sysdeps/ieee754/dbl-64/e_remainder.c

   1 /*
   2  * IBM Accurate Mathematical Library
   3  * Copyright (c) International Business Machines Corp., 2001
   4  *
   5  * This program is free software; you can redistribute it and/or modify
   6  * it under the terms of the GNU Lesser General Public License as published by
   7  * the Free Software Foundation; either version 2 of the License, or
   8  * (at your option) any later version.
   9  *
  10  * This program is distributed in the hope that it will be useful,
  11  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  12  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  13  * GNU General Public License for more details.
  14  *
  15  * You should have received a copy of the GNU Lesser General Public License
  16  * along with this program; if not, write to the Free Software
  17  * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
  18  */
  19 /**************************************************************************/
  20 /*  MODULE_NAME urem.c                                                    */
  21 /*                                                                        */
  22 /*  FUNCTION: uremainder                                                  */
  23 /*                                                                        */
  24 /* An ultimate remainder routine. Given two IEEE double machine numbers x */
  25 /* ,y   it computes the correctly rounded (to nearest) value of remainder */
  26 /* of dividing x by y.                                                    */
  27 /* Assumption: Machine arithmetic operations are performed in             */
  28 /* round to nearest mode of IEEE 754 standard.                            */
  29 /*                                                                        */
  30 /* ************************************************************************/
  31
  32 #include "endian.h"
  33 #include "mydefs.h"
  34 #include "urem.h"
  35 #include "MathLib.h"
  36 #include "math_private.h"
  37
  38 /**************************************************************************/
  39 /* An ultimate remainder routine. Given two IEEE double machine numbers x */
  40 /* ,y   it computes the correctly rounded (to nearest) value of remainder */
  41 /**************************************************************************/
  42 double __ieee754_remainder(double x, double y)
  43 {
  44   double z,d,xx;
  45 #if 0
  46   double yy;
  47 #endif
  48   int4 kx,ky,n,nn,n1,m1,l;
  49 #if 0
  50   int4 m;
  51 #endif
  52   mynumber u,t,w={{0,0}},v={{0,0}},ww={{0,0}},r;
  53   u.x=x;
  54   t.x=y;
  55   kx=u.i[HIGH_HALF]&0x7fffffff; /* no sign  for x*/
  56   t.i[HIGH_HALF]&=0x7fffffff;   /*no sign for y */
  57   ky=t.i[HIGH_HALF];
  58   /*------ |x| < 2^1023  and   2^-970 < |y| < 2^1024 ------------------*/
  59   if (kx<0x7fe00000 && ky<0x7ff00000 && ky>=0x03500000) {
  60     if (kx+0x00100000<ky) return x;
  61     if ((kx-0x01500000)<ky) {
  62       z=x/t.x;
  63       v.i[HIGH_HALF]=t.i[HIGH_HALF];
  64       d=(z+big.x)-big.x;
  65       xx=(x-d*v.x)-d*(t.x-v.x);
  66       if (d-z!=0.5&&d-z!=-0.5) return (xx!=0)?xx:((x>0)?ZERO.x:nZERO.x);
  67       else {
  68         if (ABS(xx)>0.5*t.x) return (z>d)?xx-t.x:xx+t.x;
  69         else return xx;
  70       }
  71     }   /*    (kx<(ky+0x01500000))         */
  72     else  {
  73       r.x=1.0/t.x;
  74       n=t.i[HIGH_HALF];
  75       nn=(n&0x7ff00000)+0x01400000;
  76       w.i[HIGH_HALF]=n;
  77       ww.x=t.x-w.x;
  78       l=(kx-nn)&0xfff00000;
  79       n1=ww.i[HIGH_HALF];
  80       m1=r.i[HIGH_HALF];
  81       while (l>0) {
  82         r.i[HIGH_HALF]=m1-l;
  83         z=u.x*r.x;
  84         w.i[HIGH_HALF]=n+l;
  85         ww.i[HIGH_HALF]=(n1)?n1+l:n1;
  86         d=(z+big.x)-big.x;
  87         u.x=(u.x-d*w.x)-d*ww.x;
  88         l=(u.i[HIGH_HALF]&0x7ff00000)-nn;
  89       }
  90       r.i[HIGH_HALF]=m1;
  91       w.i[HIGH_HALF]=n;
  92       ww.i[HIGH_HALF]=n1;
  93       z=u.x*r.x;
  94       d=(z+big.x)-big.x;
  95       u.x=(u.x-d*w.x)-d*ww.x;
  96       if (ABS(u.x)<0.5*t.x) return (u.x!=0)?u.x:((x>0)?ZERO.x:nZERO.x);
  97       else
  98         if (ABS(u.x)>0.5*t.x) return (d>z)?u.x+t.x:u.x-t.x;
  99         else
 100         {z=u.x/t.x; d=(z+big.x)-big.x; return ((u.x-d*w.x)-d*ww.x);}
 101     }
 102
 103   }   /*   (kx<0x7fe00000&&ky<0x7ff00000&&ky>=0x03500000)     */
 104   else {
 105     if (kx<0x7fe00000&&ky<0x7ff00000&&(ky>0||t.i[LOW_HALF]!=0)) {
 106       y=ABS(y)*t128.x;
 107       z=__ieee754_remainder(x,y)*t128.x;
 108       z=__ieee754_remainder(z,y)*tm128.x;
 109       return z;
 110     }
 111   else {
 112     if ((kx&0x7ff00000)==0x7fe00000&&ky<0x7ff00000&&(ky>0||t.i[LOW_HALF]!=0)) {
 113       y=ABS(y);
 114       z=2.0*__ieee754_remainder(0.5*x,y);
 115       d = ABS(z);
 116       if (d <= ABS(d-y)) return z;
 117       else return (z>0)?z-y:z+y;
 118     }
 119     else { /* if x is too big */
 120       if (kx == 0x7ff00000 && u.i[LOW_HALF] == 0 && y == 1.0)
 121         return x / x;
 122       if (kx>=0x7ff00000||(ky==0&&t.i[LOW_HALF]==0)||ky>0x7ff00000||
 123           (ky==0x7ff00000&&t.i[LOW_HALF]!=0))
 124         return (u.i[HIGH_HALF]&0x80000000)?nNAN.x:NAN.x;
 125       else return x;
 126     }
 127    }
 128   }
 129 }