Xorshift random number generators from primitive polynomials

Some long-period random number generators using shifts and xors

Marsaglia recently introduced a class of “xorshift” random number generators (RNGs) with periods 2n − 1 for n = 32, 64, etc. Here Marsaglia’s xorshift generators are generalised to obtain fast and highquality RNGs with extremely long periods. Whereas RNGs based on primitive trinomials may be unsatisfactory, because a trinomial has very small weight, these new generators can be chosen so that th...

Note on Marsaglia’s Xorshift Random Number Generators

Marsaglia (2003) has described a class of“xorshift”random number generators (RNGs) with periods 2 − 1 for n = 32, 64, etc. We show that the sequences generated by these RNGs are identical to the sequences generated by certain linear feedback shift register (LFSR) generators using “exclusive or” (xor) operations on n-bit words, with a recurrence defined by a primitive polynomial of degree n.

Using Magma to find good xorshift random number generators

Further scramblings of Marsaglia's xorshift generators

xorshift* generators are a variant of Marsaglia’s xorshift generators that eliminate linear artifacts typical of generators based on Z/2Z-linear operations using multiplication by a suitable constant. Shortly after high-dimensional xorshift* generators were introduced, Saito and Matsumoto suggested a different way to eliminate linear artifacts based on addition in Z/232Z, leading to the XSadd g...

On the Use of Reducible Polynomials as Random Number Generators

The randomness properties and the hierarchy of correlation coefficients are studied of approximate-maximum-length sequences, for which the characteristic polynomial is a product of several primitive polynomials. The randomness properties are almost the same as for maximum-length sequences characterized by a primitive polynomial with many terms and of the same degree. Reducible characteristic po...