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

From: Dr. Alexander Klein
Subject: [avr-libc-dev] Some question regarding FP-math
Date: Mon, 18 Jun 2012 09:53:17 +0200


I just got myself an Arduino-board to evaluate some algorithms in a more 
real-world like environment than I get with the "slowest Atom-Netbook around" 
approach. I usually prototype the algorithms in GNU-Octave, so I wondered what 
errors I'd have to expect compared to IEEE double precision math.

So, just for the fun of it, I started browsing the source of the 
FP-implementation and a few things occured to me:

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?

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?

3. In an old post 
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?

I hope this is the right place to ask these questions anyway ...

Kind regards,


Dr. Alexander Klein, Diplom-Mathematiker
Physiologisches Institut der JLU-Gießen
Aulweg 129
35392 Gießen


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