arXiv subjects

Paolo Bientinesi

Publications and source records attributed to Paolo Bientinesi.

At least 55 records · Page 3Linked to original sources

arXiv2017

Assessment of sound spatialisation algorithms for sonic rendering with headsets

Given an input sound signal and a target virtual sound source, sound spatialisation algorithms manipulate the signal so that a listener perceives it as though it were emitted from the target source. There exist several established spatialisation approaches that deliver satisfactory results when loudspeakers are used to playback the manipulated signal. As headphones have a number of desirable characteristics over loudspeakers, such as portability, isolation from the surrounding environment, cost and ease of use, it is interesting to explore how a sense of acoustic space can be conveyed through them. This article first surveys traditional spatialisation approaches intended for loudspeakers, and then reviews them with regard to their adaptability to headphones.

cs.SD↗

arXiv2017

Design of a high-performance GEMM-like Tensor-Tensor Multiplication

We present "GEMM-like Tensor-Tensor multiplication" (GETT), a novel approach to tensor contractions that mirrors the design of a high-performance general matrix-matrix multiplication (GEMM). The critical insight behind GETT is the identification of three index sets, involved in the tensor contraction, which enable us to systematically reduce an arbitrary tensor contraction to loops around a highly tuned "macro-kernel". This macro-kernel operates on suitably prepared ("packed") sub-tensors that reside in a specified level of the cache hierarchy. In contrast to previous approaches to tensor contractions, GETT exhibits desirable features such as unit-stride memory accesses, cache-awareness, as well as full vectorization, without requiring auxiliary memory. To compare our technique with other modern tensor contractions, we integrate GETT alongside the so called Transpose-Transpose-GEMM-Transpose and Loops-over-GEMM approaches into an open source "Tensor Contraction Code Generator" (TCCG). The performance results for a wide range of tensor contractions suggest that GETT has the potential of becoming the method of choice: While GETT exhibits excellent performance across the board, its effectiveness for bandwidth-bound tensor contractions is especially impressive, outperforming existing approaches by up to $12.4\times$. More precisely, GETT achieves speedups of up to $1.41\times$ over an equivalent-sized GEMM for bandwidth-bound tensor contractions while attaining up to $91.3\%$ of peak floating-point performance for compute-bound tensor contractions.

cs.MS↗

arXiv2017

MatchPy: A Pattern Matching Library

Pattern matching is a powerful tool for symbolic computations, based on the well-defined theory of term rewriting systems. Application domains include algebraic expressions, abstract syntax trees, and XML and JSON data. Unfortunately, no lightweight implementation of pattern matching as general and flexible as Mathematica exists for Python Mathics,MacroPy,patterns,PyPatt. Therefore, we created the open source module MatchPy which offers similar pattern matching functionality in Python using a novel algorithm which finds matches for large pattern sets more efficiently by exploiting similarities between patterns.

cs.PL↗

arXiv2017

The Tersoff many-body potential: Sustainable performance through vectorization

Molecular dynamics models materials by simulating each individual particle's trajectory. Many-body potentials lead to a more accurate trajectory simulation, and are used in materials science and computational chemistry. We present optimization results for one multi-body potential on a range of vector instruction sets, targeting both CPUs and accelerators like the Intel Xeon Phi. Parallelization of MD simulations is well-studied; by contrast, vectorization is relatively unexplored. Given the prevalence and power of modern vector units, exploiting them is imperative for high performance software. When running on a highly parallel machine, any improvement to the scalar performance is paid back in hundreds or thousands of saved core hours. Vectorization is already commonly used in the optimization or pair potentials; multi-body potentials pose new, unique challenges. Indeed, their optimization pushes the boundaries of current compilers, forcing us to use explicit vectorization techniques for now. In this study, we add an optimized implementation of Tersoff potential to the LAMMPS molecular dynamics simulation package. To reduce the burden of explicit vectorization, we abstract from the specific vector instruction set and desired precision: From one algorithm, we get optimized implementations for many platforms, from SSE4.2 to AVX512, and the Intel Xeon Phi. We compare the kernels across different architectures, and determine suitable architecture-dependent parameters. Our optimizations benefit any architecture, but have a disproportionate effect on the Intel Xeon Phi, which beats the CPU (2xE5-2650) after optimization.

cs.CE↗

arXiv2017

Efficient Pattern Matching in Python

Pattern matching is a powerful tool for symbolic computations. Applications include term rewriting systems, as well as the manipulation of symbolic expressions, abstract syntax trees, and XML and JSON data. It also allows for an intuitive description of algorithms in the form of rewrite rules. We present the open source Python module MatchPy, which offers functionality and expressiveness similar to the pattern matching in Mathematica. In particular, it includes syntactic pattern matching, as well as matching for commutative and/or associative functions, sequence variables, and matching with constraints. MatchPy uses new and improved algorithms to efficiently find matches for large pattern sets by exploiting similarities between patterns. The performance of MatchPy is investigated on several real-world problems.

cs.PL↗

arXiv2017

Spin Summations: A High-Performance Perspective

Besides tensor contractions, one of the most pronounced computational bottlenecks in the non-orthogonally spin-adapted forms of the quantum chemistry methods CCSDT and CCSDTQ, and their approximate forms---including CCSD(T) and CCSDT(Q)---are spin summations. At a first sight, spin summations are operations similar to tensor transpositions; a closer look instead reveals additional challenges to high-performance calculations, including temporal locality as well as scattered memory accesses. This publication explores a sequence of algorithmic solutions for spin summations, each exploiting individual properties of either the underlying hardware (e.g. caches, vectorization), or the problem itself (e.g. factorizability). The final algorithm combines the advantages of all the solutions, while avoiding their drawbacks; this algorithm, achieves high-performance through parallelization, vectorization, and by exploiting the temporal locality inherent to spin summations. Combined, these optimizations result in speedups between 2.4x and 5.5x over the NCC quantum chemistry software package. In addition to such a performance boost, our algorithm can perform the spin summations in-place, thus reducing the memory footprint by 2x over an out-of-place variant.

cs.MS↗

arXiv2017

HPTT: A High-Performance Tensor Transposition C++ Library

Recently we presented TTC, a domain-specific compiler for tensor transpositions. Despite the fact that the performance of the generated code is nearly optimal, due to its offline nature, TTC cannot be utilized in all the application codes in which the tensor sizes and the necessary tensor permutations are determined at runtime. To overcome this limitation, we introduce the open-source C++ library High-Performance Tensor Transposition (HPTT). Similar to TTC, HPTT incorporates optimizations such as blocking, multi-threading, and explicit vectorization; furthermore it decomposes any transposition into multiple loops around a so called micro-kernel. This modular design---inspired by BLIS---makes HPTT easy to port to different architectures, by only replacing the hand-vectorized micro-kernel (e.g., a 4x4 transpose). HPTT also offers an optional autotuning framework---guided by a performance model---that explores a vast search space of implementations at runtime (similar to FFTW). Across a wide range of different tensor transpositions and architectures (e.g., Intel Ivy Bridge, Intel Knights Landing, ARMv7, IBM Power7), HPTT attains a bandwidth comparable to that of SAXPY, and yields remarkable speedups over Eigen's tensor transposition implementation. Most importantly, the integration of HPTT into the Cyclops Tensor Framework (CTF) improves the overall performance of tensor contractions by up to 3.1x.

cs.MS↗

arXiv2017

LAMMPS' PPPM Long-Range Solver for the Second Generation Xeon Phi

Molecular Dynamics is an important tool for computational biologists, chemists, and materials scientists, consuming a sizable amount of supercomputing resources. Many of the investigated systems contain charged particles, which can only be simulated accurately using a long-range solver, such as PPPM. We extend the popular LAMMPS molecular dynamics code with an implementation of PPPM particularly suitable for the second generation Intel Xeon Phi. Our main target is the optimization of computational kernels by means of vectorization, and we observe speedups in these kernels of up to 12x. These improvements carry over to LAMMPS users, with overall speedups ranging between 2-3x, without requiring users to retune input parameters. Furthermore, our optimizations make it easier for users to determine optimal input parameters for attaining top performance.

cs.CE↗

arXiv2017

A Scalable, Linear-Time Dynamic Cutoff Algorithm for Molecular Dynamics

Recent results on supercomputers show that beyond 65K cores, the efficiency of molecular dynamics simulations of interfacial systems decreases significantly. In this paper, we introduce a dynamic cutoff method (DCM) for interfacial systems of arbitrarily large size. The idea consists in adopting a cutoff-based method in which the cutoff is cho- sen on a particle-by-particle basis, according to the distance from the interface. Computationally, the challenge is shifted from the long-range solvers to the detection of the interfaces and to the computation of the particle-interface distances. For these tasks, we present linear-time algorithms that do not rely on global communication patterns. As a result, the DCM algorithm is suited for large systems of particles and mas- sively parallel computers. To demonstrate its potential, we integrated DCM into the LAMMPS open-source molecular dynamics package, and simulated large liquid/vapor systems on two supercomputers: SuperMuc and JUQUEEN. In all cases, the accuracy of DCM is comparable to the traditional particle-particle particle-mesh (PPPM) algorithm, while the performance is considerably superior for large numbers of particles. For JUQUEEN, we provide timings for simulations running on the full system (458, 752 cores), and show nearly perfect strong and weak scaling.

physics.comp-ph↗

arXiv2016

The Matrix Chain Algorithm to Compile Linear Algebra Expressions

The matrix chain problem consists in finding the parenthesization of a matrix product $M := A_1 A_2 \cdots A_n$ that minimizes the number of scalar operations. In practical applications, however, one frequently encounters more complicated scenarios, where expressions involve transposition, inversion, matrices with given properties, and sequences. The computation of such expressions makes use of a set of computational kernels that offer functionality well beyond the simple matrix product. The challenge then shifts from finding an optimal parenthesization to finding an optimal mapping of the input expression to the available kernels. Furthermore, it is often the case that a solution based on the minimization of scalar operations does not result in the optimal solution in terms of execution time, and/or might be numerically unstable. In this paper, we introduce a number of generalizations of the matrix chain problem--including kernels, properties, sequences, and cost functions--and present corresponding algorithmic solutions. The motivation for this work comes from the fact that--despite great advances in the development of compilers--the task of mapping linear algebra problems to optimized kernels is still to be done manually. In order to relieve the user from this complex task, new techniques for the compilation of linear algebra expressions have to be developed.

cs.DS↗

arXiv2016

Large Scale Parallel Computations in R through Elemental

Even though in recent years the scale of statistical analysis problems has increased tremendously, many statistical software tools are still limited to single-node computations. However, statistical analyses are largely based on dense linear algebra operations, which have been deeply studied, optimized and parallelized in the high-performance-computing community. To make high-performance distributed computations available for statistical analysis, and thus enable large scale statistical computations, we introduce RElem, an open source package that integrates the distributed dense linear algebra library Elemental into R. While on the one hand, RElem provides direct wrappers of Elemental's routines, on the other hand, it overloads various operators and functions to provide an entirely native R experience for distributed computations. We showcase how simple it is to port existing R programs to Relem and demonstrate that Relem indeed allows to scale beyond the single-node limitation of R with the full performance of Elemental without any overhead.

stat.CO↗

arXiv2016

Accelerating scientific codes by performance and accuracy modeling

Scientific software is often driven by multiple parameters that affect both accuracy and performance. Since finding the optimal configuration of these parameters is a highly complex task, it extremely common that the software is used suboptimally. In a typical scenario, accuracy requirements are imposed, and attained through suboptimal performance. In this paper, we present a methodology for the automatic selection of parameters for simulation codes, and a corresponding prototype tool. To be amenable to our methodology, the target code must expose the parameters affecting accuracy and performance, and there must be formulas available for error bounds and computational complexity of the underlying methods. As a case study, we consider the particle-particle particle-mesh method (PPPM) from the LAMMPS suite for molecular dynamics, and use our tool to identify configurations of the input parameters that achieve a given accuracy in the shortest execution time. When compared with the configurations suggested by expert users, the parameters selected by our tool yield reductions in the time-to-solution ranging between 10% and 60%. In other words, for the typical scenario where a fixed number of core-hours are granted and simulations of a fixed number of timesteps are to be run, usage of our tool may allow up to twice as many simulations. While we develop our ideas using LAMMPS as computational framework and use the PPPM method for dispersion as case study, the methodology is general and valid for a range of software tools and methods.

cs.CE↗

arXiv2016

High-performance generation of the Hamiltonian and Overlap matrices in FLAPW methods

One of the greatest efforts of computational scientists is to translate the mathematical model describing a class of physical phenomena into large and complex codes. Many of these codes face the difficulty of implementing the mathematical operations in the model in terms of low level optimized kernels offering both performance and portability. Legacy codes suffer from the additional curse of rigid design choices based on outdated performance metrics (e.g. minimization of memory footprint). Using a representative code from the Materials Science community, we propose a methodology to restructure the most expensive operations in terms of an optimized combination of dense linear algebra kernels. The resulting algorithm guarantees an increased performance and an extended life span of this code enabling larger scale simulations.

cs.CE↗

arXiv2016

The Vectorization of the Tersoff Multi-Body Potential: An Exercise in Performance Portability

Molecular dynamics simulations, an indispensable research tool in computational chemistry and materials science, consume a significant portion of the supercomputing cycles around the world. We focus on multi-body potentials and aim at achieving performance portability. Compared with well-studied pair potentials, multibody potentials deliver increased simulation accuracy but are too complex for effective compiler optimization. Because of this, achieving cross-platform performance remains an open question. By abstracting from target architecture and computing precision, we develop a vectorization scheme applicable to both CPUs and accelerators. We present results for the Tersoff potential within the molecular dynamics code LAMMPS on several architectures, demonstrating efficiency gains not only for computational kernels, but also for large-scale simulations. On a cluster of Intel Xeon Phi's, our optimized solver is between 3 and 5 times faster than the pure MPI reference.

cs.CE↗

arXiv2016

TTC: A Tensor Transposition Compiler for Multiple Architectures

We consider the problem of transposing tensors of arbitrary dimension and describe TTC, an open source domain-specific parallel compiler. TTC generates optimized parallel C++/CUDA C code that achieves a significant fraction of the system's peak memory bandwidth. TTC exhibits high performance across multiple architectures, including modern AVX-based systems (e.g.,~Intel Haswell, AMD Steamroller), Intel's Knights Corner as well as different CUDA-based GPUs such as NVIDIA's Kepler and Maxwell architectures. We report speedups of TTC over a meaningful baseline implementation generated by external C++ compilers; the results suggest that a domain-specific compiler can outperform its general purpose counterpart significantly: For instance, comparing with Intel's latest C++ compiler on the Haswell and Knights Corner architecture, TTC yields speedups of up to $8\times$ and $32\times$, respectively. We also showcase TTC's support for multiple leading dimensions, making it a suitable candidate for the generation of performance-critical packing functions that are at the core of the ubiquitous BLAS 3 routines.

cs.MS↗

arXiv2016

TTC: A high-performance Compiler for Tensor Transpositions

We present TTC, an open-source parallel compiler for multidimensional tensor transpositions. In order to generate high-performance C++ code, TTC explores a number of optimizations, including software prefetching, blocking, loop-reordering, and explicit vectorization. To evaluate the performance of multidimensional transpositions across a range of possible use-cases, we also release a benchmark covering arbitrary transpositions of up to six dimensions. Performance results show that the routines generated by TTC achieve close to peak memory bandwidth on both the Intel Haswell and the AMD Steamroller architectures, and yield significant performance gains over modern compilers. By implementing a set of pruning heuristics, TTC allows users to limit the number of potential solutions; this option is especially useful when dealing with high-dimensional tensors, as the search space might become prohibitively large. Experiments indicate that when only 100 potential solutions are considered, the resulting performance is about 99% of that achieved with exhaustive search.

cs.MS↗

arXiv2016

A Note on Time Measurements in LAMMPS

We examine the issue of assessing the efficiency of components of a parallel program at the example of the MD package LAMMPS. In particular, we look at how LAMMPS deals with the issue and explain why the approach adopted might lead to inaccurate conclusions. The misleading nature of this approach is subsequently verified experimentally with a case study. Afterwards, we demonstrate how one should correctly determine the efficiency of the components and show what changes to the code base of LAMMPS are necessary in order to get the correct behavior.

cond-mat.mtrl-sci↗

arXiv2015

Large-scale linear regression: Development of high-performance routines

In statistics, series of ordinary least squares problems (OLS) are used to study the linear correlation among sets of variables of interest; in many studies, the number of such variables is at least in the millions, and the corresponding datasets occupy terabytes of disk space. As the availability of large-scale datasets increases regularly, so does the challenge in dealing with them. Indeed, traditional solvers---which rely on the use of black-box" routines optimized for one single OLS---are highly inefficient and fail to provide a viable solution for big-data analyses. As a case study, in this paper we consider a linear regression consisting of two-dimensional grids of related OLS problems that arise in the context of genome-wide association analyses, and give a careful walkthrough for the development of {\sc ols-grid}, a high-performance routine for shared-memory architectures; analogous steps are relevant for tailoring OLS solvers to other applications. In particular, we first illustrate the design of efficient algorithms that exploit the structure of the OLS problems and eliminate redundant computations; then, we show how to effectively deal with datasets that do not fit in main memory; finally, we discuss how to cast the computation in terms of efficient kernels and how to achieve scalability. Importantly, each design decision along the way is justified by simple performance models. {\sc ols-grid} enables the solution of $10^{11}$ correlated OLS problems operating on terabytes of data in a matter of hours.

cs.CE↗