Last active
August 25, 2024 01:06
-
-
Save DiTo97/d0808f41ac789ee9570b0d94153ff828 to your computer and use it in GitHub Desktop.
A collection of prime finding algorithms implemented in pure python
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| import math | |
| def sieve_of_atkin(n: int) -> list[int]: | |
| """The Sieve of Atkin prime finding algorithm, [1]_ | |
| References | |
| ---------- | |
| .. [1] A. O. L. Atkin, D. J. Bernstein, 2003 | |
| """ | |
| if n < 3: return [2] | |
| if n < 5: return [2, 3] | |
| m = n + 1 | |
| P = [2, 3] | |
| sieve = [False] * (m) | |
| sqrtn = math.isqrt(n) | |
| for x in range(1, sqrtn + 1): | |
| for y in range(1, sqrtn + 1): | |
| h = x**2 | |
| k = y**2 | |
| i = 4 * h + k | |
| if i < m and (i % 12 == 1 or i % 12 == 5): sieve[i] = not sieve[i] | |
| i = i - h | |
| if i < m and i % 12 == 7: sieve[i] = not sieve[i] | |
| i = i - 2 * k | |
| if x > y and i < m and i % 12 == 11: sieve[i] = not sieve[i] | |
| for x in range(5, sqrtn): | |
| if sieve[x]: | |
| z = x**2 | |
| for k in range(z, x + 1, z): | |
| sieve[k] = False | |
| for x in range(5, n): | |
| if sieve[x]: P.append(x) | |
| return P | |
| def sieve_of_eratosthenes(n: int) -> list[int]: | |
| """The Sieve of Eratosthenes prime finding algorithm, [1]_ | |
| References | |
| ---------- | |
| .. [1] Nicomachus of Gerasa, 2nd c. AD | |
| Introduction to Arithmetic | |
| """ | |
| sieve = [True] * (n + 1) | |
| sqrtn = math.isqrt(n) | |
| for x in range(2, sqrtn + 1): | |
| if sieve[x]: | |
| for i in range(x * x, n + 1, x): | |
| sieve[i] = False | |
| return [x for x in range(2, n) if sieve[x]] | |
| def segmented_sieve_of_eratosthenes(n: int) -> list[int]: | |
| """The page-segmented Sieve of Eratosthenes prime finding algorithm, [1]_ | |
| Notes | |
| ----- | |
| The algorithm trades space efficiency for time efficiency to the non-segmented algorithm. | |
| References | |
| ---------- | |
| .. [1] C. Bays, R. H. Hudson, 1977 | |
| The Segmented Sieve of Eratosthenes and Primes in Arithmetic Progressions to 10^12 | |
| """ | |
| shape = math.isqrt(n) + 1 | |
| sieve = [True] * shape | |
| P = [] | |
| for x in range(2, shape): | |
| if sieve[x]: | |
| P.append(x) | |
| for i in range(x * x, shape, x): | |
| sieve[i] = False | |
| lower = shape | |
| while lower < n: | |
| upper = min(lower + shape, n) | |
| segments = [True] * (upper - lower) | |
| for x in P: | |
| start = max(x * x, (lower // x) * x) | |
| if start < lower: | |
| start += x | |
| for i in range(start, upper, x): | |
| segments[i - lower] = False | |
| for x in range(lower, upper): | |
| if segments[x - lower]: | |
| P.append(x) | |
| lower = upper | |
| return P | |
| def mixed_sieve(n: int) -> list[int]: | |
| """A prime finding algorithm mixed via rule-of-thumb""" | |
| if n < 1_000: return sieve_of_atkin(n) | |
| return sieve_of_eratosthenes(n) |
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| def main(): | |
| pass | |
| if __name__ == "__main__": | |
| # Initialize the results | |
| results = { | |
| 'sieve_of_eratosthenes': {'time': [], 'space': []}, | |
| 'sieve_of_atkin': {'time': [], 'space': []}, | |
| 'mixed_sieve': {'time': [], 'space': []}, | |
| # 'segmented_sieve_of_eratosthenes': {'time': [], 'space': []}, # FIXME: too slow | |
| } | |
| for limit in tqdm(limits): | |
| print(f"Computing primes up to {limit}...") | |
| for func in [sieve_of_eratosthenes, sieve_of_atkin, mixed_sieve]: | |
| elapsed_time, mem_usage = measure(func, limit) | |
| results[func.__name__]['time'].append(elapsed_time) | |
| results[func.__name__]['space'].append(mem_usage) | |
| plot_spacetime_efficiency(limits, results) |
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| import matplotlib.pyplot as plt | |
| def plot_timespace_efficiency(limits, results): | |
| """It plots the time and space efficiency of multiple configurations""" | |
| plt.figure(figsize=(12, 6)) | |
| print(len(limits), results) | |
| plt.subplot(1, 2, 1) | |
| for func in results: | |
| plt.plot(limits, results[func]['time'], label=func) | |
| plt.xlabel('Limit') | |
| plt.ylabel('Time (seconds)') | |
| plt.xscale('log') | |
| plt.yscale('log') | |
| plt.legend() | |
| plt.title('Time Efficiency') | |
| plt.subplot(1, 2, 2) | |
| for func in results: | |
| plt.plot(limits, results[func]['space'], label=func) | |
| plt.xlabel('Limit') | |
| plt.ylabel('Space (MiB)') | |
| plt.xscale('log') | |
| plt.yscale('log') | |
| plt.legend() | |
| plt.title('Space Efficiency') | |
| plt.tight_layout() | |
| plt.show() |
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| import typing | |
| from typing import Any | |
| from memory_profiler import memory_usage | |
| def measure(closure: typing.Callable[[...], Any], *args: Any, **kwargs: Any): | |
| """It measures the time and space efficiency of a closure""" | |
| start = time.perf_counter() | |
| usage = memory_usage((closure, args, kwargs), interval=0.1, max_usage=True) | |
| elapsed = time.time() - start | |
| return elapsed, usage |
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| matplotlib | |
| memory-profiler | |
| tqdm |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment