Mathematical operators are provided for manyPostgreSQLtypes. For types without standard mathematical conventions (e.g., date/time types) we describe the actual behavior in subsequent sections.
Table 9.4shows the available mathematical operators.
Table 9.4. Mathematical Operators
Operator
Description
Example
Result
+
addition
2 + 3
5
-
subtraction
2 - 3
-1
*
multiplication
2 * 3
6
/
division (integer division truncates the result)
4 / 2
2
%
modulo (remainder)
5 % 4
1
^
exponentiation (associates left to right)
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
&
bitwise AND
91 & 15
11
`
`
bitwise OR
`32
3`
35
#
bitwise XOR
17 # 5
20
~
bitwise NOT
~1
-2
<<
bitwise shift left
1 << 4
16
>>
bitwise shift right
8 >> 2
2
The bitwise operators work only on integral data types, whereas the others are available for all numeric data types. The bitwise operators are also available for the bit string typesbitandbit varying, as shown inTable 9.13.
Table 9.5shows the available mathematical functions. In the table,dpindicatesdouble 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 data type as its argument. The functions working withdouble precisiondata are mostly implemented on top of the host system's C library; accuracy and behavior in boundary cases can therefore vary depending on the host system.
Table 9.5. Mathematical Functions
Function
Return Type
Description
Example
Result
abs(x)
(same as input)
absolute value
abs(-17.4)
17.4
cbrt(dp)
dp
cube root
cbrt(27.0)
3
ceil(dpornumeric)
(same as input)
nearest integer greater than or equal to argument
ceil(-42.8)
-42
ceiling(dpornumeric)
(same as input)
nearest integer greater than or equal to argument (same asceil)
ceiling(-95.3)
-95
degrees(dp)
dp
radians to degrees
degrees(0.5)
28.6478897565412
div(ynumeric,xnumeric)
numeric
integer quotient ofy/x
div(9,4)
2
exp(dpornumeric)
(same as input)
exponential
exp(1.0)
2.71828182845905
floor(dpornumeric)
(same as input)
nearest integer less than or equal to argument
floor(-42.8)
-43
ln(dpornumeric)
(same as input)
natural logarithm
ln(2.0)
0.693147180559945
log(dpornumeric)
(same as input)
base 10 logarithm
log(100.0)
2
log(bnumeric,xnumeric)
numeric
logarithm to baseb
log(2.0, 64.0)
6.0000000000
mod(y,x)
(same as argument types)
remainder ofy/x
mod(9,4)
1
pi()
dp
“π”constant
pi()
3.14159265358979
power(adp,bdp)
dp
a_raised to the power ofb_
power(9.0, 3.0)
729
power(anumeric,bnumeric)
numeric
a_raised to the power ofb_
power(9.0, 3.0)
729
radians(dp)
dp
degrees to radians
radians(45.0)
0.785398163397448
round(dpornumeric)
(same as input)
round to nearest integer
round(42.4)
42
round(vnumeric,sint)
numeric
round to_s_decimal places
round(42.4382, 2)
42.44
scale(numeric)
integer
scale of the argument (the number of decimal digits in the fractional part)
scale(8.41)
2
sign(dpornumeric)
(same as input)
sign of the argument (-1, 0, +1)
sign(-8.4)
-1
sqrt(dpornumeric)
(same as input)
square root
sqrt(2.0)
1.4142135623731
trunc(dpornumeric)
(same as input)
truncate toward zero
trunc(42.8)
42
trunc(vnumeric,sint)
numeric
truncate to_s_decimal places
trunc(42.4382, 2)
42.43
width_bucket(operanddp,b1dp,b2dp,countint)
int
return the bucket number to whichoperand_would be assigned in a histogram havingcountequal-width buckets spanning the rangeb1tob2; returns0orcount_+1for an input outside the range
width_bucket(5.35, 0.024, 10.06, 5)
3
width_bucket(operandnumeric,b1numeric,b2numeric,countint)
int
return the bucket number to whichoperand_would be assigned in a histogram havingcountequal-width buckets spanning the rangeb1tob2; returns0orcount_+1for an input outside the range
width_bucket(5.35, 0.024, 10.06, 5)
3
width_bucket(operandanyelement,thresholdsanyarray)
int
return the bucket number to whichoperand_would be assigned given an array listing the lower bounds of the buckets; returns0for an input less than the first lower bound; thethresholdsarray_must be sorted, smallest first, or unexpected results will be obtained
width_bucket(now(), array['yesterday', 'today', 'tomorrow']::timestamptz[])
2
Table 9.6shows functions for generating random numbers.
Table 9.6. Random Functions
Function
Return Type
Description
random()
dp
random value in the range 0.0 <= x < 1.0
setseed(dp)
void
set seed for subsequentrandom()calls (value between -1.0 and 1.0, inclusive)
The characteristics of the values returned byrandom()depend on the system implementation. It is not suitable for cryptographic applications; seepgcryptomodule for an alternative.
Finally,Table 9.7shows the available trigonometric functions. All trigonometric functions take arguments and return values of typedouble precision. Each of the trigonometric functions comes in two variants, one that measures angles in radians and one that measures angles in degrees.
Table 9.7. Trigonometric Functions
Function (radians)
Function (degrees)
Description
acos(x)
acosd(x)
inverse cosine
asin(x)
asind(x)
inverse sine
atan(x)
atand(x)
inverse tangent
atan2(y,x)
atan2d(y,x)
inverse tangent ofy/x
cos(x)
cosd(x)
cosine
cot(x)
cotd(x)
cotangent
sin(x)
sind(x)
sine
tan(x)
tand(x)
tangent
Another way to work with angles measured in degrees is to use the unit transformation functionsradians()anddegrees()shown earlier. However, using the degree-based trigonometric functions is preferred, as that way avoids roundoff error for special cases such assind(30).