Finding maximum value of a short int variable in C

Question

I was working on Exercise 2-1 of K&R, the goal is to calculate the range of different variable types, bellow is my function to calculate the maximum value a short int can contain:

short int max_short(void) {
    short int i = 1, j = 0, k = 0;
    while (i > k) {
        k = i;
        if (((short int)2 * i) > (short int)0)
            i *= 2;
        else {
            j = i;
            while (i + j <= (short int)0)
                j /= 2;
            i += j;
        }
    }
    return i;
}

My problem is that the returned value by this function is: -32768 which is obviously wrong since I'm expecting a positive value. I can't figure out where the problem is, I used the same function (with changes in the variables types) to calculate the maximum value an int can contain and it worked...

I though the problem could be caused by comparison inside the if and while statements, hence the typecasting but that didn't help...

Any ideas what is causing this ? Thanks in advance!

EDIT: Thanks to Antti Haapala for his explanations, the overflow to the sign bit results in undefined behavior NOT in negative values.

Answer 1

You can't use calculations like this to deduce the range of signed integers, because signed integer overflow has undefined behaviour, and narrowing conversion at best results in an implementation-defined value, or a signal being raised. The proper solution is to just use SHRT_MAX, INT_MAX ... of <limits.h>. Deducing the maximum value of signed integers via arithmetic is a trick question in standardized C language, and has been so ever since the first standard was published in 1989.

Note that the original edition of K&R predates the standardization of C by 11 years, and even the 2nd one - the "ANSI-C" version predates the finalized standard and differs from it somewhat - they were written for a language that wasn't almost, but not quite, entirely unlike the C language of this day.

You can do it easily for unsigned integers though:

unsigned int i = -1;
// i now holds the maximum value of `unsigned int`.