# 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 types`bit`and`bit varying`, as shown inTable 9.13.

Table 9.5shows the available mathematical functions. In the table,`dp`indicates`double 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 with`double precision`data 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(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(ynumeric`,`xnumeric`) `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` `log(bnumeric`,`xnumeric`) `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(adp`,`bdp`) `dp` `a`_raised to the power of`b`_ `power(9.0, 3.0)` `729` `power(anumeric`,`bnumeric`) `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(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(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(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 which`operand`_would be assigned in a histogram having`count`equal-width buckets spanning the range`b1`to`b2`; returns`0`or`count`_+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 which`operand`_would be assigned in a histogram having`count`equal-width buckets spanning the range`b1`to`b2`; returns`0`or`count`_+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 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 9.6shows 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 subsequent`random()`calls (value between -1.0 and 1.0, inclusive)

The characteristics of the values returned by`random()`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 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 roundoff error for special cases such as`sind(30)`.

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