Similar to the let command,
the (( ... )) construct permits
arithmetic expansion and evaluation. In its simplest
form, a=$(( 5 + 3 )) would set
a to 5 + 3, or
8. However, this double-parentheses
construct is also a mechanism for allowing C-style
manipulation of variables in Bash, for example,
(( var++ )).
Example 8.5. C-style manipulation of variables
#!/bin/bash
# c-vars.sh
# Manipulating a variable, C-style, using the (( ... )) construct.
echo
(( a = 23 )) # Setting a value, C-style,
#+ with spaces on both sides of the "=".
echo "a (initial value) = $a" # 23
(( a++ )) # Post-increment 'a', C-style.
echo "a (after a++) = $a" # 24
(( a-- )) # Post-decrement 'a', C-style.
echo "a (after a--) = $a" # 23
(( ++a )) # Pre-increment 'a', C-style.
echo "a (after ++a) = $a" # 24
(( --a )) # Pre-decrement 'a', C-style.
echo "a (after --a) = $a" # 23
echo
########################################################
# Note that, as in C, pre- and post-decrement operators
#+ have different side-effects.
n=1; let --n && echo "True" || echo "False" # False
n=1; let n-- && echo "True" || echo "False" # True
# Thanks, Jeroen Domburg.
########################################################
echo
(( t = a<45?7:11 )) # C-style trinary operator.
# ^ ^ ^
echo "If a < 45, then t = 7, else t = 11." # a = 23
echo "t = $t " # t = 7
echo
# -----------------
# Easter Egg alert!
# -----------------
# Chet Ramey seems to have snuck a bunch of undocumented C-style
#+ constructs into Bash (actually adapted from ksh, pretty much).
# In the Bash docs, Ramey calls (( ... )) shell arithmetic,
#+ but it goes far beyond that.
# Sorry, Chet, the secret is out.
# See also "for" and "while" loops using the (( ... )) construct.
# These work only with version 2.04 or later of Bash.
exit
See also Example 11.13, “A C-style for loop” and Example 8.4, “Representation of numerical constants”.