feat: make ACVM generic across fields (#5114)

# Description

Step towards #5055 

## Summary\*

This PR starts us down the road towards removing the compile-time flags
for specifying which field is being used by replacing the usage of the
`FieldElement` type with an `AcirField` trait. This trait is mostly all
of the external methods from `FieldElement` dumped into it for now but
we can break it down in future PRs (XOR and AND are looking ready for
culling)

I've taken this route rather than just using `generic_ark::FieldElement`
as we'd need to have trait bounds for `PrimeField` anyway so we might as
well have our own trait.

I've had to delete a couple of trait implementations which fall afoul of
the orphan rule now it's being implemented for a generic type (e.g. we
need to use `MemoryValue::new_field` explicitly now) but nothing too
bad.

## Additional Context


## Documentation\*

Check one:
- [x] No documentation needed.
- [ ] Documentation included in this PR.
- [ ] **[For Experimental Features]** Documentation to be submitted in a
separate PR.

# PR Checklist\*

- [x] I have tested the changes locally.
- [x] I have formatted the changes with [Prettier](https://prettier.io/)
and/or `cargo fmt` on default settings.

acvm-repo/acir/Cargo.toml

@@ -33,9 +33,8 @@ criterion.workspace = true
 pprof.workspace = true
 
 [features]
-default = ["bn254"]
-bn254 = ["acir_field/bn254", "brillig/bn254"]
-bls12_381 = ["acir_field/bls12_381", "brillig/bls12_381"]
+bn254 = ["acir_field/bn254"]
+bls12_381 = ["acir_field/bls12_381"]
 
 [[bench]]
 name = "serialization"

acvm-repo/acir/benches/serialization.rs

@@ -11,8 +11,8 @@ use pprof::criterion::{Output, PProfProfiler};
 
 const SIZES: [usize; 9] = [10, 50, 100, 500, 1000, 5000, 10000, 50000, 100000];
 
-fn sample_program(num_opcodes: usize) -> Program {
-    let assert_zero_opcodes: Vec<Opcode> = (0..num_opcodes)
+fn sample_program(num_opcodes: usize) -> Program<FieldElement> {
+    let assert_zero_opcodes: Vec<Opcode<_>> = (0..num_opcodes)
         .map(|i| {
             Opcode::AssertZero(Expression {
                 mul_terms: vec![(
@@ -83,7 +83,7 @@ fn bench_deserialization(c: &mut Criterion) {
             BenchmarkId::from_parameter(size),
             &serialized_program,
             |b, program| {
-                b.iter(|| Program::deserialize_program(program));
+                b.iter(|| Program::<FieldElement>::deserialize_program(program));
             },
         );
     }
@@ -107,7 +107,7 @@ fn bench_deserialization(c: &mut Criterion) {
             |b, program| {
                 b.iter(|| {
                     let mut deserializer = serde_json::Deserializer::from_slice(program);
-                    Program::deserialize_program_base64(&mut deserializer)
+                    Program::<FieldElement>::deserialize_program_base64(&mut deserializer)
                 });
             },
         );

acvm-repo/acir/src/circuit/brillig.rs

@@ -6,9 +6,9 @@ use serde::{Deserialize, Serialize};
 /// Inputs for the Brillig VM. These are the initial inputs
 /// that the Brillig VM will use to start.
 #[derive(Clone, PartialEq, Eq, Serialize, Deserialize, Debug)]
-pub enum BrilligInputs {
-    Single(Expression),
-    Array(Vec<Expression>),
+pub enum BrilligInputs<F> {
+    Single(Expression<F>),
+    Array(Vec<Expression<F>>),
     MemoryArray(BlockId),
 }
 
@@ -24,6 +24,6 @@ pub enum BrilligOutputs {
 /// a full Brillig function to be executed by the Brillig VM.
 /// This is stored separately on a program and accessed through a [BrilligPointer].
 #[derive(Clone, PartialEq, Eq, Serialize, Deserialize, Default, Debug)]
-pub struct BrilligBytecode {
-    pub bytecode: Vec<BrilligOpcode>,
+pub struct BrilligBytecode<F> {
+    pub bytecode: Vec<BrilligOpcode<F>>,
 }

acvm-repo/acir/src/circuit/directives.rs

@@ -5,7 +5,7 @@ use serde::{Deserialize, Serialize};
 /// Directives do not apply any constraints.
 /// You can think of them as opcodes that allow one to use non-determinism
 /// In the future, this can be replaced with asm non-determinism blocks
-pub enum Directive {
+pub enum Directive<F> {
     //decomposition of a: a=\sum b[i]*radix^i where b is an array of witnesses < radix in little endian form
-    ToLeRadix { a: Expression, b: Vec<Witness>, radix: u32 },
+    ToLeRadix { a: Expression<F>, b: Vec<Witness>, radix: u32 },
 }

acvm-repo/acir/src/circuit/mod.rs

@@ -4,7 +4,7 @@ pub mod directives;
 pub mod opcodes;
 
 use crate::native_types::{Expression, Witness};
-use acir_field::FieldElement;
+use acir_field::AcirField;
 pub use opcodes::Opcode;
 use thiserror::Error;
 
@@ -38,17 +38,17 @@ pub enum ExpressionWidth {
 /// A program represented by multiple ACIR circuits. The execution trace of these
 /// circuits is dictated by construction of the [crate::native_types::WitnessStack].
 #[derive(Clone, PartialEq, Eq, Serialize, Deserialize, Default)]
-pub struct Program {
-    pub functions: Vec<Circuit>,
-    pub unconstrained_functions: Vec<BrilligBytecode>,
+pub struct Program<F> {
+    pub functions: Vec<Circuit<F>>,
+    pub unconstrained_functions: Vec<BrilligBytecode<F>>,
 }
 
 #[derive(Clone, PartialEq, Eq, Serialize, Deserialize, Default)]
-pub struct Circuit {
+pub struct Circuit<F> {
     // current_witness_index is the highest witness index in the circuit. The next witness to be added to this circuit
     // will take on this value. (The value is cached here as an optimization.)
     pub current_witness_index: u32,
-    pub opcodes: Vec<Opcode>,
+    pub opcodes: Vec<Opcode<F>>,
     pub expression_width: ExpressionWidth,
 
     /// The set of private inputs to the circuit.
@@ -67,7 +67,7 @@ pub struct Circuit {
     // Note: This should be a BTreeMap, but serde-reflect is creating invalid
     // c++ code at the moment when it is, due to OpcodeLocation needing a comparison
     // implementation which is never generated.
-    pub assert_messages: Vec<(OpcodeLocation, AssertionPayload)>,
+    pub assert_messages: Vec<(OpcodeLocation, AssertionPayload<F>)>,
 
     /// States whether the backend should use a SNARK recursion friendly prover.
     /// If implemented by a backend, this means that proofs generated with this circuit
@@ -76,15 +76,15 @@ pub struct Circuit {
 }
 
 #[derive(Debug, Clone, PartialEq, Eq, Serialize, Deserialize)]
-pub enum ExpressionOrMemory {
-    Expression(Expression),
+pub enum ExpressionOrMemory<F> {
+    Expression(Expression<F>),
     Memory(BlockId),
 }
 
 #[derive(Debug, Clone, PartialEq, Eq, Serialize, Deserialize)]
-pub enum AssertionPayload {
+pub enum AssertionPayload<F> {
     StaticString(String),
-    Dynamic(/* error_selector */ u64, Vec<ExpressionOrMemory>),
+    Dynamic(/* error_selector */ u64, Vec<ExpressionOrMemory<F>>),
 }
 
 #[derive(Debug, Copy, PartialEq, Eq, Hash, Clone, PartialOrd, Ord)]
@@ -127,15 +127,15 @@ impl<'de> Deserialize<'de> for ErrorSelector {
 pub const STRING_ERROR_SELECTOR: ErrorSelector = ErrorSelector(0);
 
 #[derive(Clone, PartialEq, Eq, Debug, Serialize, Deserialize)]
-pub struct RawAssertionPayload {
+pub struct RawAssertionPayload<F> {
     pub selector: ErrorSelector,
-    pub data: Vec<FieldElement>,
+    pub data: Vec<F>,
 }
 
 #[derive(Clone, PartialEq, Eq, Debug)]
-pub enum ResolvedAssertionPayload {
+pub enum ResolvedAssertionPayload<F> {
     String(String),
-    Raw(RawAssertionPayload),
+    Raw(RawAssertionPayload<F>),
 }
 
 #[derive(Debug, Copy, Clone)]
@@ -204,7 +204,7 @@ impl FromStr for OpcodeLocation {
     }
 }
 
-impl Circuit {
+impl<F: AcirField> Circuit<F> {
     pub fn num_vars(&self) -> u32 {
         self.current_witness_index + 1
     }
@@ -223,7 +223,7 @@ impl Circuit {
     }
 }
 
-impl Program {
+impl<F: Serialize> Program<F> {
     fn write<W: std::io::Write>(&self, writer: W) -> std::io::Result<()> {
         let buf = bincode::serialize(self).unwrap();
         let mut encoder = flate2::write::GzEncoder::new(writer, Compression::default());
@@ -232,36 +232,38 @@ impl Program {
         Ok(())
     }
 
-    fn read<R: std::io::Read>(reader: R) -> std::io::Result<Self> {
-        let mut gz_decoder = flate2::read::GzDecoder::new(reader);
-        let mut buf_d = Vec::new();
-        gz_decoder.read_to_end(&mut buf_d)?;
-        bincode::deserialize(&buf_d)
-            .map_err(|err| std::io::Error::new(std::io::ErrorKind::InvalidInput, err))
-    }
-
-    pub fn serialize_program(program: &Program) -> Vec<u8> {
+    pub fn serialize_program(program: &Self) -> Vec<u8> {
         let mut program_bytes: Vec<u8> = Vec::new();
         program.write(&mut program_bytes).expect("expected circuit to be serializable");
         program_bytes
     }
 
-    pub fn deserialize_program(serialized_circuit: &[u8]) -> std::io::Result<Self> {
-        Program::read(serialized_circuit)
-    }
-
     // Serialize and base64 encode program
-    pub fn serialize_program_base64<S>(program: &Program, s: S) -> Result<S::Ok, S::Error>
+    pub fn serialize_program_base64<S>(program: &Self, s: S) -> Result<S::Ok, S::Error>
     where
         S: Serializer,
     {
         let program_bytes = Program::serialize_program(program);
         let encoded_b64 = base64::engine::general_purpose::STANDARD.encode(program_bytes);
         s.serialize_str(&encoded_b64)
     }
+}
+
+impl<F: for<'a> Deserialize<'a>> Program<F> {
+    fn read<R: std::io::Read>(reader: R) -> std::io::Result<Self> {
+        let mut gz_decoder = flate2::read::GzDecoder::new(reader);
+        let mut buf_d = Vec::new();
+        gz_decoder.read_to_end(&mut buf_d)?;
+        bincode::deserialize(&buf_d)
+            .map_err(|err| std::io::Error::new(std::io::ErrorKind::InvalidInput, err))
+    }
+
+    pub fn deserialize_program(serialized_circuit: &[u8]) -> std::io::Result<Self> {
+        Program::read(serialized_circuit)
+    }
 
     // Deserialize and base64 decode program
-    pub fn deserialize_program_base64<'de, D>(deserializer: D) -> Result<Program, D::Error>
+    pub fn deserialize_program_base64<'de, D>(deserializer: D) -> Result<Self, D::Error>
     where
         D: Deserializer<'de>,
     {
@@ -274,7 +276,7 @@ impl Program {
     }
 }
 
-impl std::fmt::Display for Circuit {
+impl<F: AcirField> std::fmt::Display for Circuit<F> {
     fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
         writeln!(f, "current witness index : {}", self.current_witness_index)?;
 
@@ -313,13 +315,13 @@ impl std::fmt::Display for Circuit {
     }
 }
 
-impl std::fmt::Debug for Circuit {
+impl<F: AcirField> std::fmt::Debug for Circuit<F> {
     fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
         std::fmt::Display::fmt(self, f)
     }
 }
 
-impl std::fmt::Display for Program {
+impl<F: AcirField> std::fmt::Display for Program<F> {
     fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
         for (func_index, function) in self.functions.iter().enumerate() {
             writeln!(f, "func {}", func_index)?;
@@ -333,7 +335,7 @@ impl std::fmt::Display for Program {
     }
 }
 
-impl std::fmt::Debug for Program {
+impl<F: AcirField> std::fmt::Debug for Program<F> {
     fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
         std::fmt::Display::fmt(self, f)
     }
@@ -365,21 +367,22 @@ mod tests {
         circuit::{ExpressionWidth, Program},
         native_types::Witness,
     };
-    use acir_field::FieldElement;
+    use acir_field::{AcirField, FieldElement};
+    use serde::{Deserialize, Serialize};
 
-    fn and_opcode() -> Opcode {
+    fn and_opcode<F: AcirField>() -> Opcode<F> {
         Opcode::BlackBoxFuncCall(BlackBoxFuncCall::AND {
             lhs: FunctionInput { witness: Witness(1), num_bits: 4 },
             rhs: FunctionInput { witness: Witness(2), num_bits: 4 },
             output: Witness(3),
         })
     }
-    fn range_opcode() -> Opcode {
+    fn range_opcode<F: AcirField>() -> Opcode<F> {
         Opcode::BlackBoxFuncCall(BlackBoxFuncCall::RANGE {
             input: FunctionInput { witness: Witness(1), num_bits: 8 },
         })
     }
-    fn keccakf1600_opcode() -> Opcode {
+    fn keccakf1600_opcode<F: AcirField>() -> Opcode<F> {
         let inputs: Box<[FunctionInput; 25]> = Box::new(std::array::from_fn(|i| FunctionInput {
             witness: Witness(i as u32 + 1),
             num_bits: 8,
@@ -388,7 +391,7 @@ mod tests {
 
         Opcode::BlackBoxFuncCall(BlackBoxFuncCall::Keccakf1600 { inputs, outputs })
     }
-    fn schnorr_verify_opcode() -> Opcode {
+    fn schnorr_verify_opcode<F: AcirField>() -> Opcode<F> {
         let public_key_x =
             FunctionInput { witness: Witness(1), num_bits: FieldElement::max_num_bits() };
         let public_key_y =
@@ -413,7 +416,7 @@ mod tests {
         let circuit = Circuit {
             current_witness_index: 5,
             expression_width: ExpressionWidth::Unbounded,
-            opcodes: vec![and_opcode(), range_opcode(), schnorr_verify_opcode()],
+            opcodes: vec![and_opcode::<FieldElement>(), range_opcode(), schnorr_verify_opcode()],
             private_parameters: BTreeSet::new(),
             public_parameters: PublicInputs(BTreeSet::from_iter(vec![Witness(2), Witness(12)])),
             return_values: PublicInputs(BTreeSet::from_iter(vec![Witness(4), Witness(12)])),
@@ -422,7 +425,9 @@ mod tests {
         };
         let program = Program { functions: vec![circuit], unconstrained_functions: Vec::new() };
 
-        fn read_write(program: Program) -> (Program, Program) {
+        fn read_write<F: AcirField + Serialize + for<'a> Deserialize<'a>>(
+            program: Program<F>,
+        ) -> (Program<F>, Program<F>) {
             let bytes = Program::serialize_program(&program);
             let got_program = Program::deserialize_program(&bytes).unwrap();
             (program, got_program)
@@ -475,7 +480,8 @@ mod tests {
         encoder.write_all(bad_circuit).unwrap();
         encoder.finish().unwrap();
 
-        let deserialization_result = Program::deserialize_program(&zipped_bad_circuit);
+        let deserialization_result: Result<Program<FieldElement>, _> =
+            Program::deserialize_program(&zipped_bad_circuit);
         assert!(deserialization_result.is_err());
     }
 }