9.3. 數學函式及運算子

本節提供了 PostgreSQL 的數學運算方式。對於沒有標準數學約定的型別(例如,日期/時間型別),我們將在後續部分中介紹具體的行為。

Table 9.4 列出了可用的數學運算子。

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

位元運算子僅適用於整數資料型別,也可用於位元字串型別的位元和位元變化,如 Table 9.14 所示。

Table 9.5 列出了可用的數學函數。在該表中,dp 表示雙精確度。這些函數中的許多函數都提供了多種形式,且具有不同的參數型別。除非另有說明,否則函數的任何形式都將回傳與其參數相同的資料型別。使用雙精確度資料的功能主要以主機系統的 C 函式庫實作; 因此,邊界情況下的準確性和行為可能會因主機系統而有所差異。

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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