Mathematical functions and operators#
Mathematical operators#
Operator |
Description |
---|---|
|
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
.
- ceiling(x) [same as input] #
Returns
x
rounded up to the nearest integer.
- 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.
- ln(x) double #
Returns the natural logarithm of
x
.
- log(b, x) double #
Returns the base
b
logarithm ofx
.
- 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 bym
.
- pi() double #
Returns the constant Pi.
- power(x, p) double #
Returns
x
raised to the power ofp
.
- radians(x) double #
Converts angle
x
in degrees to radians.
- round(x) [same as input] #
Returns
x
rounded to the nearest integer.
- round(x, d) [same as input]
Returns
x
rounded tod
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
.
- 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 specifiedbound1
andbound2
bounds andn
number of buckets.
- width_bucket(x, bins) bigint
Returns the 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.
Random functions#
- 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).
- random(m, n) [same as input]
Returns a pseudo-random number between m and n (exclusive).
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
.
- sinh(x) double #
Returns the hyperbolic 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.
Base conversion functions#
- from_base(string, radix) bigint #
Returns the value of
string
interpreted as a base-radix
number.
- to_base(x, radix) varchar #
Returns the base-
radix
representation ofx
.
Statistical functions#
- cosine_similarity(x, y) double #
Returns the cosine similarity between the sparse vectors
x
andy
:SELECT cosine_similarity(MAP(ARRAY['a'], ARRAY[1.0]), MAP(ARRAY['a'], ARRAY[2.0])); -- 1.0
- 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
.
Cumulative distribution functions#
- 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].
- 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].
- 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.