Re: [avr-libc-dev] Some question regarding FP-math

[David Brown]

On 07/01/2012 09:25 AM, Dmitry wrote:
> 18.06.2012 18:53, Dr. Alexander Klein:
> [...]
> > 1. Most if not all transcendental functions are implemented as power
> > series approximations, but no hints are given as to their properties
> > of approximation. Are the polynomials or maybe their derivatives
> > optimal in any L_p-sense? Can a description be found anywhere?
> Main reason was the flash usage minimization. Minor reason was a
> fast multiplication: avoid division.
>
> > 2. All we have for the time being is single precision float. Are the
> > functions for power series evaluation optimised so as to minimise
> > summation error?
> A part of internal calculations is more precision: 32-wide mantissa is
> used.
>
> > 3. In an old post
> > (http://lists.nongnu.org/archive/html/avr-libc-dev/2006-04/msg00068.html)
> > someone benchmarked basic arithmetic operations, but only for one
> > platform. How do other platforms perform? Especially, would it be
> > worthwhile to try to speed up multiplication?
> The avr-libc documention contains a good set of benchmarks. The big
> difference between avr2 and avr4 is due to multiplication.
>
> Regards,
> Dmitry.

Is there any interest in alternative implementations for some of these 
functions?  I've got some code for calculating sines and cosines using a 
table with cubic interpolation which I used on another processor.  It is 
probably a little bigger than the current avr-libc implementation, but 
not too bad - with cubic interpolation the table can be a lot smaller 
than with linear interpolation.  It is also not quite as accurate as 
power-series implementations tend to be, but it is a lot faster, and 
accurate enough for many uses.

I'm sure I could adapt the code to the avr.  But I don't know the best 
way to include such code in avr-libc - because it is not accurate enough 
for IEEE standards, it can't replace the standard implementations.

mvh.,

David