Why is the division result between two integers truncated?

Question

All experienced programmers in C# (I think this comes from C) are used to cast on of the integers in a division to get the decimal / double / float result instead of the int (the real result truncated).

I'd like to know why is this implemented like this? Is there ANY good reason to truncate the result if both numbers are integer?

Answer 1

C# traces its heritage to C, so the answer to "why is it like this in C#?" is a combination of "why is it like this in C?" and "was there no good reason to change?"

The approach of C is to have a fairly close correspondence between the high-level language and low-level operations. Processors generally implement integer division as returning a quotient and a remainder, both of which are of the same type as the operands.

(So my question would be, "why doesn't integer division in C-like languages return two integers ", not "why doesn't it return a floating point value?")

The solution was to provide separate operations for division and remainder, each of which returns an integer. In the context of C, it's not surprising that the result of each of these operations is an integer. This is frequently more accurate than floating-point arithmetic. Consider the example from your comment of 7 / 3 . This value cannot be represented by a finite binary number nor by a finite decimal number . In other words, on today's computers, we cannot accurately represent 7 / 3 unless we use integers! The most accurate representation of this fraction is "quotient 2, remainder 1".

So, was there no good reason to change? I can't think of any, and I can think of a few good reasons not to change. None of the other answers has mentioned Visual Basic which (at least through version 6) has two operators for dividing integers: / converts the integers to double, and returns a double, while \\ performs normal integer arithmetic.

I learned about the \\ operator after struggling to implement a binary search algorithm using floating-point division. It was really painful, and integer division came in like a breath of fresh air. Without it, there was lots of special handling to cover edge cases and off-by-one errors in the first draft of the procedure.

From that experience, I draw the conclusion that having different operators for dividing integers is confusing.

Another alternative would be to have only one integer operation, which always returns a double, and require programmers to truncate it. This means you have to perform two int->double conversions, a truncation and a double->int conversion every time you want integer division. And how many programmers would mistakenly round or floor the result instead of truncating it? It's a more complicated system, and at least as prone to programmer error, and slower.

Finally, in addition to binary search, there are many standard algorithms that employ integer arithmetic. One example is dividing collections of objects into sub-collections of similar size. Another is converting between indices in a 1-d array and coordinates in a 2-d matrix.

As far as I can see, no alternative to "int / int yields int" survives a cost-benefit analysis in terms of language usability, so there's no reason to change the behavior inherited from C.

In conclusion:

• Integer division is frequently useful in many standard algorithms.
• When the floating-point division of integers is needed, it may be invoked explicitly with a simple, short, and clear cast: (double)a / b rather than a / b
• Other alternatives introduce more complication both the programmer and more clock cycles for the processor.

Answer 2

Is there ANY good reason to truncate the result if both numbers are integer?

Of course; I can think of a dozen such scenarios easily. For example: you have a large image, and a thumbnail version of the image which is 10 times smaller in both dimensions. When the user clicks on a point in the large image, you wish to identify the corresponding pixel in the scaled-down image. Clearly to do so, you divide both the x and y coordinates by 10. Why would you want to get a result in decimal ? The corresponding coordinates are going to be integer coordinates in the thumbnail bitmap.

Doubles are great for physics calculations and decimals are great for financial calculations, but almost all the work I do with computers that does any math at all does it entirely in integers. I don't want to be constantly having to convert doubles or decimals back to integers just because I did some division. If you are solving physics or financial problems then why are you using integers in the first place? Use nothing but doubles or decimals. Use integers to solve finite mathematics problems.

Answer 3

Calculating on integers is faster (usually) than on floating point values. Besides, all other integer/integer operations ( + , - , * ) return an integer.

EDIT: As per the request of the OP, here's some addition:

The OP's problem is that they think of / as division in the mathematical sense, and the / operator in the language performs some other operation (which is not the math. division). By this logic they should question the validity of all other operations ( + , - , * ) as well, since those have special overflow rules, which is not the same as would be expected from their math counterparts. If this is bothersome for someone, they should find another language where the operations perform as expected by the person.

As for the claim on perfomance difference in favor of integer values: When I wrote the answer I only had "folk" knowledge and "intuition" to back up the claim (hece my "usually" disclaimer). Indeed as Gabe pointed out, there are platforms where this does not hold. On the other hand I found this link (point 12) that shows mixed performances on an Intel platform (the language used is Java, though).

The takeaway should be that with performance many claims and intuition are unsubstantiated until measured and found true.

Answer 4

Yes, if the end result needs to be a whole number. It would depend on the requirements.

If these are indeed your requirements, then you would not want to store a decimal and then truncate it. You would be wasting memory and processing time to accomplish something that is already built-in functionality.

Answer 5

The operator is designed to return the same type as it's input.

Edit (comment response): Why? I don't design languages, but I would assume most of the time you will be sticking with the data types you started with and in the remaining instance, what criteria would you use to automatically assume which type the user wants? Would you automatically expect a string when you need it? (sincerity intended)

Answer 6

If you add an int to an int, you expect to get an int. If you subtract an int from an int, you expect to get an int. If you multiple an int by an int, you expect to get an int. So why would you not expect an int result if you divide an int by an int? And if you expect an int, then you will have to truncate.

If you don't want that, then you need to cast your ints to something else first.

Edit: I'd also note that if you really want to understand why this is, then you should start looking into how binary math works and how it is implemented in an electronic circuit. It's certainly not necessary to understand it in detail, but having a quick overview of it would really help you understand how the low-level details of the hardware filter through to the details of high-level languages.