Re: Really strange problem, for very bright people

The reason is probably the rounding errors incurred during processing differ when the  
order of the values changes. 

Put the following formulas into a spreadsheet and see the differences 

ROUND(1.5 * 3) * ROUND(2.5*4)  = 50 

ROUND(1.5 * 4) * ROUND(2.5*3) = 48 

Formulas are processed in chunks, so 

x = a * b * c * d 

will probably be processed something like this: 

x = a * b 
x = x * c 
x = x * d 




On 8 Aug 2003 at 20:09, Daniel Rail wrote:

> Hi,
> 
> At August 8, 2003, 16:57, Stephen Wood wrote:
> 
> > I understand that clearly, but what I'm failing to understand is how the
> > following occurs...
> 
> > 1.035 * 4.32765 * 1.673
> 
> > gives different answers to
> 
> > 1.673 * 1.035 * 4.32765 and 4.32765 * 1.673 * 1.035
> 
> > They are the same numbers, just in a different sequence....
> 
> > (Please note, these are not the numbers in my original equation, I've just
> > written some very simplified numbers to illustrate the problem)
> 
> > The only thing I can think of, is that the order of the calculation, and
> > therefore the order of precision loss, has a different outcome on the final
> > answer....
> 
> > Very strange...
> 
> It is strange, but you have to accept it as a fact-of-life for as long
> as it is the standard for the CPU's FPU(Floating-Point Unit).
> 
> Look at your equations as follows:
> (1.035 * 4.32765) * 1.673
> (1.673 * 1.035) * 4.32765
> (4.32765 * 1.673) * 1.035
> 
> The values are considered as floating-point values, especially if the
> resulting value is a floating-point. What it sent to the CPU's
> floating-point processor, is only the multiplication of 2 numbers, not
> the whole equation. So, basically, the first 2 numbers get multiplied,
> then that result(which has been approximated by the CPU) is multiplied
> by the 3rd number. And, that result is also approximated by the CPU.
> And, not to forget that the separate numbers are also approximated,
> since they are considered to be floating-point values.
> 
> -- 
> Best regards,
>  Daniel Rail
>  Senior System Engineer
>  ACCRA Group Inc. (www.accra.ca)
>  ACCRA Med Software Inc. (www.filopto.com)
> 
> 
> 
> CodeCoffer - new Delphi code protection Tool!
> http://www.delphicollection.com/public/CodeCoffer.htm
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