1 | // SPDX-License-Identifier: LGPL-2.1-or-later |
2 | /* |
3 | * Provides fixed-point logarithm operations. |
4 | * |
5 | * Copyright (C) 2006 Christoph Pfister (christophpfister@gmail.com) |
6 | */ |
7 | |
8 | #include <linux/bitops.h> |
9 | #include <linux/export.h> |
10 | #include <linux/int_log.h> |
11 | #include <linux/kernel.h> |
12 | #include <linux/types.h> |
13 | |
14 | #include <asm/bug.h> |
15 | |
16 | static const unsigned short logtable[256] = { |
17 | 0x0000, 0x0171, 0x02e0, 0x044e, 0x05ba, 0x0725, 0x088e, 0x09f7, |
18 | 0x0b5d, 0x0cc3, 0x0e27, 0x0f8a, 0x10eb, 0x124b, 0x13aa, 0x1508, |
19 | 0x1664, 0x17bf, 0x1919, 0x1a71, 0x1bc8, 0x1d1e, 0x1e73, 0x1fc6, |
20 | 0x2119, 0x226a, 0x23ba, 0x2508, 0x2656, 0x27a2, 0x28ed, 0x2a37, |
21 | 0x2b80, 0x2cc8, 0x2e0f, 0x2f54, 0x3098, 0x31dc, 0x331e, 0x345f, |
22 | 0x359f, 0x36de, 0x381b, 0x3958, 0x3a94, 0x3bce, 0x3d08, 0x3e41, |
23 | 0x3f78, 0x40af, 0x41e4, 0x4319, 0x444c, 0x457f, 0x46b0, 0x47e1, |
24 | 0x4910, 0x4a3f, 0x4b6c, 0x4c99, 0x4dc5, 0x4eef, 0x5019, 0x5142, |
25 | 0x526a, 0x5391, 0x54b7, 0x55dc, 0x5700, 0x5824, 0x5946, 0x5a68, |
26 | 0x5b89, 0x5ca8, 0x5dc7, 0x5ee5, 0x6003, 0x611f, 0x623a, 0x6355, |
27 | 0x646f, 0x6588, 0x66a0, 0x67b7, 0x68ce, 0x69e4, 0x6af8, 0x6c0c, |
28 | 0x6d20, 0x6e32, 0x6f44, 0x7055, 0x7165, 0x7274, 0x7383, 0x7490, |
29 | 0x759d, 0x76aa, 0x77b5, 0x78c0, 0x79ca, 0x7ad3, 0x7bdb, 0x7ce3, |
30 | 0x7dea, 0x7ef0, 0x7ff6, 0x80fb, 0x81ff, 0x8302, 0x8405, 0x8507, |
31 | 0x8608, 0x8709, 0x8809, 0x8908, 0x8a06, 0x8b04, 0x8c01, 0x8cfe, |
32 | 0x8dfa, 0x8ef5, 0x8fef, 0x90e9, 0x91e2, 0x92db, 0x93d2, 0x94ca, |
33 | 0x95c0, 0x96b6, 0x97ab, 0x98a0, 0x9994, 0x9a87, 0x9b7a, 0x9c6c, |
34 | 0x9d5e, 0x9e4f, 0x9f3f, 0xa02e, 0xa11e, 0xa20c, 0xa2fa, 0xa3e7, |
35 | 0xa4d4, 0xa5c0, 0xa6ab, 0xa796, 0xa881, 0xa96a, 0xaa53, 0xab3c, |
36 | 0xac24, 0xad0c, 0xadf2, 0xaed9, 0xafbe, 0xb0a4, 0xb188, 0xb26c, |
37 | 0xb350, 0xb433, 0xb515, 0xb5f7, 0xb6d9, 0xb7ba, 0xb89a, 0xb97a, |
38 | 0xba59, 0xbb38, 0xbc16, 0xbcf4, 0xbdd1, 0xbead, 0xbf8a, 0xc065, |
39 | 0xc140, 0xc21b, 0xc2f5, 0xc3cf, 0xc4a8, 0xc580, 0xc658, 0xc730, |
40 | 0xc807, 0xc8de, 0xc9b4, 0xca8a, 0xcb5f, 0xcc34, 0xcd08, 0xcddc, |
41 | 0xceaf, 0xcf82, 0xd054, 0xd126, 0xd1f7, 0xd2c8, 0xd399, 0xd469, |
42 | 0xd538, 0xd607, 0xd6d6, 0xd7a4, 0xd872, 0xd93f, 0xda0c, 0xdad9, |
43 | 0xdba5, 0xdc70, 0xdd3b, 0xde06, 0xded0, 0xdf9a, 0xe063, 0xe12c, |
44 | 0xe1f5, 0xe2bd, 0xe385, 0xe44c, 0xe513, 0xe5d9, 0xe69f, 0xe765, |
45 | 0xe82a, 0xe8ef, 0xe9b3, 0xea77, 0xeb3b, 0xebfe, 0xecc1, 0xed83, |
46 | 0xee45, 0xef06, 0xefc8, 0xf088, 0xf149, 0xf209, 0xf2c8, 0xf387, |
47 | 0xf446, 0xf505, 0xf5c3, 0xf680, 0xf73e, 0xf7fb, 0xf8b7, 0xf973, |
48 | 0xfa2f, 0xfaea, 0xfba5, 0xfc60, 0xfd1a, 0xfdd4, 0xfe8e, 0xff47, |
49 | }; |
50 | |
51 | unsigned int intlog2(u32 value) |
52 | { |
53 | /** |
54 | * returns: log2(value) * 2^24 |
55 | * wrong result if value = 0 (log2(0) is undefined) |
56 | */ |
57 | unsigned int msb; |
58 | unsigned int logentry; |
59 | unsigned int significand; |
60 | unsigned int interpolation; |
61 | |
62 | if (unlikely(value == 0)) { |
63 | WARN_ON(1); |
64 | return 0; |
65 | } |
66 | |
67 | /* first detect the msb (count begins at 0) */ |
68 | msb = fls(x: value) - 1; |
69 | |
70 | /** |
71 | * now we use a logtable after the following method: |
72 | * |
73 | * log2(2^x * y) * 2^24 = x * 2^24 + log2(y) * 2^24 |
74 | * where x = msb and therefore 1 <= y < 2 |
75 | * first y is determined by shifting the value left |
76 | * so that msb is bit 31 |
77 | * 0x00231f56 -> 0x8C7D5800 |
78 | * the result is y * 2^31 -> "significand" |
79 | * then the highest 9 bits are used for a table lookup |
80 | * the highest bit is discarded because it's always set |
81 | * the highest nine bits in our example are 100011000 |
82 | * so we would use the entry 0x18 |
83 | */ |
84 | significand = value << (31 - msb); |
85 | logentry = (significand >> 23) % ARRAY_SIZE(logtable); |
86 | |
87 | /** |
88 | * last step we do is interpolation because of the |
89 | * limitations of the log table the error is that part of |
90 | * the significand which isn't used for lookup then we |
91 | * compute the ratio between the error and the next table entry |
92 | * and interpolate it between the log table entry used and the |
93 | * next one the biggest error possible is 0x7fffff |
94 | * (in our example it's 0x7D5800) |
95 | * needed value for next table entry is 0x800000 |
96 | * so the interpolation is |
97 | * (error / 0x800000) * (logtable_next - logtable_current) |
98 | * in the implementation the division is moved to the end for |
99 | * better accuracy there is also an overflow correction if |
100 | * logtable_next is 256 |
101 | */ |
102 | interpolation = ((significand & 0x7fffff) * |
103 | ((logtable[(logentry + 1) % ARRAY_SIZE(logtable)] - |
104 | logtable[logentry]) & 0xffff)) >> 15; |
105 | |
106 | /* now we return the result */ |
107 | return ((msb << 24) + (logtable[logentry] << 8) + interpolation); |
108 | } |
109 | EXPORT_SYMBOL(intlog2); |
110 | |
111 | unsigned int intlog10(u32 value) |
112 | { |
113 | /** |
114 | * returns: log10(value) * 2^24 |
115 | * wrong result if value = 0 (log10(0) is undefined) |
116 | */ |
117 | u64 log; |
118 | |
119 | if (unlikely(value == 0)) { |
120 | WARN_ON(1); |
121 | return 0; |
122 | } |
123 | |
124 | log = intlog2(value); |
125 | |
126 | /** |
127 | * we use the following method: |
128 | * log10(x) = log2(x) * log10(2) |
129 | */ |
130 | |
131 | return (log * 646456993) >> 31; |
132 | } |
133 | EXPORT_SYMBOL(intlog10); |
134 | |