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Rounding Functions

floor(x[, N])​

Returns the largest round number that is less than or equal to x. A round number is a multiple of 1/10N, or the nearest number of the appropriate data type if 1 / 10N isn’t exact. ‘N’ is an integer constant, optional parameter. By default it is zero, which means to round to an integer. ‘N’ may be negative.

Examples: floor(123.45, 1) = 123.4, floor(123.45, -1) = 120.

x is any numeric type. The result is a number of the same type. For integer arguments, it makes sense to round with a negative N value (for non-negative N, the function does not do anything). If rounding causes overflow (for example, floor(-128, -1)), an implementation-specific result is returned.

ceil(x[, N]), ceiling(x[, N])​

Returns the smallest round number that is greater than or equal to x. In every other way, it is the same as the floor function (see above).

trunc(x[, N]), truncate(x[, N])​

Returns the round number with largest absolute value that has an absolute value less than or equal to x‘s. In every other way, it is the same as the ’floor’ function (see above).

Syntax

trunc(input, precision)

Alias: truncate.

Parameters

Returned value

  • A data type of input.

Example

Query:

SELECT trunc(123.499, 1) as res;
┌───res─┐
│ 123.4 │
└───────┘

round(x[, N])​

Rounds a value to a specified number of decimal places.

The function returns the nearest number of the specified order. In case when given number has equal distance to surrounding numbers, the function uses banker’s rounding for float number types and rounds away from zero for the other number types (Decimal).

round(expression [, decimal_places])

Arguments

  • expression — A number to be rounded. Can be any expression returning the numeric data type.
  • decimal-places — An integer value.
    • If decimal-places > 0 then the function rounds the value to the right of the decimal point.
    • If decimal-places < 0 then the function rounds the value to the left of the decimal point.
    • If decimal-places = 0 then the function rounds the value to integer. In this case the argument can be omitted.

Returned value:

The rounded number of the same type as the input number.

Examples

Example of usage with Float:

SELECT number / 2 AS x, round(x) FROM system.numbers LIMIT 3;
┌───x─┬─round(divide(number, 2))─┐
│   0 │                        0 │
│ 0.5 │                        0 │
│   1 │                        1 │
└─────┴──────────────────────────┘

Example of usage with Decimal:

SELECT cast(number / 2 AS  Decimal(10,4)) AS x, round(x) FROM system.numbers LIMIT 3;
┌───x─┬─round(CAST(divide(number, 2), 'Decimal(10, 4)'))─┐
│   0 │                                                0 │
│ 0.5 │                                                1 │
│   1 │                                                1 │
└─────┴──────────────────────────────────────────────────┘

If you want to keep the trailing zeros, you need to enable output_format_decimal_trailing_zeros

SELECT cast(number / 2 AS  Decimal(10,4)) AS x, round(x) FROM system.numbers LIMIT 3 settings output_format_decimal_trailing_zeros=1;

┌──────x─┬─round(CAST(divide(number, 2), 'Decimal(10, 4)'))─┐
│ 0.0000 │                                           0.0000 │
│ 0.5000 │                                           1.0000 │
│ 1.0000 │                                           1.0000 │
└────────┴──────────────────────────────────────────────────┘

Examples of rounding to the nearest number:

round(3.2, 0) = 3
round(4.1267, 2) = 4.13
round(22,-1) = 20
round(467,-2) = 500
round(-467,-2) = -500

Banker’s rounding.

round(3.5) = 4
round(4.5) = 4
round(3.55, 1) = 3.6
round(3.65, 1) = 3.6

See Also

roundBankers​

Rounds a number to a specified decimal position.

  • If the rounding number is halfway between two numbers, the function uses banker’s rounding. Banker's rounding is a method of rounding fractional numbers. When the rounding number is halfway between two numbers, it's rounded to the nearest even digit at the specified decimal position. For example: 3.5 rounds up to 4, 2.5 rounds down to 2. It's the default rounding method for floating point numbers defined in IEEE 754. The round function performs the same rounding for floating point numbers. The roundBankers function also rounds integers the same way, for example, roundBankers(45, -1) = 40.

  • In other cases, the function rounds numbers to the nearest integer.

Using banker’s rounding, you can reduce the effect that rounding numbers has on the results of summing or subtracting these numbers.

For example, sum numbers 1.5, 2.5, 3.5, 4.5 with different rounding:

  • No rounding: 1.5 + 2.5 + 3.5 + 4.5 = 12.
  • Banker’s rounding: 2 + 2 + 4 + 4 = 12.
  • Rounding to the nearest integer: 2 + 3 + 4 + 5 = 14.

Syntax

roundBankers(expression [, decimal_places])

Arguments

  • expression — A number to be rounded. Can be any expression returning the numeric data type.
  • decimal-places — Decimal places. An integer number.
    • decimal-places > 0 — The function rounds the number to the given position right of the decimal point. Example: roundBankers(3.55, 1) = 3.6.
    • decimal-places < 0 — The function rounds the number to the given position left of the decimal point. Example: roundBankers(24.55, -1) = 20.
    • decimal-places = 0 — The function rounds the number to an integer. In this case the argument can be omitted. Example: roundBankers(2.5) = 2.

Returned value

A value rounded by the banker’s rounding method.

Examples

Query:

 SELECT number / 2 AS x, roundBankers(x, 0) AS b fROM system.numbers limit 10

Result:

┌───x─┬─b─┐
│   0 │ 0 │
│ 0.5 │ 0 │
│   1 │ 1 │
│ 1.5 │ 2 │
│   2 │ 2 │
│ 2.5 │ 2 │
│   3 │ 3 │
│ 3.5 │ 4 │
│   4 │ 4 │
│ 4.5 │ 4 │
└─────┴───┘

Examples of Banker’s rounding:

roundBankers(0.4) = 0
roundBankers(-3.5) = -4
roundBankers(4.5) = 4
roundBankers(3.55, 1) = 3.6
roundBankers(3.65, 1) = 3.6
roundBankers(10.35, 1) = 10.4
roundBankers(10.755, 2) = 10.76

See Also

roundToExp2​

Accepts a number. If the number is less than one, it returns 0. Otherwise, it rounds the number down to the nearest (whole non-negative) degree of two.

Syntax

roundToExp2(num)

Parameters

  • num: A number representing an age in years. UInt/Float.

Returned value

  • 0, for num <1\lt 1. UInt8.
  • num rounded down to the nearest (whole non-negative) degree of two. UInt/Float equivalent to the input type.

Example

Query:

SELECT *, roundToExp2(*) FROM system.numbers WHERE number IN (0, 2, 5, 10, 19, 50)

Result:

┌─number─┬─roundToExp2(number)─┐
│      0 │                   0 │
│      2 │                   2 │
│      5 │                   4 │
│     10 │                   8 │
│     19 │                  16 │
│     50 │                  32 │
└────────┴─────────────────────┘

roundDuration​

Accepts a number. If the number is less than one, it returns 0. Otherwise, it rounds the number down to numbers from the set of commonly used durations: 1, 10, 30, 60, 120, 180, 240, 300, 600, 1200, 1800, 3600, 7200, 18000, 36000.

Syntax

roundDuration(num)

Parameters

  • num: A number to round to one of the numbers in the set of common durations. UInt/Float.

Returned value

  • 0, for num <1\lt 1.
  • Otherwise, one of: 1, 10, 30, 60, 120, 180, 240, 300, 600, 1200, 1800, 3600, 7200, 18000, 36000. UInt16.

Example

Query:

SELECT *, roundDuration(*) FROM system.numbers WHERE number IN (0, 9, 19, 47, 101, 149, 205, 271, 421, 789, 1423, 2345, 4567, 9876, 24680, 42573)

Result:

┌─number─┬─roundDuration(number)─┐
│      0 │                     0 │
│      9 │                     1 │
│     19 │                    10 │
│     47 │                    30 │
│    101 │                    60 │
│    149 │                   120 │
│    205 │                   180 │
│    271 │                   240 │
│    421 │                   300 │
│    789 │                   600 │
│   1423 │                  1200 │
│   2345 │                  1800 │
│   4567 │                  3600 │
│   9876 │                  7200 │
│  24680 │                 18000 │
│  42573 │                 36000 │
└────────┴───────────────────────┘

roundAge​

Accepts a number within various commonly used ranges of human age and returns either a maximum or a minimum within that range.

Syntax

roundAge(num)

Parameters

  • age: A number representing an age in years. UInt/Float.

Returned value

  • Returns 0, for age<1age \lt 1.
  • Returns 17, for 1≤age≤171 \leq age \leq 17.
  • Returns 18, for 18≤age≤2418 \leq age \leq 24.
  • Returns 25, for 25≤age≤3425 \leq age \leq 34.
  • Returns 35, for 35≤age≤4435 \leq age \leq 44.
  • Returns 45, for 45≤age≤5445 \leq age \leq 54.
  • Returns 55, for age≥55age \geq 55.

Type: UInt8.

Example

Query:

SELECT *, roundAge(*) FROM system.numbers WHERE number IN (0, 5, 20, 31, 37, 54, 72);

Result:

┌─number─┬─roundAge(number)─┐
│      0 │                0 │
│      5 │               17 │
│     20 │               18 │
│     31 │               25 │
│     37 │               35 │
│     54 │               45 │
│     72 │               55 │
└────────┴──────────────────┘

roundDown​

Accepts a number and rounds it down to an element in the specified array. If the value is less than the lowest bound, the lowest bound is returned.

Syntax

roundDown(num, arr)

Parameters

  • num: A number to round down. Numeric.
  • arr: Array of elements to round age down to. Array of UInt/Float type.

Returned value

  • Number rounded down to an element in arr. If the value is less than the lowest bound, the lowest bound is returned. UInt/Float type deduced from the type of arr.

Example

Query:

SELECT *, roundDown(*, [3, 4, 5]) FROM system.numbers WHERE number IN (0, 1, 2, 3, 4, 5)

Result:

┌─number─┬─roundDown(number, [3, 4, 5])─┐
│      0 │                            3 │
│      1 │                            3 │
│      2 │                            3 │
│      3 │                            3 │
│      4 │                            4 │
│      5 │                            5 │
└────────┴──────────────────────────────┘