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I’ve been asked on numerous occasions whether we can perform mathematic computations in a Unix command line environment? And how about radix conversions and calculations? The answer to both questions is, YES, using a relatively underutilised Unix tool. Like Windows, Unix systems come equiped with a desktop calculator (dc) utility. dc is a reverse polish calculator that supports unlimited precision arithmetic. Relatively few people know about this handy tool and fewer still take advantage of it. Most rely on the stripped down functionality of the expr command which, unfortunately, only handles round number computations.

Reverse polish or postfix notation is simple enough to understand and work with. Basically, it is programmed as a stack. Every numerical value (operand) that is encountered is pushed into the stack. When an operator is encountered, values are popped from the stack in Last In First Out (LIFO) order. The computed result is then pushed back into the stack. The number of elements popped depend on the type of operator being used.

The way we usually write mathematical formulas is in the standard ordered notation (or infix notation), where operators are sandwiched by the operands that they work on. The biggest advantage of postfix over infix notation is that it works solely on operators and operands alone and does not require parentheses [’(’ and ‘)’] to determine precedence. On the downside, users need to adopt a notation method which is not immediately apparent. However, once the rules are understood, converting from one to the other is a simple procedure.

There is little benefit for me to repeat the algorithm here. Refer to the links above on postfix and infix notation for the conversion algorithms. Instead, here are some quick examples of infix formulas written in postfix notation:

Infix: 10 + 11 + 12
Postfix: 10 11 + 12 +

Infix: 10 + 11 * 12
Postfix: 10 11 12 * +

Infix: (10 + 11) * 12
Postfix: 10 11 + 12 *

Once we know how to write a formula in postfix notation, computing the result in a Unix command line environment is a simple matter of invoking the dc command. The following is an example of invoking the desktop calculator and printing the result:

$ dc -e"10 11 + p"
output: 21

The ‘p’ operator simply tells dc to print the value from the top of the operand stack. If you are writing a shell script, it would be useful to store the computation result in a variable for later use. This is achieved using the usual shell notation as follows:

myresult=`dc -e"10 11 + p"`
echo $myresult

or

myresult=$(dc -e"10 11 + p")
echo $myresult

Both achieve the same result of assigning the value of the computation to the variable ‘myresult’ which can then be reused for future operations. Some are probably thinking big deal. We can do the same using the expr command (e.g. expr 10 + 11). The thing is that expr won’t work with decimal values. ‘expr 10.5 + 11.3′ will throw out an ‘non-numeric argument’ error where as ‘dc -e”10.5 11.3 + p”‘ prints the correct result of 21.8.

One other convenient use of ‘dc’ is to convert between radices. We usually write values in a base-10 decimal format. However, we may have occasion to use a different base radix. This is especially true when dealing with computer generated input/output that may include binary, octal, decimal, or hexadecimal values. ‘dc’ provides two operators to define the input and output radix.

i: Pops the value off the top of the stack and sets it as the input radix.
o: Pops the value off the top of the stack and sets it as the output radix.

The default input and output radix is base-10. Examples for converting between the four common radices are as follows:

While these are the standard conversions, you can just as easily apply the conversion to any other base radix of your choice.

You might also like to take a look at bc which is an arbitrary precision calculator language. With a combination of dc, bc, and other math libraries and utilities, you have pretty much free reign over mathematical computation within a shell environment. As usual, read the manuals for more indepth information on the commands. I’ll leave you to discover other math utilities and their usage. Until next time, good luck and happy scripting.