2 * IBM Accurate Mathematical Library
3 * Copyright (c) International Business Machines Corp., 2001
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.
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.
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.
19 /*********************************************************************/
20 /* MODULE_NAME: uroot.c */
24 /* FILES NEEDED: dla.h endian.h mydefs.h uroot.h */
27 /* An ultimate sqrt routine. Given an IEEE double machine number x */
28 /* it computes the correctly rounded (to nearest) value of square */
30 /* Assumption: Machine arithmetic operations are performed in */
31 /* round to nearest mode of IEEE 754 standard. */
33 /*********************************************************************/
41 /*********************************************************************/
42 /* An ultimate aqrt routine. Given an IEEE double machine number x */
43 /* it computes the correctly rounded (to nearest) value of square */
45 /*********************************************************************/
46 double __ieee754_sqrt(double x
) {
49 rt0
= 9.99999999859990725855365213134618E-01,
50 rt1
= 4.99999999495955425917856814202739E-01,
51 rt2
= 3.75017500867345182581453026130850E-01,
52 rt3
= 3.12523626554518656309172508769531E-01;
53 static const double big
= 134217728.0, big1
= 134217729.0;
54 double y
,t
,del
,res
,res1
,hy
,z
,zz
,p
,hx
,tx
,ty
,s
;
60 a
.i
[HIGH_HALF
]=(k
&0x001fffff)|0x3fe00000;
61 t
=inroot
[(k
&0x001fffff)>>14];
63 /*----------------- 2^-1022 <= | x |< 2^1024 -----------------*/
64 if (k
>0x000fffff && k
<0x7ff00000) {
66 t
=t
*(rt0
+y
*(rt1
+y
*(rt2
+y
*rt3
)));
67 c
.i
[HIGH_HALF
]=0x20000000+((k
&0x7fe00000)>>1);
70 del
=0.5*t
*((s
-hy
*hy
)-(y
-hy
)*(y
+hy
));
72 if (res
== (res
+1.002*((y
-res
)+del
))) return res
*c
.x
;
74 res1
=res
+1.5*((y
-res
)+del
);
75 EMULV(res
,res1
,z
,zz
,p
,hx
,tx
,hy
,ty
); /* (z+zz)=res*res1 */
76 return ((((z
-s
)+zz
)<0)?max(res
,res1
):min(res
,res1
))*c
.x
;
80 if (k
>0x7ff00000) /* x -> infinity */
81 return (big1
-big1
)/(big
-big
);
82 if (k
<0x00100000) { /* x -> -infinity */
84 if (k
<0) return (big1
-big1
)/(big
-big
);
85 else return tm256
.x
*__ieee754_sqrt(x
*t512
.x
);
87 else return (a
.i
[LOW_HALF
]==0)?x
:(big1
-big1
)/(big
-big
);