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 /*
27 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
28 * Use is subject to license terms.
29 */
30
31 #pragma weak __hypotl = hypotl
32
33 /*
34 * long double hypotl(long double x, long double y);
35 * Method :
36 * If z=x*x+y*y has error less than sqrt(2)/2 ulp than sqrt(z) has
37 * error less than 1 ulp.
38 * So, compute sqrt(x*x+y*y) with some care as follows:
39 * Assume x>y>0;
40 * 1. save and set rounding to round-to-nearest
41 * 2. if x > 2y use
42 * x1*x1+(y*y+(x2*(x+x2))) for x*x+y*y
43 * where x1 = x with lower 64 bits cleared, x2 = x-x1; else
44 * 3. if x <= 2y use
45 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
46 * where t1 = 2x with lower 64 bits cleared, t2 = 2x-t1, y1= y with
47 * lower 64 bits chopped, y2 = y-y1.
48 *
49 * NOTE: DO NOT remove parenthsis!
50 *
51 * Special cases:
52 * hypot(x,y) is INF if x or y is +INF or -INF; else
53 * hypot(x,y) is NAN if x or y is NAN.
54 *
55 * Accuracy:
56 * hypot(x,y) returns sqrt(x^2+y^2) with error less than 1 ulps (units
57 * in the last place)
58 */
59
60 #include "libm.h"
61 #include "longdouble.h"
62
63 extern enum fp_direction_type __swapRD(enum fp_direction_type);
64
65 static const long double zero = 0.0L, one = 1.0L;
66 long double
67 hypotl(long double x, long double y)
68 {
69 int n0, n1, n2, n3;
70 long double t1, t2, y1, y2, w;
71 int *px = (int *)&x, *py = (int *)&y;
72 int *pt1 = (int *)&t1, *py1 = (int *)&y1;
73 enum fp_direction_type rd;
74 int j, k, nx, ny, nz;
75
76 if ((*(int *)&one) != 0) { /* determine word ordering */
77 n0 = 0;
78 n1 = 1;
79 n2 = 2;
80 n3 = 3;
81 } else {
82 n0 = 3;
83 n1 = 2;
84 n2 = 1;
85 n3 = 0;
86 }
87
88 px[n0] &= 0x7fffffff; /* clear sign bit of x and y */
89 py[n0] &= 0x7fffffff;
90 k = 0x7fff0000;
91 nx = px[n0] & k; /* exponent of x and y */
92 ny = py[n0] & k;
93
94 if (ny > nx) {
95 w = x;
96 x = y;
97 y = w;
98 nz = ny;
99 ny = nx;
100 nx = nz;
101 } /* force x > y */
102
103 if ((nx - ny) >= 0x00730000)
104 return (x + y); /* x/y >= 2**116 */
105
106 if (nx < 0x5ff30000 && ny > 0x205b0000) { /* medium x,y */
107 /* save and set RD to Rounding to nearest */
108 rd = __swapRD(fp_nearest);
109 w = x - y;
110
111 if (w > y) {
112 pt1[n0] = px[n0];
113 pt1[n1] = px[n1];
114 pt1[n2] = pt1[n3] = 0;
115 t2 = x - t1;
116 x = sqrtl(t1 * t1 - (y * (-y) - t2 * (x + t1)));
117 } else {
118 x = x + x;
119 py1[n0] = py[n0];
120 py1[n1] = py[n1];
121 py1[n2] = py1[n3] = 0;
122 y2 = y - y1;
123 pt1[n0] = px[n0];
124 pt1[n1] = px[n1];
125 pt1[n2] = pt1[n3] = 0;
126 t2 = x - t1;
127 x = sqrtl(t1 * y1 - (w * (-w) - (t2 * y1 + y2 * x)));
128 }
129
130 if (rd != fp_nearest)
131 (void) __swapRD(rd); /* restore rounding mode */
132
133 return (x);
134 } else {
135 if (nx == k || ny == k) { /* x or y is INF or NaN */
136 if (isinfl(x))
137 t2 = x;
138 else if (isinfl(y))
139 t2 = y;
140 else
141 t2 = x + y; /* invalid if x or y is sNaN */
142
143 return (t2);
144 }
145
146 if (ny == 0) {
147 if (y == zero || x == zero)
148 return (x + y);
149
150 t1 = scalbnl(one, 16381);
151 x *= t1;
152 y *= t1;
153 return (scalbnl(one, -16381) * hypotl(x, y));
154 }
155
156 j = nx - 0x3fff0000;
157 px[n0] -= j;
158 py[n0] -= j;
159 pt1[n0] = nx;
160 pt1[n1] = pt1[n2] = pt1[n3] = 0;
161 return (t1 * hypotl(x, y));
162 }
163 }