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。
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 |
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。
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 |
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.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 |
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
.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 |