A special matrix version of a Feedback Shift Register Generator, developed in 1997 by Matsumoto and Nishimura. The MT19937 version has a long period of .
where stands for -bit integer numbers instead of single bits, exclusive-OR is executed bitwise on -bit long words and . The matrix transforms (twists) -width words (treated as binary vectors of length ).
The twist transformation (multiplication by the matrix ) yields benefits such as reaching the maximum theoretical limit for the period of the pseudo-random number generator and better equidistribution properties in dimensions.
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