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From: Ian Kelly <ian.g.kelly@gmail.com>
Date: Fri, 4 Apr 2014 11:01:48 -0600
Subject: Re: Explanation of this Python language feature? [x for x in x for x in x] (to flatten a nested list)
To: Python <python-list@python.org>
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Xref: csiph.com comp.lang.python:69674

On Fri, Apr 4, 2014 at 4:08 AM, Steven D'Aprano
<steve+comp.lang.python@pearwood.info> wrote:
> On Fri, 04 Apr 2014 02:13:13 -0600, Ian Kelly wrote:
>
>> On Fri, Apr 4, 2014 at 1:52 AM, Steven D'Aprano
>> <steve+comp.lang.python@pearwood.info> wrote:
>>> py> from decimal import *
>>> py> getcontext().prec = 16
>>> py> x = Decimal("0.7777777777787516") py> y =
>>> Decimal("0.7777777777787518") py> (x + y) / 2
>>> Decimal('0.7777777777787515')
>>>
>>> "Guido, why can't Python do maths???"
>>
>> Well, you need to work within the system:
>>
>>>>> (5*x + 5*y) / 10
>> Decimal('0.7777777777787517')
>>
>> Actually, I have no idea whether that formula can be relied upon or the
>> correctness of the above was just luck.
>
>
> And what happens when x+y would have been calculated correctly, but one,
> or both, of 5*x or 5*y loses catastrophically loses accuracy due to
> overflow?
>
> py> x = 3.1e307
> py> y = 3.3e307
> py> (x+y)/2
> 3.2e+307
> py> (5*x+5*y)/10
> inf
>
> (I've used regular floats here out of laziness, the same principle
> applies to Decimals -- there will be *some* number x which is finite, but
> 5*x overflows to infinity.)

I thought that Decimals had arbitrary-precision exponents, at least in
the pure Python version.  Turns out that's wrong; although the
context.Emax can be set to any int in the pure Python version, it
can't be removed entirely.  One could just temporarily upgrade the
Emax for the above calculation, but the pure Python version was made
inconvenient to use voluntarily in CPython 3.3, and the C version has
strict limits.

In any event, the exponent limits for decimals are much higher than
for floats (the default Emax is 999999, and it can be set roughly
within the limits of C integer precision), so any case where you'll
get overflow with a Decimal is already far beyond the point where
you'd have gotten overflow with a float.