Numeric Functions

Operator	Description	Example	Result
`+`	addition	`2 + 3`	`5`
`-`	subtraction	`2 - 3`	`-1`
`*`	multiplication	`2 * 3`	`6`
`/`	float division	`5 / 2`	`2.5`
`//`	division	`5 // 2`	`2`
`%`	modulo (remainder)	`5 % 4`	`1`
`**`	exponent	`3 ** 4`	`81`
`^`	exponent (alias for `**`)	`3 ^ 4`	`81`
`&`	bitwise AND	`91 & 15`	`11`
`\|`	bitwise OR	`32 \| 3`	`35`
`<<`	bitwise shift left	`1 << 4`	`16`
`>>`	bitwise shift right	`8 >> 2`	`2`
`~`	bitwise negation	`~15`	`-16`
`!`	factorial of `x`	`4!`	`24`

There are two division operators: / and //. They are equivalent when at least one of the operands is a FLOAT or a DOUBLE. When both operands are integers, / performs floating points division (5 / 2 = 2.5) while // performs integer division (5 // 2 = 2).

Supported Types

The modulo, bitwise, and negation and factorial operators work only on integral data types, whereas the others are available for all numeric data types.

Numeric Functions

The table below shows the available mathematical functions.

Name	Description
`@(x)`	Absolute value. Parentheses are optional if `x` is a column name.
`abs(x)`	Absolute value.
`acos(x)`	Computes the arccosine of `x`.
`add(x, y)`	Alias for `x + y`.
`asin(x)`	Computes the arcsine of `x`.
`atan(x)`	Computes the arctangent of `x`.
`atan2(y, x)`	Computes the arctangent `(y, x)`.
`bit_count(x)`	Returns the number of bits that are set.
`cbrt(x)`	Returns the cube root of the number.
`ceil(x)`	Rounds the number up.
`ceiling(x)`	Rounds the number up. Alias of `ceil`.
`cos(x)`	Computes the cosine of `x`.
`cot(x)`	Computes the cotangent of `x`.
`degrees(x)`	Converts radians to degrees.
`divide(x, y)`	Alias for `x // y`.
`even(x)`	Round to next even number by rounding away from zero.
`exp(x)`	Computes `e ** x`.
`factorial(x)`	See `!` operator. Computes the product of the current integer and all integers below it.
`fdiv(x, y)`	Performs integer division (`x // y`) but returns a `DOUBLE` value.
`floor(x)`	Rounds the number down.
`fmod(x, y)`	Calculates the modulo value. Always returns a `DOUBLE` value.
`gamma(x)`	Interpolation of the factorial of `x - 1`. Fractional inputs are allowed.
`gcd(x, y)`	Computes the greatest common divisor of `x` and `y`.
`greatest_common_divisor(x, y)`	Computes the greatest common divisor of `x` and `y`.
`greatest(x1, x2, ...)`	Selects the largest value.
`isfinite(x)`	Returns true if the floating point value is finite, false otherwise.
`isinf(x)`	Returns true if the floating point value is infinite, false otherwise.
`isnan(x)`	Returns true if the floating point value is not a number, false otherwise.
`lcm(x, y)`	Computes the least common multiple of `x` and `y`.
`least_common_multiple(x, y)`	Computes the least common multiple of `x` and `y`.
`least(x1, x2, ...)`	Selects the smallest value.
`lgamma(x)`	Computes the log of the `gamma` function.
`ln(x)`	Computes the natural logarithm of `x`.
`log(x)`	Computes the base-10 logarithm of `x`.
`log10(x)`	Alias of `log`. Computes the base-10 logarithm of `x`.
`log2(x)`	Computes the base-2 log of `x`.
`multiply(x, y)`	Alias for `x * y`.
`nextafter(x, y)`	Return the next floating point value after `x` in the direction of `y`.
`pi()`	Returns the value of pi.
`pow(x, y)`	Computes `x` to the power of `y`.
`power(x, y)`	Alias of `pow`. computes `x` to the power of `y`.
`radians(x)`	Converts degrees to radians.
`random()`	Returns a random number `x` in the range `0.0 <= x < 1.0`.
`round_even(v NUMERIC, s INTEGER)`	Alias of `roundbankers(v, s)`. Round to `s` decimal places using the rounding half to even rule. Values `s < 0` are allowed.
`round(v NUMERIC, s INTEGER)`	Round to `s` decimal places. Values `s < 0` are allowed.
`setseed(x)`	Sets the seed to be used for the random function.
`sign(x)`	Returns the sign of `x` as -1, 0 or 1.
`signbit(x)`	Returns whether the signbit is set or not.
`sin(x)`	Computes the sin of `x`.
`sqrt(x)`	Returns the square root of the number.
`subtract(x, y)`	Alias for `x - y`.
`tan(x)`	Computes the tangent of `x`.
`trunc(x)`	Truncates the number.
`xor(x, y)`	Bitwise XOR.

`@(x)`

Description	Absolute value. Parentheses are optional if `x` is a column name.
Example	`@(-17.4)`
Result	`17.4`
Alias	`abs`

`abs(x)`

Description	Absolute value.
Example	`abs(-17.4)`
Result	`17.4`
Alias	`@`

`acos(x)`

Description	Computes the arccosine of `x`.
Example	`acos(0.5)`
Result	`1.0471975511965976`

`add(x, y)`

Description	Alias for `x + y`.
Example	`add(2, 3)`
Result	`5`

`asin(x)`

Description	Computes the arcsine of `x`.
Example	`asin(0.5)`
Result	`0.5235987755982989`

`atan(x)`

Description	Computes the arctangent of `x`.
Example	`atan(0.5)`
Result	`0.4636476090008061`

`atan2(y, x)`

Description	Computes the arctangent (y, x).
Example	`atan2(0.5, 0.5)`
Result	`0.7853981633974483`

`bit_count(x)`

Description	Returns the number of bits that are set.
Example	`bit_count(31)`
Result	`5`

`cbrt(x)`

Description	Returns the cube root of the number.
Example	`cbrt(8)`
Result	`2`

`ceil(x)`

Description	Rounds the number up.
Example	`ceil(17.4)`
Result	`18`

`ceiling(x)`

Description	Rounds the number up. Alias of `ceil`.
Example	`ceiling(17.4)`
Result	`18`

`cos(x)`

Description	Computes the cosine of `x`.
Example	`cos(90)`
Result	`-0.4480736161291701`

`cot(x)`

Description	Computes the cotangent of `x`.
Example	`cot(0.5)`
Result	`1.830487721712452`

`degrees(x)`

Description	Converts radians to degrees.
Example	`degrees(pi())`
Result	`180`

`divide(x, y)`

Description	Alias for `x // y`.
Example	`divide(5, 2)`
Result	`2`

`even(x)`

Description	Round to next even number by rounding away from zero.
Example	`even(2.9)`
Result	`4`

`exp(x)`

Description	Computes `e ** x`.
Example	`exp(0.693)`
Result	`2`

`factorial(x)`

Description	See `!` operator. Computes the product of the current integer and all integers below it.
Example	`factorial(4)`
Result	`24`

`fdiv(x, y)`

Description	Performs integer division (`x // y`) but returns a `DOUBLE` value.
Example	`fdiv(5, 2)`
Result	`2.0`

`floor(x)`

Description	Rounds the number down.
Example	`floor(17.4)`
Result	`17`

`fmod(x, y)`

Description	Calculates the modulo value. Always returns a `DOUBLE` value.
Example	`fmod(5, 2)`
Result	`1.0`

`gamma(x)`

Description	Interpolation of the factorial of `x - 1`. Fractional inputs are allowed.
Example	`gamma(5.5)`
Result	`52.34277778455352`

`gcd(x, y)`

Description	Computes the greatest common divisor of `x` and `y`.
Example	`gcd(42, 57)`
Result	`3`

`greatest_common_divisor(x, y)`

Description	Computes the greatest common divisor of `x` and `y`.
Example	`greatest_common_divisor(42, 57)`
Result	`3`

`greatest(x1, x2, ...)`

Description	Selects the largest value.
Example	`greatest(3, 2, 4, 4)`
Result	`4`

`isfinite(x)`

Description	Returns true if the floating point value is finite, false otherwise.
Example	`isfinite(5.5)`
Result	`true`

`isinf(x)`

Description	Returns true if the floating point value is infinite, false otherwise.
Example	`isinf('Infinity'::float)`
Result	`true`

`isnan(x)`

Description	Returns true if the floating point value is not a number, false otherwise.
Example	`isnan('NaN'::float)`
Result	`true`

`lcm(x, y)`

Description	Computes the least common multiple of `x` and `y`.
Example	`lcm(42, 57)`
Result	`798`

`least_common_multiple(x, y)`

Description	Computes the least common multiple of `x` and `y`.
Example	`least_common_multiple(42, 57)`
Result	`798`

`least(x1, x2, ...)`

Description	Selects the smallest value.
Example	`least(3, 2, 4, 4)`
Result	`2`

`lgamma(x)`

Description	Computes the log of the `gamma` function.
Example	`lgamma(2)`
Result	`0`

`ln(x)`

Description	Computes the natural logarithm of `x`.
Example	`ln(2)`
Result	`0.693`

`log(x)`

Description	Computes the base-10 log of `x`.
Example	`log(100)`
Result	`2`

`log10(x)`

Description	Alias of `log`. Computes the base-10 log of `x`.
Example	`log10(1000)`
Result	`3`

`log2(x)`

Description	Computes the base-2 log of `x`.
Example	`log2(8)`
Result	`3`

`multiply(x, y)`

Description	Alias for `x * y`.
Example	`multiply(2, 3)`
Result	`6`

`nextafter(x, y)`

Description	Return the next floating point value after `x` in the direction of `y`.
Example	`nextafter(1::float, 2::float)`
Result	`1.0000001`

`pi()`

Description	Returns the value of pi.
Example	`pi()`
Result	`3.141592653589793`

`pow(x, y)`

Description	Computes `x` to the power of `y`.
Example	`pow(2, 3)`
Result	`8`

`power(x, y)`

Description	Alias of `pow`. computes `x` to the power of `y`.
Example	`power(2, 3)`
Result	`8`

`radians(x)`

Description	Converts degrees to radians.
Example	`radians(90)`
Result	`1.5707963267948966`

`random()`

Description	Returns a random number `x` in the range `0.0 <= x < 1.0`.
Example	`random()`
Result	various

`round_even(v NUMERIC, s INTEGER)`

Description	Alias of `roundbankers(v, s)`. Round to `s` decimal places using the rounding half to even rule. Values `s < 0` are allowed.
Example	`round_even(24.5, 0)`
Result	`24.0`

`round(v NUMERIC, s INTEGER)`

Description	Round to `s` decimal places. Values `s < 0` are allowed.
Example	`round(42.4332, 2)`
Result	`42.43`

`setseed(x)`

Description	Sets the seed to be used for the random function.
Example	`setseed(0.42)`

`sign(x)`

Description	Returns the sign of `x` as -1, 0 or 1.
Example	`sign(-349)`
Result	`-1`

`signbit(x)`

Description	Returns whether the signbit is set or not.
Example	`signbit(-1.0)`
Result	`true`

`sin(x)`

Description	Computes the sin of `x`.
Example	`sin(90)`
Result	`0.8939966636005579`

`sqrt(x)`

Description	Returns the square root of the number.
Example	`sqrt(9)`
Result	`3`

`subtract(x, y)`

Description	Alias for `x - y`.
Example	`subtract(2, 3)`
Result	`-1`

`tan(x)`

Description	Computes the tangent of `x`.
Example	`tan(90)`
Result	`-1.995200412208242`

`trunc(x)`

Description	Truncates the number.
Example	`trunc(17.4)`
Result	`17`

`xor(x, y)`

Description	Bitwise XOR.
Example	`xor(17, 5)`
Result	`20`

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