Application-tailored Linear Algebra Algorithms: A search-based Approach

In this paper, we tackle the problem of automatically generating algorithms for linear algebra operations by taking advantage of problem-specific knowledge. In most situations, users possess much more information about the problem at hand than what current libraries and computing environments accept; evidence shows that if properly exploited, such information leads to uncommon/unexpected speedups. We introduce a knowledge-aware linear algebra compiler that allows users to input matrix equations together with properties about the operands and the problem itself; for instance, they can specify that the equation is part of a sequence, and how successive instances are related to one another. The compiler exploits all this information to guide the generation of algorithms, to limit the size of the search space, and to avoid redundant computations. We applied the compiler to equations arising as part of sensitivity and genome studies; the algorithms produced exhibit, respectively, 100- and 1000-fold speedups

Semantic mutation testing

This is the Pre-print version of the Article. The official published version can be obtained from the link below - Copyright @ 2011 ElsevierMutation testing is a powerful and flexible test technique. Traditional mutation testing makes a small change to the syntax of a description (usually a program) in order to create a mutant. A test suite is considered to be good if it distinguishes between the original description and all of the (functionally non-equivalent) mutants. These mutants can be seen as representing potential small slips and thus mutation testing aims to produce a test suite that is good at finding such slips. It has also been argued that a test suite that finds such small changes is likely to find larger changes. This paper describes a new approach to mutation testing, called semantic mutation testing. Rather than mutate the description, semantic mutation testing mutates the semantics of the language in which the description is written. The mutations of the semantics of the language represent possible misunderstandings of the description language and thus capture a different class of faults. Since the likely misunderstandings are highly context dependent, this context should be used to determine which semantic mutants should be produced. The approach is illustrated through examples with statecharts and C code. The paper also describes a semantic mutation testing tool for C and the results of experiments that investigated the nature of some semantic mutation operators for C

Variable precision arithmetic: a Fortran 95 module

Abstract. This paper describes the design and development of a software package supporting variable precision arithmetic as a semantic extension to the Fortran 95 language. The working precision of the arithmetic supported by this package can be dynamically and arbitrarily varied. The facility exploits the data-abstraction capabilities of Fortran 95 and allows the operations to be used elementally with array operands as well as with scalars. The number system is defined in such a way as to be closed under all of the basic operations of normal arithmetic; no programterminating numerical exceptions can occur. Precision loss situations like underflow and overflow are handled by defining special value representations that preserve as much of the numeric information as is practical and the operation semantics are defined so that these exceptional values propagate as appropriate to reflect this loss of information. The number system uses an essentially conventional variable precision floating-point representation. When operations can be performed exactly within the currently-set working precision limit, the excess trailing zero digits are not stored, nor do they take part in future operations. This is both economical in storage and improves efficiency

The Linear Algebra Mapping Problem

We observe a disconnect between the developers and the end users of linear algebra libraries. On the one hand, the numerical linear algebra and the high-performance communities invest significant effort in the development and optimization of highly sophisticated numerical kernels and libraries, aiming at the maximum exploitation of both the properties of the input matrices, and the architectural features of the target computing platform. On the other hand, end users are progressively less likely to go through the error-prone and time consuming process of directly using said libraries by writing their code in C or Fortran; instead, languages and libraries such as Matlab, Julia, Eigen and Armadillo, which offer a higher level of abstraction, are becoming more and more popular. Users are given the opportunity to code matrix computations with a syntax that closely resembles the mathematical description; it is then a compiler or an interpreter that internally maps the input program to lower level kernels, as provided by libraries such as BLAS and LAPACK. Unfortunately, our experience suggests that in terms of performance, this translation is typically vastly suboptimal. In this paper, we first introduce the Linear Algebra Mapping Problem, and then investigate how effectively a benchmark of test problems is solved by popular high-level programming languages. Specifically, we consider Matlab, Octave, Julia, R, Armadillo (C++), Eigen (C++), and NumPy (Python); the benchmark is meant to test both standard compiler optimizations such as common subexpression elimination and loop-invariant code motion, as well as linear algebra specific optimizations such as optimal parenthesization of a matrix product and kernel selection for matrices with properties. The aim of this study is to give concrete guidelines for the development of languages and libraries that support linear algebra computations

Chaotic Compilation for Encrypted Computing: Obfuscation but Not in Name

An `obfuscation' for encrypted computing is quantified exactly here, leading to an argument that security against polynomial-time attacks has been achieved for user data via the deliberately `chaotic' compilation required for security properties in that environment. Encrypted computing is the emerging science and technology of processors that take encrypted inputs to encrypted outputs via encrypted intermediate values (at nearly conventional speeds). The aim is to make user data in general-purpose computing secure against the operator and operating system as potential adversaries. A stumbling block has always been that memory addresses are data and good encryption means the encrypted value varies randomly, and that makes hitting any target in memory problematic without address decryption, yet decryption anywhere on the memory path would open up many easily exploitable vulnerabilities. This paper `solves (chaotic) compilation' for processors without address decryption, covering all of ANSI C while satisfying the required security properties and opening up the field for the standard software tool-chain and infrastructure. That produces the argument referred to above, which may also hold without encryption.Comment: 31 pages. Version update adds "Chaotic" in title and throughout paper, and recasts abstract and Intro and other sections of the text for better access by cryptologists. To the same end it introduces the polynomial time defense argument explicitly in the final section, having now set that denouement out in the abstract and intr

Knowledge-Based Automatic Generation of Linear Algebra Algorithms and Code

This dissertation focuses on the design and the implementation of domain-specific compilers for linear algebra matrix equations. The development of efficient libraries for such equations, which lie at the heart of most software for scientific computing, is a complex process that requires expertise in a variety of areas, including the application domain, algorithms, numerical analysis and high-performance computing. Moreover, the process involves the collaboration of several people for a considerable amount of time. With our compilers, we aim to relieve the developers from both designing algorithms and writing code, and to generate routines that match or even surpass the performance of those written by human experts.Comment: Dissertatio

INFORM: An interactive data collection and display program with debugging capability

A computer program was developed to aid ASSEMBLY language programmers of mini and micro computers in solving the man machine communications problems that exist when scaled integers are involved. In addition to producing displays of quasi-steady state values, INFORM provides an interactive mode for debugging programs, making program patches, and modifying the displays. Auxiliary routines SAMPLE and DATAO add dynamic data acquisition and high speed dynamic display capability to the program. Programming information and flow charts to aid in implementing INFORM on various machines together with descriptions of all supportive software are provided. Program modifications to satisfy the individual user's needs are considered

Advancing HAL to an operational status

The development of the HAL language and the compiler implementation of the mathematical subset of the language have been completed. On-site support, training, and maintenance of this compiler were enlarged to broaden the implementation of HAL to include all features of the language specification for NASA manned space usage. A summary of activities associated with the HAL compiler for the UNIVAC 1108 is given