1 | /* $NetBSD: dtv_math.c,v 1.5 2011/08/09 01:42:24 jmcneill Exp $ */ |
2 | |
3 | /*- |
4 | * Copyright (c) 2011 Alan Barrett <apb@NetBSD.org> |
5 | * All rights reserved. |
6 | * |
7 | * Redistribution and use in source and binary forms, with or without |
8 | * modification, are permitted provided that the following conditions |
9 | * are met: |
10 | * 1. Redistributions of source code must retain the above copyright |
11 | * notice, this list of conditions and the following disclaimer. |
12 | * 2. Redistributions in binary form must reproduce the above copyright |
13 | * notice, this list of conditions and the following disclaimer in the |
14 | * documentation and/or other materials provided with the distribution. |
15 | * |
16 | * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS |
17 | * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED |
18 | * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
19 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS |
20 | * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
21 | * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
22 | * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
23 | * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN |
24 | * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
25 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
26 | * POSSIBILITY OF SUCH DAMAGE. |
27 | */ |
28 | |
29 | #include <sys/cdefs.h> |
30 | __KERNEL_RCSID(0, "$NetBSD: dtv_math.c,v 1.5 2011/08/09 01:42:24 jmcneill Exp $" ); |
31 | |
32 | #include <sys/types.h> |
33 | #include <sys/bitops.h> |
34 | #include <sys/module.h> |
35 | |
36 | #include <dev/dtv/dtv_math.h> |
37 | |
38 | /* |
39 | * dtv_intlog10 -- return an approximation to log10(x) * 1<<24, |
40 | * using integer arithmetic. |
41 | * |
42 | * As a special case, returns 0 when x == 0. The mathematical |
43 | * result is -infinity. |
44 | * |
45 | * This function uses 0.5 + x/2 - 1/x as an approximation to |
46 | * log2(x) for x in the range [1.0, 2.0], and scales the input value |
47 | * to fit this range. The resulting error is always better than |
48 | * 0.2%. |
49 | * |
50 | * Here's a table of the desired and actual results, as well |
51 | * as the absolute and relative errors, for several values of x. |
52 | * |
53 | * x desired actual err_abs err_rel |
54 | * 0 0 0 +0 +0.00000 |
55 | * 1 0 0 +0 +0.00000 |
56 | * 2 5050445 5050122 -323 -0.00006 |
57 | * 3 8004766 7996348 -8418 -0.00105 |
58 | * 4 10100890 10100887 -3 -0.00000 |
59 | * 5 11726770 11741823 +15053 +0.00128 |
60 | * 6 13055211 13046470 -8741 -0.00067 |
61 | * 7 14178392 14158860 -19532 -0.00138 |
62 | * 8 15151335 15151009 -326 -0.00002 |
63 | * 9 16009532 16028061 +18529 +0.00116 |
64 | * 10 16777216 16792588 +15372 +0.00092 |
65 | * 11 17471670 17475454 +3784 +0.00022 |
66 | * 12 18105656 18097235 -8421 -0.00047 |
67 | * 13 18688868 18672077 -16791 -0.00090 |
68 | * 14 19228837 19209625 -19212 -0.00100 |
69 | * 15 19731537 19717595 -13942 -0.00071 |
70 | * 16 20201781 20201774 -7 -0.00000 |
71 | * 20 21827661 21842710 +15049 +0.00069 |
72 | * 24 23156102 23147357 -8745 -0.00038 |
73 | * 30 24781982 24767717 -14265 -0.00058 |
74 | * 40 26878106 26893475 +15369 +0.00057 |
75 | * 60 29832427 29818482 -13945 -0.00047 |
76 | * 100 33554432 33540809 -13623 -0.00041 |
77 | * 1000 50331648 50325038 -6610 -0.00013 |
78 | * 10000 67108864 67125985 +17121 +0.00026 |
79 | * 100000 83886080 83875492 -10588 -0.00013 |
80 | * 1000000 100663296 100652005 -11291 -0.00011 |
81 | * 10000000 117440512 117458739 +18227 +0.00016 |
82 | * 100000000 134217728 134210175 -7553 -0.00006 |
83 | * 1000000000 150994944 150980258 -14686 -0.00010 |
84 | * 4294967295 161614248 161614192 -56 -0.00000 |
85 | */ |
86 | uint32_t |
87 | dtv_intlog10(uint32_t x) |
88 | { |
89 | uint32_t ilog2x; |
90 | uint32_t t; |
91 | uint32_t t1; |
92 | |
93 | if (__predict_false(x == 0)) |
94 | return 0; |
95 | |
96 | /* |
97 | * find ilog2x = floor(log2(x)), as an integer in the range [0,31]. |
98 | */ |
99 | ilog2x = ilog2(x); |
100 | |
101 | /* |
102 | * Set "t" to the result of shifting x left or right |
103 | * until the most significant bit that was actually set |
104 | * moves into the 1<<24 position. |
105 | * |
106 | * Now we can think of "t" as representing |
107 | * x / 2**(floor(log2(x))), |
108 | * as a fixed-point value with 8 integer bits and 24 fraction bits. |
109 | * |
110 | * This value is in the semi-closed interval [1.0, 2.0) |
111 | * when interpreting it as a fixed-point number, or in the |
112 | * interval [0x01000000, 0x01ffffff] when examining the |
113 | * underlying uint32_t representation. |
114 | */ |
115 | t = (ilog2x > 24 ? x >> (ilog2x - 24) : x << (24 - ilog2x)); |
116 | |
117 | /* |
118 | * Calculate "t1 = 1 / t" in the 8.24 fixed-point format. |
119 | * This value is in the interval [0.5, 1.0] |
120 | * when interpreting it as a fixed-point number, or in the |
121 | * interval [0x00800000, 0x01000000] when examining the |
122 | * underlying uint32_t representation. |
123 | * |
124 | */ |
125 | t1 = ((uint64_t)1 << 48) / t; |
126 | |
127 | /* |
128 | * Calculate "t = ilog2x + t/2 - t1 + 0.5" in the 8.24 |
129 | * fixed-point format. |
130 | * |
131 | * If x is a power of 2, then t is now exactly equal to log2(x) |
132 | * when interpreting it as a fixed-point number, or exactly |
133 | * log2(x) << 24 when examining the underlying uint32_t |
134 | * representation. |
135 | * |
136 | * If x is not a power of 2, then t is the result of |
137 | * using the function x/2 - 1/x + 0.5 as an approximation for |
138 | * log2(x) for x in the range [1, 2], and scaling both the |
139 | * input and the result by the appropriate number of powers of 2. |
140 | */ |
141 | t = (ilog2x << 24) + (t >> 1) - t1 + (1 << 23); |
142 | |
143 | /* |
144 | * Multiply t by log10(2) to get the final result. |
145 | * |
146 | * log10(2) is approximately 643/2136 We divide before |
147 | * multiplying to avoid overflow. |
148 | */ |
149 | return t / 2136 * 643; |
150 | } |
151 | |
152 | #ifdef _KERNEL |
153 | MODULE(MODULE_CLASS_MISC, dtv_math, NULL); |
154 | |
155 | static int |
156 | dtv_math_modcmd(modcmd_t cmd, void *opaque) |
157 | { |
158 | if (cmd == MODULE_CMD_INIT || cmd == MODULE_CMD_FINI) |
159 | return 0; |
160 | return ENOTTY; |
161 | } |
162 | #endif |
163 | |
164 | #ifdef TEST_DTV_MATH |
165 | /* |
166 | * To test: |
167 | * cc -DTEST_DTV_MATH ./dtv_math.c -lm -o ./a.out && ./a.out |
168 | */ |
169 | |
170 | #include <stdio.h> |
171 | #include <inttypes.h> |
172 | #include <math.h> |
173 | |
174 | int |
175 | main(void) |
176 | { |
177 | uint32_t xlist[] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, |
178 | 14, 15, 16, 20, 24, 30, 40, 60, 100, 1000, 10000, |
179 | 100000, 1000000, 10000000, 100000000, 1000000000, |
180 | 0xffffffff}; |
181 | int i; |
182 | |
183 | printf("%11s %11s %11s %11s %s\n" , |
184 | "x" , "desired" , "actual" , "err_abs" , "err_rel" ); |
185 | for (i = 0; i < __arraycount(xlist); i++) |
186 | { |
187 | uint32_t x = xlist[i]; |
188 | uint32_t desired = (uint32_t)(log10((double)x) |
189 | * (double)(1<<24)); |
190 | uint32_t actual = dtv_intlog10(x); |
191 | int32_t err_abs = actual - desired; |
192 | double err_rel = (err_abs == 0 ? 0.0 |
193 | : err_abs / (double)actual); |
194 | |
195 | printf("%11" PRIu32" %11" PRIu32" %11" PRIu32 |
196 | " %+11" PRId32" %+.5f\n" , |
197 | x, desired, actual, err_abs, err_rel); |
198 | } |
199 | return 0; |
200 | } |
201 | |
202 | #endif /* TEST_DTV_MATH */ |
203 | |