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 #if defined(ELFOBJ)
31 #pragma weak hypot = __hypot
32 #endif
33
34 /* INDENT OFF */
35 /*
36 * Hypot(x, y)
37 * by K.C. Ng for SUN 4.0 libm, updated 3/11/2003.
38 * Method :
39 * A. When rounding is rounded-to-nearest:
40 * If z = x * x + y * y has error less than sqrt(2) / 2 ulp than
41 * sqrt(z) has error less than 1 ulp.
42 * So, compute sqrt(x*x+y*y) with some care as follows:
43 * Assume x > y > 0;
44 * 1. Check whether save and set rounding to round-to-nearest
45 * 2. if x > 2y use
46 * xh*xh+(y*y+((x-xh)*(x+xh))) for x*x+y*y
47 * where xh = x with lower 32 bits cleared; else
48 * 3. if x <= 2y use
49 * x2h*yh+((x-y)*(x-y)+(x2h*(y-yh)+(x2-x2h)*y))
50 * where x2 = 2*x, x2h = 2x with lower 32 bits cleared, yh = y with
51 * lower 32 bits chopped.
52 *
53 * B. When rounding is not rounded-to-nearest:
54 * The following (magic) formula will yield an error less than 1 ulp.
55 * z = sqrt(x * x + y * y)
56 * hypot(x, y) = x + (y / ((x + z) / y))
57 *
58 * NOTE: DO NOT remove parenthsis!
59 *
60 * Special cases:
61 * hypot(x, y) is INF if x or y is +INF or -INF; else
62 * hypot(x, y) is NAN if x or y is NAN.
63 *
64 * Accuracy:
65 * hypot(x, y) returns sqrt(x^2+y^2) with error less than 1 ulps
66 * (units in the last place)
67 */
68
69 #include "libm.h"
70
71 static const double
72 zero = 0.0,
73 onep1u = 1.00000000000000022204e+00, /* 0x3ff00000 1 = 1+2**-52 */
74 twom53 = 1.11022302462515654042e-16, /* 0x3ca00000 0 = 2**-53 */
75 twom768 = 6.441148769597133308e-232, /* 2^-768 */
76 two768 = 1.552518092300708935e+231; /* 2^768 */
77
78 /* INDENT ON */
79
80 double
81 hypot(double x, double y) {
82 double xh, yh, w, ax, ay;
83 int i, j, nx, ny, ix, iy, iscale = 0;
84 unsigned lx, ly;
85
86 ix = ((int *) &x)[HIWORD] & ~0x80000000;
87 lx = ((int *) &x)[LOWORD];
88 iy = ((int *) &y)[HIWORD] & ~0x80000000;
89 ly = ((int *) &y)[LOWORD];
90 /*
91 * Force ax = |x| ~>~ ay = |y|
92 */
93 if (iy > ix) {
94 ax = fabs(y);
95 ay = fabs(x);
96 i = ix;
97 ix = iy;
98 iy = i;
99 i = lx;
100 lx = ly;
101 ly = i;
102 } else {
103 ax = fabs(x);
104 ay = fabs(y);
105 }
106 nx = ix >> 20;
107 ny = iy >> 20;
108 j = nx - ny;
109 /*
110 * x >= 2^500 (x*x or y*y may overflow)
111 */
112 if (nx >= 0x5f3) {
113 if (nx == 0x7ff) { /* inf or NaN, signal of sNaN */
114 if (((ix - 0x7ff00000) | lx) == 0)
115 return (ax == ay ? ay : ax);
116 else if (((iy - 0x7ff00000) | ly) == 0)
117 return (ay == ax ? ax : ay);
118 else
119 return (ax * ay); /* + -> * for Cheetah */
120 } else if (j > 32) { /* x >> y */
121 if (j <= 53)
122 ay *= twom53;
123 ax += ay;
124 if (((int *) &ax)[HIWORD] == 0x7ff00000)
125 ax = _SVID_libm_err(x, y, 4);
126 return (ax);
127 }
128 ax *= twom768;
129 ay *= twom768;
130 iscale = 2;
131 ix -= 768 << 20;
132 iy -= 768 << 20;
133 }
134 /*
135 * y < 2^-450 (x*x or y*y may underflow)
136 */
137 else if (ny < 0x23d) {
138 if ((ix | lx) == 0)
139 return (ay);
140 if ((iy | ly) == 0)
141 return (ax);
142 if (j > 53) /* x >> y */
143 return (ax + ay);
144 iscale = 1;
145 ax *= two768;
146 ay *= two768;
147 if (nx == 0) {
148 if (ax == zero) /* guard subnormal flush to zero */
149 return (ax);
150 ix = ((int *) &ax)[HIWORD];
151 } else
152 ix += 768 << 20;
153 if (ny == 0) {
154 if (ay == zero) /* guard subnormal flush to zero */
155 return (ax * twom768);
156 iy = ((int *) &ay)[HIWORD];
157 } else
158 iy += 768 << 20;
159 j = (ix >> 20) - (iy >> 20);
160 if (j > 32) { /* x >> y */
161 if (j <= 53)
162 ay *= twom53;
163 return ((ax + ay) * twom768);
164 }
165 } else if (j > 32) { /* x >> y */
166 if (j <= 53)
167 ay *= twom53;
168 return (ax + ay);
169 }
170 /*
171 * Medium range ax and ay with max{|ax/ay|,|ay/ax|} bounded by 2^32
172 * First check rounding mode by comparing onep1u*onep1u with onep1u+twom53.
173 * Make sure the computation is done at run-time.
174 */
175 if (((lx | ly) << 5) == 0) {
176 ay = ay * ay;
177 ax += ay / (ax + sqrt(ax * ax + ay));
178 } else
179 if (onep1u * onep1u != onep1u + twom53) {
180 /* round-to-zero, positive, negative mode */
181 /* magic formula with less than an ulp error */
182 w = sqrt(ax * ax + ay * ay);
183 ax += ay / ((ax + w) / ay);
184 } else {
185 /* round-to-nearest mode */
186 w = ax - ay;
187 if (w > ay) {
188 ((int *) &xh)[HIWORD] = ix;
189 ((int *) &xh)[LOWORD] = 0;
190 ay = ay * ay + (ax - xh) * (ax + xh);
191 ax = sqrt(xh * xh + ay);
192 } else {
193 ax = ax + ax;
194 ((int *) &xh)[HIWORD] = ix + 0x00100000;
195 ((int *) &xh)[LOWORD] = 0;
196 ((int *) &yh)[HIWORD] = iy;
197 ((int *) &yh)[LOWORD] = 0;
198 ay = w * w + ((ax - xh) * yh + (ay - yh) * ax);
199 ax = sqrt(xh * yh + ay);
200 }
201 }
202 if (iscale > 0) {
203 if (iscale == 1)
204 ax *= twom768;
205 else {
206 ax *= two768; /* must generate side effect here */
207 if (((int *) &ax)[HIWORD] == 0x7ff00000)
208 ax = _SVID_libm_err(x, y, 4);
209 }
210 }
211 return (ax);
212 }