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PO
primarykey
Id
10984975
data
AcceptedAnswerId
0
AnswerCount
0
ClosedDate
CommentCount
5
CommunityOwnedDate
CreationDate
2012-06-11T17:44:04.150
FavoriteCount
0
LastActivityDate
2016-03-25T23:16:20.523
LastEditDate
2016-03-25T23:16:20.523
LastEditorUserId
1709587
OwnerUserId
1413793
ParentId
10984974
PostTypeId
2
Score
345
ViewCount
0
LastEditorDisplayName
text
Body
So <code>rand()</code> is a pseudo-random number generator which chooses a natural number between 0 and <code>RAND_MAX</code>, which is a constant defined in <code>cstdlib</code> (see this <a href="http://en.cppreference.com/w/cpp/numeric/random/rand" rel="noreferrer">article</a> for a general overview on <code>rand()</code>). Now what happens if you want to generate a random number between say 0 and 2? For the sake of explanation, let's say <code>RAND_MAX</code> is 10 and I decide to generate a random number between 0 and 2 by calling <code>rand()%3</code>. However, <code>rand()%3</code> does not produce the numbers between 0 and 2 with equal probability! When <code>rand()</code> returns 0, 3, 6, or 9, <code>rand()%3 == 0</code>. Therefore, P(0) = 4/11 When <code>rand()</code> returns 1, 4, 7, or 10, <code>rand()%3 == 1</code>. Therefore, P(1) = 4/11 When <code>rand()</code> returns 2, 5, or 8, <code>rand()%3 == 2</code>. Therefore, P(2) = 3/11 This does not generate the numbers between 0 and 2 with equal probability. Of course for small ranges this might not be the biggest issue but for a larger range this could skew the distribution, biasing the smaller numbers. So when does <code>rand()%n</code> return a range of numbers from 0 to n-1 with equal probability? When <code>RAND_MAX%n == n - 1</code>. In this case, along with our earlier assumption <code>rand()</code> does return a number between 0 and <code>RAND_MAX</code> with equal probability, the modulo classes of n would also be equally distributed. So how do we solve this problem? A crude way is to keep generating random numbers until you get a number in your desired range: <pre><code>int x; do { x = rand(); } while (x >= n); </code></pre> but that's inefficient for low values of <code>n</code>, since you only have a <code>n/RAND_MAX</code> chance of getting a value in your range, and so you'll need to perform <code>RAND_MAX/n</code> calls to <code>rand()</code> on average. A more efficient formula approach would be to take some large range with a length divisible by <code>n</code>, like <code>RAND_MAX - RAND_MAX % n</code>, keep generating random numbers until you get one that lies in the range, and then take the modulus: <pre><code>int x; do { x = rand(); } while (x >= (RAND_MAX - RAND_MAX % n)); x %= n; </code></pre> For small values of <code>n</code>, this will rarely require more than one call to <code>rand()</code>. <hr> Works cited and further reading: <ul> <li><a href="http://www.cplusplus.com/reference/clibrary/cstdlib/rand/" rel="noreferrer">CPlusPlus Reference</a></li> <li><a href="http://eternallyconfuzzled.com/arts/jsw_art_rand.aspx" rel="noreferrer">Eternally Confuzzled</a> </li> </ul> <hr>
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1. This table or related slice is empty.
PostParentId
1. POWhy do people say there is modulo bias when using a random number generator?
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1. PTAnswer
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1. USMark Amery
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1. USuser1413793
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1. POWhy do people say there is modulo bias when using a random number generator?
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