Re: TI-M: Re: TI-Math Digest V1 #22
[Prev][Next][Index][Thread]
Re: TI-M: Re: TI-Math Digest V1 #22
In a message dated 6/13/00 4:37:24 PM Mountain Daylight Time,
noveck@pluto.njcc.com writes:
> Well, considering how quickly you keep telling me the division is, why not
> just do the extra divisions by 2/3/5/7 and save the trouble of a congruency
> list in the first place?
The point of the congruency list is to cut down on the number of divisions,
since it's the division (or the check for divisibility as a whole) that is
the slowest process (from my experience). Dividing each potential
probable-prime would take the complete point out of wheeler algorithm, whose
purpose is to decrease the number of overall trial-divisions. If you have to
trial-divide potential probable-primes, which, if determined to be not
divisible by 2, 3, 5, 7, 11 (or whatever), would then be trial-divided into
the number, the whole process would be a hell of a lot slower. The "trouble"
of the congruency list pays off in that probable primes are quickly
calculated one after another, so most of the processing time is spent finding
factors of the inputted number, not determining the divisibility of potential
probable-primes.
> Were it merely different hardware, I'm betting that the differences would
be
> much more linear. And that document of yours even names some algorithm HP
> uses =)
Oh, musta missed that...
> 4 MHz Saturn with an extremely small bus width, too. HP's ROM is written
by
> really l33t programmers in ASM and some really low-level SysRPL language, I
> believe.
Yes, I've heard that as well.
> HP really wanted a good calc, and did something risky - yet very
> intelligent - to get it. IIRC, Jean-Yves wrote metakernel, a complete GUI
> replacement; there's also Bernard someone who used to be a French math
> professor and wrote Erable, a symbolic CAS of some kind; and the author of
> Alg48, another symbolic CAS type thingy (they all intermingle somehow). . .
So where's that Alg85 that I need...? ;)
JayEll