import math
from decimal import Decimal, getcontext
import secrets

# Set precision for Decimal to handle large numbers
getcontext().prec = 512

# Secure Random Generator for 512-bit Values
def generate_random_512bit():
    """Generate a random 512-bit number."""
    return Decimal(secrets.SystemRandom().getrandbits(512))

# Quantum-Resistant Primitives
def ECCmod(p, q):
    return (p * q) % (p + q)

def chaos(x, y):
    # Reduce x and y to the range [0, 2π] using modulo
    two_pi = Decimal(2 * math.pi)
    x = x % two_pi
    y = y % two_pi
    return Decimal(math.sin(float(x)) * math.cos(float(y)))

def FFA(n, m):
    return ((n ** 2 + m ** 2) % (n + m + 1))

def LBP(a, b):
    return ((a ** 3 + b ** 3) % (a + b + 1))

def MNPE(c, d):
    return ((c ** 2 * d ** 2 + c * d) % (c + d + 1))

def NTRU(e, f):
    return ((e * f + e ** 2) % (f ** 2 + 1))

def HBK(g, h):
    return ((g + h) % (g * h + 1))

def TQC(i, j):
    return ((i ** 2 + j ** 2) % (i + j + 1))

def FHE(k, l):
    return ((k ** 2 + l ** 2) % (k + l + 1))

def ZKP(m, n):
    return ((m * n + m + n) % (m + n + 1))

# Main Formula
def compute_formula(p, q, x, y, n, m, a, b, c, d, e, f, g, h, i, j, k, l):
    """Compute the complex quantum-resistant formula."""
    ecc = ECCmod(p, q)
    chaotic = chaos(x, y)
    ffa = FFA(n, m)
    lbp = LBP(a, b)
    mnpe = MNPE(c, d)
    ntru = NTRU(e, f)
    hbk = HBK(g, h)
    tqc = TQC(i, j)
    fhe = FHE(k, l)
    zkp = ZKP(m, n)

    # Modular reduction at intermediate steps to prevent overflow
    term1 = (ecc + chaotic + ffa + lbp) % p
    term2 = (mnpe + ntru + hbk) % p
    term3 = (tqc + fhe + zkp) % p

    # Final result
    result = (term1 + term2 + term3) % p
    return result

# Test Implementation
if __name__ == "__main__":
    # Generate large random inputs
    p = generate_random_512bit()
    q = generate_random_512bit()
    x, y = generate_random_512bit(), generate_random_512bit()
    n, m = generate_random_512bit(), generate_random_512bit()
    a, b = generate_random_512bit(), generate_random_512bit()
    c, d = generate_random_512bit(), generate_random_512bit()
    e, f = generate_random_512bit(), generate_random_512bit()
    g, h = generate_random_512bit(), generate_random_512bit()
    i, j = generate_random_512bit(), generate_random_512bit()
    k, l = generate_random_512bit(), generate_random_512bit()
