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6.3. Mathematical Functions and Operators

Mathematical operators are provided for many PostgreSQL types. For types without common mathematical conventions for all possible permutations (e.g., date/time types) we describe the actual behavior in subsequent sections.

Table 6-2 shows the available mathematical operators.

Table 6-2. 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
|/ square root |/ 25.0 5
||/ cube root ||/ 27.0 3
! factorial 5 ! 120
!! factorial (prefix operator) !! 5 120
@ absolute value @ -5.0 5
& 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, as shown in Table 6-3. Bit string arguments to &, |, and # must be of equal length. When bit shifting, the original length of the string is preserved, as shown in the table.

Table 6-3. 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

Table 6-4 shows the available mathematical functions. In the table, dp indicates double precision. Many of these functions are provided in multiple forms with different argument types. Except where noted, any given form of a function returns the same datatype as its argument. The functions working with double precision data are mostly implemented on top of the host system's C library; accuracy and behavior in boundary cases may therefore vary depending on the host system.

Table 6-4. 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
ceil(dp or numeric) (same as input) smallest integer not less than argument ceil(-42.8) -42
degrees(dp) dp radians to degrees degrees(0.5) 28.6478897565412
exp(dp or numeric) (same as input) exponential exp(1.0) 2.71828182845905
floor(dp or numeric) (same as input) largest integer not greater than argument floor(-42.8) -43
ln(dp or numeric) (same as input) natural logarithm ln(2.0) 0.693147180559945
log(dp or numeric) (same as input) base 10 logarithm log(100.0) 2
log(b numeric, x numeric) numeric logarithm to base b log(2.0, 64.0) 6.0000000000
mod(y, x) (same as argument types) remainder of y/x mod(9,4) 1
pi() dp "Pi" constant pi() 3.14159265358979
pow(x dp, e dp) dp raise a number to exponent e pow(9.0, 3.0) 729
pow(x numeric, e numeric) numeric raise a number to exponent e pow(9.0, 3.0) 729
radians(dp) dp degrees to radians radians(45.0) 0.785398163397448
random() dp random value between 0.0 and 1.0 random()  
round(dp or numeric) (same as input) 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
sign(dp or numeric) (same as input) sign of the argument (-1, 0, +1) sign(-8.4) -1
sqrt(dp or numeric) (same as input) square root sqrt(2.0) 1.4142135623731
trunc(dp or numeric) (same as input) truncate toward zero trunc(42.8) 42
trunc(v numeric, s integer) numeric truncate to s decimal places trunc(42.4382, 2) 42.43

Finally, Table 6-5 shows the available trigonometric functions. All trigonometric functions take arguments and return values of type double precision.

Table 6-5. Trigonometric Functions

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