9.3. Mathematical Functions and Operators
    Mathematical operators are provided for many
    PostgreSQL types. For types without
    standard mathematical conventions
    (e.g., date/time types) we
    describe the actual behavior in subsequent sections.
   
    Table 9.4 shows 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 and are also
    available for the bit
    string types bit and bit varying, as
    shown in Table 9.14.
   
   Table 9.5 shows 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(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 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(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 | 
| log10(dpornumeric) | (same as input) | base 10 logarithm | log10(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 | araised to the power ofb | power(9.0, 3.0) | 729 | 
| power(anumeric,bnumeric) | numeric | araised 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 sdecimal 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 sdecimal places | trunc(42.4382, 2) | 42.43 | 
| width_bucket(operanddp,b1dp,b2dp,countint) | int | return the bucket number to which operandwould
       be assigned in a histogram havingcountequal-width
       buckets spanning the rangeb1tob2;
       returns0orfor
       an input outside the rangecount+1 | width_bucket(5.35, 0.024, 10.06, 5) | 3 | 
| width_bucket(operandnumeric,b1numeric,b2numeric,countint) | int | return the bucket number to which operandwould
       be assigned in a histogram havingcountequal-width
       buckets spanning the rangeb1tob2;
       returns0orfor
       an input outside the rangecount+1 | width_bucket(5.35, 0.024, 10.06, 5) | 3 | 
| width_bucket(operandanyelement,thresholdsanyarray) | int | return the bucket number to which operandwould
       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 9.6 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()degrees()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 |