A perfect power, and then?
nisse at lysator.liu.se
Fri Oct 26 14:50:09 CEST 2012
Torbjorn Granlund <tg at gmplib.org> writes:
> I would like to avoid fp hardware in the portable parts of GMP.
I guess this means: Avoid using functions from libm, and avoid using
floating point in critical loops. Right? There's a (non-critical)
floating point operation in mpn_perfect_power_p involving some logarithm
> Looping around umul_ppmm, keeping the msb = 1 should give a few
> correct bits.
> The error will depend on the limb size and on n. For the ASL patch
> (artificially small limbs) we might not be able to make this work.
It would make some sense to introduce an mpn_powhi, which computes an
approximation of the high n (normalized?) limbs. Would be useful also
for mpfr, I guess. It would either have a documented maximum error, or
it could return an error bound (I imagine the error bound could be
slithly different for plain binary exponentiation and window based
> I need to look into the present algorithn to get completely convinced,
> though. I was under the impression that it in practice rejected bad n
> values after a b-adic run at few-word "precision".
If I understand this correctly, most bad n ought to be rejected as soon
as the precision is xn+1 or larger.
Niels Möller. PGP-encrypted email is preferred. Keyid C0B98E26.
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