A New Class of Random Number Generators

We introduce a new class of generators of two types: add-with-carry and subtract-with-borrow. Related to lagged-Fibonacci generators, the new class has interesting underlying theory, astonishingly long periods and provable uniformity for full sequences. Among several that we mention, we recommend particularly promising ones that will generate a sequence of 2¹⁷⁵¹ bits, or a sequence of 2¹³⁷⁶ 32-bit integers, or a sequence of 2⁹³¹ reals with 24-bit fractions--all using simple computer arithmetic (subtraction) and a few memory locations.