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## 7.3 Mathematical Functions and Operators

Mathematical operators are provided for many PostgreSQL types. For types without common mathematical conventions for all possible permutations (e.g., date/time types) we describe the actual behavior in subsequent sections.

Table 7-2 shows the available mathematical operators.

Table 7-2: Mathematical Operators
 Operator Description + addition e.g. 2 + 3 => 5 - subtraction e.g. 2 - 3 => -1 * multiplication e.g. 2 * 3 => 6 / division (integer division truncates results) e.g. 4 / 2 => 2 % modulo (remainder) e.g. 5 % 4 => 1 ^ exponentiation e.g. 2.0 ^ 3.0 => 8 |/ square root e.g. |/ 25.0 => 5 ||/ cube root e.g. ||/ 27.0 => 3 ! factorial e.g. 5 ! => 120 !! factorial (prefix operator) e.g. !! 5 => 120 @ absolute value e.g. @ -5.0 => 5 & bitwise AND e.g. 91 & 15 => 11 | bitwise OR e.g. 32 | 3 => 35 # bitwise XOR e.g. 17 # 5 => 20 ~ bitwise NOT e.g. ~1 => -2 << bitwise shift left e.g. 1 << 4 => 16 >> bitwise shift right e.g. 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 in Table 7-10.

Table 7-3 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 may therefore vary depending on the host system.

Table 7-3: Mathematical Functions
 Function Return Type Description abs(x) (same as x) absolute value e.g. abs(-17.4) => 17.4 cbrt(dp) dp cube root e.g. cbrt(27.0) => 3 ceil(dp or numeric) (same as input) smallest integer not less than argument e.g. ceil(-42.8) => -42 ceiling(dp or numeric) (same as input) smallest integer not less than argument (alias for ceil) e.g. ceiling(-95.3) => -95 degrees(dp) dp radians to degrees e.g. degrees(0.5) => 28.6478897565412 exp(dp or numeric) (same as input) exponential e.g. exp(1.0) => 2.71828182845905 floor(dp or numeric) (same as input) largest integer not greater than argument e.g. floor(-42.8) => -43 ln(dp or numeric) (same as input) natural logarithm e.g. ln(2.0) => 0.693147180559945 log(dp or numeric) (same as input) base 10 logarithm e.g. log(100.0) => 2 log(b numeric, x numeric) numeric logarithm to base b e.g. log(2.0, 64.0) => 6.0000000000 mod(y, x) (same as argument types) remainder of y/x e.g. mod(9,4) => 1 pi() dp “\pi” constant e.g. pi() => 3.14159265358979 power(a dp, b dp) dp a raised to the power of b e.g. power(9.0, 3.0) => 729 power(a numeric, b numeric) numeric a raised to the power of b e.g. power(9.0, 3.0) => 729 radians(dp) dp degrees to radians e.g. radians(45.0) => 0.785398163397448 random() dp random value between 0.0 and 1.0 e.g. random() round(dp or numeric) (same as input) round to nearest integer e.g. round(42.4) => 42 round(v numeric, s int) numeric round to s decimal places e.g. round(42.4382, 2) => 42.44 setseed(dp) int set seed for subsequent random() calls (value between 0 and 1.0) e.g. setseed(0.54823) => 1177314959 sign(dp or numeric) (same as input) sign of the argument (-1, 0, +1) e.g. sign(-8.4) => -1 sqrt(dp or numeric) (same as input) square root e.g. sqrt(2.0) => 1.4142135623731 trunc(dp or numeric) (same as input) truncate toward zero e.g. trunc(42.8) => 42 trunc(v numeric, s int) numeric truncate to s decimal places e.g. trunc(42.4382, 2) => 42.43 width_bucket(op numeric, b1 numeric, b2 numeric, count int) int return the bucket to which operand would be assigned in an equidepth histogram with count buckets, in the range b1 to b2 e.g. width_bucket(5.35, 0.024, 10.06, 5) => 3

Finally, Table 7-4 shows the available trigonometric functions. All trigonometric functions take arguments and return values of type double precision.

Table 7-4: Trigonometric Functions
 Function Description acos(x) inverse cosine asin(x) inverse sine atan(x) inverse tangent atan2(x, y) inverse tangent of x/y cos(x) cosine cot(x) cotangent sin(x) sine tan(x) tangent
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