Fastest sorting for a specific genre of unordered numbers

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I can confirm, mrgrnk from ORDERPACK is quite fast for this problem:

$ ./sort_benchmark 
| algorithm                     | Time for 1 sort (s) |
| ----------------------------- | ------------------- |
| futils argsort                |       2.6560636E-05 |
| stdlib sort_index             |       1.5619091E-06 |
| sorting_module quicksort      |       9.1251818E-06 |
| sorter sortedIndex            |       2.1222727E-06 |
| C++ std::sort                 |       1.5285455E-06 |
| C++ std::stable_sort          |       1.4374545E-06 |
| quicksort_own_2d_swapped      |       3.7542727E-06 |
| mrgrnk                        |       1.0954545E-06 |

It’s good to know that specialized Fortran routines can still outperform the C++ standard library. With mrgrnk we’re looking at a speed-up of ×20 (for the sorting part) already compared to the original futils subroutine.

@nicholaswogan, does this mean the other part of your computation (binning?) becomes the bottleneck?

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