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
hypotl(long double x,long double y)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
146