Big speed up in searchsorted if second input is also sorted

I have been leaning on searchsorted heavily for one of my projects and was playing around with how to speed things up. I found out that pre-sorting the second input for large arrays greatly speeds up the computation (even taking into account the up front cost of sorting).

x = np.random.randn(5000000)
y = np.random.randn(5000000)
x.sort()

%time np.searchsorted(x, y)
CPU times: user 10.3 s, sys: 36.7 ms, total: 10.4 s
Wall time: 10.4 s

%time y.sort(); np.searchsorted(x, y)
CPU times: user 959 ms, sys: 12.4 ms, total: 971 ms
Wall time: 971 ms

I was surprised because from the documentation it didn’t seem like searchsorted made any assumptions about whether y was sorted or not. Is this speedup purely because data locality is better after sorting y? Or is there actually an algorithmic reason for this speed up? I tried digging into the C code but couldn’t follow where this would be implemented.

Would it make sense to note and explain this behavior in the documentation? Would it make sense to add an additional argument to searchsorted(x, y, both_sorted=True), or something like merge_sorted(x, y) which assumes both x and y are sorted?

See also: https://stackoverflow.com/questions/27916710/numpy-merge-sorted-array-to-an-new-array

[juliantaylor]

What is actually providing the speedup here is the reduction in branch misses. With this dense list of keys to search the wanted next key is usually very close to the beginning of the remaining search space so the branch results are mostly going the same direction. As searching is all just comparing and branching, allowing the cpu to correctly predict most branches greatly improves performance.

[juliantaylor]

the optimization of reducing the search space is actually harmful for the unsorted performance here, we knew these cases exist when it was implemented, but at the time the binsearch was also untyped so in total the performance was still better for all cases. It might be worthwhile to tune this code again a bit for unsorted keys.