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.