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HyperLogLog: use LINEARCOUNTING up to 3m.
The HyperLogLog original paper suggests using LINEARCOUNTING for cardinalities < 2.5m, however for P=14 the median / max error curves show that a value of '3' is the best pick for m = 16384.
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@ -339,7 +339,7 @@ int hllAdd(uint8_t *registers, unsigned char *ele, size_t elesize) {
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uint64_t hllCount(uint8_t *registers) {
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double m = REDIS_HLL_REGISTERS;
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double alpha = 0.7213/(1+1.079/m);
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double E = 0;
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double E = 0, linearcounting_factor;
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int ez = 0; /* Number of registers equal to 0. */
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int j;
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@ -407,8 +407,16 @@ uint64_t hllCount(uint8_t *registers) {
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/* Muliply the inverse of E for alpha_m * m^2 to have the raw estimate. */
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E = (1/E)*alpha*m*m;
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/* Apply corrections for small cardinalities. */
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if (E < m*2.5 && ez != 0) {
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/* Use the LINEARCOUNTING algorithm for small cardinalities. Note that
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* the HyperLogLog paper suggests using this correction for E < m*2.5
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* while we are using it for E < m*3 since this was verified to have
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* better median / max error rate in the 40000 - 50000 cardinality
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* interval when P * is 14 (m = 16k).
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*
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* However for other values of P we resort to the paper's value of 2.5
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* since no test was performed for other values. */
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linearcounting_factor = (m == 16384) ? 3 : 2.5;
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if (E < m*linearcounting_factor && ez != 0) {
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E = m*log(m/ez); /* LINEARCOUNTING() */
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}
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/* We don't apply the correction for E > 1/30 of 2^32 since we use
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