Math from scratch, part eleven: integer division

Now we come to the controversial one. As I pointed out back in 2011, the % operator is the remainder operator. When extending the division and remainder operators from naturals to integers, I require that the following conditions be true for dividend x, non-zero divisor y, quotient q and remainder r:

  • x == y * q + r
  • if x and y are non-negative then 0 <= r < y
  • (-x) / y == x / (-y) == -(x / y)

Let’s take a look at the consequences of these three facts. Continue reading

Math from scratch, part ten: integer comparisons

I’m going to use the same technique I used for Natural comparisons to do Integer comparisons: make a helper function that returns -1 if x < y, 0 if x == y and 1 if x > y, and then have every entry point simply call that helper function. This way we know that all the operators are consistent. The big difference here of course is that I do not need to have a special case that says that null sorts before any value. Continue reading

ATBG: null coalescing precedence

In the latest episode of the Coverity Development Testing Blog‘s continuing series “Ask the Bug Guys”, I dig into two questions about the null coalescing operator. This handy little operator is probably the least well understood of all the C# operators, but it is quite useful. Unfortunately, it is easy to accidentally use it incorrectly due to precedence issues.

As always, if you have questions about a bug you’ve found in a C, C++, C# or Java program that you think would make a good episode of ATBG, please send your question along with a small reproducer of the problem to We cannot promise to answer every question or solve every problem, but we’ll take a selection of the best questions that we can answer and address them on the dev testing blog every couple of weeks.

Math from scratch, part eight: integers

The integers are an extension to the naturals that closes them over subtraction. Rather than do anything fancy, I’m simply going to say that an integer is a natural with an associated sign, and that zero is always “positive”. We don’t want to end up in a situation where there are two forms of zero, since that is confusing. (We could of course have three signs, positive, negative and zero, but, meh. We don’t gain any great benefits from having a third sign.)

This time however I’m going to make a struct. C# requires that default(SomeStruct), where all the fields are their default values, be a valid value of the type. The default should logically be zero, as it is with all the built-in number types. So rather than checking for null, as we did with the reference type Natural, I’m going to check the sign field for null, which will only be possible if we’ve got a default struct. We’ll simply replace that with zero. (I am in general opposed to modifying the formal parameters of a method; I prefer to treat them as read-only variables. I’ll make an exception in this case because it keeps the code short and clear.) Continue reading

Math from scratch, part seven: division and remainder

We have only two operators left, integer division and remainder. We’ve left the most complicated two operations for last, so let’s tread carefully here.

(Only two? I’m not going to do bit shifting operators; I don’t think of them as operations on natural numbers. If you want them, obviously they are trivial: shifting right is just taking the tail, shifting left is appending a zero bit as the new head. Similarly I am not going to implement the bitwise logical operators. Nor am I going to do the unary plus operator, which wins my award for World’s Most Useless Operator. It is a no-op on both naturals and integers; if you really want it, it’s not hard to write. The unary minus operator makes no sense on naturals; the only legal operand value would be zero.) Continue reading

Happy blogoversary

Good heavens, I blew past my tenth blogoversary without even noticing it. My first blog post was on the 12th of September, 2003 and looking back I see that I made a whopping 36 posts in the two weeks that followed. That’s craziness; my publishing rate is now about a tenth of that. But of course then I had a huge backlog of material to publish that I had been collecting for years, so there you go.

Thanks all for helping me during my fabulous adventures; I appreciate it very much. Here’s to another ten years!