Optimize select_bit #52
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ARM NEON has a byte-wise popcount instruction, which helps to optimize `select_bit` and `PopCount::count`. Use it for AArch64 (64-bit ARM). 15% speedup for `Rank1`, 4% for `Select0` and 3% for `Select1`. (60% for `PopCount::count` itself.)
This gives a 9% speedup on `select0` and 7% on `select1`. (Tested on Pixel 3 in armeabi-v7a mode.) This is likely because the branches of this unrolled linear search are more predictable than the binary search that was used previously.
Instead of computing `(counts | MASK_80) - ((i + 1) * MASK_01)`, we pre-compute a lookup table ``` PREFIX_SUM_OVERFLOW[i] = (0x80 - (i + 1)) * MASK_01 = (0x7F - i) * MASK_01 ``` then use `counts + PREFIX_SUM_OVERFLOW[i]`. This uses a `UInt64[64]` or 0.5kiB lookup table. The trick is from: Gog, Simon and Matthias Petri. “Optimized succinct data structures for massive data.” Software: Practice and Experience 44 (2014): 1287 - 1314. https://www.semanticscholar.org/paper/Optimized-succinct-data-structures-for-massive-data-Gog-Petri/c7e7f02f441ebcc0aeffdcad2964185926551ec3 This gives a 2-3% speedup for `BitVector::select0`/`select1`.
glebm
approved these changes
Aug 21, 2023
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ARM NEON has a byte-wise popcount instruction, which helps to optimize
select_bitandPopCount::count. Use it for AArch64 (64-bit ARM).15% speedup for
Rank1, 4% forSelect0and 3% forSelect1.(60% for
PopCount::countitself.)This gives a 9% speedup on
select0and 7% onselect1.(Tested on Pixel 3 in armeabi-v7a mode.)
This is likely because the branches of this unrolled linear
search are more predictable than the binary search that was
used previously.
Instead of computing
(counts | MASK_80) - ((i + 1) * MASK_01),we pre-compute a lookup table
then use
counts + PREFIX_SUM_OVERFLOW[i].This uses a
UInt64[64]or 0.5kiB lookup table. The trick is from:Gog, Simon and Matthias Petri. “Optimized succinct data structures for
massive data.” Software: Practice and Experience 44 (2014): 1287 - 1314.
https://www.semanticscholar.org/paper/Optimized-succinct-data-structures-for-massive-data-Gog-Petri/c7e7f02f441ebcc0aeffdcad2964185926551ec3
This gives a 2-3% speedup for
BitVector::select0/select1.