On Thu, Jul 12, 2018 at 02:55:58PM +0300, Serhiy Storchaka wrote:

What are your thoughts about adding a new imath module for integer mathematics?

I'm not sure that we need a specific module for integer-valued maths. I think a more important change would be to allow math functions to be written in Python, not just C: - move the current math library to a private _math library; - add math.py, which calls "from _math import *". I often miss having a good, fast, integer square root function in the stdlib. I have a slow implementation here: http://code.activestate.com/recipes/577821-integer-square-root-function/ and as the commentary discusses, a lot of implementations on the internet are buggy. As well as isqrt(n), there's also nsqrt(n), to return the integer nearest to the square root of n. They're equivalent to: isqrt = floor sqrt nsqrt = round sqrt without overflowing for large n. (Presumably there's a ceiling sqrt function too, but I've never needed it, or seen anyone else use it.) As far as your other suggestions: * factorial(n) * gcd(n, m) Moving those seem like a fairly pedantic change. But if we did it, we could allow gcd to take an arbitrary number of values: gcd(*args) and add a least common multiple function to match. * as_integer_ration(x) I think that's mispelled "ratio" :-) There's currently a private function statistics._exact_ratio which does that. * binom(n, k) If we have number of combinations, I'd like to have number of permutations as well. * isprime(n) * primes() Primality testing and generation of primes is a bigger job than it might seem, probably deserving of an entire library. (Not necessarily in the std lib.) But if we did provide a "batteries included" solution, it should also include next prime and previous prime functions. For isprime(), I have a pure-Python solution which is not too shabby, capable of giving exact results for all integers up to 2**64 and probabilitistic results above that. Despite being pure Python, it's reasonably fast. In the REPL, these are essentially instantaneous to the naked eye: py> pyprimes.prev_prime(2**64) 18446744073709551557L py> pyprimes.is_prime(18446744073709551557L) True py> pyprimes.next_prime(2**64) pyprimes/__init__.py:278: MaybeComposite: 18446744073709551629 is only only probably prime warnings.warn(message, MaybeComposite) 18446744073709551629L At the moment this is Python 2 only and frankly overkill for the stdlib. I have something like a dozen different implementations for generating or testing primes, some of which are (intentionally) just awful. One of my favourite so-awful-it's-good algorithms is this one for testing whether a number is prime: def isprime(n): # Kids: don't try this at home! return not re.match(r'^1?$|^(11+?)\1+$', '1'*n) But if there is interest in a pure-Python solution, I might be able to find time to clean it up to stdlib quality. (Not the regex solution, obviously.) -- Steve