1 /*
2 * CDDL HEADER START
3 *
4 * The contents of this file are subject to the terms of the
5 * Common Development and Distribution License (the "License").
6 * You may not use this file except in compliance with the License.
7 *
8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 * or http://www.opensolaris.org/os/licensing.
10 * See the License for the specific language governing permissions
11 * and limitations under the License.
12 *
13 * When distributing Covered Code, include this CDDL HEADER in each
14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 * If applicable, add the following below this CDDL HEADER, with the
16 * fields enclosed by brackets "[]" replaced with your own identifying
17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 *
19 * CDDL HEADER END
20 */
21
22 /*
23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
24 */
25
26 /*
27 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
28 * Use is subject to license terms.
29 */
30
31 #pragma weak __hypotl = hypotl
32
33 /*
34 * hypotl(x,y)
35 * Method :
36 * If z=x*x+y*y has error less than sqrt(2)/2 ulp than sqrt(z) has
37 * error less than 1 ulp.
38 * So, compute sqrt(x*x+y*y) with some care as follows:
39 * Assume x>y>0;
40 * 1. save and set rounding to round-to-nearest
41 * 2. if x > 2y use
42 * x1*x1+(y*y+(x2*(x+x2))) for x*x+y*y
43 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else
44 * 3. if x <= 2y use
45 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
46 * where t1 = 2x with lower 64 bits cleared, t2 = 2x-t1, y1= y with
47 * lower 32 bits cleared, y2 = y-y1.
48 *
49 * NOTE: DO NOT remove parenthsis!
50 *
51 * Special cases:
52 * hypot(x,y) is INF if x or y is +INF or -INF; else
53 * hypot(x,y) is NAN if x or y is NAN.
54 *
55 * Accuracy:
56 * hypot(x,y) returns sqrt(x^2+y^2) with error less than 1 ulps (units
57 * in the last place)
58 */
59
60 #include "libm.h"
61
62 #if defined(__x86)
63 extern enum fp_direction_type __swap87RD(enum fp_direction_type);
64
65 #define k 0x7fff
66
67 long double
68 hypotl(long double x, long double y)
69 {
70 long double t1, t2, y1, y2, w;
71 int *px = (int *)&x, *py = (int *)&y;
72 int *pt1 = (int *)&t1, *py1 = (int *)&y1;
73 enum fp_direction_type rd;
74 int j, nx, ny, nz;
75
76 px[2] &= 0x7fff; /* clear sign bit and padding bits of x and y */
77 py[2] &= 0x7fff;
78 nx = px[2]; /* biased exponent of x and y */
79 ny = py[2];
80
81 if (ny > nx) {
82 w = x;
83 x = y;
84 y = w;
85 nz = ny;
86 ny = nx;
87 nx = nz;
88 } /* force nx >= ny */
89
90 if (nx - ny >= 66)
91 return (x + y); /* x / y >= 2**65 */
92
93 if (nx < 0x5ff3 && ny > 0x205b) { /* medium x,y */
94 /* save and set RD to Rounding to nearest */
95 rd = __swap87RD(fp_nearest);
96 w = x - y;
97
98 if (w > y) {
99 pt1[2] = px[2];
100 pt1[1] = px[1];
101 pt1[0] = 0;
102 t2 = x - t1;
103 x = sqrtl(t1 * t1 - (y * (-y) - t2 * (x + t1)));
104 } else {
105 x += x;
106 py1[2] = py[2];
107 py1[1] = py[1];
108 py1[0] = 0;
109 y2 = y - y1;
110 pt1[2] = px[2];
111 pt1[1] = px[1];
112 pt1[0] = 0;
113 t2 = x - t1;
114 x = sqrtl(t1 * y1 - (w * (-w) - (t2 * y1 + y2 * x)));
115 }
116
117 if (rd != fp_nearest)
118 __swap87RD(rd); /* restore rounding mode */
119
120 return (x);
121 } else {
122 if (nx == k || ny == k) { /* x or y is INF or NaN */
123 /* since nx >= ny; nx is always k within this block */
124 if (px[1] == 0x80000000 && px[0] == 0)
125 return (x);
126 else if (ny == k && py[1] == 0x80000000 && py[0] == 0)
127 return (y);
128 else
129 return (x + y);
130 }
131
132 if (ny == 0) {
133 if (y == 0.L || x == 0.L)
134 return (x + y);
135
136 pt1[2] = 0x3fff + 16381;
137 pt1[1] = 0x80000000;
138 pt1[0] = 0;
139 py1[2] = 0x3fff - 16381;
140 py1[1] = 0x80000000;
141 py1[0] = 0;
142 x *= t1;
143 y *= t1;
144 return (y1 * hypotl(x, y));
145 }
146
147 j = nx - 0x3fff;
148 px[2] -= j;
149 py[2] -= j;
150 pt1[2] = nx;
151 pt1[1] = 0x80000000;
152 pt1[0] = 0;
153 return (t1 * hypotl(x, y));
154 }
155 }
156 #endif