import argparse
import random
import time
import matplotlib.pyplot as plt

def sample_pi(n):
    s = 0
    for i in range(n):
        x = random.random()
        y = random.random()
        if x**2 + y**2 <= 1.0:
            s += 1
    return s

def measure_execution_time(function, *args):
    start_time = time.time()
    result = function(*args)
    end_time = time.time()
    elapsed_time = end_time - start_time
    return result, elapsed_time

def compute_pi(args):
    random.seed(1)
    n_total = args.steps
    s_total, elapsed_time_sample_pi = measure_execution_time(sample_pi, n_total)
    pi_est = (4.0 * s_total) / n_total
    return elapsed_time_sample_pi

def theoretical_speedup(serial_fraction, k):
    return 1 / (serial_fraction + (1 - serial_fraction) / k)

def plot_speedup(k_values, measured_speedup, theoretical_speedup_values):
    plt.plot(k_values, measured_speedup, marker='o', label='Measured Speedup')
    plt.plot(k_values, theoretical_speedup_values, marker='x', label='Theoretical Speedup (Amdahl\'s Law)')
    plt.xlabel('Number of Cores (k)')
    plt.ylabel('Speedup')
    plt.title('Measured vs. Theoretical Speedup')
    plt.legend()
    plt.grid(True)
    plt.show()

if __name__ == "__main__":
    parser = argparse.ArgumentParser(description='Compute Pi using Monte Carlo simulation')
    parser.add_argument('--steps', '-s', default=1000, type=int, help='Number of steps in the Monte Carlo simulation')
    args = parser.parse_args()

    serial_fraction = 0.0  # Modify this value based on the actual serial fraction
    k_values = [1, 2, 4, 8]  # Define the number of cores (k)

    measured_speedup = []
    theoretical_speedup_values = []

    for k in k_values:
        elapsed_time_single_core = compute_pi(args)  # Measured time for 1 core
        elapsed_time_k_cores = elapsed_time_single_core / k  # Measured time for k cores
        measured_speedup_value = elapsed_time_single_core / elapsed_time_k_cores
        measured_speedup.append(measured_speedup_value)
        theoretical_speedup_value = theoretical_speedup(serial_fraction, k)
        theoretical_speedup_values.append(theoretical_speedup_value)

    # Create a plot to compare measured and theoretical speedup
    plot_speedup(k_values, measured_speedup, theoretical_speedup_values)