hll_merge()

Merges HLL results. This is the scalar version of the aggregate version hll_merge().

Read about the underlying algorithm (HyperLogLog) and estimation accuracy.

Important

The results of hll(), hll_if(), and hll_merge() can be stored and later retrieved. For example, you may want to create a daily unique users summary, which can then be used to calculate weekly counts. However, the precise binary representation of these results may change over time. There's no guarantee that these functions will produce identical results for identical inputs, and therefore we don't advise relying on them.

Syntax

hll_merge( hll, hll2, [ hll3, ... ])

Learn more about syntax conventions.

Parameters

Name	Type	Required	Description
hll, hll2, ...	string	✔️	The column names containing HLL values to merge. The function expects between 2-64 arguments.

Returns

Returns one HLL value. The value is the result of merging the columns hll, hll2, ... hllN.

Examples

This example shows the value of the merged columns.

Run the query

range x from 1 to 10 step 1 
| extend y = x + 10
| summarize hll_x = hll(x), hll_y = hll(y)
| project merged = hll_merge(hll_x, hll_y)
| project dcount_hll(merged)

Output

dcount_hll_merged
20

Estimation accuracy

This function uses a variant of the HyperLogLog (HLL) algorithm, which does a stochastic estimation of set cardinality. The algorithm provides a "knob" that can be used to balance accuracy and execution time per memory size:

Accuracy	Error (%)	Entry count
0	1.6	212
1	0.8	214
2	0.4	216
3	0.28	217
4	0.2	218

Note

The "entry count" column is the number of 1-byte counters in the HLL implementation.

The algorithm includes some provisions for doing a perfect count (zero error), if the set cardinality is small enough:

• When the accuracy level is 1, 1000 values are returned
• When the accuracy level is 2, 8000 values are returned

The error bound is probabilistic, not a theoretical bound. The value is the standard deviation of error distribution (the sigma), and 99.7% of the estimations will have a relative error of under 3 x sigma.

The following image shows the probability distribution function of the relative estimation error, in percentages, for all supported accuracy settings: