Why there is unexpected result in arc4random() % n?

Question

i have

for (int i = 0; i< 10; i++) {
    CGFloat longerA = ((arc4random() % 80) - 40) / 100.0f;
    NSLog(@"%f",longerA);
}

and the result is

2013-09-20 11:41:30.801 ****[7025:a0b] 0.390000
2013-09-20 11:41:30.801 ****[7025:a0b] 0.080000
2013-09-20 11:41:30.801 ****[7025:a0b] 0.380000
2013-09-20 11:41:30.801 ****[7025:a0b] 42949672.000000
2013-09-20 11:41:30.802 ****[7025:a0b] 0.060000
2013-09-20 11:41:30.802 ****[7025:a0b] 0.080000
2013-09-20 11:41:30.802 ****[7025:a0b] 0.290000
2013-09-20 11:41:30.802 ****[7025:a0b] 42949672.000000
2013-09-20 11:41:30.803 ****[7025:a0b] 0.350000
2013-09-20 11:41:30.803 ****[7025:a0b] 0.180000

i just cant understand why there are results 42949672.000000

Please explain me why this is happening

As i "understand" It must take random(80) - 40 and result / 100.0f so i just don't understand how this (arc4random() % 80) can be more then 79.

Answer 1

The arc4random function is documented to return and u_int32_t. That sounds like an unsigned type, so that when you roll a number < 40 and then subtract 40, you get an arithmetic underflow. That’s where the big number comes from (2^32 – something).

Answer 2

arc4random returns unsigned integers, which can not be below 0. Subtracting 40 will underflow and wrap around to something close to the maximum value.

You also have modulo bias in your function (some values will be more common than others). Correct for this by using arc4random_uniform(80) instead of doing % 80. Thus the correct solution is:

for (int i = 0; i< 10; i++) {
    CGFloat longerA = (((int)arc4random_uniform(80)) - 40) / 100.0f;
    NSLog(@"%f",longerA);
}