70         for (i=0;i<=jk;i++) {
  71             for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
  72         }
  73
  74         jz = jk;
  75 recompute:
  76     /* distill q[] into iq[] reversingly */
  77         for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
  78             fw    =  (float)((int32_t)(twon8* z));
  79             iq[i] =  (int32_t)(z-two8*fw);
  80             z     =  q[j-1]+fw;
  81         }
  82
  83     /* compute n */
  84         z  = scalbnf(z,q0);             /* actual value of z */
  85         z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */
  86         n  = (int32_t) z;
  87         z -= (float)n;
  88         ih = 0;
  89         if(q0>0) {      /* need iq[jz-1] to determine n */
  90             i  = (iq[jz-1]>>(8-q0)); n += i;
  91             iq[jz-1] -= i<<(8-q0);
  92             ih = iq[jz-1]>>(7-q0);
  93         }
  94         else if(q0==0) ih = iq[jz-1]>>8;
  95         else if(z>=(float)0.5) ih=2;
  96
  97         if(ih>0) {      /* q > 0.5 */
  98             n += 1; carry = 0;
  99             for(i=0;i<jz ;i++) {        /* compute 1-q */
 100                 j = iq[i];
 101                 if(carry==0) {
 102                     if(j!=0) {
 103                         carry = 1; iq[i] = 0x100- j;
 104                     }
 105                 } else  iq[i] = 0xff - j;
 106             }
 107             if(q0>0) {          /* rare case: chance is 1 in 12 */
 108                 switch(q0) {
 109                 case 1:
 110                    iq[jz-1] &= 0x7f; break;
 111                 case 2:
 112                    iq[jz-1] &= 0x3f; break;
 113                 }
 114             }
 115             if(ih==2) {
 116                 z = one - z;
 117                 if(carry!=0) z -= scalbnf(one,q0);
 118             }
 119         }
 120
 121     /* check if recomputation is needed */
 122         if(z==zero) {
 123             j = 0;
 124             for (i=jz-1;i>=jk;i--) j |= iq[i];
 125             if(j==0) { /* need recomputation */
 126                 for(k=1;iq[jk-k]==0;k++);   /* k = no. of terms needed */
 127
 128                 for(i=jz+1;i<=jz+k;i++) {   /* add q[jz+1] to q[jz+k] */
 129                     f[jx+i] = (float) ipio2[jv+i];
 130                     for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
 131                     q[i] = fw;
 132                 }
 133                 jz += k;
 134                 goto recompute;
 135             }
 136         }
 137
 138     /* chop off zero terms */
 139         if(z==(float)0.0) {
 140             jz -= 1; q0 -= 8;
 141             while(iq[jz]==0) { jz--; q0-=8;}
 142         } else { /* break z into 8-bit if necessary */
 143             z = scalbnf(z,-q0);
 144             if(z>=two8) {
 145                 fw = (float)((int32_t)(twon8*z));
 146                 iq[jz] = (int32_t)(z-two8*fw);
 147                 jz += 1; q0 += 8;
 148                 iq[jz] = (int32_t) fw;
 149             } else iq[jz] = (int32_t) z ;
 150         }
 151
 152     /* convert integer "bit" chunk to floating-point value */
 153         fw = scalbnf(one,q0);
 154         for(i=jz;i>=0;i--) {
 155             q[i] = fw*(float)iq[i]; fw*=twon8;
 156         }
 157
 158     /* compute PIo2[0,...,jp]*q[jz,...,0] */
 159         for(i=jz;i>=0;i--) {
 160             for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
 161             fq[jz-i] = fw;
 162         }
 163
 164     /* compress fq[] into y[] */
 165         switch(prec) {
 166             case 0:
 167                 fw = 0.0;
 168                 for (i=jz;i>=0;i--) fw += fq[i];
 169                 y[0] = (ih==0)? fw: -fw;
 170                 break;
 171             case 1:
 172             case 2:
 173                 fw = 0.0;
 174                 for (i=jz;i>=0;i--) fw += fq[i];
 175                 y[0] = (ih==0)? fw: -fw;
 176                 fw = fq[0]-fw;
 177                 for (i=1;i<=jz;i++) fw += fq[i];
 178                 y[1] = (ih==0)? fw: -fw;
 179                 break;
 180             case 3:     /* painful */
 181                 for (i=jz;i>0;i--) {
 182                     fw      = fq[i-1]+fq[i];
 183                     fq[i]  += fq[i-1]-fw;
 184                     fq[i-1] = fw;
 185                 }
 186                 for (i=jz;i>1;i--) {
 187                     fw      = fq[i-1]+fq[i];
 188                     fq[i]  += fq[i-1]-fw;
 189                     fq[i-1] = fw;
 190                 }
 191                 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
 192                 if(ih==0) {
 193                     y[0] =  fq[0]; y[1] =  fq[1]; y[2] =  fw;
 194                 } else {
 195                     y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
 196                 }
 197         }
 198         return n&7;
 199 }