Bit twiddling in JDK to generate random number

Some time back a friend asked me an algorithm question:
Given an integer random number generator randomN() that can generate random number in the range [0, N), how will you generate random numbers in the range [0, M) where M
I used modulo arithmetic to generate the desired random numbers in the range [0, M). And I reasoned out that if N = q*M + r, every number in the range [0, r] has an occurrence probability of (q+1)/N, but the numbers in the range [r+1, M) has an occurrence probability of only q/N.

It is easy to visualize this. See the diagram below:

You can see that we can divide line of length N units (given in green) by lines of length M units (given in black). When N is not exactly divisible by M, in the last part alone we have only r units.

So if we choose a random integer in the line represented in green, and then take a modulo M on the value, all the values except the values in the range [r+1, M) (represented in red) will occur q+1 times. But the values in that interval will occur only q times.

So how do we generate uniform random numbers? Solution is very simple: when the generated random number is in the last segment, just discard the number and regenerate another random number. My solution looked like this:

 maxAllowed = N - (N mod M)
do {
    randValue = randomN()
} while (randValue >= maxAllowed)
return maxAllowed mod M

 Recently I was reading the Java API documentation for Random.nextInt(M). And I stumbled upon a clever trick that actually does what I did using some bit twiddling. The next(numBits) in Java code generates random numbers of length numBits. Since signed integers are 31 bits, internally nextInt(M) calls next(31). This will return values in the range of [0, MAX_INT + 1). Now using this the code generates a random number in the range of [0, M). What is the clever trick here? Look at how integer overflow is used to detect boundary condition.
do { 
 bits = next(31); 
 val = bits % n; 
} while (bits - val + (n-1) < 0);

This boundary condition is similar to "randValue >= maxAllowed" condition in my code.

Personally I feel that my code is easier to understand and (I guess) performs better. The reason why I guess my code performs better is due to the fact that it does modulo arithmetic exactly two times. But JDK's code performs modulo arithmetic every time in the loop. Also for checking the condition it performs addition of four values, while my boundary condition is a straight forward comparison. 

Yet it was interesting to see this piece of code and spend some time to understand what it is actually doing.

Comments

Post a Comment

Popular posts from this blog

The mysterious ORA-03111 error

Recently one of the applications that I developed started throwing exceptions, that had the following message: SQL state [72000]; error code [1013]; ORA-03111: break received on communication channel When I googled around, I couldn't come across anything useful. Sadly enough most of the sites just showed the documentation for that error, without any explanation from anyone experiencing that issues. So here you go, with the best possible explanation that I could come up with. My application sets two things on the connection that is throwing this exception: It sets the fetchSize to be 2500 rows It sets the query timeout to be 10 seconds The database server and the application are separated over a long latency network (actually there is a NetEm box that emulates the long latency between these two boxes) which has a latency characteristic of 50+/-5 milliseconds. This is the whole setup. It is important to understand how the timeout is handled by the Oracle client (in my case JDBC clien...
Read more

Note on allocationSize parameter of @SequenceGenerator while using JPA

I ran into what I thought as an issue while I was using the sequence ID generation strategy in JPA. The JPA provider I am using is Hibernate. I think sharing my experience will save someone some time. To use a sequence (For e.g. Oracle sequence) to generate values and assign them to the ID field of your persistence object, you will following something like this: @Id @Column(name = "ITEM_ID") @GeneratedValue(strategy = GenerationType.SEQUENCE, generator="ItemIdSeqGenerator") @SequenceGenerator(name="ItemIdSeqGenerator", sequenceName="ITEM_ID_SEQ", allocationSize=1) private long itemId; This means the following things: The @Id annotation says that the field itemId is a primary key. The @Column annotation says that the corresponding column in the database is ITEM_ID. The @GeneratedValue says that the value that needs to be populated in the itemId should be generated, while that object is persisted. The strategy to generate the value is to...
Read more

xVM's vboxmanage.exe command

You can view and edit the configuration of your guest OSs using the vboxmanage command. To view the list of guest OSs you have, give the following command: C:\Program Files\Sun\xVM VirtualBox>VBoxManage.exe list vms VirtualBox Command Line Management Interface Version 2.2.2 (C) 2005-2009 Sun Microsystems, Inc. All rights reserved. "MySolaris" {dc6dc85f-5583-4a1b-bf3e-969941a2cd91} "Ubuntu" {eb973bbf-d86e-4579-85eb-6ea2cd12bf95} "Debian" {3e784597-89d8-4f17-90cb-63e866c651a3} "openSUSE" {6862884e-60e1-4c65-8aab-b57ec38a3922} "Debian-Lenny" {4b561432-abac-4a27-a501-b42af956b96b} To view the specific guest, you can use the UUID of the guest. For e.g. C:\Program Files\Sun\xVM VirtualBox>VBoxManage.exe showvminfo eb973bbf-d86e-4579-85eb-6ea2cd12bf95 VirtualBox Command Line Management Interface Version 2.2.2 (C) 2005-2009 Sun Microsystems, Inc. All rights reserved. Name: Ubuntu Guest OS: Ubuntu UUID: eb973bb...
Read more