## Signed Division In Python (and Vial)

### Friday, April 18th, 2008:

As I was working on Vial to implement the IDIV instruction, I needed to have a signed division operator in Python. And since the x86 is a 2’s complement based, I first have to convert the number into Python’s negative (from unsigned) and only then make the operation, in my case a simple division. It was supposed to be a matter of a few minutes to code this function which gets the two operands of IDIV and return the result, but in practice it took a few bad hours.

The conversion is really easy, say we mess with 8 bits integers, then 0xff is -1, and 0×80 is -128 etc. The equation to convert it to a Python’s negative is: val – (1 << sizeof(val)*8). Of course, you do that only if the most significant bit, sign bit, is set. Eventually you return the result of val1 / val2. So far so good, but no, as I was trying to feed my IDIV with random input numbers, I saw that the result my Python’s code returns is not the same as the processor’s. This was when I started to freak out. Trying to figure out what’s the problem with my very simple snippet of code. And alas, later on I realized nothing was wrong with my code, it’s all Python’s fault.

What’s wrong with Python’s divide operator? Well, to be strict, it does not round the negative result toward 0, but towards negative infinity. Now, to be honest, I’m not really into math stuff, but all x86 processors rounds negative numbers (and positive also to be accurate) toward 0. So one would really assume Python does the same, as would C, for instance. The simple case to show what I mean is: 5/-3, in Python results in -2. Rather than -1, as the x86 IDIV instruction is expected and should return. And besides -(5/3) is not 5/-3 in Python, now it’s the time you say WTF. Which is another annoying point. But again, as I’m not a math guy, though I was speaking with many friends about this behavior, that equality (or to be accurate, inequality) is ok in real world. Seriously, what we, coders, care about real world math now? I just want to simulate a simple instruction. I really wanted to go and shout “hey there’s a bug in Python divide operator” and how come nobody saw it before? But after some digging, this behavior is really documented in Python. As much as I would hate it and many other people I know, that’s that. I even took a look at the source code of the integer division algorithm, and saw a ‘patch’ to fix the numbers to be floored if the result is negative because of C89 doesn’t define the rounding well enough.

While you’re coding something and you have a bug, you usually just start debugging your code and track it down and then fix it easily while keeping on working on the code. Because you’re in the middle of the coding phase. There are those rare times that you really get crazy when you’re absolutely sure your code is supposed to work (which it does not) and then you realize that the layer you should trust is broken (in a way). Really you want kill someone  … being a good guy I won’t do that.

Did I hear anyone say modulo?? Oh don’t even bother, but this time I think that Python returns the (math) expected result rather than the CPU. But what does it matter now? I really want only to imitate the processor’s behavior. So I had to hack that one too.

The solution after all, was to make the Python’s negative number to be absolute and remember its original sign, that we do for both operands. And then we make an unsigned division and if the signs of the input are not the same we change the sign of the result. This is because we know that the unsigned division works as the processor does and we can then use it safely.

res = x/y; if (sign_of_x != sign_of_y) res = -res;

The bottom line is that I really hate this behavior in Python and it’s not a bug, after all. I’m not sure how many people like me encountered this issue. But it’s really annoying. I don’t believe they are going to fix it in Python 3, never know though.

Anyway, I got my IDIV working now, and that was the last instruction I had to cover in my unit tests. Now It’s analysis time

### 2 Responses to “Signed Division In Python (and Vial)”

1. Matthew O'Meara says:

Just out of curiosity, how did you extract the sign of a number in python? Is there some clever bit operator that will do it? I guess,

if x < 0: sign_of_x = -1
elif not x: sign_of_x = 0
else: sign_of_x = 1

works it seems there has got to be a shorter, faster way…

cheers

-matt

2. arkon says:

Hi, thanks.
Same way as you would have done in C.
Bitwise and the number you got with a mask of the number of bits you support, for example: 2**32 – 1. This is in order to convert the number into unsigned representation.
Afterwards test the MSB by just shifting the number to the right and test the LSB.

if (((x & (2**32-1)) >> 31) & 1) == 1: print “negative number”