Talk:Rare numbers: Difference between revisions

== the 1^st REXX version ==

This is the 1^st REXX version,   before all the optimizations were added:

numeric digits 20; w= digits() + digits() % 3 /*ensure enough decimal digs for calcs.*/

parse arg many start . /*obtain optional argument from the CL.*/

if _>=0 then do; x= _; $= $ + q

end

Pretty simple,   but slow as molasses in January.

 

of   ''rare''   numbers)   within Shyam Sunder Gupta's

<br>[http://www.shyamsundergupta.com/rare.htm <u>webpage</u>] &nbsp; have been incorporated in this REXX program.

numeric digits 20; w= digits() + digits() % 3 /*ensure enough decimal digs for calcs.*/

parse arg many start . /*obtain optional argument from the CL.*/

if _>=0 then do; x= _; $= $ + q

end

Still pretty sluggish, &nbsp; like molasses in March.

 

square containing the combination 9 or 14 as the first/last digit.

 

import (

bStart = time.Now() // restart block timing

}

{{out}}

Results on the core i7-7700 @ 3.6Ghz.

:I've also updated Nigel's C++ version with the same tweaks:

 

#include <functional>

#include <bitset>

int main(){

Rare(19);

:Compiling this with g++ brings the overall execution time down from 30 to 21 minutes in round figures. So the figures for clang or mingw may well come in at below 10 minutes now.

 

== Tweaks, C++ ==

Wringing out some more performance here, just over 5 minutes for 19 digits by themselves, and just over 6 minutes for digits 2 thru 19. See the code comments for details on what was tweaked. Curiously, I found that the g++ version executes faster than the clang++ version. Compiler arguments used: <code>g++ rare.cpp -o rare.exe -std=c++17 -O3</code><br/>Curious to see if it can go faster on a different platform - But the original executed faster on g++ than clang++ for me on my platform too. Perhaps I don't have clang++ set up the same as others?

 

/*

printf("%4s %19s %11s %10s %5s %11s %9s\n", "nth", "forward", "rt.sum", "rt.diff", "digs", "block.et", "total.et");

for (int nd = 2; nd <= max; nd++) Rare(int(nd));

{{out}}

Results on the core i7-7700 @ 3.6Ghz.

--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 14:09, 4 January 2021 (UTC)

* Do 2 through 11 digits by only looking at "middles" (no "outers") - accomplished by adding an additional definition for nLH() that takes only the function of optional long when doing less that 12 digits, limit diffs to be above zero, and sums to be above a limit at which smaller squares produced are less than the forward number itself (pow10[n-1] * 4) makeL(), makeH() return nLH() now, instead of nLH() components: Okay but no need for an extra global variable. It is really a parameter to nLH's constructor (single) as now only one constructor is required.--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 14:09, 4 January 2021 (UTC)

 

== 21+ digit rare numbers ==