# Mathematical Functions and Operators

## Mathematical Operators

OperatorDescription
`+`Addition
`-`Subtraction
`*`Multiplication
`/`Division (integer division performs truncation)
`%`Modulus (remainder)

## Mathematical Functions

abs(x) -> [same as input]

Returns the absolute value of `x`.

cbrt(x) -> double

Returns the cube root of `x`.

ceil(x) -> [same as input]

This is an alias for `ceiling`.

ceiling(x) -> [same as input]

Returns `x` rounded up to the nearest integer.

cosine_similarity(x, y) -> double

Returns the cosine similarity between the sparse vectors `x` and `y`:

``````SELECT cosine_similarity(MAP(ARRAY['a'], ARRAY[1.0]), MAP(ARRAY['a'], ARRAY[2.0])); -- 1.0
``````

degrees(x) -> double

Converts angle `x` in radians to degrees.

e() -> double

Returns the constant Euler's number.

exp(x) -> double

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

floor(x) -> [same as input]

Returns `x` rounded down to the nearest integer.

Returns the value of `string` interpreted as a base-`radix` number.

inverse_normal_cdf(mean, sd, p) -> double

Compute the inverse of the Normal cdf with given mean and standard deviation (sd) for the cumulative probability (p): P(N < n). The mean must be a real value and the standard deviation must be a real and positive value. The probability p must lie on the interval (0, 1).

normal_cdf(mean, sd, v) -> double

Compute the Normal cdf with given mean and standard deviation (sd): P(N < v; mean, sd). The mean and value v must be real values and the standard deviation must be a real and positive value.

inverse_beta_cdf(a, b, p) -> double

Compute the inverse of the Beta cdf with given a, b parameters for the cumulative probability (p): P(N < n). The a, b parameters must be positive real values. The probability p must lie on the interval [0, 1].

beta_cdf(a, b, v) -> double

Compute the Beta cdf with given a, b parameters: P(N < v; a, b). The a, b parameters must be positive real numbers and value v must be a real value. The value v must lie on the interval [0, 1].

ln(x) -> double

Returns the natural logarithm of `x`.

log(b, x) -> double

Returns the base `b` logarithm of `x`.

log2(x) -> double

Returns the base 2 logarithm of `x`.

log10(x) -> double

Returns the base 10 logarithm of `x`.

mod(n, m) -> [same as input]

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

pi() -> double

Returns the constant Pi.

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.

random(n) -> [same as input]

Returns a pseudo-random number between 0 and n (exclusive).

round(x) -> [same as input]

Returns `x` rounded to the nearest integer.

round(x, d) -> [same as input]

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

sign(x) -> [same as input]

Returns the signum function of `x`, that is:

• 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 returns:

• 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`.

Returns the base-`radix` representation of `x`.

truncate(x) -> double

Returns `x` rounded to integer by dropping digits after 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 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.

## Statistical Functions

wilson_interval_lower(successes, trials, z) -> double

Returns the lower bound of the Wilson score interval of a Bernoulli trial process at a confidence specified by the z-score `z`.

wilson_interval_upper(successes, trials, z) -> double

Returns the upper bound of the Wilson score interval of a Bernoulli trial process at a confidence specified by the z-score `z`.

## Trigonometric Functions

All trigonometric function arguments are expressed in radians. See unit conversion functions `degrees` and `radians`.

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.