README.inner_loop_reduce

Vectorization Example: Inner Loop Reduce
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Consider an example where we vectorize an outer loop, and a inner loop is iterated through.
We need to accumulate a value within to a memory location dependent on variables in the inner loop.
The simd pragma can specify a reduction clause for arrays.
However, this means that the array will be augmented with another dimension of size <vector length>, and the code below the pragma will just add into that.
The reduction happens only in the end.
This may actually be desireable behaviour if we often accumulate into relatively few distinct memory locations.
It however is unsuited if we accumulate only a few times per memory location, if we are constrained in terms of memory usage, or if we need to allocate on the heap.

The mitigation strategies herein circle around the idea to "hide" code from the compiler in function calls.
These function calls have to be serialized by the compiler, and we get the desired behaviour.
Note that it is crucial to annotate the function (memory_reduce_add) with __declspec(noinline).
If inlined, it will not work: The code will compute invalid results.
As another additional step, we can make use of the vector_variant annotation, and perform the reduction using compiler intrinsics.

Measurement
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Note: none has no pragma-based vectorization, simd is explicitly vectorized, and vector_variant uses vector_variant-declarations additionally.
It is clear that performance benefits on both the Phi and the Host.

           none.x-mic: Time   : 3.473042000000000e+06
           none.x-mic: Correct: 4.835128784179688e-04
           simd.x-mic: Time   : 1.219468000000000e+06
           simd.x-mic: Correct: 1.049041748046875e-04
 vector_variant.x-mic: Time   : 3.594990000000000e+05
 vector_variant.x-mic: Correct: 3.814697265625000e-05
          none.x-host: Time   : 1.234876000000000e+06
          none.x-host: Correct: 4.835128784179688e-04
          simd.x-host: Time   : 4.378800000000000e+05
          simd.x-host: Correct: 3.433227539062500e-05
vector_variant.x-host: Time   : 2.689560000000000e+05
vector_variant.x-host: Correct: -6.866455078125000e-05