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 2005 Sun Microsystems, Inc. All rights reserved.
28 * Use is subject to license terms.
29 */
30
31 #pragma weak __logf = logf
32
33 /*
34 * Algorithm:
35 *
36 * Let y = x rounded to six significant bits. Then for any choice
37 * of e and z such that y = 2^e z, we have
38 *
39 * log(x) = e log(2) + log(z) + log(1+(x-y)/y)
40 *
41 * Note that (x-y)/y = (x'-y')/y' for any scaled x' = sx, y' = sy;
42 * in particular, we can take s to be the power of two that makes
43 * ulp(x') = 1.
44 *
45 * From a table, obtain l = log(z) and r = 1/y'. For |s| <= 2^-6,
46 * approximate log(1+s) by a polynomial p(s) where p(s) := s+s*s*
47 * (K1+s*(K2+s*K3)). Then we compute the expression above as
48 * e*ln2 + l + p(r*(x'-y')) all evaluated in double precision.
49 *
50 * When x is subnormal, we first scale it to the normal range,
51 * adjusting e accordingly.
52 *
53 * Accuracy:
54 *
55 * The largest error is less than 0.6 ulps.
56 */
57
58 #include "libm.h"
59
60 /*
61 * For i = 0, ..., 12,
62 * TBL[2i] = log(1 + i/32) and TBL[2i+1] = 2^-23 / (1 + i/32)
63 *
64 * For i = 13, ..., 32,
65 * TBL[2i] = log(1/2 + i/64) and TBL[2i+1] = 2^-23 / (1 + i/32)
66 */
67 static const double TBL[] = {
68 0.000000000000000000e+00, 1.192092895507812500e-07,
69 3.077165866675368733e-02, 1.155968868371212153e-07,
70 6.062462181643483994e-02, 1.121969784007352926e-07,
71 8.961215868968713805e-02, 1.089913504464285680e-07,
72 1.177830356563834557e-01, 1.059638129340277719e-07,
73 1.451820098444978890e-01, 1.030999260979729787e-07,
74 1.718502569266592284e-01, 1.003867701480263102e-07,
75 1.978257433299198675e-01, 9.781275040064102225e-08,
76 2.231435513142097649e-01, 9.536743164062500529e-08,
77 2.478361639045812692e-01, 9.304139672256097884e-08,
78 2.719337154836417580e-01, 9.082612537202380448e-08,
79 2.954642128938358980e-01, 8.871388989825581272e-08,
80 3.184537311185345887e-01, 8.669766512784091150e-08,
81 -3.522205935893520934e-01, 8.477105034722222546e-08,
82 -3.302416868705768671e-01, 8.292820142663043248e-08,
83 -3.087354816496132859e-01, 8.116377160904255122e-08,
84 -2.876820724517809014e-01, 7.947285970052082892e-08,
85 -2.670627852490452536e-01, 7.785096460459183052e-08,
86 -2.468600779315257843e-01, 7.629394531250000159e-08,
87 -2.270574506353460753e-01, 7.479798560049019504e-08,
88 -2.076393647782444896e-01, 7.335956280048077330e-08,
89 -1.885911698075500298e-01, 7.197542010613207272e-08,
90 -1.698990367953974734e-01, 7.064254195601851460e-08,
91 -1.515498981272009327e-01, 6.935813210227272390e-08,
92 -1.335313926245226268e-01, 6.811959402901785336e-08,
93 -1.158318155251217008e-01, 6.692451343201754014e-08,
94 -9.844007281325252434e-02, 6.577064251077586116e-08,
95 -8.134563945395240081e-02, 6.465588585805084723e-08,
96 -6.453852113757117814e-02, 6.357828776041666578e-08,
97 -4.800921918636060631e-02, 6.253602074795082293e-08,
98 -3.174869831458029812e-02, 6.152737525201612732e-08,
99 -1.574835696813916761e-02, 6.055075024801586965e-08,
100 0.000000000000000000e+00, 5.960464477539062500e-08,
101 };
102
103 static const double C[] = {
104 6.931471805599452862e-01,
105 -2.49887584306188944706e-01,
106 3.33368809981254554946e-01,
107 -5.00000008402474976565e-01
108 };
109
110 #define ln2 C[0]
111 #define K3 C[1]
112 #define K2 C[2]
113 #define K1 C[3]
114
115 float
116 logf(float x)
117 {
118 double v, t;
119 float f;
120 int hx, ix, i, exp, iy;
121
122 hx = *(int *)&x;
123 ix = hx & ~0x80000000;
124
125 if (ix >= 0x7f800000) /* nan or inf */
126 return ((hx < 0) ? x * 0.0f : x *x);
127
128 exp = 0;
129
130 if (hx < 0x00800000) { /* negative, zero, or subnormal */
131 if (hx <= 0) {
132 f = 0.0f;
133 return ((ix == 0) ? -1.0f / f : f / f);
134 }
135
136 /* subnormal; scale by 2^149 */
137 f = (float)ix;
138 ix = *(int *)&f;
139 exp = -149;
140 }
141
142 exp += (ix - 0x3f320000) >> 23;
143 ix &= 0x007fffff;
144 iy = (ix + 0x20000) & 0xfffc0000;
145 i = iy >> 17;
146 t = ln2 * (double)exp + TBL[i];
147 v = (double)(ix - iy) * TBL[i + 1];
148 v += (v * v) * (K1 + v * (K2 + v * K3));
149 f = (float)(t + v);
150 return (f);
151 }