Mathematical Functions¶
- abs(x) [same as x] ¶
Returns the absolute value of
x
.
- cbrt(x) double ¶
Returns the cube root of
x
.
- ceiling(x) [same as x] ¶
Returns
x
rounded up to the nearest integer.
- clamp(x, low, high) [same as x] ¶
Returns
low
ifx
is less thanlow
. Returnshigh
ifx
is greater thanhigh
. Returnsx
otherwise.low
is expected to be less than or equal tohigh
. This expection is not verified for performance reasons. Returnshigh
for all values ofx
whenlow
is greater thanhigh
.
- 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.
- from_base(string, radix) bigint ¶
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 bym
.
- 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.
- power(x, p) double ¶
Returns
x
raised to the power ofp
.
- radians(x) double ¶
Converts angle x in degrees to radians.
- 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 tod
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
. Ifx
is negative,NaN
is returned.
- to_base(x, radix) varchar ¶
Returns the base-
radix
representation ofx
.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 specifiedbound1
andbound2
bounds andn
number of buckets.
- width_bucket(x, bins) bigint
Returns the zero-based bin number of
x
according to the bins specified by the arraybins
. Thebins
parameter must be an array of doubles and is assumed to be in sorted ascending order.For example, if
bins
isARRAY[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.
- 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.
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.