arXiv subjects

Fabio Cannizzo

Publications and source records attributed to Fabio Cannizzo.

2 recordsLinked to original sources

arXiv2023

VMT19937: A SIMD-Friendly Pseudo Random Number Generator based on Mersenne Twister 19937

Many simulation applications require the generation of long sequences of pseudo-random numbers. Linear recurrences modulo 2 are commonly used as the fundamental building block for constructing pseudo-random number generators with extended periods and excellent statistical properties. These generators consist of a lengthy binary state vector that evolves iteratively through linear transformations. One widely accepted pseudo-random generator in this category is the Mersenne twister 19937 (MT19937), proposed by Matsumoto and Nishimura, which has been implemented in numerous software libraries and numerical packages. The MT19937's popularity stems from its favorable distribution properties and the simplicity and speed of its algorithm. The linear transformation responsible for evolving the binary state vector can be expressed as a concise set of elementary bit manipulations. However, this transformation does not fully utilize the potential for parallelization through SIMD instructions available on modern hardware, limiting further speed enhancements. This paper introduces a new SIMD-friendly random number generator, which maintains the same statistical properties and period as the MT19937. It combines the random streams of multiple MT19937 instances with state vectors de-phased via jump-ahead transformations, then polls each instance in a round-robin fashion. By evolving their vector states simultaneously, the new generator achieves perfect vectorization, fully leveraging on SIMD hardware capabilities. Comprehensive test results demonstrate that the throughput of the new generator scales approximately linearly with the width of the SIMD registers used. This provides significant speed improvements, especially on modern CPUs equipped with larger SIMD registers, and allows for efficient generation of random numbers for various simulation applications.

cs.DC↗

arXiv2017

Fast and Vectorizable Alternative to Binary Search in O(1) Applicable to a Wide Domain of Sorted Arrays of Floating Point Numbers

Given an array $X$ of $N+1$ strictly ordered floating point numbers and a floating point number $z$ in the interval $[X_0,X_N)$, a common problem is to find the index $i$ of the interval $[X_{i},X_{i+1})$ containing $z$. This problem arises for instance in the context of spline interpolation or the computation of empirical probability distribution from empirical data. Often it needs to be solved for a large number of different values $z$ and the same array $X$, which makes it worth investing resources upfront in pre-processing the array $X$ with the goal of speeding up subsequent search operations. In some cases the values $z$ to be processed are known simultaneously in blocks of size $M$, which offers the opportunity to solve the problem vectorially, exploiting the parallel capabilities of modern CPUs. The common solution is to sequentially invoke $M$ times the well known binary search algorithm, which has complexity $O(log_2 N)$ per individual search and, in its classic formulation, is not vectorizable, i.e. is not SIMD friendly. This paper describes technical improvements to the binary search algorithm, which make it faster and vectorizable. Next it proposes a new vectorizable algorithm, based on an indexing technique, applicable to a wide family of $X$ partitions, which solves the problem with complexity $O(1)$ per individual search at the cost of introducing an initial overhead to compute the index and requiring extra memory for its storage. Test results using streaming SIMD extensions compare the performance of the algorithm versus various benchmarks and demonstrate its effectiveness. Depending on the test case, the algorithm can produce a throughput up to two orders of magnitude larger than the classic binary search. Applicability limitations and cache-friendliness related aspects are also discussed.

cs.DS↗