![]() Under the hood it is using a good C bignum library. : Here is a Python program to compute very large Fibonacci numbers, modified to now accept an optional modulus. If you use exponentiation by squaring (which works for matrix powers as well since matrix multiplication is associative) together with a good big int library - it becomes perfectly feasible to compute the millionth Fibonacci number. It is well known (see this) that the nth Fibonacci number is one of the 4 entries of the nth power of the matrix ,]. On the other hand - if you want to simply compute the millionth number, you can do so - though it would be better to use a method which doesn't compute all of the intermediate numbers (as simply computing rather than printing them all would still be infeasible for large enough n). I think that you will need more than a big int library to do that. You are thus trying to print 10^11 = 100 billion digits. The average length of one of the first million Fibonacci numbers is thus over 100,000 = 10^5. A simple use of logarithms shows that the millionth Fibonacci number thus has over 200,000 digits. Be patient, you'll need ten years to learn programming.īy Binet's Formula the nth Fibonacci Number is approximately the golden ratio (roughly 1.618) raised to the power n and then divided by the square root of 5. 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. If you work on software developement, you'll be first asked to solve real-world problems (e.g. Understanding and thinking about the problem (and sub-problems too!) is an interesting part of software development. 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. 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. A cheap calculator, a pencil and a paper should be enough, and probably the calculator is not needed at all.) (I guess that with slightly more thinking, you don't need any computer or any C program to compute that. A 10 digits integer fits in a 64 bits int64_t so with some thinking you don't need any bignum library. The modulus of a sum (or a product) is congruent to the sum (resp. ![]() Read some math textbook about modular arithmetic. Clever algorithms exist for bignum arithmetic which are much more efficient than the naive one you would imagine.Īctually, you don't need any bigints. Notice that efficient bignum arithmetic is a hard subject. (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) As John Coleman answered it has about 200K digits (i.e. Of course, you won't print all the fibonacci numbers, only the last 1000000 th one (so a cheap laptop today has enough memory, and would spit that number in less than an hour). 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). Without thinking much, you could use some bignum library like GMPlib. Read much more about Fibonacci numbers (and read twice). You want the last 10 digits of Fib(1000000). 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). I don't understand how to stop it in all honesty.Ĭan anybody point me in the right direction to how to actually handle numbers of this size? 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. This is the output for the first 100 numbers: First 100 terms of Fibonacci series are :. I am using long long to try and make sure there are enough bits to store the number. Printf("First %d terms of Fibonacci series are :-\n",n) Unsigned long long n, first = 0, second = 1, next, c 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. UPDATE: The actual problem is I want to get the last 10 digits of F(1,000,000) I am trying to write C code which will print the first 1million Fibonacci numbers.
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