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 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27 * Use is subject to license terms.
28 */
29
30 #pragma weak hypotl = __hypotl
31
32 /*
33 * hypotl(x,y)
34 * Method :
35 * If z=x*x+y*y has error less than sqrt(2)/2 ulp than sqrt(z) has
36 * error less than 1 ulp.
37 * So, compute sqrt(x*x+y*y) with some care as follows:
38 * Assume x>y>0;
39 * 1. save and set rounding to round-to-nearest
40 * 2. if x > 2y use
41 * x1*x1+(y*y+(x2*(x+x2))) for x*x+y*y
42 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else
43 * 3. if x <= 2y use
44 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
45 * where t1 = 2x with lower 64 bits cleared, t2 = 2x-t1, y1= y with
46 * lower 32 bits cleared, y2 = y-y1.
47 *
48 * NOTE: DO NOT remove parenthsis!
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 than 1 ulps (units
56 * in the last place)
57 */
58
59 #include "libm.h"
60
61 #if defined(__x86)
62 extern enum fp_direction_type __swap87RD(enum fp_direction_type);
63
64 #define k 0x7fff
65
66 long double
67 hypotl(long double x, long double y) {
68 long double t1, t2, y1, y2, w;
69 int *px = (int *) &x, *py = (int *) &y;
70 int *pt1 = (int *) &t1, *py1 = (int *) &y1;
71 enum fp_direction_type rd;
72 int j, nx, ny, nz;
73
74 px[2] &= 0x7fff; /* clear sign bit and padding bits of x and y */
75 py[2] &= 0x7fff;
76 nx = px[2]; /* biased exponent of x and y */
77 ny = py[2];
78 if (ny > nx) {
79 w = x;
80 x = y;
81 y = w;
82 nz = ny;
83 ny = nx;
84 nx = nz;
85 } /* force nx >= ny */
86 if (nx - ny >= 66)
87 return (x + y); /* x / y >= 2**65 */
88 if (nx < 0x5ff3 && ny > 0x205b) { /* medium x,y */
89 /* save and set RD to Rounding to nearest */
90 rd = __swap87RD(fp_nearest);
91 w = x - y;
92 if (w > y) {
93 pt1[2] = px[2];
94 pt1[1] = px[1];
95 pt1[0] = 0;
96 t2 = x - t1;
97 x = sqrtl(t1 * t1 - (y * (-y) - t2 * (x + t1)));
98 } else {
99 x += x;
100 py1[2] = py[2];
101 py1[1] = py[1];
102 py1[0] = 0;
103 y2 = y - y1;
104 pt1[2] = px[2];
105 pt1[1] = px[1];
106 pt1[0] = 0;
107 t2 = x - t1;
108 x = sqrtl(t1 * y1 - (w * (-w) - (t2 * y1 + y2 * x)));
109 }
110 if (rd != fp_nearest)
111 __swap87RD(rd); /* restore rounding mode */
112 return (x);
113 } else {
114 if (nx == k || ny == k) { /* x or y is INF or NaN */
115 /* since nx >= ny; nx is always k within this block */
116 if (px[1] == 0x80000000 && px[0] == 0)
117 return (x);
118 else if (ny == k && py[1] == 0x80000000 && py[0] == 0)
119 return (y);
120 else
121 return (x + y);
122 }
123 if (ny == 0) {
124 if (y == 0.L || x == 0.L)
125 return (x + y);
126 pt1[2] = 0x3fff + 16381;
127 pt1[1] = 0x80000000;
128 pt1[0] = 0;
129 py1[2] = 0x3fff - 16381;
130 py1[1] = 0x80000000;
131 py1[0] = 0;
132 x *= t1;
133 y *= t1;
134 return (y1 * hypotl(x, y));
135 }
136 j = nx - 0x3fff;
137 px[2] -= j;
138 py[2] -= j;
139 pt1[2] = nx;
140 pt1[1] = 0x80000000;
141 pt1[0] = 0;
142 return (t1 * hypotl(x, y));
143 }
144 }
145 #endif