sysdeps/ieee754/flt-32/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 #if defined(LIBM_SCCS) && !defined(lint)
  17 static char rcsid[] = "$NetBSD: k_rem_pio2f.c,v 1.4 1995/05/10 20:46:28 jtc 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 #ifdef __STDC__
  27 static const int init_jk[] = {4,7,9}; /* initial value for jk */
  28 #else
  29 static int init_jk[] = {4,7,9};
  30 #endif
  31
  32 #ifdef __STDC__
  33 static const float PIo2[] = {
  34 #else
  35 static float PIo2[] = {
  36 #endif
  37   1.5703125000e+00, /* 0x3fc90000 */
  38   4.5776367188e-04, /* 0x39f00000 */
  39   2.5987625122e-05, /* 0x37da0000 */
  40   7.5437128544e-08, /* 0x33a20000 */
  41   6.0026650317e-11, /* 0x2e840000 */
  42   7.3896444519e-13, /* 0x2b500000 */
  43   5.3845816694e-15, /* 0x27c20000 */
  44   5.6378512969e-18, /* 0x22d00000 */
  45   8.3009228831e-20, /* 0x1fc40000 */
  46   3.2756352257e-22, /* 0x1bc60000 */
  47   6.3331015649e-25, /* 0x17440000 */
  48 };
  49
  50 #ifdef __STDC__
  51 static const float
  52 #else
  53 static float
  54 #endif
  55 zero   = 0.0,
  56 one    = 1.0,
  57 two8   =  2.5600000000e+02, /* 0x43800000 */
  58 twon8  =  3.9062500000e-03; /* 0x3b800000 */
  59
  60 #ifdef __STDC__
  61         int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2)
  62 #else
  63         int __kernel_rem_pio2f(x,y,e0,nx,prec,ipio2)
  64         float x[], y[]; int e0,nx,prec; int32_t ipio2[];
  65 #endif
  66 {
  67         int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
  68         float z,fw,f[20],fq[20],q[20];
  69
  70     /* initialize jk*/
  71         jk = init_jk[prec];
  72         jp = jk;
  73
  74     /* determine jx,jv,q0, note that 3>q0 */
  75         jx =  nx-1;
  76         jv = (e0-3)/8; if(jv<0) jv=0;
  77         q0 =  e0-8*(jv+1);
  78
  79     /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
  80         j = jv-jx; m = jx+jk;
  81         for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
  82
  83     /* compute q[0],q[1],...q[jk] */
  84         for (i=0;i<=jk;i++) {
  85             for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
  86         }
  87
  88         jz = jk;
  89 recompute:
  90     /* distill q[] into iq[] reversingly */
  91         for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
  92             fw    =  (float)((int32_t)(twon8* z));
  93             iq[i] =  (int32_t)(z-two8*fw);
  94             z     =  q[j-1]+fw;
  95         }
  96
  97     /* compute n */
  98         z  = __scalbnf(z,q0);           /* actual value of z */
  99         z -= (float)8.0*__floorf(z*(float)0.125);       /* trim off integer >= 8 */
 100         n  = (int32_t) z;
 101         z -= (float)n;
 102         ih = 0;
 103         if(q0>0) {      /* need iq[jz-1] to determine n */
 104             i  = (iq[jz-1]>>(8-q0)); n += i;
 105             iq[jz-1] -= i<<(8-q0);
 106             ih = iq[jz-1]>>(7-q0);
 107         }
 108         else if(q0==0) ih = iq[jz-1]>>8;
 109         else if(z>=(float)0.5) ih=2;
 110
 111         if(ih>0) {      /* q > 0.5 */
 112             n += 1; carry = 0;
 113             for(i=0;i<jz ;i++) {        /* compute 1-q */
 114                 j = iq[i];
 115                 if(carry==0) {
 116                     if(j!=0) {
 117                         carry = 1; iq[i] = 0x100- j;
 118                     }
 119                 } else  iq[i] = 0xff - j;
 120             }
 121             if(q0>0) {          /* rare case: chance is 1 in 12 */
 122                 switch(q0) {
 123                 case 1:
 124                    iq[jz-1] &= 0x7f; break;
 125                 case 2:
 126                    iq[jz-1] &= 0x3f; break;
 127                 }
 128             }
 129             if(ih==2) {
 130                 z = one - z;
 131                 if(carry!=0) z -= __scalbnf(one,q0);
 132             }
 133         }
 134
 135     /* check if recomputation is needed */
 136         if(z==zero) {
 137             j = 0;
 138             for (i=jz-1;i>=jk;i--) j |= iq[i];
 139             if(j==0) { /* need recomputation */
 140                 for(k=1;iq[jk-k]==0;k++);   /* k = no. of terms needed */
 141
 142                 for(i=jz+1;i<=jz+k;i++) {   /* add q[jz+1] to q[jz+k] */
 143                     f[jx+i] = (float) ipio2[jv+i];
 144                     for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
 145                     q[i] = fw;
 146                 }
 147                 jz += k;
 148                 goto recompute;
 149             }
 150         }
 151
 152     /* chop off zero terms */
 153         if(z==(float)0.0) {
 154             jz -= 1; q0 -= 8;
 155             while(iq[jz]==0) { jz--; q0-=8;}
 156         } else { /* break z into 8-bit if necessary */
 157             z = __scalbnf(z,-q0);
 158             if(z>=two8) {
 159                 fw = (float)((int32_t)(twon8*z));
 160                 iq[jz] = (int32_t)(z-two8*fw);
 161                 jz += 1; q0 += 8;
 162                 iq[jz] = (int32_t) fw;
 163             } else iq[jz] = (int32_t) z ;
 164         }
 165
 166     /* convert integer "bit" chunk to floating-point value */
 167         fw = __scalbnf(one,q0);
 168         for(i=jz;i>=0;i--) {
 169             q[i] = fw*(float)iq[i]; fw*=twon8;
 170         }
 171
 172     /* compute PIo2[0,...,jp]*q[jz,...,0] */
 173         for(i=jz;i>=0;i--) {
 174             for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
 175             fq[jz-i] = fw;
 176         }
 177
 178     /* compress fq[] into y[] */
 179         switch(prec) {
 180             case 0:
 181                 fw = 0.0;
 182                 for (i=jz;i>=0;i--) fw += fq[i];
 183                 y[0] = (ih==0)? fw: -fw;
 184                 break;
 185             case 1:
 186             case 2:
 187                 fw = 0.0;
 188                 for (i=jz;i>=0;i--) fw += fq[i];
 189                 y[0] = (ih==0)? fw: -fw;
 190                 fw = fq[0]-fw;
 191                 for (i=1;i<=jz;i++) fw += fq[i];
 192                 y[1] = (ih==0)? fw: -fw;
 193                 break;
 194             case 3:     /* painful */
 195                 for (i=jz;i>0;i--) {
 196                     fw      = fq[i-1]+fq[i];
 197                     fq[i]  += fq[i-1]-fw;
 198                     fq[i-1] = fw;
 199                 }
 200                 for (i=jz;i>1;i--) {
 201                     fw      = fq[i-1]+fq[i];
 202                     fq[i]  += fq[i-1]-fw;
 203                     fq[i-1] = fw;
 204                 }
 205                 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
 206                 if(ih==0) {
 207                     y[0] =  fq[0]; y[1] =  fq[1]; y[2] =  fw;
 208                 } else {
 209                     y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
 210                 }
 211         }
 212         return n&7;
 213 }