Commits on Mar 26, 2024

1. implements weighted shuffle using N-ary tree (#259) …

   This is port of firedancer's implementation of weighted shuffle:
   https://github.com/firedancer-io/firedancer/blob/3401bfc26/src/ballet/wsample/fd_wsample.c
   
   #185
   implemented weighted shuffle using binary tree. Though asymptotically a
   binary tree has better performance, compared to a Fenwick tree, it has
   less cache locality resulting in smaller improvements and in particular
   slower WeightedShuffle::new.
   
   In order to improve cache locality and reduce the overheads of
   traversing the tree, this commit instead uses a generalized N-ary tree
   with fanout of 16, showing significant improvements in both
   WeightedShuffle::new and WeightedShuffle::shuffle.
   
   With 4000 weights:
   
   N-ary tree (fanout 16):
   
       test bench_weighted_shuffle_new     ... bench:      36,244 ns/iter (+/- 243)
       test bench_weighted_shuffle_shuffle ... bench:     149,082 ns/iter (+/- 1,474)
   
   Binary tree:
   
       test bench_weighted_shuffle_new     ... bench:      58,514 ns/iter (+/- 229)
       test bench_weighted_shuffle_shuffle ... bench:     269,961 ns/iter (+/- 16,446)
   
   Fenwick tree:
   
       test bench_weighted_shuffle_new     ... bench:      39,413 ns/iter (+/- 179)
       test bench_weighted_shuffle_shuffle ... bench:     364,771 ns/iter (+/- 2,078)
   
   The improvements become even more significant as there are more items to
   shuffle. With 20_000 weights:
   
   N-ary tree (fanout 16):
   
       test bench_weighted_shuffle_new     ... bench:     200,659 ns/iter (+/- 4,395)
       test bench_weighted_shuffle_shuffle ... bench:     941,928 ns/iter (+/- 26,492)
   
   Binary tree:
   
       test bench_weighted_shuffle_new     ... bench:     881,114 ns/iter (+/- 12,343)
       test bench_weighted_shuffle_shuffle ... bench:   1,822,257 ns/iter (+/- 12,772)
   
   Fenwick tree:
   
       test bench_weighted_shuffle_new     ... bench:     276,936 ns/iter (+/- 14,692)
       test bench_weighted_shuffle_shuffle ... bench:   2,644,713 ns/iter (+/- 49,252)
   
   (cherry picked from commit 30eecd6)

   

   behzadnouri authored and mergify[bot] committed Mar 26, 2024
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