# 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.