9.3. Mathematical Functions and Operators
Mathematical operators are provided for manyPostgres Pro 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, usefactorial() instead) | 5 ! | 120 |
!! | factorial as a prefix operator (deprecated, usefactorial() 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 typesbit andbit varying, as shown inTable 9.14.
Table 9.5 shows the available mathematical functions. In the table,dp indicatesdouble 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 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 ornumeric) | (same as input) | nearest integer greater than or equal to argument | ceil(-42.8) | -42 |
ceiling(dp ornumeric) | (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(dp ornumeric) | (same as input) | exponential | exp(1.0) | 2.71828182845905 |
factorial(bigint) | numeric | factorial | factorial(5) | 120 |
floor(dp ornumeric) | (same as input) | nearest integer less than or equal to argument | floor(-42.8) | -43 |
ln(dp ornumeric) | (same as input) | natural logarithm | ln(2.0) | 0.693147180559945 |
log(dp ornumeric) | (same as input) | base 10 logarithm | log(100.0) | 2 |
log10(dp ornumeric) | (same as input) | base 10 logarithm | log10(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(dp ornumeric) | (same as input) | round to nearest integer | round(42.4) | 42 |
round(vnumeric,sint) | numeric | round tos 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 ornumeric) | (same as input) | sign of the argument (-1, 0, +1) | sign(-8.4) | -1 |
sqrt(dp ornumeric) | (same as input) | square root | sqrt(2.0) | 1.4142135623731 |
trunc(dp ornumeric) | (same as input) | truncate toward zero | trunc(42.8) | 42 |
trunc(vnumeric,sint) | numeric | truncate tos 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 havingcount equal-width buckets spanning the rangeb1 tob2; returns0 orcount+1 | 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 havingcount equal-width buckets spanning the rangeb1 tob2; returns0 orcount+1 | 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; returns0 for an input less than the first lower bound; thethresholds arraymust 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 subsequentrandom() calls (value between -1.0 and 1.0, inclusive) |
Therandom() function uses a simple linear congruential algorithm. It is fast but not suitable for cryptographic applications; see thepgcrypto module for a more secure alternative. Ifsetseed() is called, the results of subsequentrandom() calls in the current session are repeatable by re-issuingsetseed() with the same argument. Without any priorsetseed() call in the same session, the firstrandom() 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 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 |
Note
Another way to work with angles measured in degrees is to use the unit transformation functionsradians()degrees()sind(30).
Table 9.8 shows the available hyperbolic functions. All these functions take arguments and return values of typedouble 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 |
