roots

Jason Moxham J.L.Moxham@maths.soton.ac.uk
Fri, 1 Nov 2002 20:47:31 +0000


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Attached is a mainly mpn-ified version , its still preliminary with a few=
=20
thing still to do.For cube roots and higher the cutoff point is about 200=
=20
bits now , I should be able to lower this some more , and perhaps increas=
e=20
the speed for large n and k.
If gmp is going to have a high half multiplication then I can take advant=
age=20
of that (really easy).
One thing should be considered , is that the algortihm does not calculate=
 the=20
remainder , which can take much longer than the root , although still fas=
ter=20
than the current code.
The current mpz_root fn returns an integer indicating whether the root is=
=20
exact , perhaps a new mpz_roots fn which just does the root calculation=20
should be added to take advantage of this.The mpz_perfect_power_p fn is a=
lso=20
better to write in terms of p-adic or the underlying nroot fns rather tha=
n=20
the much slower mpn_rootrem and I have a go at this soon.

I was going to mention that the inversion can be faster than the existing=
=20
mpz_tdiv_qr , but that is probably wrong now .=20

Note: when I get the snapshot all I get is the current 4.1.1 , not the 4.=
2-pre=20
?

Aside from the quick division test above , I an concentrating on cube roo=
ts or=20
higher , for sqrts or inversion my code is slower (so far)

jason





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