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chapter(Arithmetic Evaluation)
ifzman(\
sect(Arithmetic Evaluation)
)\
cindex(arithmetic evaluation)
cindex(evaluation, arithmetic)
An ability to perform integer arithmetic is provided with the builtin tt(let).
findex(let, use of)
Evaluations are performed using em(long) arithmetic.
A leading `tt(0x)' or `tt(0X)' denotes hexadecimal.
Otherwise, numbers are of the form `[var(base)tt(#)]var(n)',
where var(base) is a decimal number between two and thirty-six
representing the arithmetic base and var(n)
is a number in that base (for example, `tt(16#ff)' is 255 in hexadecimal).
If var(base) is omitted
then base 10 is used.  For backwards compatibility the form
`tt([)var(base)tt(])var(n)' is also accepted.

cindex(arithmetic operators)
cindex(operators, arithmetic)
An arithmetic expression uses nearly the same syntax, precedence, and
associativity of expressions in C.
The following operators are supported (listed in decreasing order
of precedence):

startsitem()
sitem(tt(PLUS() - ! ~ PLUS()PLUS() --))(unary plus/minus, logical NOT, complement, {pre,post}{in,de}crement)
sitem(tt(<< >>))(bitwise shift left, right)
sitem(tt(&))(bitwise AND)
sitem(tt(^))(bitwise XOR)
sitem(tt(|))(bitwise OR)
sitem(tt(**))(exponentiation)
sitem(tt(* / %))(multiplication, division, modulus (remainder))
sitem(tt(PLUS() -))(addition, subtraction)
sitem(tt(< > <= >=))(comparison)
sitem(tt(== !=))(equality and inequality)
sitem(tt(&&))(logical AND)
sitem(tt(|| ^^))(logical OR, XOR)
sitem(tt(? :))(ternary operator)
sitem(tt(= PLUS()= -= *= /= %= &= ^= |= <<= >>= &&= ||= ^^= **=))(assignment)
sitem(tt(,))(comma operator)
endsitem()

The operators `tt(&&)', `tt(||)', `tt(&&=)', and `tt(||=)' are short-circuiting,
and only one of the latter two expressions in a ternary operator
is evaluated.  Note the precedence of the bitwise AND, OR,
and XOR operators.

An expression of the form `tt(#\)var(x)' where var(x) is any character
gives the ascii value of this character and an expression of the form
`tt(#)var(foo)' gives the ascii value of the first character of the value
of the parameter var(foo).

Named parameters and subscripted arrays can be referenced by name within an
arithmetic expression without using the parameter expansion syntax.

An internal integer representation of a named parameter
can be specified with the tt(integer) builtin.
cindex(parameters, integer)
cindex(integer parameters)
findex(integer, use of)
Arithmetic evaluation is performed on the value of each
assignment to a named parameter declared integer
in this manner.

Since many of the arithmetic operators require
quoting, an alternative form of the tt(let) command is provided.
For any command which begins with a tt(LPAR()LPAR()),
all the characters until a matching tt(RPAR()RPAR())
are treated as a quoted expression.
More precisely, `tt(LPAR()LPAR()) ... tt(RPAR()RPAR())'
is equivalent to `tt(let ")...tt(")'.