[Haskell-cafe] Re: Is logBase right?

[Eugene Kirpichov]

2009/8/22 Roberto López <plastermoso at hotmail.com>:
> If 4.0 / 2.0 was 1.9999999999999999999998, it would be ok?

I think yes. However, hardware can afford to do computations "as
accurately as possible", whereas software like Haskell Prelude can't.

>
> The real value of log10 1000 is 3 (3.0). It can be represented with accuracy
> and it should be.

Doing so would not be of much use and would impose a performance
penalty required to achieve this accuracy.

I looked into the Prelude source and saw that logBase is implemented
like x`logBase`y = log x / log y. I think it is quite a sensible
definition, and there's no point in modifying it just to make accuracy
even better than 0.000000000000000004 in certain cases where it is
possible.

To my mind, an accuracy of "the representable number closest to the
exact answer" is only required in very specific circumstances, for
example when you are converting a string to a float.

If you have a good reason to need exact real numbers, you can use a
corresponding package for exact reals.

However, if you propose an equivalently fast definition of logBase
that achieves better accuracy, I am sure it will be much welcomed.

>
> You get the accuracy value in Perl, but there is the same problem in Python.
> It's a bit discouraging.
>
>
> Eugene Kirpichov wrote:
>
>> What do you consider to be the specification of logBase? Exact
>> floating-point numbers don't exist, so it has to return an
>> approximation. The standard doesn't give any guarantees as to the
>> precision of the approximation. Is a precision of 0.00000000000004 not
>> satisfactory for you?
>>
>
>
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-- 
Eugene Kirpichov
Web IR developer, market.yandex.ru