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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6

All sources NASA NTRS DOE OSTI

DOE OSTI2020

Dynamic variable precision computation

A conversion unit converts operands from a conventional number system that represents each binary number in the operands as one bit to redundant number system (RNS) operands that represent each binary number as a plurality of bits. An arithmetic logic unit performs an arithmetic operation on the RNS operands in a direction from a most significant bit (MSB) to a least significant bit (LSB). The arithmetic logic unit stops performing the arithmetic operation prior to performing the arithmetic operation on a target binary number indicated by a dynamic precision associated with the RNS operands. In some cases, a power supply provides power to bit slices in the arithmetic logic unit and a clock signal generator provides clock signals to the bit slices. Gate logic is configured to gate the power or the clock signals provided to a subset of the bit slices.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Fine-Grained Exploitation of Mixed Precision for Faster CNN Training

As deep convolutional neural networks (CNNs) have become increasingly popular and successful at an ever-widening number of machine learning tasks specialized hardware has become increasingly available for training and deploying them. NVIDIA's recent Volta architecture includes tensor cores which perform a fused operation reduced and mixed precision (16-bit multiply, 32-bit accumulate). Recent research indicates that, typically, very little is lost (in terms of training accuracy) when half precision is used in place of single precision, and performance gains can be made by doing arithmetic in reduced precision. In this work we demonstrate that making layer-by-layer choices as to the arithmetic/data precision can lead to further performance improvement. In our study of 25,200 CNNs we demonstrate an average speedup (over purely half precision) of 1.27x and speedups as high as 3.64x by appropriately combining single and half precision arithmetic and data types on a layer-by-layer basis.

Johnston, Travis↗

NASA NTRS1977

An improved algorithm for the isolation of polynomial real zeros

THe Collins-Loos algorithm for computing isolating intervals for the zeros of an integer polynomial requires the evaluation of polynomials at rational points. This implies the use of arbitrary precision integer arithmetic. It is shown how careful use of single precision, floating point arithmetic within the context of a slightly modified algorithm can make the calculation considerably faster and no less exact. Typically, 95% or more of the evaluations can be done without exact arithmetic. The precise speedup depends on the relative costs of the arithmetic in a given implementation. The implementation on DEC KL-10 computer is some 5 to 10 times faster than the original Univac 1110 implementation in SAC-I.

Fateman, R. J.↗

NASA NTRS1983

Verification of Numerical Algorithms

The following strategy is suggested for specification and proof: (1) Defer the construction of a formal program specification with respect to I/O assertions unit the correctness of the program with respect to an abstract mathematical model of program intent is demonstrated. (2) Prove that an abstract machine (using infinite precision arithmetic) would compute that object exactly. (3) Prove that the computational sequences of arithmetic operations that occur in the abstract machine must be precisely the same at every step as those occurring on an actual machine (with finite precision arithmetic), executing the same program. (4) Use a Verification Conditions VC-generator that knows about the semantics of arithmetic operations to annotate the program with assertions that bound (or in some circumstances estimate) the difference between the actual machine state variables and the corresponding ones of the abstract machine. Construct the formal program specification by combining the verification conditions into theorems about computational error that can be proved with mechanical assistance.

Source record↗

NASA NTRS1994

A componential model of human interaction with graphs: 1. Linear regression modeling

Task analyses served as the basis for developing the Mixed Arithmetic-Perceptual (MA-P) model, which proposes (1) that people interacting with common graphs to answer common questions apply a set of component processes-searching for indicators, encoding the value of indicators, performing arithmetic operations on the values, making spatial comparisons among indicators, and repsonding; and (2) that the type of graph and user's task determine the combination and order of the components applied (i.e., the processing steps). Two experiments investigated the prediction that response time will be linearly related to the number of processing steps according to the MA-P model. Subjects used line graphs, scatter plots, and stacked bar graphs to answer comparison questions and questions requiring arithmetic calculations. A one-parameter version of the model (with equal weights for all components) and a two-parameter version (with different weights for arithmetic and nonarithmetic processes) accounted for 76%-85% of individual subjects' variance in response time and 61%-68% of the variance taken across all subjects. The discussion addresses possible modifications in the MA-P model, alternative models, and design implications from the MA-P model.

Gillan, Douglas J.↗

NASA NTRS1992

Phase-locked loop FM demodulator

A conventional phase-locked loop is improved by replacing its phase detector with one comprising a linear ramp generator and a sample-and-hold circuit, thus eliminating the need for a lowpass loop filter, although the output of the sample-and-hold circuit may be filtered in the case of a very low level modulating signal on the incoming FM signal, but then filtering is not a difficult problem as in a conventional phase-locked loop. The result is FM demodulation by zero-order estimation. For FM demodulation by first-order estimation, the arithmetic difference between adjacent samples is formed, and using a second sample-and-hold circuit an arithmetic difference signal is produced as an input to a second ramp generator that is reset after each sampling cycle to generate a ramp the slope of which is a function of the arithmetic difference signal stored in the second sample-and-hold circuit. The ramp thus generated by the second ramp generator is arithmetically summed with the zero-estimation signal from the first sample-and-hold circuit to form a first-order estimation signal. Filtering such a first-order estimation signal is less of a problem than filtering a zero-order estimation signal.

Kirkham, Harold↗

DOE OSTI2015

TabVar: Tabulated Variables

TabVar: A Python library for manipulating datasets in the form of tabulated variables. Tables in tabvar contain many columns representing independent variables, but exactly one distinguished column for the dependent variable. Having a single distinguished column allows a natural lifting of arithmetic operators to tables, much (and in fact fully generalizing) multidimensional array arithmetic. The convenient syntax of whole-table arithmetic, along with the usual operations of filtering and aggregation, and all in the setting of python's interactive REPL allows for rapid exploration of datasets.

Bachan, John↗

DOE OSTI2016

Technology Performance Level (TPL) Scoring Tool

Three different ways of combining scores are used in the revised formulation. These are arithmetic mean, geometric mean and multiplication with normalisation. Arithmetic mean is used when combining scores that measure similar attributes, e.g. used for combining costs. The arithmetic mean has the property that it is similar to a logical OR, e.g. when combining costs it does not matter what the individual costs are only what the combined cost is. Geometric mean and Multiplication are used when combining scores that measure disparate attributes. Multiplication is similar to a logical AND, it is used to combine ‘must haves.’ As a result, this method is more punitive than the geometric mean; to get a good score in the combined result it is necessary to have a good score in ALL of the inputs. e.g. the different types of survivability are ‘must haves.’ On balance, the revised TPL is probably less punitive than the previous spreadsheet, multiplication is used sparingly as a method of combining scores. This is in line with the feedback of the Wave Energy Prize judges.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Technical report: Design of the accessor

As we have seen the arithmetic power of hardware architectures growing much faster than the memory bandwidth, there is an urgent need to rethink the way we operate, communicate, and store data. A promising strategy for overcoming the “memory wall” is the decoupling of memory precision from arithmetic precision as proposed in Anzt et al. Such a decoupling of memory precision and arithmetic precision requires an “accessor” that handles the conversion between formats (resp. compression of the data) on the fly in registers. Such an accessor has to be general in the sense that it can handle a wide range of floating point formats and compression strategies, and still allows for further extension. At the same time, is important that the use of the accessor is not a burden for the developer. Therefore, it is important to abstract all implementation details from the user, hide the underlying storage format from the user, and make the accessor cross-platform portable. In this document we present the design of an accessor that aims at fulfilling all these requirements.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Technical Report: Accessor Realization

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

The Implications of 3D Thermal Structure on 1D Atmospheric Retrieval

Using the atmospheric structure from a 3D global radiation-hydrodynamic simulation of HD 189733b and the open-source Bayesian Atmospheric Radiative Transfer (BART) code, we investigate the difference between the secondary-eclipse temperature structure produced with a 3D simulation and the best-fit 1D retrieved model. Synthetic data are generated by integrating the 3D models over the Spitzer , the Hubble Space Telescope ( HST ), and the James Web Space Telescope ( JWST ) bandpasses, covering the wavelength range between 1 and 11 μ m where most spectroscopically active species have pronounced features. Using the data from different observing instruments, we present detailed comparisons between the temperature–pressure profiles recovered by BART and those from the 3D simulations. We calculate several averages of the 3D thermal structure and explore which particular thermal profile matches the retrieved temperature structure. We implement two temperature parameterizations that are commonly used in retrieval to investigate different thermal profile shapes. To assess which part of the thermal structure is best constrained by the data, we generate contribution functions for our theoretical model and each of our retrieved models. Our conclusions are strongly affected by the spectral resolution of the instruments included, their wavelength coverage, and the number of data points combined. We also see some limitations in each of the temperature parametrizations, as they are not able to fully match the complex curvatures that are usually produced in hydrodynamic simulations. The results show that our 1D retrieval is recovering a temperature and pressure profile that most closely matches the arithmetic average of the 3D thermal structure. When we use a higher resolution, more data points, and a parametrized temperature profile that allows more flexibility in the middle part of the atmosphere, we find a better match between the retrieved temperature and pressure profile and the arithmetic average. The Spitzer and HST simulated observations sample deep parts of the planetary atmosphere and provide fewer constraints on the temperature and pressure profile, while the JWST observations sample the middle part of the atmosphere, providing a good match with the middle and most complex part of the arithmetic average of the 3D temperature structure.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1977

Fault tolerant computing: A preamble for assuring viability of large computer systems

The need for fault-tolerant computing is addressed from the viewpoints of (1) why it is needed, (2) how to apply it in the current state of technology, and (3) what it means in the context of the Phoenix computer system and other related systems. To this end, the value of concurrent error detection and correction is described. User protection, program retry, and repair are among the factors considered. The technology of algebraic codes to protect memory systems and arithmetic codes to protect memory systems and arithmetic codes to protect arithmetic operations is discussed.

Lim, R. S.↗

NASA NTRS1984

Research in the design of high-performance reconfigurable systems

An initial design for the Bit Processor (BP) referred to in prior reports as the Processing Element or PE has been completed. Eight BP's, together with their supporting random-access memory, a 64 k x 9 ROM to perform addition, routing logic, and some additional logic, constitute the components of a single stage. An initial stage design is given. Stages may be combined to perform high-speed fixed or floating point arithmetic. Stages can be configured into a range of arithmetic modules that includes bit-serial one or two-dimensional arrays; one or two dimensional arrays fixed or floating point processors; and specialized uniprocessors, such as long-word arithmetic units. One to eight BP's represent a likely initial chip level. The Stage would then correspond to a first-level pluggable module. As both this project and VLSI CAD/CAM progress, however, it is expected that the chip level would migrate upward to the stage and, perhaps, ultimately the box level. The BP RAM, consisting of two banks, holds only operands and indices. Programs are at the box (high-level function) and system level. At the system level initial effort has been concentrated on specifying the tools needed to evaluate design alternatives.

Slotnick, D. L.↗

NASA NTRS1985

Research in the design of high-performance reconfigurable systems

The initial control and programming philosophies of the RELAPSE are discussed. A block diagram showing the relationship of the Arithmetic Units (composed of Stages and Bit Processors), to the Functional Units, and other components of the RELAPSE is used to guide this discussion. The latest version of the Bit Processor design is presented. Included is a detailed discussion of the Bit Processor's new scratch pad memory component. The section also clarifies the usage of the Bit Processor's processing registers, and Input/Output functions. The final design phase of the Arithmetic Unit is underway by a study of the Proposed IEEE Floating Point Standard. The decisions on conformation to this standard will be used as inputs into the finalization of the designs of the Bit Processor, Stage, and Arithmetic Units of the RELAPSE.

Slotnick, D. L.↗

NASA NTRS1989

Noiseless compression using non-Markov models

Adaptive data compression techniques can be viewed as consisting of a model specified by a database common to the encoder and decoder, an encoding rule and a rule for updating the model to ensure that the encoder and decoder always agree on the interpretation of the next transmission. The techniques which fit this framework range from run-length coding, to adaptive Huffman and arithmetic coding, to the string-matching techniques of Lempel and Ziv. The compression obtained by arithmetic coding is dependent on the generality of the source model. For many sources, an independent-letter model is clearly insufficient. Unfortunately, a straightforward implementation of a Markov model requires an amount of space exponential in the number of letters remembered. The Directed Acyclic Word Graph (DAWG) can be constructed in time and space proportional to the text encoded, and can be used to estimate the probabilities required for arithmetic coding based on an amount of memory which varies naturally depending on the encoded text. The tail of that portion of the text which was encoded is the longest suffix that has occurred previously. The frequencies of letters following these previous occurrences can be used to estimate the probability distribution of the next letter. Experimental results indicate that compression is often far better than that obtained using independent-letter models, and sometimes also significantly better than other non-independent techniques.

Blumer, Anselm↗

NASA NTRS1989

Basic mathematical function libraries for scientific computation

Ada packages implementing selected mathematical functions for the support of scientific and engineering applications were written. The packages provide the Ada programmer with the mathematical function support found in the languages Pascal and FORTRAN as well as an extended precision arithmetic and a complete complex arithmetic. The algorithms used are fully described and analyzed. Implementation assumes that the Ada type FLOAT objects fully conform to the IEEE 754-1985 standard for single binary floating-point arithmetic, and that INTEGER objects are 32-bit entities. Codes for the Ada packages are included as appendixes.

Galant, David C.↗

NASA NTRS1991

A 640-MHz 32-megachannel real-time polyphase-FFT spectrum analyzer

A polyphase fast Fourier transform (FFT) spectrum analyzer being designed for NASA's Search for Extraterrestrial Intelligence (SETI) Sky Survey at the Jet Propulsion Laboratory is described. By replacing the time domain multiplicative window preprocessing with polyphase filter processing, much of the processing loss of windowed FFTs can be eliminated. Polyphase coefficient memory costs are minimized by effective use of run length compression. Finite word length effects are analyzed, producing a balanced system with 8 bit inputs, 16 bit fixed point polyphase arithmetic, and 24 bit fixed point FFT arithmetic. Fixed point renormalization midway through the computation is seen to be naturally accommodated by the matrix FFT algorithm proposed. Simulation results validate the finite word length arithmetic analysis and the renormalization technique.

Zimmerman, G. A.↗

NASA NTRS1995

A seismic data compression system using subband coding

This article presents a study of seismic data compression techniques and a compression algorithm based on subband coding. The algorithm includes three stages: a decorrelation stage, a quantization stage that introduces a controlled amount of distortion to allow for high compression ratios, and a lossless entropy coding stage based on a simple but efficient arithmetic coding method. Subband coding methods are particularly suited to the decorrelation of nonstationary processes such as seismic events. Adaptivity to the nonstationary behavior of the waveform is achieved by dividing the data into separate blocks that are encoded separately with an adaptive arithmetic encoder. This is done with high efficiency due to the low overhead introduced by the arithmetic encoder in specifying its parameters. The technique could be used as a progressive transmission system, where successive refinements of the data can be requested by the user. This allows seismologists to first examine a coarse version of waveforms with minimal usage of the channel and then decide where refinements are required. Rate-distortion performance results are presented and comparisons are made with two block transform methods.

Kiely, A. B.↗