On Fri, May 7, 2010 at 9:19 AM, Xavier Ho wrote:

2010/5/7 spir ☣

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The following discussion in the article does not tell whether one solution is the _official_ one. But: that   -4/3 != -(4/3)   looks simply wrong for me.

Denis

I believe the official decision relates to PEP 238:

No: PEP 238 is (partly) about how integer division is expressed in Python; not about its semantics. Python's choice for integer division with negative arguments goes back much further. From Misc/HISTORY: ================================== ==> RELEASE 0.9.6 (6 Apr 1992) <== ================================== [...] New features in 0.9.6: [...] - Division and modulo for long and plain integers with negative operands have changed; a/b is now floor(float(a)/float(b)) and a%b is defined as a-(a/b)*b. So now the outcome of divmod(a,b) is the same as (a/b, a%b) for integers. For floats, % is also changed, but of course / is unchanged, and divmod(x,y) does not yield (x/y, x%y)... [...] Personally, I've always liked Python's behaviour in this regard: for the few times that I've needed an 'x % y' operation that works with both positive and negative x, more often than not x-y*floor(x/y) turns out to be what I need. I've lost count of the number times I've had to write something awkward like: /* adjust for the exponent; first reduce it modulo _PyHASH_BITS */ e = e >= 0 ? e % _PyHASH_BITS : _PyHASH_BITS-1-((-1-e) % _PyHASH_BITS); in C. -- Mark

If I can diffidently put myself forward as a mathematician of sorts (not a professional one): I agree with everything that Jason says here. Mathematics is the study of abstract patterns. (No doubt, this is not an original observation.) Rob Cliffe ----- Original Message ----- From: "Jason Orendorff" To: "spir ☣" Cc: "python ideas" Sent: Friday, May 07, 2010 3:20 PM Subject: Re: [Python-ideas] integer dividion in R -- PS

2010/5/7 spir ☣ :

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I searched the def of int division in R. I could not find it in the english wikipedia,

On page 4 of Gallian, "Contemporary Abstract Algebra", we have:

Division Algorithm

Let a and b be integers with b > 0. Then there exist unique integers q and r with the property that a = bq + r where 0 <= r < b.

This is, of course, the definition Python uses. I think this is pretty standard. What might mathematicians like about this definition? Well, I think the fundamentally important thing about integer division (or any mathematical object really) is the patterns it makes:

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[a % 5 for a in range(20)] [0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4] [a // 5 for a in range(20)] [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3]

Those patterns show up in both C and Python. Do the patterns continue as you go into the negative numbers? In Python they do:

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[a % 5 for a in range(-10, 10)] [0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4] [a // 5 for a in range(-10, 10)] [-2, -2, -2, -2, -2, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1]

In C, the patterns change as you pass 0.

That is, the Python definition satisfies these mathematical properties, and the C definition doesn't:

(a + b) // b == a // b + 1 (a + b) % b == a % b

The Python definition agrees with modulo arithmetic:

-3 ≡ 2 (mod 5) http://en.wikipedia.org/wiki/Modular_arithmetic

In Python, -3 % 5 == 2 % 5 is true. In C it is false.

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But: that -4/3 != -(4/3) looks simply wrong for me.

You can either have the mirror symmetry about 0 that you want, or you can have the translational symmetry shown above. I think translational symmetry is the defining thing about integer division and therefore more important.

Of course for a programming language the question of which definition to use is a practical one: which is more useful? Ultimately practicality beats purity. But as far as purity goes (and it goes along with practicality a good long way) I think Python's integer division wins by a wide margin.

Cheers, -j _______________________________________________ Python-ideas mailing list Python-ideas@python.org http://mail.python.org/mailman/listinfo/python-ideas