# Optimization: AVX2 vectorization of the ped-ped loop

- **Author**: Linus
- **Predecessor**: variant_inlining_7_SoA.cpp
- **File(s)**: variants/variant_inlining_7_SoA_AVX2.cpp
- **Status**: TBD, positive locally (approx.2 times)

## What this changes

First AVX2 pass through the ped-ped inner loop. The `j` loop strides by
4 and processes 4 pedestrians at once on `__m256d` registers. SoA from
the predecessor variant is what makes the loads contiguous, otherwise
this would not have been clean to write.

The `i == j` skip is now a mask instead of `continue`. I also pad all
the per-pedestrian arrays to a multiple of 4 (`n_p_pad`) so the loop
doesn't need a scalar tail. Padding positions are set to `1e9` so even
without the mask the lane would contribute ~0 via exp(very negative),
but the mask makes it deterministic. Same mask is also used to zero out
the i==j lane after the body.

The scalar `exp()` is still called 4 times per j step into a scratch
array. 

## Code (relevant snippet)

See `variants/variant_inlining_7_SoA_AVX2.cpp` for the full inner loop.
Structure is: build the active mask from `j_idx` vs `i` and `n_p`, run
the vector body on 4 lanes at a time, blend in a safe denom so the
i==j lane does not produce a NaN, mask the per-lane force contribution,
then accumulate into `acc_x` and `acc_y`. After the j loop a horizontal
sum folds the accumulators into the scalar `f_alpha_dt`.

## Benchmark

Conditions: min of N runs (TBD), N_ITER=1000, -O3 -march=native -flto.
Diff is vs `variant_inlining_7_SoA`.

local runs show a clear speedup over the SoA-only predecessor. exact
numbers TBD on the test machine, but the qualitative picture is that
the 4 scalar `exp()` calls inside the j loop now dominate.
### x86

**Machine**: TBD

**Frequency**: TBD

| N    | W(n) [Flops] | T(n) [Cycles] | Performance [Flops/Cycle] | Diff vs Predecessor |
| ---- | ------------ | ------------- | ------------------------- | ------------------- |
| 50   |              |               |                           |                     |
| 100  |              |               |                           |                     |
| 200  |              |               |                           |                     |
| 500  |              |               |                           |                     |
| 1000 |              |               |                           |                     |

### ARM (Apple)

Not applicable, this variant uses AVX2 intrinsics
## Analysis

The win comes from doing 4 ped-ped interactions per j step instead of 1.
Loads are contiguous thanks to SoA, and the inner body is mostly
straight-line `sub`, `fmadd`, `mul`, `sqrt`, one `div`, plus a `blendv`
and a couple of `cmp`/`and` for the mask. No branches in the j loop
other than the loop counter.

I expected `exp()` to become the bottleneck once everything around it
was vectorized, and the profile confirmed it. The horizontal sum at the
end of the j loop only happens once per outer iter, not per j step, so
its cost is small.



## Takeaway

First real perf jump for the ped-ped force, but limited by the scalar
`exp` call still inside the loop. Sets up the polyexp variant.