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 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
23 */
24 /*
25 * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
26 * Use is subject to license terms.
27 */
28
29 #pragma weak __logf = logf
30
31 /*
32 * Algorithm:
33 *
34 * Let y = x rounded to six significant bits. Then for any choice
35 * of e and z such that y = 2^e z, we have
36 *
37 * log(x) = e log(2) + log(z) + log(1+(x-y)/y)
38 *
39 * Note that (x-y)/y = (x'-y')/y' for any scaled x' = sx, y' = sy;
40 * in particular, we can take s to be the power of two that makes
41 * ulp(x') = 1.
42 *
43 * From a table, obtain l = log(z) and r = 1/y'. For |s| <= 2^-6,
44 * approximate log(1+s) by a polynomial p(s) where p(s) := s+s*s*
45 * (K1+s*(K2+s*K3)). Then we compute the expression above as
46 * e*ln2 + l + p(r*(x'-y')) all evaluated in double precision.
47 *
48 * When x is subnormal, we first scale it to the normal range,
49 * adjusting e accordingly.
50 *
51 * Accuracy:
52 *
53 * The largest error is less than 0.6 ulps.
54 */
55
56 #include "libm.h"
57
58 /*
59 * For i = 0, ..., 12,
60 * TBL[2i] = log(1 + i/32) and TBL[2i+1] = 2^-23 / (1 + i/32)
61 *
62 * For i = 13, ..., 32,
63 * TBL[2i] = log(1/2 + i/64) and TBL[2i+1] = 2^-23 / (1 + i/32)
64 */
65 static const double TBL[] = {
66 0.000000000000000000e+00, 1.192092895507812500e-07,
67 3.077165866675368733e-02, 1.155968868371212153e-07,
68 6.062462181643483994e-02, 1.121969784007352926e-07,
69 8.961215868968713805e-02, 1.089913504464285680e-07,
70 1.177830356563834557e-01, 1.059638129340277719e-07,
71 1.451820098444978890e-01, 1.030999260979729787e-07,
72 1.718502569266592284e-01, 1.003867701480263102e-07,
73 1.978257433299198675e-01, 9.781275040064102225e-08,
74 2.231435513142097649e-01, 9.536743164062500529e-08,
75 2.478361639045812692e-01, 9.304139672256097884e-08,
76 2.719337154836417580e-01, 9.082612537202380448e-08,
77 2.954642128938358980e-01, 8.871388989825581272e-08,
78 3.184537311185345887e-01, 8.669766512784091150e-08,
79 -3.522205935893520934e-01, 8.477105034722222546e-08,
80 -3.302416868705768671e-01, 8.292820142663043248e-08,
81 -3.087354816496132859e-01, 8.116377160904255122e-08,
82 -2.876820724517809014e-01, 7.947285970052082892e-08,
83 -2.670627852490452536e-01, 7.785096460459183052e-08,
84 -2.468600779315257843e-01, 7.629394531250000159e-08,
85 -2.270574506353460753e-01, 7.479798560049019504e-08,
86 -2.076393647782444896e-01, 7.335956280048077330e-08,
87 -1.885911698075500298e-01, 7.197542010613207272e-08,
88 -1.698990367953974734e-01, 7.064254195601851460e-08,
89 -1.515498981272009327e-01, 6.935813210227272390e-08,
90 -1.335313926245226268e-01, 6.811959402901785336e-08,
91 -1.158318155251217008e-01, 6.692451343201754014e-08,
92 -9.844007281325252434e-02, 6.577064251077586116e-08,
93 -8.134563945395240081e-02, 6.465588585805084723e-08,
94 -6.453852113757117814e-02, 6.357828776041666578e-08,
95 -4.800921918636060631e-02, 6.253602074795082293e-08,
96 -3.174869831458029812e-02, 6.152737525201612732e-08,
97 -1.574835696813916761e-02, 6.055075024801586965e-08,
98 0.000000000000000000e+00, 5.960464477539062500e-08,
99 };
100
101 static const double C[] = {
102 6.931471805599452862e-01,
103 -2.49887584306188944706e-01,
104 3.33368809981254554946e-01,
105 -5.00000008402474976565e-01
106 };
107
108 #define ln2 C[0]
109 #define K3 C[1]
110 #define K2 C[2]
111 #define K1 C[3]
112
113 float
114 logf(float x)
115 {
116 double v, t;
117 float f;
118 int hx, ix, i, exp, iy;
119
120 hx = *(int *)&x;
121 ix = hx & ~0x80000000;
122
123 if (ix >= 0x7f800000) /* nan or inf */
124 return ((hx < 0)? x * 0.0f : x * x);
125
126 exp = 0;
127 if (hx < 0x00800000) { /* negative, zero, or subnormal */
128 if (hx <= 0) {
129 f = 0.0f;
130 return ((ix == 0)? -1.0f / f : f / f);
131 }
132
133 /* subnormal; scale by 2^149 */
134 f = (float)ix;
135 ix = *(int *)&f;
136 exp = -149;
137 }
138
139 exp += (ix - 0x3f320000) >> 23;
140 ix &= 0x007fffff;
141 iy = (ix + 0x20000) & 0xfffc0000;
142 i = iy >> 17;
143 t = ln2 * (double)exp + TBL[i];
144 v = (double)(ix - iy) * TBL[i + 1];
145 v += (v * v) * (K1 + v * (K2 + v * K3));
146 f = (float)(t + v);
147 return (f);
148 }