* feat; benchmark compressed SNARK with computational commitments

- labeled types for compressed SNARKs in benchmarks, both with and without computational commitments, enhancing the functionality.
- Extended benchmark testing to include compressed SNARK with computational commtiments

* fix: use flat sampling mode for computational commitments, reduce circuit sizes

* reorganize different variants of spartan and make direct snark more generic

* cargo fmt

* test: compute_path

* refactor: path computation

- Improve path concatenation by utilizing built-in `join` method

* refactor: replace `PartialEq` with derived instance

- Derive `PartialEq` for `SatisfyingAssignment` struct
- Remove redundant manual implementation of `PartialEq`

Cargo-expand generates:
```
        #[automatically_derived]
        impl<G: ::core::cmp::PartialEq + Group> ::core::cmp::PartialEq
        for SatisfyingAssignment<G>
        where
            G::Scalar: PrimeField,
            G::Scalar: ::core::cmp::PartialEq,
            G::Scalar: ::core::cmp::PartialEq,
            G::Scalar: ::core::cmp::PartialEq,
            G::Scalar: ::core::cmp::PartialEq,
            G::Scalar: ::core::cmp::PartialEq,
        {
            #[inline]
            fn eq(&self, other: &SatisfyingAssignment<G>) -> bool {
                self.a_aux_density == other.a_aux_density
                    && self.b_input_density == other.b_input_density
                    && self.b_aux_density == other.b_aux_density && self.a == other.a
                    && self.b == other.b && self.c == other.c
                    && self.input_assignment == other.input_assignment
                    && self.aux_assignment == other.aux_assignment
            }
        }
```

* refactor: avoid default for PhantomData Unit type

* refactor: replace fold with sum where applicable

- Simplify code by replacing `fold` with `sum` in various instances

* refactor: decompression method in sumcheck.rs

* refactor: test functions to use slice instead of vector conversion

* refactor: use more references in functions

- Update parameter types to use references instead of owned values in various functions that do not need them
- Replace cloning instances with references

* feat: Integrate flamegraph profiling in benchmarks

- Introduce "flamegraph" feature flag for optional profiling integration
- Add benchmark profiling support in `compressed_snark` and `recursive_snark` groups
- Update Cargo.toml with `pprof` and `cfg-if` dependencies

* ci: Build benches to make sure they don't bit-rot

- Integrate bench build step into GitHub Actions workflow

* Improve performance of recursive

* Fix the test after rebase

* Fix CI/CD warnings

* Update benchmark to work with new interface of RecursiveSNARK

* Fix example to make sure step 1 is correct

* refactor: Removes unneeded pass-by value in verification

- Update function arguments to use borrowing instead of passing ownership

* Resolve the conflict with upstream branch

* refactor: Avoid extra input cloning in RecursiveSNARK::new

* Update criterion to 0.5.1 to prevent the panic with its plot

* Fix benchmark issue with new recursive_snark instance

* Fix CI/CD warning with

* refactor: Make mutation easier to observe

- Utilize mutable references to Points for better memory management

* chore: Downgrade clippy dependency for compatibility

---------

Co-authored-by: François Garillot <francois@garillot.net>

* a more optimal preprocessing SNARK

* update version

* cleanup; address clippy

* spark-based commitments to R1CS matrices

* small fixes

* checkpoint

* simplify further

* checkpoint

* gens --> ck

* update benches

* address clippy

* cleanup

* update version

make spartan generic over the evaluation engine

update version

disable Wasm CI check

* Clippy with Rust 1.67

* Clippy/Rustfmt with Rust 1.66.1

* support for arbitrary arity for F

* revive MinRoot example

* revive tests

* revive ecdsa

* remove unused code

* use None instead of Some(1u32)

* revive benches

* fix clippy warning

* rename methods for better clarity

* rename

* Bump version

* vary the number of constraints in the step circuit

* use a different starting state

* fix name

* Add 14

use a default implementation for step circuit

* support non-determinism with small changes to the interface

* update benches to use the new API

* add an example that exercises non-deterministic advice at each step of recursion

* tiny rename

* Address clippy; update version

* cleanup code

* compiles

* additional plumbing

* add padding

* Add missing file

* integrate

* add a separate test

* cleanup

* cleanup

* add checks for outer sum-check

* sum-checks pass

* sum-checks pass

* sum-checks pass

* Add polycommit checks to the end

* switch to pasta_msm

* clippy

* remove int_log

* switch to pasta_curves

* clippy

* clippy

* add a special case for bases.len() = 1

* use naive MSM to avoid SIGFE error for smaller MSMs

* add rayon parallelism to naive MSM

* update comment since we already implement it

* address clippy

* cleanup map and reduce code

* add parallelism to final SNARK creation and verification

* add par

* add par

* add par

* add par

* store padded shapes in the parameters

* Address clippy

* pass padded shape in params

* pass padded shape in params

* cargo fmt

* add par

* add par

* Add par

* cleanup with a reorg

* factor out spartan-based snark into a separate module

* create traits for RelaxedR1CSSNARK

* make CompressedSNARK parameterized by a SNARK satisfying our new trait

* fix benches

* cleanup code

* remove unused

* move code to Spartan-based SNARK

* make unused function private

* rename IPA types for clarity

* cleanup

* return error types; rename r_j to r_i

* fix duplicate code

* add benches

* fix error

* put snark in a black_box when benchmarking verification time

* fix error in benches