7,106 research outputs found
Exact Sparse Matrix-Vector Multiplication on GPU's and Multicore Architectures
We propose different implementations of the sparse matrix--dense vector
multiplication (\spmv{}) for finite fields and rings \Zb/m\Zb. We take
advantage of graphic card processors (GPU) and multi-core architectures. Our
aim is to improve the speed of \spmv{} in the \linbox library, and henceforth
the speed of its black box algorithms. Besides, we use this and a new
parallelization of the sigma-basis algorithm in a parallel block Wiedemann rank
implementation over finite fields
FooPar: A Functional Object Oriented Parallel Framework in Scala
We present FooPar, an extension for highly efficient Parallel Computing in
the multi-paradigm programming language Scala. Scala offers concise and clean
syntax and integrates functional programming features. Our framework FooPar
combines these features with parallel computing techniques. FooPar is designed
modular and supports easy access to different communication backends for
distributed memory architectures as well as high performance math libraries. In
this article we use it to parallelize matrix matrix multiplication and show its
scalability by a isoefficiency analysis. In addition, results based on a
empirical analysis on two supercomputers are given. We achieve close-to-optimal
performance wrt. theoretical peak performance. Based on this result we conclude
that FooPar allows to fully access Scala's design features without suffering
from performance drops when compared to implementations purely based on C and
MPI
Parallel Integer Polynomial Multiplication
We propose a new algorithm for multiplying dense polynomials with integer
coefficients in a parallel fashion, targeting multi-core processor
architectures. Complexity estimates and experimental comparisons demonstrate
the advantages of this new approach
Enhancing an Embedded Processor Core with a Cryptographic Unit for Performance and Security
We present a set of low-cost architectural enhancements to accelerate the execution of certain arithmetic operations common in cryptographic applications on an extensible embedded processor core. The proposed enhancements are generic in the sense that they can be beneficially applied in almost any RISC processor. We implemented the enhancements in form of a cryptographic unit (CU) that offers the programmer an extended instruction set. The CU features a 128-bit wide register file and datapath, which enables it to process 128-bit words and perform 128-bit loads/stores. We analyze the speed-up factors for some arithmetic operations and public-key cryptographic algorithms obtained through
these enhancements. In addition, we evaluate the hardware overhead (i.e. silicon area) of integrating the CU into an embedded RISC processor. Our experimental results show that the proposed architectural enhancements allow for a
significant performance gain for both RSA and ECC at the expense of an acceptable increase in silicon area. We also demonstrate that the proposed enhancements facilitate the protection of cryptographic algorithms against certain types of side-channel attacks and present an AES implementation
hardened against cache-based attacks as a case study
A Scalable Correlator Architecture Based on Modular FPGA Hardware, Reuseable Gateware, and Data Packetization
A new generation of radio telescopes is achieving unprecedented levels of
sensitivity and resolution, as well as increased agility and field-of-view, by
employing high-performance digital signal processing hardware to phase and
correlate large numbers of antennas. The computational demands of these imaging
systems scale in proportion to BMN^2, where B is the signal bandwidth, M is the
number of independent beams, and N is the number of antennas. The
specifications of many new arrays lead to demands in excess of tens of PetaOps
per second.
To meet this challenge, we have developed a general purpose correlator
architecture using standard 10-Gbit Ethernet switches to pass data between
flexible hardware modules containing Field Programmable Gate Array (FPGA)
chips. These chips are programmed using open-source signal processing libraries
we have developed to be flexible, scalable, and chip-independent. This work
reduces the time and cost of implementing a wide range of signal processing
systems, with correlators foremost among them,and facilitates upgrading to new
generations of processing technology. We present several correlator
deployments, including a 16-antenna, 200-MHz bandwidth, 4-bit, full Stokes
parameter application deployed on the Precision Array for Probing the Epoch of
Reionization.Comment: Accepted to Publications of the Astronomy Society of the Pacific. 31
pages. v2: corrected typo, v3: corrected Fig. 1
Reproducibility, accuracy and performance of the Feltor code and library on parallel computer architectures
Feltor is a modular and free scientific software package. It allows
developing platform independent code that runs on a variety of parallel
computer architectures ranging from laptop CPUs to multi-GPU distributed memory
systems. Feltor consists of both a numerical library and a collection of
application codes built on top of the library. Its main target are two- and
three-dimensional drift- and gyro-fluid simulations with discontinuous Galerkin
methods as the main numerical discretization technique. We observe that
numerical simulations of a recently developed gyro-fluid model produce
non-deterministic results in parallel computations. First, we show how we
restore accuracy and bitwise reproducibility algorithmically and
programmatically. In particular, we adopt an implementation of the exactly
rounded dot product based on long accumulators, which avoids accuracy losses
especially in parallel applications. However, reproducibility and accuracy
alone fail to indicate correct simulation behaviour. In fact, in the physical
model slightly different initial conditions lead to vastly different end
states. This behaviour translates to its numerical representation. Pointwise
convergence, even in principle, becomes impossible for long simulation times.
In a second part, we explore important performance tuning considerations. We
identify latency and memory bandwidth as the main performance indicators of our
routines. Based on these, we propose a parallel performance model that predicts
the execution time of algorithms implemented in Feltor and test our model on a
selection of parallel hardware architectures. We are able to predict the
execution time with a relative error of less than 25% for problem sizes between
0.1 and 1000 MB. Finally, we find that the product of latency and bandwidth
gives a minimum array size per compute node to achieve a scaling efficiency
above 50% (both strong and weak)
Realizing arbitrary-precision modular multiplication with a fixed-precision multiplier datapath
Within the context of cryptographic hardware, the term scalability refers to the ability to process operands of any size, regardless of the precision of the underlying data path or registers. In this paper we present a simple yet effective technique for increasing the scalability of a fixed-precision Montgomery multiplier. Our idea is to extend the datapath of a Montgomery multiplier in such a way that it can also perform an ordinary multiplication of two n-bit operands (without modular reduction), yielding a 2n-bit result. This
conventional (nxn->2n)-bit multiplication is then used as a “sub-routine” to realize arbitrary-precision Montgomery multiplication according to standard software algorithms such as Coarsely Integrated Operand Scanning (CIOS). We
show that performing a 2n-bit modular multiplication on an n-bit multiplier can be done in 5n clock cycles, whereby we assume that the n-bit modular multiplication takes n cycles. Extending a Montgomery multiplier for this extra
functionality requires just some minor modifications of the datapath and entails a slight increase in silicon area
- …