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 * long double hypotl(long double x, long double 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 64 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 64 bits chopped, 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#include "longdouble.h"
61
62extern enum fp_direction_type __swapRD(enum fp_direction_type);
63
64static const long double zero = 0.0L, one = 1.0L;
65
66long double
67hypotl(long double x, long double y) {
68	int n0, n1, n2, n3;
69	long double t1, t2, y1, y2, w;
70	int *px = (int *) &x, *py = (int *) &y;
71	int *pt1 = (int *) &t1, *py1 = (int *) &y1;
72	enum fp_direction_type rd;
73	int j, k, nx, ny, nz;
74
75	if ((*(int *) &one) != 0) {	/* determine word ordering */
76		n0 = 0;
77		n1 = 1;
78		n2 = 2;
79		n3 = 3;
80	} else {
81		n0 = 3;
82		n1 = 2;
83		n2 = 1;
84		n3 = 0;
85	}
86
87	px[n0] &= 0x7fffffff;	/* clear sign bit of x and y */
88	py[n0] &= 0x7fffffff;
89	k = 0x7fff0000;
90	nx = px[n0] & k;	/* exponent of x and y */
91	ny = py[n0] & k;
92	if (ny > nx) {
93		w = x;
94		x = y;
95		y = w;
96		nz = ny;
97		ny = nx;
98		nx = nz;
99	}			/* force x > y */
100	if ((nx - ny) >= 0x00730000)
101		return (x + y);	/* x/y >= 2**116 */
102	if (nx < 0x5ff30000 && ny > 0x205b0000) {	/* medium x,y */
103		/* save and set RD to Rounding to nearest */
104		rd = __swapRD(fp_nearest);
105		w = x - y;
106		if (w > y) {
107			pt1[n0] = px[n0];
108			pt1[n1] = px[n1];
109			pt1[n2] = pt1[n3] = 0;
110			t2 = x - t1;
111			x = sqrtl(t1 * t1 - (y * (-y) - t2 * (x + t1)));
112		} else {
113			x = x + x;
114			py1[n0] = py[n0];
115			py1[n1] = py[n1];
116			py1[n2] = py1[n3] = 0;
117			y2 = y - y1;
118			pt1[n0] = px[n0];
119			pt1[n1] = px[n1];
120			pt1[n2] = pt1[n3] = 0;
121			t2 = x - t1;
122			x = sqrtl(t1 * y1 - (w * (-w) - (t2 * y1 + y2 * x)));
123		}
124		if (rd != fp_nearest)
125			(void) __swapRD(rd);	/* restore rounding mode */
126		return (x);
127	} else {
128		if (nx == k || ny == k) {	/* x or y is INF or NaN */
129			if (isinfl(x))
130				t2 = x;
131			else if (isinfl(y))
132				t2 = y;
133			else
134				t2 = x + y;	/* invalid if x or y is sNaN */
135			return (t2);
136		}
137		if (ny == 0) {
138			if (y == zero || x == zero)
139				return (x + y);
140			t1 = scalbnl(one, 16381);
141			x *= t1;
142			y *= t1;
143			return (scalbnl(one, -16381) * hypotl(x, y));
144		}
145		j = nx - 0x3fff0000;
146		px[n0] -= j;
147		py[n0] -= j;
148		pt1[n0] = nx;
149		pt1[n1] = pt1[n2] = pt1[n3] = 0;
150		return (t1 * hypotl(x, y));
151	}
152}
153