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