未用函式封裝造成的Julia和c相同演算法執行時間的巨大差異

c

#include <cstdio>
int r=100;
int main()
{
    int cnt=0;

    for(int a=-r; a<=r; a++)
        for(int b=-r; b<=r ; b++)
            for(int c=-r; c<=r; c++)
                for(int d=-r; d<=r ; d++)
                    if(a*a+b*b+c*c+d*d-r*r<=0)
                    {
                        //printf("%d %d %d %d %d\n",cnt,a,b,c,d);
                        cnt++;
                    }

    printf("%d",cnt);
}

julia

r,cnt=100,0
for a=-r:r,b=-r:r,c=-r:r,d=-r:r
if a*a+b*b+c*c+d*d-r*r<=0 cnt=cnt+1 end
end
println(cnt)

比較

D:\>g++ p596.cpp -O3

D:\>a\timer a

Timer 3.01  Copyright (c) 2002-2003 Igor Pavlov  2003-07-10
493490641
Kernel Time  =     0.015 = 00:00:00.015 =   0%
User Time    =     1.544 = 00:00:01.544 =  49%
Process Time =     1.560 = 00:00:01.560 =  50%
Global Time  =     3.105 = 00:00:03.105 = 100%

julia> @time include("d:\\p596.jl")
493490641
757.315780 seconds (12.00 G allocations: 101.719 GiB, 3.11% gc time)

不明白巢狀迴圈為什麼分配這麼多記憶體
改用while迴圈

r,cnt=100,0
a=-r
while a<=r
b=-r
while b<=r
c=-r
while c<=r
d=-r
while d<=r
if a*a+b*b+c*c+d*d-r*r<=0 cnt=cnt+1 end
d=d+1
end
c=c+1
end
b=b+1
end
a=a+1
end

println(cnt)

在r=20時，記憶體，時間都比for小一些

julia> @time include("d:\\p596a.jl")  #for
789905
  1.263037 seconds (5.57 M allocations: 65.239 MiB, 0.63% gc time)

julia> @time include("d:\\p596b.jl") #while
789905
  1.044400 seconds (2.60 M allocations: 19.921 MiB, 0.37% gc time)

python的表現很正常

r,cnt=100,0
for a in range(-r,r+1):
 for b in range(-r,r+1):
  for c in range(-r,r+1):
   for d in range(-r,r+1):
    if a*a+b*b+c*c+d*d-r*r<=0:
     cnt=cnt+1
print(cnt)

D:\>a\timer \pypy256\pypy p596.py

Timer 3.01  Copyright (c) 2002-2003 Igor Pavlov  2003-07-10
493490641

Kernel Time  =     0.078 = 00:00:00.078 =   0%
User Time    =    10.218 = 00:00:10.218 =  87%
Process Time =    10.296 = 00:00:10.296 =  87%
Global Time  =    11.716 = 00:00:11.716 = 100%

聯想到上次把python改寫成julia的經過，把上述演算法包含在一個函式裡，然後呼叫函式，速度極大地提高，這個問題得解。

function f5()
r,cnt=100,0
e=-r:r
for a in e,b in e,c in e,d in e
if a*a+b*b+c*c+d*d-r*r<=0 cnt=cnt+1 end
end
println(cnt)
end
@time  f5()
-----
493490641
  1.334010 seconds (6.82 k allocations: 205.733 KiB)

0.51文件中提到

Avoid global variables
A global variable might have its value, and therefore its type, change at any point. This makes it difficult for the compiler to optimize code using global variables. Variables should be local, or passed as arguments to functions, whenever possible.
Any code that is performance critical or being benchmarked should be inside a function.

避免全域性變數
全域性變數的值、型別，都可能變化。這使編譯器難優化使用全域性變數 的程式碼。應使用具部變數 ， 或者把 變數當 做引數傳遞給函式。
對效能至關重要的程式碼，應放入函式中。