> -----Original Message-----
> From: piclist-bounces@mit.edu [mailto:piclist-bounces@mit.edu] On
Behalf
> Of William "Chops" Westfield
> Sent: 10 May 2008 01:15
> To: Microcontroller discussion list - Public.
> Subject: Re: [PIC] - Need fast divide by 14 constant routine? ( Random
> access8-bit data in PIC16F flash )
> 
> 
> On May 9, 2008, at 12:39 PM, Harold Hallikainen wrote:
> > There's a nice code generator for multiply and divide by a constant
at
> > http://www.piclist.com/techref/piclist/codegen/constdivmul.htm .
> 
> The algorithm it produces does not seem to work very well in this
> case, even if I use extra bits to produce less error in intermediate
> steps.
> I'm having trouble grasping why not :-(
> 
> It says:
> 
> ; ALGORITHM:
> ; Clear accumulator
> ; Add input / 16 to accumulator
> ; Add input / 128 to accumulator
> ; Add input / 1024 to accumulator
> ; Add input / 8192 to accumulator
> ; Add input / 65536 to accumulator
> 
> The first error is at 14.  (ALL the factors are obviously zero.)
> Even if I do:
> 
> 	(i/2 + i/16 + i/128 + i/1024 + i/8192) / 8
> 
> The first error is still at 14.
> 
> Going at it backwards isn't going to work either:
> 	x/14 = x/8 - x/32 - x/64 - x/256...
> 

This problem very often occurs with small input values when using
shift/add type multiplications.  Often you can add a fudge factor which
gives acceptable performance with small inputs (but will give the odd
off-by-one error with large values).

((i/2 + i/16 + i/128 + i/1024 + i/8192) + 1 ) / 8

Mike

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