[DO NOT MERGE] Memory Profiler

[zhiyong1997]

From the implementation side:

The most extensive part of memory usage now:

1. PCS Peak: ~60GB (root only).
2. GKR Peak: ~5.59 GB/core

• Export to Expander Format: ~1.2GB
• ScratchPad: ~2.7 GB
• Input Intermediate Result: ~0.5 GB
• All witness: ~1.2 GB

1. PCS Target: TBD
2. GKR Target:

• Export to Expander Format: 0. (Store shared expander circuit instead of ECC circuit in the very beginning)
• ScratchPad: ~1.4GB
• Input Intermediate Result: 0 (Simply drop it)
• All witness: ~1.2GB (No change)

[zhiyong1997]

From system design:

Backend

1. Goldilocks, but what PCS?.
2. Variable-length BN Field.
3. Optimize Sumcheck (Currently 4X input size overhead).
4. (Fallback) Auto detect available memory and split large parallelism into several smaller ones (will either hurt proving time or proof size and verification time).

Frontend

1. Minimize circuit and witness size.