The spectral test is a statistical test for the quality of a class of

pseudorandom number generator A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. The PRNG-generate ...

s (PRNGs), the

linear congruential generator A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation. The method represents one of the oldest and best-known pseudorandom number generat ...

s (LCGs). LCGs have a property that when plotted in 2 or more dimensions, lines or hyperplanes will form, on which all possible outputs can be found. The spectral test compares the distance between these planes; the further apart they are, the worse the generator is. As this test is devised to study the lattice structures of LCGs, it can not be applied to other families of PRNGs. According to

Donald Knuth Donald Ervin Knuth ( ; born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University. He is the 1974 recipient of the ACM Turing Award, informally considered the Nobel Prize of computer sc ...

, this is by far the most powerful test known, because it can fail LCGs which pass most statistical tests. The IBM subroutine

RANDU RANDUCompaq Fortran Language Reference Manual (Order Number: AA-Q66SD-TK) September 1999 (formerly DIGITAL Fortran and DEC Fortran 90) is a linear congruential pseudorandom number generator (LCG) of the Park–Miller type, which was used primar ...

LCG fails in this test for 3 dimensions and above.

References

Pseudorandom number generators {{comp-sci-theory-stub