To implement the continuation

[grandchildrice]

Hello jolt team. I am interested in implementing continuation to jolt related to this issue #211. In SP1, RISC Zero and Ceno, continuation is at the most central to the parallelization strategy. According to my benchmarks, I can expect up to 10x speedup on a Mac Studio M2 64GB Memory machine.

I am aware that jolt has a strategy to reduce the memory usage to 10GB by implementing continuations in a folding manner. I would like to actually implement it and run some benchmarks.

I have previously worked on that for 5 days. Our efforts are as follows.

1. add segment_trace() function to jolt/vm/read_write_memory.rs and split the trace evenly
2. add functions prove_segment() and verify_segment() to jolt/vm/mod.rs to verify that per-segment proving works.
3. add functions to lasso/memory_checking.rs, lasso/surge.rs, subprotocols/grand_product.rs to aggregate instructionLookup's memory_checking proofs, and Test the aggregation

• Trace segmentation grandchildrice/jolt#14
• GKR Folding grandchildrice/jolt#2

The goal was to test up to 3 and then implement the folding function and compare it with the aggregation function.
In the end, I stumbled on the implementation of trace segmentation. Implementing consistent init and final values for each segment was extremely difficult. I wondered if it would be better to directly modify the trace()function injolt/trace/src/lib.rs.

I would like to first implement and test it with the least amount of changes, and would appreciate any ideas for the design of continuation in Jolt.