1 | /* hyperloglog.c - Redis HyperLogLog probabilistic cardinality approximation. |
2 | * This file implements the algorithm and the exported Redis commands. |
3 | * |
4 | * Copyright (c) 2014, Salvatore Sanfilippo <antirez at gmail dot com> |
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 are met: |
9 | * |
10 | * * Redistributions of source code must retain the above copyright notice, |
11 | * this list of conditions and the following disclaimer. |
12 | * * 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 | * * Neither the name of Redis nor the names of its contributors may be used |
16 | * to endorse or promote products derived from this software without |
17 | * specific prior written permission. |
18 | * |
19 | * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" |
20 | * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
21 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
22 | * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE |
23 | * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
24 | * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
25 | * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
26 | * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN |
27 | * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
28 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
29 | * POSSIBILITY OF SUCH DAMAGE. |
30 | */ |
31 | |
32 | #include "duckdb/common/vector.hpp" |
33 | #include "duckdb/common/types/hyperloglog.hpp" |
34 | |
35 | #include "hyperloglog.hpp" |
36 | #include "sds.hpp" |
37 | |
38 | #include <assert.h> |
39 | #include <stdint.h> |
40 | #include <math.h> |
41 | #include <stddef.h> |
42 | #include <string.h> |
43 | #include <stdlib.h> |
44 | |
45 | |
46 | |
47 | namespace duckdb_hll { |
48 | |
49 | #define HLL_SPARSE_MAX_BYTES 3000 |
50 | |
51 | /* The Redis HyperLogLog implementation is based on the following ideas: |
52 | * |
53 | * * The use of a 64 bit hash function as proposed in [1], in order to don't |
54 | * limited to cardinalities up to 10^9, at the cost of just 1 additional |
55 | * bit per register. |
56 | * * The use of 16384 6-bit registers for a great level of accuracy, using |
57 | * a total of 12k per key. |
58 | * * The use of the Redis string data type. No new type is introduced. |
59 | * * No attempt is made to compress the data structure as in [1]. Also the |
60 | * algorithm used is the original HyperLogLog Algorithm as in [2], with |
61 | * the only difference that a 64 bit hash function is used, so no correction |
62 | * is performed for values near 2^32 as in [1]. |
63 | * |
64 | * [1] Heule, Nunkesser, Hall: HyperLogLog in Practice: Algorithmic |
65 | * Engineering of a State of The Art Cardinality Estimation Algorithm. |
66 | * |
67 | * [2] P. Flajolet, Éric Fusy, O. Gandouet, and F. Meunier. Hyperloglog: The |
68 | * analysis of a near-optimal cardinality estimation algorithm. |
69 | * |
70 | * Redis uses two representations: |
71 | * |
72 | * 1) A "dense" representation where every entry is represented by |
73 | * a 6-bit integer. |
74 | * 2) A "sparse" representation using run length compression suitable |
75 | * for representing HyperLogLogs with many registers set to 0 in |
76 | * a memory efficient way. |
77 | * |
78 | * |
79 | * HLL header |
80 | * === |
81 | * |
82 | * Both the dense and sparse representation have a 16 byte header as follows: |
83 | * |
84 | * +------+---+-----+----------+ |
85 | * | HYLL | E | N/U | Cardin. | |
86 | * +------+---+-----+----------+ |
87 | * |
88 | * The first 4 bytes are a magic string set to the bytes "HYLL". |
89 | * "E" is one byte encoding, currently set to HLL_DENSE or |
90 | * HLL_SPARSE. N/U are three not used bytes. |
91 | * |
92 | * The "Cardin." field is a 64 bit integer stored in little endian format |
93 | * with the latest cardinality computed that can be reused if the data |
94 | * structure was not modified since the last computation (this is useful |
95 | * because there are high probabilities that HLLADD operations don't |
96 | * modify the actual data structure and hence the approximated cardinality). |
97 | * |
98 | * When the most significant bit in the most significant byte of the cached |
99 | * cardinality is set, it means that the data structure was modified and |
100 | * we can't reuse the cached value that must be recomputed. |
101 | * |
102 | * Dense representation |
103 | * === |
104 | * |
105 | * The dense representation used by Redis is the following: |
106 | * |
107 | * +--------+--------+--------+------// //--+ |
108 | * |11000000|22221111|33333322|55444444 .... | |
109 | * +--------+--------+--------+------// //--+ |
110 | * |
111 | * The 6 bits counters are encoded one after the other starting from the |
112 | * LSB to the MSB, and using the next bytes as needed. |
113 | * |
114 | * Sparse representation |
115 | * === |
116 | * |
117 | * The sparse representation encodes registers using a run length |
118 | * encoding composed of three opcodes, two using one byte, and one using |
119 | * of two bytes. The opcodes are called ZERO, XZERO and VAL. |
120 | * |
121 | * ZERO opcode is represented as 00xxxxxx. The 6-bit integer represented |
122 | * by the six bits 'xxxxxx', plus 1, means that there are N registers set |
123 | * to 0. This opcode can represent from 1 to 64 contiguous registers set |
124 | * to the value of 0. |
125 | * |
126 | * XZERO opcode is represented by two bytes 01xxxxxx yyyyyyyy. The 14-bit |
127 | * integer represented by the bits 'xxxxxx' as most significant bits and |
128 | * 'yyyyyyyy' as least significant bits, plus 1, means that there are N |
129 | * registers set to 0. This opcode can represent from 0 to 16384 contiguous |
130 | * registers set to the value of 0. |
131 | * |
132 | * VAL opcode is represented as 1vvvvvxx. It contains a 5-bit integer |
133 | * representing the value of a register, and a 2-bit integer representing |
134 | * the number of contiguous registers set to that value 'vvvvv'. |
135 | * To obtain the value and run length, the integers vvvvv and xx must be |
136 | * incremented by one. This opcode can represent values from 1 to 32, |
137 | * repeated from 1 to 4 times. |
138 | * |
139 | * The sparse representation can't represent registers with a value greater |
140 | * than 32, however it is very unlikely that we find such a register in an |
141 | * HLL with a cardinality where the sparse representation is still more |
142 | * memory efficient than the dense representation. When this happens the |
143 | * HLL is converted to the dense representation. |
144 | * |
145 | * The sparse representation is purely positional. For example a sparse |
146 | * representation of an empty HLL is just: XZERO:16384. |
147 | * |
148 | * An HLL having only 3 non-zero registers at position 1000, 1020, 1021 |
149 | * respectively set to 2, 3, 3, is represented by the following three |
150 | * opcodes: |
151 | * |
152 | * XZERO:1000 (Registers 0-999 are set to 0) |
153 | * VAL:2,1 (1 register set to value 2, that is register 1000) |
154 | * ZERO:19 (Registers 1001-1019 set to 0) |
155 | * VAL:3,2 (2 registers set to value 3, that is registers 1020,1021) |
156 | * XZERO:15362 (Registers 1022-16383 set to 0) |
157 | * |
158 | * In the example the sparse representation used just 7 bytes instead |
159 | * of 12k in order to represent the HLL registers. In general for low |
160 | * cardinality there is a big win in terms of space efficiency, traded |
161 | * with CPU time since the sparse representation is slower to access: |
162 | * |
163 | * The following table shows average cardinality vs bytes used, 100 |
164 | * samples per cardinality (when the set was not representable because |
165 | * of registers with too big value, the dense representation size was used |
166 | * as a sample). |
167 | * |
168 | * 100 267 |
169 | * 200 485 |
170 | * 300 678 |
171 | * 400 859 |
172 | * 500 1033 |
173 | * 600 1205 |
174 | * 700 1375 |
175 | * 800 1544 |
176 | * 900 1713 |
177 | * 1000 1882 |
178 | * 2000 3480 |
179 | * 3000 4879 |
180 | * 4000 6089 |
181 | * 5000 7138 |
182 | * 6000 8042 |
183 | * 7000 8823 |
184 | * 8000 9500 |
185 | * 9000 10088 |
186 | * 10000 10591 |
187 | * |
188 | * The dense representation uses 12288 bytes, so there is a big win up to |
189 | * a cardinality of ~2000-3000. For bigger cardinalities the constant times |
190 | * involved in updating the sparse representation is not justified by the |
191 | * memory savings. The exact maximum length of the sparse representation |
192 | * when this implementation switches to the dense representation is |
193 | * configured via the define server.hll_sparse_max_bytes. |
194 | */ |
195 | |
196 | struct hllhdr { |
197 | char magic[4]; /* "HYLL" */ |
198 | uint8_t encoding; /* HLL_DENSE or HLL_SPARSE. */ |
199 | uint8_t notused[3]; /* Reserved for future use, must be zero. */ |
200 | uint8_t card[8]; /* Cached cardinality, little endian. */ |
201 | uint8_t registers[1]; /* Data bytes. */ |
202 | }; |
203 | |
204 | /* The cached cardinality MSB is used to signal validity of the cached value. */ |
205 | #define HLL_INVALIDATE_CACHE(hdr) (hdr)->card[7] |= (1<<7) |
206 | #define HLL_VALID_CACHE(hdr) (((hdr)->card[7] & (1<<7)) == 0) |
207 | |
208 | #define HLL_P 12 /* The greater is P, the smaller the error. */ |
209 | #define HLL_Q (64-HLL_P) /* The number of bits of the hash value used for |
210 | determining the number of leading zeros. */ |
211 | #define HLL_REGISTERS (1<<HLL_P) /* With P=14, 16384 registers. */ |
212 | #define HLL_P_MASK (HLL_REGISTERS-1) /* Mask to index register. */ |
213 | #define HLL_BITS 6 /* Enough to count up to 63 leading zeroes. */ |
214 | #define HLL_REGISTER_MAX ((1<<HLL_BITS)-1) |
215 | #define HLL_HDR_SIZE sizeof(struct hllhdr) |
216 | #define HLL_DENSE_SIZE (HLL_HDR_SIZE+((HLL_REGISTERS*HLL_BITS+7)/8)) |
217 | #define HLL_DENSE 0 /* Dense encoding. */ |
218 | #define HLL_SPARSE 1 /* Sparse encoding. */ |
219 | #define HLL_RAW 255 /* Only used internally, never exposed. */ |
220 | #define HLL_MAX_ENCODING 1 |
221 | |
222 | /* =========================== Low level bit macros ========================= */ |
223 | |
224 | /* Macros to access the dense representation. |
225 | * |
226 | * We need to get and set 6 bit counters in an array of 8 bit bytes. |
227 | * We use macros to make sure the code is inlined since speed is critical |
228 | * especially in order to compute the approximated cardinality in |
229 | * HLLCOUNT where we need to access all the registers at once. |
230 | * For the same reason we also want to avoid conditionals in this code path. |
231 | * |
232 | * +--------+--------+--------+------// |
233 | * |11000000|22221111|33333322|55444444 |
234 | * +--------+--------+--------+------// |
235 | * |
236 | * Note: in the above representation the most significant bit (MSB) |
237 | * of every byte is on the left. We start using bits from the LSB to MSB, |
238 | * and so forth passing to the next byte. |
239 | * |
240 | * Example, we want to access to counter at pos = 1 ("111111" in the |
241 | * illustration above). |
242 | * |
243 | * The index of the first byte b0 containing our data is: |
244 | * |
245 | * b0 = 6 * pos / 8 = 0 |
246 | * |
247 | * +--------+ |
248 | * |11000000| <- Our byte at b0 |
249 | * +--------+ |
250 | * |
251 | * The position of the first bit (counting from the LSB = 0) in the byte |
252 | * is given by: |
253 | * |
254 | * fb = 6 * pos % 8 -> 6 |
255 | * |
256 | * Right shift b0 of 'fb' bits. |
257 | * |
258 | * +--------+ |
259 | * |11000000| <- Initial value of b0 |
260 | * |00000011| <- After right shift of 6 pos. |
261 | * +--------+ |
262 | * |
263 | * Left shift b1 of bits 8-fb bits (2 bits) |
264 | * |
265 | * +--------+ |
266 | * |22221111| <- Initial value of b1 |
267 | * |22111100| <- After left shift of 2 bits. |
268 | * +--------+ |
269 | * |
270 | * OR the two bits, and finally AND with 111111 (63 in decimal) to |
271 | * clean the higher order bits we are not interested in: |
272 | * |
273 | * +--------+ |
274 | * |00000011| <- b0 right shifted |
275 | * |22111100| <- b1 left shifted |
276 | * |22111111| <- b0 OR b1 |
277 | * | 111111| <- (b0 OR b1) AND 63, our value. |
278 | * +--------+ |
279 | * |
280 | * We can try with a different example, like pos = 0. In this case |
281 | * the 6-bit counter is actually contained in a single byte. |
282 | * |
283 | * b0 = 6 * pos / 8 = 0 |
284 | * |
285 | * +--------+ |
286 | * |11000000| <- Our byte at b0 |
287 | * +--------+ |
288 | * |
289 | * fb = 6 * pos % 8 = 0 |
290 | * |
291 | * So we right shift of 0 bits (no shift in practice) and |
292 | * left shift the next byte of 8 bits, even if we don't use it, |
293 | * but this has the effect of clearing the bits so the result |
294 | * will not be affacted after the OR. |
295 | * |
296 | * ------------------------------------------------------------------------- |
297 | * |
298 | * Setting the register is a bit more complex, let's assume that 'val' |
299 | * is the value we want to set, already in the right range. |
300 | * |
301 | * We need two steps, in one we need to clear the bits, and in the other |
302 | * we need to bitwise-OR the new bits. |
303 | * |
304 | * Let's try with 'pos' = 1, so our first byte at 'b' is 0, |
305 | * |
306 | * "fb" is 6 in this case. |
307 | * |
308 | * +--------+ |
309 | * |11000000| <- Our byte at b0 |
310 | * +--------+ |
311 | * |
312 | * To create a AND-mask to clear the bits about this position, we just |
313 | * initialize the mask with the value 63, left shift it of "fs" bits, |
314 | * and finally invert the result. |
315 | * |
316 | * +--------+ |
317 | * |00111111| <- "mask" starts at 63 |
318 | * |11000000| <- "mask" after left shift of "ls" bits. |
319 | * |00111111| <- "mask" after invert. |
320 | * +--------+ |
321 | * |
322 | * Now we can bitwise-AND the byte at "b" with the mask, and bitwise-OR |
323 | * it with "val" left-shifted of "ls" bits to set the new bits. |
324 | * |
325 | * Now let's focus on the next byte b1: |
326 | * |
327 | * +--------+ |
328 | * |22221111| <- Initial value of b1 |
329 | * +--------+ |
330 | * |
331 | * To build the AND mask we start again with the 63 value, right shift |
332 | * it by 8-fb bits, and invert it. |
333 | * |
334 | * +--------+ |
335 | * |00111111| <- "mask" set at 2&6-1 |
336 | * |00001111| <- "mask" after the right shift by 8-fb = 2 bits |
337 | * |11110000| <- "mask" after bitwise not. |
338 | * +--------+ |
339 | * |
340 | * Now we can mask it with b+1 to clear the old bits, and bitwise-OR |
341 | * with "val" left-shifted by "rs" bits to set the new value. |
342 | */ |
343 | |
344 | /* Note: if we access the last counter, we will also access the b+1 byte |
345 | * that is out of the array, but sds strings always have an implicit null |
346 | * term, so the byte exists, and we can skip the conditional (or the need |
347 | * to allocate 1 byte more explicitly). */ |
348 | |
349 | /* Store the value of the register at position 'regnum' into variable 'target'. |
350 | * 'p' is an array of unsigned bytes. */ |
351 | #define HLL_DENSE_GET_REGISTER(target,p,regnum) do { \ |
352 | uint8_t *_p = (uint8_t*) p; \ |
353 | unsigned long _byte = regnum*HLL_BITS/8; \ |
354 | unsigned long _fb = regnum*HLL_BITS&7; \ |
355 | unsigned long _fb8 = 8 - _fb; \ |
356 | unsigned long b0 = _p[_byte]; \ |
357 | unsigned long b1 = _p[_byte+1]; \ |
358 | target = ((b0 >> _fb) | (b1 << _fb8)) & HLL_REGISTER_MAX; \ |
359 | } while(0) |
360 | |
361 | /* Set the value of the register at position 'regnum' to 'val'. |
362 | * 'p' is an array of unsigned bytes. */ |
363 | #define HLL_DENSE_SET_REGISTER(p,regnum,val) do { \ |
364 | uint8_t *_p = (uint8_t*) p; \ |
365 | unsigned long _byte = regnum*HLL_BITS/8; \ |
366 | unsigned long _fb = regnum*HLL_BITS&7; \ |
367 | unsigned long _fb8 = 8 - _fb; \ |
368 | unsigned long _v = val; \ |
369 | _p[_byte] &= ~(HLL_REGISTER_MAX << _fb); \ |
370 | _p[_byte] |= _v << _fb; \ |
371 | _p[_byte+1] &= ~(HLL_REGISTER_MAX >> _fb8); \ |
372 | _p[_byte+1] |= _v >> _fb8; \ |
373 | } while(0) |
374 | |
375 | /* Macros to access the sparse representation. |
376 | * The macros parameter is expected to be an uint8_t pointer. */ |
377 | #define HLL_SPARSE_XZERO_BIT 0x40 /* 01xxxxxx */ |
378 | #define HLL_SPARSE_VAL_BIT 0x80 /* 1vvvvvxx */ |
379 | #define HLL_SPARSE_IS_ZERO(p) (((*(p)) & 0xc0) == 0) /* 00xxxxxx */ |
380 | #define HLL_SPARSE_IS_XZERO(p) (((*(p)) & 0xc0) == HLL_SPARSE_XZERO_BIT) |
381 | #define HLL_SPARSE_IS_VAL(p) ((*(p)) & HLL_SPARSE_VAL_BIT) |
382 | #define HLL_SPARSE_ZERO_LEN(p) (((*(p)) & 0x3f)+1) |
383 | #define HLL_SPARSE_XZERO_LEN(p) (((((*(p)) & 0x3f) << 8) | (*((p)+1)))+1) |
384 | #define HLL_SPARSE_VAL_VALUE(p) ((((*(p)) >> 2) & 0x1f)+1) |
385 | #define HLL_SPARSE_VAL_LEN(p) (((*(p)) & 0x3)+1) |
386 | #define HLL_SPARSE_VAL_MAX_VALUE 32 |
387 | #define HLL_SPARSE_VAL_MAX_LEN 4 |
388 | #define HLL_SPARSE_ZERO_MAX_LEN 64 |
389 | #define HLL_SPARSE_XZERO_MAX_LEN 16384 |
390 | #define HLL_SPARSE_VAL_SET(p,val,len) do { \ |
391 | *(p) = (((val)-1)<<2|((len)-1))|HLL_SPARSE_VAL_BIT; \ |
392 | } while(0) |
393 | #define HLL_SPARSE_ZERO_SET(p,len) do { \ |
394 | *(p) = (len)-1; \ |
395 | } while(0) |
396 | #define HLL_SPARSE_XZERO_SET(p,len) do { \ |
397 | int _l = (len)-1; \ |
398 | *(p) = (_l>>8) | HLL_SPARSE_XZERO_BIT; \ |
399 | *((p)+1) = (_l&0xff); \ |
400 | } while(0) |
401 | #define HLL_ALPHA_INF 0.721347520444481703680 /* constant for 0.5/ln(2) */ |
402 | |
403 | /* ========================= HyperLogLog algorithm ========================= */ |
404 | |
405 | /* Our hash function is MurmurHash2, 64 bit version. |
406 | * It was modified for Redis in order to provide the same result in |
407 | * big and little endian archs (endian neutral). */ |
408 | uint64_t MurmurHash64A (const void * key, int len, unsigned int seed) { |
409 | const uint64_t m = 0xc6a4a7935bd1e995; |
410 | const int r = 47; |
411 | uint64_t h = seed ^ (len * m); |
412 | const uint8_t *data = (const uint8_t *)key; |
413 | const uint8_t *end = data + (len-(len&7)); |
414 | |
415 | while(data != end) { |
416 | uint64_t k; |
417 | |
418 | #if (BYTE_ORDER == LITTLE_ENDIAN) |
419 | #ifdef USE_ALIGNED_ACCESS |
420 | memcpy(&k,data,sizeof(uint64_t)); |
421 | #else |
422 | k = *((uint64_t*)data); |
423 | #endif |
424 | #else |
425 | k = (uint64_t) data[0]; |
426 | k |= (uint64_t) data[1] << 8; |
427 | k |= (uint64_t) data[2] << 16; |
428 | k |= (uint64_t) data[3] << 24; |
429 | k |= (uint64_t) data[4] << 32; |
430 | k |= (uint64_t) data[5] << 40; |
431 | k |= (uint64_t) data[6] << 48; |
432 | k |= (uint64_t) data[7] << 56; |
433 | #endif |
434 | |
435 | k *= m; |
436 | k ^= k >> r; |
437 | k *= m; |
438 | h ^= k; |
439 | h *= m; |
440 | data += 8; |
441 | } |
442 | |
443 | switch(len & 7) { |
444 | case 7: h ^= (uint64_t)data[6] << 48; /* fall-thru */ |
445 | case 6: h ^= (uint64_t)data[5] << 40; /* fall-thru */ |
446 | case 5: h ^= (uint64_t)data[4] << 32; /* fall-thru */ |
447 | case 4: h ^= (uint64_t)data[3] << 24; /* fall-thru */ |
448 | case 3: h ^= (uint64_t)data[2] << 16; /* fall-thru */ |
449 | case 2: h ^= (uint64_t)data[1] << 8; /* fall-thru */ |
450 | case 1: h ^= (uint64_t)data[0]; |
451 | h *= m; /* fall-thru */ |
452 | }; |
453 | |
454 | h ^= h >> r; |
455 | h *= m; |
456 | h ^= h >> r; |
457 | return h; |
458 | } |
459 | |
460 | /* Given a string element to add to the HyperLogLog, returns the length |
461 | * of the pattern 000..1 of the element hash. As a side effect 'regp' is |
462 | * set to the register index this element hashes to. */ |
463 | int hllPatLen(unsigned char *ele, size_t elesize, long *regp) { |
464 | uint64_t hash, bit, index; |
465 | int count; |
466 | |
467 | /* Count the number of zeroes starting from bit HLL_REGISTERS |
468 | * (that is a power of two corresponding to the first bit we don't use |
469 | * as index). The max run can be 64-P+1 = Q+1 bits. |
470 | * |
471 | * Note that the final "1" ending the sequence of zeroes must be |
472 | * included in the count, so if we find "001" the count is 3, and |
473 | * the smallest count possible is no zeroes at all, just a 1 bit |
474 | * at the first position, that is a count of 1. |
475 | * |
476 | * This may sound like inefficient, but actually in the average case |
477 | * there are high probabilities to find a 1 after a few iterations. */ |
478 | hash = MurmurHash64A(key: ele,len: elesize,seed: 0xadc83b19ULL); |
479 | index = hash & HLL_P_MASK; /* Register index. */ |
480 | hash >>= HLL_P; /* Remove bits used to address the register. */ |
481 | hash |= ((uint64_t)1<<HLL_Q); /* Make sure the loop terminates |
482 | and count will be <= Q+1. */ |
483 | bit = 1; |
484 | count = 1; /* Initialized to 1 since we count the "00000...1" pattern. */ |
485 | while((hash & bit) == 0) { |
486 | count++; |
487 | bit <<= 1; |
488 | } |
489 | *regp = (int) index; |
490 | return count; |
491 | } |
492 | |
493 | /* ================== Dense representation implementation ================== */ |
494 | |
495 | /* Low level function to set the dense HLL register at 'index' to the |
496 | * specified value if the current value is smaller than 'count'. |
497 | * |
498 | * 'registers' is expected to have room for HLL_REGISTERS plus an |
499 | * additional byte on the right. This requirement is met by sds strings |
500 | * automatically since they are implicitly null terminated. |
501 | * |
502 | * The function always succeed, however if as a result of the operation |
503 | * the approximated cardinality changed, 1 is returned. Otherwise 0 |
504 | * is returned. */ |
505 | static inline int hllDenseSet(uint8_t *registers, long index, uint8_t count) { |
506 | uint8_t oldcount; |
507 | |
508 | HLL_DENSE_GET_REGISTER(oldcount,registers,index); |
509 | if (count > oldcount) { |
510 | HLL_DENSE_SET_REGISTER(registers,index,count); |
511 | return 1; |
512 | } else { |
513 | return 0; |
514 | } |
515 | } |
516 | |
517 | /* "Add" the element in the dense hyperloglog data structure. |
518 | * Actually nothing is added, but the max 0 pattern counter of the subset |
519 | * the element belongs to is incremented if needed. |
520 | * |
521 | * This is just a wrapper to hllDenseSet(), performing the hashing of the |
522 | * element in order to retrieve the index and zero-run count. */ |
523 | int hllDenseAdd(uint8_t *registers, unsigned char *ele, size_t elesize) { |
524 | long index; |
525 | uint8_t count = hllPatLen(ele,elesize,regp: &index); |
526 | /* Update the register if this element produced a longer run of zeroes. */ |
527 | return hllDenseSet(registers,index,count); |
528 | } |
529 | |
530 | /* Compute the register histogram in the dense representation. */ |
531 | void hllDenseRegHisto(uint8_t *registers, int* reghisto) { |
532 | int j; |
533 | |
534 | /* Redis default is to use 16384 registers 6 bits each. The code works |
535 | * with other values by modifying the defines, but for our target value |
536 | * we take a faster path with unrolled loops. */ |
537 | if (HLL_REGISTERS == 16384 && HLL_BITS == 6) { |
538 | uint8_t *r = registers; |
539 | unsigned long r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, |
540 | r10, r11, r12, r13, r14, r15; |
541 | for (j = 0; j < 1024; j++) { |
542 | /* Handle 16 registers per iteration. */ |
543 | r0 = r[0] & 63; |
544 | r1 = (r[0] >> 6 | r[1] << 2) & 63; |
545 | r2 = (r[1] >> 4 | r[2] << 4) & 63; |
546 | r3 = (r[2] >> 2) & 63; |
547 | r4 = r[3] & 63; |
548 | r5 = (r[3] >> 6 | r[4] << 2) & 63; |
549 | r6 = (r[4] >> 4 | r[5] << 4) & 63; |
550 | r7 = (r[5] >> 2) & 63; |
551 | r8 = r[6] & 63; |
552 | r9 = (r[6] >> 6 | r[7] << 2) & 63; |
553 | r10 = (r[7] >> 4 | r[8] << 4) & 63; |
554 | r11 = (r[8] >> 2) & 63; |
555 | r12 = r[9] & 63; |
556 | r13 = (r[9] >> 6 | r[10] << 2) & 63; |
557 | r14 = (r[10] >> 4 | r[11] << 4) & 63; |
558 | r15 = (r[11] >> 2) & 63; |
559 | |
560 | reghisto[r0]++; |
561 | reghisto[r1]++; |
562 | reghisto[r2]++; |
563 | reghisto[r3]++; |
564 | reghisto[r4]++; |
565 | reghisto[r5]++; |
566 | reghisto[r6]++; |
567 | reghisto[r7]++; |
568 | reghisto[r8]++; |
569 | reghisto[r9]++; |
570 | reghisto[r10]++; |
571 | reghisto[r11]++; |
572 | reghisto[r12]++; |
573 | reghisto[r13]++; |
574 | reghisto[r14]++; |
575 | reghisto[r15]++; |
576 | |
577 | r += 12; |
578 | } |
579 | } else { |
580 | for(j = 0; j < HLL_REGISTERS; j++) { |
581 | unsigned long reg; |
582 | HLL_DENSE_GET_REGISTER(reg,registers,j); |
583 | reghisto[reg]++; |
584 | } |
585 | } |
586 | } |
587 | |
588 | /* ================== Sparse representation implementation ================= */ |
589 | |
590 | /* Convert the HLL with sparse representation given as input in its dense |
591 | * representation. Both representations are represented by SDS strings, and |
592 | * the input representation is freed as a side effect. |
593 | * |
594 | * The function returns C_OK if the sparse representation was valid, |
595 | * otherwise C_ERR is returned if the representation was corrupted. */ |
596 | int hllSparseToDense(robj *o) { |
597 | sds sparse = (sds) o->ptr, dense; |
598 | struct hllhdr *hdr, *oldhdr = (struct hllhdr*)sparse; |
599 | int idx = 0, runlen, regval; |
600 | uint8_t *p = (uint8_t*)sparse, *end = p+sdslen(s: sparse); |
601 | |
602 | /* If the representation is already the right one return ASAP. */ |
603 | hdr = (struct hllhdr*) sparse; |
604 | if (hdr->encoding == HLL_DENSE) return HLL_C_OK; |
605 | |
606 | /* Create a string of the right size filled with zero bytes. |
607 | * Note that the cached cardinality is set to 0 as a side effect |
608 | * that is exactly the cardinality of an empty HLL. */ |
609 | dense = sdsnewlen(NULL,HLL_DENSE_SIZE); |
610 | hdr = (struct hllhdr*) dense; |
611 | *hdr = *oldhdr; /* This will copy the magic and cached cardinality. */ |
612 | hdr->encoding = HLL_DENSE; |
613 | |
614 | /* Now read the sparse representation and set non-zero registers |
615 | * accordingly. */ |
616 | p += HLL_HDR_SIZE; |
617 | while(p < end) { |
618 | if (HLL_SPARSE_IS_ZERO(p)) { |
619 | runlen = HLL_SPARSE_ZERO_LEN(p); |
620 | idx += runlen; |
621 | p++; |
622 | } else if (HLL_SPARSE_IS_XZERO(p)) { |
623 | runlen = HLL_SPARSE_XZERO_LEN(p); |
624 | idx += runlen; |
625 | p += 2; |
626 | } else { |
627 | runlen = HLL_SPARSE_VAL_LEN(p); |
628 | regval = HLL_SPARSE_VAL_VALUE(p); |
629 | while(runlen--) { |
630 | HLL_DENSE_SET_REGISTER(hdr->registers + 1,idx,regval); |
631 | idx++; |
632 | } |
633 | p++; |
634 | } |
635 | } |
636 | |
637 | /* If the sparse representation was valid, we expect to find idx |
638 | * set to HLL_REGISTERS. */ |
639 | if (idx != HLL_REGISTERS) { |
640 | sdsfree(s: dense); |
641 | return HLL_C_ERR; |
642 | } |
643 | |
644 | /* Free the old representation and set the new one. */ |
645 | sdsfree(s: (sds) o->ptr); |
646 | o->ptr = dense; |
647 | return HLL_C_OK; |
648 | } |
649 | |
650 | /* Low level function to set the sparse HLL register at 'index' to the |
651 | * specified value if the current value is smaller than 'count'. |
652 | * |
653 | * The object 'o' is the String object holding the HLL. The function requires |
654 | * a reference to the object in order to be able to enlarge the string if |
655 | * needed. |
656 | * |
657 | * On success, the function returns 1 if the cardinality changed, or 0 |
658 | * if the register for this element was not updated. |
659 | * On error (if the representation is invalid) -1 is returned. |
660 | * |
661 | * As a side effect the function may promote the HLL representation from |
662 | * sparse to dense: this happens when a register requires to be set to a value |
663 | * not representable with the sparse representation, or when the resulting |
664 | * size would be greater than server.hll_sparse_max_bytes. */ |
665 | int hllSparseSet(robj *o, long index, uint8_t count) { |
666 | struct hllhdr *hdr; |
667 | uint8_t oldcount, *sparse, *end, *p, *prev, *next; |
668 | long first, span; |
669 | long is_zero = 0, is_xzero = 0, is_val = 0, runlen = 0; |
670 | uint8_t seq[5], *n; |
671 | int last; |
672 | int len; |
673 | int seqlen; |
674 | int oldlen; |
675 | int deltalen; |
676 | |
677 | /* If the count is too big to be representable by the sparse representation |
678 | * switch to dense representation. */ |
679 | if (count > HLL_SPARSE_VAL_MAX_VALUE) goto promote; |
680 | |
681 | /* When updating a sparse representation, sometimes we may need to |
682 | * enlarge the buffer for up to 3 bytes in the worst case (XZERO split |
683 | * into XZERO-VAL-XZERO). Make sure there is enough space right now |
684 | * so that the pointers we take during the execution of the function |
685 | * will be valid all the time. */ |
686 | o->ptr = (sds) sdsMakeRoomFor(s: (sds) o->ptr,addlen: 3); |
687 | |
688 | /* Step 1: we need to locate the opcode we need to modify to check |
689 | * if a value update is actually needed. */ |
690 | sparse = p = ((uint8_t*)o->ptr) + HLL_HDR_SIZE; |
691 | end = p + sdslen(s: (sds) o->ptr) - HLL_HDR_SIZE; |
692 | |
693 | first = 0; |
694 | prev = NULL; /* Points to previous opcode at the end of the loop. */ |
695 | next = NULL; /* Points to the next opcode at the end of the loop. */ |
696 | span = 0; |
697 | while(p < end) { |
698 | long oplen; |
699 | |
700 | /* Set span to the number of registers covered by this opcode. |
701 | * |
702 | * This is the most performance critical loop of the sparse |
703 | * representation. Sorting the conditionals from the most to the |
704 | * least frequent opcode in many-bytes sparse HLLs is faster. */ |
705 | oplen = 1; |
706 | if (HLL_SPARSE_IS_ZERO(p)) { |
707 | span = HLL_SPARSE_ZERO_LEN(p); |
708 | } else if (HLL_SPARSE_IS_VAL(p)) { |
709 | span = HLL_SPARSE_VAL_LEN(p); |
710 | } else { /* XZERO. */ |
711 | span = HLL_SPARSE_XZERO_LEN(p); |
712 | oplen = 2; |
713 | } |
714 | /* Break if this opcode covers the register as 'index'. */ |
715 | if (index <= first+span-1) break; |
716 | prev = p; |
717 | p += oplen; |
718 | first += span; |
719 | } |
720 | if (span == 0) return -1; /* Invalid format. */ |
721 | |
722 | next = HLL_SPARSE_IS_XZERO(p) ? p+2 : p+1; |
723 | if (next >= end) next = NULL; |
724 | |
725 | /* Cache current opcode type to avoid using the macro again and |
726 | * again for something that will not change. |
727 | * Also cache the run-length of the opcode. */ |
728 | if (HLL_SPARSE_IS_ZERO(p)) { |
729 | is_zero = 1; |
730 | runlen = HLL_SPARSE_ZERO_LEN(p); |
731 | } else if (HLL_SPARSE_IS_XZERO(p)) { |
732 | is_xzero = 1; |
733 | runlen = HLL_SPARSE_XZERO_LEN(p); |
734 | } else { |
735 | is_val = 1; |
736 | runlen = HLL_SPARSE_VAL_LEN(p); |
737 | } |
738 | |
739 | /* Step 2: After the loop: |
740 | * |
741 | * 'first' stores to the index of the first register covered |
742 | * by the current opcode, which is pointed by 'p'. |
743 | * |
744 | * 'next' ad 'prev' store respectively the next and previous opcode, |
745 | * or NULL if the opcode at 'p' is respectively the last or first. |
746 | * |
747 | * 'span' is set to the number of registers covered by the current |
748 | * opcode. |
749 | * |
750 | * There are different cases in order to update the data structure |
751 | * in place without generating it from scratch: |
752 | * |
753 | * A) If it is a VAL opcode already set to a value >= our 'count' |
754 | * no update is needed, regardless of the VAL run-length field. |
755 | * In this case PFADD returns 0 since no changes are performed. |
756 | * |
757 | * B) If it is a VAL opcode with len = 1 (representing only our |
758 | * register) and the value is less than 'count', we just update it |
759 | * since this is a trivial case. */ |
760 | if (is_val) { |
761 | oldcount = HLL_SPARSE_VAL_VALUE(p); |
762 | /* Case A. */ |
763 | if (oldcount >= count) return 0; |
764 | |
765 | /* Case B. */ |
766 | if (runlen == 1) { |
767 | HLL_SPARSE_VAL_SET(p,count,1); |
768 | goto updated; |
769 | } |
770 | } |
771 | |
772 | /* C) Another trivial to handle case is a ZERO opcode with a len of 1. |
773 | * We can just replace it with a VAL opcode with our value and len of 1. */ |
774 | if (is_zero && runlen == 1) { |
775 | HLL_SPARSE_VAL_SET(p,count,1); |
776 | goto updated; |
777 | } |
778 | |
779 | /* D) General case. |
780 | * |
781 | * The other cases are more complex: our register requires to be updated |
782 | * and is either currently represented by a VAL opcode with len > 1, |
783 | * by a ZERO opcode with len > 1, or by an XZERO opcode. |
784 | * |
785 | * In those cases the original opcode must be split into multiple |
786 | * opcodes. The worst case is an XZERO split in the middle resuling into |
787 | * XZERO - VAL - XZERO, so the resulting sequence max length is |
788 | * 5 bytes. |
789 | * |
790 | * We perform the split writing the new sequence into the 'new' buffer |
791 | * with 'newlen' as length. Later the new sequence is inserted in place |
792 | * of the old one, possibly moving what is on the right a few bytes |
793 | * if the new sequence is longer than the older one. */ |
794 | n = seq; |
795 | last = first+span-1; /* Last register covered by the sequence. */ |
796 | |
797 | if (is_zero || is_xzero) { |
798 | /* Handle splitting of ZERO / XZERO. */ |
799 | if (index != first) { |
800 | len = index-first; |
801 | if (len > HLL_SPARSE_ZERO_MAX_LEN) { |
802 | HLL_SPARSE_XZERO_SET(n,len); |
803 | n += 2; |
804 | } else { |
805 | HLL_SPARSE_ZERO_SET(n,len); |
806 | n++; |
807 | } |
808 | } |
809 | HLL_SPARSE_VAL_SET(n,count,1); |
810 | n++; |
811 | if (index != last) { |
812 | len = last-index; |
813 | if (len > HLL_SPARSE_ZERO_MAX_LEN) { |
814 | HLL_SPARSE_XZERO_SET(n,len); |
815 | n += 2; |
816 | } else { |
817 | HLL_SPARSE_ZERO_SET(n,len); |
818 | n++; |
819 | } |
820 | } |
821 | } else { |
822 | /* Handle splitting of VAL. */ |
823 | int curval = HLL_SPARSE_VAL_VALUE(p); |
824 | |
825 | if (index != first) { |
826 | len = index-first; |
827 | HLL_SPARSE_VAL_SET(n,curval,len); |
828 | n++; |
829 | } |
830 | HLL_SPARSE_VAL_SET(n,count,1); |
831 | n++; |
832 | if (index != last) { |
833 | len = last-index; |
834 | HLL_SPARSE_VAL_SET(n,curval,len); |
835 | n++; |
836 | } |
837 | } |
838 | |
839 | /* Step 3: substitute the new sequence with the old one. |
840 | * |
841 | * Note that we already allocated space on the sds string |
842 | * calling sdsMakeRoomFor(). */ |
843 | seqlen = n-seq; |
844 | oldlen = is_xzero ? 2 : 1; |
845 | deltalen = seqlen-oldlen; |
846 | |
847 | if (deltalen > 0 && |
848 | sdslen(s: (sds) o->ptr)+deltalen > HLL_SPARSE_MAX_BYTES) goto promote; |
849 | if (deltalen && next) memmove(dest: next+deltalen,src: next,n: end-next); |
850 | sdsIncrLen(s: (sds) o->ptr,incr: deltalen); |
851 | memcpy(dest: p,src: seq,n: seqlen); |
852 | end += deltalen; |
853 | |
854 | updated: { |
855 | /* Step 4: Merge adjacent values if possible. |
856 | * |
857 | * The representation was updated, however the resulting representation |
858 | * may not be optimal: adjacent VAL opcodes can sometimes be merged into |
859 | * a single one. */ |
860 | p = prev ? prev : sparse; |
861 | int scanlen = 5; /* Scan up to 5 upcodes starting from prev. */ |
862 | while (p < end && scanlen--) { |
863 | if (HLL_SPARSE_IS_XZERO(p)) { |
864 | p += 2; |
865 | continue; |
866 | } else if (HLL_SPARSE_IS_ZERO(p)) { |
867 | p++; |
868 | continue; |
869 | } |
870 | /* We need two adjacent VAL opcodes to try a merge, having |
871 | * the same value, and a len that fits the VAL opcode max len. */ |
872 | if (p+1 < end && HLL_SPARSE_IS_VAL(p+1)) { |
873 | int v1 = HLL_SPARSE_VAL_VALUE(p); |
874 | int v2 = HLL_SPARSE_VAL_VALUE(p+1); |
875 | if (v1 == v2) { |
876 | int len = HLL_SPARSE_VAL_LEN(p)+HLL_SPARSE_VAL_LEN(p+1); |
877 | if (len <= HLL_SPARSE_VAL_MAX_LEN) { |
878 | HLL_SPARSE_VAL_SET(p+1,v1,len); |
879 | memmove(dest: p,src: p+1,n: end-p); |
880 | sdsIncrLen(s: (sds) o->ptr,incr: -1); |
881 | end--; |
882 | /* After a merge we reiterate without incrementing 'p' |
883 | * in order to try to merge the just merged value with |
884 | * a value on its right. */ |
885 | continue; |
886 | } |
887 | } |
888 | } |
889 | p++; |
890 | } |
891 | |
892 | /* Invalidate the cached cardinality. */ |
893 | hdr = (struct hllhdr *) o->ptr; |
894 | HLL_INVALIDATE_CACHE(hdr); |
895 | return 1; |
896 | } |
897 | promote: /* Promote to dense representation. */ |
898 | if (hllSparseToDense(o) == HLL_C_ERR) return -1; /* Corrupted HLL. */ |
899 | hdr = (struct hllhdr *) o->ptr; |
900 | |
901 | /* We need to call hllDenseAdd() to perform the operation after the |
902 | * conversion. However the result must be 1, since if we need to |
903 | * convert from sparse to dense a register requires to be updated. |
904 | * |
905 | * Note that this in turn means that PFADD will make sure the command |
906 | * is propagated to slaves / AOF, so if there is a sparse -> dense |
907 | * conversion, it will be performed in all the slaves as well. */ |
908 | int dense_retval = hllDenseSet(registers: hdr->registers + 1,index,count); |
909 | assert(dense_retval == 1); |
910 | return dense_retval; |
911 | } |
912 | |
913 | /* "Add" the element in the sparse hyperloglog data structure. |
914 | * Actually nothing is added, but the max 0 pattern counter of the subset |
915 | * the element belongs to is incremented if needed. |
916 | * |
917 | * This function is actually a wrapper for hllSparseSet(), it only performs |
918 | * the hashshing of the elmenet to obtain the index and zeros run length. */ |
919 | int hllSparseAdd(robj *o, unsigned char *ele, size_t elesize) { |
920 | long index; |
921 | uint8_t count = hllPatLen(ele,elesize,regp: &index); |
922 | /* Update the register if this element produced a longer run of zeroes. */ |
923 | return hllSparseSet(o,index,count); |
924 | } |
925 | |
926 | /* Compute the register histogram in the sparse representation. */ |
927 | void hllSparseRegHisto(uint8_t *sparse, int sparselen, int *invalid, int* reghisto) { |
928 | int idx = 0, runlen, regval; |
929 | uint8_t *end = sparse+sparselen, *p = sparse; |
930 | |
931 | while(p < end) { |
932 | if (HLL_SPARSE_IS_ZERO(p)) { |
933 | runlen = HLL_SPARSE_ZERO_LEN(p); |
934 | idx += runlen; |
935 | reghisto[0] += runlen; |
936 | p++; |
937 | } else if (HLL_SPARSE_IS_XZERO(p)) { |
938 | runlen = HLL_SPARSE_XZERO_LEN(p); |
939 | idx += runlen; |
940 | reghisto[0] += runlen; |
941 | p += 2; |
942 | } else { |
943 | runlen = HLL_SPARSE_VAL_LEN(p); |
944 | regval = HLL_SPARSE_VAL_VALUE(p); |
945 | idx += runlen; |
946 | reghisto[regval] += runlen; |
947 | p++; |
948 | } |
949 | } |
950 | if (idx != HLL_REGISTERS && invalid) *invalid = 1; |
951 | } |
952 | |
953 | /* ========================= HyperLogLog Count ============================== |
954 | * This is the core of the algorithm where the approximated count is computed. |
955 | * The function uses the lower level hllDenseRegHisto() and hllSparseRegHisto() |
956 | * functions as helpers to compute histogram of register values part of the |
957 | * computation, which is representation-specific, while all the rest is common. */ |
958 | |
959 | /* Implements the register histogram calculation for uint8_t data type |
960 | * which is only used internally as speedup for PFCOUNT with multiple keys. */ |
961 | void hllRawRegHisto(uint8_t *registers, int* reghisto) { |
962 | uint64_t *word = (uint64_t*) registers; |
963 | uint8_t *bytes; |
964 | int j; |
965 | |
966 | for (j = 0; j < HLL_REGISTERS/8; j++) { |
967 | if (*word == 0) { |
968 | reghisto[0] += 8; |
969 | } else { |
970 | bytes = (uint8_t*) word; |
971 | reghisto[bytes[0]]++; |
972 | reghisto[bytes[1]]++; |
973 | reghisto[bytes[2]]++; |
974 | reghisto[bytes[3]]++; |
975 | reghisto[bytes[4]]++; |
976 | reghisto[bytes[5]]++; |
977 | reghisto[bytes[6]]++; |
978 | reghisto[bytes[7]]++; |
979 | } |
980 | word++; |
981 | } |
982 | } |
983 | |
984 | // somehow this is missing on some platforms |
985 | #ifndef INFINITY |
986 | // from math.h |
987 | #define INFINITY 1e50f |
988 | #endif |
989 | |
990 | |
991 | /* Helper function sigma as defined in |
992 | * "New cardinality estimation algorithms for HyperLogLog sketches" |
993 | * Otmar Ertl, arXiv:1702.01284 */ |
994 | double hllSigma(double x) { |
995 | if (x == 1.) return INFINITY; |
996 | double zPrime; |
997 | double y = 1; |
998 | double z = x; |
999 | do { |
1000 | x *= x; |
1001 | zPrime = z; |
1002 | z += x * y; |
1003 | y += y; |
1004 | } while(zPrime != z); |
1005 | return z; |
1006 | } |
1007 | |
1008 | /* Helper function tau as defined in |
1009 | * "New cardinality estimation algorithms for HyperLogLog sketches" |
1010 | * Otmar Ertl, arXiv:1702.01284 */ |
1011 | double hllTau(double x) { |
1012 | if (x == 0. || x == 1.) return 0.; |
1013 | double zPrime; |
1014 | double y = 1.0; |
1015 | double z = 1 - x; |
1016 | do { |
1017 | x = sqrt(x: x); |
1018 | zPrime = z; |
1019 | y *= 0.5; |
1020 | z -= pow(x: 1 - x, y: 2)*y; |
1021 | } while(zPrime != z); |
1022 | return z / 3; |
1023 | } |
1024 | |
1025 | /* Return the approximated cardinality of the set based on the harmonic |
1026 | * mean of the registers values. 'hdr' points to the start of the SDS |
1027 | * representing the String object holding the HLL representation. |
1028 | * |
1029 | * If the sparse representation of the HLL object is not valid, the integer |
1030 | * pointed by 'invalid' is set to non-zero, otherwise it is left untouched. |
1031 | * |
1032 | * hllCount() supports a special internal-only encoding of HLL_RAW, that |
1033 | * is, hdr->registers will point to an uint8_t array of HLL_REGISTERS element. |
1034 | * This is useful in order to speedup PFCOUNT when called against multiple |
1035 | * keys (no need to work with 6-bit integers encoding). */ |
1036 | uint64_t hllCount(struct hllhdr *hdr, int *invalid) { |
1037 | double m = HLL_REGISTERS; |
1038 | double E; |
1039 | int j; |
1040 | int reghisto[HLL_Q+2] = {0}; |
1041 | |
1042 | /* Compute register histogram */ |
1043 | if (hdr->encoding == HLL_DENSE) { |
1044 | hllDenseRegHisto(registers: hdr->registers + 1,reghisto); |
1045 | } else if (hdr->encoding == HLL_SPARSE) { |
1046 | hllSparseRegHisto(sparse: hdr->registers + 1, |
1047 | sparselen: sdslen(s: (sds)hdr)-HLL_HDR_SIZE,invalid,reghisto); |
1048 | } else if (hdr->encoding == HLL_RAW) { |
1049 | hllRawRegHisto(registers: hdr->registers + 1,reghisto); |
1050 | } else { |
1051 | *invalid = 1; |
1052 | return 0; |
1053 | //serverPanic("Unknown HyperLogLog encoding in hllCount()"); |
1054 | } |
1055 | |
1056 | /* Estimate cardinality form register histogram. See: |
1057 | * "New cardinality estimation algorithms for HyperLogLog sketches" |
1058 | * Otmar Ertl, arXiv:1702.01284 */ |
1059 | double z = m * hllTau(x: (m-reghisto[HLL_Q+1])/(double)m); |
1060 | for (j = HLL_Q; j >= 1; --j) { |
1061 | z += reghisto[j]; |
1062 | z *= 0.5; |
1063 | } |
1064 | z += m * hllSigma(x: reghisto[0]/(double)m); |
1065 | E = llroundl(HLL_ALPHA_INF*m*m/z); |
1066 | |
1067 | return (uint64_t) E; |
1068 | } |
1069 | |
1070 | /* Call hllDenseAdd() or hllSparseAdd() according to the HLL encoding. */ |
1071 | int hll_add(robj *o, unsigned char *ele, size_t elesize) { |
1072 | struct hllhdr *hdr = (struct hllhdr *) o->ptr; |
1073 | switch(hdr->encoding) { |
1074 | case HLL_DENSE: return hllDenseAdd(registers: hdr->registers + 1,ele,elesize); |
1075 | case HLL_SPARSE: return hllSparseAdd(o,ele,elesize); |
1076 | default: return -1; /* Invalid representation. */ |
1077 | } |
1078 | } |
1079 | |
1080 | /* Merge by computing MAX(registers[i],hll[i]) the HyperLogLog 'hll' |
1081 | * with an array of uint8_t HLL_REGISTERS registers pointed by 'max'. |
1082 | * |
1083 | * The hll object must be already validated via isHLLObjectOrReply() |
1084 | * or in some other way. |
1085 | * |
1086 | * If the HyperLogLog is sparse and is found to be invalid, C_ERR |
1087 | * is returned, otherwise the function always succeeds. */ |
1088 | int hllMerge(uint8_t *max, robj *hll) { |
1089 | struct hllhdr *hdr = (struct hllhdr *) hll->ptr; |
1090 | int i; |
1091 | |
1092 | if (hdr->encoding == HLL_DENSE) { |
1093 | uint8_t val; |
1094 | |
1095 | for (i = 0; i < HLL_REGISTERS; i++) { |
1096 | HLL_DENSE_GET_REGISTER(val,hdr->registers + 1,i); |
1097 | if (val > max[i]) max[i] = val; |
1098 | } |
1099 | } else { |
1100 | uint8_t *p = (uint8_t *) hll->ptr, *end = p + sdslen(s: (sds) hll->ptr); |
1101 | long runlen, regval; |
1102 | |
1103 | p += HLL_HDR_SIZE; |
1104 | i = 0; |
1105 | while(p < end) { |
1106 | if (HLL_SPARSE_IS_ZERO(p)) { |
1107 | runlen = HLL_SPARSE_ZERO_LEN(p); |
1108 | i += runlen; |
1109 | p++; |
1110 | } else if (HLL_SPARSE_IS_XZERO(p)) { |
1111 | runlen = HLL_SPARSE_XZERO_LEN(p); |
1112 | i += runlen; |
1113 | p += 2; |
1114 | } else { |
1115 | runlen = HLL_SPARSE_VAL_LEN(p); |
1116 | regval = HLL_SPARSE_VAL_VALUE(p); |
1117 | while(runlen--) { |
1118 | if (regval > max[i]) max[i] = regval; |
1119 | i++; |
1120 | } |
1121 | p++; |
1122 | } |
1123 | } |
1124 | if (i != HLL_REGISTERS) return HLL_C_ERR; |
1125 | } |
1126 | return HLL_C_OK; |
1127 | } |
1128 | |
1129 | /* ========================== robj creation ========================== */ |
1130 | robj *createObject(void *ptr) { |
1131 | robj *result = (robj*) malloc(size: sizeof(robj)); |
1132 | result->ptr = ptr; |
1133 | return result; |
1134 | } |
1135 | |
1136 | void destroyObject(robj *obj) { |
1137 | free(ptr: obj); |
1138 | } |
1139 | |
1140 | /* ========================== HyperLogLog commands ========================== */ |
1141 | |
1142 | /* Create an HLL object. We always create the HLL using sparse encoding. |
1143 | * This will be upgraded to the dense representation as needed. */ |
1144 | robj *hll_create(void) { |
1145 | robj *o; |
1146 | struct hllhdr *hdr; |
1147 | sds s; |
1148 | uint8_t *p; |
1149 | int sparselen = HLL_HDR_SIZE + |
1150 | (((HLL_REGISTERS+(HLL_SPARSE_XZERO_MAX_LEN-1)) / |
1151 | HLL_SPARSE_XZERO_MAX_LEN)*2); |
1152 | int aux; |
1153 | |
1154 | /* Populate the sparse representation with as many XZERO opcodes as |
1155 | * needed to represent all the registers. */ |
1156 | aux = HLL_REGISTERS; |
1157 | s = sdsnewlen(NULL,initlen: sparselen); |
1158 | p = (uint8_t*)s + HLL_HDR_SIZE; |
1159 | while(aux) { |
1160 | int xzero = HLL_SPARSE_XZERO_MAX_LEN; |
1161 | if (xzero > aux) xzero = aux; |
1162 | HLL_SPARSE_XZERO_SET(p,xzero); |
1163 | p += 2; |
1164 | aux -= xzero; |
1165 | } |
1166 | assert((p-(uint8_t*)s) == sparselen); |
1167 | |
1168 | /* Create the actual object. */ |
1169 | o = createObject(ptr: s); |
1170 | hdr = (struct hllhdr *) o->ptr; |
1171 | memcpy(dest: hdr->magic,src: "HYLL" ,n: 4); |
1172 | hdr->encoding = HLL_SPARSE; |
1173 | return o; |
1174 | } |
1175 | |
1176 | void hll_destroy(robj *obj) { |
1177 | if (!obj) { |
1178 | return; |
1179 | } |
1180 | sdsfree(s: (sds) obj->ptr); |
1181 | destroyObject(obj); |
1182 | } |
1183 | |
1184 | |
1185 | |
1186 | int hll_count(robj *o, size_t *result) { |
1187 | int invalid = 0; |
1188 | *result = hllCount(hdr: (struct hllhdr*) o->ptr, invalid: &invalid); |
1189 | return invalid == 0 ? HLL_C_OK : HLL_C_ERR; |
1190 | } |
1191 | |
1192 | robj *hll_merge(robj **hlls, size_t hll_count) { |
1193 | uint8_t max[HLL_REGISTERS]; |
1194 | struct hllhdr *hdr; |
1195 | size_t j; |
1196 | /* Use dense representation as target? */ |
1197 | int use_dense = 0; |
1198 | |
1199 | /* Compute an HLL with M[i] = MAX(M[i]_j). |
1200 | * We store the maximum into the max array of registers. We'll write |
1201 | * it to the target variable later. */ |
1202 | memset(s: max, c: 0, n: sizeof(max)); |
1203 | for (j = 0; j < hll_count; j++) { |
1204 | /* Check type and size. */ |
1205 | robj *o = hlls[j]; |
1206 | if (o == NULL) continue; /* Assume empty HLL for non existing var. */ |
1207 | |
1208 | /* If at least one involved HLL is dense, use the dense representation |
1209 | * as target ASAP to save time and avoid the conversion step. */ |
1210 | hdr = (struct hllhdr *) o->ptr; |
1211 | if (hdr->encoding == HLL_DENSE) use_dense = 1; |
1212 | |
1213 | /* Merge with this HLL with our 'max' HHL by setting max[i] |
1214 | * to MAX(max[i],hll[i]). */ |
1215 | if (hllMerge(max, hll: o) == HLL_C_ERR) { |
1216 | return NULL; |
1217 | } |
1218 | } |
1219 | |
1220 | /* Create the destination key's value. */ |
1221 | robj *result = hll_create(); |
1222 | if (!result) { |
1223 | return NULL; |
1224 | } |
1225 | |
1226 | /* Convert the destination object to dense representation if at least |
1227 | * one of the inputs was dense. */ |
1228 | if (use_dense && hllSparseToDense(o: result) == HLL_C_ERR) { |
1229 | hll_destroy(obj: result); |
1230 | return NULL; |
1231 | } |
1232 | |
1233 | /* Write the resulting HLL to the destination HLL registers and |
1234 | * invalidate the cached value. */ |
1235 | for (j = 0; j < HLL_REGISTERS; j++) { |
1236 | if (max[j] == 0) continue; |
1237 | hdr = (struct hllhdr *) result->ptr; |
1238 | switch(hdr->encoding) { |
1239 | case HLL_DENSE: hllDenseSet(registers: hdr->registers + 1,index: j,count: max[j]); break; |
1240 | case HLL_SPARSE: hllSparseSet(o: result,index: j,count: max[j]); break; |
1241 | } |
1242 | } |
1243 | return result; |
1244 | } |
1245 | |
1246 | uint64_t get_size() { |
1247 | return HLL_DENSE_SIZE; |
1248 | } |
1249 | |
1250 | } |
1251 | |
1252 | namespace duckdb { |
1253 | |
1254 | static inline int AddToLog(void *log, const uint64_t &index, const uint8_t &count) { |
1255 | auto o = (duckdb_hll::robj *)log; |
1256 | duckdb_hll::hllhdr *hdr = (duckdb_hll::hllhdr *)o->ptr; |
1257 | D_ASSERT(hdr->encoding == HLL_DENSE); |
1258 | return duckdb_hll::hllDenseSet(registers: hdr->registers + 1, index, count); |
1259 | } |
1260 | |
1261 | void AddToLogsInternal(UnifiedVectorFormat &vdata, idx_t count, uint64_t indices[], uint8_t counts[], void ***logs[], |
1262 | const SelectionVector *log_sel) { |
1263 | // 'logs' is an array of pointers to AggregateStates |
1264 | // AggregateStates have a pointer to a HyperLogLog object |
1265 | // HyperLogLog objects have a pointer to a 'robj', which we need |
1266 | for (idx_t i = 0; i < count; i++) { |
1267 | auto log = logs[log_sel->get_index(idx: i)]; |
1268 | if (log && vdata.validity.RowIsValid(row_idx: vdata.sel->get_index(idx: i))) { |
1269 | AddToLog(log: **log, index: indices[i], count: counts[i]); |
1270 | } |
1271 | } |
1272 | } |
1273 | |
1274 | void AddToSingleLogInternal(UnifiedVectorFormat &vdata, idx_t count, uint64_t indices[], uint8_t counts[], void *log) { |
1275 | const auto o = (duckdb_hll::robj *)log; |
1276 | duckdb_hll::hllhdr *hdr = (duckdb_hll::hllhdr *)o->ptr; |
1277 | D_ASSERT(hdr->encoding == HLL_DENSE); |
1278 | |
1279 | const auto registers = hdr->registers + 1; |
1280 | for (idx_t i = 0; i < count; i++) { |
1281 | if (vdata.validity.RowIsValid(row_idx: vdata.sel->get_index(idx: i))) { |
1282 | duckdb_hll::hllDenseSet(registers, index: indices[i], count: counts[i]); |
1283 | } |
1284 | } |
1285 | } |
1286 | |
1287 | } // namespace duckdb |
1288 | |