9.3. Mathematical Functions and Operators

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

Table 9-2 shows the available mathematical operators.

Table 9-2. Mathematical Operators

Operator	Description	Example	Result
`+`	addition	`2 + 3`	`5`
`-`	subtraction	`2 - 3`	`-1`
`*`	multiplication	`2 * 3`	`6`
`/`	division (integer division truncates results)	`4 / 2`	`2`
`%`	modulo (remainder)	`5 % 4`	`1`
`^`	exponentiation	`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 types bit and bit varying, as shown in Table 9-10.

Table 9-3 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 may therefore vary depending on the host system.

Table 9-3. Mathematical Functions

Function	Return Type	Description	Example	Result
`abs(x)`	(same as `x`)	absolute value	`abs(-17.4)`	`17.4`
`cbrt(dp)`	`dp`	cube root	`cbrt(27.0)`	`3`
`ceil(dp or numeric)`	(same as input)	smallest integer not less than argument	`ceil(-42.8)`	`-42`
`ceiling(dp or numeric)`	(same as input)	smallest integer not less than argument (alias for `ceil`)	`ceiling(-95.3)`	`-95`
`degrees(dp)`	`dp`	radians to degrees	`degrees(0.5)`	`28.6478897565412`
`exp(dp or numeric)`	(same as input)	exponential	`exp(1.0)`	`2.71828182845905`
`floor(dp or numeric)`	(same as input)	largest integer not greater than 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`
`random()`	`dp`	random value between 0.0 and 1.0	`random()`
`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`
`setseed(dp)`	`int`	set seed for subsequent `random()` calls (value between 0 and 1.0)	`setseed(0.54823)`	`1177314959`
`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(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`	`width_bucket(5.35, 0.024, 10.06, 5)`	`3`

Finally, Table 9-4 shows the available trigonometric functions. All trigonometric functions take arguments and return values of type double precision.

Table 9-4. Trigonometric Functions

Function	Description
`acos(x)`	inverse cosine
`asin(x)`	inverse sine
`atan(x)`	inverse tangent
`atan2(x, y)`	inverse tangent of `x/y`
`cos(x)`	cosine
`cot(x)`	cotangent
`sin(x)`	sine
`tan(x)`	tangent

9.3. Mathematical Functions and Operators

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