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result accumulation - Monitoring progress of long calculations


I've came upon a few methods of how to display "processing" information while Mathematica is running. But, from what I've understood, this only works in between lines of codes. Is it possible to display a "how far is something being processed"-information during a line of code?


For example, I wish to Map a function g over a very large list, for example:


Map[ g , Sort[Apply[Join, Table[Range[1000000], {1000}]]] ],

which will take quite some time. Now, because the list consists of 1000 times every number between 1 and 1000000, could it be possible do display (as a temporary display), which number is being processed?



I have thought of using Print and changing the function being mapped to


Map[ (Print[#]; g[#]) &, Sort[Apply[Join, Table[Range[1000000], {1000}]]] ],

but I was wondering if there was any "faster" method, which wouldn't print out every number of the list, but for example every 1000th number. I have thought about If before Print, but I think this method would take too much extra time.



Answer



Or you can use something like this:


Monitor[
    Table[Length@FactorInteger[2^n - 1], {n, 50, 500, 50}], 
    Grid[{{Text[Style["Integer Factorization :", Darker[Blue, 0.66]]],
        ProgressIndicator[n, {50, 500}]},

    {Text[Style["Factoring 2^n-1 with n : ", Darker[Blue, 0.66]]], n}},
Alignment -> Left, Dividers -> Center]]

enter image description here


Sorry for not using your computation, since it did not make sense to me, which is my fault. That's why I've chosen another, just to display my approach.


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