Array programming provides a powerful, compact and expressive syntax for accessing, manipulating and operating on data in vectors, matrices and higher-dimensional arrays. NumPy is the primary array programming library for the Python language. It has an essential role in research analysis pipelines in fields as diverse as physics, chemistry, astronomy, geoscience, biology, psychology, materials science, engineering, finance and economics. For example, in astronomy, NumPy was an important part of the software stack used in the discovery of gravitational waves1 and in the first imaging of a black hole2. Here we review how a few fundamental array concepts lead to a simple and powerful programming paradigm for organizing, exploring and analysing scientific data. NumPy is the foundation upon which the scientific Python ecosystem is constructed. It is so pervasive that several projects, targeting audiences with specialized needs, have developed their own NumPy-like interfaces and array objects. Owing to its central position in the ecosystem, NumPy increasingly acts as an interoperability layer between such array computation libraries and, together with its application programming interface (API), provides a flexible framework to support the next decade of scientific and industrial analysis. NumPy is the primary array programming library for Python; here its fundamental concepts are reviewed and its evolution into a flexible interoperability layer between increasingly specialized computational libraries is discussed.

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Array programming with NumPy

We describe LLVM (low level virtual machine), a compiler framework designed to support transparent, lifelong program analysis and transformation for arbitrary programs, by providing high-level information to compiler transformations at compile-time, link-time, run-time, and in idle time between runs. LLVM defines a common, low-level code representation in static single assignment (SSA) form, with several novel features: a simple, language-independent type-system that exposes the primitives commonly used to implement high-level language features; an instruction for typed address arithmetic; and a simple mechanism that can be used to implement the exception handling features of high-level languages (and setjmp/longjmp in C) uniformly and efficiently. The LLVM compiler framework and code representation together provide a combination of key capabilities that are important for practical, lifelong analysis and transformation of programs. To our knowledge, no existing compilation approach provides all these capabilities. We describe the design of the LLVM representation and compiler framework, and evaluate the design in three ways: (a) the size and effectiveness of the representation, including the type information it provides; (b) compiler performance for several interprocedural problems; and (c) illustrative examples of the benefits LLVM provides for several challenging compiler problems.

/pdf/llvm-a-compilation-framework-for-lifelong-program-analysis-2e1wwcps42.pdf

LLVM: a compilation framework for lifelong program analysis & transformation

Array programming provides a powerful, compact, expressive syntax for accessing, manipulating, and operating on data in vectors, matrices, and higher-dimensional arrays. NumPy is the primary array programming library for the Python language. It plays an essential role in research analysis pipelines in fields as diverse as physics, chemistry, astronomy, geoscience, biology, psychology, material science, engineering, finance, and economics. For example, in astronomy, NumPy was an important part of the software stack used in the discovery of gravitational waves and the first imaging of a black hole. Here we show how a few fundamental array concepts lead to a simple and powerful programming paradigm for organizing, exploring, and analyzing scientific data. NumPy is the foundation upon which the entire scientific Python universe is constructed. It is so pervasive that several projects, targeting audiences with specialized needs, have developed their own NumPy-like interfaces and array objects. Because of its central position in the ecosystem, NumPy increasingly plays the role of an interoperability layer between these new array computation libraries.

/pdf/array-programming-with-numpy-4gbytt9sw2.pdf

Array Programming with NumPy

Bridging cultures that have often been distant, Julia combines expertise from the diverse fields of computer science and computational science to create a new approach to numerical computing. Julia is designed to be easy and fast and questions notions generally held to be “laws of nature" by practitioners of numerical computing: \beginlist \item High-level dynamic programs have to be slow. \item One must prototype in one language and then rewrite in another language for speed or deployment. \item There are parts of a system appropriate for the programmer, and other parts that are best left untouched as they have been built by the experts. \endlist We introduce the Julia programming language and its design---a dance between specialization and abstraction. Specialization allows for custom treatment. Multiple dispatch, a technique from computer science, picks the right algorithm for the right circumstance. Abstraction, which is what good computation is really about, recognizes what remains the same after dif...

Julia: A Fresh Approach to Numerical Computing

We present a new symbolic execution tool, KLEE, capable of automatically generating tests that achieve high coverage on a diverse set of complex and environmentally-intensive programs. We used KLEE to thoroughly check all 89 stand-alone programs in the GNU COREUTILS utility suite, which form the core user-level environment installed on millions of Unix systems, and arguably are the single most heavily tested set of open-source programs in existence. KLEE-generated tests achieve high line coverage -- on average over 90% per tool (median: over 94%) -- and significantly beat the coverage of the developers' own hand-written test suite. When we did the same for 75 equivalent tools in the BUSYBOX embedded system suite, results were even better, including 100% coverage on 31 of them.We also used KLEE as a bug finding tool, applying it to 452 applications (over 430K total lines of code), where it found 56 serious bugs, including three in COREUTILS that had been missed for over 15 years. Finally, we used KLEE to crosscheck purportedly identical BUSYBOX and COREUTILS utilities, finding functional correctness errors and a myriad of inconsistencies.

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KLEE: unassisted and automatic generation of high-coverage tests for complex systems programs

Context-sensitive pointer analysis algorithms with full "heapcloning" are powerful but are widely considered to be too expensive to include in production compilers. This paper shows, for the first time, that a context-sensitive, field-sensitive algorithm with fullheap cloning (by acyclic call paths) can indeed be both scalable and extremely fast in practice. Overall, the algorithm is able to analyze programs in the range of 100K-200K lines of C code in 1-3 seconds,takes less than 5% of the time it takes for GCC to compile the code (which includes no whole-program analysis), and scales well across five orders of magnitude of code size. It is also able to analyze the Linux kernel (about 355K linesof code) in 3.1 seconds. The paper describes the major algorithmic and engineering design choices that are required to achieve these results, including (a) using flow-insensitive and unification-basedanalysis, which are essential to avoid exponential behavior in practice;(b) sacrificing context-sensitivity within strongly connected components of the call graph; and (c) carefully eliminating several kinds of O(N2) behaviors (largely without affecting precision). The techniques used for (b) and (c) eliminated several major bottlenecks to scalability, and both are generalizable to other context-sensitive algorithms. We show that the engineering choices collectively reduce analysis time by factors of up to 10x-15xin our larger programs, and have found that the savings grow strongly with program size. Finally, we briefly summarize results demonstrating the precision of the analysis.

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Making context-sensitive points-to analysis with heap cloning practical for the real world

This paper describes Automatic Pool Allocation, a transformation framework that segregates distinct instances of heap-based data structures into seperate memory pools and allows heuristics to be used to partially control the internal layout of those data structures. The primary goal of this work is performance improvement, not automatic memory management, and the paper makes several new contributions. The key contribution is a new compiler algorithm for partitioning heap objects in imperative programs based on a context-sensitive pointer analysis, including a novel strategy for correct handling of indirect (and potentially unsafe) function calls. The transformation does not require type safe programs and works for the full generality of C and C++. Second, the paper describes several optimizations that exploit data structure partitioning to further improve program performance. Third, the paper evaluates how memory hierarchy behavior and overall program performance are impacted by the new transformations. Using a number of benchmarks and a few applications, we find that compilation times are extremely low, and overall running times for heap intensive programs speed up by 10-25% in many cases, about 2x in two cases, and more than 10x in two small benchmarks. Overall, we believe this work provides a new framework for optimizing pointer intensive programs by segregating and controlling the layout of heap-based data structures.

/pdf/automatic-pool-allocation-improving-performance-by-3h88v4k4el.pdf

Automatic pool allocation: improving performance by controlling data structure layout in the heap

Traditional approaches to enforcing memory safety of programs rely heavily on runtime checks of memory accesses and on garbage collection, both of which are unattractive for embedded applications. The long-term goal of our work is to enable 100% static enforcement of memory safety for embedded programs through advanced compiler techniques and minimal semantic restrictions on programs. The key result of this paper is a compiler technique that ensures memory safety of dynamically allocated memory without programmer annotations, runtime checks, or garbage collection, and works for a large subclass of type-safe C programs. The technique is based on a fully automatic pool allocation (i.e., region-inference) algorithm for C programs we developed previously, and it ensures safety of dynamically allocated memory while retaining explicit deallocation of individual objects within regions (to avoid garbage collection). For a diverse set of embedded C programs (and using a previous technique to avoid null pointer checks), we show that we are able to statically ensure the safety of pointer and dynamic memory usage in all these programs. We also describe some improvements over our previous work in static checking of array accesses. Overall, we achieve 100% static enforcement of memory safety without new language syntax for a significant subclass of embedded C programs, and the subclass is much broader if array bounds checks are ignored. Overall, these techniques greatly expand the class of embedded programs for which 100% static enforcement of memory safety is possible, and furthermore can be achieved without new language support.

Memory safety without runtime checks or garbage collection

The LLVM Compiler Infrastructure (http://llvm.cs. uiuc.edu) is a robust system that is well suited for a wide variety of research and development work. This brief paper introduces the LLVM system and provides pointers to more extensive documentation, complementing the tutorial presented at LCPC.

Chris Lattner

Papers

LLVM: a compilation framework for lifelong program analysis & transformation

Making context-sensitive points-to analysis with heap cloning practical for the real world

Automatic pool allocation: improving performance by controlling data structure layout in the heap

Memory safety without runtime checks or garbage collection

The LLVM compiler framework and infrastructure tutorial