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### 49.5 L’Ecuyer’s MRG32k3a generator

The default randomness source of (vicare crypto randomisations) is Pierre L’Ecuyer’s MRG32k3a generator:

P. L’Ecuyer. “Good Parameter Sets for Combined Multiple Recursive Random Number Generators”, Shorter version in Operations Research, 47, 1 (1999), 159–164.

P. L’Ecuyer, R. Simard, E. J. Chen, W. D. Kelton. “An Object–Oriented Random–Number Package With Many Long Streams and Substreams”. 2001. To appear in Operations Research.

Function: make-random-source/mrg32k3a

Create and return a new randomness source using MRG32k3a, representing a deterministic stream of random bits. Each returned randomness source generates the same stream of values, unless the state is modified with random-source-seed!.

The state returned by random-source-state-ref is a Scheme vector of length 7, whose first value is the symbol random-source-state/mrg32k3a. All the other values in the vector are positive integers.

#### The algorithm

The MRG32k3a generator produces values N in the range 0 <= N < 2^{32} - 209. A new pseudo–random number N is generated with the following computation starting from the state vectors [A1, A2, A3] and [B1, B2, B3]:

M1 = 4294967087 = 2^32 - 209
M2 = 4294944443 = 2^32 - 22853

c2 =  1403580
c3 =  -810728
d1 =   527612
d3 = -1370589

A0 = (          c2 * A2 + c3 * A3) mod M1
B0 = (d1 * B1 +           d3 * B3) mod M2

; right-shift A, purging the old A3
A3 = A2
A2 = A1
A1 = A0

; right-shift B, purging the old B3
B3 = B2
B2 = B1
B1 = B0

N = (A0 - B0) mod M1

notice that M1 and M2 are two prime numbers just below 2^{32}; c2, c3, d1 and d3 are called recursion coefficients. The (vicare crypto randomisations) library defines the initial state vectors as:

A1 = 1062452522
A2 = 2961816100
A3 =  342112271

B1 = 2854655037
B2 = 3321940838
B3 = 3542344109

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