Resuming an old post......................while crunching numberes

[aurelio]

Hi all!
I was looking for informations about the HP32sII and related benchmarks when I found this old post in the archives, a long discussion expecially between Norm and Valentin Albillo..........very, very interesting matter, then while searching I stopped on Namir Shammas site with his HP67 emulator and I agreed, reading words like:"These programs run MUCH FASTER THAN ON THE ORIGINAL CALCULATOR!!! The simulator combines the speed and power of the personal computer with the vintage technology of the HP-67 calculator. No more taking coffee breaks while the calculator is busy crunching numbers!!"

just a couple of days ago, I was trying to calculate with programs written for hp67 (stat pac), HP41c and HP42s (J.Baillard, thanks) n! of an integer (5.850 or 5,850 for the ones who use the comma in place of dot)....

Here below the porformances (crunching time)

HP67 >>>>>>>>>>>>>> 2h 15'

HP41c >>>>>>>>>>>>> 20 '

HP41c emulator>>>>> 14'

HP42s >>>>>>>>>>>>> 11'

Hp42s emulator>>>>> 3'' (woah!)

HP49g+(build in fn) 20'

not yet tested with WP34s

Really we moved in the last years from the moon to mars!

Edited: 26 Sept 2012, 9:05 a.m. after one or more responses were posted

[Gerson W. Barbosa]

Quote:

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not yet tested with WP42s

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Because there is not such a calculator, I presume :-)

[aurelio]

Quote:

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Because there is not such a calculator, I presume :-)

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sorry wp34 I meant, post edited.........

[Gerson W. Barbosa]

I know you meant the WP 34S, sorry! This only reflects our desire to have the WP 42S one day :-)

[jerome ibanes]

Hm, I'd really like to know how long this takes on the WP.

[Paul Dale]

5850! overflows double precision, although the internal numeric format will represent this just fine -- it supports truly huge exponents. The answer is of the order of 10¹⁹⁴⁹⁹ which is tiny in comparison.

We can do better of course. Log gamma just happens to be a built-in function. LnGamma of 5851 takes under a second and returns 44899.3081516.... divide this by Ln(10) and get 19499.5217715.... take the fractional portion and raising 10 to this power gives: 3.324845739721310138138472210374560 x 10¹⁹⁴⁹⁹. So 29 accurate digits in a few seconds manually and under a second from a program. I did all this in double precision mode -- single precision won't be any faster.

I'm not going to find the precise overflow threshold for factorial, however 2000! doesn't overflow double precision mode.

- Pauli

Edited: 26 Sept 2012, 6:48 a.m.

[Walter B]

2123! is the last working before an overflow error in double precision.

[Paul Dale]

What about the fractional part? Factorial is really a gamma function :-)

- Pauli

[Gerson W. Barbosa]

The program below gives a very rough approximation of x (x > 1.5), given x!:

6145 10^x A  -->  2123.51     x!  -->  7.64e6144

  EEX 100 A  -->    69.95     x!  -->  9.56e99

   EEX 10 A  -->    13.17     x!  -->  9.81e9

Gerson.

-----------------------------

001 LBL A

002 LN

003 FILL

004 1 

005 e^x

006 / 

007 Wp

008 /

009 .

010 5

011 -

012 STO 00

013 x<> Y

014 Wp

015 1/x

016 LN

017 FILL

018 1

019 0

020 LN

021 2

022 10^x

023 /

024 *

025 6

026 EEX

027 +/-

028 4

029 *

030 +/-

031 .

032 1

033 SQRT

034 +

035 *

036 1

037 +/-

038 e^x

039 SQRT

040 +

041 +/-

042 RCL+ 00

043 END

[Walter B]

By nested intervals, I get 1^HIG in double precision
(i.e. 9.999 999 999 997 216 877...E6144)
for 2 123.549 956 662 463 2!, FWIW.

Edited: 27 Sept 2012, 5:05 a.m.

[Olivier De Smet]

Tested on go49g (built-in in exact mode) on a galaxy tab10.1: 180 seconds :)

(a number of 19500 digits with 1460 '0' at the end)

P.S. I'm curious about the HP67/97 program for testing it on my emulators ...

Edited: 24 Sept 2012, 6:22 p.m.

[Frido Bohn]

<10 '' Galaxy Tab 7'' using Wolfram Alpha App (Android)

Don't tell me that's unfair advantage. I know.