Add selection algorithms nthElement heapSelect and median

[oittaa]

Selection algorithms come up from time to time, for example here: #9890

This pull request adds the following public functions to std.select. Is this the correct place or should we put them to std.sort even though they aren't exactly sorting algorithms?

• nthElement
• nthElementContext
• heapSelect
• heapSelectContext
• median

I tried to check how the current sorting algorithm work and more or less copy their behavior, but there are still couple of open questions.

• How to handle empty arrays? Currently we use assert.
• Is the argument order correct for nthElement and heapSelect, especially n?
• Are the arguments for median good enough or what should be done to them?
• There are two private functions that are exactly the same in std.sort or std.sort.pdq: partitionEqual and siftDown should we share the implementations somehow?
• And couple of functions are almost the same, but since we don't care about the exact order here we drop some functionality: sort3, chosePivot, partition Same as above, do we implement them here with the minor modifications (and possible minor speedups), but duplicate code?
• Are there enough tests?

[adworacz]

Any thoughts on additional inclusion of sorting networks, particularly for finding things like median?

Ref:

1. https://github.com/bertdobbelaere/SorterHunter
2. https://bertdobbelaere.github.io/sorting_networks.html
3. https://bertdobbelaere.github.io/median_networks.html

Disclaimer: I implemented some of the above in comptime for my video processing plugin: https://github.com/adworacz/zsmooth/blob/master/src/common/sorting_networks.zig

[alichraghi]

• How to handle empty arrays? Currently we use assert.
  Sounds about right. It's better to catch invalid usage at the call site to prevent UB.

• Is the argument order correct for nthElement and heapSelect, especially n?
  LGTM.

• Are the arguments for median good enough or what should be done to them?
  LGTM.

• There are two private functions that are exactly the same in std.sort or std.sort.pdq: partitionEqual and siftDown should we share the implementations somehow?
  Yes.

• And couple of functions are almost the same, but since we don't care about the exact order here we drop some functionality: sort3, chosePivot, partition Same as above, do we implement them here with the minor modifications (and possible minor speedups), but duplicate code?
  I think they should be public and the duplicated code must be removed.

[oittaa]

• I think they should be public and the duplicated code must be removed.

EDIT:
I put them to std.sort. If there are better ideas, they're welcomed. At first I put them under std.sort.utils but I noticed that for example std.crypto.utils will be removed in the future.

[oittaa]

Since I didn't find anything from the math library that calculates a mean in an overflow safe manner, in the median function for integers it's now done with the common bit manipulation (a&b) + ((a^b)>>1). Mean for two floats is calculated a/2 + b/2 where we might lose some precision since I have no idea how the compiler will optimize that.