Question

I am trying to multiply two vectors together where each element of one vector is multiplied by the element in the same index at the other vector. I then want to sum all the elements of the resulting vector to obtain one number. For instance, the calculation would look like this for the vectors {1,2,3,4} and {5,6,7,8}:

1*5 + 2*6 + 3*7 + 4*8

Essentially, I am taking the dot product of the two vectors. I know there is an SSE command to do this, but the command doesn’t have an intrinsic function associated with it. At this point, I don’t want to write inline assembly in my C code, so I want to use only intrinsic functions. This seems like a common calculation so I am surprised by myself that I couldn’t find the answer on Google.

Note: I am optimizing for a specific micro architecture which supports up to SSE 4.2.

Answer 1

If you’re doing a dot-product of longer vectors, use multiply and regular _mm_add_ps (or FMA) inside the inner loop. Save the horizontal sum until the end.

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But if you are doing a dot product of just a single pair of SIMD vectors:

GCC (at least version 4.3) includes <smmintrin.h> with SSE4.1 level intrinsics, including the single and double-precision dot products:

_mm_dp_ps (__m128 __X, __m128 __Y, const int __M);
_mm_dp_pd (__m128d __X, __m128d __Y, const int __M);

On Intel mainstream CPUs (not Atom/Silvermont) these are somewhat faster than doing it manually with multiple instructions.

But on AMD (including Ryzen), dpps is significantly slower. (See Agner Fog’s instruction tables)

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As a fallback for older processors, you can use this algorithm to create the dot product of the vectors a and b:

__m128 r1 = _mm_mul_ps(a, b);

and then horizontal sum r1 using Fastest way to do horizontal float vector sum on x86 (see there for a commented version of this, and why it’s faster.)

__m128 shuf   = _mm_shuffle_ps(r1, r1, _MM_SHUFFLE(2, 3, 0, 1));
__m128 sums   = _mm_add_ps(r1, shuf);
shuf          = _mm_movehl_ps(shuf, sums);
sums          = _mm_add_ss(sums, shuf);
float result =  _mm_cvtss_f32(sums);

A slow alternative costs 2 shuffles per hadd, which will easily bottleneck on shuffle throughput, especially on Intel CPUs.

r2 = _mm_hadd_ps(r1, r1);
r3 = _mm_hadd_ps(r2, r2);
_mm_store_ss(&result, r3);