feat: add support for functions

air-script/tests/codegen/masm.rs

@@ -84,6 +84,16 @@ fn evaluators() {
     expected.assert_eq(&generated_masm);
 }
 
+#[test]
+fn functions() {
+    let generated_masm = Test::new("tests/functions/functions.air".to_string())
+        .transpile(Target::Masm)
+        .unwrap();
+
+    let expected = expect_file!["../functions/functions.masm"];
+    expected.assert_eq(&generated_masm);
+}
+
 #[test]
 fn variables() {
     let generated_masm = Test::new("tests/variables/variables.air".to_string())

air-script/tests/codegen/winterfell.rs

@@ -84,6 +84,16 @@ fn evaluators() {
     expected.assert_eq(&generated_air);
 }
 
+#[test]
+fn functions() {
+    let generated_air = Test::new("tests/functions/functions.air".to_string())
+        .transpile(Target::Winterfell)
+        .unwrap();
+
+    let expected = expect_file!["../functions/functions.rs"];
+    expected.assert_eq(&generated_air);
+}
+
 #[test]
 fn variables() {
     let generated_air = Test::new("tests/variables/variables.air".to_string())

air-script/tests/functions/functions.air

@@ -0,0 +1,36 @@
+def FunctionsAir
+
+fn get_multiplicity_flags(s0: felt, s1: felt) -> felt[4]:
+    return [!s0 & !s1, s0 & !s1, !s0 & s1, s0 & s1]
+
+fn fold_vec(a: felt[12]) -> felt:
+   return sum([x for x in a])
+
+fn fold_scalar_and_vec(a: felt, b: felt[12]) -> felt:
+    let m = fold_vec(b)
+    let n = m + 1
+    let o = n * 2
+    return o
+
+trace_columns:
+    main: [t, s0, s1, v, b[12]]
+    aux: [b_range]
+
+public_inputs:
+    stack_inputs: [16]
+
+random_values:
+    alpha: [16]
+
+boundary_constraints:
+    enf v.first = 0
+
+integrity_constraints:
+    let val = $alpha[0] + v
+    let f = get_multiplicity_flags(s0, s1)
+    let z = val^4 * f[3] + val^2 * f[2] + val * f[1] + f[0]
+    let folded_value = fold_scalar_and_vec(v, b)
+    enf b_range' = b_range * (z * t - t + 1)
+    let d = fold_scalar_and_vec(v, b)
+    let c = fold_scalar_and_vec(t, b)
+    enf v' = d

air-script/tests/functions/functions.masm

@@ -0,0 +1,166 @@
+# Procedure to efficiently compute the required exponentiations of the out-of-domain point `z` and cache them for later use.
+#
+# This computes the power of `z` needed to evaluate the periodic polynomials and the constraint divisors
+#
+# Input: [...]
+# Output: [...]
+proc.cache_z_exp
+    padw mem_loadw.4294903304 drop drop # load z
+    # => [z_1, z_0, ...]
+    # Exponentiate z trace_len times
+    mem_load.4294903307 neg
+    # => [count, z_1, z_0, ...] where count = -log2(trace_len)
+    dup.0 neq.0
+    while.true
+        movdn.2 dup.1 dup.1 ext2mul
+        # => [(e_1, e_0)^n, i, ...]
+        movup.2 add.1 dup.0 neq.0
+        # => [b, i+1, (e_1, e_0)^n, ...]
+    end # END while
+    push.0 mem_storew.500000100 # z^trace_len
+    # => [0, 0, (z_1, z_0)^trace_len, ...]
+    dropw # Clean stack
+end # END PROC cache_z_exp
+
+# Procedure to compute the exemption points.
+#
+# Input: [...]
+# Output: [g^{-2}, g^{-1}, ...]
+proc.get_exemptions_points
+    mem_load.4294799999
+    # => [g, ...]
+    push.1 swap div
+    # => [g^{-1}, ...]
+    dup.0 dup.0 mul
+    # => [g^{-2}, g^{-1}, ...]
+end # END PROC get_exemptions_points
+
+# Procedure to compute the integrity constraint divisor.
+#
+# The divisor is defined as `(z^trace_len - 1) / ((z - g^{trace_len-2}) * (z - g^{trace_len-1}))`
+# Procedure `cache_z_exp` must have been called prior to this.
+#
+# Input: [...]
+# Output: [divisor_1, divisor_0, ...]
+proc.compute_integrity_constraint_divisor
+    padw mem_loadw.500000100 drop drop # load z^trace_len
+    # Comments below use zt = `z^trace_len`
+    # => [zt_1, zt_0, ...]
+    push.1 push.0 ext2sub
+    # => [zt_1-1, zt_0-1, ...]
+    padw mem_loadw.4294903304 drop drop # load z
+    # => [z_1, z_0, zt_1-1, zt_0-1, ...]
+    exec.get_exemptions_points
+    # => [g^{trace_len-2}, g^{trace_len-1}, z_1, z_0, zt_1-1, zt_0-1, ...]
+    dup.0 mem_store.500000101 # Save a copy of `g^{trace_len-2} to be used by the boundary divisor
+    dup.3 dup.3 movup.3 push.0 ext2sub
+    # => [e_1, e_0, g^{trace_len-1}, z_1, z_0, zt_1-1, zt_0-1, ...]
+    movup.4 movup.4 movup.4 push.0 ext2sub
+    # => [e_3, e_2, e_1, e_0, zt_1-1, zt_0-1, ...]
+    ext2mul
+    # => [denominator_1, denominator_0, zt_1-1, zt_0-1, ...]
+    ext2div
+    # => [divisor_1, divisor_0, ...]
+end # END PROC compute_integrity_constraint_divisor
+
+# Procedure to evaluate numerators of all integrity constraints.
+#
+# All the 1 main and 1 auxiliary constraints are evaluated.
+# The result of each evaluation is kept on the stack, with the top of the stack
+# containing the evaluations for the auxiliary trace (if any) followed by the main trace.
+#
+# Input: [...]
+# Output: [(r_1, r_0)*, ...]
+# where: (r_1, r_0) is the quadratic extension element resulting from the integrity constraint evaluation.
+#        This procedure pushes 2 quadratic extension field elements to the stack
+proc.compute_integrity_constraints
+    # integrity constraint 0 for main
+    padw mem_loadw.4294900003 drop drop padw mem_loadw.4294900004 movdn.3 movdn.3 drop drop padw mem_loadw.4294900005 movdn.3 movdn.3 drop drop ext2add padw mem_loadw.4294900006 movdn.3 movdn.3 drop drop ext2add padw mem_loadw.4294900007 movdn.3 movdn.3 drop drop ext2add padw mem_loadw.4294900008 movdn.3 movdn.3 drop drop ext2add padw mem_loadw.4294900009 movdn.3 movdn.3 drop drop ext2add padw mem_loadw.4294900010 movdn.3 movdn.3 drop drop ext2add padw mem_loadw.4294900011 movdn.3 movdn.3 drop drop ext2add padw mem_loadw.4294900012 movdn.3 movdn.3 drop drop ext2add padw mem_loadw.4294900013 movdn.3 movdn.3 drop drop ext2add padw mem_loadw.4294900014 movdn.3 movdn.3 drop drop ext2add padw mem_loadw.4294900015 movdn.3 movdn.3 drop drop ext2add push.1 push.0 ext2add push.2 push.0 ext2mul ext2sub
+    # Multiply by the composition coefficient
+    padw mem_loadw.4294900200 movdn.3 movdn.3 drop drop ext2mul
+    # integrity constraint 0 for aux
+    padw mem_loadw.4294900072 drop drop padw mem_loadw.4294900072 movdn.3 movdn.3 drop drop padw mem_loadw.4294900150 movdn.3 movdn.3 drop drop padw mem_loadw.4294900003 movdn.3 movdn.3 drop drop ext2add
+    # push the accumulator to the stack
+    push.1 movdn.2 push.0 movdn.2
+    # => [b1, b0, r1, r0, ...]
+    # square 2 times
+    dup.1 dup.1 ext2mul dup.1 dup.1 ext2mul
+    # multiply
+    dup.1 dup.1 movdn.5 movdn.5
+    # => [b1, b0, r1, r0, b1, b0, ...] (4 cycles)
+    ext2mul movdn.3 movdn.3
+    # => [b1, b0, r1', r0', ...] (5 cycles)
+    # clean stack
+    drop drop
+    # => [r1, r0, ...] (2 cycles)
+    padw mem_loadw.4294900001 movdn.3 movdn.3 drop drop padw mem_loadw.4294900002 movdn.3 movdn.3 drop drop ext2mul ext2mul padw mem_loadw.4294900150 movdn.3 movdn.3 drop drop padw mem_loadw.4294900003 movdn.3 movdn.3 drop drop ext2add
+    # push the accumulator to the stack
+    push.1 movdn.2 push.0 movdn.2
+    # => [b1, b0, r1, r0, ...]
+    # square 1 times
+    dup.1 dup.1 ext2mul
+    # multiply
+    dup.1 dup.1 movdn.5 movdn.5
+    # => [b1, b0, r1, r0, b1, b0, ...] (4 cycles)
+    ext2mul movdn.3 movdn.3
+    # => [b1, b0, r1', r0', ...] (5 cycles)
+    # clean stack
+    drop drop
+    # => [r1, r0, ...] (2 cycles)
+    push.1 push.0 padw mem_loadw.4294900001 movdn.3 movdn.3 drop drop ext2sub padw mem_loadw.4294900002 movdn.3 movdn.3 drop drop ext2mul ext2mul ext2add padw mem_loadw.4294900150 movdn.3 movdn.3 drop drop padw mem_loadw.4294900003 movdn.3 movdn.3 drop drop ext2add padw mem_loadw.4294900001 movdn.3 movdn.3 drop drop push.1 push.0 padw mem_loadw.4294900002 movdn.3 movdn.3 drop drop ext2sub ext2mul ext2mul ext2add push.1 push.0 padw mem_loadw.4294900001 movdn.3 movdn.3 drop drop ext2sub push.1 push.0 padw mem_loadw.4294900002 movdn.3 movdn.3 drop drop ext2sub ext2mul ext2add padw mem_loadw.4294900000 movdn.3 movdn.3 drop drop ext2mul padw mem_loadw.4294900000 movdn.3 movdn.3 drop drop ext2sub push.1 push.0 ext2add ext2mul ext2sub
+    # Multiply by the composition coefficient
+    padw mem_loadw.4294900200 drop drop ext2mul
+end # END PROC compute_integrity_constraints
+
+# Procedure to evaluate the boundary constraint numerator for the first row of the main trace
+#
+# Input: [...]
+# Output: [(r_1, r_0)*, ...]
+# Where: (r_1, r_0) is one quadratic extension field element for each constraint
+proc.compute_boundary_constraints_main_first
+    # boundary constraint 0 for main
+    padw mem_loadw.4294900003 movdn.3 movdn.3 drop drop push.0 push.0 ext2sub
+    # Multiply by the composition coefficient
+    padw mem_loadw.4294900201 movdn.3 movdn.3 drop drop ext2mul
+end # END PROC compute_boundary_constraints_main_first
+
+# Procedure to evaluate all integrity constraints.
+#
+# Input: [...]
+# Output: [(r_1, r_0), ...]
+# Where: (r_1, r_0) is the final result with the divisor applied
+proc.evaluate_integrity_constraints
+    exec.compute_integrity_constraints
+    # Numerator of the transition constraint polynomial
+    ext2add ext2add
+    # Divisor of the transition constraint polynomial
+    exec.compute_integrity_constraint_divisor
+    ext2div # divide the numerator by the divisor
+end # END PROC evaluate_integrity_constraints
+
+# Procedure to evaluate all boundary constraints.
+#
+# Input: [...]
+# Output: [(r_1, r_0), ...]
+# Where: (r_1, r_0) is the final result with the divisor applied
+proc.evaluate_boundary_constraints
+    exec.compute_boundary_constraints_main_first
+    # => [(first1, first0), ...]
+    # Compute the denominator for domain FirstRow
+    padw mem_loadw.4294903304 drop drop # load z
+    push.1 push.0 ext2sub
+    # Compute numerator/denominator for first row
+    ext2div
+end # END PROC evaluate_boundary_constraints
+
+# Procedure to evaluate the integrity and boundary constraints.
+#
+# Input: [...]
+# Output: [(r_1, r_0), ...]
+export.evaluate_constraints
+    exec.cache_z_exp
+    exec.evaluate_integrity_constraints
+    exec.evaluate_boundary_constraints
+    ext2add
+end # END PROC evaluate_constraints
+

air-script/tests/functions/functions.rs

@@ -0,0 +1,91 @@
+use winter_air::{Air, AirContext, Assertion, AuxTraceRandElements, EvaluationFrame, ProofOptions as WinterProofOptions, TransitionConstraintDegree, TraceInfo};
+use winter_math::fields::f64::BaseElement as Felt;
+use winter_math::{ExtensionOf, FieldElement};
+use winter_utils::collections::Vec;
+use winter_utils::{ByteWriter, Serializable};
+
+pub struct PublicInputs {
+    stack_inputs: [Felt; 16],
+}
+
+impl PublicInputs {
+    pub fn new(stack_inputs: [Felt; 16]) -> Self {
+        Self { stack_inputs }
+    }
+}
+
+impl Serializable for PublicInputs {
+    fn write_into<W: ByteWriter>(&self, target: &mut W) {
+        target.write(self.stack_inputs.as_slice());
+    }
+}
+
+pub struct FunctionsAir {
+    context: AirContext<Felt>,
+    stack_inputs: [Felt; 16],
+}
+
+impl FunctionsAir {
+    pub fn last_step(&self) -> usize {
+        self.trace_length() - self.context().num_transition_exemptions()
+    }
+}
+
+impl Air for FunctionsAir {
+    type BaseField = Felt;
+    type PublicInputs = PublicInputs;
+
+    fn context(&self) -> &AirContext<Felt> {
+        &self.context
+    }
+
+    fn new(trace_info: TraceInfo, public_inputs: PublicInputs, options: WinterProofOptions) -> Self {
+        let main_degrees = vec![TransitionConstraintDegree::new(1)];
+        let aux_degrees = vec![TransitionConstraintDegree::new(8)];
+        let num_main_assertions = 1;
+        let num_aux_assertions = 0;
+
+        let context = AirContext::new_multi_segment(
+            trace_info,
+            main_degrees,
+            aux_degrees,
+            num_main_assertions,
+            num_aux_assertions,
+            options,
+        )
+        .set_num_transition_exemptions(2);
+        Self { context, stack_inputs: public_inputs.stack_inputs }
+    }
+
+    fn get_periodic_column_values(&self) -> Vec<Vec<Felt>> {
+        vec![]
+    }
+
+    fn get_assertions(&self) -> Vec<Assertion<Felt>> {
+        let mut result = Vec::new();
+        result.push(Assertion::single(3, 0, Felt::ZERO));
+        result
+    }
+
+    fn get_aux_assertions<E: FieldElement<BaseField = Felt>>(&self, aux_rand_elements: &AuxTraceRandElements<E>) -> Vec<Assertion<E>> {
+        let mut result = Vec::new();
+        result
+    }
+
+    fn evaluate_transition<E: FieldElement<BaseField = Felt>>(&self, frame: &EvaluationFrame<E>, periodic_values: &[E], result: &mut [E]) {
+        let main_current = frame.current();
+        let main_next = frame.next();
+        result[0] = main_next[3] - (main_current[4] + main_current[5] + main_current[6] + main_current[7] + main_current[8] + main_current[9] + main_current[10] + main_current[11] + main_current[12] + main_current[13] + main_current[14] + main_current[15] + E::ONE) * E::from(2_u64);
+    }
+
+    fn evaluate_aux_transition<F, E>(&self, main_frame: &EvaluationFrame<F>, aux_frame: &EvaluationFrame<E>, _periodic_values: &[F], aux_rand_elements: &AuxTraceRandElements<E>, result: &mut [E])
+    where F: FieldElement<BaseField = Felt>,
+          E: FieldElement<BaseField = Felt> + ExtensionOf<F>,
+    {
+        let main_current = main_frame.current();
+        let main_next = main_frame.next();
+        let aux_current = aux_frame.current();
+        let aux_next = aux_frame.next();
+        result[0] = aux_next[0] - aux_current[0] * (((aux_rand_elements.get_segment_elements(0)[0] + E::from(main_current[3])).exp(E::PositiveInteger::from(4_u64)) * E::from(main_current[1]) * E::from(main_current[2]) + (aux_rand_elements.get_segment_elements(0)[0] + E::from(main_current[3])).exp(E::PositiveInteger::from(2_u64)) * (E::ONE - E::from(main_current[1])) * E::from(main_current[2]) + (aux_rand_elements.get_segment_elements(0)[0] + E::from(main_current[3])) * E::from(main_current[1]) * (E::ONE - E::from(main_current[2])) + (E::ONE - E::from(main_current[1])) * (E::ONE - E::from(main_current[2]))) * E::from(main_current[0]) - E::from(main_current[0]) + E::ONE);
+    }
+}

parser/src/ast/declarations.rs

@@ -41,6 +41,10 @@ pub enum Declaration {
     ///
     /// Evaluator functions can be defined in any module of the program
     EvaluatorFunction(EvaluatorFunction),
+    /// A pure function definition
+    ///
+    /// Pure functions can be defined in any module of the program
+    Function(Function),
     /// A `periodic_columns` section declaration
     ///
     /// This may appear any number of times in the program, and may be declared in any module.
@@ -523,3 +527,47 @@ impl PartialEq for EvaluatorFunction {
         self.name == other.name && self.params == other.params && self.body == other.body
     }
 }
+
+/// Functions take a group of expressions as parameters and returns a group of expressions. These
+/// values can be a Felt, a Vector or a Matrix. Functions do not take trace bindings as parameters.
+#[derive(Debug, Clone, Spanned)]
+pub struct Function {
+    #[span]
+    pub span: SourceSpan,
+    pub name: Identifier,
+    pub params: Vec<(Identifier, Type)>,
+    pub return_type: Type,
+    pub body: Vec<Statement>,
+}
+impl Function {
+    /// Creates a new function.
+    pub const fn new(
+        span: SourceSpan,
+        name: Identifier,
+        params: Vec<(Identifier, Type)>,
+        return_type: Type,
+        body: Vec<Statement>,
+    ) -> Self {
+        Self {
+            span,
+            name,
+            params,
+            return_type,
+            body,
+        }
+    }
+
+    pub fn param_types(&self) -> Vec<Type> {
+        self.params.iter().map(|(_, ty)| *ty).collect::<Vec<_>>()
+    }
+}
+
+impl Eq for Function {}
+impl PartialEq for Function {
+    fn eq(&self, other: &Self) -> bool {
+        self.name == other.name
+            && self.params == other.params
+            && self.return_type == other.return_type
+            && self.body == other.body
+    }
+}