On Tue, Oct 20, 2020 at 01:59:25PM +0100, Dima Pasechnik wrote:
>
> Why don't you use an already available fast implementation in C or C++?
> In this case, SageMath uses NTL https://shoup.net/ntl/
> which is very fast, and written by an expert in computational number theory.
Well, in this case it would help. However, many computations
in FriCAS use operations on polynomials with finite field
coefficients. Delegating all those users of polynomials
with finite field coefficients to external libraries is
unrealistic (I think that is some cases FriCAS is the
only system which can do given computation). More attractive
would be to delegate say polynomial multiplication to
external library. But this is tricky performancewise.
FriCAS performs a lot of operations on relativly small
polynomials. For such polynomials cost of external
call and (usually) data convertion is significant.
To illustrate what I mean let me say that whan I
implemented U32VectorPolynomialOperations I did some
benchmarks comparing it with Sage. For small degrees
FriCAS was faster. I am pretty sure that low level
C libraries used by Sage were faster than FriCAS
routines. But Sage overhead apparently was enough
to change which routines where faster when used from
higher level code. It is quite likely that calls
from FriCAS to C would cause similar overhead.
--
Waldek Hebisch
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