在BASH中进行数学运算

以前只知道expr，今天发现了BASH内置的let：
let: let arg [arg ...]
Each ARG is an arithmetic expression to be evaluated.  Evaluation
is done in fixed-width integers with no check for overflow, though
division by 0 is trapped and flagged as an error.  The following
list of operators is grouped into levels of equal-precedence operators.
The levels are listed in order of decreasing precedence.
id++, id–      variable post-increment, post-decrement
++id, –id      variable pre-increment, pre-decrement
-, +            unary minus, plus
!, ~            logical and bitwise negation
**              exponentiation
*, /, %         multiplication, division, remainder
+, -            addition, subtraction
<<, >>          left and right bitwise shifts
<=, >=, <, >    comparison
==, !=          equality, inequality
&               bitwise AND
^               bitwise XOR
|               bitwise OR
&&              logical AND
||              logical OR
expr ? expr : expr
conditional operator
=, *=, /=, %=,
+=, -=, <<=, >>=,
&=, ^=, |=      assignment
Shell variables are allowed as operands.  The name of the variable
is replaced by its value (coerced to a fixed-width integer) within
an expression.  The variable need not have its integer attribute
turned on to be used in an expression.
Operators are evaluated in order of precedence.  Sub-expressions in
parentheses are evaluated first and may override the precedence
rules above.
If the last ARG evaluates to 0, let returns 1; 0 is returned
otherwise.

又有新的发现：
(( … )): (( expression ))
The EXPRESSION is evaluated according to the rules for arithmetic
evaluation.  Equivalent to “let EXPRESSION”.
$a=1
$(( a++ ))
$echo $a
2
2011-07-23
一个有意思的用法：
$ echo $((2#11111111))
255
二进制11111111的值（十进制）是多少？