Mathematical Functions

This page summarizes mathematical functions in Machbase.

Function Matrix

Function	Syntax	Return type	Arguments	Behavior
PI	`PI()`	`DOUBLE`	No arguments	Returns π constant (`3.141592653589793`).
SQRT	`SQRT(n)`	`DOUBLE`	1 numeric argument	Returns the square root of `n`.
POWER	`POWER(base, exponent)`	`DOUBLE`	2 numeric arguments	Returns `base` raised to `exponent`.
POW	`POW(base, exponent)`	`DOUBLE`	2 numeric arguments	Alias of `POWER`.
LOG	`LOG(n)`	`DOUBLE`	1 numeric argument	Returns natural logarithm `ln(n)`.
LOG	`LOG(base, n)`	`DOUBLE`	2 numeric arguments	Returns logarithm with base and argument, `log_base(n)`.
LN	`LN(n)`	`DOUBLE`	1 numeric argument	Returns natural logarithm `ln(n)`.
EXP	`EXP(n)`	`DOUBLE`	1 numeric argument	Returns `e^n`.
FLOOR	`FLOOR(n)`	`DOUBLE`	1 numeric argument	Rounds down toward negative infinity.
CEIL	`CEIL(n)`	`DOUBLE`	1 numeric argument	Rounds up toward positive infinity.
SIN	`SIN(radian)`	`DOUBLE`	1 numeric argument	Returns sine (argument is in radians).
COS	`COS(radian)`	`DOUBLE`	1 numeric argument	Returns cosine (argument is in radians).
TAN	`TAN(radian)`	`DOUBLE`	1 numeric argument	Returns tangent (argument is in radians).
MOD	`MOD(dividend, divisor)`	`DOUBLE`	2 numeric arguments	Returns remainder using truncation toward zero of quotient.
RAND	`RAND()`	`DOUBLE`	No arguments	Pseudo random in range `[0, 1)`, stateful per session.
RAND	`RAND(seed)`	`DOUBLE`	1 integer argument	Deterministic pseudo random in `[0, 1)` for a given seed.

SELECT PI() FROM m$sys_users WHERE name = 'SYS';

Returns a DOUBLE value. Passing arguments is not allowed.

SELECT SQRT(9)
FROM m$sys_users WHERE name = 'SYS';

SELECT FLOOR(3.2), FLOOR(-1.2)
FROM m$sys_users WHERE name = 'SYS';

SELECT CEIL(3.2), CEIL(-1.2)
FROM m$sys_users WHERE name = 'SYS';

SELECT SIN(PI()/2), SIN(0)
FROM m$sys_users WHERE name = 'SYS';

SELECT COS(0), COS(PI())
FROM m$sys_users WHERE name = 'SYS';

SELECT TAN(0), TAN(PI()/4)
FROM m$sys_users WHERE name = 'SYS';

SELECT LN(2), LN(10)
FROM m$sys_users WHERE name = 'SYS';

SELECT EXP(2), EXP(-1)
FROM m$sys_users WHERE name = 'SYS';

All trigonometric and logarithmic/exponential functions require numeric input and return DOUBLE.

SELECT SQRT(9), LN(2), EXP(2), SIN(PI()/2)
FROM m$sys_users WHERE name = 'SYS';

POWER and POW are identical.

SELECT POWER(3, 4), POW(2, -1) FROM m$sys_users WHERE name = 'SYS';

Alias of POWER().

SELECT POW(2, 3)
FROM m$sys_users WHERE name = 'SYS';

SELECT LOG(2, 8), LOG(100) FROM m$sys_users WHERE name = 'SYS';

For negative values, quotient truncation uses zero-centered truncation.

SELECT MOD(-10, 3), MOD(10, -3), MOD(-10, -3)
FROM m$sys_users WHERE name = 'SYS';

RAND(seed) requires an integer seed. Passing the same seed repeatedly returns the same value.
RAND() uses internal state, so successive calls in one statement return different values.
Output is DOUBLE in [0, 1).

SELECT RAND(), RAND(), RAND(5), RAND(5), RAND() FROM m$sys_users WHERE name = 'SYS';

Error kind	Error code	Triggered when
Argument type mismatch	`ERR-02036` / `ERR-02037`	`PI` with arguments, or any numeric-function input is non-numeric.
Execution failure	`ERR-02317`	Domain/range error while calculating value, for example negative input to `SQRT`, zero in `MOD` divisor, invalid `LOG` base, or overflow in `EXP`/`POWER`.

When an argument is NULL, the result is NULL.

Last updated on Mar 14, 2026