Re: TI-M: Re: TI-Math Digest V1 #22

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Re: TI-M: Re: TI-Math Digest V1 #22


> and it shouldn't be too hard to create the congruency list on the fly
instead
> of hard-storing it.  Just set up a list of the numbers from 2 to 2310 (for
> example), then cancel all multiples of 2, then 3, then 5, then 7, then 11,
> and then your congruency list is composed of all the uncancelled elements.

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?

> Wow, either the guy that made these tests didn't have full juice in the
> batteries or TI actually did some work in they're latest hardware or ROM
> version...

Actually, my batteries weren't too full =)  HW2 is 2 MHz faster and isn't
hampered by the screen's DMA (it's now buffered in a hardware gate array).

> Well, i think the differences can be accounted for by differenct
algorithms,
> as well as differenct calculators?  Just a thought... ;)

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 =)

> Amazing how well the little 4 mhz Saturn in the HP does compared
> to the 10 mhz m68k in the TI, though.  An engineering marvel?  Maybe...the
> Saturn does have a big advantage in that its registers are 64-bits in
length
> and have tons of ways to access different portions of those registers,
more
> so than the m68k...

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.

> Plenty more speed comparisons, mostly stuff you'd never want to enter into
> your calculator, though...

And some odd factoring in there I'd never think of - who ever woulda thought
to factor x^40 - x^30 + x^20 - x^10 + x - 1 = 0 ???????

> Yeah, kinda figured that...

That's what I want outta TI.

> Yeah, I read that somewhere; I remember the name Jean-Yves Avenard, or
> soemthing like that...  Interesting story, though, guess HP really wanted
> something out of their next graphing calculator.

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). . .

    -Scott
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