sysdeps/ieee754/dbl-64/e_remainder.c

   1 /*
   2  * IBM Accurate Mathematical Library
   3  * written by International Business Machines Corp.
   4  * Copyright (C) 2001 Free Software Foundation
   5  *
   6  * This program is free software; you can redistribute it and/or modify
   7  * it under the terms of the GNU Lesser General Public License as published by
   8  * the Free Software Foundation; either version 2.1 of the License, or
   9  * (at your option) any later version.
  10  *
  11  * This program is distributed in the hope that it will be useful,
  12  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  13  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14  * GNU Lesser General Public License for more details.
  15  *
  16  * You should have received a copy of the GNU Lesser General Public License
  17  * along with this program; if not, write to the Free Software
  18  * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
  19  */
  20 /**************************************************************************/
  21 /*  MODULE_NAME urem.c                                                    */
  22 /*                                                                        */
  23 /*  FUNCTION: uremainder                                                  */
  24 /*                                                                        */
  25 /* An ultimate remainder routine. Given two IEEE double machine numbers x */
  26 /* ,y   it computes the correctly rounded (to nearest) value of remainder */
  27 /* of dividing x by y.                                                    */
  28 /* Assumption: Machine arithmetic operations are performed in             */
  29 /* round to nearest mode of IEEE 754 standard.                            */
  30 /*                                                                        */
  31 /* ************************************************************************/
  32
  33 #include "endian.h"
  34 #include "mydefs.h"
  35 #include "urem.h"
  36 #include "MathLib.h"
  37 #include "math_private.h"
  38
  39 /**************************************************************************/
  40 /* An ultimate remainder routine. Given two IEEE double machine numbers x */
  41 /* ,y   it computes the correctly rounded (to nearest) value of remainder */
  42 /**************************************************************************/
  43 double __ieee754_remainder(double x, double y)
  44 {
  45   double z,d,xx;
  46 #if 0
  47   double yy;
  48 #endif
  49   int4 kx,ky,n,nn,n1,m1,l;
  50 #if 0
  51   int4 m;
  52 #endif
  53   mynumber u,t,w={{0,0}},v={{0,0}},ww={{0,0}},r;
  54   u.x=x;
  55   t.x=y;
  56   kx=u.i[HIGH_HALF]&0x7fffffff; /* no sign  for x*/
  57   t.i[HIGH_HALF]&=0x7fffffff;   /*no sign for y */
  58   ky=t.i[HIGH_HALF];
  59   /*------ |x| < 2^1023  and   2^-970 < |y| < 2^1024 ------------------*/
  60   if (kx<0x7fe00000 && ky<0x7ff00000 && ky>=0x03500000) {
  61     if (kx+0x00100000<ky) return x;
  62     if ((kx-0x01500000)<ky) {
  63       z=x/t.x;
  64       v.i[HIGH_HALF]=t.i[HIGH_HALF];
  65       d=(z+big.x)-big.x;
  66       xx=(x-d*v.x)-d*(t.x-v.x);
  67       if (d-z!=0.5&&d-z!=-0.5) return (xx!=0)?xx:((x>0)?ZERO.x:nZERO.x);
  68       else {
  69         if (ABS(xx)>0.5*t.x) return (z>d)?xx-t.x:xx+t.x;
  70         else return xx;
  71       }
  72     }   /*    (kx<(ky+0x01500000))         */
  73     else  {
  74       r.x=1.0/t.x;
  75       n=t.i[HIGH_HALF];
  76       nn=(n&0x7ff00000)+0x01400000;
  77       w.i[HIGH_HALF]=n;
  78       ww.x=t.x-w.x;
  79       l=(kx-nn)&0xfff00000;
  80       n1=ww.i[HIGH_HALF];
  81       m1=r.i[HIGH_HALF];
  82       while (l>0) {
  83         r.i[HIGH_HALF]=m1-l;
  84         z=u.x*r.x;
  85         w.i[HIGH_HALF]=n+l;
  86         ww.i[HIGH_HALF]=(n1)?n1+l:n1;
  87         d=(z+big.x)-big.x;
  88         u.x=(u.x-d*w.x)-d*ww.x;
  89         l=(u.i[HIGH_HALF]&0x7ff00000)-nn;
  90       }
  91       r.i[HIGH_HALF]=m1;
  92       w.i[HIGH_HALF]=n;
  93       ww.i[HIGH_HALF]=n1;
  94       z=u.x*r.x;
  95       d=(z+big.x)-big.x;
  96       u.x=(u.x-d*w.x)-d*ww.x;
  97       if (ABS(u.x)<0.5*t.x) return (u.x!=0)?u.x:((x>0)?ZERO.x:nZERO.x);
  98       else
  99         if (ABS(u.x)>0.5*t.x) return (d>z)?u.x+t.x:u.x-t.x;
 100         else
 101         {z=u.x/t.x; d=(z+big.x)-big.x; return ((u.x-d*w.x)-d*ww.x);}
 102     }
 103
 104   }   /*   (kx<0x7fe00000&&ky<0x7ff00000&&ky>=0x03500000)     */
 105   else {
 106     if (kx<0x7fe00000&&ky<0x7ff00000&&(ky>0||t.i[LOW_HALF]!=0)) {
 107       y=ABS(y)*t128.x;
 108       z=__ieee754_remainder(x,y)*t128.x;
 109       z=__ieee754_remainder(z,y)*tm128.x;
 110       return z;
 111     }
 112   else {
 113     if ((kx&0x7ff00000)==0x7fe00000&&ky<0x7ff00000&&(ky>0||t.i[LOW_HALF]!=0)) {
 114       y=ABS(y);
 115       z=2.0*__ieee754_remainder(0.5*x,y);
 116       d = ABS(z);
 117       if (d <= ABS(d-y)) return z;
 118       else return (z>0)?z-y:z+y;
 119     }
 120     else { /* if x is too big */
 121       if (kx == 0x7ff00000 && u.i[LOW_HALF] == 0 && y == 1.0)
 122         return x / x;
 123       if (kx>=0x7ff00000||(ky==0&&t.i[LOW_HALF]==0)||ky>0x7ff00000||
 124           (ky==0x7ff00000&&t.i[LOW_HALF]!=0))
 125         return (u.i[HIGH_HALF]&0x80000000)?nNAN.x:NAN.x;
 126       else return x;
 127     }
 128    }
 129   }
 130 }