Mathematical Functions and Operators
| PostgreSQL 9.6.21 Documentation | |||
|---|---|---|---|
| Prev | Up | Chapter 9. Functions and Operators | Next |
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 9-4 shows 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
(deprecated, use
factorial()
instead)
|
5 ! | 120 |
| !! |
factorial as a prefix operator
(deprecated, use
factorial()
instead)
|
!! 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 and are also available for the bit string types bit and bit varying , as shown in Table 9-13 .
Table 9-5 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 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(
dp
or
numeric
)
|
(same as input) | nearest integer greater than or equal to argument | ceil(-42.8) | -42 |
ceiling(
dp
or
numeric
)
|
(same as input) |
nearest integer greater than or equal to argument (same as
ceil
)
|
ceiling(-95.3) | -95 |
degrees(
dp
)
|
dp | radians to degrees | degrees(0.5) | 28.6478897565412 |
div(
y
numeric
,
x
numeric
)
|
numeric | integer quotient of y / x | div(9,4) | 2 |
exp(
dp
or
numeric
)
|
(same as input) | exponential | exp(1.0) | 2.71828182845905 |
factorial(
bigint
)
|
numeric | factorial | factorial(5) | 120 |
floor(
dp
or
numeric
)
|
(same as input) | nearest integer less than or equal to 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 | "π" constant | pi() | 3.14159265358979 |
power(
a
dp
,
b
dp
)
|
dp | a raised to the power of b | power(9.0, 3.0) | 729 |
power(
a
numeric
,
b
numeric
)
|
numeric | a raised to the power of b | power(9.0, 3.0) | 729 |
radians(
dp
)
|
dp | degrees to radians | radians(45.0) | 0.785398163397448 |
round(
dp
or
numeric
)
|
(same as input) | round to nearest integer | round(42.4) | 42 |
round(
v
numeric
,
s
int
)
|
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(
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
int
)
|
numeric | truncate to s decimal places | trunc(42.4382, 2) | 42.43 |
width_bucket(
operand
dp
,
b1
dp
,
b2
dp
,
count
int
)
|
int | return the bucket number to which operand would be assigned in a histogram having count equal-width buckets spanning the range b1 to b2 ; returns 0 or count +1 for an input outside the range | width_bucket(5.35, 0.024, 10.06, 5) | 3 |
width_bucket(
operand
numeric
,
b1
numeric
,
b2
numeric
,
count
int
)
|
int | return the bucket number to which operand would be assigned in a histogram having count equal-width buckets spanning the range b1 to b2 ; returns 0 or count +1 for an input outside the range | width_bucket(5.35, 0.024, 10.06, 5) | 3 |
width_bucket(
operand
anyelement
,
thresholds
anyarray
)
|
int | return the bucket number to which operand would be assigned given an array listing the lower bounds of the buckets; returns 0 for an input less than the first lower bound; the thresholds array must be sorted , smallest first, or unexpected results will be obtained | width_bucket(now(), array['yesterday', 'today', 'tomorrow']::timestamptz[]) | 2 |
Table 9-6 shows 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 subsequent random() calls (value between -1.0 and 1.0, inclusive) |
The characteristics of the values returned by
random()
depend
on the system implementation. It is not suitable for cryptographic
applications; see
pgcrypto
module for an alternative.
Finally, Table 9-7 shows the available trigonometric functions. All trigonometric functions take arguments and return values of type double 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 of y / x |
cos(
x
)
|
cosd(
x
)
|
cosine |
cot(
x
)
|
cotd(
x
)
|
cotangent |
sin(
x
)
|
sind(
x
)
|
sine |
tan(
x
)
|
tand(
x
)
|
tangent |
Note: Another way to work with angles measured in degrees is to use the unit transformation functions
radians()anddegrees()shown earlier. However, using the degree-based trigonometric functions is preferred, as that way avoids roundoff error for special cases such as sind(30) .