6.6. Mathematical Functions and Operators

Mathematical Operators

OperatorDescription
+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.

  • ceil(x) → [same as input]

  • This is an alias for ceiling().

  • ceiling(x) → [same as input]

  • Returns x rounded up to the nearest integer.

  • cosinesimilarity(_x, y) → double

  • Returns the cosine similarity between the sparse vectors x and y:
  1. 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.

  • frombase(_string, radix) → bigint

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

  • inversenormal_cdf(_mean, sd, p) → double

  • Compute the inverse of the Normal cdf with given mean and standarddeviation (sd) for the cumulative probability (p): P(N < n). The mean must bea real value and the standard deviation must be a real and positive value.The probability p must lie on the interval (0, 1).

  • normalcdf(_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 realand positive value.

  • inversebeta_cdf(_a, b, p) → double

  • Compute the inverse of the Beta cdf with given a, b parameters for the cumulativeprobability (p): P(N < n). The a, b parameters must be positive real values.The probability p must lie on the interval [0, 1].

  • betacdf(_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.

  • 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.

  • tobase(_x, radix) → varchar

  • Returns the base-radix representation of x.

  • truncate(x) → double

  • Returns x rounded to integer by dropping digits after decimal point.

  • widthbucket(_x, bound1, bound2, n) → bigint

  • Returns the bin number of x in an equi-width histogram with thespecified bound1 and bound2 bounds and n number of buckets.

  • widthbucket(_x, bins) → bigint

  • Returns the bin number of x according to the bins specified by thearray bins. The bins parameter must be an array of doubles and isassumed to be in sorted ascending order.

Statistical Functions

  • wilsoninterval_lower(_successes, trials, z) → double

  • Returns the lower bound of the Wilson score interval of a Bernoulli trial processat a confidence specified by the z-score z.

  • wilsoninterval_upper(_successes, trials, z) → double

  • Returns the upper bound of the Wilson score interval of a Bernoulli trial processat 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.

  • isfinite(_x) → boolean

  • Determine if x is finite.

  • isinfinite(_x) → boolean

  • Determine if x is infinite.

  • isnan(_x) → boolean

  • Determine if x is not-a-number.

  • nan() → double

  • Returns the constant representing not-a-number.