[word-lo-hi] fine tune copy circuit to reduce degree

[hero78119]

Description

[PR description]

Issue Link

#1499

Type of change

• Bug fix (non-breaking change which fixes an issue)

Contents

This pr is to rewrite/split copy circuit constrains to trade more gates with less degree.
copy table tag field is binary number decomposition with degree N (N represent number of bits, in copy table case N = 3). Once put in or::expr([#num_or_condition]), gate degrees will be exploded quickly by N*#num_or_condition.

Before PR, copy circuit max is degree 12,
After PR, copy circuit max 6 degree with 2 more gates.

However, circuit degree upper bound still increase by 1 (9 -> 10) for word-lo-hi refactor, due to state-circuit batch_is_zero-"is_zero is 1 if values are all zero"> gate degrees from 6 -> 10 Due to we fold 2 extra column, each contribute 2 degrees
https://github.com/privacy-scaling-explorations/zkevm-circuits/blob/word-lo-hi/zkevm-circuits/src/state_circuit.rs#L129-L141.

State circuit need some discussion, as I thought rewrite it might be a bit over-engineering.

[hero78119]

+ @adria0, might have thought on state-circuit case

[ed255]

This solution looks good to me!

[ChihChengLiang]

LGTM

[hero78119]

Will merge it first to unblock word-lo-hi back to main. state circuit case can fine tune later

[adria0]

+ @adria0, might have thought on state-circuit case

Nice improvment! What do you have in mind (overengineered?) for the 4-batched zero check in state circuit?

[hero78119]

+ @adria0, might have thought on state-circuit case

Nice improvment! What do you have in mind (overengineered?) for the 4-batched zero check in state circuit?

Hi @adria0 my option is intuitively quick fix is separating into 4 zero check then and 4 is_zero expr() naturally. It lead to 4 extra is_zero config fields. It also implies BatchedIsZeroChip usage easily to lead to degree booming pitfall. Maybe we need to remove or redesign BatchedIsZeroChip

[adria0]

BatchedIsZeroChip usage easily to lead to degree booming pitfall.

fortunately I see that only is used in state circuit :) Maybe 4 extra is_zero it's ok for now.
Crazy tradeoffs