Generating optimized Fourier interpolation routines for density function theory using SPIRAL

© 2015 IEEE.Upsampling of a multi-dimensional data-set is an operation with wide application in image processing and quantum mechanical calculations using density functional theory. For small up sampling factors as seen in the quantum chemistry code ONETEP, a time-shift based implementation that shifts samples by a fraction of the original grid spacing to fill in the intermediate values using a frequency domain Fourier property can be a good choice. Readily available highly optimized multidimensional FFT implementations are leveraged at the expense of extra passes through the entire working set. In this paper we present an optimized variant of the time-shift based up sampling. Since ONETEP handles threading, we address the memory hierarchy and SIMD vectorization, and focus on problem dimensions relevant for ONETEP. We present a formalization of this operation within the SPIRAL framework and demonstrate auto-generated and auto-tuned interpolation libraries. We compare the performance of our generated code against the previous best implementations using highly optimized FFT libraries (FFTW and MKL). We demonstrate speed-ups in isolation averaging 3x and within ONETEP of up to 15%

Identification and classification of off-vertex critical points for contour tree construction on unstructured meshes of hexahedra

The topology of isosurfaces changes at isovalues of critical points, making such points an important feature when building contour trees or Morse-Smale complexes. Hexahedral elements with linear interpolants can contain additional off-vertex critical points in element bodies and on element faces. Moreover, a point on the face of a hexahedron which is critical in the element-local context is not necessarily critical in the global context. In ‘`Exploring Scalar Fields Using Critical Isovalues’' Weber et al. introduce a method to determine whether critical points on faces are also critical in the global context, based on the gradient of the asymptotic decider in each element that shares the face. However, as defined, the method of Weber et al. contains an error, and can lead to incorrect results. In this work we correct the error

Convolutional kernel function algebra

Many systems for image manipulation, signal analysis, machine learning, and scientific computing make use of discrete convolutional filters that are known before computation begins. These contexts benefit from common sub-expression elimination to reduce the number of calculations required, both multiplications and additions. We present an algebra for describing convolutional kernels and filters at a sufficient level of abstraction to enable intuitive common sub-expression based optimizations through decomposing filters into smaller, repeated, kernels. This enables the creation of an enormous search space of potential implementations of filters via algebraic manipulation. We demonstrate how integral image and sliding window optimizations can be expressed in the context of common sub-expression elimination as well as show the direct use case for this algebra in massively SIMD multiply-free contexts such as in cellular processor arrays. We then show that this algebra is general enough to express and optimize kernels that use non-standard semi-rings to enable shortest path algorithms

Adaptive-resolution octree-based volumetric SLAM

We introduce a novel volumetric SLAM pipeline for the integration and rendering of depth images at an adaptive level of detail. Our core contribution is a fusion algorithm which dynamically selects the appropriate integration scale based on the effective sensor resolution given the distance from the observed scene, addressing aliasing issues, reconstruction quality, and efficiency simultaneously. We implement our approach using an efficient octree structure which supports multi-resolution rendering allowing for online frame-to-model alignment. Our qualitative and quantitative experiments demonstrate significantly improved reconstruction quality and up to six-fold execution time speed-ups compared to single resolution grids

Precise event sampling on AMD versus intel: quantitative and qualitative comparison

Precise event sampling is a profiling feature in commodity processors that can sample hardware events and accurately locate the instructions that trigger the events. This feature has been used in a large number of tools to detect application performance issues. Although precise event sampling is readily supported in modern multicore architectures, vendor supports exhibit great differences that affect their accuracy, stability, overhead, and functionality. This work presents the most comprehensive study to date on benchmarking the event sampling features of Intel PEBS and AMD IBS and performs in-depth analysis on key differences through series of microbenchmarks. Our qualitative and quantitative analysis shows that PEBS allows finer-grained and more accurate sampling of hardware events, while IBS offers richer set of information at each sample though it suffers from lower accuracy and stability. Moreover, OS signal delivery, which is a common method used by the profiling software, introduces significant time overhead to the original overhead incurred by the hardware mechanisms in both PEBS and IBS. We also found that both PEBS and IBS have bias in sampling events across multiple different locations in a code. Lastly, we demonstrate how our findings on microbenchmarks under different thread counts hold for a full-fledged profiling tool that runs on the state-of-the-art Intel and AMD machines. Overall our detailed comparisons serve as a great reference and provide invaluable information for hardware designers and profiling tool developers

High-frame rate homography and visual odometry by tracking binary features from the focal plane

Robotics faces a long-standing obstacle in which the speed of the vision system’s scene understanding is insufficient, impeding the robot’s ability to perform agile tasks. Consequently, robots must often rely on interpolation and extrapolation of the vision data to accomplish tasks in a timely and effective manner. One of the primary reasons for these delays is the analog-to-digital conversion that occurs on a per-pixel basis across the image sensor, along with the transfer of pixel-intensity information to the host device. This results in significant delays and power consumption in modern visual processing pipelines. The SCAMP-5—a general-purpose Focal-plane Sensor-processor array (FPSP)—used in this research performs computations in the analog domain prior to analog-to-digital conversion. By extracting features from the image on the focal plane, the amount of data that needs to be digitised and transferred is reduced. This allows for a high frame rate and low energy consumption for the SCAMP-5. The focus of our work is on localising the camera within the scene, which is crucial for scene understanding and for any downstream robotics tasks. We present a localisation system that utilise the FPSP in two parts. First, a 6-DoF odometry system is introduced, which efficiently estimates its position against a known marker at over 400 FPS. Second, our work is extended to implement BIT-VO—6-DoF visual odometry system which operates under an unknown natural environment at 300 FPS

Temporal blocking of finite-difference stencil operators with sparse "off-the-grid" sources

Stencil kernels dominate a range of scientific applications, including seismic and medical imaging, image processing, and neural networks. Temporal blocking is a performance optimization that aims to reduce the required memory bandwidth of stencil computations by re-using data from the cache for multiple time steps. It has already been shown to be beneficial for this class of algorithms. However, applying temporal blocking to practical applications' stencils remains challenging. These computations often consist of sparsely located operators not aligned with the computational grid (“off-the-grid”). Our work is motivated by modelling problems in which source injections result in wavefields that must then be measured at receivers by interpolation from the grided wavefield. The resulting data dependencies make the adoption of temporal blocking much more challenging. We propose a methodology to inspect these data dependencies and reorder the computation, leading to performance gains in stencil codes where temporal blocking has not been applicable. We implement this novel scheme in the Devito domain-specific compiler toolchain. Devito implements a domain-specific language embedded in Python to generate optimized partial differential equation solvers using the finite-difference method from high-level symbolic problem definitions. We evaluate our scheme using isotropic acoustic, anisotropic acoustic, and isotropic elastic wave propagators of industrial significance. After auto-tuning, performance evaluation shows that this enables substantial performance improvement through temporal blocking over highly-optimized vectorized spatially-blocked code of up to 1.6x