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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/C/log2.c
+++ new/usr/src/lib/libm/common/C/log2.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 log2 = __log2
30 +#pragma weak __log2 = log2
31 31
32 32 /* INDENT OFF */
33 33 /*
34 34 * log2(x) = log(x)/log2
35 35 *
36 36 * Base on Table look-up algorithm with product polynomial
37 37 * approximation for log(x).
38 38 *
39 39 * By K.C. Ng, Nov 29, 2004
40 40 *
41 41 * (a). For x in [1-0.125, 1+0.125], from log.c we have
42 42 * log(x) = f + ((a1*f^2) *
43 43 * ((a2 + (a3*f)*(a4+f)) + (f^3)*(a5+f))) *
44 44 * (((a6 + f*(a7+f)) + (f^3)*(a8+f)) *
45 45 * ((a9 + (a10*f)*(a11+f)) + (f^3)*(a12+f)))
46 46 * where f = x - 1.
47 47 * (i) modify a1 <- a1 / log2
48 48 * (ii) 1/log2 = 1.4426950408889634...
49 49 * = 1.5 - 0.057304959... (4 bit shift)
50 50 * Let lv = 1.5 - 1/log2, then
51 51 * lv = 0.057304959111036592640075318998107956665325,
52 52 * (iii) f*1.5 is exact because f has 3 trailing zero.
53 53 * (iv) Thus, log2(x) = f*1.5 - (lv*f - PPoly)
54 54 *
55 55 * (b). For 0.09375 <= x < 24
56 56 * Let j = (ix - 0x3fb80000) >> 15. Look up Y[j], 1/Y[j], and log(Y[j])
57 57 * from _TBL_log.c. Then
58 58 * log2(x) = log2(Y[j]) + log2(1 + (x-Y[j])*(1/Y[j]))
59 59 * = log(Y[j])(1/log2) + log2(1 + s)
60 60 * where
61 61 * s = (x-Y[j])*(1/Y[j])
62 62 * From log.c, we have log(1+s) =
63 63 * 2 2 2
64 64 * (b s) (b + b s + s ) [b + b s + s (b + s)] (b + b s + s )
65 65 * 1 2 3 4 5 6 7 8
66 66 *
67 67 * By setting b1 <- b1/log2, we have
68 68 * log2(x) = 1.5 * T - (lv * T - POLY(s))
69 69 *
70 70 * (c). Otherwise, get "n", the exponent of x, and then normalize x to
71 71 * z in [1,2). Then similar to (b) find a Y[i] that matches z to 5.5
72 72 * significant bits. Then
73 73 * log2(x) = n + log2(z).
74 74 *
75 75 * Special cases:
76 76 * log2(x) is NaN with signal if x < 0 (including -INF) ;
77 77 * log2(+INF) is +INF; log2(0) is -INF with signal;
78 78 * log2(NaN) is that NaN with no signal.
79 79 *
80 80 * Maximum error observed: less than 0.84 ulp
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81 81 *
82 82 * Constants:
83 83 * The hexadecimal values are the intended ones for the following constants.
84 84 * The decimal values may be used, provided that the compiler will convert
85 85 * from decimal to binary accurately enough to produce the hexadecimal values
86 86 * shown.
87 87 */
88 88 /* INDENT ON */
89 89
90 90 #include "libm.h"
91 -#include "libm_synonyms.h"
92 91 #include "libm_protos.h"
93 92
94 93 extern const double _TBL_log[];
95 94
96 95 static const double P[] = {
97 96 /* ONE */ 1.0,
98 97 /* TWO52 */ 4503599627370496.0,
99 98 /* LN10V */ 1.4426950408889634073599246810018920433347, /* 1/log10 */
100 99 /* ZERO */ 0.0,
101 100 /* A1 */ -9.6809362455249638217841932228967194640116e-02,
102 101 /* A2 */ 1.99628461483039965074226529395673424005508422852e+0000,
103 102 /* A3 */ 2.26812367662950720159642514772713184356689453125e+0000,
104 103 /* A4 */ -9.05030639084976384900471657601883634924888610840e-0001,
105 104 /* A5 */ -1.48275767132434044270894446526654064655303955078e+0000,
106 105 /* A6 */ 1.88158320939722756293122074566781520843505859375e+0000,
107 106 /* A7 */ 1.83309386046986411145098827546462416648864746094e+0000,
108 107 /* A8 */ 1.24847063988317086291601754055591300129890441895e+0000,
109 108 /* A9 */ 1.98372421445537705508854742220137268304824829102e+0000,
110 109 /* A10 */ -3.94711735767898475035764249696512706577777862549e-0001,
111 110 /* A11 */ 3.07890395362954372160402272129431366920471191406e+0000,
112 111 /* A12 */ -9.60099585275022149311041630426188930869102478027e-0001,
113 112 /* B1 */ -1.8039695622547469514898963204616532885451e-01,
114 113 /* B2 */ 1.87161713283355151891381127914642725337613123482e+0000,
115 114 /* B3 */ -1.89082956295731507978530316904652863740921020508e+0000,
116 115 /* B4 */ -2.50562891673640253387134180229622870683670043945e+0000,
117 116 /* B5 */ 1.64822828085258366037635369139024987816810607910e+0000,
118 117 /* B6 */ -1.24409107065868340669112512841820716857910156250e+0000,
119 118 /* B7 */ 1.70534231658220414296067701798165217041969299316e+0000,
120 119 /* B8 */ 1.99196833784655646937267192697618156671524047852e+0000,
121 120 /* LGH */ 1.5,
122 121 /* LGL */ 0.057304959111036592640075318998107956665325,
123 122 };
124 123
125 124 #define ONE P[0]
126 125 #define TWO52 P[1]
127 126 #define LN10V P[2]
128 127 #define ZERO P[3]
129 128 #define A1 P[4]
130 129 #define A2 P[5]
131 130 #define A3 P[6]
132 131 #define A4 P[7]
133 132 #define A5 P[8]
134 133 #define A6 P[9]
135 134 #define A7 P[10]
136 135 #define A8 P[11]
137 136 #define A9 P[12]
138 137 #define A10 P[13]
139 138 #define A11 P[14]
140 139 #define A12 P[15]
141 140 #define B1 P[16]
142 141 #define B2 P[17]
143 142 #define B3 P[18]
144 143 #define B4 P[19]
145 144 #define B5 P[20]
146 145 #define B6 P[21]
147 146 #define B7 P[22]
148 147 #define B8 P[23]
149 148 #define LGH P[24]
150 149 #define LGL P[25]
151 150
152 151 double
153 152 log2(double x) {
154 153 int i, hx, ix, n, lx;
155 154
156 155 n = 0;
157 156 hx = ((int *) &x)[HIWORD]; ix = hx & 0x7fffffff;
158 157 lx = ((int *) &x)[LOWORD];
159 158
160 159 /* subnormal,0,negative,inf,nan */
161 160 if ((hx + 0x100000) < 0x200000) {
162 161 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
163 162 if (ix >= 0x7ff80000) /* assumes sparc-like QNaN */
164 163 return (x); /* for Cheetah when x is QNaN */
165 164 #endif
166 165 if (((hx << 1) | lx) == 0) /* log(0.0) = -inf */
167 166 return (A5 / fabs(x));
168 167 if (hx < 0) { /* x < 0 */
169 168 if (ix >= 0x7ff00000)
170 169 return (x - x); /* x is -inf or NaN */
171 170 else
172 171 return (ZERO / (x - x));
173 172 }
174 173 if (((hx - 0x7ff00000) | lx) == 0) /* log(inf) = inf */
175 174 return (x);
176 175 if (ix >= 0x7ff00000) /* log(NaN) = NaN */
177 176 return (x - x);
178 177 x *= TWO52;
179 178 n = -52;
180 179 hx = ((int *) &x)[HIWORD]; ix = hx & 0x7fffffff;
181 180 lx = ((int *) &x)[LOWORD];
182 181 }
183 182
184 183 /* 0.09375 (0x3fb80000) <= x < 24 (0x40380000) */
185 184 i = ix >> 19;
186 185 if (i >= 0x7f7 && i <= 0x806) {
187 186 /* 0.875 <= x < 1.125 */
188 187 if (ix >= 0x3fec0000 && ix < 0x3ff20000) {
189 188 double s, z, r, w;
190 189 s = x - ONE; z = s * s; r = (A10 * s) * (A11 + s);
191 190 w = z * s;
192 191 if (((ix << 12) | lx) == 0)
193 192 return (z);
194 193 else
195 194 return (LGH * s - (LGL * s - ((A1 * z) *
196 195 ((A2 + (A3 * s) * (A4 + s)) + w * (A5 + s))) *
197 196 (((A6 + s * (A7 + s)) + w * (A8 + s)) *
198 197 ((A9 + r) + w * (A12 + s)))));
199 198 } else {
200 199 double *tb, s;
201 200 i = (ix - 0x3fb80000) >> 15;
202 201 tb = (double *) _TBL_log + (i + i + i);
203 202 if (((ix << 12) | lx) == 0) /* 2's power */
204 203 return ((double) ((ix >> 20) - 0x3ff));
205 204 s = (x - tb[0]) * tb[1];
206 205 return (LGH * tb[2] - (LGL * tb[2] - ((B1 * s) *
207 206 (B2 + s * (B3 + s))) *
208 207 (((B4 + s * B5) + (s * s) * (B6 + s)) *
209 208 (B7 + s * (B8 + s)))));
210 209 }
211 210 } else {
212 211 double *tb, dn, s;
213 212 dn = (double) (n + ((ix >> 20) - 0x3ff));
214 213 ix <<= 12;
215 214 if ((ix | lx) == 0)
216 215 return (dn);
217 216 i = ((unsigned) ix >> 12) | 0x3ff00000; /* scale x to [1,2) */
218 217 ((int *) &x)[HIWORD] = i;
219 218 i = (i - 0x3fb80000) >> 15;
220 219 tb = (double *) _TBL_log + (i + i + i);
221 220 s = (x - tb[0]) * tb[1];
222 221 return (dn + (tb[2] * LN10V + ((B1 * s) *
223 222 (B2 + s * (B3 + s))) *
224 223 (((B4 + s * B5) + (s * s) * (B6 + s)) *
225 224 (B7 + s * (B8 + s)))));
226 225 }
227 226 }
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