1.4 倍遅いは嘘な件

mc_divrem.jl

# Linear congruential generators (LCGs)
# Parameters are provided by Park and Miller
# See https://c-faq.com/lib/rand.html

function LCGs(seed::Integer)
    a = 48271
    m = 2147483647

    q, r = divrem(m, a)

    hi, lo = divrem(seed, q)
    test = a * lo - r * hi

    seed = ifelse(test > 0, test, test + m)
 
    return seed, Float64(seed) / m
end

function main()
    seed = 20231226
    num_points = 1000000000
    num_inside = 0
 
    for i in eachindex(Base.OneTo(num_points))
        seed, x = LCGs(seed)
        seed, y = LCGs(seed)
        r2 = x^2 + y^2
        num_inside += (r2 < 1.0)
    end
 
    println("pi=", 4.0 * num_inside / num_points)
end
 
if abspath(PROGRAM_FILE) == @__FILE__
    @time main()
end

mc_jit.py

from numba import jit
import time

# Linear congruential generators (LCGs)
# Parameters are provided by Park and Miller
# See https://c-faq.com/lib/rand.html
@jit(nopython=True)
def LCGs(seed):
    a = 48271
    m = 2147483647

    q, r = divmod(m, a)

    hi, lo = divmod(seed, q)
    test = a * lo - r * hi

    if test > 0:
        seed = test
    else:
        seed = test + m

    rand_num = seed / m
    return seed, rand_num


@jit(nopython=True)
def main():
    seed = 20231226
    num_points = 1000000000
    num_inside = 0

    for i in range(num_points):
        seed, x = LCGs(seed)
        seed, y = LCGs(seed)
        r2 = x**2 + y**2
        num_inside += r2 < 1.0

    print("pi =", 4.0 * float(num_inside) / num_points)


if __name__ == "__main__":
    for _ in range(3):
        s = time.perf_counter()
        main()
        e = time.perf_counter()
        print(f"elapsed {e - s}")

参考にした記事

https://kamemori.com/research/fortran/speed_montecarlo_lcgs_ja.html

$ gfortran -O3 mc.f90
$ time ./a.out
 pi=   3.1415463479999999
./a.out  7.74s user 0.02s system 99% cpu 7.786 total

確かに Fortran は速いのですが

Python

Numba ぐらいは試しましょう．

docker run --rm -it -v $PWD:/work -w /work python:3.11.7 bash
root@8d4708baf43d:/work# pip3 install numba >/dev/null 2>&1
root@8d4708baf43d:/work# python mc.py
pi = 3.141546348
elapsed 11.547261276999961
pi = 3.141546348
elapsed 11.642988100000025
pi = 3.141546348
elapsed 11.440575886999966

Julia

せめて divrem ぐらいの存在は常識にしましょう．

https://docs.julialang.org/en/v1/base/math/#Base.divrem

書き方を統一したいという固執によって柔軟さに欠ける特定のプログラミング言語の実行速度を目立たせるような印象操作はかなり悪意を感じます．

また，使用している Julia が 1.7.3 らしいのですが，コミュニテイではすでにメンテナンスされていないバージョンのものです．
https://julialang.org/blog/2019/08/release-process/ の存在すら知らない素人でしょう．Julia のダウンロードページ　https://julialang.org/downloads/ からリンクが付けられているので気づいて欲しいです．

julia> versioninfo()
Julia Version 1.10.0
Commit 3120989f39b (2023-12-25 18:01 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (x86_64-apple-darwin22.4.0)
  CPU: 16 × Intel(R) Core(TM) i9-9980HK CPU @ 2.40GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, skylake)
  Threads: 1 on 16 virtual cores
Environment:
  JULIA_EDITOR = subl
  JULIA_PROJECT = @.
  JULIA_PKG_USE_CLI_GIT = true

julia mc.jl
pi=3.141546348
  9.639376 seconds (11.28 k allocations: 879.625 KiB, 0.24% compilation time)
pi=3.141546348
  9.365997 seconds (10 allocations: 576 bytes)
pi=3.141546348
  9.267306 seconds (11 allocations: 880 bytes)

https://gist.github.com/terasakisatoshi/783f227994c7cc2f83d40a9071c65ce1