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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