1.1 The universal expr arithmetic helper commandIndex

The oldest and most universal arithmetic helper command is the expr command, and it is often used in older scripts inside the historic back-quote form of Command Substitution to capture its output value:

$ expr 2 + 2 \* 9
20

$ x=`expr 2 + 2 \* 9`                 # historic `...` command substitution syntax
$ echo "$x"
20

The individual arguments to the expr command constitute the arithmetic expression to be evaluated and the value is printed on standard output. Shell meta-characters such as * (GLOB) must be quoted to hide them from the shell. All numbers and operators must be individual arguments, separated by blanks, otherwise expr simply echoes the unrecognized expression back to the user without any error message and without doing any mathematics:

$ expr 2 + 2
4

$ expr 2+2
2+2

The expr command is the original shell arithmetic helper command. It is standard and works in all Unix/Linux shells ever written.

Because expr is often an external command in many shells, not a shell built-in, it is slow. Using it in a loop that has to iterate hundreds or thousands of times will not be fast.

You can read more in the manual page expr(1).

Don’t use the legacy expr command in modern shell scripts.

1.2 The occasional let built-in arithmetic helper commandIndex

Some later Bourne shells invented and used the let built-in helper command to do arithmetic:

$ let x=4 y=5 z=x+y
$ echo "$x $y $z"
4 5 9

• Each argument is an arithmetic expression to evaluate
• Shell variables are allowed with or without leading $
• Arithmetic expressions can involve assignment of values to variables, where = is the basic assignment operator
• See the ARITHMETIC EVALUATION section of the bash man page

The let helper command is not universally available in all Bourne shells. (In particular, the dash shell used as /bin/sh under Ubuntu does not support it!) Don’t use it in new scripts.

You can read more in the BASH shell help page help let.

Don’t use the legacy let command in modern shell scripts.

1.3 The modern $((...)) syntax for Arithmetic ExpansionIndex

The modern way to do arithmetic that we will use in this course does away with all the old helper commands. Arithmetic expressions are done directly by the shell using a special dollar-and-double-parenthesis Arithmetic Expansion syntax: $((expression))

The enclosed expression is designed for arithmetic and is not GLOB expanded. Arguments do not need surrounding spaces or special quoting and variables do not need leading $:

$ echo $(( 2 + 2 * 9 ))
20

$ echo $((2+2*9))
20

$ x=2 y=3 ; echo $((x*y))
6

• The $((expression))is an Arithmetic Expansion, like a variable expansion, and it can be used anywhere that you might use a variable.
• Just as with variable substitution, the $((expression))is is replaced by the results of the evaluated Arithmetic Expression

Here is a small example shell script using basic arithmetic:

#!/bin/sh -u
linkcount=$( ls -ld "$1" | awk '{print $2}' )
subdir=$(( linkcount - 2 ))
echo "Directory $1 has link count $linkcount and $subdir sub-directories"

Running the above script:

$ ./example.sh /etc
Directory /etc has link count 183 and 181 sub-directories

$ ./example.sh /
Directory / has link count 25 and 23 sub-directories

The same script could be written as a single line, but it would have to execute the ls pipeline twice and would be be much harder to read (remember blanks are optional inside the expression):

#!/bin/sh -u
echo "Directory $1 has link count $(ls -ld "$1"|awk '{print $2}') and $(($(ls -ld "$1"|awk '{print $2}')-2)) sub-directories"

Yes, that line contains a Command Substitution inside an Arithmetic Expression. Don’t write hard-to-read code like this! Write the script on separate (shorter) lines so you can read it.

1.4 Legacy $[...] syntax for Arithmetic ExpansionIndex

Some older versions of the Bourne shells use the old syntax $[expression] for Arithmetic Expansion, but this is now obsolete and deprecated:

$ echo $[2+2*9]                     # deprecated; do not use this syntax
20

Don’t use the legacy $[...] syntax in modern shell scripts.