High-performance vectorised positional popcount routines for Go
===============================================================

This repository contains implementations of the positional population
count functions for Go.  Details on the algorithms used will be
published in a future research paper.

To use this library, import it as follows:

    import "github.com/clausecker/pospop"

You can then count populations using the Count8, Count16, Count32,
and Count64 functions:

    var counts [8]int
    pospop.Count8(&counts, buf)

The positional population count for buf is added to the contents of
counts.

Supported Platforms
-------------------

The kernels works on a block size of 240 or 480 bytes (depending on
whether AVX2 is available or not).  A buffer size that is a multiple
of 480 bytes and at least 10 kB in size is recommended.

Implementations are provided for the following SIMD extensions:

 * AVX-512 F/BW (amd64)
 * AVX2 (amd64, 386)
 * SSE2 (amd64, 386)
 * NEON (arm64)
 * generic kernel (all architectures)

The three kernels for amd64 correspond to the v4, v3, and v1 values
of the upcoming GOAMD64 environment variable.

Due to some required improvements in the assembler, the NEON kernel will
only be available on Go 1.16 or newer.  When building with earlier
versions of the tool chain, only the generic kernel is available.

The library automatically chooses the fastest available kernel for
the system it is running on.

Performance
-----------

As all functions
(Count8, Count16, Count32, Count64) of one set are based on the
same kernel with a different accumulation function, they all perform
equally well.  This does not apply to the generic implementations
whose performance is therefore given for every function individually.

The following performance table is grouped by the instruction set used
and the architecture it runs on.  A buffer size of 100 kB was used to
find these results.


		amd64		386		arm64		arm
avx512		82.1 GB/s	---		---		---
avx2		34.8 GB/s	31.6 GB/s	---		---
sse2		16.0 GB/s	15.6 GB/s	---		---
neon		---		---		36.9 GB/s	---
generic8	1.02 GB/s	297 MB/s	1.68 GB/s	49.0 MB/s
generic16	1.71 GB/s	1.36 GB/s	3.03 GB/s	67.1 MB/s
generic32	2.66 GB/s	2.21 GB/s	3.83 GB/s	105 MB/s
generic64	3.43 GB/s	1.89 GB/s	6.56 GB/s	82.9 MB/s

The following systems were used for benchmarks, all using Go 1.16:

 * amd64, 386: Intel(R) Xeon(R) Gold 6138 CPU @ 2.00GHz
 * arm64: Apple M1
 * arm: ARM Cortex-A72 r0p3 (Raspberry Pi 4B)

Remaining Work
--------------

 * provide assembly kernels for arm, ppcle, and others
   (hardware donations appreciated for further targets)
 * provide variants of Count16, Count32, and Count64 working on byte
   arrays

(c) 2020--2024 Robert Clausecker <[email protected]>.  All Rights Reserved.

This code is published under a 2-clause BSD license.  See the file
COPYING for details.