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Optimize select_bit #52

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Optimize select_bit #52

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Commits on Aug 21, 2023

  1. select_bit: Optimize for AArch64 

    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.)
    @jmr
    jmr committed Aug 21, 2023
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  2. select_bit: Use byte-serial version for 32-bit 

    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.
    @jmr
    jmr committed Aug 21, 2023
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  3. select_bit: Use a lookup table 

    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`.
    @jmr
    jmr committed Aug 21, 2023
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