Re: Optimizing Memory Allocation in a Simple, but Long Function

From	Peter Otten <__peter__@web.de>
Newsgroups	comp.lang.python
Subject	Re: Optimizing Memory Allocation in a Simple, but Long Function
Date	2016-04-25 10:16 +0200
Organization	None
Message-ID	<mailman.66.1461572195.32212.python-list@python.org> (permalink)
References	(7 earlier) <CAHVvXxSwb8=a+b5WQfd3KeXTe8VuL4RMnwu3TSNp8129FJHJGw@mail.gmail.com> <CAGuRns911cXoppsS_8f657UDdCtVFhAzwY7ohafOqrsEuRq7vQ@mail.gmail.com> <CAGuRns9byxLC3pGrkPG8m-qLTzB1+PYxLHNy2=fOHcwWR21x6A@mail.gmail.com> <CAGuRns9yCR8FP9-wV5OYRKUHVtEVMsYgrtQtoB2Up-C4CTOkUw@mail.gmail.com> <nfkjop$tui$1@ger.gmane.org>

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Derek Klinge wrote:

> I found that the pattern of an additional digit of accuracy corresponding
> to 10*n did not hold as strongly for that value (I can post data if
> desired). I also got some results that seem to contradict the mathematical
> definition. For example try EulersNumber(10**15).LimitMethod(), the
> definition places this limit at e, and yet the (python) answer is >3.035.
> Please let me know if I've fouled up the implementation somehow.

There's nothing wrong with the formula, but floating point numbers have 
limited precision. At some point your calculation will become mostly a 
rounding error.

You'll see the surprising

>>> n = 10**14
>>> (1+1/n)**n
2.716110034087023
>>> n = 10**15
>>> (1+1/n)**n
3.035035206549262

on most modern computers with most programming langagues.

https://docs.python.org/3.5/tutorial/floatingpoint.html

has some introductory information.

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Re: Optimizing Memory Allocation in a Simple, but Long Function Peter Otten <__peter__@web.de> - 2016-04-25 10:16 +0200

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