[ODE] Length calculation

[Jon Watte (ODE)]

I am saying that the change you propose is not any more precise, for 
exactly the reasons you suggest -- but the additional work for the CPU 
is measurable. Thus, leave dLength3() the way it is. And if there is a 
precision difference, then there's one more operation in the chain in 
the proposed change case, which thus will be slightly less precise.

Cheers,

          / h+


Oleh Derevenko wrote:
> Hi Jon
>
> ----- Original Message ----- 
> From: "Jon Watte (ODE)"
> To: "Oleh Derevenko"
> Sent: 12 жовтня 2007 р. 05:30
> Subject: Re: [ODE] Length calculation
>
>   
>> Oleh Derevenko wrote:
>>     
>>> Why? Multiplications and divisions do not introduce substantial error. At 
>>> the same time, length calculation, as seen from dNormalize3, is much more 
>>> precise after you divide by largest vector component.
>>>
>>>       
>> Do the analysis: it doesn't help. It may hurt. With the normal 
>> formulation, you do math on the basic quantities. With the "normalized" 
>> components, multiplied by the largest value, for very long vectors, you're 
>> getting small-by-large multiplication (not any more precise), and for very 
>> short vectors you're getting division-by-small-value (not any more 
>> precise).
>>     
>
> Could you explain why is small-by-large multiplication not precise? In FPU 
> numbers are stored in exponential form. The mantissa is always in range 
> [1.0b...10.0b). So, you always multiply mantissas from range [1..2) and do 
> the addition for integer exponents. Why is it less precise to multiply small 
> by large rather than two numbers of same order? There is only loss of 
> precision if one or both numbers are denormalized. But I don't think we 
> should consider operating denormalized numbers to be a common practice. It's 
> a FPU exception condition, after all, and denormalized numbers are supported 
> just to save at least something from failed computation.
>
> Oleh Derevenko
> -- ICQ: 36361783
>
>
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