Does rand() / RAND_MAX return[0, 1) or [0,1]?

Question

I have looked at many places and cannot seem to find the answer. I understand that the probability of rand() / RAND_MAX == 1 is low because rand() is unlikely to equal RAND_MAX.
However is it theoretically possible?
I saw someone write, on something similar, that the range is [0, 1), however I do not understand why.

Thanks!

This is integer division as written. Making it floating point division opens other cans of worms though... — StoryTeller - Unslander Monica, Jun 12 '18 at 07:25
[c++reference](http://en.cppreference.com/w/cpp/numeric/random/rand) says the upper bound is included. — HolyBlackCat, Jun 12 '18 at 07:25

Bathsheba · Accepted Answer · 2018-06-12T07:28:55.267

5

Bizarrely rand() / RAND_MAX will only draw 0 or 1 due to the effects of integer division.

Did you mean 1.0 * rand() / RAND_MAX? That can draw 0 and 1; the reason being that rand() is allowed to return RAND_MAX.

That's an unusual way of having things. Normally you don't want to draw 1, so quite often you'll see

rand() / (RAND_MAX + 1.0)

instead. Note that the 1.0 forces the denominator to assume a floating point type, and the numerator will also therefore be promoted. On its own, RAND_MAX + 1 is liable to overflow an integral type, which could have undefined results.

edited Jun 12 '18 at 07:28

answered Jun 12 '18 at 07:24

Bathsheba

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Well... unless you want to have an *extremely* biased coin simulation. – StoryTeller - Unslander Monica Jun 12 '18 at 07:26
I have edited to clarify. The code was `(double) rand() / RAND_MAX`. – dng Jun 12 '18 at 14:41
1

@dng: I'd be inclined to roll it back: it doesn't really add anything to the question, and it invalidates this and the other answer. – Bathsheba Jun 12 '18 at 14:43
So how do you take a `rand()` result and convert it to, say, a 6-sided die value of 1 to 6? If it can return 0, and it can return 1, then that's quite difficult. – PhilHibbs Jun 30 '20 at 18:39

Yunnosch · Answer 2 · 2018-06-12T07:38:21.607

Quoting from here:
http://en.cppreference.com/w/c/numeric/random/rand

Returns a pseudo-random integer value between 0 and RAND_MAX (0 and RAND_MAX included).

Quoting from standard:
http://port70.net/~nsz/c/c11/n1570.html#7.22
(bold by me)

RAND_MAX which expands to an integer constant expression that is the maximum value returned by the rand function

Those quotes show that RAND_MAX can be returned, but as you say, very unlikely.

For rand() / RAND_MAX it means that 1 is actually a possible result, though because of integer division, 0 is the only other possible result.

However, if you calculate in floating points, in order to aslo get the values in between, then be careful with the problems described here:
Is floating point math broken?

Does rand() / RAND_MAX return[0, 1) or [0,1]?

2 Answers2