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.pyt...@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.)
--
Steven D'Aprano
http://import-that.dreamwidth.org/
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