SSE reduction of float vector

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Typically you generate 4 partial sums in your loop and then just sum horizontally across the 4 elements after the loop, e.g.

#include <cassert>
#include <cstdint>
#include <emmintrin.h>

float vsum(const float *a, int n)
{
    float sum;
    __m128 vsum = _mm_set1_ps(0.0f);
    assert((n & 3) == 0);
    assert(((uintptr_t)a & 15) == 0);
    for (int i = 0; i < n; i += 4)
    {
        __m128 v = _mm_load_ps(&a[i]);
        vsum = _mm_add_ps(vsum, v);
    }
    vsum = _mm_hadd_ps(vsum, vsum);
    vsum = _mm_hadd_ps(vsum, vsum);
    _mm_store_ss(&sum, vsum);
    return sum;
}

Note: for the above example a must be 16 byte aligned and n must be a multiple of 4. If the alignment of a can not be guaranteed then use _mm_loadu_ps instead of _mm_load_ps. If n is not guaranteed to be a multiple of 4 then add a scalar loop at the end of the function to accumulate any remaining elements.

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