Introduction to Unix 

Math in Shell Scripts¶
Shell script variables are by default treated as strings, not numbers, which adds some complexity to doing math in shell script. To keep with script programming paradigm and allow for better math support, languages such Perl or Python would be better suited when math is desired. However, it is possible to do math with shell script. In fact, over the years, multiple facilities have been added to Unix to support working with numbers.
Note
As we will see, some of the commands used to facilitate math are a little picky about things like spaces around operators.
declare¶
You may recall, that when the text book introduced the declare statement, it said that it is not always needed. So what do you get by declaring a variable to be an integer? The following example illustrates that a declared integer is not treated as a string.
$ n=6/3
$ echo $n
6/3
$ declare i n
$ n=6/3
$ echo $n
2
When you do not need the declare statement is when you will use a program or builtin command to evaluate a math statement.
expr¶
An old Unix program that can evaluate math is expr. expr became popular in the days of the Bourne Shell, which did not support math. With Bash and Korn shell, it is generally not needed. Since it is a command, command substitution is needed. We are still treating the variable as a string. As you can see, it is picky about spaces.
$ z=5
$ z=`expr $z+1`  Need spaces around + sign.
$ echo $z
5+1
$ z=`expr $z + 1`
$ echo $z
6
let¶
A Bash and Korn shell builtin command for math is let. As you can see, it is also a little picky about spaces, but it wants the opposite of what expr wanted. let also relaxes the normal rule of needing a $ in front of variables to be read.
$ let z=5
$ echo $z
5
$ let z=$z+1
$ echo $z
6
$ let z=$z + 1 #  Spaces around + sign are bad with let
bash: let: +: syntax error: operand expected (error token is "+")
$let z=z+1 #  look Mom, no $ to read a variable.
$echo $z
7
BASH Arithmetic¶
With the BASH shell, whole arithmetic expressions may be placed inside double parenthesis. This form is more forgiving about spaces.
$ ((e=5))
$ echo $e
5
$ (( e = e + 3 ))
$ echo $e
8
$ (( e=e+4 )) #  spaces or no spaces, it doesn't matter
$ echo $e
12
+  
Addition, subtration 
++  
Increment, decrement 
* / % 
Multiplication, division, remainder 
** 
Exponentiation 
Numerical boolean expressions in Control Constructs are also expressed using double parenthesis.
if (( x > y )); then
echo "x > y"
fi
<= >= < > 
Less than or equal, greater than or equal, less than, greater than 
== != 
Equal, not equal 
! 
Logical NOT 
&& 
Logical AND 
 
Logical OR 
bc¶
What if you want to do math with floating point numbers or you have some fairly complicated math to do? Neither form of let, supports floating point numbers. The bc command is needed. But you have to treat the variables as strings.
Here is what happens when we try to do floating point math with the shell:
$let r=3.5
bash: let: r=3.5: syntax error in expression (error token is ".5")
$(( r = 3.5 ))
bash: ((: r = 3.5 : syntax error in expression (error token is ".5 ")

bc
An arbitrary precision calculator language. bc may either be run interactively, or as a shell script command. In interactive mode, type cntrld (EOF) to exit.
SYNOPSIS
bc
bc EXPRESSION
Here are some examples:
$ bc
bc 1.06
Copyright 19911994, 1997, 1998, 2000 Free Software Foundation, Inc.
This is free software with ABSOLUTELY NO WARRANTY.
For details type `warranty'.
3 + 2
5
obase=2
12
1100
<cntrld>
Remember to type cntrld (EOF) to exit from interactive mode.
$r=3.5
$s=`echo "$r + 2.2"  bc`
$echo $s
5.7
$ z = `echo $z + 1  bc`
bash: z: command not found
#  spaces around = sign are bad
(shell thing, not bc)
$ z=`echo "$z + 1"  bc`
$ echo $z
8
$ z=`echo "$z+1"  bc`  spaces don't matter with bc
$ echo $z
9
Numeric Boolean expressions:¶
If BASH double parenthesis are not used, then the test command must be used to compare integer variables. See test.
 INTEGER1 eq INTEGER2
 INTEGER1 is equal to INTEGER2
 INTEGER1 ge INTEGER2
 INTEGER1 is greater than or equal to INTEGER2
 INTEGER1 gt INTEGER2
 INTEGER1 is greater than INTEGER2
 INTEGER1 le INTEGER2
 INTEGER1 is less than or equal to INTEGER2
 INTEGER1 lt INTEGER2
 INTEGER1 is less than INTEGER2
 INTEGER1 ne INTEGER2
 INTEGER1 is not equal to INTEGER2
That is to say, the following two if
statements are identical:
if (( x < y )); then
statements
fi
if [ $x lt $y ]; then
statements
fi
And for logical expressions using floating point math, the bc command returns 1 for logical true expressions and 0 for false expressions, thus testing for result of 1 achieves a logical expression:
if [ $( echo "$t < 3.4"  bc ) eq 1 ]; then
statements
fi