C++ - how to find the length of an integer

Question

I\'m trying to find a way to find the length of an integer (number of digits) and then place it in an integer array. The assignment also calls for doing this without the use

Answer 1

Closed formula for the longest int (I used int here, but works for any signed integral type):

1 + (int) ceil((8*sizeof(int)-1) * log10(2))

Explanation:

                  sizeof(int)                 // number bytes in int
                8*sizeof(int)                 // number of binary digits (bits)
                8*sizeof(int)-1               // discount one bit for the negatives
               (8*sizeof(int)-1) * log10(2)   // convert to decimal, because:
                                              // 1 bit == log10(2) decimal digits
    (int) ceil((8*sizeof(int)-1) * log10(2))  // round up to whole digits
1 + (int) ceil((8*sizeof(int)-1) * log10(2))  // make room for the minus sign

For an int type of 4 bytes, the result is 11. An example of 4 bytes int with 11 decimal digits is: "-2147483648".

If you want the number of decimal digits of some int value, you can use the following function:

unsigned base10_size(int value)
{
    if(value == 0) {
        return 1u;
    }

    unsigned ret;
    double dval;
    if(value > 0) {
        ret = 0;
        dval = value;
    } else {
        // Make room for the minus sign, and proceed as if positive.
        ret = 1;
        dval = -double(value);
    }

    ret += ceil(log10(dval+1.0));

    return ret;
}

I tested this function for the whole range of int in g++ 9.3.0 for x86-64.