R_Python_C_Rust效率对比(蒙特卡洛方法)

蒙特卡洛计算圆周率 PI

蒙特卡洛计算圆周率 PI 其实是一个非常经典的案例，在 R 仿真里面，也都有。

基本上案例如下：

在一个边长为 1 的正方形里面，有一个半径为 1/2 的圆。
正方形和圆共一个中心点。圆内切正方形。
向这个正方形里面投点，计算点落在圆内的数量。落在圆内点的数量比上总点数就是等于 $\pi/4$ 。

那么按照这个思想，只要是不断的生成若干个点，计算占比即可。

C 代码

这里先分享一个 C 语言的代码：

#include 
#include 
#include 
#include 

#define N_POINTS 10000000
#define N_REPEATS 5

float estimate_pi(int n_points) {
   double x, y, radius_squared, pi;
   int within_circle=0;

   for (int i=0; i < n_points; i++) {
      x = (double)rand() / RAND_MAX;
      y = (double)rand() / RAND_MAX;

      radius_squared = x*x + y*y;
      if (radius_squared <= 1) within_circle++;
   }

   pi=(double)within_circle/N_POINTS * 4;
   return pi;
}

int main() {
    double avg_time = 0;

    srand(42);

    for (int i=0; i < N_REPEATS; i++) {
        auto begin = std::chrono::high_resolution_clock::now();
        double pi = estimate_pi(N_POINTS);
        auto end = std::chrono::high_resolution_clock::now();
        auto elapsed = std::chrono::duration_cast(end - begin);
        avg_time += elapsed.count() * 1e-9;
        printf("Pi is approximately %g and took %.5f seconds to calculate.\n", pi, elapsed.count() * 1e-9);
    }

    printf("\nEach loop took on average %.5f seconds to calculate.\n", avg_time / N_REPEATS);
}


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这里在 clion 里面运行一下，可以看到非常的快，基本上都是在 0.19 秒左右。

python 代码

既然 c 语言这么快，那 python 是什么情况，运行效率如何，这里给到 python 代码：

import random
import time
import argparse


def estimate_pi(
    n_points: int,
    show_estimate: bool,
) -> None:
    """
    Simple Monte Carlo Pi estimation calculation.

    Parameters
    ----------
    n_points
        number of random numbers used to for estimation.
    show_estimate
        if True, will show the estimation of Pi, otherwise
        will not output anything.
    """
    within_circle = 0

    for _ in range(n_points):
        x, y = (random.uniform(-1, 1) for v in range(2))
        radius_squared = x**2 + y**2

        if radius_squared <= 1:
            within_circle += 1

    pi_estimate = 4 * within_circle / n_points

    if not show_estimate:
        print("Final Estimation of Pi=", pi_estimate)


def run_test(
    n_points: int,
    n_repeats: int,
    only_time: bool,
) -> None:
    """
    Perform the tests and measure required time.

    Parameters
    ----------
    n_points
        number of random numbers used to for estimation.
    n_repeats
        number of times the test is repeated.
    only_time
        if True will only print the time, otherwise
        will also show the Pi estimate and a neat formatted
        time.
    """
    start_time = time.time()

    for _ in range(n_repeats):
        estimate_pi(n_points, only_time)

    if only_time:
        print(f"{(time.time() - start_time)/n_repeats:.4f}")
    else:
        print(
            f"Estimating pi took {(time.time() - start_time)/n_repeats:.4f} seconds per run."
        )


def positive_integer(value: str) -> int:
    """Check for positive integer in arg_parse."""
    int_value = int(value)

    if int_value <= 0:
        raise argparse.ArgumentTypeError(f"{value} is an invalid positive int value")

    return int_value


def main(arguments=None):
    """Main loop in arg parser."""
    parser = argparse.ArgumentParser()
    parser.add_argument(
        "-p",
        "--n_points",
        help="Number of random points to use for estimating Pi.",
        type=positive_integer,
        default=1_000_000,
    )
    parser.add_argument(
        "-r",
        "--n_repeats",
        help="Number of times to repeat the calculation.",
        type=positive_integer,
        default=5,
    )
    parser.add_argument(
            "--only-time",
            action='store_true',
            default=False,
    )
    args = parser.parse_args()

    run_test(
        args.n_points,
        args.n_repeats,
        args.only_time,
    )


if __name__ == "__main__":
    main()


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这里是 python 的运行结果，基本上在 1.5 秒左右

rust 代码

[package]
name = "code091501"
version = "0.1.0"
edition = "2021"

[dependencies]
rand = "0.8.5"

[profile.release]
opt-level = 3

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use rand::Rng;
use std::time::Instant;
// use std::time::Duration;
// use std::thread::sleep;

fn calculate_pi(sample_n: usize) -> f32 {
    let mut in_circile = 0;
    let mut rng = rand::thread_rng();

    for _ in 0..sample_n {
        let x = rng.gen_range(0.0..1.0);
        let y = rng.gen_range(0.0..1.0);
        let r = x * x + y * y;
        if r < 1.0 {
            in_circile += 1;
        }
    }
    let pi = in_circile as f32 / sample_n as f32 * 4.0;
    pi
}

fn main() {
    for _ in 0..10 {
        let now = Instant::now();
        let pi = calculate_pi(10000000);
        // let pi = 2.00;
        // sleep(Duration::new(2, 0));
        let ela = now.elapsed();
        let use_time = ela.subsec_nanos() as f64 * 1e-9 + ela.as_secs() as f64;
        println!("the pi is : {} use time is: {:.3} s", pi, use_time);
    }
}

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rust 运行效果如下：

R 语言

我的第一个入门语言，那这里我也展示一下 R 的运行效率。

library(tidyverse)


calculate_pi <- function(sample_n) {
  in_circle = 0
  for (index in 1:sample_n) {
    x = runif(1, min = 0, max = 1)
    y = runif(1, min = 0, max = 1)
    r = x*x + y*y
    if (r <1) {
      in_circle = in_circle+1
    }

  }
  pi = in_circle / sample_n * 4
  return(pi)
}


for (index in 1:10) {
  start = Sys.time()

  pi = calculate_pi(10000000)
  end = Sys.time()

  els = end - start

  cat("the pi is :", pi, "use time is : ", els, '\n')
}

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R语言的运行结果：

结论

C 和 rust 运行时间基本在 0.15 秒左右。
python 运行时间基本在 1.5 秒左右。
R 语言运行时间基本在 43 秒左右。

这里要说明一下

C是在window11系统的wsl2虚拟机下面运行的。cpu：17-8750H，内存16G
python是在window11系统下的anaconda下运行的，python版本是3.8。cpu：17-8750H，内存16G
rust是在mac系统下运行的。rust版本是1.62。机器版本是macbook 16寸2019款，cpu：2.6 GHz 六核Intel Core i7
R是在mac系统下运行的。R版本是4.2.1。机器版本是macbook 16寸2019款，cpu：2.6 GHz 六核Intel Core i7

整理表格如下：

语言	运行时间｜
C 语言	0.19s
Rust	0.15s
python	1.5s
R	43.0s