`np.bincount` benchmarking

gistfile1.txt

-------------+---------+-----------------+-----------------
 bins   len  |   old   |   new (naive)   |   new (opt.)
-------------+---------+-----------------+-----------------
    3      3 | 8.2e-07 | 8.2e-07 (1.00x) | 8.2e-07 (1.00x)
    3     10 | 8.2e-07 | 8.2e-07 (1.00x) | 8.2e-07 (1.00x)
    3     30 | 8.2e-07 | 8.2e-07 (1.00x) | 8.2e-07 (1.00x)
    3    100 | 9.8e-07 | 8.3e-07 (1.18x) | 8.2e-07 (1.20x)
    3    300 | 1.6e-06 | 1.2e-06 (1.33x) | 1.2e-06 (1.33x)
    3   1000 | 3.0e-06 | 2.5e-06 (1.20x) | 2.5e-06 (1.20x)
    3   3000 | 7.3e-06 | 6.3e-06 (1.16x) | 7.9e-06 (0.92x)
    3  10000 | 2.3e-05 | 1.9e-05 (1.21x) | 2.7e-05 (0.85x)
    3  30000 | 6.6e-05 | 5.6e-05 (1.18x) | 8.3e-05 (0.80x)
    3 100000 | 2.2e-04 | 1.9e-04 (1.16x) | 2.8e-04 (0.79x)
   10      3 | 8.2e-07 | 8.2e-07 (1.00x) | 8.2e-07 (1.00x)
   10     10 | 8.3e-07 | 8.2e-07 (1.01x) | 8.2e-07 (1.01x)
   10     30 | 8.2e-07 | 8.2e-07 (1.00x) | 8.2e-07 (1.00x)
   10    100 | 1.2e-06 | 8.3e-07 (1.45x) | 8.2e-07 (1.46x)
   10    300 | 1.3e-06 | 1.2e-06 (1.08x) | 1.2e-06 (1.08x)
   10   1000 | 2.9e-06 | 2.5e-06 (1.16x) | 2.5e-06 (1.16x)
   10   3000 | 7.0e-06 | 5.8e-06 (1.21x) | 8.3e-06 (0.84x)
   10  10000 | 2.1e-05 | 1.8e-05 (1.17x) | 2.9e-05 (0.72x)
   10  30000 | 6.2e-05 | 5.2e-05 (1.19x) | 8.9e-05 (0.70x)
   10 100000 | 2.1e-04 | 1.7e-04 (1.24x) | 3.0e-04 (0.70x)
   30      3 | 8.2e-07 | 8.2e-07 (1.00x) | 8.2e-07 (1.00x)
   30     10 | 8.2e-07 | 8.2e-07 (1.00x) | 8.2e-07 (1.00x)
   30     30 | 8.2e-07 | 8.2e-07 (1.00x) | 8.2e-07 (1.00x)
   30    100 | 1.2e-06 | 8.4e-07 (1.43x) | 8.2e-07 (1.46x)
   30    300 | 1.5e-06 | 1.2e-06 (1.25x) | 1.2e-06 (1.25x)
   30   1000 | 2.9e-06 | 2.5e-06 (1.16x) | 2.5e-06 (1.16x)
   30   3000 | 6.8e-06 | 5.9e-06 (1.15x) | 8.3e-06 (0.82x)
   30  10000 | 2.1e-05 | 1.8e-05 (1.17x) | 2.9e-05 (0.72x)
   30  30000 | 6.3e-05 | 5.2e-05 (1.21x) | 9.1e-05 (0.69x)
   30 100000 | 2.1e-04 | 1.7e-04 (1.24x) | 3.0e-04 (0.70x)
  100      3 | 8.2e-07 | 8.2e-07 (1.00x) | 8.2e-07 (1.00x)
  100     10 | 8.2e-07 | 8.2e-07 (1.00x) | 8.2e-07 (1.00x)
  100     30 | 8.2e-07 | 8.2e-07 (1.00x) | 8.2e-07 (1.00x)
  100    100 | 1.2e-06 | 8.9e-07 (1.35x) | 8.2e-07 (1.46x)
  100    300 | 1.6e-06 | 1.2e-06 (1.33x) | 1.3e-06 (1.23x)
  100   1000 | 2.9e-06 | 2.5e-06 (1.16x) | 2.6e-06 (1.12x)
  100   3000 | 6.8e-06 | 5.9e-06 (1.15x) | 8.2e-06 (0.83x)
  100  10000 | 2.1e-05 | 1.8e-05 (1.17x) | 3.0e-05 (0.70x)
  100  30000 | 6.2e-05 | 5.3e-05 (1.17x) | 9.0e-05 (0.69x)
  100 100000 | 2.1e-04 | 1.8e-04 (1.17x) | 3.1e-04 (0.68x)
  300      3 | 8.2e-07 | 8.2e-07 (1.00x) | 8.2e-07 (1.00x)
  300     10 | 8.3e-07 | 8.3e-07 (1.00x) | 8.3e-07 (1.00x)
  300     30 | 8.4e-07 | 8.4e-07 (1.00x) | 8.3e-07 (1.01x)
  300    100 | 1.2e-06 | 9.6e-07 (1.25x) | 8.6e-07 (1.40x)
  300    300 | 1.7e-06 | 1.2e-06 (1.42x) | 1.2e-06 (1.42x)
  300   1000 | 2.9e-06 | 2.5e-06 (1.16x) | 2.5e-06 (1.16x)
  300   3000 | 7.1e-06 | 5.9e-06 (1.20x) | 8.2e-06 (0.87x)
  300  10000 | 2.1e-05 | 1.8e-05 (1.17x) | 2.9e-05 (0.72x)
  300  30000 | 6.1e-05 | 5.0e-05 (1.22x) | 8.9e-05 (0.69x)
  300 100000 | 2.1e-04 | 1.7e-04 (1.24x) | 3.0e-04 (0.70x)
 1000      3 | 8.3e-07 | 8.3e-07 (1.00x) | 8.3e-07 (1.00x)
 1000     10 | 8.3e-07 | 8.3e-07 (1.00x) | 8.3e-07 (1.00x)
 1000     30 | 1.0e-06 | 8.3e-07 (1.20x) | 8.3e-07 (1.20x)
 1000    100 | 1.2e-06 | 1.2e-06 (1.00x) | 1.1e-06 (1.09x)
 1000    300 | 1.6e-06 | 1.4e-06 (1.14x) | 1.2e-06 (1.33x)
 1000   1000 | 3.1e-06 | 2.6e-06 (1.19x) | 2.6e-06 (1.19x)
 1000   3000 | 6.9e-06 | 5.8e-06 (1.19x) | 8.2e-06 (0.84x)
 1000  10000 | 2.1e-05 | 1.8e-05 (1.17x) | 2.9e-05 (0.72x)
 1000  30000 | 6.3e-05 | 5.1e-05 (1.24x) | 8.8e-05 (0.72x)
 1000 100000 | 2.0e-04 | 1.7e-04 (1.18x) | 3.0e-04 (0.67x)
 3000      3 | 1.2e-06 | 1.1e-06 (1.09x) | 1.2e-06 (1.00x)
 3000     10 | 1.2e-06 | 1.2e-06 (1.00x) | 1.2e-06 (1.00x)
 3000     30 | 1.2e-06 | 1.3e-06 (0.92x) | 1.2e-06 (1.00x)
 3000    100 | 1.6e-06 | 1.3e-06 (1.23x) | 1.2e-06 (1.33x)
 3000    300 | 2.1e-06 | 1.7e-06 (1.24x) | 1.7e-06 (1.24x)
 3000   1000 | 3.7e-06 | 2.9e-06 (1.28x) | 2.9e-06 (1.28x)
 3000   3000 | 7.6e-06 | 6.2e-06 (1.23x) | 8.7e-06 (0.87x)
 3000  10000 | 2.1e-05 | 1.8e-05 (1.17x) | 3.0e-05 (0.70x)
 3000  30000 | 6.2e-05 | 5.1e-05 (1.22x) | 8.9e-05 (0.70x)
 3000 100000 | 2.0e-04 | 1.7e-04 (1.18x) | 3.0e-04 (0.67x)
10000      3 | 2.2e-06 | 2.5e-06 (0.88x) | 2.5e-06 (0.88x)
10000     10 | 2.2e-06 | 2.6e-06 (0.85x) | 2.5e-06 (0.88x)
10000     30 | 2.5e-06 | 2.6e-06 (0.96x) | 2.5e-06 (1.00x)
10000    100 | 2.5e-06 | 2.8e-06 (0.89x) | 2.6e-06 (0.96x)
10000    300 | 3.1e-06 | 3.0e-06 (1.03x) | 3.1e-06 (1.00x)
10000   1000 | 8.7e-06 | 8.1e-06 (1.07x) | 1.0e-05 (0.87x)
10000  10000 | 2.3e-05 | 2.0e-05 (1.15x) | 3.2e-05 (0.72x)
10000  30000 | 6.4e-05 | 5.5e-05 (1.16x) | 9.3e-05 (0.69x)
10000 100000 | 2.1e-04 | 1.8e-04 (1.17x) | 3.1e-04 (0.68x)
-------------+---------+-----------------+-----------------
(*) Timings are averages of 100 runs of `np.bincount(x)` where
    `x = np.random.randint(bins, size=len)`. The naive method
    simply checks each item against the min and max in a single
    loop of the array, while the optimized one takes items in
    pairs, compares them to each other, then checks the smaller
    against the min and the largest against the max, so it does
    only 3 comparisons for every 2 items, instead of 3 per item.