src/fdlibm/e_hypot.c

/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
 *
 * ***** BEGIN LICENSE BLOCK *****
 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
 *
 * The contents of this file are subject to the Mozilla Public License Version
 * 1.1 (the "License"); you may not use this file except in compliance with
 * the License. You may obtain a copy of the License at
 * http://www.mozilla.org/MPL/
 *
 * Software distributed under the License is distributed on an "AS IS" basis,
 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
 * for the specific language governing rights and limitations under the
 * License.
 *
 * The Original Code is Mozilla Communicator client code, released
 * March 31, 1998.
 *
 * The Initial Developer of the Original Code is
 * Sun Microsystems, Inc.
 * Portions created by the Initial Developer are Copyright (C) 1998
 * the Initial Developer. All Rights Reserved.
 *
 * Contributor(s):
 *
 * Alternatively, the contents of this file may be used under the terms of
 * either of the GNU General Public License Version 2 or later (the "GPL"),
 * or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
 * in which case the provisions of the GPL or the LGPL are applicable instead
 * of those above. If you wish to allow use of your version of this file only
 * under the terms of either the GPL or the LGPL, and not to allow others to
 * use your version of this file under the terms of the MPL, indicate your
 * decision by deleting the provisions above and replace them with the notice
 * and other provisions required by the GPL or the LGPL. If you do not delete
 * the provisions above, a recipient may use your version of this file under
 * the terms of any one of the MPL, the GPL or the LGPL.
 *
 * ***** END LICENSE BLOCK ***** */

/* @(#)e_hypot.c 1.3 95/01/18 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

/* __ieee754_hypot(x,y)
 *
 * Method :                  
 *      If (assume round-to-nearest) z=x*x+y*y 
 *      has error less than sqrt(2)/2 ulp, than 
 *      sqrt(z) has error less than 1 ulp (exercise).
 *
 *      So, compute sqrt(x*x+y*y) with some care as 
 *      follows to get the error below 1 ulp:
 *
 *      Assume x>y>0;
 *      (if possible, set rounding to round-to-nearest)
 *      1. if x > 2y  use
 *              x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
 *      where x1 = x with lower 32 bits cleared, x2 = x-x1; else
 *      2. if x <= 2y use
 *              t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
 *      where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, 
 *      y1= y with lower 32 bits chopped, y2 = y-y1.
 *              
 *      NOTE: scaling may be necessary if some argument is too 
 *            large or too tiny
 *
 * Special cases:
 *      hypot(x,y) is INF if x or y is +INF or -INF; else
 *      hypot(x,y) is NAN if x or y is NAN.
 *
 * Accuracy:
 *      hypot(x,y) returns sqrt(x^2+y^2) with error less 
 *      than 1 ulps (units in the last place) 
 */

#include "fdlibm.h"

#ifdef __STDC__
        double __ieee754_hypot(double x, double y)
#else
        double __ieee754_hypot(x,y)
        double x, y;
#endif
{
        fd_twoints ux, uy;
        double a=x,b=y,t1,t2,y1,y2,w;
        int j,k,ha,hb;
        
        ux.d = x; uy.d = y;
        ha = __HI(ux)&0x7fffffff;       /* high word of  x */
        hb = __HI(uy)&0x7fffffff;       /* high word of  y */
        if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
        ux.d = a; uy.d = b;
        __HI(ux) = ha;  /* a <- |a| */
        __HI(uy) = hb;  /* b <- |b| */
        a = ux.d; b = uy.d;
        if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
        k=0;
        if(ha > 0x5f300000) {   /* a>2**500 */
           if(ha >= 0x7ff00000) {       /* Inf or NaN */
               w = a+b;                 /* for sNaN */
               ux.d = a; uy.d = b;
               if(((ha&0xfffff)|__LO(ux))==0) w = a;
               if(((hb^0x7ff00000)|__LO(uy))==0) w = b;
               return w;
           }
           /* scale a and b by 2**-600 */
           ha -= 0x25800000; hb -= 0x25800000;  k += 600;
           ux.d = a; uy.d = b;
           __HI(ux) = ha;
           __HI(uy) = hb;
           a = ux.d; b = uy.d;
        }
        if(hb < 0x20b00000) {   /* b < 2**-500 */
            if(hb <= 0x000fffff) {      /* subnormal b or 0 */  
                uy.d = b;
                if((hb|(__LO(uy)))==0) return a;
                t1=0;
                ux.d = t1;
                __HI(ux) = 0x7fd00000;  /* t1=2^1022 */
                t1 = ux.d;
                b *= t1;
                a *= t1;
                k -= 1022;
            } else {            /* scale a and b by 2^600 */
                ha += 0x25800000;       /* a *= 2^600 */
                hb += 0x25800000;       /* b *= 2^600 */
                k -= 600;
                ux.d = a; uy.d = b;
                __HI(ux) = ha;
                __HI(uy) = hb;
                a = ux.d; b = uy.d;
            }
        }
    /* medium size a and b */
        w = a-b;
        if (w>b) {
            t1 = 0;
            ux.d = t1;
            __HI(ux) = ha;
            t1 = ux.d;
            t2 = a-t1;
            w  = fd_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
        } else {
            a  = a+a;
            y1 = 0;
            ux.d = y1;
            __HI(ux) = hb;
            y1 = ux.d;
            y2 = b - y1;
            t1 = 0;
            ux.d = t1;
            __HI(ux) = ha+0x00100000;
            t1 = ux.d;
            t2 = a - t1;
            w  = fd_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
        }
        if(k!=0) {
            t1 = 1.0;
            ux.d = t1;
            __HI(ux) += (k<<20);
            t1 = ux.d;
            return t1*w;
        } else return w;
}
1	/* -- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 --
2	*
3	* *** BEGIN LICENSE BLOCK ***
4	* Version: MPL 1.1/GPL 2.0/LGPL 2.1
5	*
6	* The contents of this file are subject to the Mozilla Public License Version
7	* 1.1 (the "License"); you may not use this file except in compliance with
8	* the License. You may obtain a copy of the License at
9	* http://www.mozilla.org/MPL/
10	*
11	* Software distributed under the License is distributed on an "AS IS" basis,
12	* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
13	* for the specific language governing rights and limitations under the
14	* License.
15	*
16	* The Original Code is Mozilla Communicator client code, released
17	* March 31, 1998.
18	*
19	* The Initial Developer of the Original Code is
20	* Sun Microsystems, Inc.
21	* Portions created by the Initial Developer are Copyright (C) 1998
22	* the Initial Developer. All Rights Reserved.
23	*
24	* Contributor(s):
25	*
26	* Alternatively, the contents of this file may be used under the terms of
27	* either of the GNU General Public License Version 2 or later (the "GPL"),
28	* or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
29	* in which case the provisions of the GPL or the LGPL are applicable instead
30	* of those above. If you wish to allow use of your version of this file only
31	* under the terms of either the GPL or the LGPL, and not to allow others to
32	* use your version of this file under the terms of the MPL, indicate your
33	* decision by deleting the provisions above and replace them with the notice
34	* and other provisions required by the GPL or the LGPL. If you do not delete
35	* the provisions above, a recipient may use your version of this file under
36	* the terms of any one of the MPL, the GPL or the LGPL.
37	*
38	* *** END LICENSE BLOCK *** */
39
40	/* @(#)e_hypot.c 1.3 95/01/18 */
41	/*
42	* ====================================================
43	* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
44	*
45	* Developed at SunSoft, a Sun Microsystems, Inc. business.
46	* Permission to use, copy, modify, and distribute this
47	* software is freely granted, provided that this notice
48	* is preserved.
49	* ====================================================
50	*/
51
52	/* __ieee754_hypot(x,y)
53	*
54	* Method :
55	* If (assume round-to-nearest) z=xx+yy
56	* has error less than sqrt(2)/2 ulp, than
57	* sqrt(z) has error less than 1 ulp (exercise).
58	*
59	* So, compute sqrt(xx+yy) with some care as
60	* follows to get the error below 1 ulp:
61	*
62	* Assume x>y>0;
63	* (if possible, set rounding to round-to-nearest)
64	* 1. if x > 2y use
65	* x1x1+(yy+(x2(x+x1))) for xx+y*y
66	* where x1 = x with lower 32 bits cleared, x2 = x-x1; else
67	* 2. if x <= 2y use
68	* t1y1+((x-y)(x-y)+(t1y2+t2y))
69	* where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
70	* y1= y with lower 32 bits chopped, y2 = y-y1.
71	*
72	* NOTE: scaling may be necessary if some argument is too
73	* large or too tiny
74	*
75	* Special cases:
76	* hypot(x,y) is INF if x or y is +INF or -INF; else
77	* hypot(x,y) is NAN if x or y is NAN.
78	*
79	* Accuracy:
80	* hypot(x,y) returns sqrt(x^2+y^2) with error less
81	* than 1 ulps (units in the last place)
82	*/
83
84	#include "fdlibm.h"
85
86	#ifdef __STDC__
87	double __ieee754_hypot(double x, double y)
88	#else
89	double __ieee754_hypot(x,y)
90	double x, y;
91	#endif
92	{
93	fd_twoints ux, uy;
94	double a=x,b=y,t1,t2,y1,y2,w;
95	int j,k,ha,hb;
96
97	ux.d = x; uy.d = y;
98	ha = __HI(ux)&0x7fffffff; /* high word of x */
99	hb = __HI(uy)&0x7fffffff; /* high word of y */
100	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
101	ux.d = a; uy.d = b;
102	__HI(ux) = ha; /* a <- \|a\| */
103	__HI(uy) = hb; /* b <- \|b\| */
104	a = ux.d; b = uy.d;
105	if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2*60 /
106	k=0;
107	if(ha > 0x5f300000) { /* a>2*500 /
108	if(ha >= 0x7ff00000) { /* Inf or NaN */
109	w = a+b; /* for sNaN */
110	ux.d = a; uy.d = b;
111	if(((ha&0xfffff)\|__LO(ux))==0) w = a;
112	if(((hb^0x7ff00000)\|__LO(uy))==0) w = b;
113	return w;
114	}
115	/* scale a and b by 2*-600 /
116	ha -= 0x25800000; hb -= 0x25800000; k += 600;
117	ux.d = a; uy.d = b;
118	__HI(ux) = ha;
119	__HI(uy) = hb;
120	a = ux.d; b = uy.d;
121	}
122	if(hb < 0x20b00000) { /* b < 2*-500 /
123	if(hb <= 0x000fffff) { /* subnormal b or 0 */
124	uy.d = b;
125	if((hb\|(__LO(uy)))==0) return a;
126	t1=0;
127	ux.d = t1;
128	__HI(ux) = 0x7fd00000; /* t1=2^1022 */
129	t1 = ux.d;
130	b *= t1;
131	a *= t1;
132	k -= 1022;
133	} else { /* scale a and b by 2^600 */
134	ha += 0x25800000; /* a = 2^600 /
135	hb += 0x25800000; /* b = 2^600 /
136	k -= 600;
137	ux.d = a; uy.d = b;
138	__HI(ux) = ha;
139	__HI(uy) = hb;
140	a = ux.d; b = uy.d;
141	}
142	}
143	/* medium size a and b */
144	w = a-b;
145	if (w>b) {
146	t1 = 0;
147	ux.d = t1;
148	__HI(ux) = ha;
149	t1 = ux.d;
150	t2 = a-t1;
151	w = fd_sqrt(t1t1-(b(-b)-t2*(a+t1)));
152	} else {
153	a = a+a;
154	y1 = 0;
155	ux.d = y1;
156	__HI(ux) = hb;
157	y1 = ux.d;
158	y2 = b - y1;
159	t1 = 0;
160	ux.d = t1;
161	__HI(ux) = ha+0x00100000;
162	t1 = ux.d;
163	t2 = a - t1;
164	w = fd_sqrt(t1y1-(w(-w)-(t1y2+t2b)));
165	}
166	if(k!=0) {
167	t1 = 1.0;
168	ux.d = t1;
169	__HI(ux) += (k<<20);
170	t1 = ux.d;
171	return t1*w;
172	} else return w;
173	}