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5261 libm should stop using synonyms.h
5298 fabs is 0-sized, confuses dis(1) and others
Reviewed by: Josef 'Jeff' Sipek <jeffpc@josefsipek.net>
Approved by: Gordon Ross <gwr@nexenta.com>
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--- old/usr/src/lib/libm/common/complex/ctanh.c
+++ new/usr/src/lib/libm/common/complex/ctanh.c
1 1 /*
2 2 * CDDL HEADER START
3 3 *
4 4 * The contents of this file are subject to the terms of the
5 5 * Common Development and Distribution License (the "License").
6 6 * You may not use this file except in compliance with the License.
7 7 *
8 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 9 * or http://www.opensolaris.org/os/licensing.
10 10 * See the License for the specific language governing permissions
11 11 * and limitations under the License.
12 12 *
13 13 * When distributing Covered Code, include this CDDL HEADER in each
14 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 15 * If applicable, add the following below this CDDL HEADER, with the
16 16 * fields enclosed by brackets "[]" replaced with your own identifying
17 17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 18 *
19 19 * CDDL HEADER END
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20 20 */
21 21
22 22 /*
23 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
24 24 */
25 25 /*
26 26 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27 27 * Use is subject to license terms.
28 28 */
29 29
30 -#pragma weak ctanh = __ctanh
30 +#pragma weak __ctanh = ctanh
31 31
32 32 /* INDENT OFF */
33 33 /*
34 34 * dcomplex ctanh(dcomplex z);
35 35 *
36 36 * tanh x + i tan y sinh 2x + i sin 2y
37 37 * ctanh z = --------------------- = --------------------
38 38 * 1 + i tanh(x)tan(y) cosh 2x + cos 2y
39 39 *
40 40 * For |x| >= prec/2 (14,28,34,60 for single, double, double extended, quad),
41 41 * we use
42 42 *
43 43 * 1 2x 2 sin 2y
44 44 * cosh 2x = sinh 2x = --- e and hence ctanh z = 1 + i -----------;
45 45 * 2 2x
46 46 * e
47 47 *
48 48 * otherwise, to avoid cancellation, for |x| < prec/2,
49 49 * 2x 2
50 50 * (e - 1) 2 2
51 51 * cosh 2x + cos 2y = 1 + ------------ + cos y - sin y
52 52 * 2x
53 53 * 2 e
54 54 *
55 55 * 1 2x 2 -2x 2
56 56 * = --- (e - 1) e + 2 cos y
57 57 * 2
58 58 * and
59 59 *
60 60 * [ 2x ]
61 61 * 1 [ 2x e - 1 ]
62 62 * sinh 2x = --- [ e - 1 + --------- ]
63 63 * 2 [ 2x ]
64 64 * [ e ]
65 65 * 2x
66 66 * Implementation notes: let t = expm1(2x) = e - 1, then
67 67 *
68 68 * 1 [ t*t 2 ] 1 [ t ]
69 69 * cosh 2x + cos 2y = --- * [ ----- + 4 cos y ]; sinh 2x = --- * [ t + --- ]
70 70 * 2 [ t+1 ] 2 [ t+1 ]
71 71 *
72 72 * Hence,
73 73 *
74 74 *
75 75 * t*t+2t [4(t+1)(cos y)]*(sin y)
76 76 * ctanh z = --------------------------- + i --------------------------
77 77 * t*t+[4(t+1)(cos y)](cos y) t*t+[4(t+1)(cos y)](cos y)
78 78 *
79 79 * EXCEPTION (conform to ISO/IEC 9899:1999(E)):
80 80 * ctanh(0,0)=(0,0)
81 81 * ctanh(x,inf) = (NaN,NaN) for finite x
82 82 * ctanh(x,NaN) = (NaN,NaN) for finite x
83 83 * ctanh(inf,y) = 1+ i*0*sin(2y) for positive-signed finite y
84 84 * ctanh(inf,inf) = (1, +-0)
85 85 * ctanh(inf,NaN) = (1, +-0)
86 86 * ctanh(NaN,0) = (NaN,0)
87 87 * ctanh(NaN,y) = (NaN,NaN) for non-zero y
88 88 * ctanh(NaN,NaN) = (NaN,NaN)
89 89 */
90 90 /* INDENT ON */
91 91
92 92 #include "libm.h" /* exp/expm1/fabs/sin/tanh/sincos */
93 93 #include "complex_wrapper.h"
94 94
95 95 static const double four = 4.0, two = 2.0, one = 1.0, zero = 0.0;
96 96
97 97 dcomplex
98 98 ctanh(dcomplex z) {
99 99 double t, r, v, u, x, y, S, C;
100 100 int hx, ix, lx, hy, iy, ly;
101 101 dcomplex ans;
102 102
103 103 x = D_RE(z);
104 104 y = D_IM(z);
105 105 hx = HI_WORD(x);
106 106 lx = LO_WORD(x);
107 107 ix = hx & 0x7fffffff;
108 108 hy = HI_WORD(y);
109 109 ly = LO_WORD(y);
110 110 iy = hy & 0x7fffffff;
111 111 x = fabs(x);
112 112 y = fabs(y);
113 113
114 114 if ((iy | ly) == 0) { /* ctanh(x,0) = (x,0) for x = 0 or NaN */
115 115 D_RE(ans) = tanh(x);
116 116 D_IM(ans) = zero;
117 117 } else if (iy >= 0x7ff00000) { /* y is inf or NaN */
118 118 if (ix < 0x7ff00000) /* catanh(finite x,inf/nan) is nan */
119 119 D_RE(ans) = D_IM(ans) = y - y;
120 120 else if (((ix - 0x7ff00000) | lx) == 0) { /* x is inf */
121 121 D_RE(ans) = one;
122 122 D_IM(ans) = zero;
123 123 } else {
124 124 D_RE(ans) = x + y;
125 125 D_IM(ans) = y - y;
126 126 }
127 127 } else if (ix >= 0x403c0000) {
128 128 /*
129 129 * |x| > 28 = prec/2 (14,28,34,60)
130 130 * ctanh z ~ 1 + i (sin2y)/(exp(2x))
131 131 */
132 132 D_RE(ans) = one;
133 133 if (iy < 0x7fe00000) /* t = sin(2y) */
134 134 S = sin(y + y);
135 135 else {
136 136 (void) sincos(y, &S, &C);
137 137 S = (S + S) * C;
138 138 }
139 139 if (ix >= 0x7fe00000) { /* |x| > max/2 */
140 140 if (ix >= 0x7ff00000) { /* |x| is inf or NaN */
141 141 if (((ix - 0x7ff00000) | lx) != 0)
142 142 D_RE(ans) = D_IM(ans) = x + y;
143 143 /* x is NaN */
144 144 else
145 145 D_IM(ans) = zero * S; /* x is inf */
146 146 } else
147 147 D_IM(ans) = S * exp(-x); /* underflow */
148 148 } else
149 149 D_IM(ans) = (S + S) * exp(-(x + x));
150 150 /* 2 sin 2y / exp(2x) */
151 151 } else {
152 152 /* INDENT OFF */
153 153 /*
154 154 * t*t+2t
155 155 * ctanh z = --------------------------- +
156 156 * t*t+[4(t+1)(cos y)](cos y)
157 157 *
158 158 * [4(t+1)(cos y)]*(sin y)
159 159 * i --------------------------
160 160 * t*t+[4(t+1)(cos y)](cos y)
161 161 */
162 162 /* INDENT ON */
163 163 (void) sincos(y, &S, &C);
164 164 t = expm1(x + x);
165 165 r = (four * C) * (t + one);
166 166 u = t * t;
167 167 v = one / (u + r * C);
168 168 D_RE(ans) = (u + two * t) * v;
169 169 D_IM(ans) = (r * S) * v;
170 170 }
171 171 if (hx < 0)
172 172 D_RE(ans) = -D_RE(ans);
173 173 if (hy < 0)
174 174 D_IM(ans) = -D_IM(ans);
175 175 return (ans);
176 176 }
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