quantileBFloat16

Computes an approximate quantile of a sample consisting of bfloat16 numbers. bfloat16 is a floating-point data type with 1 sign bit, 8 exponent bits and 7 fraction bits. The function converts input values to 32-bit floats and takes the most significant 16 bits. Then it calculates bfloat16 quantile value and converts the result to a 64-bit float by appending zero bits. The function is a fast quantile estimator with a relative error no more than 0.390625%.

Syntax

quantileBFloat16[(level)](expr)

Alias: medianBFloat16

Arguments

• expr — Column with numeric data. Integer, Float.

Parameters

• level — Level of quantile. Optional. Possible values are in the range from 0 to 1. Default value: 0.5. Float.

Returned value

• Approximate quantile of the specified level.

Type: Float64.

Example

Input table has an integer and a float columns:

┌─a─┬─────b─┐
│ 1 │ 1.001 │
│ 2 │ 1.002 │
│ 3 │ 1.003 │
│ 4 │ 1.004 │
└───┴───────┘

Query to calculate 0.75-quantile (third quartile):

SELECT quantileBFloat16(0.75)(a), quantileBFloat16(0.75)(b) FROM example_table;

Result:

┌─quantileBFloat16(0.75)(a)─┬─quantileBFloat16(0.75)(b)─┐
│                         3 │                         1 │
└───────────────────────────┴───────────────────────────┘

Note that all floating point values in the example are truncated to 1.0 when converting to bfloat16.

quantileBFloat16Weighted

Like quantileBFloat16 but takes into account the weight of each sequence member.

See Also

• median
• quantiles