PostgreSQL

9.3. Mathematical Functions and Operators
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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

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`

+

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

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`	“[.quote]#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`

+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

“[.quote]#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

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

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)

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

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

+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

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`

+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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