1
2 /*
3 * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
4 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
5 *
6 * This code is free software; you can redistribute it and/or modify it
7 * under the terms of the GNU General Public License version 2 only, as
8 * published by the Free Software Foundation. Oracle designates this
9 * particular file as subject to the "Classpath" exception as provided
10 * by Oracle in the LICENSE file that accompanied this code.
11 *
12 * This code is distributed in the hope that it will be useful, but WITHOUT
13 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
14 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
15 * version 2 for more details (a copy is included in the LICENSE file that
16 * accompanied this code).
17 *
18 * You should have received a copy of the GNU General Public License version
19 * 2 along with this work; if not, write to the Free Software Foundation,
20 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
21 *
22 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
23 * or visit www.oracle.com if you need additional information or have any
24 * questions.
25 */
26
27 /* __ieee754_hypot(x,y)
28 *
29 * Method :
30 * If (assume round-to-nearest) z=x*x+y*y
31 * has error less than sqrt(2)/2 ulp, than
32 * sqrt(z) has error less than 1 ulp (exercise).
33 *
34 * So, compute sqrt(x*x+y*y) with some care as
35 * follows to get the error below 1 ulp:
36 *
37 * Assume x>y>0;
38 * (if possible, set rounding to round-to-nearest)
39 * 1. if x > 2y use
40 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
41 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else
42 * 2. if x <= 2y use
43 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
44 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
45 * y1= y with lower 32 bits chopped, y2 = y-y1.
46 *
47 * NOTE: scaling may be necessary if some argument is too
48 * large or too tiny
49 *
50 * Special cases:
51 * hypot(x,y) is INF if x or y is +INF or -INF; else
52 * hypot(x,y) is NAN if x or y is NAN.
53 *
54 * Accuracy:
55 * hypot(x,y) returns sqrt(x^2+y^2) with error less
56 * than 1 ulps (units in the last place)
57 */
58
59 #include "fdlibm.h"
60
61 #ifdef __STDC__
62 double __ieee754_hypot(double x, double y)
63 #else
64 double __ieee754_hypot(x,y)
65 double x, y;
66 #endif
67 {
68 double a=x,b=y,t1,t2,y1,y2,w;
69 int j,k,ha,hb;
70
71 ha = __HI(x)&0x7fffffff; /* high word of x */
72 hb = __HI(y)&0x7fffffff; /* high word of y */
73 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
74 __HI(a) = ha; /* a <- |a| */
75 __HI(b) = hb; /* b <- |b| */
76 if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
77 k=0;
78 if(ha > 0x5f300000) { /* a>2**500 */
79 if(ha >= 0x7ff00000) { /* Inf or NaN */
80 w = a+b; /* for sNaN */
81 if(((ha&0xfffff)|__LO(a))==0) w = a;
82 if(((hb^0x7ff00000)|__LO(b))==0) w = b;
83 return w;
84 }
85 /* scale a and b by 2**-600 */
86 ha -= 0x25800000; hb -= 0x25800000; k += 600;
87 __HI(a) = ha;
88 __HI(b) = hb;
89 }
90 if(hb < 0x20b00000) { /* b < 2**-500 */
91 if(hb <= 0x000fffff) { /* subnormal b or 0 */
92 if((hb|(__LO(b)))==0) return a;
93 t1=0;
94 __HI(t1) = 0x7fd00000; /* t1=2^1022 */
95 b *= t1;
96 a *= t1;
97 k -= 1022;
98 } else { /* scale a and b by 2^600 */
99 ha += 0x25800000; /* a *= 2^600 */
100 hb += 0x25800000; /* b *= 2^600 */
101 k -= 600;
102 __HI(a) = ha;
103 __HI(b) = hb;
104 }
105 }
106 /* medium size a and b */
107 w = a-b;
108 if (w>b) {
109 t1 = 0;
110 __HI(t1) = ha;
111 t2 = a-t1;
112 w = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
113 } else {
114 a = a+a;
115 y1 = 0;
116 __HI(y1) = hb;
117 y2 = b - y1;
118 t1 = 0;
119 __HI(t1) = ha+0x00100000;
120 t2 = a - t1;
121 w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
122 }
123 if(k!=0) {
124 t1 = 1.0;
125 __HI(t1) += (k<<20);
126 return t1*w;
127 } else return w;
128 }