Intel AVX: 256-bits version of dot product for double precision floating point variables

The Intel Advanced Vector Extensions (AVX) offers no dot product in the 256-bit version (YMM register) for double precision floating point variables. The "Why?" question have been very briefly treated in another forum (here) and on Stack Overflow (here). But the question I am facing is how to replace this missing instruction with other AVX instructions in an efficient way?

The dot product in 256-bit version exists for single precision floating point variables (reference here):

 __m256 _mm256_dp_ps(__m256 m1, __m256 m2, const int mask);

The idea is to find an efficient equivalent for this missing instruction:

 __m256d _mm256_dp_pd(__m256d m1, __m256d m2, const int mask);

To be more specific, the code I would like to transform from __m128 (four floats) to __m256d (4 doubles) use the following instructions:

   __m128 val0 = ...; // Four float values
   __m128 val1 = ...; //
   __m128 val2 = ...; //
   __m128 val3 = ...; //
   __m128 val4 = ...; //

   __m128 res = _mm_or_ps( _mm_dp_ps(val1,  val0,   0xF1),
                _mm_or_ps( _mm_dp_ps(val2,  val0,   0xF2),
                _mm_or_ps( _mm_dp_ps(val3,  val0,   0xF4),
                           _mm_dp_ps(val4,  val0,   0xF8) )));

The result of this code is a _m128 vector of four floats containing the results of the dot products between val1 and val0, val2 and val0, val3 and val0, val4 and val0<