The following is a list of all available mathematical functions. They are divided into several sections:
PI, DEGREES, RADIANS.FLOOR, CEIL, ROUND, TRUNC.EXP, SQRT, LN).SIN, ASIN).COSH, ACOSH).RANDOM, RANDINT.PI() -> float64Returns the value of the PI constant.
Notes
The precision of the value of PI is no less than 12 decimal places.
Examples
SELECT PI();
--> 3.14159265358979
DEGREES(x: float64) -> float64Converts the argument from radians to degrees.
Null handling
If the argument is NULL, the function will also return NULL.
Examples
SELECT DEGREES(3.1415);
--> 179.99469134034814
SELECT DEGREES(0);
--> 0.0
SELECT DEGREES(-1.5708);
--> -90.00021045914971
See also
RADIANS(x: float64) -> float64Converts the argument from degrees to radians.
Null handling
If the argument is NULL, the function will also return NULL.
Examples
SELECT RADIANS(180);
--> 3.14159265358979
SELECT RADIANS(0);
--> 0.0
SELECT RADIANS(-90);
--> -1.5707963267949
See also
CEIL(x: float64) -> int64Returns the nearest integer greater or equal to the argument.
Null handling
If the argument is NULL, the function will also return NULL.
Notes
When the argument is negative, CEIL rounds it towards zero, which, even though mathematically correct, can be suprising to some.
Examples
SELECT CEIL(4.2);
--> 5
SELECT CEIL(2.7);
--> 3
SELECT CEIL(-3.1);
--> -3
See also
FLOOR(x: float64) -> int64Returns the nearest integer less than or equal to the argument.
Null handling
If the argument is NULL, the function will also return NULL.
Notes
When the argument is negative, FLOOR rounds it towards negative infinity, which, even though mathematically correct, can be suprising to some. If rounding towards zero is desired in all cases, use the TRUNC function.
Examples
SELECT FLOOR(4.2);
--> 4
SELECT FLOOR(2.7);
--> 2
SELECT FLOOR(-3.1);
--> -4
See also
ROUND(x: float64) -> int64ROUND(x: float64, n: int64) -> float64Rounds the argument to the nearest integer, or to n decimal places.
Null handling
If any of the arguments is NULL, the function will also return NULL.
Examples
SELECT ROUND(4.2);
--> 4
SELECT ROUND(2.7);
--> 3
SELECT ROUND(-3.1);
--> -3
With specified number of decimal places:
SELECT ROUND(4.2573, 1);
--> 4.3
SELECT ROUND(2.7418, 1);
--> 2.7
SELECT ROUND(-3.1201, 1);
--> -3.1
TRUNC(x: float64) -> int64TRUNC(x: float64, n: int64) -> float64Truncates the argument to an integer, or to n decimal places.
Null handling
If any of the arguments is NULL, the function will also return NULL.
Notes
TRUNC always rounds the argument towards zero.
Examples
SELECT TRUNC(4.2);
--> 4
SELECT TRUNC(2.7);
--> 2
SELECT TRUNC(-3.1);
--> -3
With specified number of decimal places:
SELECT TRUNC(4.2573, 1);
--> 4.2
SELECT TRUNC(2.7418, 1);
--> 2.7
SELECT TRUNC(-3.1201, 1);
--> -3.1
FMOD(x: f64, y: f64) -> f64Returns the floating-point remainder of the division operation x / y.
Null handling
If any of the arguments is NULL, the function will also return NULL.
Error handling
If the value of the divisor y is 0, the function will return an error Division by zero.
Notes
The function behaves the same as C++ std::fmod function.
Examples
SELECT fmod(+5.1, +3.0)
--> 2.1
SELECT fmod(-5.1, +3.0)
--> -2.1
SELECT fmod(+5.1, -3.0)
--> 2.1
SELECT fmod(-5.1, -3.0)
--> -2.1
CBRT(x: float64) -> float64Returns the cubic root of the argument.
Arguments
The function accepts negative numbers as valid arguments.
Null handling
If the argument is NULL, the function will also return NULL.
Notes
The CBRT function is logically equivalent to POWER(x, 1/3), but unlike POWER, CBRT works correctly for negative arguments (while the POWER function doesn't allow raising negative values to a decimal power).
Examples
SELECT CBRT(27);
--> 3.0
SELECT CBRT(-8);
--> -2.0
SELECT CBRT(15.625);
--> 2.5
See also
EXP(x: float64) -> float64Returns the value of the exponential function, e^x, for the given argument.
Null handling
If the argument is NULL, the function will also return NULL.
Error handling
If the value of e^x exceeds the maximum value representable by a 64-bit floating-point number (~1.8e+308), the function will return an error: Result out of representable range.
Examples
SELECT EXP(1);
--> 2.71828182845905
SELECT EXP(-0.5);
--> 0.60653065971263
SELECT EXP(0.0001);
--> 1.00010000500017
See also
LN(x: float64) -> float64Returns the value of the natural logarithm of the argument.
Null handling
If the argument is NULL, the function will also return NULL.
Error handling
As logarithms are defined only for positive numbers, for a non-positive argument the function will return an error: Argument out of domain.
Examples
SELECT LN(2.718);
--> 0.99989631572895
SELECT LN(0.135);
--> -2.00248050054371
SELECT LN(10);
--> 2.30258509299405
See also
LOG10(x: float64) -> float64Returns the value of the base-10 logarithm of the argument.
Null handling
If the argument is NULL, the function will also return NULL.
Error handling
As logarithms are defined only for positive numbers, for a non-positive argument the function will return an error: Argument out of domain.
Examples
SELECT LOG10(10);
--> 1.0
SELECT LOG10(0.01);
--> -2.0
SELECT LOG10(2);
--> 0.30102999566398
See also
LOG2(x: float64) -> float64Returns the value of the base-2 logarithm of the argument.
Null handling
If the argument is NULL, the function will also return NULL.
Error handling
As logarithms are defined only for positive numbers, for a non-positive argument the function will return an error: Argument out of domain.
Examples
SELECT LOG2(2);
--> 1.0
SELECT LOG2(0.125);
--> -3.0
SELECT LOG2(10);
--> 3.32192809488736
See also
POWER(x: float64, y: float64) -> float64Returns the value of the first argument raised to the power of the second argument, i.e. x^y.
Null handling
If any of the arguments is NULL, the function will also return NULL.
Error handling
If the first argument is negative, the second argument must be an integer, otherwise the function will return an error: Cannot raise a negative number to decimal power.
If the first argument is 0 and the second argument is negative, the function will return an error: Division by zero.
If the value of x^y exceeds the maximum value representable by a 64-bit floating-point number (~1.8e+308), the function will return an error: Result out of representable range.
Examples
SELECT POWER(3, 2);
--> 9.0
SELECT POWER(27, 0.33333);
--> 2.99996704181238
SELECT POWER(6.25, -0.5);
--> 0.4
See also
SQRT(x: float64) -> float64Returns the square root of the argument.
Null handling
If the argument is NULL, the function will also return NULL.
Error handling
As the square root of a negative number is not real, for negative arguments the function returns an error: Argument out of domain.
Examples
SELECT SQRT(9);
--> 3.0
SELECT SQRT(0.25);
--> 0.5
SELECT SQRT(256);
--> 16.0
See also
ACOS(x: float64) -> float64Returns the arc cosine of the argument, i.e. the number for which the cosine is equal to x.
Null handling
If the argument is NULL, the function will also return NULL.
Error handling
As arc cosine is defined only for arguments from the range [-1, 1], for values outside of that range the function will return an error: Argument out of domain.
Notes
The result is always from the range [0, pi].
ACOS is the inverse function of COS, so it holds that ACOS(COS(x)) = x, but only for arguments from the range [0, pi] and up to rounding errors.
Examples
SELECT ACOS(0.5);
--> 1.0471975511966
SELECT ACOS(-0.707);
--> 2.3560434901900
SELECT ACOS(0);
--> 1.5707963267949
See also
ASIN(x: float64) -> float64Returns the arc sine of the argument, i.e. the number for which the sine is equal to x.
Null handling
If the argument is NULL, the function will also return NULL.
Error handling
As arc sine is defined only for arguments from the range [-1, 1], for values outside of that range the function will return an error: Argument out of domain.
Notes
The result is always from the range [-pi/2, pi/2].
ASIN is the inverse function of SIN, so it holds that ASIN(SIN(x)) = x, but only arguments from the range [-pi/2, pi/2] and up to rounding errors.
Examples
SELECT ASIN(0.5);
--> 0.5235987755983
SELECT ASIN(-0.707);
--> -0.7852471633951
SELECT ASIN(0);
--> 0.0
See also
ATAN(x: float64) -> float64Returns the arc tangent of the argument, i.e. the number for which the tangent is equal to x.
Null handling
If the argument is NULL, the function will also return NULL.
Notes
The result is always from the range [-pi/2, pi/2].
ATAN is the inverse function of TAN, so it holds that ATAN(TAN(x)) = x, but only for arguments from the range [-pi/2, pi/2] and up to rounding errors.
Examples
SELECT ATAN(SQRT(3));
--> 1.0471975511966
SELECT ATAN(-1);
--> -0.7853981633974
SELECT ATAN(0);
--> 0.0
See also
ATAN2(y: float64, x: float64) -> float64Return the arc tangent of the y/x, using the signs of the arguments to determine the correct quadrant.
Null handling
If any of the arguments is NULL, the function will also return NULL.
Notes
The result is always from the range [-pi, pi].
For the special case x=0, y=0, the function returns 0.
Examples
SELECT ATAN2(SQRT(3)/2, 0.5);
--> 1.0471975511966
SELECT ATAN2(2, 2);
--> 0.7853981633974
SELECT ATAN2(1, 0);
--> 1.5707963267949
See also
COS(x: float64) -> float64Returns the cosine of the argument.
Null handling
If the argument is NULL, the function will also return NULL.
Examples
SELECT COS(PI()/3);
--> 0.5
SELECT COS(3*PI()/4);
--> -0.70710678118655
SELECT COS(PI()/2);
--> 6.12323399573677e-17
See also
SIN(x: float64) -> float64Returns the sine of the argument.
Null handling
If the argument is NULL, the function will also return NULL.
Examples
SELECT SIN(PI()/6);
--> 0.5
SELECT SIN(-PI()/4);
--> -0.70710678118655
SELECT SIN(0);
--> 0.0
See also
TAN(x: float64) -> float64Returns the tangent of the argument.
Null handling
If the argument is NULL, the function will also return NULL.
Examples
SELECT TAN(PI()/3);
--> 1.73205080756888
SELECT TAN(-PI()/4);
--> -1.0
SELECT TAN(0);
--> 0.0
See also
ACOSH(x: float64) -> float64Returns the area hyperbolic cosine of the argument, i.e. the number for which the hyperbolic cosine is equal to x.
Null handling
If the argument is NULL, the function will also return NULL.
Error handling
As area hyperbolic cosine is defined only for x >= 1, for arguments smaller than 1 the function will return an error: Argument out of domain.
Notes
The result is always non-negative.
ACOSH is the inverse function of COSH, so it holds that ACOSH(COSH(x)) = x, but only for x >= 1 and up to rounding errors.
Examples
SELECT ACOSH(1);
--> 0.0
SELECT ACOSH(2);
--> 1.3169578969248
SELECT ACOSH(5);
--> 2.2924316695612
See also
ASINH(x: float64) -> float64Returns the area hyperbolic sine of the argument, i.e. the number for which the hyperbolic sine is equal to x.
Null handling
If the argument is NULL, the function will also return NULL.
Notes
ASINH is the inverse function of SINH, so it holds that ASINH(SINH(x)) = x for all values of x.
Examples
SELECT ASINH(1);
--> 0.8813735870195
SELECT ASINH(0);
--> 0.0
SELECT ASINH(-1);
--> -0.8813735870195
See also
ATANH(x: float64) -> float64Returns the area hyperbolic tangent of the argument, i.e. the number for which the hyperbolic tangent is equal to x.
Null handling
If the argument is NULL, the function will also return NULL.
Error handling
As area hyperbolic tangent is only defined for arguments from the open range <-1, 1>, for arguments outside of this range the function will return an error: Argument out of domain.
Notes
ATANH is the inverse function of TANH, so it holds that ATANH(TANH(x)) = x (up to rounding errors) for all values of x from the domain.
Examples
SELECT ATANH(0.5);
--> 0.5493061443340
SELECT ATANH(0);
--> 0.0
SELECT ATANH(-0.5);
--> -0.5493061443340
See also
COSH(x: float64) -> float64Returns the hyperbolic cosine of the argument.
Null handling
If the argument is NULL, the function will also return NULL.
Error handling
If the value of COSH(x) exceeds the maximum value representable by a 64-bit floating-point number (~1.8e+308), the function will return an error: Result out of representable range.
Examples
SELECT COSH(1);
--> 1.54308063481524
SELECT COSH(0);
--> 1.0
SELECT COSH(-1);
--> 1.54308063481524
See also
SINH(x: float64) -> float64Returns the hyperbolic sine of the argument.
Null handling
If the argument is NULL, the function will also return NULL.
Error handling
If the value of SINH(x) exceeds the maximum value representable by a 64-bit floating-point number (~1.8e+308), the function will return an error: Result out of representable range.
Examples
SELECT SINH(1);
--> 1.1752011936438
SELECT SINH(0);
--> 0.0
SELECT SINH(-1);
--> -1.1752011936438
See also
TANH(x: float64) -> float64Returns the hyperbolic tangent of the argument.
Null handling
If the argument is NULL, the function will also return NULL.
Examples
SELECT TANH(1);
--> 0.76159415595576
SELECT TANH(0);
--> 0.0
SELECT TANH(-1);
--> -0.76159415595576
See also
RANDINT(max: int64) -> int64Returns a random integer between 0 (inclusive) and the given argument (exclusive).
Null handling
If the argument is NULL, the function will also return NULL.
Examples
SELECT RANDINT(10);
--> 7
See also
RANDOM() -> float64Returns a random number between 0 and 1.
Examples
SELECT RANDOM();
--> 0.23679588880354
See also