Accelerating scientific computations with mixed precision algorithms

On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. The approach presented here can apply not only to conventional processors but also to other technologies such as Field Programmable Gate Arrays (FPGA), Graphical Processing Units (GPU), and the STI Cell BE processor. Results on modern processor architectures and the STI Cell BE are presented.

Program summary

Program title: ITER-REFCatalogue identifier: AECO_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECO_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 7211No. of bytes in distributed program, including test data, etc.: 41 862Distribution format: tar.gzProgramming language: FORTRAN 77Computer: desktop, serverOperating system: Unix/LinuxRAM: 512 MbytesClassification: 4.8External routines: BLAS (optional)Nature of problem: On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution.Solution method: Mixed precision algorithms stem from the observation that, in many cases, a single precision solution of a problem can be refined to the point where double precision accuracy is achieved. A common approach to the solution of linear systems, either dense or sparse, is to perform the LU factorization of the coefficient matrix using Gaussian elimination. First, the coefficient matrix A is factored into the product of a lower triangular matrix L and an upper triangular matrix U. Partial row pivoting is in general used to improve numerical stability resulting in a factorization PA=LU, where P is a permutation matrix. The solution for the system is achieved by first solving Ly=Pb (forward substitution) and then solving Ux=y (backward substitution). Due to round-off errors, the computed solution, x, carries a numerical error magnified by the condition number of the coefficient matrix A. In order to improve the computed solution, an iterative process can be applied, which produces a correction to the computed solution at each iteration, which then yields the method that is commonly known as the iterative refinement algorithm. Provided that the system is not too ill-conditioned, the algorithm produces a solution correct to the working precision.Running time: seconds/minutes     

The interaction between skill, postures, forces and back pain in wool handling

Wool handling is an important rural occupation where workers process 200 or more fleeces daily, separating them into various quality components. Loads and postures they experience carry substantial risk of low back pain (LBP). Although a formal skill training structure exists, interaction with loads and LBP is unknown. We examined whether skill and LBP influenced trunk postures and loads of 60 wool handlers representing 3 skill levels. LBP prevalence ranged from 20% for junior (lowest skill) to 45% for open class (highest skill) wool handlers. Open class wool handlers demonstrated increased lateral bend and more axially twisted postures, generating greater medio-lateral shear forces and lateral bend and axial twist moments. LBP was associated with open class wool handlers spending more time in severe axially twisted postures. These findings suggest that skill-based training needs to be reviewed to reduce the quantity of axially twisted posture which may help reduce the prevalence of LBP in this workforce.     

Algorithm-Based Fault Tolerance for Fail-Stop Failures

Fail-stop failures in distributed environments are often tolerated by checkpointing or message logging. In this paper, we show that fail-stop process failures in ScaLAPACK matrix-matrix multiplication kennel can be tolerated without checkpointing or message logging. It has been proved in previous algorithm-based fault tolerance that, for matrix-matrix multiplication, the checksum relationship in the input checksum matrices is preserved at the end of the computation no mater which algorithm is chosen. From this checksum relationship in the final computation results, processor miscalculations can be detected, located, and corrected at the end of the computation. However, whether this checksum relationship can be maintained in the middle of the computation or not remains open. In this paper, we first demonstrate that, for many matrix matrix multiplication algorithms, the checksum relationship in the input checksum matrices is not maintained in the middle of the computation. We then prove that, however, for the outer product version algorithm, the checksum relationship in the input checksum matrices can be maintained in the middle of the computation. Based on this checksum relationship maintained in the middle of the computation, we demonstrate that fail-stop process failures (which are often tolerated by checkpointing or message logging) in ScaLAPACK matrix-matrix multiplication can be tolerated without checkpointing or message logging.     

Parametric embedding for class visualization

We propose a new method, parametric embedding (PE), that embeds objects with the class structure into a low-dimensional visualization space. PE takes as input a set of class conditional probabilities for given data points and tries to preserve the structure in an embedding space by minimizing a sum of Kullback-Leibler divergences, under the assumption that samples are generated by a gaussian mixture with equal covariances in the embedding space. PE has many potential uses depending on the source of the input data, providing insight into the classifier's behavior in supervised, semisupervised, and unsupervised settings. The PE algorithm has a computational advantage over conventional embedding methods based on pairwise object relations since its complexity scales with the product of the number of objects and the number of classes. We demonstrate PE by visualizing supervised categorization of Web pages, semisupervised categorization of digits, and the relations of words and latent topics found by an unsupervised algorithm, latent Dirichlet allocation.     

On aggregate available bandwidth in many-to-one data transfer—modeling and applications

This work investigates the modeling of aggregate available bandwidth in multi-sender network applications. Unlike the well-established client–server model, where there is only one server sending the requested data, the available bandwidth of multiple senders when combined together does exhibit consistent properties and thus can be modeled and estimated. Through extensive experiments conducted in the Internet this work proposed to model the aggregate available bandwidth using a normal distribution and then illustrates its application through a hybrid download-streaming algorithm and a playback-adaptive streaming algorithm for video delivery under different bandwidth availability scenarios. This new multi-source bandwidth model opens a new way to provide probabilistic performance guarantee in best-effort networks such as the Internet, and is particularly suitable for the emerging peer-to-peer applications, where having multiple sources is the norm rather than the exception.

Stability ball versus office chair: comparison of muscle activation and lumbar spine posture during prolonged sitting

OBJECTIVE: The objective of the study was to evaluate the differences between sitting on a stability ball and in an office chair in terms of trunk muscle activation and lumbar spine posture. BACKGROUND: Stability balls have become increasingly popular as an alternative to office chairs to help reduce the prevalence of low back pain; however, little research has been conducted on their use as office chairs. METHODS: The 14 participants (7 men, 7 women) were required to sit on both a stability ball and an office chair for 1 hour each while performing various computer workstation tasks throughout the sitting periods. The activation of eight muscles and lumbar spine posture were measured and analyzed. RESULTS: Increased muscle activation in thoracic erector spinae (p = .0352), decreased pelvic tilt (p = .0114), and increased perceived discomfort (p < .0001) while sitting on the stability ball were observed. CONCLUSIONS: The small changes in biological responses when sitting on a stability ball as compared with an office chair, combined with the increased reported discomfort while on the ball, suggests its use for prolonged sitting may not be advantageous. APPLICATION: Prolonged sitting on a stability ball does not greatly alter the manner in which an individual sits, yet it appears to increase the level of discomfort. Therefore, it is important to fully explore a new chair design and consult scientific research before implementing its use.     

Evidence for transient composition variations at GaAs/Ga1−xAlxAs heterostructure interfaces prepared by metal-organic chemical vapour deposition

The composition profiles of GaAs/Ga_1?xAl_xAs heterostructures prepared in two different Metal-Organic Chemical Vapour Deposition (MOCVD) reactors have been studied. Transmission electron microscopy (TEM). and Auger and secondary ion mass spectrometry (SIMS) sputter profiling results are in good agreement and interface widths below 20 å have been achieved. Significant new results on transient phenomena have been obtained. showing that large and sometimes very sharp excursions in composition can be associated with valve switching actions. Direct evidence is presented that gas pressure or flow transients can occur during valve operations. and it is suggested that such instabilities are the cause of the effects observed.     

Percolation and the resistive transition of the critical temperature Tc of Nb3Sn

The relationship between the distribution of the critical temperature, the percolation function, and the resistive transition of the critical temperature is explored for polycrystalline Nb₃Sn. In the neighborhood of the critical temperature, Nb₃Sn is assumed to be a random mixture of superconducting and normal grains. Percolation concepts are applied to a study of the resistivity. A general analysis is made showing that the onset and shape of the resistive transition for composite conductors are determined by the percolation function and the distribution of the critical temperature. An approximate form of the percolation function is determined based on a linear FEM analysis. Example resistive transitions are calculated for an assumed normal distribution of the critical temperature. An argument is presented that relates grain orientation and strain dependence in Nb₃Sn. It is noted that a dependence of the distribution of T_c with strain, in addition to the usual shift in T_c with strain, would be the result of a strain dependence that is a function of grain orientation. The analysis shows the extent to which the slope of the resistive transition is a measure of the distribution of the critical temperature, and therefore a measure of the grain orientation strain sensitivity. Finally, a method is described to determine the percolation function experimentally.