9.3. 數學函式及運算子

Mathematical operators are provided for manyPostgreSQLtypes. For types without standard mathematical conventions (e.g., date/time types) we describe the actual behavior in subsequent sections.

Table 9.4shows 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 typesbitandbit varying, as shown inTable 9.13.

Table 9.5shows the available mathematical functions. In the table,dpindicatesdouble 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 precisiondata 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(dpornumeric)

(same as input)

nearest integer greater than or equal to argument

ceil(-42.8)

-42

ceiling(dpornumeric)

(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(dpornumeric)

(same as input)

exponential

exp(1.0)

2.71828182845905

floor(dpornumeric)

(same as input)

nearest integer less than or equal to argument

floor(-42.8)

-43

ln(dpornumeric)

(same as input)

natural logarithm

ln(2.0)

0.693147180559945

log(dpornumeric)

(same as input)

base 10 logarithm

log(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(dpornumeric)

(same as input)

round to nearest integer

round(42.4)

42

round(vnumeric,sint)

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(dpornumeric)

(same as input)

sign of the argument (-1, 0, +1)

sign(-8.4)

-1

sqrt(dpornumeric)

(same as input)

square root

sqrt(2.0)

1.4142135623731

trunc(dpornumeric)

(same as input)

truncate toward zero

trunc(42.8)

42

trunc(vnumeric,sint)

numeric

truncate to_s_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 havingcountequal-width buckets spanning the rangeb1tob2; returns0orcount_+1for an input outside the range

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 havingcountequal-width buckets spanning the rangeb1tob2; returns0orcount_+1for an input outside the range

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; returns0for an input less than the first lower bound; thethresholdsarray_must be sorted, smallest first, or unexpected results will be obtained

width_bucket(now(), array['yesterday', 'today', 'tomorrow']::timestamptz[])

2

Table 9.6shows 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)

The characteristics of the values returned byrandom()depend on the system implementation. It is not suitable for cryptographic applications; seepgcryptomodule for an alternative.

Finally,Table 9.7shows the available trigonometric functions. All trigonometric 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()anddegrees()shown earlier. However, using the degree-based trigonometric functions is preferred, as that way avoids roundoff error for special cases such assind(30).