Quick and dirty calculator for the largest fibonacci sequence number which can be held in common integer widths and in a JavaScript Number. Likely only compiles on a 64 bit machine with a reasonably modern gcc or clang.

fibonacci_limits.c

#include <stdio.h>
#include <stdint.h>
#include <inttypes.h>

// Uses the fibonacci sequence defined
// in http://oeis.org/A000045

__uint128_t fib(__uint128_t n) {
	if (n == 0) {
		return 0;
	}
	
	__uint128_t prev = 0;
	__uint128_t result = 1;
	__uint128_t sum;
	
	for(size_t i = 2; i <= n; ++i)
	{
		sum = result + prev;
		prev = result;
		result = sum;
	}
	
	return result;
}

int main(int argc, char *argv[]) {
	int hit[] = {0, 0, 0, 0};
	int next_hit = 0;
	int was_hit;
	
	for (int i = 0; i < 100; i++) {
		was_hit = 0;
		
		__uint128_t result = fib(i);
		
		if (result > INT32_MAX && !hit[0]) {
			was_hit = 1;
			printf("^-- 32 bit signed int max ------------------------------\n");
		} else if (result > UINT32_MAX && !hit[1]) {
			was_hit = 1;
			printf("^-- 32 bit unsigned int max ------------------------------\n");
		} else if (result > UINT64_C(9007199254740992) && !hit[2]) {
			was_hit = 1;
			printf("^-- JavaScript Number (53 bit signed int) max ------------------------------\n");
		} else if (result > INT64_MAX && !hit[3]) {
			was_hit = 1;
			printf("^-- 64 bit signed int max ------------------------------\n");
		} else if (result > UINT64_MAX) {
			printf("^-- 64 bit unsigned int max ------------------------------\n");
			return 0;
		}
		
		if (was_hit) {
			hit[next_hit] = 1;
			++next_hit;
		}
		
		printf("%d:\t%" PRIu64 "\n", i, (uint64_t)result);
	}
	
	return 0;
}

output.txt

0:	0
1:	1
2:	1
3:	2
4:	3
5:	5
6:	8
7:	13
8:	21
9:	34
10:	55
11:	89
12:	144
13:	233
14:	377
15:	610
16:	987
17:	1597
18:	2584
19:	4181
20:	6765
21:	10946
22:	17711
23:	28657
24:	46368
25:	75025
26:	121393
27:	196418
28:	317811
29:	514229
30:	832040
31:	1346269
32:	2178309
33:	3524578
34:	5702887
35:	9227465
36:	14930352
37:	24157817
38:	39088169
39:	63245986
40:	102334155
41:	165580141
42:	267914296
43:	433494437
44:	701408733
45:	1134903170
46:	1836311903
^-- 32 bit signed int max ------------------------------
47:	2971215073
^-- 32 bit unsigned int max ------------------------------
48:	4807526976
49:	7778742049
50:	12586269025
51:	20365011074
52:	32951280099
53:	53316291173
54:	86267571272
55:	139583862445
56:	225851433717
57:	365435296162
58:	591286729879
59:	956722026041
60:	1548008755920
61:	2504730781961
62:	4052739537881
63:	6557470319842
64:	10610209857723
65:	17167680177565
66:	27777890035288
67:	44945570212853
68:	72723460248141
69:	117669030460994
70:	190392490709135
71:	308061521170129
72:	498454011879264
73:	806515533049393
74:	1304969544928657
75:	2111485077978050
76:	3416454622906707
77:	5527939700884757
78:	8944394323791464
^-- JavaScript Number (53 bit signed int) max ------------------------------
79:	14472334024676221
80:	23416728348467685
81:	37889062373143906
82:	61305790721611591
83:	99194853094755497
84:	160500643816367088
85:	259695496911122585
86:	420196140727489673
87:	679891637638612258
88:	1100087778366101931
89:	1779979416004714189
90:	2880067194370816120
91:	4660046610375530309
92:	7540113804746346429
^-- 64 bit signed int max ------------------------------
93:	12200160415121876738
^-- 64 bit unsigned int max ------------------------------