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	`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 9.14.

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`
`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` 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 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.

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() and degrees() shown earlier. However, using the degree-based trigonometric functions is preferred, as that way avoids round-off error for special cases such as 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`

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