feat: add per-lane popcount on batch

[DiamonDinoia]

Count the bits set in each element of an integer batch. The common kernel is the SWAR fold; NEON uses CNT with pairwise widening adds, SVE uses svcnt_x, and WASM uses i8x16.popcnt with pairwise widening extends, falling back to the common kernel for 64-bit elements.

I will add kernels in the future too when I have more of this. I need the bitwise operation for a Morton transform library I am writing.

Creating a new file because I plan to add more functions in the future:
countl_zero/countr_zero, bit_reverse, multishift, bit_deposit/bit_extract, bit_permute + bit_permute_constant, bit_matmul, GFNI kernels.

Reviewed by: Claude Opus 5 noreply@anthropic.com

[serge-sans-paille]

With the appropriate credits, https://github.com/WojciechMula/sse-popcount seems to provide relevant implementation for arch-specifics

[DiamonDinoia]

Good point. I also should have listed that the algorithm I implemented I found it on wikipedia.

[serge-sans-paille]

See also https://github.com/kimwalisch/libpopcnt/tree/master based on the paper above for an AVX2 implementation you could add to this PR (with proper credit of course)

[DiamonDinoia]

@serge-sans-paille you know about arm more than I do. Is this a good idea? should this be a new architecture entirely? If so I will purge it from here and add it in a separate PR.

[serge-sans-paille]

yeah, it should be a proper architecture :-/

[DiamonDinoia]

Okay I will do a follow up PR with the missing architectures.

[serge-sans-paille]

Could you please add (and test) a scalar version for this, that uses the version you provide in xsimd_common_bitwise.hpp?

[serge-sans-paille]

I'm not a big fan of neither the name, nor the explanation, nor the implementation.
What about the more generic:

// Create an integer of type U with Pattern P repeated as much as possible within U
template<class U, class P>
constexpr U repeat_pattern() {
    static_assert(P!=0);
    constexpr size_t pattern_size = sizeof(U) * CHAR_BITS - std::count_lzero(P); // FIXME: need to provide our implementation
    static_assert(sizeof(U) * CHAR_BIT % pattern_size == 0);
    constexpr size_t rep_count = sizeof(U) * CHAR_BIT % pattern_size;
    U result = P;
    for(size_t i = 1; i < rep_count; ++i) {
        result |= P << ( pattern_size * i );
    }
}

[DiamonDinoia]

Good point. I was wondering how to simplify this

[serge-sans-paille]

you could / should check if __builtin_popcount is available and if so, use it.

[DiamonDinoia]

We fallback on it in the scalar case. Am I missing something? This is the fallback in case that builtin is not available. I am thinking of msvc.