[VA] SRC #013 - Pi Day 2023 Special

[Valentin Albillo]

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Hi, J-F and 2old2randr,

J-F Garnier Wrote:

I Wrote:[...] Same here, right ?

Understood !

Good.

J-F Garnier Wrote:Certainly.

Below are the timings for a HP-71B 1BBBB (636kHz), a HP-71B 2CDCC (650kHz) and Emu71/Win in Authentic Speed, respectively. [...] Emu71/Win in Authentic Calculator Speed mode gives reproducible timings [...] So your implementation seems to be about 2x faster than mine. I see some ways to gain maybe 25%, but not much more. Interesting.

More results on Emu71/Win only:  

  N    Count      PI approx.        Timings (fast/auth.)
10E6  6079291 3.14158749068 0.8s/813s
25E6 15198180 3.14159239999 1.2s/1308s
33E6 20061593 3.14159276017 1.4s/1511s

Very good, thanks. In reciprocity, here are more of my results for you, obtained with my original Solution 1 (my original Solution 2 is slower):

      N         Count    \(\pi\) approx    |Error|     go71b  Emu71/Win  Physical
                                                 @128x    @976x     HP-71B
----------------------------------------------------------------------------
10,000,000   6,079,291  3.14158749  0.00000516    3.03"    0.40"     6' 28"
25,000,000  15,198,180  3.14159240  0.00000025    4.87"    0.64"    10' 23"
33,000,000  20,061,593  3.14159276  0.00000011    5.61"    0.74"    11' 58"

    1E8     60,792,694  3.14159307  0.00000042    9.93"    1.30"    21' 11"
    1E9    607,927,124  3.14159260  0.00000006   32.45"    4.26"    69' 14"

It would seem that my results for Emu71/Win @ 976x are ~ 2x faster than yours but please provide the speed factor (976x in mine) for comparison purposes. Also and for the same reason, please provide your timings for N = 10⁸ and 10⁹, if at all possible.

2old2randr Wrote:I have updated the run times in my original post using the Sys RPL version of the Möbius function written by Gerald H (thanks, John Keith). This turns out to be twice as fast as the times obtained on the physical HP-71B.

Thanks but unless I'm mistaken (I don't know the first word about RPL, let alone Sys RPL) you didn't include the Sys RPL code in your edited post and I think you should, lest the posted code and timings aren't synchronized with one another.

Also, as I told J-F above, please provide your timings for N = 10⁸ and 10⁹, if at all possible.

Best regards.
V.