# Mathematical Functions and Operators#

## Mathematical Operators#

Operator

Description

+

-

Subtraction

*

Multiplication

/

Division (integer division performs truncation)

%

Modulus (remainder)

## Mathematical Functions#

abs(x) → [same as input]#

Returns the absolute value of x.

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].

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.

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 positive real numbers and value must be a real value. The value must be non-negative.

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.

from_base(string, radix) → bigint#

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

inverse_binomial_cdf(numberOfTrials, successProbability, p) → int#

Compute the inverse of the Binomial cdf with given numberOfTrials and successProbability (of a single trial) the cumulative probability (p): P(N <= n). The successProbability and p must be real values in [0, 1] and the numberOfTrials must be a positive integer.

inverse_cauchy_cdf(median, scale, p) → double#

Compute the inverse of the Cauchy cdf with given parameters median and scale (gamma) for the probability p. The scale parameter must be a positive double. The probability p must be a double on the interval [0, 1].

inverse_chi_squared_cdf(df, p) → double#

Compute the inverse of the Chi-square cdf with given df (degrees of freedom) parameter for the cumulative probability (p): P(N < n). The df parameter must be positive real values. The probability p must lie on the interval [0, 1].

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).

inverse_poisson_cdf(lambda, p) → integer#

Compute the inverse of the Poisson cdf with given lambda (mean) parameter for the cumulative probability (p). It returns the value of n so that: P(N <= n; lambda) = p. The lambda parameter must be a positive real number (of type DOUBLE). 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.

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.

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.

pow(x, p) → double#

This is an alias for power().

power(x, p) → double#

Returns x raised to the power of p.

radians(x) → double#

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.

to_base(x, radix) → varchar#

Returns the base-radix representation of x.

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.

Example: truncate(REAL '12.333', -1) -> result is 10.0 truncate(REAL '12.333', 0) -> result is 12.0 truncate(REAL '12.333', 1) -> result is 12.3

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.