quantileBFloat16

Introduced in: v21.7.0

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 maximum relative error of 0.78125% (and an average relative error of approximately 0.27%), corresponding to the 7-bit mantissa precision of bfloat16.

Syntax

quantileBFloat16[(level)](expr)

Aliases: medianBFloat16

Parameters

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

Arguments

expr — Expression over the column values resulting in numeric data types, Date or DateTime. (U)Int* or Float* or Date or DateTime

Returned value

Approximate quantile of the specified level. For Date and DateTime inputs the output format matches the input format. Float64 or Date or DateTime

Examples

Computing quantile with bfloat16

CREATE TABLE example_table (a UInt32, b Float32) ENGINE = Memory;
INSERT INTO example_table VALUES (1, 1.001), (2, 1.002), (3, 1.003), (4, 1.004);

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

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

See Also

quantileBFloat16​

quantileBFloat16