Calculator
Recently I was asked to complete our state machine designs presented on our web site by an example of an application controlling a user interface. The suggestion was to show an calculator design similar to the example of the Visual Basic calculator, as described in the book by Horrocks: “Constructing the User Interface with Statecharts” and also discussed by Samek in his more recent book: “Practical Statecharts in C/C++”. Samek does at least establish a strong case for basing such a design on a finite state machine, after discussing many defects of the Microsoft solution, but his design can and should be improved upon.
My first idea was just to repeat this example. Before I started I made a short analysis of the topic “calculator” discovering some interesting points. Using calculators I imagined that something like a standard user interface existed. I have been sometimes confused when getting into my hands a new calculator whose behavior is different to other ones. Anyway, I never worried much about this as my interest is limited to very simple operations. If my calculations are a bit longer or more complex I use spreadsheets.
Let’s then define the calculator to be designed. The simplest calculator possesses the keys:

to define the operands: digits (0..9), number sign (±) and decimal point (.)

to define the operations: add (+), subtract (), multiply (*), divide (/), equals (=)
It has a display to show the operand typed in and the calculation result.
The few calculators I had at hand are similar but the use of the keys is not standardized:

the role of keys C and CE are interchanged; sometimes they get other names

the equals key (=) allows sometimes the calculation to be continued

the continuation of calculation after termination may be done using operation keys +*/
The calculation scheme of Samek’s example adheres to the standard one: an actuation of an operation key (+*/) is unique and defines the next operation, the following actuation of operation keys are ignored and the calculator awaits the operand. The limitation has been introduced to show that in such a case it is possible to use the key “” in a double role: as an operation key (subtract) and as a sign of the operand. The other simplification is the priority of operations: they are performed in the sequence in which they are entered, let’s call it the “arithmetic for dummies”. It means that typing “1+2*3=” you get 9 instead of the expected 7. Maybe for people who terminated their education in the first class of the grammar school such calculations make sense but most of us respect the usual priority of arithmetic operations and such calculator would be rather useless for them. Imagine you want to calculate your shopping expenses: a piece of butter, 4 bottles of beer, 3 bars of chocolate, etc; no chances to do it with such a calculator (unless it has an addtomemory feature of course). You find this kind of arithmetic in “simple” calculators. A curiosity of the Windows calculator is that in the Standard mode uses the “arithmetic for dummies” and if you switch to the Scientific mode it uses the arithmetic priority rules. Strange, the use of normal arithmetic is considered as a scientific approach! This limitation in the Samek example is obvious: to make the example as simple as possible, otherwise it will be too difficult. This is a artificial example, used to explain how to use statecharts in UML design. Obviously, UML statecharts does not work for any more practical problem.
As we prefer to work with examples taken from practice I had to decide which calculator from the few ones on my table and screen should be emulated. Eventually, I decided to design the calculator similar to one found on any computer running Windows.
Playing a little bit with this calculator I have found it has rather strange behavior in some situations. It is fairly easy to get the calculator to produce random results without any indication that the only way out is to reset it using the key “C”. For instance, trying “2/0+” you get expected “Cannot divide by 0″ but continuing with keys “CE” and “=” you get 10 (!). Maybe it is the code number of the software bug! Typing “2/0”= you get the same expected “Cannot divide by 0″ but continuing with keys “CE” and any new operand the calculator is in a loop generating “Cannot divide by 0″ which is in a way better. Of course the only solution is again the reset with the key “C”. Another example: “5+9/=” produces 10 which corresponds to “5+=” the pretended algorithm of using equals key “=”. But typing “5+9/CE=” produces an error message “Cannot divide by 0” (i.e. the clear key introduces 0 as an operand!). And now try “5+9/0=CE” and you get 100!
The calculator has another problems with unexpected sequences of operation keys. For instance, if you type “2+7*=” you get 4 (in Scientific mode). The Windows calculator manifests also a specific behavior after terminating the calculation with the equals key “=”. Repeating the key “=” performs the last operation using the result and the last operand; effectively it is the cash register function which is done normally using the key “+”. But if you change the operation and continue with the key “=” it continues using in the first step the last result as both operands. No idea what is this function for. I could not find any explanation of the described (faulty?) behavior in the voluminous Help which describes many obvious topics but does not explain how the calculator is to behave in the above described situations. In this situation the calculator ignores also entered numbers without informing the user about it. So if you type for instance”1+2=” you get 3. Entering then “4=” you get 5 which is OK in relation to the cash registration function but is confusing for the user who entered 4 having something else in mind. Investigating more carefully the behavior after entering the key “=” you will find also an algorithm that explains the strange result of previously shown operation “2+7*=”. This algorithm says: forget the last operator and operand and perform the cashier function. This might explain the behavior but what is this functionality for? Of course, the results in examples discussed in this section are different for Scientific and Standard modes. A possible use for this feature is to calculate compound interest: try 1.06 * = = = = = ; each = shows the effect of an extra 6% compound interest.
The calculator seems also to have difficulties with operation on and presentation of floating point numbers. By typing the sequence “9 sqrt =” you get 6 (as expected). By repeating the Equal sign you expect to get values decreasing by 3. It works but the 0 value is not correctly displayed. Namely the results are: 3, 3,46391…e37, 3, 6, etc. I have not investigated this problem further as the numerical computation is not my favorite topic but it is a rather strange effect.
To get a more complete picture I have taken another calculator that I have in my drawer and repeated the same exercises getting different results but also partly erroneous!
I have to admit that after that experience I was a bit shocked. I have been convinced that a calculator is a mature product delivering correct results, not only for operations like 2+2. Obviously the software in these tested examples fails in “unexpected” situations. It is more or less a known problem in software implemented according to “use cases”, where the adequacy of the set of “cases” is left to the good will, time and ability of programmers.
After that introductory work I decided to take the problem seriously and design it with StateWORKS. I have been convinced that it is possible to get a calculator which behaves as required in all situations. I will present it in few steps. You find the discussion in the Case study section in a document “Calculator”.
Tags: Calculator, Calculator design, state machine, stateworks