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 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 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 aqrt 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, big1 = 134217729.0;
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) /* x -> infinity */
83 return (big1-big1)/(big-big);
84 if (k<0x00100000) { /* x -> -infinity */
86 if (k<0) return (big1-big1)/(big-big);
87 else return tm256.x*__ieee754_sqrt(x*t512.x);
89 else return (a.i[LOW_HALF]==0)?x:(big1-big1)/(big-big);