Sadly, the interviewee was... misfortunate, and couldn't solve this, even though I practically wrote the answer on the white board.
An answer (in PHP):
function truemod($num, $mod) { $return = $num % $mod; if ($return < 0) { $return += $mod; } return $return; }
The follow-up to this (what I thought was a decidedly easy) question was going to be, "now do it without a conditional."
An answer (in PHP):
function truemod($num, $mod) { return ($mod + ($num % $mod)) % $mod; }
We didn't quite get that far, however, since the interviewee gave up instead of translating "-5 + 7" (what I wrote on the board as I was trying to prod him into an answer) into a function.
Anyway, I had run into this problem before, mainly when dealing with calendars, and had to hack my way to a solution. I brought it up to my coworkers, and what followed was a heated argument about whether "Tommy is wrong because -5 % 7 in Java is -5" (paraphrased). Since my coworker was slightly belligerent, and I found it kind of insulting, I gave him the mathematical answer, which is correct-ish, since I took group theory two and a half years ago and haven't used it since:
However inaccurate that explanation was, they didn't really buy it, but I only wrote it up to be facetious, and wasn't really meant to be taken seriously.
We ended up finding "bug" reports for both Java and PHP where people were complaining that the modulus operator wasn't accurate: it was returning negative numbers when that's not possible (for the very reasons that I so eloquently stated above). We eventually discovered the reason:
Some languages truncate integer division toward zero, which means that, for example, 15/7 = 2 and -15/7 = -2. Java, PHP, JavaScript, C#, SQL and probably (I don't have a C compiler) C/C++ work this way. These are the languages in which -5 % 7 = -5. Other languages truncate toward negative infinity (i.e. they always take the floor), which means that 15/7 = 2 and -15/7 = -3. Perl, Python, Ruby, Lisp, Haskell and Lua all work this way. These are the languages in which -5 % 7 = 2.
In conclusion, it was a stimulating exercise. Can anybody give examples of other languages and their modulus operators?
Fun time!! Try it yourself! (No, I don't know Haskell; I learned enough of it in 10 minutes to install a compiler and run one command)
PHP: <?php echo -5%7; ?> JavaScript : (why do I need a space there to be able to write "JavaScript" as one word?) alert(-5%7) Java: public class mod { public static void main(String [] args) { System.out.println(-5%7); } } C#: class mod { static void Main(string[] args) { System.Console.WriteLine(-5 % 7); } } SQL: SELECT -5%7 Ruby: puts -5%7 Perl/Python: print -5%7 Lua: io.write(-5%7); Lisp: (mod -5 7) Haskell: -5 `mod` 7
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