Line data Source code
1 : /*-------------------------------------------------------------------------
2 : *
3 : * hyperloglog.c
4 : * HyperLogLog cardinality estimator
5 : *
6 : * Portions Copyright (c) 2014-2024, PostgreSQL Global Development Group
7 : *
8 : * Based on Hideaki Ohno's C++ implementation. This is probably not ideally
9 : * suited to estimating the cardinality of very large sets; in particular, we
10 : * have not attempted to further optimize the implementation as described in
11 : * the Heule, Nunkesser and Hall paper "HyperLogLog in Practice: Algorithmic
12 : * Engineering of a State of The Art Cardinality Estimation Algorithm".
13 : *
14 : * A sparse representation of HyperLogLog state is used, with fixed space
15 : * overhead.
16 : *
17 : * The copyright terms of Ohno's original version (the MIT license) follow.
18 : *
19 : * IDENTIFICATION
20 : * src/backend/lib/hyperloglog.c
21 : *
22 : *-------------------------------------------------------------------------
23 : */
24 :
25 : /*
26 : * Copyright (c) 2013 Hideaki Ohno <hide.o.j55{at}gmail.com>
27 : *
28 : * Permission is hereby granted, free of charge, to any person obtaining a copy
29 : * of this software and associated documentation files (the 'Software'), to
30 : * deal in the Software without restriction, including without limitation the
31 : * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
32 : * sell copies of the Software, and to permit persons to whom the Software is
33 : * furnished to do so, subject to the following conditions:
34 : *
35 : * The above copyright notice and this permission notice shall be included in
36 : * all copies or substantial portions of the Software.
37 : *
38 : * THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
39 : * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
40 : * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
41 : * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
42 : * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
43 : * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
44 : * IN THE SOFTWARE.
45 : */
46 :
47 : #include "postgres.h"
48 :
49 : #include <math.h>
50 :
51 : #include "lib/hyperloglog.h"
52 : #include "port/pg_bitutils.h"
53 :
54 : #define POW_2_32 (4294967296.0)
55 : #define NEG_POW_2_32 (-4294967296.0)
56 :
57 : static inline uint8 rho(uint32 x, uint8 b);
58 :
59 : /*
60 : * Initialize HyperLogLog track state, by bit width
61 : *
62 : * bwidth is bit width (so register size will be 2 to the power of bwidth).
63 : * Must be between 4 and 16 inclusive.
64 : */
65 : void
66 96472 : initHyperLogLog(hyperLogLogState *cState, uint8 bwidth)
67 : {
68 : double alpha;
69 :
70 96472 : if (bwidth < 4 || bwidth > 16)
71 0 : elog(ERROR, "bit width must be between 4 and 16 inclusive");
72 :
73 96472 : cState->registerWidth = bwidth;
74 96472 : cState->nRegisters = (Size) 1 << bwidth;
75 96472 : cState->arrSize = sizeof(uint8) * cState->nRegisters + 1;
76 :
77 : /*
78 : * Initialize hashes array to zero, not negative infinity, per discussion
79 : * of the coupon collector problem in the HyperLogLog paper
80 : */
81 96472 : cState->hashesArr = palloc0(cState->arrSize);
82 :
83 : /*
84 : * "alpha" is a value that for each possible number of registers (m) is
85 : * used to correct a systematic multiplicative bias present in m ^ 2 Z (Z
86 : * is "the indicator function" through which we finally compute E,
87 : * estimated cardinality).
88 : */
89 96472 : switch (cState->nRegisters)
90 : {
91 0 : case 16:
92 0 : alpha = 0.673;
93 0 : break;
94 50424 : case 32:
95 50424 : alpha = 0.697;
96 50424 : break;
97 0 : case 64:
98 0 : alpha = 0.709;
99 0 : break;
100 46048 : default:
101 46048 : alpha = 0.7213 / (1.0 + 1.079 / cState->nRegisters);
102 : }
103 :
104 : /*
105 : * Precalculate alpha m ^ 2, later used to generate "raw" HyperLogLog
106 : * estimate E
107 : */
108 96472 : cState->alphaMM = alpha * cState->nRegisters * cState->nRegisters;
109 96472 : }
110 :
111 : /*
112 : * Initialize HyperLogLog track state, by error rate
113 : *
114 : * Instead of specifying bwidth (number of bits used for addressing the
115 : * register), this method allows sizing the counter for particular error
116 : * rate using a simple formula from the paper:
117 : *
118 : * e = 1.04 / sqrt(m)
119 : *
120 : * where 'm' is the number of registers, i.e. (2^bwidth). The method
121 : * finds the lowest bwidth with 'e' below the requested error rate, and
122 : * then uses it to initialize the counter.
123 : *
124 : * As bwidth has to be between 4 and 16, the worst possible error rate
125 : * is between ~25% (bwidth=4) and 0.4% (bwidth=16).
126 : */
127 : void
128 0 : initHyperLogLogError(hyperLogLogState *cState, double error)
129 : {
130 0 : uint8 bwidth = 4;
131 :
132 0 : while (bwidth < 16)
133 : {
134 0 : double m = (Size) 1 << bwidth;
135 :
136 0 : if (1.04 / sqrt(m) < error)
137 0 : break;
138 0 : bwidth++;
139 : }
140 :
141 0 : initHyperLogLog(cState, bwidth);
142 0 : }
143 :
144 : /*
145 : * Free HyperLogLog track state
146 : *
147 : * Releases allocated resources, but not the state itself (in case it's not
148 : * allocated by palloc).
149 : */
150 : void
151 26910 : freeHyperLogLog(hyperLogLogState *cState)
152 : {
153 : Assert(cState->hashesArr != NULL);
154 26910 : pfree(cState->hashesArr);
155 26910 : }
156 :
157 : /*
158 : * Adds element to the estimator, from caller-supplied hash.
159 : *
160 : * It is critical that the hash value passed be an actual hash value, typically
161 : * generated using hash_any(). The algorithm relies on a specific bit-pattern
162 : * observable in conjunction with stochastic averaging. There must be a
163 : * uniform distribution of bits in hash values for each distinct original value
164 : * observed.
165 : */
166 : void
167 5708680 : addHyperLogLog(hyperLogLogState *cState, uint32 hash)
168 : {
169 : uint8 count;
170 : uint32 index;
171 :
172 : /* Use the first "k" (registerWidth) bits as a zero based index */
173 5708680 : index = hash >> (BITS_PER_BYTE * sizeof(uint32) - cState->registerWidth);
174 :
175 : /* Compute the rank of the remaining 32 - "k" (registerWidth) bits */
176 5708680 : count = rho(hash << cState->registerWidth,
177 5708680 : BITS_PER_BYTE * sizeof(uint32) - cState->registerWidth);
178 :
179 5708680 : cState->hashesArr[index] = Max(count, cState->hashesArr[index]);
180 5708680 : }
181 :
182 : /*
183 : * Estimates cardinality, based on elements added so far
184 : */
185 : double
186 29050 : estimateHyperLogLog(hyperLogLogState *cState)
187 : {
188 : double result;
189 29050 : double sum = 0.0;
190 : int i;
191 :
192 3081530 : for (i = 0; i < cState->nRegisters; i++)
193 : {
194 3052480 : sum += 1.0 / pow(2.0, cState->hashesArr[i]);
195 : }
196 :
197 : /* result set to "raw" HyperLogLog estimate (E in the HyperLogLog paper) */
198 29050 : result = cState->alphaMM / sum;
199 :
200 29050 : if (result <= (5.0 / 2.0) * cState->nRegisters)
201 : {
202 : /* Small range correction */
203 28276 : int zero_count = 0;
204 :
205 2901236 : for (i = 0; i < cState->nRegisters; i++)
206 : {
207 2872960 : if (cState->hashesArr[i] == 0)
208 2131780 : zero_count++;
209 : }
210 :
211 28276 : if (zero_count != 0)
212 28276 : result = cState->nRegisters * log((double) cState->nRegisters /
213 : zero_count);
214 : }
215 774 : else if (result > (1.0 / 30.0) * POW_2_32)
216 : {
217 : /* Large range correction */
218 0 : result = NEG_POW_2_32 * log(1.0 - (result / POW_2_32));
219 : }
220 :
221 29050 : return result;
222 : }
223 :
224 : /*
225 : * Worker for addHyperLogLog().
226 : *
227 : * Calculates the position of the first set bit in first b bits of x argument
228 : * starting from the first, reading from most significant to least significant
229 : * bits.
230 : *
231 : * Example (when considering fist 10 bits of x):
232 : *
233 : * rho(x = 0b1000000000) returns 1
234 : * rho(x = 0b0010000000) returns 3
235 : * rho(x = 0b0000000000) returns b + 1
236 : *
237 : * "The binary address determined by the first b bits of x"
238 : *
239 : * Return value "j" used to index bit pattern to watch.
240 : */
241 : static inline uint8
242 5708680 : rho(uint32 x, uint8 b)
243 : {
244 5708680 : uint8 j = 1;
245 :
246 5708680 : if (x == 0)
247 0 : return b + 1;
248 :
249 5708680 : j = 32 - pg_leftmost_one_pos32(x);
250 :
251 5708680 : if (j > b)
252 0 : return b + 1;
253 :
254 5708680 : return j;
255 : }
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