limits.c:
#include <stdio.h>

#ifndef CHECK_TYPE
#  define CHECK_TYPE unsigned long
#endif

int overflowed(CHECK_TYPE number, long long inc) {
    CHECK_TYPE sum = (CHECK_TYPE)((long long)number + inc);
    if (inc > 0 && sum <= number)  /* incrementing does not increase value */
        return 1;
    if (inc < 0 && sum >= number)  /* decrementing does not decrease value */
        return 1;
    return 0;
}

CHECK_TYPE find_limit(long long inc) {
    CHECK_TYPE number;
    for (number = 0;
         !overflowed(number, inc);
         number = (CHECK_TYPE)((long long)number + inc),
         inc += (long long)number / 4);
    /* now (number + inc) gives overflow of checked type */
    for ( ;inc > 1 || inc < -1; ) {
        if (overflowed(number, inc/2))
            inc = inc/2;
        else
            number = (CHECK_TYPE)((long long)number + inc/2);
    }
    return number;
}

int main() {
    int size = sizeof(CHECK_TYPE);
    printf("Size of type: %d byte(s)\n", size);
    printf("Supposed upper limit: %llu (signed) or %llu (unsigned)\n",
           (1LL << (size * 8 - 1)) - 1LL, (1LL << (size * 8 - 1))*2LL - 1LL);
    printf("Supposed lower limit: %lld (signed) or %lld (unsigned)\n",
           -(1LL << (size * 8 - 1)), 0LL);
    printf("Calculated upper limit: %llu\n", (unsigned long long)find_limit(1));
    printf("Calculated lower limit: %lld\n", (long long)find_limit(-1));
    return 0;
}

limits.sh:
#!/bin/bash

qualifiers=( "" "signed" "unsigned" )
types=( "char" "short" "int" "long" "long long" )

for type in "${types[@]}"
do
    for qualifier in "${qualifiers[@]}"
    do
        echo "**** check <$qualifier $type>"
        gcc -D"CHECK_TYPE=$qualifier $type" limits.c -o limits
        ./limits
    done
done

./limits.sh > limits.out
limits.out:
**** check < char>
Size of type: 1 byte(s)
Supposed upper limit: 127 (signed) or 255 (unsigned)
Supposed lower limit: -128 (signed) or 0 (unsigned)
Calculated upper limit: 127
Calculated lower limit: -128
**** check <signed char>
Size of type: 1 byte(s)
Supposed upper limit: 127 (signed) or 255 (unsigned)
Supposed lower limit: -128 (signed) or 0 (unsigned)
Calculated upper limit: 127
Calculated lower limit: -128
**** check <unsigned char>
Size of type: 1 byte(s)
Supposed upper limit: 127 (signed) or 255 (unsigned)
Supposed lower limit: -128 (signed) or 0 (unsigned)
Calculated upper limit: 255
Calculated lower limit: 0
**** check < short>
Size of type: 2 byte(s)
Supposed upper limit: 32767 (signed) or 65535 (unsigned)
Supposed lower limit: -32768 (signed) or 0 (unsigned)
Calculated upper limit: 32767
Calculated lower limit: -32768
**** check <signed short>
Size of type: 2 byte(s)
Supposed upper limit: 32767 (signed) or 65535 (unsigned)
Supposed lower limit: -32768 (signed) or 0 (unsigned)
Calculated upper limit: 32767
Calculated lower limit: -32768
**** check <unsigned short>
Size of type: 2 byte(s)
Supposed upper limit: 32767 (signed) or 65535 (unsigned)
Supposed lower limit: -32768 (signed) or 0 (unsigned)
Calculated upper limit: 65535
Calculated lower limit: 0
**** check < int>
Size of type: 4 byte(s)
Supposed upper limit: 2147483647 (signed) or 4294967295 (unsigned)
Supposed lower limit: -2147483648 (signed) or 0 (unsigned)
Calculated upper limit: 2147483647
Calculated lower limit: -2147483648
**** check <signed int>
Size of type: 4 byte(s)
Supposed upper limit: 2147483647 (signed) or 4294967295 (unsigned)
Supposed lower limit: -2147483648 (signed) or 0 (unsigned)
Calculated upper limit: 2147483647
Calculated lower limit: -2147483648
**** check <unsigned int>
Size of type: 4 byte(s)
Supposed upper limit: 2147483647 (signed) or 4294967295 (unsigned)
Supposed lower limit: -2147483648 (signed) or 0 (unsigned)
Calculated upper limit: 4294967295
Calculated lower limit: 0
**** check < long>
Size of type: 8 byte(s)
Supposed upper limit: 9223372036854775807 (signed) or 18446744073709551615 (unsigned)
Supposed lower limit: -9223372036854775808 (signed) or 0 (unsigned)
Calculated upper limit: 9223372036854775807
Calculated lower limit: -9223372036854775808
**** check <signed long>
Size of type: 8 byte(s)
Supposed upper limit: 9223372036854775807 (signed) or 18446744073709551615 (unsigned)
Supposed lower limit: -9223372036854775808 (signed) or 0 (unsigned)
Calculated upper limit: 9223372036854775807
Calculated lower limit: -9223372036854775808
**** check <unsigned long>
Size of type: 8 byte(s)
Supposed upper limit: 9223372036854775807 (signed) or 18446744073709551615 (unsigned)
Supposed lower limit: -9223372036854775808 (signed) or 0 (unsigned)
Calculated upper limit: 18446744073709551615
Calculated lower limit: 0
**** check < long long>
Size of type: 8 byte(s)
Supposed upper limit: 9223372036854775807 (signed) or 18446744073709551615 (unsigned)
Supposed lower limit: -9223372036854775808 (signed) or 0 (unsigned)
Calculated upper limit: 9223372036854775807
Calculated lower limit: -9223372036854775808
**** check <signed long long>
Size of type: 8 byte(s)
Supposed upper limit: 9223372036854775807 (signed) or 18446744073709551615 (unsigned)
Supposed lower limit: -9223372036854775808 (signed) or 0 (unsigned)
Calculated upper limit: 9223372036854775807
Calculated lower limit: -9223372036854775808
**** check <unsigned long long>
Size of type: 8 byte(s)
Supposed upper limit: 9223372036854775807 (signed) or 18446744073709551615 (unsigned)
Supposed lower limit: -9223372036854775808 (signed) or 0 (unsigned)
Calculated upper limit: 18446744073709551615
Calculated lower limit: 0