Re precision, etc.
Waldemar Horwat
waldemar at google.com
Fri Aug 22 13:23:52 PDT 2008
Mike Cowlishaw wrote:
> Re:
>
>> ----- Message from Waldemar Horwat <waldemar at google.com> on Fri, 22
>> Aug 2008 11:39:57 -0700 -----
>
>> Contrary to some beliefs, the different cohort members in IEEE P754
>> are *not* a valid indicator of precision. To prove this, assume
>> that the different cohort members are an indicator of precision.
>> Then evaluate:
>>
>> 3.00 + 1.00000
>>
>> IEEE P754 returns 4.00000, while the result is actually precise to
>> only two digits after the decimal point. Hence a contradiction. QED.
>
> The preservation of exponents in IEEE 754 is indeed not an indication of
> 'precision' in the significance arithmetic sense, and it was never
> intended to be. See:
>
> http://speleotrove.com/decimal/decifaq2.html#precision
>
> for some of the uses of the word 'precision' -- it is best avoided -- and
> see:
>
> http://speleotrove.com/decimal/decifaq4.html#signif
>
> for why 'significance arithmetic' makes no sense at all, beyond single
> operations and rules-of-thumb.
>
> The rules in 754 codify current 'best' practice (the rule for division,
> for example, came from the .Net and C# division operator in its decimal
> class; it has the very desirable property that 2.40/2 gives 1.20, etc.).
> The result of 1/.1 is a necessary consequence of that .. and a lesser evil
> than not preserving the information that's available. There might well be
> a better rule for division, but that was the best proposal (and that has
> been in the public drafts since 2003, so there has been plenty of time to
> make alternative proposals).
You're still making the unjustified assumption that the choice of cohort member is productive information. The examples here have shown that it is not, and it leads to bad results. Things are much simpler by not trying to make questionable distinctions between 1000000000000 and 1e12.
Waldemar
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