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Mathematical operators

OperatorDescription
+Addition
-Subtraction
*Multiplication
/Division (integer division performs truncation)
%Modulus (remainder)

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Mathematical functions

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abs()

abs(x) → same as input
Returns the absolute value of x.

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cbrt()

cbrt(x) → double
Returns the cube root of x.

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ceil()

ceil(x) → same as input
This is an alias for ceiling.

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ceiling()

ceiling(x) → same as input
Returns x rounded up to the nearest integer.

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degrees()

degrees(x) → double
Converts angle x in radians to degrees.

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e()

e() → double
Returns the constant Euler’s number.

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exp()

exp(x) → double
Returns Euler’s number raised to the power of x.

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floor()

floor(x) → same as input
Returns x rounded down to the nearest integer.

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ln()

ln(x) → double
Returns the natural logarithm of x.

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log()

log(b, x) → double
Returns the base b logarithm of x.

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log2()

log2(x) → double
Returns the base 2 logarithm of x.

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log10()

log10(x) → double
Returns the base 10 logarithm of x.

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mod()

mod(n, m) → same as input
Returns the modulus (remainder) of n divided by m.

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pi()

pi() → double
Returns the constant Pi.

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pow()

pow(x, p) → double
This is an alias for power.

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power()

power(x, p) → double
Returns x raised to the power of p.

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radians()

radians(x) → double
Converts angle x in degrees to radians.

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round()

round(x) → same as input
Returns x rounded to the nearest integer.

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round()

round(x, d) → same as input
Returns x rounded to d decimal places.

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sign()

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.

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sqrt()

sqrt(x) → double
Returns the square root of x.

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truncate()

truncate(x) → double
Returns x rounded to integer by dropping digits after decimal point.

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width_bucket()

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.

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width_bucket()

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.

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Random functions

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rand()

rand() → double
This is an alias for random().

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random()

random() → double
Returns a pseudo-random value in the range 0.0 <= x < 1.0.

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random()

random(n) → same as input
Returns a pseudo-random number between 0 and n (exclusive).

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random()

random(m, n) → same as input
Returns a pseudo-random number between m and n (exclusive).

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Trigonometric functions

All trigonometric function arguments are expressed in radians. See unit conversion functions degrees and radians.

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acos()

acos(x) → double
Returns the arc cosine of x.

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asin()

asin(x) → double
Returns the arc sine of x.

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atan()

atan(x) → double
Returns the arc tangent of x.

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atan2()

atan2(y, x) → double
Returns the arc tangent of y / x.

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cos()

cos(x) → double
Returns the cosine of x.

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cosh()

cosh(x) → double
Returns the hyperbolic cosine of x.

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sin()

sin(x) → double
Returns the sine of x.

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tan()

tan(x) → double
Returns the tangent of x.

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sinh()

sinh(x) → double Returns the hyperbolic sine of x.

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tanh()

tanh(x) → double
Returns the hyperbolic tangent of x.

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Floating point functions

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infinity()

infinity() → double
Returns the constant representing positive infinity.

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is_finite()

is_finite(x) → boolean
Determine if x is finite.

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is_infinite()

is_infinite(x) → boolean
Determine if x is infinite.

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is_nan()

is_nan(x) → boolean
Determine if x is not-a-number.

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nan()

nan() → double
Returns the constant representing not-a-number.

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Base conversion functions

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from_base()

from_base(string, radix) → bigint
Returns the value of string interpreted as a base-radix number.

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to_base()

to_base(x, radix) → varchar
Returns the base-radix representation of x.

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Statistical functions

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cosine_similarity()

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

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wilson_interval_lower()

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.

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wilson_interval_upper()

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.

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Cumulative distribution functions

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beta_cdf()

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].

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inverse_beta_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. The probability p must lie on the interval [0, 1].

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inverse_normal_cdf()

inverse_normal_cdf(mean, sd, p) → double
Compute the inverse of the Normal cdf with given mean and standard

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normal_cdf()

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.

​
Mathematical operators

OperatorDescription
+Addition
-Subtraction
*Multiplication
/Division (integer division performs truncation)
%Modulus (remainder)

​
Mathematical functions

​
abs()

abs(x) → same as input
Returns the absolute value of x.

​
cbrt()

cbrt(x) → double
Returns the cube root of x.

​
ceil()

ceil(x) → same as input
This is an alias for ceiling.

​
ceiling()

ceiling(x) → same as input
Returns x rounded up to the nearest integer.

​
degrees()

degrees(x) → double
Converts angle x in radians to degrees.

​
e()

e() → double
Returns the constant Euler’s number.

​
exp()

exp(x) → double
Returns Euler’s number raised to the power of x.

​
floor()

floor(x) → same as input
Returns x rounded down to the nearest integer.

​
ln()

ln(x) → double
Returns the natural logarithm of x.

​
log()

log(b, x) → double
Returns the base b logarithm of x.

​
log2()

log2(x) → double
Returns the base 2 logarithm of x.

​
log10()

log10(x) → double
Returns the base 10 logarithm of x.

​
mod()

mod(n, m) → same as input
Returns the modulus (remainder) of n divided by m.

​
pi()

pi() → double
Returns the constant Pi.

​
pow()

pow(x, p) → double
This is an alias for power.

​
power()

power(x, p) → double
Returns x raised to the power of p.

​
radians()

radians(x) → double
Converts angle x in degrees to radians.

​
round()

round(x) → same as input
Returns x rounded to the nearest integer.

​
round()

round(x, d) → same as input
Returns x rounded to d decimal places.

​
sign()

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()

sqrt(x) → double
Returns the square root of x.

​
truncate()

truncate(x) → double
Returns x rounded to integer by dropping digits after decimal point.

​
width_bucket()

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()

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.

​
Random functions

​
rand()

rand() → double
This is an alias for random().

​
random()

random() → double
Returns a pseudo-random value in the range 0.0 <= x < 1.0.

​
random()

random(n) → same as input
Returns a pseudo-random number between 0 and n (exclusive).

​
random()

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()

acos(x) → double
Returns the arc cosine of x.

​
asin()

asin(x) → double
Returns the arc sine of x.

​
atan()

atan(x) → double
Returns the arc tangent of x.

​
atan2()

atan2(y, x) → double
Returns the arc tangent of y / x.

​
cos()

cos(x) → double
Returns the cosine of x.

​
cosh()

cosh(x) → double
Returns the hyperbolic cosine of x.

​
sin()

sin(x) → double
Returns the sine of x.

​
tan()

tan(x) → double
Returns the tangent of x.

​
sinh()

sinh(x) → double Returns the hyperbolic sine of x.

​
tanh()

tanh(x) → double
Returns the hyperbolic tangent of x.

​
Floating point functions

​
infinity()

infinity() → double
Returns the constant representing positive infinity.

​
is_finite()

is_finite(x) → boolean
Determine if x is finite.

​
is_infinite()

is_infinite(x) → boolean
Determine if x is infinite.

​
is_nan()

is_nan(x) → boolean
Determine if x is not-a-number.

​
nan()

nan() → double
Returns the constant representing not-a-number.

​
Base conversion functions

​
from_base()

from_base(string, radix) → bigint
Returns the value of string interpreted as a base-radix number.

​
to_base()

to_base(x, radix) → varchar
Returns the base-radix representation of x.

​
Statistical functions

​
cosine_similarity()

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

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wilson_interval_lower()

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()

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()

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()

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()

inverse_normal_cdf(mean, sd, p) → double
Compute the inverse of the Normal cdf with given mean and standard

​
normal_cdf()

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.