Optimization and Parallelization of B-Spline Based Orbital Evaluations in QMC on Multi/Many-Core Shared Memory Processors

Abstract

B-spline based orbital representations are widely used in Quantum Monte Carlo (QMC) simulations of solids, historically taking as much as 50% of the total run time. Random accesses to a large four-dimensional array make it challenging to efficiently utilize caches and wide vector units of modern CPUs. We present node-level optimizations of B-spline evaluations on multi/many-core shared memory processors. To increase SIMD efficiency and bandwidth utilization, we first apply data layout transformation from array-of-structures to structure-of-arrays (SoA). Then by blocking SoA objects, we optimize cache reuse and get sustained throughput for a range of problem sizes. We implement efficient nested threading in B-spline orbital evaluation kernels, paving the way towards enabling strong scaling of QMC simulations. These optimizations are portable on four distinct cache-coherent architectures and result in up to 5.6x performance enhancements on Intel R Xeon Phi TM processor 7250P (KNL), 5.7x on Intel R Xeon Phi TM coprocessor 7120P, 10x on an Intel R Xeon R processor E5v4 CPU and 9.5x on BlueGene/Q processor. Our nested threading implementation shows nearly ideal parallel efficiency on KNL up to 16 threads. We employ roofline performance analysis to model the impacts of our optimizations. This work combined with our current efforts of optimizing other QMC kernels, result in greater than 4.5x speedup of miniQMC on KNL.

Optimizations of Unstructured Aerodynamics Computations for Many-core Architectures

“…Residual and Gradient Data Layout: We implement a variant of the hybrid/tiled Array-of-Structs (Array-of-Structsof-Arrays (AoSoA)) [21], [22], [23] data structure layout to store the residual and gradient vectors. For simplicity, we call it Array-of-Structs-of-Strided-Arrays memory layout, in which the struct's arrays are tiled (see Figure 2).…”

Honing and proofing Astrophysical codes on the road to Exascale. Experiences from code modernization on many-core systems

“…Additional physics modules use different sub-resolution models, to properly treat processes which are far below the resolution limit in galaxy simulations. Our work is performed on a code version dubbed as P-GADGET3 [14], based on the latest public release GADGET-2 [13] 2 . Some of the core parts of the code recently underwent a modernization, as reported by [6].…”

“…The optimization of simulation code, or the ab initio development of modern applications have arisen to be an urgent task in the scientific community [1], [2], [3], [4], [5], [6], [7]. An underlying and often implicit point in this process is the identification of a target computing architecture for the optimization.…”

Embracing a new era of highly efficient and productive quantum Monte Carlo simulations

“…We use them to narrow the solution space for the optimization and parallelization of QMCPACK. Our previous work [8] showed performance improvement in 3D B-spline routines using a SoA data type. In this work, we implement the SoA data types in the full QMCPACK code for the top kernels.…”

“…Our previous work [8] demonstrated that tiling of the big Bspline table and parallel execution over the array-of-SoA (AoSoA) objects can reduce the time to complete a QMC step. We propose to extend those ideas to full QMCPACK.…”