Causal set generator and action computer

William J. Cunningham

doi:10.1016/j.cpc.2018.06.008

2018-12-01

William J. Cunningham *

Dmitri Krioukov

DOI：10.1016/j.cpc.2018.06.008

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摘要

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The causal set approach to quantum gravity has gained traction over the past three decades, but numerical experiments involving causal sets have been limited to relatively small scales. The software suite presented here provides a new framework for the generation and study of causal sets. Its efficiency surpasses previous implementations by several orders of magnitude. We highlight several important features of the code, including the compact data structures, the O(N-2) causal set generation process, and several implementations of the O(N-3) algorithm to compute the Benincasa-Dowker action of compact regions of spacetime. We show that by tailoring the data structures and algorithms to take advantage of low-level CPU and GPU architecture designs, we are able to increase the efficiency and reduce the amount of required memory significantly. The presented algorithms and their implementations rely on methods that use CUDA, OpenMP, x86 Assembly, SSE/AVX, Pthreads, and MPI. We also analyze the scaling of the algorithms' running times with respect to the problem size and available resources, with suggestions on how to modify the code for future hardware architectures. Program summary Program Title: Causal Set Generator and Action Computer Program Files doi : http://dx.doi.org/10.17632/5k8wjrhgwh.1 Licensing Provisions: MIT Programming Language: C++/CUDA, x86 Assembly Nature of Problem: Generate causal sets and compute the Benincasa-Dowker action. Solution Method: We generate causal sets sprinkled on a Lorentzian manifold by randomly sampling element coordinates using OpenMP and linking elements using CUDA. Causal sets are stored in a minimal binary representation via the FastBitset class. We measure the action in parallel using OpenMP, SSE/AVX and x86 Assembly. When multiple computers are available, MPI and POSIX threads are also incorporated. Additional Comments: The program runs most efficiently with an Intel processor supporting AVX2 and an NVIDIA GPU with compute capability greater than or equal to 3.0. (C) 2018 Elsevier B.V. All rights reserved.

Keyword:

Causal sets

Lorentzian geometry

CUDA

x86 Assembly