Redis随记--HyperLogLog的代码学习01

基础结构和常量

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
#define HLL_ALPHA_INF 0.721347520444481703680 /* constant for 0.5/ln(2) */

相关函数

hllCount 函数

/* 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, becuase 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 form 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;
}

hllRawRegHisto函数

/* 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++;
    }
}

hllTau函数

/* 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;
}

hllSigma函数

/* 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;
}