[libc++] Add introsort to avoid O(n^2) behavior

This commit adds a benchmark that tests std::sort on an adversarial inputs,
and uses introsort in std::sort to avoid O(n^2) behavior on adversarial
inputs.

Inputs where partitions are unbalanced even after 2 log(n) pivots have
been selected, the algorithm switches to heap sort to avoid the
possibility of spending O(n^2) time on sorting the input.
Benchmark results show that the intro sort implementation does
significantly better.

Benchmarking results before this change. Time represents the sorting
time required per element:

----------------------------------------------------------------------------------------------------------
Benchmark                                                                Time             CPU   Iterations
----------------------------------------------------------------------------------------------------------
BM_Sort_uint32_QuickSortAdversary_1                                   3.75 ns         3.74 ns    187432960
BM_Sort_uint32_QuickSortAdversary_4                                   3.05 ns         3.05 ns    231211008
BM_Sort_uint32_QuickSortAdversary_16                                  2.45 ns         2.45 ns    288096256
BM_Sort_uint32_QuickSortAdversary_64                                  32.8 ns         32.8 ns     21495808
BM_Sort_uint32_QuickSortAdversary_256                                  132 ns          132 ns      5505024
BM_Sort_uint32_QuickSortAdversary_1024                                 498 ns          497 ns      1572864
BM_Sort_uint32_QuickSortAdversary_16384                               3846 ns         3845 ns       262144
BM_Sort_uint32_QuickSortAdversary_262144                             61431 ns        61400 ns       262144
BM_Sort_uint64_QuickSortAdversary_1                                   3.93 ns         3.92 ns    181141504
BM_Sort_uint64_QuickSortAdversary_4                                   3.10 ns         3.09 ns    222560256
BM_Sort_uint64_QuickSortAdversary_16                                  2.50 ns         2.50 ns    283639808
BM_Sort_uint64_QuickSortAdversary_64                                  33.2 ns         33.2 ns     21757952
BM_Sort_uint64_QuickSortAdversary_256                                  132 ns          132 ns      5505024
BM_Sort_uint64_QuickSortAdversary_1024                                 478 ns          477 ns      1572864
BM_Sort_uint64_QuickSortAdversary_16384                               3932 ns         3930 ns       262144
BM_Sort_uint64_QuickSortAdversary_262144                             61646 ns        61615 ns       262144

Benchmarking results after this change:

----------------------------------------------------------------------------------------------------------
Benchmark                                                                Time             CPU   Iterations
----------------------------------------------------------------------------------------------------------
BM_Sort_uint32_QuickSortAdversary_1                                   6.31 ns         6.30 ns    107741184
BM_Sort_uint32_QuickSortAdversary_4                                   4.51 ns         4.50 ns    158859264
BM_Sort_uint32_QuickSortAdversary_16                                  3.00 ns         3.00 ns    223608832
BM_Sort_uint32_QuickSortAdversary_64                                  44.8 ns         44.8 ns     15990784
BM_Sort_uint32_QuickSortAdversary_256                                 69.0 ns         68.9 ns      9961472
BM_Sort_uint32_QuickSortAdversary_1024                                 118 ns          118 ns      6029312
BM_Sort_uint32_QuickSortAdversary_16384                                175 ns          175 ns      4194304
BM_Sort_uint32_QuickSortAdversary_262144                               210 ns          210 ns      3407872
BM_Sort_uint64_QuickSortAdversary_1                                   6.75 ns         6.73 ns    103809024
BM_Sort_uint64_QuickSortAdversary_4                                   4.53 ns         4.53 ns    160432128
BM_Sort_uint64_QuickSortAdversary_16                                  2.98 ns         2.97 ns    234356736
BM_Sort_uint64_QuickSortAdversary_64                                  44.3 ns         44.3 ns     15990784
BM_Sort_uint64_QuickSortAdversary_256                                 69.2 ns         69.2 ns     10223616
BM_Sort_uint64_QuickSortAdversary_1024                                 119 ns          119 ns      6029312
BM_Sort_uint64_QuickSortAdversary_16384                                173 ns          173 ns      4194304
BM_Sort_uint64_QuickSortAdversary_262144                               212 ns          212 ns      3407872

Differential Revision: https://reviews.llvm.org/D113413

0 files changed, 0 insertions, 0 deletions