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use alloc::vec::Vec;
use super::{op_flags::OpFlags, EvaluationFrame, Felt, FieldElement, TransitionConstraintDegree};
use crate::{
stack::EvaluationFrameExt,
utils::{are_equal, is_binary},
};
#[cfg(test)]
pub mod tests;
// CONSTANTS
// ================================================================================================
/// The number of unique transition constraints in stack manipulation operations.
pub const NUM_CONSTRAINTS: usize = 13;
// The co-efficient of the most significant 16-bit limb in the helper register during aggregation.
pub const TWO_48: Felt = Felt::new(2u64.pow(48));
// The co-efficient of the 2nd most significant 16-bit limb in the helper register during
// aggregation.
pub const TWO_32: Felt = Felt::new(2u64.pow(32));
// The co-efficient of the 3rd significant 16-bit limb in the helper register during aggregation.
pub const TWO_16: Felt = Felt::new(2u64.pow(16));
// The co-efficient of the least significant 16-bit bit in the helper register during aggregation.
pub const TWO_0: Felt = Felt::new(1);
/// The degrees of constraints in individual u32 operations.
pub const CONSTRAINT_DEGREES: [usize; NUM_CONSTRAINTS] = [
// Given it is a degree 6 operation, 6 is added to all the individual constraints
// degree.
9, // constraint for element validity check
7, 7, // 2 constraints in the agg of lower and upper limbs
7, // constraint for U32SPLIT operation
7, // constraint for U32ADD operation
7, // constraint for U32ADD3 operation
7, 8, // 2 constraints for U32SUB operation
8, // constraint for U32MUL operation
8, // constraint for U32MADD operation
8, 7, 7, // constraint for U32DIV operation
];
// U32 OPERATIONS TRANSITION CONSTRAINTS
// ================================================================================================
/// Builds the transition constraint degrees for the u32 operations.
pub fn get_transition_constraint_degrees() -> Vec<TransitionConstraintDegree> {
CONSTRAINT_DEGREES
.iter()
.map(|°ree| TransitionConstraintDegree::new(degree))
.collect()
}
/// Returns the number of transition constraints for the u32 operations.
pub fn get_transition_constraint_count() -> usize {
NUM_CONSTRAINTS
}
/// Enforces constraints for the u32 operations.
pub fn enforce_constraints<E: FieldElement<BaseField = Felt>>(
frame: &EvaluationFrame<E>,
result: &mut [E],
op_flag: &OpFlags<E>,
) -> usize {
let mut index = 0;
let limbs = LimbCompositions::new(frame);
index += enforce_check_element_validity(frame, result, op_flag, &limbs);
// Enforce general constaints of the u32 arithmetic operations.
index += enforce_limbs_agg(frame, &mut result[index..], op_flag, &limbs);
// Enforce constaints of the U32SPLIT operations.
index += enforce_u32split_constraints(frame, &mut result[index..], op_flag.u32split(), &limbs);
// Enforce constaints of the U32ADD operations.
index += enforce_u32add_constraints(frame, &mut result[index..], op_flag.u32add(), &limbs);
// Enforce constaints of the U32ADD3 operations.
index += enforce_u32add3_constraints(frame, &mut result[index..], op_flag.u32add3(), &limbs);
// Enforce constaints of the U32SUB operations.
index += enforce_u32sub_constraints(frame, &mut result[index..], op_flag.u32sub());
// Enforce constaints of the U32MUL operations.
index += enforce_u32mul_constraints(frame, &mut result[index..], op_flag.u32mul(), &limbs);
// Enforce constaints of the U32MADD operations.
index += enforce_u32madd_constraints(frame, &mut result[index..], op_flag.u32madd(), &limbs);
// Enforce constaints of the U32DIV operations.
index += enforce_u32div_constraints(frame, &mut result[index..], op_flag.u32div(), &limbs);
index
}
// TRANSITION CONSTRAINT HELPERS
// ================================================================================================
/// Enforces constraints of the U32SPLIT operation. The U32SPLIT operation splits the top element
/// into two 32-bit numbers. Therefore, the following constraints are enforced:
/// - The aggregation of limbs from the helper registers forms the top element in the stack.
pub fn enforce_u32split_constraints<E: FieldElement<BaseField = Felt>>(
frame: &EvaluationFrame<E>,
result: &mut [E],
op_flag: E,
limbs: &LimbCompositions<E>,
) -> usize {
// Enforces the aggregation of limbs from the helper registers forms the top element in the
// current trace.
result[0] = op_flag * are_equal(frame.stack_item(0), limbs.v64());
1
}
/// Enforces constraints of the U32ADD operation. The U32ADD operation adds the top two
/// elements in the current trace of the stack. Therefore, the following constraints are
/// enforced:
/// - The aggregation of limbs from the helper registers is equal to the sum of the top two element
/// in the stack.
pub fn enforce_u32add_constraints<E: FieldElement<BaseField = Felt>>(
frame: &EvaluationFrame<E>,
result: &mut [E],
op_flag: E,
limbs: &LimbCompositions<E>,
) -> usize {
let a = frame.stack_item(0);
let b = frame.stack_item(1);
// Enforces the aggregation of the least three significant limbs from the helper registers forms
// the sum of a and b.
result[0] = op_flag * are_equal(a + b, limbs.v48());
1
}
/// Enforces constraints of the U32ADD3 operation. The U32ADD3 operation adds the top three
/// elements in the current trace of the stack. Therefore, the following constraints are
/// enforced:
/// - The aggregation of limbs from the helper registers is equal to the sum of the top three
/// elements in the stack.
pub fn enforce_u32add3_constraints<E: FieldElement<BaseField = Felt>>(
frame: &EvaluationFrame<E>,
result: &mut [E],
op_flag: E,
limbs: &LimbCompositions<E>,
) -> usize {
let a = frame.stack_item(0);
let b = frame.stack_item(1);
let c = frame.stack_item(2);
// Enforces the aggregation of the least three significant limbs from the helper registers forms
// the combined sum of a, b and c.
result[0] = op_flag * are_equal(a + b + c, limbs.v48());
1
}
/// Enforces constraints of the U32SUB operation. The U32SUB operation subtracts the first
/// element from the second in the current trace of the stack. Therefore, the following
/// constraints are enforced:
/// - The aggregation of limbs from helper registers is equal to the difference of the top two
/// elements in the stack.
/// - The first element in the next trace should be a binary.
pub fn enforce_u32sub_constraints<E: FieldElement<BaseField = Felt>>(
frame: &EvaluationFrame<E>,
result: &mut [E],
op_flag: E,
) -> usize {
let a = frame.stack_item(0);
let b = frame.stack_item(1);
let c = frame.stack_item_next(0);
let d = frame.stack_item_next(1);
let sub_limb_aggregation = a + d - E::from(TWO_32) * c;
// Enforces the aggregation of the limbs from the helper registers is equal to the difference
// of b and a.
result[0] = op_flag * are_equal(b, sub_limb_aggregation);
// Enforces that c is a binary.
result[1] = op_flag * is_binary(c);
2
}
/// Enforces constraints of the U32MUL operation. The U32MUL operation multiplies the top two
/// elements in the current trace of the stack. Therefore, the following constraints are
/// enforced:
/// - The aggregation of all the limbs in the helper registers is equal to the product of the top
/// two elements in the stack.
pub fn enforce_u32mul_constraints<E: FieldElement<BaseField = Felt>>(
frame: &EvaluationFrame<E>,
result: &mut [E],
op_flag: E,
limbs: &LimbCompositions<E>,
) -> usize {
let a = frame.stack_item(0);
let b = frame.stack_item(1);
// Enforces the aggregation of all the limbs in the helper registers is the product of
// a and b.
result[0] = op_flag * are_equal(a * b, limbs.v64());
1
}
/// Enforces constraints of the U32MADD operation. The U32MADD operation adds the third
/// element to the product of the first two elements in the current trace. Therefore, the
/// following constraints are enforced:
/// - The aggregation of all the limbs in the helper registers is equal to the sum of the third
/// element with the product of the first two elements in the current trace.
pub fn enforce_u32madd_constraints<E: FieldElement<BaseField = Felt>>(
frame: &EvaluationFrame<E>,
result: &mut [E],
op_flag: E,
limbs: &LimbCompositions<E>,
) -> usize {
let a = frame.stack_item(0);
let b = frame.stack_item(1);
let c = frame.stack_item(2);
// Enforces the aggregation of all the limbs in the helper registers is equal to the
// addition of c with the product of a and b.
result[0] = op_flag * are_equal(a * b + c, limbs.v64());
1
}
/// Enforces constraints of the U32DIV operation. The U32DIV operation divides the second element
/// with the first element in the current trace. Therefore, the following constraints are enforced:
/// - The second element in the current trace should be equal to the sum of the first element in the
/// next trace with the product of the first element in the current trace and second element in
/// the next trace.
/// - The difference between the second elements in the current and next trace should be equal to
/// the aggregation of the lower 16-bits limbs.
/// - The difference between the second elements in the current and next trace and one should be
/// equal to the aggregation of the upper 16-bits limbs.
pub fn enforce_u32div_constraints<E: FieldElement<BaseField = Felt>>(
frame: &EvaluationFrame<E>,
result: &mut [E],
op_flag: E,
limbs: &LimbCompositions<E>,
) -> usize {
let a = frame.stack_item(0);
let b = frame.stack_item(1);
let c = frame.stack_item_next(0);
let d = frame.stack_item_next(1);
// Enforces that adding c with the product of a and d is equal to b.
result[0] = op_flag * are_equal(a * d + c, b);
// Enforces the aggregation of the lower limbs is equal to the difference between b and d.
result[1] = op_flag * are_equal(b - d, limbs.v_lo());
// Enforces the aggregation of the upper limbs is equal to the difference between a and c + 1.
result[2] = op_flag * are_equal(a - c, limbs.v_hi() + E::ONE);
3
}
// GENERAL U32 OPERATION CONSTRAINTS
// ===============================================================================================================
/// The constraint checks if the top four element in the trace on aggregating forms a valid field
/// element. no not. This constraint is applicable in `U32SPLIT`, `U32MADD` and `U32MUL`.
pub fn enforce_check_element_validity<E: FieldElement<BaseField = Felt>>(
frame: &EvaluationFrame<E>,
result: &mut [E],
op_flag: &OpFlags<E>,
limbs: &LimbCompositions<E>,
) -> usize {
let m = frame.user_op_helper(4);
// composite flag for u32split, u32madd and u32mul.
let u32_split_mul_madd = op_flag.u32mul() + op_flag.u32split() + op_flag.u32madd();
let v_hi_comp = E::ONE - m * (E::from(TWO_32) - E::ONE - limbs.v_hi());
// Enforces that the agggregation of the limbs forms a valid field element.
result[0] = u32_split_mul_madd * are_equal(v_hi_comp * limbs.v_lo(), E::ZERO);
1
}
/// Enforces constraints of the general operation. The constaints checks if the lower 16-bits limbs
/// are aggregated correctly or not. Therefore, the following constraints are enforced:
/// - The aggregation of lower two lower 16-bits limbs in the helper registers is equal to the
/// second element in the next row.
/// - The aggregation of lower two upper 16-bits limbs in the helper registers is equal to the first
/// element in the next row.
pub fn enforce_limbs_agg<E: FieldElement<BaseField = Felt>>(
frame: &EvaluationFrame<E>,
result: &mut [E],
op_flag: &OpFlags<E>,
limbs: &LimbCompositions<E>,
) -> usize {
// flag of u32 arithmetic operation excluding the `U32DIV` operation.
let u32op_ex_div_assert2 = op_flag.u32_rc_op() - op_flag.u32div() - op_flag.u32assert2();
let u32op_ex_div_assert2_sub = u32op_ex_div_assert2 - op_flag.u32sub();
// Enforces that aggregation of the two lower 16-bits limbs is equal to the second stack element
// in the next row.
result[0] = u32op_ex_div_assert2 * are_equal(frame.stack_item_next(1), limbs.v_lo());
// Enforces that aggregation of the two upper 16-bits limbs is equal to the first stack element
// in the next row.
result[1] = u32op_ex_div_assert2_sub * are_equal(frame.stack_item_next(0), limbs.v_hi());
2
}
// U32 HELPERS
// ================================================================================================
/// Contains intermediate limbs values required in u32 constraint checks.
pub struct LimbCompositions<E: FieldElement> {
v_hi: E,
v_lo: E,
v48: E,
v64: E,
}
impl<E: FieldElement<BaseField = Felt>> LimbCompositions<E> {
// Returns a new instance of [LimbCompositions] instantiated with all the intermediate limbs
// values.
pub fn new(frame: &EvaluationFrame<E>) -> Self {
let v_lo =
E::from(TWO_16) * frame.user_op_helper(1) + E::from(TWO_0) * frame.user_op_helper(0);
let v_hi =
E::from(TWO_16) * frame.user_op_helper(3) + E::from(TWO_0) * frame.user_op_helper(2);
let v48 = E::from(TWO_32) * frame.user_op_helper(2) + v_lo;
let v64 = E::from(TWO_48) * frame.user_op_helper(3) + v48;
Self { v_hi, v_lo, v48, v64 }
}
/// Returns v_hi intermediate flag value.
fn v_hi(&self) -> E {
self.v_hi
}
/// Returns v_lo intermediate flag value.
fn v_lo(&self) -> E {
self.v_lo
}
/// Returns v48 intermediate flag value.
fn v48(&self) -> E {
self.v48
}
/// Returns v64 intermediate flag value.
fn v64(&self) -> E {
self.v64
}
}