# 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`.

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.

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.

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).

secure_rand() double#

This is an alias for `secure_random()`.

secure_random() double#

Returns a cryptographically secure random value in the range 0.0 <= x < 1.0.

secure_random(lower, upper) [same as input]#

Returns a cryptographically secure random value in the range lower <= x < upper, where lower < upper.

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.

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.

## 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.

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].

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_gamma_cdf(shape, scale, p) double#

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

inverse_f_cdf(df1, df2, p) double#

Compute the inverse of the F cdf with a given df1 (numerator degrees of freedom) and df2 (denominator degrees of freedom) parameters for the cumulative probability (p): P(N < n). The numerator and denominator df parameters must be positive real numbers. The probability p must lie on the interval [0, 1].

inverse_laplace_cdf(mean, scale, p) double#

Compute the inverse of the Laplace cdf with given mean and scale parameters for the cumulative probability (p): P(N < n). The mean must be a real value and the scale must be a positive real value (both of type DOUBLE). 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 (both of type DOUBLE). 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).

inverse_weibull_cdf(a, b, p) double#

Compute the inverse of the Weibull cdf with given parameters `a`, `b` for the probability `p`. The `a`, `b` parameters must be positive double values. The probability `p` must be a double 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`.

## 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.