libgcc-math/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_private.h"
  21
  22 /* In the float version, the input parameter x contains 8 bit
  23    integers, not 24 bit integers.  113 bit precision is not supported.  */
  24
  25 #ifdef __STDC__
  26 static const int init_jk[] = {4,7,9}; /* initial value for jk */
  27 #else
  28 static int init_jk[] = {4,7,9};
  29 #endif
  30
  31 #ifdef __STDC__
  32 static const float PIo2[] = {
  33 #else
  34 static float PIo2[] = {
  35 #endif
  36   1.5703125000e+00, /* 0x3fc90000 */
  37   4.5776367188e-04, /* 0x39f00000 */
  38   2.5987625122e-05, /* 0x37da0000 */
  39   7.5437128544e-08, /* 0x33a20000 */
  40   6.0026650317e-11, /* 0x2e840000 */
  41   7.3896444519e-13, /* 0x2b500000 */
  42   5.3845816694e-15, /* 0x27c20000 */
  43   5.6378512969e-18, /* 0x22d00000 */
  44   8.3009228831e-20, /* 0x1fc40000 */
  45   3.2756352257e-22, /* 0x1bc60000 */
  46   6.3331015649e-25, /* 0x17440000 */
  47 };
  48
  49 #ifdef __STDC__
  50 static const float
  51 #else
  52 static float
  53 #endif
  54 zero   = 0.0,
  55 one    = 1.0,
  56 two8   =  2.5600000000e+02, /* 0x43800000 */
  57 twon8  =  3.9062500000e-03; /* 0x3b800000 */
  58
  59 #ifdef __STDC__
  60         int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2)
  61 #else
  62         int __kernel_rem_pio2f(x,y,e0,nx,prec,ipio2)
  63         float x[], y[]; int e0,nx,prec; int32_t ipio2[];
  64 #endif
  65 {
  66         int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
  67         float z,fw,f[20],fq[20],q[20];
  68
  69     /* initialize jk*/
  70         jk = init_jk[prec];
  71         jp = jk;
  72
  73     /* determine jx,jv,q0, note that 3>q0 */
  74         jx =  nx-1;
  75         jv = (e0-3)/8; if(jv<0) jv=0;
  76         q0 =  e0-8*(jv+1);
  77
  78     /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
  79         j = jv-jx; m = jx+jk;
  80         for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
  81
  82     /* compute q[0],q[1],...q[jk] */
  83         for (i=0;i<=jk;i++) {
  84             for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
  85         }
  86
  87         jz = jk;
  88 recompute:
  89     /* distill q[] into iq[] reversingly */
  90         for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
  91             fw    =  (float)((int32_t)(twon8* z));
  92             iq[i] =  (int32_t)(z-two8*fw);
  93             z     =  q[j-1]+fw;
  94         }
  95
  96     /* compute n */
  97         z  = __scalbnf(z,q0);           /* actual value of z */
  98         z -= (float)8.0*__floorf(z*(float)0.125);       /* trim off integer >= 8 */
  99         n  = (int32_t) z;
 100         z -= (float)n;
 101         ih = 0;
 102         if(q0>0) {      /* need iq[jz-1] to determine n */
 103             i  = (iq[jz-1]>>(8-q0)); n += i;
 104             iq[jz-1] -= i<<(8-q0);
 105             ih = iq[jz-1]>>(7-q0);
 106         }
 107         else if(q0==0) ih = iq[jz-1]>>8;
 108         else if(z>=(float)0.5) ih=2;
 109
 110         if(ih>0) {      /* q > 0.5 */
 111             n += 1; carry = 0;
 112             for(i=0;i<jz ;i++) {        /* compute 1-q */
 113                 j = iq[i];
 114                 if(carry==0) {
 115                     if(j!=0) {
 116                         carry = 1; iq[i] = 0x100- j;
 117                     }
 118                 } else  iq[i] = 0xff - j;
 119             }
 120             if(q0>0) {          /* rare case: chance is 1 in 12 */
 121                 switch(q0) {
 122                 case 1:
 123                    iq[jz-1] &= 0x7f; break;
 124                 case 2:
 125                    iq[jz-1] &= 0x3f; break;
 126                 }
 127             }
 128             if(ih==2) {
 129                 z = one - z;
 130                 if(carry!=0) z -= __scalbnf(one,q0);
 131             }
 132         }
 133
 134     /* check if recomputation is needed */
 135         if(z==zero) {
 136             j = 0;
 137             for (i=jz-1;i>=jk;i--) j |= iq[i];
 138             if(j==0) { /* need recomputation */
 139                 for(k=1;iq[jk-k]==0;k++);   /* k = no. of terms needed */
 140
 141                 for(i=jz+1;i<=jz+k;i++) {   /* add q[jz+1] to q[jz+k] */
 142                     f[jx+i] = (float) ipio2[jv+i];
 143                     for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
 144                     q[i] = fw;
 145                 }
 146                 jz += k;
 147                 goto recompute;
 148             }
 149         }
 150
 151     /* chop off zero terms */
 152         if(z==(float)0.0) {
 153             jz -= 1; q0 -= 8;
 154             while(iq[jz]==0) { jz--; q0-=8;}
 155         } else { /* break z into 8-bit if necessary */
 156             z = __scalbnf(z,-q0);
 157             if(z>=two8) {
 158                 fw = (float)((int32_t)(twon8*z));
 159                 iq[jz] = (int32_t)(z-two8*fw);
 160                 jz += 1; q0 += 8;
 161                 iq[jz] = (int32_t) fw;
 162             } else iq[jz] = (int32_t) z ;
 163         }
 164
 165     /* convert integer "bit" chunk to floating-point value */
 166         fw = __scalbnf(one,q0);
 167         for(i=jz;i>=0;i--) {
 168             q[i] = fw*(float)iq[i]; fw*=twon8;
 169         }
 170
 171     /* compute PIo2[0,...,jp]*q[jz,...,0] */
 172         for(i=jz;i>=0;i--) {
 173             for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
 174             fq[jz-i] = fw;
 175         }
 176
 177     /* compress fq[] into y[] */
 178         switch(prec) {
 179             case 0:
 180                 fw = 0.0;
 181                 for (i=jz;i>=0;i--) fw += fq[i];
 182                 y[0] = (ih==0)? fw: -fw;
 183                 break;
 184             case 1:
 185             case 2:
 186                 fw = 0.0;
 187                 for (i=jz;i>=0;i--) fw += fq[i];
 188                 y[0] = (ih==0)? fw: -fw;
 189                 fw = fq[0]-fw;
 190                 for (i=1;i<=jz;i++) fw += fq[i];
 191                 y[1] = (ih==0)? fw: -fw;
 192                 break;
 193             case 3:     /* painful */
 194                 for (i=jz;i>0;i--) {
 195                     fw      = fq[i-1]+fq[i];
 196                     fq[i]  += fq[i-1]-fw;
 197                     fq[i-1] = fw;
 198                 }
 199                 for (i=jz;i>1;i--) {
 200                     fw      = fq[i-1]+fq[i];
 201                     fq[i]  += fq[i-1]-fw;
 202                     fq[i-1] = fw;
 203                 }
 204                 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
 205                 if(ih==0) {
 206                     y[0] =  fq[0]; y[1] =  fq[1]; y[2] =  fw;
 207                 } else {
 208                     y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
 209                 }
 210         }
 211         return n&7;
 212 }