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


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




In a message dated 6/12/00 6:47:26 PM Mountain Daylight Time, 
noveck@pluto.njcc.com writes:

> > Well, you wouldn't really need to divide the probable primes by anything,
>  > just trial-dividing the number by the probable primes.  485
>  trial-divisions
>  > takes maybe 2 or 3 seconds on the Z80 with assembly integer functions
>  (less
>  > with faster routines); much faster with an m68k, I'm sure.
>  
>  Well, if you say it's that fast, I suppose that it would be best to wheeler
>  all the way - use a modified version of the division algorithm to mod 30?

Well, actually, I would suggest to at least use a modulus 210, and with the 
89/92+'s memory, why not go as far as 2310 or 2310*13?  The memory's there, 
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.

>  Let me try it on my 89 HW2, too - last data I checked said the 89 was 
faster
>  for most anything that's just brute force work, like trial division, yet
>  loses on BCD and some of the complex stuff.

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...

>  So what accounts for these non-linear differences?  Another algorithm
>  involved somewhere?  Different size congruency tables in wheeler?

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

I actually wouldn't put any money on the fact that either HP or TI uses 
wheeler.  You'd actually have to physically "decode" the ROM routines that 
does this.  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...

>  If there's anything else interesting in there - speed differenced for other
>  operations, maybe? - can you send it to me off the list?

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

>  Yeah, you don't know the story of why HP is such a cool company???  The 
main
>  reason boils down to this one neat little story:
>  
>  The HP48, as you may know, is, by default, just a simple graphing 
calculator
>  like the z80 calcs.  But it has some very, very powerful mid-level 
scripting
>  languages that are high level, but extremely fast.  So people were actually
>  able to write their own symbolic CAS's for the 48, which brings it up to
>  almost the equivalent level of the 89.  They're actually pretty amazing.
>  And since HP releases the full specs and documents every single ROM entry
>  point, people are able to replace all of HP's interface - matrix editors,
>  text editors, menus, fonts, etc - with their own.

Yeah, kinda figured that...

>  So when the time came for HP to design their next calc, they didn't hire a
>  bunch of engineers and mathematicians who may or may not be the best at
>  their jobs - they hired these hoby coders!  Yup, they paid all these guys,
>  moved them down to Australia, and set them up to write the HP49 ROM.  At
>  first, I thought it was the most absurd thing I've ever heard, but these
>  guys wrote a great calculator what with the hardware limitations they face.
>  I commend them =)

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.

JayEll