Empirically Tuning HPC Kernels with iFKO

iFKO (iterative Floating point Kernel Optimizer) is an open-source iterative empirical compilation framework which can be used to tune high performance computing (HPC) kernels. The goal of our research is to advance iterative empirical compilation to the degree that the performance it can achieve is comparable to that delivered by painstaking hand tuning in assembly. This will allow many HPC researchers to spend precious development time on higher level aspects of tuning such as parallelization, as well as enabling computational scientists to develop new algorithms that demand new high performance kernels. At present, algorithms that cannot use hand-tuned performance libraries tend to lose to even inferior algorithms that can. We discuss our new autovectorization technique (speculative vectorization) which can autovectorize loops past dependent branches by speculating along frequently taken paths, even when other paths cannot be effectively vectorized. We implemented this technique in iFKO and demonstrated significant speedup for kernels that prior vectorization techniques could not optimize. We have developed an optimization for two dimensional array indexing that is critical for allowing us to heavily unroll and jam loops without restriction from integer register pressure. We then extended the state of the art single basic block vectorization method, SLP, to vectorize nested loops. We have also introduced optimized reductions that can retain full SIMD parallelization for the entire reduction, as well as doing loop specialization and unswitching as needed to address vector alignment issues and paths inside the loops which inhibit autovectorization. We have also implemented a critical transformation for optimal vectorization of mixed-type data. Combining all these techniques we can now fully vectorize the loopnests for our most complicated kernels, allowing us to achieve performance very close to that of hand-tuned assembly

Optimizing SIMD execution in HW/SW co-designed processors

SIMD accelerators are ubiquitous in microprocessors from different computing domains. Their high compute power and hardware simplicity improve overall performance in an energy efficient manner. Moreover, their replicated functional units and simple control mechanism make them amenable to scaling to higher vector lengths. However, code generation for these accelerators has been a challenge from the days of their inception. Compilers generate vector code conservatively to ensure correctness. As a result they lose significant vectorization opportunities and fail to extract maximum benefits out of SIMD accelerators. This thesis proposes to vectorize the program binary at runtime in a speculative manner, in addition to the compile time static vectorization. There are different environments that support runtime profiling and optimization support required for dynamic vectorization, one of most prominent ones being: 1) Dynamic Binary Translators and Optimizers (DBTO) and 2) Hardware/Software (HW/SW) Co-designed Processors. HW/SW co-designed environment provides several advantages over DBTOs like transparent incorporations of new hardware features, binary compatibility, etc. Therefore, we use HW/SW co-designed environment to assess the potential of speculative dynamic vectorization. Furthermore, we analyze vector code generation for wider vector units and find out that even though SIMD accelerators are amenable to scaling from the hardware point of view, vector code generation at higher vector length is even more challenging. The two major factors impeding vectorization for wider SIMD units are: 1) Reduced dynamic instruction stream coverage for vectorization and 2) Large number of permutation instructions. To solve the first problem we propose Variable Length Vectorization that iteratively vectorizes for multiple vector lengths to improve dynamic instruction stream coverage. Secondly, to reduce the number of permutation instructions we propose Selective Writing that selectively writes to different parts of a vector register and avoids permutations. Finally, we tackle the problem of leakage energy in SIMD accelerators. Since SIMD accelerators consume significant amount of real estate on the chip, they become the principle source of leakage if not utilized judiciously. Power gating is one of the most widely used techniques to reduce leakage energy of functional units. However, power gating has its own energy and performance overhead associated with it. We propose to selectively devectorize the vector code when higher SIMD lanes are used intermittently. This selective devectorization keeps the higher SIMD lanes idle and power gated for maximum duration. Therefore, resulting in overall leakage energy reduction.Postprint (published version

Assisting Static Compiler Vectorization with a Speculative Dynamic Vectorizer in an HW/SW Codesigned Environment

Compiler-based static vectorization is used widely to extract data-level parallelism from computation-intensive applications. Static vectorization is very effective in vectorizing traditional array-based applications. However, compilers' inability to do accurate interprocedural pointer disambiguation and interprocedural array dependence analysis severely limits vectorization opportunities. HW/SW codesigned processors provide an excellent opportunity to optimize the applications at runtime. The availability of dynamic application behavior at runtime helps in capturing vectorization opportunities generally missed by the compilers. This article proposes to complement the static vectorization with a speculative dynamic vectorizer in an HW/SW codesigned processor. We present a speculative dynamic vectorization algorithm that speculatively reorders ambiguous memory references to uncover vectorization opportunities. The speculative reordering of memory instructions avoids the need for accurate interprocedural pointer disambiguation and interprocedural array dependence analysis. The hardware checks for any memory dependence violation due to speculative vectorization and takes corrective action in case of violation. Our experiments show that the combined (static + dynamic) vectorization approach provides a 2× performance benefit compared to the static GCC vectorization alone, for SPECFP2006. Furthermore, the speculative dynamic vectorizer is able to vectorize 48% of the loops that ICC failed to vectorize due to conservative dependence analysis in the TSVC benchmark suite. Moreover, the dynamic vectorization scheme is as effective in vectorization of pointer-based applications as for the array-based ones, whereas compilers lose significant vectorization opportunities in pointer-based applications. Furthermore, we show that speculation is not only a luxury but also a necessity for runtime vectorization.Peer ReviewedPostprint (author's final draft

Effective data parallel computing on multicore processors

The rise of chip multiprocessing or the integration of multiple general purpose processing cores on a single chip (multicores), has impacted all computing platforms including high performance, servers, desktops, mobile, and embedded processors. Programmers can no longer expect continued increases in software performance without developing parallel, memory hierarchy friendly software that can effectively exploit the chip level multiprocessing paradigm of multicores. The goal of this dissertation is to demonstrate a design process for data parallel problems that starts with a sequential algorithm and ends with a high performance implementation on a multicore platform. Our design process combines theoretical algorithm analysis with practical optimization techniques. Our target multicores are quad-core processors from Intel and the eight-SPE IBM Cell B.E. Target applications include Matrix Multiplications (MM), Finite Difference Time Domain (FDTD), LU Decomposition (LUD), and Power Flow Solver based on Gauss-Seidel (PFS-GS) algorithms. These applications are popular computation methods in science and engineering problems and are characterized by unit-stride (MM, LUD, and PFS-GS) or 2-point stencil (FDTD) memory access pattern. The main contributions of this dissertation include a cache- and space-efficient algorithm model, integrated data pre-fetching and caching strategies, and in-core optimization techniques. Our multicore efficient implementations of the above described applications outperform nai¨ve parallel implementations by at least 2x and scales well with problem size and with the number of processing cores

Riemannian Reading: Using Manifolds to Calculate and Unfold Narrative

The purpose of this study is to investigate the space where readers and texts interact. By applying non-Euclidean geometry to the modern subgenre of science fiction known as steampunk, we can see that narratives have no intrinsic geometry. Instead, what we can understand is that readers unflatten inherently flat narratives by applying their own metric of understanding to a narrative. Steampunk acts a primer to considering this mathematical process by explicitly flattening its settings and characters, as well as the historical accounts founding the narrative. Mark Hodder\u27s novel, The Strange Affair of Spring-Heeled Jack, offers two characters that unsuccessfully attempt to act as non-Euclidean readers. Through manipulation of agency, Hodder\u27s novel demonstrates the unflattening process as we read novels. However, our unflattening process distorts a narrative through the application of our metric of understanding. The study first gives a short historical account of non-Euclidean geometry in the 19th century. The analysis stems from the application of non-Euclidean geometric thinking to narrative structures

Riemannian Reading: Using Manifolds to Calculate and Unfold Narrative

The purpose of this study is to investigate the space where readers and texts interact. By applying non-Euclidean geometry to the modern subgenre of science fiction known as steampunk, we can see that narratives have no intrinsic geometry. Instead, what we can understand is that readers unflatten inherently flat narratives by applying their own metric of understanding to a narrative. Steampunk acts a primer to considering this mathematical process by explicitly flattening its settings and characters, as well as the historical accounts founding the narrative. Mark Hodder\u27s novel, The Strange Affair of Spring-Heeled Jack, offers two characters that unsuccessfully attempt to act as non-Euclidean readers. Through manipulation of agency, Hodder\u27s novel demonstrates the unflattening process as we read novels. However, our unflattening process distorts a narrative through the application of our metric of understanding. The study first gives a short historical account of non-Euclidean geometry in the 19th century. The analysis stems from the application of non-Euclidean geometric thinking to narrative structures

Curve41417: Karatsuba Revisited

Abstract. This paper introduces constant-time ARM Cortex-A8 ECDH software that (1) is faster than the fastest ECDH option in the latest version of OpenSSL but (2) achieves a security level above 2200 using a prime above 2400. For comparison, this OpenSSL ECDH option is not constant-time and has a security level of only 280. The new speeds are achieved in a quite different way from typical prime-field ECC software: they rely on a synergy between Karatsuba’s method and choices of radix smaller than the CPU word size