Docs: explain prover's design for precompiles

[kunxian-xia]

No description provided.

[kunxian-xia]

trigger the integration test for gkr keccak

[kunxian-xia]

@hero78119 It seems to me that eq_left / eq_right / eq_target is not checked at all.

[hero78119]

rotation eq will be re-construct when the random point was derived from previous layer

ceno/gkr_iop/src/gkr/layer/cpu/mod.rs

Lines 178 to 198 in ca7b038

	.chain(rotation_left.par_iter().map(|rotation_left| {
	MultilinearExtension::from_evaluations_ext_vec(
	rotation_left.len(),
	build_eq_x_r_vec(rotation_left),
	)
	}))
	// for rotation right point
	.chain(rotation_right.par_iter().map(|rotation_right| {
	MultilinearExtension::from_evaluations_ext_vec(
	rotation_right.len(),
	build_eq_x_r_vec(rotation_right),
	)
	}))
	// for rotation point
	.chain(rotation_point.par_iter().map(|rotation_point| {
	MultilinearExtension::from_evaluations_ext_vec(
	rotation_point.len(),
	build_eq_x_r_vec(rotation_point),
	)
	}))
	.collect::<Vec<_>>();

in summary, eq will transform from A to B format

• format A: each eq will be assign as selector with only 0, 1 during witness generation to serve layer by layer witness inference
• format B: once random point $$r$$ derive from previous layer, each eq will be constructed via build_eq(r) then proceed sumcheck

[kunxian-xia]

I think the array self.out_sel_and_eval_exprs does not include eq_left / eq_right / eq.

ceno/gkr_iop/src/gkr/layer/zerocheck_layer.rs

Lines 287 to 297 in ca7b038

	izip!(&self.out_sel_and_eval_exprs, &eval_and_dedup_points).for_each(
	|((sel_type, _), (_, out_point))| {
	sel_type.evaluate(
	&mut main_evals,
	out_point.as_ref().unwrap(),
	&in_point,
	num_instances,
	self.n_witin,
	);
	},
	);