brillig: Use register liveness to deallocate registers

[ludamad]

Problem

Current brillig gen strategy uses a pattern of register allocation that does not reuse registers as values go out of scope/livenesss. We should use a deallocate_register method and a free list to deallocate registers when no longer used for a certain value, and reuse them in an allocate_register method.

Happy Case

Registers are tightly reused the moment it's valid to do so.

Alternatives Considered

No response

Additional Context

No response

Would you like to submit a PR for this Issue?

No

Support Needs

No response