On May 9, 2008, at 6:27 PM, John Coppens wrote:
> I believe this is not a precise division. What is being done is  
> multiply
> really by 1/14 in decimal, or 0.071...  You selected a precision of 16
> bits (?), so the error will probably be in the order of 1. It's quite
> probable that the first one fails.

Right, that's PART of it.  But multiplying (floatingpoint) by
	(1.0/16 + 1.0/128 + 1.0/1024 + 1.0/8192 + 1.0/65536)

over the input range (1..65535) gives only 1/3 the number of errors  
(about 7000) as adding the set of integer divisions. Note that this  
point is about as far as it makes sense to take the binary fractions;  
for the 16bit input, anything smaller than i/65536 is going to be  
zero anyway; that's one of the factors that led me to expect better  
results.  :-(

> The error will always be +/- 1, but if you selected 16 bit precision,
> that means only an error of 1 in 4000 or so (65536/14). Which, if you
> look to replace fractional division by a simple algorithm, is quite  
> good.


Sounds good, doesn't it?  But 14/14 = 0 is 100% error !

It seems like a similar algorithm ought to be able to do better.

BillW

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