Random Object Generation [HB 1]

Magma V2.7 contains an implementation of the new MONSTER random number generator due to G. Marsaglia [FSU, Tallahassee, FL]. The Monster generator has period 2²⁹⁴³⁰ - 2²⁷³⁸² (approximately 10⁸⁸⁵⁹) and passes all of the stringent tests in Marsaglia's Diehard test suite (available online at http://stat.fsu.edu/pub/diehard/).

The new generator is thus very much better than the previous linear congruential generator, whose period was only 2³¹-1 (for which the full period could be easily exhausted).

Changes:

• Because the new Monster generator uses an internal array of machine integers, one `seed' variable no longer expresses the whole state, so the method for setting or getting the generator state is now by way of a pair of values: (1) the seed for initializing the array, and (2) the number of steps performed since the initialization. In detail:
• The procedure SetSeed(s, c) now takes the initial seed s and a step number c to advance to. SetSeed(s) is equivalent to SetSeed(s, 0).
• The function GetSeed() now returns the initial seed s used to initialize the random-number generator and also the current step c.
• Starting from a given seed s, randomly generating any kind of object using any random functions (including multi-precision integers) will now produce exactly the same result, no matter which machine type is used (including 64-bit machines versus 32-bit machines).