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Re: Some question regarding FP-math
by David Brown-4
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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
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> 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
_______________________________________________
AVR-libc-dev mailing list
AVR-libc-dev@...
https://lists.nongnu.org/mailman/listinfo/avr-libc-dev
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