horizontal sum of 8 packed 32bit floats

问题:

If I have 8 packed 32-bit floating point numbers (__m256), what's the fastest way to extract the horizontal sum of all 8 elements? Similarly, how to obtain the horizontal maximum and minimum? In other words, what's the best implementation for the following C++ functions?

float sum(__m256 x);  ///< returns sum of all 8 elements
float max(__m256 x);  ///< returns the maximum of all 8 elements
float min(__m256 x);  ///< returns the minimum of all 8 elements

回答1:

Quickly jotted down here (and hence untested):

float sum(__m256 x) {
    __m128 hi = _mm256_extractf128_ps(x, 1);
    __m128 lo = _mm256_extractf128_ps(x, 0);
    lo = _mm_add_ps(hi, lo);
    hi = _mm_movehl_ps(hi, lo);
    lo = _mm_add_ps(hi, lo);
    hi = _mm_shuffle_ps(lo, lo, 1);
    lo = _mm_add_ss(hi, lo);
    return _mm_cvtss_f32(lo);
}

For min/max, replace _mm_add_ps and _mm_add_ss with _mm_max_* or _mm_min_*.

Note that this is a lot of work for a few operations; AVX isn't really intended to do horizontal operations efficiently. If you can batch up this work for multiple vectors, then more efficient solutions are possible.

回答2:

While Stephen Canon's answer is probably ideal for finding the horizontal maximum/minimum I think a better solution can be found for the horizontal sum.

float horizontal_add (__m256 a) {
    __m256 t1 = _mm256_hadd_ps(a,a);
    __m256 t2 = _mm256_hadd_ps(t1,t1);
    __m128 t3 = _mm256_extractf128_ps(t2,1);
    __m128 t4 = _mm_add_ss(_mm256_castps256_ps128(t2),t3);
    return _mm_cvtss_f32(t4);        
}

回答3:

I tried to write code that avoids mixing avx and non-avx instructions and the horizontal sum of an avx register containing floats can be done avx-only by

• 1x vperm2f128,
• 2x vshufps and
• 3x vaddps,

resulting in a register where all entries contain the sum of all elements in the original register.

// permute
//  4, 5, 6, 7, 0, 1, 2, 3
// add
//  0+4, 1+5, 2+6, 3+7, 4+0, 5+1, 6+2, 7+3
// shuffle
//  1+5, 0+4, 3+7, 2+6, 5+1, 4+0, 7+3, 6+2
// add
//  1+5+0+4, 0+4+1+5, 3+7+2+6, 2+6+3+7, 
//  5+1+4+0, 4+0+5+1, 7+3+6+2, 6+2+7+3
// shuffle
//  3+7+2+6, 2+6+3+7, 1+5+0+4, 0+4+1+5, 
//  7+3+6+2, 6+2+7+3, 5+1+4+0, 4+0+5+1
// add
//  3+7+2+6+1+5+0+4, 2+6+3+7+0+4+1+5, 1+5+0+4+3+7+2+6, 0+4+1+5+2+6+3+7,
//  7+3+6+2+5+1+4+0, 6+2+7+3+4+0+5+1, 5+1+4+0+7+3+6+2, 4+0+5+1+6+2+7+3

static inline __m256 hsums(__m256 const& v)
{
    auto x = _mm256_permute2f128_ps(v, v, 1);
    auto y = _mm256_add_ps(v, x);
    x = _mm256_shuffle_ps(y, y, _MM_SHUFFLE(2, 3, 0, 1));
    x = _mm256_add_ps(x, y);
    y = _mm256_shuffle_ps(x, x, _MM_SHUFFLE(1, 0, 3, 2));
    return _mm256_add_ps(x, y);
}

Obtaining the value is then easy by using _mm256_castps256_ps128 and _mm_cvtss_f32:

static inline float hadd(__m256 const& v)
{
    return _mm_cvtss_f32(_mm256_castps256_ps128(hsums(v)));
}

I did some basic benchmarks against the other solutions with __rdtscp and did not find one to be superior in terms of mean cpu cycle count on my Intel i5-2500k.

Looking at the Agner Instruction Tables I found (for Sandy-Bridge processors):

                µops    lat.    1/tp    count

this:

vperm2f128      1       2       1       1
vaddps          1       3       1       3
vshufps         1       1       1       2

sum             6       13      6       6

Z boson:

vhaddps         3       5       2       2
vextractf128    1       2       1       1
addss           1       3       1       1

sum             8       15      6       4

Stephen Canon:

vextractf128    1       2       1       1
addps           1       3       1       2
movhlps         1       1       1       1
shufps          1       1       1       1
addss           1       3       1       1

sum             8       13      6       6

where to me (due to the values being rather similar) none is clearly superior (as I cannot forsee whether instruction count, µop count, latency or throughput matters most). edit, note: The potential problem I assumed to exist in the following is not true. I suspected, that -if having the result in the ymm register is sufficient- my hsums could be useful as it doesn't require vzeroupper to prevent state switching penalty and can thus interleave / execute concurrently with other avx computations using different registers without introducing some kind of sequence point.

回答4:

union ymm {
    __m256 m256;
    struct {
        __m128 m128lo;
        __m128 m128hi;
    };
};

union ymm result = {1,2,3,4,5,6,7,8};
__m256 a = {9,10,11,12,13,14,15,16};

result.m256 = _mm256_add_ps (result.m256, a);
result.m128lo = _mm_hadd_ps (result.m128lo, result.m128hi);
result.m128lo = _mm_hadd_ps (result.m128lo, result.m128hi);
result.m128lo = _mm_hadd_ps (result.m128lo, result.m128hi);