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The PostgreSQL 9.0 Reference Manual - Volume 1A - SQL Language Reference
by The PostgreSQL Global Development Group
Paperback (6"x9"), 454 pages
ISBN 9781906966041
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7.3 Mathematical Functions and Operators

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

Table 7-2 shows the available mathematical operators.

Table 7-2: Mathematical Operators
Operator Description
+ addition
e.g. 2 + 3 => 5
- subtraction
e.g. 2 - 3 => -1
* multiplication
e.g. 2 * 3 => 6
/ division (integer division truncates the result)
e.g. 4 / 2 => 2
% modulo (remainder)
e.g. 5 % 4 => 1
^ exponentiation
e.g. 2.0 ^ 3.0 => 8
|/ square root
e.g. |/ 25.0 => 5
||/ cube root
e.g. ||/ 27.0 => 3
! factorial
e.g. 5 ! => 120
!! factorial (prefix operator)
e.g. !! 5 => 120
@ absolute value
e.g. @ -5.0 => 5
& bitwise AND
e.g. 91 & 15 => 11
| bitwise OR
e.g. 32 | 3 => 35
# bitwise XOR
e.g. 17 # 5 => 20
~ bitwise NOT
e.g. ~1 => -2
<< bitwise shift left
e.g. 1 << 4 => 16
>> bitwise shift right
e.g. 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 types bit and bit varying, as shown in Table 7-10.

Table 7-3 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 data type 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 can therefore vary depending on the host system.

Table 7-3: Mathematical Functions
Function Return Type Description
abs(x) (same as input) absolute value
e.g. abs(-17.4) => 17.4
cbrt(dp) dp cube root
e.g. cbrt(27.0) => 3
ceil(dp or numeric) (same as input) smallest integer not less than argument
e.g. ceil(-42.8) => -42
ceiling(dp or numeric) (same as input) smallest integer not less than argument (alias for ceil)
e.g. ceiling(-95.3) => -95
degrees(dp) dp radians to degrees
e.g. degrees(0.5) => 28.6478897565412
div(y numeric, x numeric) numeric integer quotient of y/x
e.g. div(9,4) => 2
exp(dp or numeric) (same as input) exponential
e.g. exp(1.0) => 2.71828182845905
floor(dp or numeric) (same as input) largest integer not greater than argument
e.g. floor(-42.8) => -43
ln(dp or numeric) (same as input) natural logarithm
e.g. ln(2.0) => 0.693147180559945
log(dp or numeric) (same as input) base 10 logarithm
e.g. log(100.0) => 2
log(b numeric, x numeric) numeric logarithm to base b
e.g. log(2.0, 64.0) => 6.0000000000
mod(y, x) (same as argument types) remainder of y/x
e.g. mod(9,4) => 1
pi() dp “\pi” constant
e.g. pi() => 3.14159265358979
power(a dp, b dp) dp a raised to the power of b
e.g. power(9.0, 3.0) => 729
power(a numeric, b numeric) numeric a raised to the power of b
e.g. power(9.0, 3.0) => 729
radians(dp) dp degrees to radians
e.g. radians(45.0) => 0.785398163397448
random() dp random value in the range 0.0 <= x < 1.0
e.g. random()
round(dp or numeric) (same as input) round to nearest integer
e.g. round(42.4) => 42
round(v numeric, s int) numeric round to s decimal places
e.g. round(42.4382, 2) => 42.44
setseed(dp) void set seed for subsequent random() calls (value between -1.0 and 1.0, inclusive)
e.g. setseed(0.54823)
sign(dp or numeric) (same as input) sign of the argument (-1, 0, +1)
e.g. sign(-8.4) => -1
sqrt(dp or numeric) (same as input) square root
e.g. sqrt(2.0) => 1.4142135623731
trunc(dp or numeric) (same as input) truncate toward zero
e.g. trunc(42.8) => 42
trunc(v numeric, s int) numeric truncate to s decimal places
e.g. trunc(42.4382, 2) => 42.43
width_bucket(op numeric, b1 numeric, b2 numeric, count int) int return the bucket to which operand would be assigned in an equidepth histogram with count buckets, in the range b1 to b2
e.g. width_bucket(5.35, 0.024, 10.06, 5) => 3
width_bucket(op dp, b1 dp, b2 dp, count int) int return the bucket to which operand would be assigned in an equidepth histogram with count buckets, in the range b1 to b2
e.g. width_bucket(5.35, 0.024, 10.06, 5) => 3

Finally, Table 7-4 shows the available trigonometric functions. All trigonometric functions take arguments and return values of type double precision. Trigonometric functions arguments are expressed in radians. Inverse functions return values are expressed in radians. See unit transformation functions radians() and degrees() above.

Table 7-4: Trigonometric Functions
Function Description
acos(x) inverse cosine
asin(x) inverse sine
atan(x) inverse tangent
atan2(y, x) inverse tangent of y/x
cos(x) cosine
cot(x) cotangent
sin(x) sine
tan(x) tangent
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