Optimize c code to calculate pi

Question

I have written C code to calculate pi on https://github.com/gongchengra/hacker/blob/master/c/16_pi.c

The code without comments is listed as follows:

#include <stdio.h>
#define NUMBER 100000
int array_divide_number(int *array, int number, int size)
{
    int i,tmp;
    int modulo=0;
    for(i=0;i<size;i++)
    {
    tmp = array[i]+modulo*10;
    array[i] = tmp/number;
    modulo = tmp%number;
    }
    return 0;
}
void print_array(int *array, int size)
{
    int i,last;
    for(last=size-1;last>=0;last--)
    {
    if(array[last] != 0)
    {
        break;
    }
    }
    for(i=0;i<=last;i++)
    {
    printf("%d",array[i]);
    }
    printf("\n");
}
void copy_array(int *source, int *target, int size)
{
    int i;
    for(i=0;i<size;i++)
    {
    target[i] = source[i];
    }
}
void plus_array(int *augend, int *addend, int *sum, int size)
{
    int i;
    for(i=size-1;i>=0;i--)
    {
    sum[i] = augend[i] + addend[i];
    if(sum[i]>9)
    {
        sum[i] = sum[i] % 10;
        sum[i-1]++;
    }
    }
}
void minus_array(int *minuend, int *subtracter, int *answer, int size)
{
    int i;
    for(i=size-1;i>=0;i--)
    {
    if(minuend[i] >= subtracter[i] || i == 0)
    {
        answer[i] = minuend[i] - subtracter[i];
    }
    else
    {
        if(minuend[i-1] == 0)
        {
            minuend[i-2]--;
            minuend[i-1] = 10;
        }
        minuend[i-1]--;
        answer[i] = 10 + minuend[i] - subtracter[i];
    }
    }
}
int main()
{
    int i;
    int flag=1;
    int d5[NUMBER]={0};
    int t5[NUMBER]={0};
    int d239[NUMBER]={0};
    int t239[NUMBER]={0};
    int pi[NUMBER]={0};
    d5[0]=16;
    d239[0]=4;
    array_divide_number(d5,5,NUMBER);
    array_divide_number(d239,239,NUMBER);
    //every iteration will increase three valid digitals
    for(i=1;i<NUMBER*3/2;i+=2)
    {
    copy_array(d5, t5, NUMBER);
    copy_array(d239, t239, NUMBER);
    array_divide_number(t5,i,NUMBER);
    array_divide_number(t239,i,NUMBER);
    if(flag > 0)
    {
        plus_array(pi,t5,pi,NUMBER);
        minus_array(pi,t239,pi,NUMBER);
    }
    else
    {
        minus_array(pi,t5,pi,NUMBER);
        plus_array(pi,t239,pi,NUMBER);
    }
    flag = -1*flag;
    array_divide_number(d5,5*5,NUMBER);
    array_divide_number(d239,239*239,NUMBER);
    }
    print_array(pi, NUMBER);
    return 0;
}

It works, but takes too long:

$time ./16_pi.exe >pi3.log ./16_pi.exe > pi3.log 617.76s user 0.15s system 98% cpu 10:27.94 total

You can see, in order to calculate 100000 digits of pi, it take more than 10 minutes. Is there a way to optimize the code without changing the algorithm of calculate pi (The algorithm used here is pi=(16/5-4/239)-1/3*(16/5^3-4/239^3)+1/5*(16/5^5-4/239^5)+...)

Answer 1

Optimizing the code is changing somehow the algorithm (even if the formula is the same).

You are doing some bignum arithmetic. Bignum algorithms are hard and clever. You should use a bignum library like GMPlib (which probably also profits from special carry-propagating machine instructions; the major gain is clever bignum arithmetic algorithms), it probably should run faster than your naive bignum routines.

Of course, don't forget to ask the compiler to optimize (e.g. gcc -O3 -Wall -mtune=native) when benchmarking

FWIW, see also Fabrice Bellard's page about Pi. And GMP has a page with code about Pi: computing 100,000 digits takes a small fraction of a second.