How to Calculate Vector Dot Product Using SSE Intrinsic Functions in C

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.

Thanks for your help.

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);

Answer 2

I'd say the fastest SSE method would be:

static inline float CalcDotProductSse(__m128 x, __m128 y) {
    __m128 mulRes, shufReg, sumsReg;
    mulRes = _mm_mul_ps(x, y);

    // Calculates the sum of SSE Register - https://stackoverflow.com/a/35270026/195787
    shufReg = _mm_movehdup_ps(mulRes);        // Broadcast elements 3,1 to 2,0
    sumsReg = _mm_add_ps(mulRes, shufReg);
    shufReg = _mm_movehl_ps(shufReg, sumsReg); // High Half -> Low Half
    sumsReg = _mm_add_ss(sumsReg, shufReg);
    return  _mm_cvtss_f32(sumsReg); // Result in the lower part of the SSE Register
}

I followed - Fastest Way to Do Horizontal Float Vector Sum On x86.

Answer 3

I wrote this and compiled it with gcc -O3 -S -ftree-vectorize -ftree-vectorizer-verbose=2 sse.c

void f(int * __restrict__ a, int * __restrict__ b, int * __restrict__ c, int * __restrict__ d,
       int * __restrict__ e, int * __restrict__ f, int * __restrict__ g, int * __restrict__ h,
       int * __restrict__ o)
{
    int i;

    for (i = 0; i < 8; ++i)
        o[i] = a[i]*e[i] + b[i]*f[i] + c[i]*g[i] + d[i]*h[i];
}

And GCC 4.3.0 auto-vectorized it:

sse.c:5: note: LOOP VECTORIZED.
sse.c:2: note: vectorized 1 loops in function.

However, it would only do that if I used a loop with enough iterations -- otherwise the verbose output would clarify that vectorization was unprofitable or the loop was too small. Without the __restrict__ keywords it has to generate separate, non-vectorized versions to deal with cases where the output o may point into one of the inputs.

I would paste the instructions as an example, but since part of the vectorization unrolled the loop it's not very readable.

Answer 4

There is an article by Intel here which touches on dot-product implementations.