Arithmetic expansions

Arithmetic expansion provides a mechanism for evaluating an arithmetic expression and substituting its value. The format for arithmetic expansion is:

$((expression))

The expression is treated as if it were in double quotation marks, except that a double quotation mark inside expression is not treated specially. The shell expands all tokens in expression for parameter expansion, command substitution, and quote removal. qsh treats the result as an arithmetic expression and substitutes the value of the expression.

Arithmetic expressions

An arithmetic expression can be specified in the following situations:

in an arithmetic expansion
for each argument of the let utility
for the argument of the shift utility
for the operands of the arithmetic formats of the printf utility
for the operands to the arithmetic comparison operators of the test utility
for the argument of the ulimit utility
in the "Substring Starting at Offset" parameter expansion

qsh performs either integer or floating point arithmetic based on the setting of the float option. When the float option is set on, qsh performs floating point arithmetic.

An integer number has the format [base#]number where:

base is a decimal integer between 2 and 36 that specifies the arithmetic base. The default is base 10.
number is a non-negative number. For a base greater than 10, numbers greater than 9 or represented using a letter of the alphabet. For example, when using base 16, the decimal number 10 is represented using A.

A floating point number has the format [+|-] number[.number] [exponent] where:

number is a non-negative decimal number.
exponent is E or e followed by + or - and a non-negative decimal number.

Arithmetic expressions use the following ANSI C language operators and precedence.

(expression): Parenthesis overrides precedence rules
Unary operators: +expression Unary +; -expression Unary -; ~expression Bitwise negation; !expression Logical negation
Multiplicative operators: expression * expression Multiplication; expression / expression Division; expression % expression Remainder
Additive operators: expression + expression Addition; expression - expression Subtraction
Bitwise shift operators: expression << expression Left shift the first expression by the number of bits given in the second expression; expression >> expression Right shift the first expression by the number of bits given in the second expression
Relational operators: expression < expression Less than; expression <= expression Less than or equal to; expression > expression Greater than; expression >= expression Greater than or equal to
Bitwise AND operator: expression & expression Bitwise and where the result contains a 1 in each bit position where there is a 1 in both expressions and a 0 in all other bit positions.
Bitwise Exclusive OR operator: expression ^ expression Bitwise exclusive or where the result contains a 1 in each bit position where there is a 1 in only one of the expressions and a 0 in all other bit positions.
Bitwise OR operator: expression | expression Bitwise or where the result contains a 1 in each bit position where there is a 1 in either expression and a 0 in all other bit positions.
Logical AND operator: expression && expression Logical and where the result is true if both expressions are true
Logical OR operator: expression || expression Logical or where the result is true if one of the expressions is true
Conditional operator: expression ? expression : expression Conditional operator where when the first expression is true, the second expression is evaluated. Otherwise the third expression is evaluated.
Assignment operators: expression = expression Simple assignment; expression *= expression Assign and multiply; expression /= expression Assign and divide; expression %= expression Assign and remainder; expression += expression Assign and add; expression -= expression Assign and subtract; expression <<= expression Assign and shift left; expression >>= expression Assign and shift right; expression &= expression Assign and bitwise AND; expression ^= expression Assign and bitwise exclusive OR; expression |= expression Assign and bitwise OR

Note:

When using floating point arithmetic the remainder, left shift, right shift, bitwise AND, bitwise exclusive OR, and bitwise OR operators are not supported.

Examples

Add two decimal numbers:
```
echo $((2+2))
```
Add two hexadecimal numbers:
```
echo $((16#A + 16#20))
```
Increment the variable index by one:
```
let index+=1
```
Evaluate a complex expression:
```
echo $((5+9-2*3/2))
```
Add two floating point numbers:
```
set -F
echo $((5.75+9.157))
set +F
```