syphilis:

I poked around with it and came up with something for you to figure it out without the looping.

$ cat funky_bits.cc
// funky_bits.cpp
//
// experiment with odd bit handling?
//
// 20200227

#include <stdio.h>

// Some test cases
unsigned long long foo[] = {
    0xcab312,
    0xdeadbeef,
    0xdeadbeef0,
    0xdeadbeef000,
    0x138,
    9007199254740992ULL,
    18446744073709551615ULL
};

// Needs a good name, and the type shenanigans should be cleaned up
bool duzzit_fit(unsigned long long t) {

    // First we need to identify the lowest bit set
    long long neg_t = -(long long)t;
    long long last_set = t & neg_t;

    // Shift it left 52 bits to get location of lowest invalid bit
    // NOTE: If smallest invalid bit is far enough left, then this wil
+l turn into 0
    // making the invalid bits also 0, which happens to be OK!
    long long smallest_invalid = last_set << 52;

    // Convert it to a bit mask for the smallest invalid bit and those
+ to the left.
    unsigned long long valid_bits = smallest_invalid - 1;
    unsigned long long invalid_bits = ~valid_bits;

    // Uncomment for debugging
    //printf( "               t:%16llx\n"
    //        "        last_set:%16llx\n"
    //        "           neg_t:%16llx\n"
    //        "smallest_invalid:%16llx\n"
    //        "      valid_bits:%16llx\n"
    //        "    invalid_bits:%16llx\n",
    //        t, last_set, neg_t, smallest_invalid,
    //        valid_bits, invalid_bits);

    // It's a 'valid' number unless one of the upper-order invalid bit
+s are set
    return ! (t & invalid_bits);
}

int main(int, char **) {
    for (int z=0; z<sizeof(foo)/sizeof(foo[0]); ++z) {
        unsigned long long i = foo[z];
        bool b = duzzit_fit(i);
        printf("%lld: %s\n", i, b ? "OK" : "**NOPE**");
    }
    return 0;
}

$ clang -o funky_bits funky_bits.cc

$ ./funky_bits
13284114: OK
3735928559: OK
59774856944: OK
15302363377664: OK
312: OK
9007199254740992: OK
-1: **NOPE**
[download]

Cleaning it up, adding more test cases, further testing, debugging and simplification are all left as exercises for the reader... ;^D

I was originally thinking of making a lookup table, but thought of this along the way.

Update: fixed the abomination that was the first sentence.

...roboticus

When your only tool is a hammer, all problems look like your thumb.