# 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`.

cosine_similarity(map(varchar, double), map(varchar, double)) double

Returns the cosine similarity between the vectors represented as map(varchar, double). If any input map is empty, the function returns NaN.

SELECT cosine_similarity(MAP(ARRAY[‘a’], ARRAY[1.0]), MAP(ARRAY[‘a’], ARRAY[2.0])); – 1.0

SELECT cosine_similarity(MAP(ARRAY[‘a’, ‘b’], ARRAY[1.0, 2.0]), MAP(ARRAY[‘a’, ‘b’], ARRAY[NULL, 3.0])); – NULL

SELECT cosine_similarity(MAP(ARRAY[], ARRAY[]), MAP(ARRAY[‘a’, ‘b’], ARRAY[2, 3])); – NaN

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.

random(n) [same as n]

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

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) [same as x]

Returns x rounded to integer by dropping digits after decimal point. Supported types of `x` are: REAL and DOUBLE.

truncate(x, n) [same as x]

Returns x truncated to n decimal places. n can be negative to truncate n digits left of the decimal point. Supported types of `x` are: REAL and DOUBLE. `n` is an INTEGER.

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.

# Probability Functions: cdf¶

beta_cdf(a, b, value) double

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

binomial_cdf(numberOfTrials, successProbability, value) double

Compute the Binomial cdf with given numberOfTrials and successProbability (for a single trial): P(N < value). The successProbability must be real value in [0, 1], numberOfTrials and value must be positive integers with numberOfTrials greater or equal to value

cauchy_cdf(median, scale, value) double

Compute the Cauchy cdf with given parameters median and scale (gamma): P(N; median, scale). The scale parameter must be a positive double. The value parameter must be a double on the interval [0, 1].

chi_squared_cdf(df, value) double

Compute the Chi-square cdf with given df (degrees of freedom) parameter: P(N < value; df). The df parameter must be a positive real number, and value must be a non-negative real value (both of type DOUBLE).

f_cdf(df1, df2, value) double

Compute the F cdf with given df1 (numerator degrees of freedom) and df2 (denominator degrees of freedom) parameters: P(N < value; df1, df2). The numerator and denominator df parameters must be positive real numbers. The value must be a non-negative real number.

gamma_cdf(shape, scale, value) double

Compute the Gamma cdf with given shape and scale parameters: P(N < value; shape, scale). The shape and scale parameters must be positive real numbers. The value must be a non-negative real 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 (both of type DOUBLE). The probability p must lie on the interval (0, 1).

laplace_cdf(mean, scale, value) double

Compute the Laplace cdf with given mean and scale parameters: P(N < value; mean, scale). The mean and value must be real values and the scale parameter must be a positive value (all of type DOUBLE).

normal_cdf(mean, sd, value) double

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

poisson_cdf(lambda, value) double

Compute the Poisson cdf with given lambda (mean) parameter: P(N <= value; lambda). The lambda parameter must be a positive real number (of type DOUBLE) and value must be a non-negative integer.

weibull_cdf(a, b, value) double

Compute the Weibull cdf with given parameters a, b: P(N <= value). The `a` and `b` parameters must be positive doubles and `value` must also be a double.

# Probability Functions: inverse_cdf¶

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 (all of type DOUBLE). The probability p must lie on the interval [0, 1].

# 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.