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diff --git a/src/hyperloglog.c b/src/hyperloglog.c new file mode 100644 index 0000000..84fd6b6 --- /dev/null +++ b/src/hyperloglog.c @@ -0,0 +1,1607 @@ +/* hyperloglog.c - Redis HyperLogLog probabilistic cardinality approximation. + * This file implements the algorithm and the exported Redis commands. + * + * Copyright (c) 2014, Salvatore Sanfilippo <antirez at gmail dot com> + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions are met: + * + * * Redistributions of source code must retain the above copyright notice, + * this list of conditions and the following disclaimer. + * * Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * * Neither the name of Redis nor the names of its contributors may be used + * to endorse or promote products derived from this software without + * specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" + * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE + * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "server.h" + +#include <stdint.h> +#include <math.h> + +/* The Redis HyperLogLog implementation is based on the following ideas: + * + * * The use of a 64 bit hash function as proposed in [1], in order to estimate + * cardinalities larger than 10^9, at the cost of just 1 additional bit per + * register. + * * The use of 16384 6-bit registers for a great level of accuracy, using + * a total of 12k per key. + * * The use of the Redis string data type. No new type is introduced. + * * No attempt is made to compress the data structure as in [1]. Also the + * algorithm used is the original HyperLogLog Algorithm as in [2], with + * the only difference that a 64 bit hash function is used, so no correction + * is performed for values near 2^32 as in [1]. + * + * [1] Heule, Nunkesser, Hall: HyperLogLog in Practice: Algorithmic + * Engineering of a State of The Art Cardinality Estimation Algorithm. + * + * [2] P. Flajolet, Éric Fusy, O. Gandouet, and F. Meunier. Hyperloglog: The + * analysis of a near-optimal cardinality estimation algorithm. + * + * Redis uses two representations: + * + * 1) A "dense" representation where every entry is represented by + * a 6-bit integer. + * 2) A "sparse" representation using run length compression suitable + * for representing HyperLogLogs with many registers set to 0 in + * a memory efficient way. + * + * + * HLL header + * === + * + * Both the dense and sparse representation have a 16 byte header as follows: + * + * +------+---+-----+----------+ + * | HYLL | E | N/U | Cardin. | + * +------+---+-----+----------+ + * + * The first 4 bytes are a magic string set to the bytes "HYLL". + * "E" is one byte encoding, currently set to HLL_DENSE or + * HLL_SPARSE. N/U are three not used bytes. + * + * The "Cardin." field is a 64 bit integer stored in little endian format + * with the latest cardinality computed that can be reused if the data + * structure was not modified since the last computation (this is useful + * because there are high probabilities that HLLADD operations don't + * modify the actual data structure and hence the approximated cardinality). + * + * When the most significant bit in the most significant byte of the cached + * cardinality is set, it means that the data structure was modified and + * we can't reuse the cached value that must be recomputed. + * + * Dense representation + * === + * + * The dense representation used by Redis is the following: + * + * +--------+--------+--------+------// //--+ + * |11000000|22221111|33333322|55444444 .... | + * +--------+--------+--------+------// //--+ + * + * The 6 bits counters are encoded one after the other starting from the + * LSB to the MSB, and using the next bytes as needed. + * + * Sparse representation + * === + * + * The sparse representation encodes registers using a run length + * encoding composed of three opcodes, two using one byte, and one using + * of two bytes. The opcodes are called ZERO, XZERO and VAL. + * + * ZERO opcode is represented as 00xxxxxx. The 6-bit integer represented + * by the six bits 'xxxxxx', plus 1, means that there are N registers set + * to 0. This opcode can represent from 1 to 64 contiguous registers set + * to the value of 0. + * + * XZERO opcode is represented by two bytes 01xxxxxx yyyyyyyy. The 14-bit + * integer represented by the bits 'xxxxxx' as most significant bits and + * 'yyyyyyyy' as least significant bits, plus 1, means that there are N + * registers set to 0. This opcode can represent from 0 to 16384 contiguous + * registers set to the value of 0. + * + * VAL opcode is represented as 1vvvvvxx. It contains a 5-bit integer + * representing the value of a register, and a 2-bit integer representing + * the number of contiguous registers set to that value 'vvvvv'. + * To obtain the value and run length, the integers vvvvv and xx must be + * incremented by one. This opcode can represent values from 1 to 32, + * repeated from 1 to 4 times. + * + * The sparse representation can't represent registers with a value greater + * than 32, however it is very unlikely that we find such a register in an + * HLL with a cardinality where the sparse representation is still more + * memory efficient than the dense representation. When this happens the + * HLL is converted to the dense representation. + * + * The sparse representation is purely positional. For example a sparse + * representation of an empty HLL is just: XZERO:16384. + * + * An HLL having only 3 non-zero registers at position 1000, 1020, 1021 + * respectively set to 2, 3, 3, is represented by the following three + * opcodes: + * + * XZERO:1000 (Registers 0-999 are set to 0) + * VAL:2,1 (1 register set to value 2, that is register 1000) + * ZERO:19 (Registers 1001-1019 set to 0) + * VAL:3,2 (2 registers set to value 3, that is registers 1020,1021) + * XZERO:15362 (Registers 1022-16383 set to 0) + * + * In the example the sparse representation used just 7 bytes instead + * of 12k in order to represent the HLL registers. In general for low + * cardinality there is a big win in terms of space efficiency, traded + * with CPU time since the sparse representation is slower to access: + * + * The following table shows average cardinality vs bytes used, 100 + * samples per cardinality (when the set was not representable because + * of registers with too big value, the dense representation size was used + * as a sample). + * + * 100 267 + * 200 485 + * 300 678 + * 400 859 + * 500 1033 + * 600 1205 + * 700 1375 + * 800 1544 + * 900 1713 + * 1000 1882 + * 2000 3480 + * 3000 4879 + * 4000 6089 + * 5000 7138 + * 6000 8042 + * 7000 8823 + * 8000 9500 + * 9000 10088 + * 10000 10591 + * + * The dense representation uses 12288 bytes, so there is a big win up to + * a cardinality of ~2000-3000. For bigger cardinalities the constant times + * involved in updating the sparse representation is not justified by the + * memory savings. The exact maximum length of the sparse representation + * when this implementation switches to the dense representation is + * configured via the define server.hll_sparse_max_bytes. + */ + +struct hllhdr { + char magic[4]; /* "HYLL" */ + uint8_t encoding; /* HLL_DENSE or HLL_SPARSE. */ + uint8_t notused[3]; /* Reserved for future use, must be zero. */ + uint8_t card[8]; /* Cached cardinality, little endian. */ + uint8_t registers[]; /* Data bytes. */ +}; + +/* The cached cardinality MSB is used to signal validity of the cached value. */ +#define HLL_INVALIDATE_CACHE(hdr) (hdr)->card[7] |= (1<<7) +#define HLL_VALID_CACHE(hdr) (((hdr)->card[7] & (1<<7)) == 0) + +#define HLL_P 14 /* The greater is P, the smaller the error. */ +#define HLL_Q (64-HLL_P) /* The number of bits of the hash value used for + determining the number of leading zeros. */ +#define HLL_REGISTERS (1<<HLL_P) /* With P=14, 16384 registers. */ +#define HLL_P_MASK (HLL_REGISTERS-1) /* Mask to index register. */ +#define HLL_BITS 6 /* Enough to count up to 63 leading zeroes. */ +#define HLL_REGISTER_MAX ((1<<HLL_BITS)-1) +#define HLL_HDR_SIZE sizeof(struct hllhdr) +#define HLL_DENSE_SIZE (HLL_HDR_SIZE+((HLL_REGISTERS*HLL_BITS+7)/8)) +#define HLL_DENSE 0 /* Dense encoding. */ +#define HLL_SPARSE 1 /* Sparse encoding. */ +#define HLL_RAW 255 /* Only used internally, never exposed. */ +#define HLL_MAX_ENCODING 1 + +static char *invalid_hll_err = "-INVALIDOBJ Corrupted HLL object detected"; + +/* =========================== Low level bit macros ========================= */ + +/* Macros to access the dense representation. + * + * We need to get and set 6 bit counters in an array of 8 bit bytes. + * We use macros to make sure the code is inlined since speed is critical + * especially in order to compute the approximated cardinality in + * HLLCOUNT where we need to access all the registers at once. + * For the same reason we also want to avoid conditionals in this code path. + * + * +--------+--------+--------+------// + * |11000000|22221111|33333322|55444444 + * +--------+--------+--------+------// + * + * Note: in the above representation the most significant bit (MSB) + * of every byte is on the left. We start using bits from the LSB to MSB, + * and so forth passing to the next byte. + * + * Example, we want to access to counter at pos = 1 ("111111" in the + * illustration above). + * + * The index of the first byte b0 containing our data is: + * + * b0 = 6 * pos / 8 = 0 + * + * +--------+ + * |11000000| <- Our byte at b0 + * +--------+ + * + * The position of the first bit (counting from the LSB = 0) in the byte + * is given by: + * + * fb = 6 * pos % 8 -> 6 + * + * Right shift b0 of 'fb' bits. + * + * +--------+ + * |11000000| <- Initial value of b0 + * |00000011| <- After right shift of 6 pos. + * +--------+ + * + * Left shift b1 of bits 8-fb bits (2 bits) + * + * +--------+ + * |22221111| <- Initial value of b1 + * |22111100| <- After left shift of 2 bits. + * +--------+ + * + * OR the two bits, and finally AND with 111111 (63 in decimal) to + * clean the higher order bits we are not interested in: + * + * +--------+ + * |00000011| <- b0 right shifted + * |22111100| <- b1 left shifted + * |22111111| <- b0 OR b1 + * | 111111| <- (b0 OR b1) AND 63, our value. + * +--------+ + * + * We can try with a different example, like pos = 0. In this case + * the 6-bit counter is actually contained in a single byte. + * + * b0 = 6 * pos / 8 = 0 + * + * +--------+ + * |11000000| <- Our byte at b0 + * +--------+ + * + * fb = 6 * pos % 8 = 0 + * + * So we right shift of 0 bits (no shift in practice) and + * left shift the next byte of 8 bits, even if we don't use it, + * but this has the effect of clearing the bits so the result + * will not be affected after the OR. + * + * ------------------------------------------------------------------------- + * + * Setting the register is a bit more complex, let's assume that 'val' + * is the value we want to set, already in the right range. + * + * We need two steps, in one we need to clear the bits, and in the other + * we need to bitwise-OR the new bits. + * + * Let's try with 'pos' = 1, so our first byte at 'b' is 0, + * + * "fb" is 6 in this case. + * + * +--------+ + * |11000000| <- Our byte at b0 + * +--------+ + * + * To create an AND-mask to clear the bits about this position, we just + * initialize the mask with the value 63, left shift it of "fs" bits, + * and finally invert the result. + * + * +--------+ + * |00111111| <- "mask" starts at 63 + * |11000000| <- "mask" after left shift of "ls" bits. + * |00111111| <- "mask" after invert. + * +--------+ + * + * Now we can bitwise-AND the byte at "b" with the mask, and bitwise-OR + * it with "val" left-shifted of "ls" bits to set the new bits. + * + * Now let's focus on the next byte b1: + * + * +--------+ + * |22221111| <- Initial value of b1 + * +--------+ + * + * To build the AND mask we start again with the 63 value, right shift + * it by 8-fb bits, and invert it. + * + * +--------+ + * |00111111| <- "mask" set at 2&6-1 + * |00001111| <- "mask" after the right shift by 8-fb = 2 bits + * |11110000| <- "mask" after bitwise not. + * +--------+ + * + * Now we can mask it with b+1 to clear the old bits, and bitwise-OR + * with "val" left-shifted by "rs" bits to set the new value. + */ + +/* Note: if we access the last counter, we will also access the b+1 byte + * that is out of the array, but sds strings always have an implicit null + * term, so the byte exists, and we can skip the conditional (or the need + * to allocate 1 byte more explicitly). */ + +/* Store the value of the register at position 'regnum' into variable 'target'. + * 'p' is an array of unsigned bytes. */ +#define HLL_DENSE_GET_REGISTER(target,p,regnum) do { \ + uint8_t *_p = (uint8_t*) p; \ + unsigned long _byte = regnum*HLL_BITS/8; \ + unsigned long _fb = regnum*HLL_BITS&7; \ + unsigned long _fb8 = 8 - _fb; \ + unsigned long b0 = _p[_byte]; \ + unsigned long b1 = _p[_byte+1]; \ + target = ((b0 >> _fb) | (b1 << _fb8)) & HLL_REGISTER_MAX; \ +} while(0) + +/* Set the value of the register at position 'regnum' to 'val'. + * 'p' is an array of unsigned bytes. */ +#define HLL_DENSE_SET_REGISTER(p,regnum,val) do { \ + uint8_t *_p = (uint8_t*) p; \ + unsigned long _byte = regnum*HLL_BITS/8; \ + unsigned long _fb = regnum*HLL_BITS&7; \ + unsigned long _fb8 = 8 - _fb; \ + unsigned long _v = val; \ + _p[_byte] &= ~(HLL_REGISTER_MAX << _fb); \ + _p[_byte] |= _v << _fb; \ + _p[_byte+1] &= ~(HLL_REGISTER_MAX >> _fb8); \ + _p[_byte+1] |= _v >> _fb8; \ +} while(0) + +/* Macros to access the sparse representation. + * The macros parameter is expected to be an uint8_t pointer. */ +#define HLL_SPARSE_XZERO_BIT 0x40 /* 01xxxxxx */ +#define HLL_SPARSE_VAL_BIT 0x80 /* 1vvvvvxx */ +#define HLL_SPARSE_IS_ZERO(p) (((*(p)) & 0xc0) == 0) /* 00xxxxxx */ +#define HLL_SPARSE_IS_XZERO(p) (((*(p)) & 0xc0) == HLL_SPARSE_XZERO_BIT) +#define HLL_SPARSE_IS_VAL(p) ((*(p)) & HLL_SPARSE_VAL_BIT) +#define HLL_SPARSE_ZERO_LEN(p) (((*(p)) & 0x3f)+1) +#define HLL_SPARSE_XZERO_LEN(p) (((((*(p)) & 0x3f) << 8) | (*((p)+1)))+1) +#define HLL_SPARSE_VAL_VALUE(p) ((((*(p)) >> 2) & 0x1f)+1) +#define HLL_SPARSE_VAL_LEN(p) (((*(p)) & 0x3)+1) +#define HLL_SPARSE_VAL_MAX_VALUE 32 +#define HLL_SPARSE_VAL_MAX_LEN 4 +#define HLL_SPARSE_ZERO_MAX_LEN 64 +#define HLL_SPARSE_XZERO_MAX_LEN 16384 +#define HLL_SPARSE_VAL_SET(p,val,len) do { \ + *(p) = (((val)-1)<<2|((len)-1))|HLL_SPARSE_VAL_BIT; \ +} while(0) +#define HLL_SPARSE_ZERO_SET(p,len) do { \ + *(p) = (len)-1; \ +} while(0) +#define HLL_SPARSE_XZERO_SET(p,len) do { \ + int _l = (len)-1; \ + *(p) = (_l>>8) | HLL_SPARSE_XZERO_BIT; \ + *((p)+1) = (_l&0xff); \ +} while(0) +#define HLL_ALPHA_INF 0.721347520444481703680 /* constant for 0.5/ln(2) */ + +/* ========================= HyperLogLog algorithm ========================= */ + +/* Our hash function is MurmurHash2, 64 bit version. + * It was modified for Redis in order to provide the same result in + * big and little endian archs (endian neutral). */ +REDIS_NO_SANITIZE("alignment") +uint64_t MurmurHash64A (const void * key, int len, unsigned int seed) { + const uint64_t m = 0xc6a4a7935bd1e995; + const int r = 47; + uint64_t h = seed ^ (len * m); + const uint8_t *data = (const uint8_t *)key; + const uint8_t *end = data + (len-(len&7)); + + while(data != end) { + uint64_t k; + +#if (BYTE_ORDER == LITTLE_ENDIAN) + #ifdef USE_ALIGNED_ACCESS + memcpy(&k,data,sizeof(uint64_t)); + #else + k = *((uint64_t*)data); + #endif +#else + k = (uint64_t) data[0]; + k |= (uint64_t) data[1] << 8; + k |= (uint64_t) data[2] << 16; + k |= (uint64_t) data[3] << 24; + k |= (uint64_t) data[4] << 32; + k |= (uint64_t) data[5] << 40; + k |= (uint64_t) data[6] << 48; + k |= (uint64_t) data[7] << 56; +#endif + + k *= m; + k ^= k >> r; + k *= m; + h ^= k; + h *= m; + data += 8; + } + + switch(len & 7) { + case 7: h ^= (uint64_t)data[6] << 48; /* fall-thru */ + case 6: h ^= (uint64_t)data[5] << 40; /* fall-thru */ + case 5: h ^= (uint64_t)data[4] << 32; /* fall-thru */ + case 4: h ^= (uint64_t)data[3] << 24; /* fall-thru */ + case 3: h ^= (uint64_t)data[2] << 16; /* fall-thru */ + case 2: h ^= (uint64_t)data[1] << 8; /* fall-thru */ + case 1: h ^= (uint64_t)data[0]; + h *= m; /* fall-thru */ + }; + + h ^= h >> r; + h *= m; + h ^= h >> r; + return h; +} + +/* Given a string element to add to the HyperLogLog, returns the length + * of the pattern 000..1 of the element hash. As a side effect 'regp' is + * set to the register index this element hashes to. */ +int hllPatLen(unsigned char *ele, size_t elesize, long *regp) { + uint64_t hash, bit, index; + int count; + + /* Count the number of zeroes starting from bit HLL_REGISTERS + * (that is a power of two corresponding to the first bit we don't use + * as index). The max run can be 64-P+1 = Q+1 bits. + * + * Note that the final "1" ending the sequence of zeroes must be + * included in the count, so if we find "001" the count is 3, and + * the smallest count possible is no zeroes at all, just a 1 bit + * at the first position, that is a count of 1. + * + * This may sound like inefficient, but actually in the average case + * there are high probabilities to find a 1 after a few iterations. */ + hash = MurmurHash64A(ele,elesize,0xadc83b19ULL); + index = hash & HLL_P_MASK; /* Register index. */ + hash >>= HLL_P; /* Remove bits used to address the register. */ + hash |= ((uint64_t)1<<HLL_Q); /* Make sure the loop terminates + and count will be <= Q+1. */ + bit = 1; + count = 1; /* Initialized to 1 since we count the "00000...1" pattern. */ + while((hash & bit) == 0) { + count++; + bit <<= 1; + } + *regp = (int) index; + return count; +} + +/* ================== Dense representation implementation ================== */ + +/* Low level function to set the dense HLL register at 'index' to the + * specified value if the current value is smaller than 'count'. + * + * 'registers' is expected to have room for HLL_REGISTERS plus an + * additional byte on the right. This requirement is met by sds strings + * automatically since they are implicitly null terminated. + * + * The function always succeed, however if as a result of the operation + * the approximated cardinality changed, 1 is returned. Otherwise 0 + * is returned. */ +int hllDenseSet(uint8_t *registers, long index, uint8_t count) { + uint8_t oldcount; + + HLL_DENSE_GET_REGISTER(oldcount,registers,index); + if (count > oldcount) { + HLL_DENSE_SET_REGISTER(registers,index,count); + return 1; + } else { + return 0; + } +} + +/* "Add" the element in the dense hyperloglog data structure. + * Actually nothing is added, but the max 0 pattern counter of the subset + * the element belongs to is incremented if needed. + * + * This is just a wrapper to hllDenseSet(), performing the hashing of the + * element in order to retrieve the index and zero-run count. */ +int hllDenseAdd(uint8_t *registers, unsigned char *ele, size_t elesize) { + long index; + uint8_t count = hllPatLen(ele,elesize,&index); + /* Update the register if this element produced a longer run of zeroes. */ + return hllDenseSet(registers,index,count); +} + +/* Compute the register histogram in the dense representation. */ +void hllDenseRegHisto(uint8_t *registers, int* reghisto) { + int j; + + /* Redis default is to use 16384 registers 6 bits each. The code works + * with other values by modifying the defines, but for our target value + * we take a faster path with unrolled loops. */ + if (HLL_REGISTERS == 16384 && HLL_BITS == 6) { + uint8_t *r = registers; + unsigned long r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, + r10, r11, r12, r13, r14, r15; + for (j = 0; j < 1024; j++) { + /* Handle 16 registers per iteration. */ + r0 = r[0] & 63; + r1 = (r[0] >> 6 | r[1] << 2) & 63; + r2 = (r[1] >> 4 | r[2] << 4) & 63; + r3 = (r[2] >> 2) & 63; + r4 = r[3] & 63; + r5 = (r[3] >> 6 | r[4] << 2) & 63; + r6 = (r[4] >> 4 | r[5] << 4) & 63; + r7 = (r[5] >> 2) & 63; + r8 = r[6] & 63; + r9 = (r[6] >> 6 | r[7] << 2) & 63; + r10 = (r[7] >> 4 | r[8] << 4) & 63; + r11 = (r[8] >> 2) & 63; + r12 = r[9] & 63; + r13 = (r[9] >> 6 | r[10] << 2) & 63; + r14 = (r[10] >> 4 | r[11] << 4) & 63; + r15 = (r[11] >> 2) & 63; + + reghisto[r0]++; + reghisto[r1]++; + reghisto[r2]++; + reghisto[r3]++; + reghisto[r4]++; + reghisto[r5]++; + reghisto[r6]++; + reghisto[r7]++; + reghisto[r8]++; + reghisto[r9]++; + reghisto[r10]++; + reghisto[r11]++; + reghisto[r12]++; + reghisto[r13]++; + reghisto[r14]++; + reghisto[r15]++; + + r += 12; + } + } else { + for(j = 0; j < HLL_REGISTERS; j++) { + unsigned long reg; + HLL_DENSE_GET_REGISTER(reg,registers,j); + reghisto[reg]++; + } + } +} + +/* ================== Sparse representation implementation ================= */ + +/* Convert the HLL with sparse representation given as input in its dense + * representation. Both representations are represented by SDS strings, and + * the input representation is freed as a side effect. + * + * The function returns C_OK if the sparse representation was valid, + * otherwise C_ERR is returned if the representation was corrupted. */ +int hllSparseToDense(robj *o) { + sds sparse = o->ptr, dense; + struct hllhdr *hdr, *oldhdr = (struct hllhdr*)sparse; + int idx = 0, runlen, regval; + uint8_t *p = (uint8_t*)sparse, *end = p+sdslen(sparse); + + /* If the representation is already the right one return ASAP. */ + hdr = (struct hllhdr*) sparse; + if (hdr->encoding == HLL_DENSE) return C_OK; + + /* Create a string of the right size filled with zero bytes. + * Note that the cached cardinality is set to 0 as a side effect + * that is exactly the cardinality of an empty HLL. */ + dense = sdsnewlen(NULL,HLL_DENSE_SIZE); + hdr = (struct hllhdr*) dense; + *hdr = *oldhdr; /* This will copy the magic and cached cardinality. */ + hdr->encoding = HLL_DENSE; + + /* Now read the sparse representation and set non-zero registers + * accordingly. */ + p += HLL_HDR_SIZE; + while(p < end) { + if (HLL_SPARSE_IS_ZERO(p)) { + runlen = HLL_SPARSE_ZERO_LEN(p); + idx += runlen; + p++; + } else if (HLL_SPARSE_IS_XZERO(p)) { + runlen = HLL_SPARSE_XZERO_LEN(p); + idx += runlen; + p += 2; + } else { + runlen = HLL_SPARSE_VAL_LEN(p); + regval = HLL_SPARSE_VAL_VALUE(p); + if ((runlen + idx) > HLL_REGISTERS) break; /* Overflow. */ + while(runlen--) { + HLL_DENSE_SET_REGISTER(hdr->registers,idx,regval); + idx++; + } + p++; + } + } + + /* If the sparse representation was valid, we expect to find idx + * set to HLL_REGISTERS. */ + if (idx != HLL_REGISTERS) { + sdsfree(dense); + return C_ERR; + } + + /* Free the old representation and set the new one. */ + sdsfree(o->ptr); + o->ptr = dense; + return C_OK; +} + +/* Low level function to set the sparse HLL register at 'index' to the + * specified value if the current value is smaller than 'count'. + * + * The object 'o' is the String object holding the HLL. The function requires + * a reference to the object in order to be able to enlarge the string if + * needed. + * + * On success, the function returns 1 if the cardinality changed, or 0 + * if the register for this element was not updated. + * On error (if the representation is invalid) -1 is returned. + * + * As a side effect the function may promote the HLL representation from + * sparse to dense: this happens when a register requires to be set to a value + * not representable with the sparse representation, or when the resulting + * size would be greater than server.hll_sparse_max_bytes. */ +int hllSparseSet(robj *o, long index, uint8_t count) { + struct hllhdr *hdr; + uint8_t oldcount, *sparse, *end, *p, *prev, *next; + long first, span; + long is_zero = 0, is_xzero = 0, is_val = 0, runlen = 0; + + /* If the count is too big to be representable by the sparse representation + * switch to dense representation. */ + if (count > HLL_SPARSE_VAL_MAX_VALUE) goto promote; + + /* When updating a sparse representation, sometimes we may need to + * enlarge the buffer for up to 3 bytes in the worst case (XZERO split + * into XZERO-VAL-XZERO). Make sure there is enough space right now + * so that the pointers we take during the execution of the function + * will be valid all the time. */ + o->ptr = sdsMakeRoomFor(o->ptr,3); + + /* Step 1: we need to locate the opcode we need to modify to check + * if a value update is actually needed. */ + sparse = p = ((uint8_t*)o->ptr) + HLL_HDR_SIZE; + end = p + sdslen(o->ptr) - HLL_HDR_SIZE; + + first = 0; + prev = NULL; /* Points to previous opcode at the end of the loop. */ + next = NULL; /* Points to the next opcode at the end of the loop. */ + span = 0; + while(p < end) { + long oplen; + + /* Set span to the number of registers covered by this opcode. + * + * This is the most performance critical loop of the sparse + * representation. Sorting the conditionals from the most to the + * least frequent opcode in many-bytes sparse HLLs is faster. */ + oplen = 1; + if (HLL_SPARSE_IS_ZERO(p)) { + span = HLL_SPARSE_ZERO_LEN(p); + } else if (HLL_SPARSE_IS_VAL(p)) { + span = HLL_SPARSE_VAL_LEN(p); + } else { /* XZERO. */ + span = HLL_SPARSE_XZERO_LEN(p); + oplen = 2; + } + /* Break if this opcode covers the register as 'index'. */ + if (index <= first+span-1) break; + prev = p; + p += oplen; + first += span; + } + if (span == 0 || p >= end) return -1; /* Invalid format. */ + + next = HLL_SPARSE_IS_XZERO(p) ? p+2 : p+1; + if (next >= end) next = NULL; + + /* Cache current opcode type to avoid using the macro again and + * again for something that will not change. + * Also cache the run-length of the opcode. */ + if (HLL_SPARSE_IS_ZERO(p)) { + is_zero = 1; + runlen = HLL_SPARSE_ZERO_LEN(p); + } else if (HLL_SPARSE_IS_XZERO(p)) { + is_xzero = 1; + runlen = HLL_SPARSE_XZERO_LEN(p); + } else { + is_val = 1; + runlen = HLL_SPARSE_VAL_LEN(p); + } + + /* Step 2: After the loop: + * + * 'first' stores to the index of the first register covered + * by the current opcode, which is pointed by 'p'. + * + * 'next' ad 'prev' store respectively the next and previous opcode, + * or NULL if the opcode at 'p' is respectively the last or first. + * + * 'span' is set to the number of registers covered by the current + * opcode. + * + * There are different cases in order to update the data structure + * in place without generating it from scratch: + * + * A) If it is a VAL opcode already set to a value >= our 'count' + * no update is needed, regardless of the VAL run-length field. + * In this case PFADD returns 0 since no changes are performed. + * + * B) If it is a VAL opcode with len = 1 (representing only our + * register) and the value is less than 'count', we just update it + * since this is a trivial case. */ + if (is_val) { + oldcount = HLL_SPARSE_VAL_VALUE(p); + /* Case A. */ + if (oldcount >= count) return 0; + + /* Case B. */ + if (runlen == 1) { + HLL_SPARSE_VAL_SET(p,count,1); + goto updated; + } + } + + /* C) Another trivial to handle case is a ZERO opcode with a len of 1. + * We can just replace it with a VAL opcode with our value and len of 1. */ + if (is_zero && runlen == 1) { + HLL_SPARSE_VAL_SET(p,count,1); + goto updated; + } + + /* D) General case. + * + * The other cases are more complex: our register requires to be updated + * and is either currently represented by a VAL opcode with len > 1, + * by a ZERO opcode with len > 1, or by an XZERO opcode. + * + * In those cases the original opcode must be split into multiple + * opcodes. The worst case is an XZERO split in the middle resulting into + * XZERO - VAL - XZERO, so the resulting sequence max length is + * 5 bytes. + * + * We perform the split writing the new sequence into the 'new' buffer + * with 'newlen' as length. Later the new sequence is inserted in place + * of the old one, possibly moving what is on the right a few bytes + * if the new sequence is longer than the older one. */ + uint8_t seq[5], *n = seq; + int last = first+span-1; /* Last register covered by the sequence. */ + int len; + + if (is_zero || is_xzero) { + /* Handle splitting of ZERO / XZERO. */ + if (index != first) { + len = index-first; + if (len > HLL_SPARSE_ZERO_MAX_LEN) { + HLL_SPARSE_XZERO_SET(n,len); + n += 2; + } else { + HLL_SPARSE_ZERO_SET(n,len); + n++; + } + } + HLL_SPARSE_VAL_SET(n,count,1); + n++; + if (index != last) { + len = last-index; + if (len > HLL_SPARSE_ZERO_MAX_LEN) { + HLL_SPARSE_XZERO_SET(n,len); + n += 2; + } else { + HLL_SPARSE_ZERO_SET(n,len); + n++; + } + } + } else { + /* Handle splitting of VAL. */ + int curval = HLL_SPARSE_VAL_VALUE(p); + + if (index != first) { + len = index-first; + HLL_SPARSE_VAL_SET(n,curval,len); + n++; + } + HLL_SPARSE_VAL_SET(n,count,1); + n++; + if (index != last) { + len = last-index; + HLL_SPARSE_VAL_SET(n,curval,len); + n++; + } + } + + /* Step 3: substitute the new sequence with the old one. + * + * Note that we already allocated space on the sds string + * calling sdsMakeRoomFor(). */ + int seqlen = n-seq; + int oldlen = is_xzero ? 2 : 1; + int deltalen = seqlen-oldlen; + + if (deltalen > 0 && + sdslen(o->ptr)+deltalen > server.hll_sparse_max_bytes) goto promote; + if (deltalen && next) memmove(next+deltalen,next,end-next); + sdsIncrLen(o->ptr,deltalen); + memcpy(p,seq,seqlen); + end += deltalen; + +updated: + /* Step 4: Merge adjacent values if possible. + * + * The representation was updated, however the resulting representation + * may not be optimal: adjacent VAL opcodes can sometimes be merged into + * a single one. */ + p = prev ? prev : sparse; + int scanlen = 5; /* Scan up to 5 upcodes starting from prev. */ + while (p < end && scanlen--) { + if (HLL_SPARSE_IS_XZERO(p)) { + p += 2; + continue; + } else if (HLL_SPARSE_IS_ZERO(p)) { + p++; + continue; + } + /* We need two adjacent VAL opcodes to try a merge, having + * the same value, and a len that fits the VAL opcode max len. */ + if (p+1 < end && HLL_SPARSE_IS_VAL(p+1)) { + int v1 = HLL_SPARSE_VAL_VALUE(p); + int v2 = HLL_SPARSE_VAL_VALUE(p+1); + if (v1 == v2) { + int len = HLL_SPARSE_VAL_LEN(p)+HLL_SPARSE_VAL_LEN(p+1); + if (len <= HLL_SPARSE_VAL_MAX_LEN) { + HLL_SPARSE_VAL_SET(p+1,v1,len); + memmove(p,p+1,end-p); + sdsIncrLen(o->ptr,-1); + end--; + /* After a merge we reiterate without incrementing 'p' + * in order to try to merge the just merged value with + * a value on its right. */ + continue; + } + } + } + p++; + } + + /* Invalidate the cached cardinality. */ + hdr = o->ptr; + HLL_INVALIDATE_CACHE(hdr); + return 1; + +promote: /* Promote to dense representation. */ + if (hllSparseToDense(o) == C_ERR) return -1; /* Corrupted HLL. */ + hdr = o->ptr; + + /* We need to call hllDenseAdd() to perform the operation after the + * conversion. However the result must be 1, since if we need to + * convert from sparse to dense a register requires to be updated. + * + * Note that this in turn means that PFADD will make sure the command + * is propagated to slaves / AOF, so if there is a sparse -> dense + * conversion, it will be performed in all the slaves as well. */ + int dense_retval = hllDenseSet(hdr->registers,index,count); + serverAssert(dense_retval == 1); + return dense_retval; +} + +/* "Add" the element in the sparse hyperloglog data structure. + * Actually nothing is added, but the max 0 pattern counter of the subset + * the element belongs to is incremented if needed. + * + * This function is actually a wrapper for hllSparseSet(), it only performs + * the hashing of the element to obtain the index and zeros run length. */ +int hllSparseAdd(robj *o, unsigned char *ele, size_t elesize) { + long index; + uint8_t count = hllPatLen(ele,elesize,&index); + /* Update the register if this element produced a longer run of zeroes. */ + return hllSparseSet(o,index,count); +} + +/* Compute the register histogram in the sparse representation. */ +void hllSparseRegHisto(uint8_t *sparse, int sparselen, int *invalid, int* reghisto) { + int idx = 0, runlen, regval; + uint8_t *end = sparse+sparselen, *p = sparse; + + while(p < end) { + if (HLL_SPARSE_IS_ZERO(p)) { + runlen = HLL_SPARSE_ZERO_LEN(p); + idx += runlen; + reghisto[0] += runlen; + p++; + } else if (HLL_SPARSE_IS_XZERO(p)) { + runlen = HLL_SPARSE_XZERO_LEN(p); + idx += runlen; + reghisto[0] += runlen; + p += 2; + } else { + runlen = HLL_SPARSE_VAL_LEN(p); + regval = HLL_SPARSE_VAL_VALUE(p); + idx += runlen; + reghisto[regval] += runlen; + p++; + } + } + if (idx != HLL_REGISTERS && invalid) *invalid = 1; +} + +/* ========================= HyperLogLog Count ============================== + * This is the core of the algorithm where the approximated count is computed. + * The function uses the lower level hllDenseRegHisto() and hllSparseRegHisto() + * functions as helpers to compute histogram of register values part of the + * computation, which is representation-specific, while all the rest is common. */ + +/* Implements the register histogram calculation for uint8_t data type + * which is only used internally as speedup for PFCOUNT with multiple keys. */ +void hllRawRegHisto(uint8_t *registers, int* reghisto) { + uint64_t *word = (uint64_t*) registers; + uint8_t *bytes; + int j; + + for (j = 0; j < HLL_REGISTERS/8; j++) { + if (*word == 0) { + reghisto[0] += 8; + } else { + bytes = (uint8_t*) word; + reghisto[bytes[0]]++; + reghisto[bytes[1]]++; + reghisto[bytes[2]]++; + reghisto[bytes[3]]++; + reghisto[bytes[4]]++; + reghisto[bytes[5]]++; + reghisto[bytes[6]]++; + reghisto[bytes[7]]++; + } + word++; + } +} + +/* Helper function sigma as defined in + * "New cardinality estimation algorithms for HyperLogLog sketches" + * Otmar Ertl, arXiv:1702.01284 */ +double hllSigma(double x) { + if (x == 1.) return INFINITY; + double zPrime; + double y = 1; + double z = x; + do { + x *= x; + zPrime = z; + z += x * y; + y += y; + } while(zPrime != z); + return z; +} + +/* Helper function tau as defined in + * "New cardinality estimation algorithms for HyperLogLog sketches" + * Otmar Ertl, arXiv:1702.01284 */ +double hllTau(double x) { + if (x == 0. || x == 1.) return 0.; + double zPrime; + double y = 1.0; + double z = 1 - x; + do { + x = sqrt(x); + zPrime = z; + y *= 0.5; + z -= pow(1 - x, 2)*y; + } while(zPrime != z); + return z / 3; +} + +/* Return the approximated cardinality of the set based on the harmonic + * mean of the registers values. 'hdr' points to the start of the SDS + * representing the String object holding the HLL representation. + * + * If the sparse representation of the HLL object is not valid, the integer + * pointed by 'invalid' is set to non-zero, otherwise it is left untouched. + * + * hllCount() supports a special internal-only encoding of HLL_RAW, that + * is, hdr->registers will point to an uint8_t array of HLL_REGISTERS element. + * This is useful in order to speedup PFCOUNT when called against multiple + * keys (no need to work with 6-bit integers encoding). */ +uint64_t hllCount(struct hllhdr *hdr, int *invalid) { + double m = HLL_REGISTERS; + double E; + int j; + /* Note that reghisto size could be just HLL_Q+2, because HLL_Q+1 is + * the maximum frequency of the "000...1" sequence the hash function is + * able to return. However it is slow to check for sanity of the + * input: instead we history array at a safe size: overflows will + * just write data to wrong, but correctly allocated, places. */ + int reghisto[64] = {0}; + + /* Compute register histogram */ + if (hdr->encoding == HLL_DENSE) { + hllDenseRegHisto(hdr->registers,reghisto); + } else if (hdr->encoding == HLL_SPARSE) { + hllSparseRegHisto(hdr->registers, + sdslen((sds)hdr)-HLL_HDR_SIZE,invalid,reghisto); + } else if (hdr->encoding == HLL_RAW) { + hllRawRegHisto(hdr->registers,reghisto); + } else { + serverPanic("Unknown HyperLogLog encoding in hllCount()"); + } + + /* Estimate cardinality from register histogram. See: + * "New cardinality estimation algorithms for HyperLogLog sketches" + * Otmar Ertl, arXiv:1702.01284 */ + double z = m * hllTau((m-reghisto[HLL_Q+1])/(double)m); + for (j = HLL_Q; j >= 1; --j) { + z += reghisto[j]; + z *= 0.5; + } + z += m * hllSigma(reghisto[0]/(double)m); + E = llroundl(HLL_ALPHA_INF*m*m/z); + + return (uint64_t) E; +} + +/* Call hllDenseAdd() or hllSparseAdd() according to the HLL encoding. */ +int hllAdd(robj *o, unsigned char *ele, size_t elesize) { + struct hllhdr *hdr = o->ptr; + switch(hdr->encoding) { + case HLL_DENSE: return hllDenseAdd(hdr->registers,ele,elesize); + case HLL_SPARSE: return hllSparseAdd(o,ele,elesize); + default: return -1; /* Invalid representation. */ + } +} + +/* Merge by computing MAX(registers[i],hll[i]) the HyperLogLog 'hll' + * with an array of uint8_t HLL_REGISTERS registers pointed by 'max'. + * + * The hll object must be already validated via isHLLObjectOrReply() + * or in some other way. + * + * If the HyperLogLog is sparse and is found to be invalid, C_ERR + * is returned, otherwise the function always succeeds. */ +int hllMerge(uint8_t *max, robj *hll) { + struct hllhdr *hdr = hll->ptr; + int i; + + if (hdr->encoding == HLL_DENSE) { + uint8_t val; + + for (i = 0; i < HLL_REGISTERS; i++) { + HLL_DENSE_GET_REGISTER(val,hdr->registers,i); + if (val > max[i]) max[i] = val; + } + } else { + uint8_t *p = hll->ptr, *end = p + sdslen(hll->ptr); + long runlen, regval; + + p += HLL_HDR_SIZE; + i = 0; + while(p < end) { + if (HLL_SPARSE_IS_ZERO(p)) { + runlen = HLL_SPARSE_ZERO_LEN(p); + i += runlen; + p++; + } else if (HLL_SPARSE_IS_XZERO(p)) { + runlen = HLL_SPARSE_XZERO_LEN(p); + i += runlen; + p += 2; + } else { + runlen = HLL_SPARSE_VAL_LEN(p); + regval = HLL_SPARSE_VAL_VALUE(p); + if ((runlen + i) > HLL_REGISTERS) break; /* Overflow. */ + while(runlen--) { + if (regval > max[i]) max[i] = regval; + i++; + } + p++; + } + } + if (i != HLL_REGISTERS) return C_ERR; + } + return C_OK; +} + +/* ========================== HyperLogLog commands ========================== */ + +/* Create an HLL object. We always create the HLL using sparse encoding. + * This will be upgraded to the dense representation as needed. */ +robj *createHLLObject(void) { + robj *o; + struct hllhdr *hdr; + sds s; + uint8_t *p; + int sparselen = HLL_HDR_SIZE + + (((HLL_REGISTERS+(HLL_SPARSE_XZERO_MAX_LEN-1)) / + HLL_SPARSE_XZERO_MAX_LEN)*2); + int aux; + + /* Populate the sparse representation with as many XZERO opcodes as + * needed to represent all the registers. */ + aux = HLL_REGISTERS; + s = sdsnewlen(NULL,sparselen); + p = (uint8_t*)s + HLL_HDR_SIZE; + while(aux) { + int xzero = HLL_SPARSE_XZERO_MAX_LEN; + if (xzero > aux) xzero = aux; + HLL_SPARSE_XZERO_SET(p,xzero); + p += 2; + aux -= xzero; + } + serverAssert((p-(uint8_t*)s) == sparselen); + + /* Create the actual object. */ + o = createObject(OBJ_STRING,s); + hdr = o->ptr; + memcpy(hdr->magic,"HYLL",4); + hdr->encoding = HLL_SPARSE; + return o; +} + +/* Check if the object is a String with a valid HLL representation. + * Return C_OK if this is true, otherwise reply to the client + * with an error and return C_ERR. */ +int isHLLObjectOrReply(client *c, robj *o) { + struct hllhdr *hdr; + + /* Key exists, check type */ + if (checkType(c,o,OBJ_STRING)) + return C_ERR; /* Error already sent. */ + + if (!sdsEncodedObject(o)) goto invalid; + if (stringObjectLen(o) < sizeof(*hdr)) goto invalid; + hdr = o->ptr; + + /* Magic should be "HYLL". */ + if (hdr->magic[0] != 'H' || hdr->magic[1] != 'Y' || + hdr->magic[2] != 'L' || hdr->magic[3] != 'L') goto invalid; + + if (hdr->encoding > HLL_MAX_ENCODING) goto invalid; + + /* Dense representation string length should match exactly. */ + if (hdr->encoding == HLL_DENSE && + stringObjectLen(o) != HLL_DENSE_SIZE) goto invalid; + + /* All tests passed. */ + return C_OK; + +invalid: + addReplyError(c,"-WRONGTYPE Key is not a valid " + "HyperLogLog string value."); + return C_ERR; +} + +/* PFADD var ele ele ele ... ele => :0 or :1 */ +void pfaddCommand(client *c) { + robj *o = lookupKeyWrite(c->db,c->argv[1]); + struct hllhdr *hdr; + int updated = 0, j; + + if (o == NULL) { + /* Create the key with a string value of the exact length to + * hold our HLL data structure. sdsnewlen() when NULL is passed + * is guaranteed to return bytes initialized to zero. */ + o = createHLLObject(); + dbAdd(c->db,c->argv[1],o); + updated++; + } else { + if (isHLLObjectOrReply(c,o) != C_OK) return; + o = dbUnshareStringValue(c->db,c->argv[1],o); + } + /* Perform the low level ADD operation for every element. */ + for (j = 2; j < c->argc; j++) { + int retval = hllAdd(o, (unsigned char*)c->argv[j]->ptr, + sdslen(c->argv[j]->ptr)); + switch(retval) { + case 1: + updated++; + break; + case -1: + addReplyError(c,invalid_hll_err); + return; + } + } + hdr = o->ptr; + if (updated) { + signalModifiedKey(c,c->db,c->argv[1]); + notifyKeyspaceEvent(NOTIFY_STRING,"pfadd",c->argv[1],c->db->id); + server.dirty += updated; + HLL_INVALIDATE_CACHE(hdr); + } + addReply(c, updated ? shared.cone : shared.czero); +} + +/* PFCOUNT var -> approximated cardinality of set. */ +void pfcountCommand(client *c) { + robj *o; + struct hllhdr *hdr; + uint64_t card; + + /* Case 1: multi-key keys, cardinality of the union. + * + * When multiple keys are specified, PFCOUNT actually computes + * the cardinality of the merge of the N HLLs specified. */ + if (c->argc > 2) { + uint8_t max[HLL_HDR_SIZE+HLL_REGISTERS], *registers; + int j; + + /* Compute an HLL with M[i] = MAX(M[i]_j). */ + memset(max,0,sizeof(max)); + hdr = (struct hllhdr*) max; + hdr->encoding = HLL_RAW; /* Special internal-only encoding. */ + registers = max + HLL_HDR_SIZE; + for (j = 1; j < c->argc; j++) { + /* Check type and size. */ + robj *o = lookupKeyRead(c->db,c->argv[j]); + if (o == NULL) continue; /* Assume empty HLL for non existing var.*/ + if (isHLLObjectOrReply(c,o) != C_OK) return; + + /* Merge with this HLL with our 'max' HLL by setting max[i] + * to MAX(max[i],hll[i]). */ + if (hllMerge(registers,o) == C_ERR) { + addReplyError(c,invalid_hll_err); + return; + } + } + + /* Compute cardinality of the resulting set. */ + addReplyLongLong(c,hllCount(hdr,NULL)); + return; + } + + /* Case 2: cardinality of the single HLL. + * + * The user specified a single key. Either return the cached value + * or compute one and update the cache. + * + * Since a HLL is a regular Redis string type value, updating the cache does + * modify the value. We do a lookupKeyRead anyway since this is flagged as a + * read-only command. The difference is that with lookupKeyWrite, a + * logically expired key on a replica is deleted, while with lookupKeyRead + * it isn't, but the lookup returns NULL either way if the key is logically + * expired, which is what matters here. */ + o = lookupKeyRead(c->db,c->argv[1]); + if (o == NULL) { + /* No key? Cardinality is zero since no element was added, otherwise + * we would have a key as HLLADD creates it as a side effect. */ + addReply(c,shared.czero); + } else { + if (isHLLObjectOrReply(c,o) != C_OK) return; + o = dbUnshareStringValue(c->db,c->argv[1],o); + + /* Check if the cached cardinality is valid. */ + hdr = o->ptr; + if (HLL_VALID_CACHE(hdr)) { + /* Just return the cached value. */ + card = (uint64_t)hdr->card[0]; + card |= (uint64_t)hdr->card[1] << 8; + card |= (uint64_t)hdr->card[2] << 16; + card |= (uint64_t)hdr->card[3] << 24; + card |= (uint64_t)hdr->card[4] << 32; + card |= (uint64_t)hdr->card[5] << 40; + card |= (uint64_t)hdr->card[6] << 48; + card |= (uint64_t)hdr->card[7] << 56; + } else { + int invalid = 0; + /* Recompute it and update the cached value. */ + card = hllCount(hdr,&invalid); + if (invalid) { + addReplyError(c,invalid_hll_err); + return; + } + hdr->card[0] = card & 0xff; + hdr->card[1] = (card >> 8) & 0xff; + hdr->card[2] = (card >> 16) & 0xff; + hdr->card[3] = (card >> 24) & 0xff; + hdr->card[4] = (card >> 32) & 0xff; + hdr->card[5] = (card >> 40) & 0xff; + hdr->card[6] = (card >> 48) & 0xff; + hdr->card[7] = (card >> 56) & 0xff; + /* This is considered a read-only command even if the cached value + * may be modified and given that the HLL is a Redis string + * we need to propagate the change. */ + signalModifiedKey(c,c->db,c->argv[1]); + server.dirty++; + } + addReplyLongLong(c,card); + } +} + +/* PFMERGE dest src1 src2 src3 ... srcN => OK */ +void pfmergeCommand(client *c) { + uint8_t max[HLL_REGISTERS]; + struct hllhdr *hdr; + int j; + int use_dense = 0; /* Use dense representation as target? */ + + /* Compute an HLL with M[i] = MAX(M[i]_j). + * We store the maximum into the max array of registers. We'll write + * it to the target variable later. */ + memset(max,0,sizeof(max)); + for (j = 1; j < c->argc; j++) { + /* Check type and size. */ + robj *o = lookupKeyRead(c->db,c->argv[j]); + if (o == NULL) continue; /* Assume empty HLL for non existing var. */ + if (isHLLObjectOrReply(c,o) != C_OK) return; + + /* If at least one involved HLL is dense, use the dense representation + * as target ASAP to save time and avoid the conversion step. */ + hdr = o->ptr; + if (hdr->encoding == HLL_DENSE) use_dense = 1; + + /* Merge with this HLL with our 'max' HLL by setting max[i] + * to MAX(max[i],hll[i]). */ + if (hllMerge(max,o) == C_ERR) { + addReplyError(c,invalid_hll_err); + return; + } + } + + /* Create / unshare the destination key's value if needed. */ + robj *o = lookupKeyWrite(c->db,c->argv[1]); + if (o == NULL) { + /* Create the key with a string value of the exact length to + * hold our HLL data structure. sdsnewlen() when NULL is passed + * is guaranteed to return bytes initialized to zero. */ + o = createHLLObject(); + dbAdd(c->db,c->argv[1],o); + } else { + /* If key exists we are sure it's of the right type/size + * since we checked when merging the different HLLs, so we + * don't check again. */ + o = dbUnshareStringValue(c->db,c->argv[1],o); + } + + /* Convert the destination object to dense representation if at least + * one of the inputs was dense. */ + if (use_dense && hllSparseToDense(o) == C_ERR) { + addReplyError(c,invalid_hll_err); + return; + } + + /* Write the resulting HLL to the destination HLL registers and + * invalidate the cached value. */ + for (j = 0; j < HLL_REGISTERS; j++) { + if (max[j] == 0) continue; + hdr = o->ptr; + switch(hdr->encoding) { + case HLL_DENSE: hllDenseSet(hdr->registers,j,max[j]); break; + case HLL_SPARSE: hllSparseSet(o,j,max[j]); break; + } + } + hdr = o->ptr; /* o->ptr may be different now, as a side effect of + last hllSparseSet() call. */ + HLL_INVALIDATE_CACHE(hdr); + + signalModifiedKey(c,c->db,c->argv[1]); + /* We generate a PFADD event for PFMERGE for semantical simplicity + * since in theory this is a mass-add of elements. */ + notifyKeyspaceEvent(NOTIFY_STRING,"pfadd",c->argv[1],c->db->id); + server.dirty++; + addReply(c,shared.ok); +} + +/* ========================== Testing / Debugging ========================== */ + +/* PFSELFTEST + * This command performs a self-test of the HLL registers implementation. + * Something that is not easy to test from within the outside. */ +#define HLL_TEST_CYCLES 1000 +void pfselftestCommand(client *c) { + unsigned int j, i; + sds bitcounters = sdsnewlen(NULL,HLL_DENSE_SIZE); + struct hllhdr *hdr = (struct hllhdr*) bitcounters, *hdr2; + robj *o = NULL; + uint8_t bytecounters[HLL_REGISTERS]; + + /* Test 1: access registers. + * The test is conceived to test that the different counters of our data + * structure are accessible and that setting their values both result in + * the correct value to be retained and not affect adjacent values. */ + for (j = 0; j < HLL_TEST_CYCLES; j++) { + /* Set the HLL counters and an array of unsigned byes of the + * same size to the same set of random values. */ + for (i = 0; i < HLL_REGISTERS; i++) { + unsigned int r = rand() & HLL_REGISTER_MAX; + + bytecounters[i] = r; + HLL_DENSE_SET_REGISTER(hdr->registers,i,r); + } + /* Check that we are able to retrieve the same values. */ + for (i = 0; i < HLL_REGISTERS; i++) { + unsigned int val; + + HLL_DENSE_GET_REGISTER(val,hdr->registers,i); + if (val != bytecounters[i]) { + addReplyErrorFormat(c, + "TESTFAILED Register %d should be %d but is %d", + i, (int) bytecounters[i], (int) val); + goto cleanup; + } + } + } + + /* Test 2: approximation error. + * The test adds unique elements and check that the estimated value + * is always reasonable bounds. + * + * We check that the error is smaller than a few times than the expected + * standard error, to make it very unlikely for the test to fail because + * of a "bad" run. + * + * The test is performed with both dense and sparse HLLs at the same + * time also verifying that the computed cardinality is the same. */ + memset(hdr->registers,0,HLL_DENSE_SIZE-HLL_HDR_SIZE); + o = createHLLObject(); + double relerr = 1.04/sqrt(HLL_REGISTERS); + int64_t checkpoint = 1; + uint64_t seed = (uint64_t)rand() | (uint64_t)rand() << 32; + uint64_t ele; + for (j = 1; j <= 10000000; j++) { + ele = j ^ seed; + hllDenseAdd(hdr->registers,(unsigned char*)&ele,sizeof(ele)); + hllAdd(o,(unsigned char*)&ele,sizeof(ele)); + + /* Make sure that for small cardinalities we use sparse + * encoding. */ + if (j == checkpoint && j < server.hll_sparse_max_bytes/2) { + hdr2 = o->ptr; + if (hdr2->encoding != HLL_SPARSE) { + addReplyError(c, "TESTFAILED sparse encoding not used"); + goto cleanup; + } + } + + /* Check that dense and sparse representations agree. */ + if (j == checkpoint && hllCount(hdr,NULL) != hllCount(o->ptr,NULL)) { + addReplyError(c, "TESTFAILED dense/sparse disagree"); + goto cleanup; + } + + /* Check error. */ + if (j == checkpoint) { + int64_t abserr = checkpoint - (int64_t)hllCount(hdr,NULL); + uint64_t maxerr = ceil(relerr*6*checkpoint); + + /* Adjust the max error we expect for cardinality 10 + * since from time to time it is statistically likely to get + * much higher error due to collision, resulting into a false + * positive. */ + if (j == 10) maxerr = 1; + + if (abserr < 0) abserr = -abserr; + if (abserr > (int64_t)maxerr) { + addReplyErrorFormat(c, + "TESTFAILED Too big error. card:%llu abserr:%llu", + (unsigned long long) checkpoint, + (unsigned long long) abserr); + goto cleanup; + } + checkpoint *= 10; + } + } + + /* Success! */ + addReply(c,shared.ok); + +cleanup: + sdsfree(bitcounters); + if (o) decrRefCount(o); +} + +/* Different debugging related operations about the HLL implementation. + * + * PFDEBUG GETREG <key> + * PFDEBUG DECODE <key> + * PFDEBUG ENCODING <key> + * PFDEBUG TODENSE <key> + */ +void pfdebugCommand(client *c) { + char *cmd = c->argv[1]->ptr; + struct hllhdr *hdr; + robj *o; + int j; + + o = lookupKeyWrite(c->db,c->argv[2]); + if (o == NULL) { + addReplyError(c,"The specified key does not exist"); + return; + } + if (isHLLObjectOrReply(c,o) != C_OK) return; + o = dbUnshareStringValue(c->db,c->argv[2],o); + hdr = o->ptr; + + /* PFDEBUG GETREG <key> */ + if (!strcasecmp(cmd,"getreg")) { + if (c->argc != 3) goto arityerr; + + if (hdr->encoding == HLL_SPARSE) { + if (hllSparseToDense(o) == C_ERR) { + addReplyError(c,invalid_hll_err); + return; + } + server.dirty++; /* Force propagation on encoding change. */ + } + + hdr = o->ptr; + addReplyArrayLen(c,HLL_REGISTERS); + for (j = 0; j < HLL_REGISTERS; j++) { + uint8_t val; + + HLL_DENSE_GET_REGISTER(val,hdr->registers,j); + addReplyLongLong(c,val); + } + } + /* PFDEBUG DECODE <key> */ + else if (!strcasecmp(cmd,"decode")) { + if (c->argc != 3) goto arityerr; + + uint8_t *p = o->ptr, *end = p+sdslen(o->ptr); + sds decoded = sdsempty(); + + if (hdr->encoding != HLL_SPARSE) { + sdsfree(decoded); + addReplyError(c,"HLL encoding is not sparse"); + return; + } + + p += HLL_HDR_SIZE; + while(p < end) { + int runlen, regval; + + if (HLL_SPARSE_IS_ZERO(p)) { + runlen = HLL_SPARSE_ZERO_LEN(p); + p++; + decoded = sdscatprintf(decoded,"z:%d ",runlen); + } else if (HLL_SPARSE_IS_XZERO(p)) { + runlen = HLL_SPARSE_XZERO_LEN(p); + p += 2; + decoded = sdscatprintf(decoded,"Z:%d ",runlen); + } else { + runlen = HLL_SPARSE_VAL_LEN(p); + regval = HLL_SPARSE_VAL_VALUE(p); + p++; + decoded = sdscatprintf(decoded,"v:%d,%d ",regval,runlen); + } + } + decoded = sdstrim(decoded," "); + addReplyBulkCBuffer(c,decoded,sdslen(decoded)); + sdsfree(decoded); + } + /* PFDEBUG ENCODING <key> */ + else if (!strcasecmp(cmd,"encoding")) { + char *encodingstr[2] = {"dense","sparse"}; + if (c->argc != 3) goto arityerr; + + addReplyStatus(c,encodingstr[hdr->encoding]); + } + /* PFDEBUG TODENSE <key> */ + else if (!strcasecmp(cmd,"todense")) { + int conv = 0; + if (c->argc != 3) goto arityerr; + + if (hdr->encoding == HLL_SPARSE) { + if (hllSparseToDense(o) == C_ERR) { + addReplyError(c,invalid_hll_err); + return; + } + conv = 1; + server.dirty++; /* Force propagation on encoding change. */ + } + addReply(c,conv ? shared.cone : shared.czero); + } else { + addReplyErrorFormat(c,"Unknown PFDEBUG subcommand '%s'", cmd); + } + return; + +arityerr: + addReplyErrorFormat(c, + "Wrong number of arguments for the '%s' subcommand",cmd); +} + |