Non-zero arithmetic check in Python

Question

This math equation...

(4195835 / 3145727) * 3145727 - 4195835

is supposed to equate to 0. According to the book Software Testing (2nd Ed),

If you get anything else, you have an old Intel Pentium CPU with a floating-point division buga software bug burned into a computer chip and reproduced over and over in the manufacturing process.

Using Python 2.7, I get -1050108 in command line.

Using Node I get 0, just as I would in the calculator

Any deeper explanation for this? This was originally brought up due to a bug in the video game Disney's Lion King, 1994. I thought I would test the equation on a few things.

Note that just because a mathematical expression equals zero does not mean that the same computation done with floating-point has to equal zero, and that's not a bug, that's how standard floating-point computations work. You make it sound as if your book is not explaining this very clearly. — Pascal Cuoq
– Pascal Cuoq, Commented Sep 18, 2013 at 8:32
@PascalCuoq I believe my title had some info about the book that related to the question and someone modified this title. Either way the book was not trying to explain floating points or anything more than sharing "Infamous Software Error Case Studies". I just took the computation and tried myself, with at the time odd results until it was obviously rounding the division. So, no the book had no reason to explain these details or should have based on this chapter. A very good book and worth the read. — Shane
– Shane, Commented Sep 18, 2013 at 16:39

Brian Cain · Accepted Answer · 2013-09-18 02:20:45Z

12

You did integer math and not floating point math.

>>> (4195835 / 3145727) * 3145727 - 4195835
-1050108
>>> (4195835. / 3145727.) * 3145727. - 4195835.
0.0

Note that you can get the behavior you want from integers using py3k or PEP238 division.

>>> from __future__ import division
>>> (4195835 / 3145727) * 3145727 - 4195835
0.0

answered Sep 18, 2013 at 2:20

Brian Cain

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paxdiablo · Accepted Answer · 2013-09-18 02:28:25Z

9

With integer math (which is what you're using), (4195835 / 3145727) will give you 1.33382... rounded down to the integer 1.

So you effectively end up with:

  (4195835 / 3145727) * 3145727 - 4195835
=          1          * 3145727 - 4195835
=                       3145727 - 4195835
=                           -1050108

which is why you get that negative number.

You can force it to use floating point just by making one of the values floating point:

>>> (4195835. / 3145727) * 3145727 - 4195835
0.0

edited Sep 18, 2013 at 2:28

answered Sep 18, 2013 at 2:22

paxdiablo

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