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Register a new userSIMD Vectorization for the Lennard-Jones Potential with AVX2 and AVX-512 instructions
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Added by
Hiroshi Watanabe
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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This work describes the SIMD vectorization of the force calculation of the Lennard-Jones potential with Intel AVX2 and AVX-512 instruction sets. Since the force-calculation kernel of the molecular dynamics method involves indirect access to memory, the data layout is one of the most important factors in vectorization. We find that the Array of Structures (AoS) with padding exhibits better performance than Structure of Arrays (SoA) with appropriate vectorization and optimizations. In particular, AoS with 512-bit width exhibits the best performance among the architectures. While the difference in performance between AoS and SoA is significant for the vectorization with AVX2, that with AVX-512 is minor. The effect of other optimization techniques, such as software pipelining together with vectorization, is also discussed. We present results for benchmarks on three CPU architectures: Intel Haswell (HSW), Knights Landing (KNL), and Skylake (SKL). The performance gains by vectorization are about 42% on HSW compared with the code optimized without vectorization. On KNL, the hand-vectorized codes exhibit 34% better performance than the codes vectorized automatically by the Intel compiler. On SKL, the code vectorized with AVX2 exhibits slightly better performance than that with vectorized AVX-512.
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We publish an extension of openQCD-1.6 with AVX-512 vector instructions using Intel intrinsics. Recent Intel processors support extended instruction sets with operations on 512-bit wide vectors, increasing both the capacity for floating point operations and register memory. Optimal use of the new capabilities requires reorganising data and floating point operations into these wider vector units. We report on the implementation and performance of the AVX-512 OpenQCD extension on clusters using Intel Knights Landing and Xeon Scalable (Skylake) CPUs. In complete HMC trajectories with physically relevant parameters we observe a performance increase of 5% to 10%.
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This paper investigates the relation between the density-scaling exponent $gamma$ and the virial potential-energy correlation coefficient $R$ at several thermodynamic state points in three dimensions for the generalized $(2n,n)$ Lennard-Jones (LJ) system for $n=4, 9, 12, 18$, as well as for the standard $n=6$ LJ system in two, three, and four dimensions. The state points studied include many low-density states at which the virial potential-energy correlations are not strong. For these state points we find the roughly linear relation $gammacong 3nR/d$ in $d$ dimensions. This result is discussed in light of the approximate extended inverse power law description of generalized LJ potentials [N. P. Bailey et al., J. Chem. Phys. 129, 184508 (2008)]. In the plot of $gamma$ versus $R$ there is in all cases a transition around $Rapprox 0.9$, above which $gamma$ starts to decrease as $R$ approaches unity. This is consistent with the fact that $gammarightarrow 2n/d$ for $Rrightarrow 1$, a limit that is approached at high densities and/or temperatures at which the repulsive $r^{-2n}$ term dominates the physics.
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