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[remytuyeras]

@CodiumAI-Agent /review

[CodiumAI-Agent]

PR Reviewer Guide 🔍

Here are some key observations to aid the review process:

⏱️ Estimated effort to review: 5 🔵🔵🔵🔵🔵

🧪 No relevant tests

🔒 No security concerns identified

⚡ Recommended focus areas for review Possible Issue In the ArithChannel.generate_u method, the adjustment to ensure the evaluation at arg=1 is zero modulo q might not handle edge cases where randpoly(arg=1) equals self.q. This could lead to incorrect polynomial generation. def generate_u(self) -> Polynomial: """ Generates a random polynomial `u` whose evaluation at `arg=1` is zero modulo `self.q`. This method generates a random polynomial and adjusts it so that its evaluation at `arg = 1` is zero modulo `self.q`. The polynomial is shifted so that the evaluation at `arg = 1` equals zero modulo `q`. Outputs: - Polynomial: The generated polynomial `u` with the required properties. """ # Generate a random polynomial randpoly = Polynomial.random(self.q, self.deg_u) # Append the leading coefficient as 1 randpoly.coefs.append(1) # Adjust to ensure evaluation at 1 is zero modulo q shift = Polynomial.randshift(self.q - randpoly(arg=1), self.q, self.deg_u) # Return the polynomial with the desired properties return shift + randpoly Performance Concern The Polynomial.__mod__ method uses a loop for repeated reductions, which could lead to performance issues for high-degree polynomials. Consider optimizing the reduction process. def __mod__(self, other: Polynomial) -> Polynomial: """ Computes the remainder of the Euclidean division of the current polynomial by another polynomial. This method computes the remainder of polynomial division by utilizing a (Gröbner basis-like) reduction (`<<`) operation. It repeatedly performs reduction until the degree of the remainder is smaller than that of the divisor. The result is the final remainder obtained at the end of the Euclidean division process. Inputs: - other (Polynomial): The polynomial by which to compute the modulus of the current polynomial. Outputs: - Polynomial: The remainder after the Euclidean division of the current polynomial by the other. Notes: - This method uses the `__lshift__` method for polynomial reduction, repeating the process until the degree of the remainder is smaller than that of the divisor. - The modulus operation ensures that the result is a polynomial of lower degree than the divisor, adhering to the principles of polynomial Euclidean division. """ # Perform the (Gröbner basis-like) reduction and extract the remainder. r, _, t = self << other while t: r, _, t = r << other # Return the final remainder after all reduction steps. return r Inefficient Prime Generation The Primes.get_primes method uses trial division for prime generation, which may not scale well for large upper bounds. Consider implementing a more efficient algorithm like the Sieve of Eratosthenes. def get_primes(upperbound: int, cache: list[int] =[]) -> list[int]: """ Generates a list of prime factors for numbers up to a given upper bound using trial division. This method builds on any previously provided list of primes (via `cache`) to optimize prime generation by skipping known non-prime numbers. Inputs: - upperbound (int): The maximum integer (inclusive) for which prime factors are generated. - cache (list, optional): A list of previously generated primes. Defaults to an empty list. Outputs: - list: A list of prime numbers for numbers up to `upperbound`. """ # Initialize the list of primes with the previously cached primes, if provided. previous = cache # Determine the starting point for prime generation: # - If `cache` is provided, start from the next integer after the last cached prime. # - Otherwise, start from 2, the smallest prime number. i = max(2, previous[-1]) if previous else 2 # Iterate over integers from the starting point (`i`) up to the square root of the upper bound. # The range limit is chosen because any composite number `n` must have at least one divisor smaller than or equal to `sqrt(n)`. for k in range(i, int(math.sqrt(upperbound)) + 1): # Assume `k` is prime until proven otherwise. is_prime = True # Check if `k` is divisible by any of the previously identified primes. If divisible, `k` is not a prime, and we exit the loop early. for p in previous: # `k` is divisible by a smaller prime `p`. if k % p == 0: is_prime = False # Stop further checks; `k` is confirmed non-prime. break # If no divisors were found, `k` is a prime number. if is_prime: # Add `k` to the list of primes. previous.append(k) # Return the updated list of primes, including both cached and newly identified primes. return previous