[Python-ideas] [Brainstorm] Testing with Documented ABCs

[Abe Dillon]

OK. I know I made a mistake by saying, "computers are very good at
*exhaustively* searching multidimensional spaces." I should have said,
"computers are very good at enumerating examples from multi-dimensional
spaces" or something to that effect. Now that we've had our fun, can you
guys please continue in a forked conversation so it doesn't derail the
conversation?

On Wed, Nov 28, 2018 at 7:47 PM David Mertz <mertz at gnosis.cx> wrote:

> 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 <antoine at 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 <solipsis at pitrou.net
>> > <mailto:solipsis at pitrou.net> wrote:
>> >
>> >     On Wed, 28 Nov 2018 15:58:24 -0600
>> >     Abe Dillon <abedillon at gmail.com <mailto:abedillon at 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.
>> >
>> >
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