Why does rand() + rand() produce negative numbers?

Question

I observed that `rand()` library function when it is called just once within a loop, it almost always produces positive numbers. for (i = 0; i < 100; i++) { printf("%d\\n", rand()); }But when I add two `rand()` calls, the numbers generated now have more negative numbers. for (i = 0; i < 100; i++) { printf("%d = %d\\n", rand(), (rand() + rand())); }Can someone explain why I am seeing negative numbers in the second case?PS: I initialize the seed before the loop as `srand(time(NULL))`.

Answer 1

The output of rand() is a positive integer. For this problem to occur it means that the RAND_MAX must be 0x7FFF if the integer is a 16 bit integer or 0x7FFFFFFF for a 32 bit integer.

Looking at the 32 bit case: 50% of the time the returned value will be in the range 0x7FFFFFFF - 0x40000000. If you add two return values from rand() the result will often be in the range 0xFFFFFFFF - 0x80000000. That is where the problem comes up, negative numbers have the high bit set to 1 and are represented as 1s complement. Numbers in that range are negative:

hex value integer value

0xFFFFFFFF -1

0xFFFFFFFE -2

...

0xFFA92743 -5691581

...

0x80000000 -2147483648

The same logic holds for the 16 bit case.

As an aside: in Microsoft Visual studio 2022 C the RAND_MAX is 0x7FFF so in that case it never comes up.