2 * IBM Accurate Mathematical Library
3 * written by International Business Machines Corp.
4 * Copyright (C) 2001 Free Software Foundation
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.
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.
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.
20 /*********************************************************************/
21 /* MODULE_NAME: uroot.c */
25 /* FILES NEEDED: dla.h endian.h mydefs.h uroot.h */
28 /* An ultimate sqrt routine. Given an IEEE double machine number x */
29 /* it computes the correctly rounded (to nearest) value of square */
31 /* Assumption: Machine arithmetic operations are performed in */
32 /* round to nearest mode of IEEE 754 standard. */
34 /*********************************************************************/
41 #include "math_private.h"
43 /*********************************************************************/
44 /* An ultimate sqrt routine. Given an IEEE double machine number x */
45 /* it computes the correctly rounded (to nearest) value of square */
47 /*********************************************************************/
48 double __ieee754_sqrt(double x
) {
51 rt0
= 9.99999999859990725855365213134618E-01,
52 rt1
= 4.99999999495955425917856814202739E-01,
53 rt2
= 3.75017500867345182581453026130850E-01,
54 rt3
= 3.12523626554518656309172508769531E-01;
55 static const double big
= 134217728.0;
56 double y
,t
,del
,res
,res1
,hy
,z
,zz
,p
,hx
,tx
,ty
,s
;
62 a
.i
[HIGH_HALF
]=(k
&0x001fffff)|0x3fe00000;
63 t
=inroot
[(k
&0x001fffff)>>14];
65 /*----------------- 2^-1022 <= | x |< 2^1024 -----------------*/
66 if (k
>0x000fffff && k
<0x7ff00000) {
68 t
=t
*(rt0
+y
*(rt1
+y
*(rt2
+y
*rt3
)));
69 c
.i
[HIGH_HALF
]=0x20000000+((k
&0x7fe00000)>>1);
72 del
=0.5*t
*((s
-hy
*hy
)-(y
-hy
)*(y
+hy
));
74 if (res
== (res
+1.002*((y
-res
)+del
))) return res
*c
.x
;
76 res1
=res
+1.5*((y
-res
)+del
);
77 EMULV(res
,res1
,z
,zz
,p
,hx
,tx
,hy
,ty
); /* (z+zz)=res*res1 */
78 return ((((z
-s
)+zz
)<0)?max(res
,res1
):min(res
,res1
))*c
.x
;
82 if ((k
& 0x7ff00000) == 0x7ff00000)
83 return x
*x
+x
; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
84 if (x
==0) return x
; /* sqrt(+0)=+0, sqrt(-0)=-0 */
85 if (k
<0) return (x
-x
)/(x
-x
); /* sqrt(-ve)=sNaN */
86 return tm256
.x
*__ieee754_sqrt(x
*t512
.x
);