# Mathematical Functions¶

abs(x) [same as x]

Returns the absolute value of `x`.

cbrt(x) double

Returns the cube root of `x`.

ceil(x) [same as x]

This is an alias for `ceiling()`.

ceiling(x) [same as x]

Returns `x` rounded up to the nearest integer.

clamp(x, low, high) [same as x]

Returns `low` if `x` is less than `low`. Returns `high` if `x` is greater than `high`. Returns `x` otherwise.

`low` is expected to be less than or equal to `high`. This expection is not verified for performance reasons. Returns `high` for all values of `x` when `low` is greater than `high`.

degrees(x) double

Converts angle x in radians to degrees.

divide(x, y) [same as x]

Returns the results of dividing x by y. The types of x and y must be the same. The result of dividing by zero depends on the input types. For integral types, division by zero results in an error. For floating point types, division by zero returns positive infinity if x is greater than zero, negative infinity if x if less than zero and NaN if x is equal to zero.

e() double

Returns the value of Euler’s Constant.

exp(x) double

Returns Euler’s number raised to the power of `x`.

floor(x) [same as x]

Returns `x` rounded down to the nearest integer.

Returns the value of `string` interpreted as a base-`radix` number. `radix` must be between 2 and 36.

ln(x) double

Returns the natural logarithm of `x`.

log2(x) double

Returns the base 2 logarithm of `x`.

log10(x) double

Returns the base 10 logarithm of `x`.

minus(x, y) [same as x]

Returns the result of subtracting y from x. The types of x and y must be the same. For integral types, overflow results in an error.

mod(n, m) [same as n]

Returns the modulus (remainder) of `n` divided by `m`.

multiply(x, y) [same as x]

Returns the result of multiplying x by y. The types of x and y must be the same. For integral types, overflow results in an error.

negate(x) [same as x]

Returns the additive inverse of x, e.g. the number that, when added to x, yields zero.

pi() double

Returns the value of Pi.

plus(x, y) [same as x]

Returns the result of adding x to y. The types of x and y must be the same. For integral types, overflow results in an error.

pow(x, p) double

This is an alias for `power()`.

power(x, p) double

Returns `x` raised to the power of `p`.

Converts angle x in degrees to radians.

rand() double

This is an alias for `random()`.

random() double

Returns a pseudo-random value in the range 0.0 <= x < 1.0.

round(x) [same as x]

Returns `x` rounded to the nearest integer.

round(x, d) [same as x]

Returns `x` rounded to `d` decimal places.

sign(x) [same as x]

Returns the signum function of `x`. For both integer and floating point arguments, it returns: * 0 if the argument is 0, * 1 if the argument is greater than 0, * -1 if the argument is less than 0.

For double arguments, the function additionally return: * NaN if the argument is NaN, * 1 if the argument is +Infinity, * -1 if the argument is -Infinity.

sqrt(x) double

Returns the square root of `x` . If `x` is negative, `NaN` is returned.

Returns the base-`radix` representation of `x`. `radix` must be between 2 and 36.

truncate(x) double

Returns x rounded to integer by dropping digits after decimal point.

truncate(x, n) double

Returns x truncated to n decimal places. n can be negative to truncate n digits left of the decimal point.

width_bucket(x, bound1, bound2, n) bigint

Returns the bin number of `x` in an equi-width histogram with the specified `bound1` and `bound2` bounds and `n` number of buckets.

width_bucket(x, bins) bigint

Returns the zero-based bin number of `x` according to the bins specified by the array `bins`. The `bins` parameter must be an array of doubles and is assumed to be in sorted ascending order.

For example, if `bins` is `ARRAY[0, 2, 4]`, then we have four bins: `(-infinity(), 0)`, `[0, 2)`, `[2, 4)` and `[4, infinity())`.

# Trigonometric Functions¶

acos(x) double

Returns the arc cosine of `x`.

asin(x) double

Returns the arc sine of `x`.

atan(x) double

Returns the arc tangent of `x`.

atan2(y, x) double

Returns the arc tangent of `y / x`.

cos(x) double

Returns the cosine of `x`.

cosh(x) double

Returns the hyperbolic cosine of `x`.

sin(x) double

Returns the sine of `x`.

tan(x) double

Returns the tangent of `x`.

tanh(x) double

Returns the hyperbolic tangent of `x`.

# Floating Point Functions¶

infinity() double

Returns the constant representing positive infinity.

is_finite(x) boolean

Determine if x is finite.

is_infinite(x) boolean

Determine if x is infinite.

is_nan(x) boolean

Determine if x is not-a-number.

nan() double

Returns the constant representing not-a-number.