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# 4.3. Mathematical Functions and Operators

Table 4-2. Mathematical Operators

Name Description Example Result
+ Addition 2 + 3 5
- Subtraction 2 - 3 -1
* Multiplication 2 * 3 6
/ Division (integer division truncates results) 4 / 2 2
% Modulo (remainder) 5 % 4 1
^ Exponentiation 2.0 ^ 3.0 8.0
|/ Square root |/ 25.0 5.0
||/ Cube root ||/ 27.0 3
! Factorial 5 ! 120
!! Factorial (prefix operator) !! 5 120
@ Absolute value @ -5.0 5.0
& Binary AND 91 & 15 11
| Binary OR 32 | 3 35
# Binary XOR 17 # 5 20
~ Binary NOT ~1 -2
<< Binary shift left 1 << 4 16
>> Binary shift right 8 >> 2 2

The "binary" operators are also available for the bit string types BIT and BIT VARYING.

Table 4-3. Bit String Binary Operators

Example Result
B'10001' & B'01101' 00001
B'10001' | B'01101' 11101
B'10001' # B'01101' 11110
~ B'10001' 01110
B'10001' << 3 01000
B'10001' >> 2 00100
Bit string arguments to &, |, and # must be of equal length. When bit shifting, the original length of the string is preserved, as shown here.

Table 4-4. Mathematical Functions

Function Return Type Description Example Result
abs(x) (same as x) absolute value abs(-17.4) 17.4
cbrt(dp) dp cube root cbrt(27.0) 3.0
ceil(numeric) numeric smallest integer not less than argument ceil(-42.8) -42
degrees(dp) dp radians to degrees degrees(0.5) 28.6478897565412
exp(dp) dp exponential exp(1.0) 2.71828182845905
floor(numeric) numeric largest integer not greater than argument floor(-42.8) -43
ln(dp) dp natural logarithm ln(2.0) 0.693147180559945
log(dp) dp base 10 logarithm log(100.0) 2.0
log(b numeric, x numeric) numeric logarithm to base b log(2.0, 64.0) 6.0
mod(y, x) (same as argument types) remainder of y/x mod(9,4) 1
pi() dp "Pi" constant pi() 3.14159265358979
pow(e dp, n dp) dp raise a number to exponent e pow(9.0, 3.0) 729.0
random() dp value between 0.0 to 1.0 random()
round(dp) dp round to nearest integer round(42.4) 42
round(v numeric, s integer) numeric round to s decimal places round(42.4382, 2) 42.44
sqrt(dp) dp square root sqrt(2.0) 1.4142135623731
trunc(dp) dp truncate toward zero trunc(42.8) 42
trunc(numeric, s integer) numeric truncate to s decimal places round(42.4382, 2) 42.43

In the table above, "dp" indicates double precision. The functions exp, ln, log, pow, round (1 argument), sqrt, and trunc (1 argument) are also available for the type numeric in place of double precision. Functions returning a numeric result take numeric input arguments, unless otherwise specified. Many of these functions are implemented on top of the host system's C library and behavior in boundary cases could therefore vary depending on the operating system.

Table 4-5. Trigonometric Functions

Function Description
acos(x) inverse cosine
asin(x) inverse sine
atan(x) inverse tangent
atan2(x, y) inverse tangent of y/x
cos(x) cosine
cot(x) cotangent
sin(x) sine
tan(x) tangent

All trigonometric functions have arguments and return values of type double precision.