I was assuming it was a Numba-ized function since it's purely numeric. ;-) FWIW, the theoretical limit of Python ints is limited by the fact 'int.bit_length()' is a platform native int. So my system cannot store ints larger than (2**(2**63-1)). It'll take a lot more memory than my measly 4GiB to store that number though.
So yes, that's way longer that heat-death-of-universe even before 128-bit machines are widespread. On Wed, Nov 28, 2018, 6:43 PM Antoine Pitrou <anto...@python.org wrote: > > But Python integers are variable-sized, and their size is basically > limited by available memory or address space. > > Let's take a typical 64-bit Python build, assuming 4 GB RAM available. > Let's also assume that 90% of those 4 GB can be readily allocated for > Python objects (there's overhead, etc.). > > Also let's take a look at the Python integer representation: > > >>> sys.int_info > sys.int_info(bits_per_digit=30, sizeof_digit=4) > > This means that every 4 bytes of integer object store 30 bit of actual > integer data. > > So, how many bits has the largest allocatable integer on that system, > assuming 90% of 4 GB are available for allocation? > > >>> nbits = (2**32)*0.9*30/4 > >>> nbits > 28991029248.0 > > Now how many possible integers are there in that number of bits? > > >>> x = 1 << int(nbits) > >>> x.bit_length() > 28991029249 > > (yes, that number was successfully allocated in full. And the Python > process occupies 3.7 GB RAM at that point, which validates the estimate.) > > Let's try to have a readable approximation of that number. Convert it > to a float perhaps? > > >>> float(x) > Traceback (most recent call last): > File "<stdin>", line 1, in <module> > OverflowError: int too large to convert to float > > Well, of course. So let's just extract a power of 10: > > >>> math.log10(x) > 8727169408.819794 > >>> 10**0.819794 > 6.603801339268099 > > (yes, math.log10() works on non-float-convertible integers. I'm > impressed!) > > So the number of representable integers on that system is approximately > 6.6e8727169408. Let's hope the Sun takes its time. > > (and of course, what is true for ints is true for any variable-sized > input, such as strings, lists, dicts, sets, etc.) > > Regards > > Antoine. > > > Le 29/11/2018 à 00:24, David Mertz a écrit : > > That's easy, Antoine. On a reasonable modern multi-core workstation, I > > can do 4 billion additions per second. A year is just over 30 million > > seconds. For 32-bit ints, I can whiz through the task in only 130,000 > > years. We have at least several hundred million years before the sun > > engulfs us. > > > > On Wed, Nov 28, 2018, 5:09 PM Antoine Pitrou <solip...@pitrou.net > > <mailto:solip...@pitrou.net> wrote: > > > > On Wed, 28 Nov 2018 15:58:24 -0600 > > Abe Dillon <abedil...@gmail.com <mailto:abedil...@gmail.com>> wrote: > > > Thirdly, Computers are very good at exhaustively searching > > multidimensional > > > spaces. > > > > How long do you think it will take your computer to exhaustively > search > > the space of possible input values to a 2-integer addition function? > > > > Do you think it can finish before the Earth gets engulfed by the Sun? > > > > Regards > > > > Antoine. > > > > > > _______________________________________________ > > Python-ideas mailing list > > Python-ideas@python.org <mailto:Python-ideas@python.org> > > https://mail.python.org/mailman/listinfo/python-ideas > > Code of Conduct: http://python.org/psf/codeofconduct/ > > > _______________________________________________ > Python-ideas mailing list > Python-ideas@python.org > https://mail.python.org/mailman/listinfo/python-ideas > Code of Conduct: http://python.org/psf/codeofconduct/ >
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