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).