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
62 extern enum fp_direction_type __swapRD(enum fp_direction_type);
63
64 static const long double zero = 0.0L, one = 1.0L;
65
66 long double
67 hypotl(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 }