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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>
5262 libm needs to be carefully unifdef'd
5268 libm doesn't need to hide symbols which are already local
Reviewed by: Josef 'Jeff' Sipek <jeffpc@josefsipek.net>
Reviewed by: Igor Kozhukhov <ikozhukhov@gmail.com>
Reviewed by: Gordon Ross <gwr@nexenta.com>
Approved by: Gordon Ross <gwr@nexenta.com>
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--- old/usr/src/lib/libm/common/Q/expm1l.c
+++ new/usr/src/lib/libm/common/Q/expm1l.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 -#if defined(ELFOBJ)
31 -#pragma weak expm1l = __expm1l
32 -#endif
30 +#pragma weak __expm1l = expm1l
31 +
33 32 #if !defined(__sparc)
34 33 #error Unsupported architecture
35 34 #endif
36 35
37 36 /*
38 37 * expm1l(x)
39 38 *
40 39 * Table driven method
41 40 * Written by K.C. Ng, June 1995.
42 41 * Algorithm :
43 42 * 1. expm1(x) = x if x<2**-114
44 43 * 2. if |x| <= 0.0625 = 1/16, use approximation
45 44 * expm1(x) = x + x*P/(2-P)
46 45 * where
47 46 * P = x - z*(P1+z*(P2+z*(P3+z*(P4+z*(P5+z*P6+z*P7))))), z = x*x;
48 47 * (this formula is derived from
49 48 * 2-P+x = R = x*(exp(x)+1)/(exp(x)-1) ~ 2 + x*x/6 - x^4/360 + ...)
50 49 *
51 50 * P1 = 1.66666666666666666666666666666638500528074603030e-0001
52 51 * P2 = -2.77777777777777777777777759668391122822266551158e-0003
53 52 * P3 = 6.61375661375661375657437408890138814721051293054e-0005
54 53 * P4 = -1.65343915343915303310185228411892601606669528828e-0006
55 54 * P5 = 4.17535139755122945763580609663414647067443411178e-0008
56 55 * P6 = -1.05683795988668526689182102605260986731620026832e-0009
57 56 * P7 = 2.67544168821852702827123344217198187229611470514e-0011
58 57 *
59 58 * Accuracy: |R-x*(exp(x)+1)/(exp(x)-1)|<=2**-119.13
60 59 *
61 60 * 3. For 1/16 < |x| < 1.125, choose x(+-i) ~ +-(i+4.5)/64, i=0,..,67
62 61 * since
63 62 * exp(x) = exp(xi+(x-xi))= exp(xi)*exp((x-xi))
64 63 * we have
65 64 * expm1(x) = expm1(xi)+(exp(xi))*(expm1(x-xi))
66 65 * where
67 66 * |s=x-xi| <= 1/128
68 67 * and
69 68 * expm1(s)=2s/(2-R), R= s-s^2*(T1+s^2*(T2+s^2*(T3+s^2*(T4+s^2*T5))))
70 69 *
71 70 * T1 = 1.666666666666666666666666666660876387437e-1L,
72 71 * T2 = -2.777777777777777777777707812093173478756e-3L,
73 72 * T3 = 6.613756613756613482074280932874221202424e-5L,
74 73 * T4 = -1.653439153392139954169609822742235851120e-6L,
75 74 * T5 = 4.175314851769539751387852116610973796053e-8L;
76 75 *
77 76 * 4. For |x| >= 1.125, return exp(x)-1.
78 77 * (see algorithm for exp)
79 78 *
80 79 * Special cases:
81 80 * expm1l(INF) is INF, expm1l(NaN) is NaN;
82 81 * expm1l(-INF)= -1;
83 82 * for finite argument, only expm1l(0)=0 is exact.
84 83 *
85 84 * Accuracy:
86 85 * according to an error analysis, the error is always less than
87 86 * 2 ulp (unit in the last place).
88 87 *
89 88 * Misc. info.
90 89 * For 113 bit long double
91 90 * if x > 1.135652340629414394949193107797076342845e+4
92 91 * then expm1l(x) overflow;
93 92 *
94 93 * Constants:
95 94 * Only decimal values are given. We assume that the compiler will convert
96 95 * from decimal to binary accurately enough to produce the correct
97 96 * hexadecimal values.
98 97 */
99 98
100 99 #include "libm.h"
101 100
102 101 extern const long double _TBL_expl_hi[], _TBL_expl_lo[];
103 102 extern const long double _TBL_expm1lx[], _TBL_expm1l[];
104 103
105 104 static const long double
106 105 zero = +0.0L,
107 106 one = +1.0L,
108 107 two = +2.0L,
109 108 ln2_64 = +1.083042469624914545964425189778400898568e-2L,
110 109 ovflthreshold = +1.135652340629414394949193107797076342845e+4L,
111 110 invln2_32 = +4.616624130844682903551758979206054839765e+1L,
112 111 ln2_32hi = +2.166084939249829091928849858592451515688e-2L,
113 112 ln2_32lo = +5.209643502595475652782654157501186731779e-27L,
114 113 huge = +1.0e4000L,
115 114 tiny = +1.0e-4000L,
116 115 P1 = +1.66666666666666666666666666666638500528074603030e-0001L,
117 116 P2 = -2.77777777777777777777777759668391122822266551158e-0003L,
118 117 P3 = +6.61375661375661375657437408890138814721051293054e-0005L,
119 118 P4 = -1.65343915343915303310185228411892601606669528828e-0006L,
120 119 P5 = +4.17535139755122945763580609663414647067443411178e-0008L,
121 120 P6 = -1.05683795988668526689182102605260986731620026832e-0009L,
122 121 P7 = +2.67544168821852702827123344217198187229611470514e-0011L,
123 122 /* rational approximation coeffs for [-(ln2)/64,(ln2)/64] */
124 123 T1 = +1.666666666666666666666666666660876387437e-1L,
125 124 T2 = -2.777777777777777777777707812093173478756e-3L,
126 125 T3 = +6.613756613756613482074280932874221202424e-5L,
127 126 T4 = -1.653439153392139954169609822742235851120e-6L,
128 127 T5 = +4.175314851769539751387852116610973796053e-8L;
129 128
130 129 long double
131 130 expm1l(long double x) {
132 131 int hx, ix, j, k, m;
133 132 long double t, r, s, w;
134 133
135 134 hx = ((int *) &x)[HIXWORD];
136 135 ix = hx & ~0x80000000;
137 136 if (ix >= 0x7fff0000) {
138 137 if (x != x)
139 138 return (x + x); /* NaN */
140 139 if (x < zero)
141 140 return (-one); /* -inf */
142 141 return (x); /* +inf */
143 142 }
144 143 if (ix < 0x3fff4000) { /* |x| < 1.25 */
145 144 if (ix < 0x3ffb0000) { /* |x| < 0.0625 */
146 145 if (ix < 0x3f8d0000) {
147 146 if ((int) x == 0)
148 147 return (x); /* |x|<2^-114 */
149 148 }
150 149 t = x * x;
151 150 r = (x - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t *
152 151 (P5 + t * (P6 + t * P7)))))));
153 152 return (x + (x * r) / (two - r));
154 153 }
155 154 /* compute i = [64*x] */
156 155 m = 0x4009 - (ix >> 16);
157 156 j = ((ix & 0x0000ffff) | 0x10000) >> m; /* j=4,...,67 */
158 157 if (hx < 0)
159 158 j += 82; /* negative */
160 159 s = x - _TBL_expm1lx[j];
161 160 t = s * s;
162 161 r = s - t * (T1 + t * (T2 + t * (T3 + t * (T4 + t * T5))));
163 162 r = (s + s) / (two - r);
164 163 w = _TBL_expm1l[j];
165 164 return (w + (w + one) * r);
166 165 }
167 166 if (hx > 0) {
168 167 if (x > ovflthreshold)
169 168 return (huge * huge);
170 169 k = (int) (invln2_32 * (x + ln2_64));
171 170 } else {
172 171 if (x < -80.0)
173 172 return (tiny - x / x);
174 173 k = (int) (invln2_32 * (x - ln2_64));
175 174 }
176 175 j = k & 0x1f;
177 176 m = k >> 5;
178 177 t = (long double) k;
179 178 x = (x - t * ln2_32hi) - t * ln2_32lo;
180 179 t = x * x;
181 180 r = (x - t * (T1 + t * (T2 + t * (T3 + t * (T4 + t * T5))))) - two;
182 181 x = _TBL_expl_hi[j] - ((_TBL_expl_hi[j] * (x + x)) / r -
183 182 _TBL_expl_lo[j]);
184 183 return (scalbnl(x, m) - one);
185 184 }
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