Pseudorandom number generator

The pseudorandom number generator used by the Doom engine is simplistic yet adequate for gameplay. Its simplicity has the virtue of speed.

Implementation

The file m_random.c in the Doom source code contains a static table 256 bytes long containing numbers between 0 and 255 in a fixed, scrambled order. There is an index to this table which starts at zero. Each call to the function P_Random advances the index by one, wrapping around to zero after 255, and returns the table entry at that index.

There is another function, M_Random, that is identical except that it uses its own independent index. P_Random is used in play simulation situations, such as calculating hit damage. M_Random is used otherwise.

The reason for the existence of two individual indexes is to maintain multiplayer synchronisation: for example, M_Random is used to apply a random pitch variation to sounds. As two players may not hear the same sound effect (they may be in different parts of the level), using a single index would cause the game to become desynchronised. To use a model-view-controller analogy, P_Random is used for random number generation at the 'model', while M_Random is used for random number generation at the 'view'.

The function M_ClearRandom resets both functions' indexes to zero. It is called during initialization of each new game so that demos will be the same each time they are played, and so that multiplayer games are synchronised.

Although the table is 256 bytes long, it does not contain all of the numbers between 0 and 255 inclusive. For example, 0 appears twice and 1 does not appear at all; 145 appears five times, more than any other number. Thus the values are not uniformly distributed, but in fact they are nearly so. The mean value is 128.852, whereas it would be 127.500 if all values were equally likely. All of this suggests that the table was generated using a conventional pseudorandom number generator of reasonable quality.

Source algorithm

The values in Doom's random number table are the output from a linear congruential generator, one of the most well-known algorithms for pseudorandom number generators. The multiplier and increment are 134775813 and 1 respectively, which were used in the random number generators found in various compilers from Borland in the late 80s/early 90s.

The following is an example Python program that produces the contents of the random number table:

 state = 1
 for _ in range(256):
     print(state >> 16)
     state = (134775813 * state + 1) % (1 << 24)

In pure mathematical terms, the sequence can be calculated by the following formula (through the closed-form sum of a geometric series), though for an implementation in software it is likely to be impractical:

 a(n) = floor((134775813 ^ (n + 1) - 1) / 8832667615232) mod 2^8

History

The same table of random numbers used by Doom is also found in the The Catacomb, Hovertank 3D, Catacomb 3D, Commander Keen 1-3, Keen Dreams, Commander Keen 4-6, Wolfenstein 3D, In Pursuit of Greed and Duke Nukem II code bases.

External links

• "Random number table used by Doom" in the On-Line Encyclopedia of Integer Sequences (entry A259233)
• Pseudorandom number generator article at Wikipedia
• Linear congruential generator article at Wikipedia