[Python-ideas] Add the imath module

[Tim Peters]

[Chris Angelico, on "probable prime" testers]

> You can say that about algorithms easily enough. My point is that this
> ought to be a constraint on the function - implementations may choose
> other algorithms, but they MUST follow one pattern or the other,
> meaning that a Python script can depend on it without knowing the
> implementation. Like guaranteeing that list.sort() is stable without
> stipulating the actual sort algo used.
>

I agree!  Don't worry about it - if this module gets added, I'll make sure
of it.  My own "probable prime" function starts like so:

def pp(n, k=10):
    """
    Return True iff n is a probable prime, using k Miller-Rabin tests.

    When False, n is definitely composite.
    """

In the context of algorithmic number theory, "no false negatives" is
implied by that context, but it should be spelled out anyway.  A "probable
prime", by definition, is an integer that satisfies some property that
_all_ primes satisfy, but that some composites may satisfy too.  The
variation among probable prime algorithms is in which specific
property(ies) they test for.

For example:

def pp1(n):
    return True

meets the promise, but is useless ;-)

def pp2(n):
    return  n % 3 != 0 or n == 3

is slightly less useless.

But

def pp3(n):
    return n % 3 != 0

would be incorrect, because pp3(3) returns False - `n % 3 != 0` is not a
property that all primes satisfy.
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