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)
62extern enum fp_direction_type __swap87RD(enum fp_direction_type);
63
64#define	k	0x7fff
65
66long double
67hypotl(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