C print first million Fibonacci numbers
I am trying to write C code which will print the first 1million Fibonacci numbers.
The actual problem is I want to get the last 10 digits of F(1,000,000)
I understand how the sequence works and how to write the code to achieve that however as F(1,000,000) is very large I am struggling to find a way to represent it.
This is code I am using:
#include<stdio.h>
int main()
{
unsigned long long n, first = 0, second = 1, next, c;
printf("Enter the number of terms\n");
scanf("%d",&n);
printf("First %d terms of Fibonacci series are :-\n",n);
for ( c = 0 ; c < n ; c++ )
{
if ( c <= 1 )
next = c;
else
{
next = first + second;
first = second;
second = next;
}
printf("%d\n",next);
}
return 0;
}
I am using long long to try and make sure there are enough bits to store the number.
This is the output for the first 100 numbers:
First 100 terms of Fibonacci series are :-
0
1
1
2
3
5
8
13
21
34
55
89
144
233
377
610
987
1597
2584
4181
6765
10946
17711
28657
46368
75025
121393
196418
317811
514229
832040
1346269
2178309
3524578
5702887
9227465
14930352
24157817
39088169
63245986
102334155
165580141
267914296
433494437
701408733
1134903170
1836311903
-1323752223
512559680
-811192543
-298632863
-1109825406
-1408458269
...
Truncated the output but you can see the problem, I believe the size of the number generated is causing the value to overflow to negative. I don't understand how to stop it in all honesty.
Can anybody point me in the right direction to how to actually handle numbers of this size?
I haven't tried to print the first million because if it fails on printing F(100) there isn't much hope of it printing F(1,000,000).
Answer
You want the last 10 digits of Fib(1000000). Read much more about Fibonacci numbers (and read twice).
Without thinking much, you could use some bignum library like GMPlib. You would loop to compute Fib(1000000) using a few mpz_t bigint variables (you certainly don't need an array of a million mpz_t, but less mpz_t variables than you have fingers in your hand). Of course, you won't print all the fibonacci numbers, only the last 1000000th one (so a cheap laptop today has enough memory, and would spit that number in less than an hour). As John Coleman answered it has about 200K digits (i.e. 2500 lines of 80 digits each).
(BTW, when thinking of a program producing some big output, you'll better guess-estimate the typical size of that output and the typical time to get it; if it does not fit in your desktop room -or your desktop computer-, you have a problem, perhaps an economical one: you need to buy more computing resources)
Notice that efficient bignum arithmetic is a hard subject. Clever algorithms exist for bignum arithmetic which are much more efficient than the naive one you would imagine.
Actually, you don't need any bigints. Read some math textbook about modular arithmetic. The modulus of a sum (or a product) is congruent to the sum (resp. the product) of the modulus. Use that property. A 10 digits integer fits in a 64 bits int64_t so with some thinking you don't need any bignum library.
(I guess that with slightly more thinking, you don't need any computer or any C program to compute that. A cheap calculator, a pencil and a paper should be enough, and probably the calculator is not needed at all.)
The lesson to learn when programming (or when solving math exercises) is to think about the problem and try to reformulate the question before starting coding. J.Pitrat (an Artificial Intelligence pioneer in France, now retired, but still working on his computer) has several interesting blog entries related to that: Is it possible to define a problem?, When Donald and Gerald meet Robert, etc.
Understanding and thinking about the problem (and sub-problems too!) is an interesting part of software development. If you work on software developement, you'll be first asked to solve real-world problems (e.g. make a selling website, or an autonomous vacuum cleaner) and you'll need to think to transform that problem into something which is codable on a computer. Be patient, you'll need ten years to learn programming.