# nir/search: Search for all combinations of commutative ops

Consider the following search expression and NIR sequence:

```
('iadd', ('imul', a, b), b)
ssa_2 = imul ssa_0, ssa_1
ssa_3 = iadd ssa_2, ssa_0
```

The current algorithm is greedy and, the moment the imul finds a match, it commits those variable names and returns success. In the above example, it maps a -> ssa_0 and b -> ssa_1. When we then try to match the iadd, it sees that ssa_0 is not b and fails to match. The iadd match will attempt to flip itself and try again (which won't work) but it cannot ask the imul to try a flipped match.

This commit instead counts the number of commutative ops in each expression and assigns an index to each. It then does a loop and loops over the full combinatorial matrix of commutative operations. In order to keep things sane, we limit it to at most 4 commutative operations (16 combinations). There is only one optimization in opt_algebraic that goes over this limit and it's the bitfieldReverse detection for some UE4 demo.

Shader-db results on Kaby Lake:

```
total instructions in shared programs: 15310125 -> 15302469 (-0.05%)
instructions in affected programs: 1797123 -> 1789467 (-0.43%)
helped: 6751
HURT: 2264
total cycles in shared programs: 357346617 -> 357202526 (-0.04%)
cycles in affected programs: 15931005 -> 15786914 (-0.90%)
helped: 6024
HURT: 3436
total loops in shared programs: 4360 -> 4360 (0.00%)
loops in affected programs: 0 -> 0
helped: 0
HURT: 0
total spills in shared programs: 23675 -> 23666 (-0.04%)
spills in affected programs: 235 -> 226 (-3.83%)
helped: 5
HURT: 1
total fills in shared programs: 32040 -> 32032 (-0.02%)
fills in affected programs: 190 -> 182 (-4.21%)
helped: 6
HURT: 2
LOST: 18
GAINED: 5
```