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/*
* IBM Accurate Mathematical Library
* Copyright (c) International Business Machines Corp., 2001
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/**************************************************************************/
/* MODULE_NAME urem.c */
/* */
/* FUNCTION: uremainder */
/* */
/* An ultimate remainder routine. Given two IEEE double machine numbers x */
/* ,y it computes the correctly rounded (to nearest) value of remainder */
/* of dividing x by y. */
/* Assumption: Machine arithmetic operations are performed in */
/* round to nearest mode of IEEE 754 standard. */
/* */
/* ************************************************************************/
#include "endian.h"
#include "mydefs.h"
#include "urem.h"
#include "MathLib.h"
#include "math_private.h"
/**************************************************************************/
/* An ultimate remainder routine. Given two IEEE double machine numbers x */
/* ,y it computes the correctly rounded (to nearest) value of remainder */
/**************************************************************************/
double __ieee754_remainder(double x, double y)
{
double z,d,xx;
#if 0
double yy;
#endif
int4 kx,ky,n,nn,n1,m1,l;
#if 0
int4 m;
#endif
mynumber u,t,w={{0,0}},v={{0,0}},ww={{0,0}},r;
u.x=x;
t.x=y;
kx=u.i[HIGH_HALF]&0x7fffffff; /* no sign for x*/
t.i[HIGH_HALF]&=0x7fffffff; /*no sign for y */
ky=t.i[HIGH_HALF];
/*------ |x| < 2^1023 and 2^-970 < |y| < 2^1024 ------------------*/
if (kx<0x7fe00000 && ky<0x7ff00000 && ky>=0x03500000) {
if (kx+0x00100000<ky) return x;
if ((kx-0x01500000)<ky) {
z=x/t.x;
v.i[HIGH_HALF]=t.i[HIGH_HALF];
d=(z+big.x)-big.x;
xx=(x-d*v.x)-d*(t.x-v.x);
if (d-z!=0.5&&d-z!=-0.5) return (xx!=0)?xx:((x>0)?ZERO.x:nZERO.x);
else {
if (ABS(xx)>0.5*t.x) return (z>d)?xx-t.x:xx+t.x;
else return xx;
}
} /* (kx<(ky+0x01500000)) */
else {
r.x=1.0/t.x;
n=t.i[HIGH_HALF];
nn=(n&0x7ff00000)+0x01400000;
w.i[HIGH_HALF]=n;
ww.x=t.x-w.x;
l=(kx-nn)&0xfff00000;
n1=ww.i[HIGH_HALF];
m1=r.i[HIGH_HALF];
while (l>0) {
r.i[HIGH_HALF]=m1-l;
z=u.x*r.x;
w.i[HIGH_HALF]=n+l;
ww.i[HIGH_HALF]=(n1)?n1+l:n1;
d=(z+big.x)-big.x;
u.x=(u.x-d*w.x)-d*ww.x;
l=(u.i[HIGH_HALF]&0x7ff00000)-nn;
}
r.i[HIGH_HALF]=m1;
w.i[HIGH_HALF]=n;
ww.i[HIGH_HALF]=n1;
z=u.x*r.x;
d=(z+big.x)-big.x;
u.x=(u.x-d*w.x)-d*ww.x;
if (ABS(u.x)<0.5*t.x) return (u.x!=0)?u.x:((x>0)?ZERO.x:nZERO.x);
else
if (ABS(u.x)>0.5*t.x) return (d>z)?u.x+t.x:u.x-t.x;
else
{z=u.x/t.x; d=(z+big.x)-big.x; return ((u.x-d*w.x)-d*ww.x);}
}
} /* (kx<0x7fe00000&&ky<0x7ff00000&&ky>=0x03500000) */
else {
if (kx<0x7fe00000&&ky<0x7ff00000&&(ky>0||t.i[LOW_HALF]!=0)) {
y=ABS(y)*t128.x;
z=__ieee754_remainder(x,y)*t128.x;
z=__ieee754_remainder(z,y)*tm128.x;
return z;
}
else {
if ((kx&0x7ff00000)==0x7fe00000&&ky<0x7ff00000&&(ky>0||t.i[LOW_HALF]!=0)) {
y=ABS(y);
z=2.0*__ieee754_remainder(0.5*x,y);
d = ABS(z);
if (d <= ABS(d-y)) return z;
else return (z>0)?z-y:z+y;
}
else { /* if x is too big */
if (kx == 0x7ff00000 && u.i[LOW_HALF] == 0 && y == 1.0)
return x / x;
if (kx>=0x7ff00000||(ky==0&&t.i[LOW_HALF]==0)||ky>0x7ff00000||
(ky==0x7ff00000&&t.i[LOW_HALF]!=0))
return (u.i[HIGH_HALF]&0x80000000)?nNAN.x:NAN.x;
else return x;
}
}
}
}
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