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/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001-2013 Free Software Foundation, Inc.
*
* 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 2.1 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 Lesser 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, see <http://www.gnu.org/licenses/>.
*/
/**************************************************************************/
/* 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;
int4 kx,ky,n,nn,n1,m1,l;
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) {
SET_RESTORE_ROUND_NOEX (FE_TONEAREST);
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 (ky==0 && t.i[LOW_HALF] == 0) /* y = 0 */
return (x * y) / (x * y);
else if (kx >= 0x7ff00000 /* x not finite */
|| (ky>0x7ff00000 /* y is NaN */
|| (ky == 0x7ff00000 && t.i[LOW_HALF] != 0)))
return (x * y) / (x * y);
else
return x;
}
}
}
}
strong_alias (__ieee754_remainder, __remainder_finite)
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