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