A revision of the subtract-with-borrow random number generators

The most popular and widely used subtract-with-borrow generator, also known as RANLUX, is reimplemented as a linear congruential generator using large integer arithmetic with the modulus size of 576 bits. Modern computers, as well as the specific structure of the modulus inferred from RANLUX, allow for the development of a fast modular multiplication – the core of the procedure. This was previously believed to be slow and have too high cost in terms of computing resources. Our tests show a significant gain in generation speed which is comparable with other fast, high quality random number generators. An additional feature is the fast skipping of generator states leading to a seeding scheme which guarantees the uniqueness of random number sequences.