[Python-bugs-list] [ python-Bugs-457066 ] pow(a,b,c) should accept b<0

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Bugs item #457066, was opened at 2001-08-30 18:17
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Category: Python Library
Group: Feature Request
>Status: Closed
>Resolution: Rejected
Priority: 5
Submitted By: Nobody/Anonymous (nobody)
Assigned to: Tim Peters (tim_one)
Summary: pow(a,b,c) should accept b<0

Initial Comment:
You should be able to raise integers to negative powers
mod n.  If b<0, pow(a,b,c)==pow(pow(a,-1,c),-b,c)
where pow(a,-1,c) is a's multiplicative inverse mod c,
computed with the extended Euclid algorithm.  This
would be in Python's spirit of math completeness and
would save people from the trouble of having to figure
out the algorithm over and over.  

I can come up with a patch for this if it's agreed on
as desirable.


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>Comment By: Tim Peters (tim_one)
Date: 2001-08-30 22:23

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The desire is understandable but this isn't the right way 
to do it, so I'm rejecting this.  While 2.2a2 changed the 
specifics, the general rule remains that

pow(a, b, c) == a**b % c

except that the LHS may be very much faster for large 
integer arguments.

"The right way" to do modular arithmetic is to define a 
class for it, and do the full job (+ - * /, not just 
modular pow).  egcd is easy to code in Python, and because 
it's an obscure speciality need (it gets asked about maybe 
twice per year on c.l.py) doesn't really belong in the core 
even if it weren't.  I'm not even sure how 3-argument pow 
got in, but am grateful it did and don't want to press our 
luck <wink>.

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Comment By: Guido van Rossum (gvanrossum)
Date: 2001-08-30 18:49

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Of course I meant (1.0/(a**-b))%c. Sorry!

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Comment By: Guido van Rossum (gvanrossum)
Date: 2001-08-30 18:46

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Hm.

In 2.2a2, currently, pow(a, b, c) for ints a, b, c where b <
0 is defined as pow(float(a), float(b), float(c)), IOW
(1.0/(a**b))%c. This doesn't make a lot of sense for the
three-argument version though, because the result tends to
be between 0.0 and 1.0...  But it is consistent with the
(future) rule that operations on integers and floats should
give results with the same value only a different type.

Assigning to Tim, whose mathematical sensibilities are more
refined than mine...

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