Question

I have written a code which calculates Fibonacci number using my own arbitrary precision functions for multiplication and addition.

#include<iostream>
#include<cstdio>
#include<map>
#include<cstring>

using namespace std;

#define max 3000

struct data_type{
   int string[max]; 
};

struct data_type mul(struct data_type a,struct data_type b) {
   struct data_type c;
   memset(c.string,0,sizeof(int)*max);
   int k;
   int i,j;
   for(i=max-1;i>0;i--) {
      int num=a.string[i];
      int carry=0;
      int rem=0;
      k=i;

      for(j=max-1;j>0;j--) {
         int n=b.string[j]*num + carry;
         int r=n%10;
         carry=n/10;
         int p=(c.string[k]+r+rem)%10;
         rem=(c.string[k]+r+rem)/10;
         c.string[k]=p;  
         k--;
      }
   }

   return c;
}

struct data_type add(struct data_type a,struct data_type b) {
   struct data_type c;
   memset(c.string,0,sizeof(int)*max);
   int carry=0;
   int i,j;
   int k=max-1;

   for(i=max-1,j=max-1;i>0 && j>0;i--,j--) {
      int res=(a.string[i] + b.string[j])+carry;
      carry=res/10;
      c.string[k--]=res%10;
   }

   return c;
}

void multiply(struct data_type f[2][2],struct data_type m[2][2]){

   struct data_type x,y,z,t;
   x=add(mul(f[0][0],m[0][0]),mul(f[0][1],m[1][0]));    
   y=add(mul(f[0][0],m[0][1]),mul(f[0][1],m[1][1]));    
   z=add(mul(f[1][0],m[0][0]),mul(f[1][1],m[1][0]));    
   t=add(mul(f[1][0],m[0][1]),mul(f[1][1],m[1][1]));    

   f[0][0]=x;
   f[0][1]=y;
   f[1][0]=z;
   f[1][1]=t;       
}

void power(struct data_type f[2][2],unsigned long long n){

   if((n==0)||(n==1))
      return ;
   struct data_type a,b;
   memset(a.string,0,sizeof(int)*max);
   memset(b.string,0,sizeof(int)*max);
   a.string[max-1]=1;
   b.string[max-1]=0;
   struct data_type m[2][2]={{a,a},{a,b}};  

   power(f,n/2);

   multiply(f,f);

   if(n%2 != 0)
       multiply(f,m);
   }

   struct data_type fib(unsigned long long n){
   struct data_type a,b;
   memset(a.string,0,sizeof(int)*max);
   memset(b.string,0,sizeof(int)*max);
   a.string[max-1]=1;
   b.string[max-1]=0;

   struct data_type f[2][2]={{a,a},{a,b}};

   if(n==0)
      return b;

   power(f,n-1);
   return f[0][0];
}

int main()
{   
   int t;
   cin>>t;

   for(int w=0;w<t;w++){
      unsigned long long n;
      cin>>n;
      struct data_type a,b,c;

      a=fib(n-1);
      b=fib(n+2);
      c=add(a,b);

      int ck=0;

      for(int i=0;i<max;i++) {
         if(c.string[i] && !ck)
            ck=1;

         if(ck)
            cout<<c.string[i];
      }

      cout<<"\n";
   }

   return 0;
}

My problem is that it’s showing SIGSEGV on running but sometimes runs correctly say for example I have tested it on fib(50000) for max=4000 but as soon as I change max=5000 it stops working. I’m breaking my head for hours but still unabled to figure out the problem.

Please tell me what might be possibly wrong with my code.

Is there any logical mistake in the code which is causing runtime error ?

Answer 1

I think the problem is in the mul() function as the index k in the inner for loop can become a negative integer and k is used to index an array.

k is decremented max - 1 times always but it is only set to max - 1 on the first iteration of the outer for loop. In subsequent iterations of the outer for loop it is set to a value less than max - 1 resulting in k becoming negative.

EDIT:

I modified the inner for loop:

for(j=max-1;j>0;j--){
    if (k < 0)
        std::cout << k << "\n";
    ...
}

and supplied 1 and 4 when prompted during execution and many negative values were displayed: so this is definitely one problem.