9.3. 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 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 9.14.
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 |
log10(dp or numeric) | (same as input) | base 10 logarithm | log10(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 | 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 | 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 random() function uses a simple linear
congruential algorithm. It is fast but not suitable for cryptographic
applications; see the pgcrypto module for a more
secure alternative.
If setseed() is called, the results of
subsequent random() calls in the current session are
repeatable by re-issuing setseed() with the same
argument.
Without any prior setseed() call in the same
session, the first random() call obtains a seed
from a platform-dependent source of random bits.
Table 9.7 shows the
available trigonometric functions. All these 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()degrees()sind(30).
Table 9.8 shows the
available hyperbolic functions. All these functions
take arguments and return values of type double
precision.
Table 9.8. Hyperbolic Functions
| Function | Description | Example | Result |
|---|
sinh(x) | hyperbolic sine | sinh(0) | 0 |
cosh(x) | hyperbolic cosine | cosh(0) | 1 |
tanh(x) | hyperbolic tangent | tanh(0) | 0 |
asinh(x) | inverse hyperbolic sine | asinh(0) | 0 |
acosh(x) | inverse hyperbolic cosine | acosh(1) | 0 |
atanh(x) | inverse hyperbolic tangent | atanh(0) | 0 |