random

© 2011-2013 John Abbott, Anna M. Bigatti; code by John Abbott
GNU Free Documentation License, Version 1.2

CoCoALib Documentation Index

Examples

Here is a typical example of how to use a RandomSeqLong; note that we create the generator before entering the loop, then inside the loop we use the function NextValue to get 100 successive random values (between -9 and 9) from the generator: 

    RandomSeqLong rnd(-9,9);
    for (int i=0; i < 100; ++i)
      cout << NextValue(rnd) << endl;

User documentation

Below, in random RandomSourceOperations we list these handy functions for generating random values:

RandomBool(), RandomLong(lo, hi), RandomBigInt(lo, hi)

they are probably just what you want in a simple program, but using them will make your code thread-unsafe (which is quite acceptable in a small program for personal use).

For a thread-safe solution you should create your own random generator. If you just want to generate many random values of the same type, you should consider using one of the three specialized random sequence generators (which are faster than the more general RandomSource):

There are also RandomNBitPrime and RandomSmallPrime in NumTheory.

Constructors

All constructors have an optional argument which is the initial seed -- it determines the initial state of the generator. If you do not give a seed, the default is 0.

If you create several random sequence generators of the same kind and with the same seed, they will each produce exactly the same sequence of values. If you want to obtain different results each time a program is run, you can seed the generator with the system time (e.g. by supplying as argument time(0)); this is likely desirable unless you're trying to debug a randomized algorithm.

For RandomSource there is also the reseed function documented below (see random reseed).

RandomSource

RandomSource() seeded with 0
RandomSource(n) seeded with n

For convenience, there is a global RandomSource object (belonging to GlobalManager); you can get a reference to it by calling GlobalRandomSource(), but using it will make your code thread-unsafe.

RandomSeqXXXX

There are two families of constructors.

Constructors with default seed (0):

RandomSeqBigInt(lo,hi) seeded with 0
RandomSeqLong(lo,hi) seeded with 0
RandomSeqBool() seeded with 0

Constructors with given (small integer) seed:

RandomSeqBigInt(lo,hi, n) seeded with abs(n)
RandomSeqLong(lo,hi, n) seeded with abs(n)
RandomSeqBool(n) seeded with abs(n)

Each RandomSeqBigInt (or RandomSeqLong) will produce (pseudo) random values uniformly distributed in the range from lo to hi (with both extremes included). An ERR::BadArg exception is thrown if lo > hi; the case lo == hi is allowed.

RandomSource Operations

These are the most convenient functions for generating random values; but they use GlobalRandomSource, so they are thread-unsafe:

A cleaner way is to pass as an argument the specific RandomSource object to be used (in these examples we call it RndSrc):

Reseed

A RandomSource object may be reseeded at any time; immediately after reseeding it will generate the same random sequence as a newly created RandomSource initialized with that same seed. The seed must be an integer value.

Note about thread-safety: the various operations on a fixed RandomSource object are not thread-safe; to achieve thread safety, you should use different objects in different threads. In particular, it is best not to use GlobalRandomSource() in a multi-threaded environment.

RandomSeqXXXX Operations

Once you have created a RandomSeqXXXX you may perform the following operations on it:

You may assign or create copies of RandomSeqXXXX objects; the copies acquire the complete state of the original, so will go on to produce exactly the same sequence of values as the original will produce.

Maintainer documentation

RandomSource

The impl is mostly quite straightforward since almost all the work is done by GMP.

RandomLong(RndSrc, lo, hi) is a bit messy for two reasons:

  1. CoCoALib uses signed longs while GMP uses unsigned longs;
  2. the case when (lo,hi) specify the whole range of representable longs requires special handling.

RandomSeqLong and RandomSeqBigInt

The idea is very simple: use the pseudo-random number generator of GMP to generate a random machine integer in the range 0 to myRange-1 (where myRange was set in the ctor to be 1+myUpb-myLwb) and then add that to myLwb. The result is stored in the data member myValue so that input iterator syntax can be supported.

There are two non essential data members: mySeed and myCounter. I put these in to help any poor blighter who has to debug a randomized algorithm, and who may want to fast forward the random sequence to the right place.

The data member myState holds all the state information used by the GMP generator. Its presence makes the ctors, dtor and assignment messier than they would have been otherwise.

The advancing and reading member functions (i.e. operator++ and operator*) are inline for efficiency, as is the NextValue function.

myGetValue is a little messy because the value generated by the GMP function gmp_urandomm_ui cannot generate the full range of unsigned long values. Instead I have to call gmp_urandomb_ui if the full range is needed.

The data members myLwb, myUpb and myRange are morally constant, but I cannot make them const because I wanted to allow assignment of RandomSeqLong objects.

RandomSeqBool

The idea is very simple: use the pseudo-random number generator of GMP to generate a random integer, and then give out the bits of this integer one at at time; when the last bit has been given out, get a new random integer from the GMP generator. The random integer is kept in the data member myBuffer, and myBitIndex is used to read the bits one at a time.

The condition for refilling myBuffer is when the index goes beyond the number of bits held in myBuffer.

myFillBuffer also sets the data member myBitIndex to zero; it seemed most sensible to do this here.

The function prob is nifty; if you think about it for a moment, it is obviously right (and economical on random bits). It would be niftier still if the probability were specified as an unsigned long -- on a 64-bit machine this ought to be sufficient for almost all purposes. If the requested probability is of the form N/2^k for some odd integer N, then the average number of bits consumed by prob is 2-2^(1-k), which always lies between 1 and 2. If the requested probability is 0 or 1, no bits are consumed.

Bugs, shortcomings and other ideas

The printing function gives only partial information; e.g. two RandomSource objects with different internal states might be printed out identically.

The implementation simply calls the GMP pseudo-random generator; this generator is deterministic (so always produces the same sequence), but if you change versions of GMP, the sequence of generated values may change. You will have to read the GMP documentation to know more.

Discarded idea: have a ctor which takes a ref to a RandomSource, and which uses that to obtain randomness. I discarded the idea because of the risks of an invisible external reference (e.g. a dangling reference, or problems in multithreaded code). Instead of passing a reference to a RandomSource to the ctor, you can use the RandomSource to create an initial seed which is handed to the ctor -- this gives better separation.

Why can RandomSource be seeded with a BigInt but the others not? Does anyone really care?

Doubts common to RandomSeqBigInt, RandomSeqBool, RandomSeqLong

It might be neater to put ++myCounter inside myGenValue, though this would mean that myCounter gets incremented inside the ctor.

Should NextValue advance before or after getting the value?

Is the information printed by myOutputSelf adequate? Time will tell.

Is there a better way of writing the four ctors (for RandomSeqBigInt) without repeating many lines of essentially identical source code?

Are there too many inline fns? Is run-time speed so important here? How many algorithms really consume millions of random bits/numbers? Surely the computations on the random values should exceed the cost of generating them, shouldn't they?

Main changes