Search NASA⌕ Search

SEARCH · Search NASA

Results for “Arithmetic”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 343 records · Page 19

Testing interconnected VLSI circuits in the Big Viterbi Decoder

The Big Viterbi Decoder (BVD) is a powerful error-correcting hardware device for the Deep Space Network (DSN), in support of the Galileo and Comet Rendezvous Asteroid Flyby (CRAF)/Cassini Missions. Recently, a prototype was completed and run successfully at 400,000 or more decoded bits per second. This prototype is a complex digital system whose core arithmetic unit consists of 256 identical very large scale integration (VLSI) gate-array chips, 16 on each of 16 identical boards which are connected through a 28-layer, printed-circuit backplane using 4416 wires. Special techniques were developed for debugging, testing, and locating faults inside individual chips, on boards, and within the entire decoder. The methods are based upon hierarchical structure in the decoder, and require that chips or boards be wired themselves as Viterbi decoders. The basic procedure consists of sending a small set of known, very noisy channel symbols through a decoder, and matching observables against values computed by a software simulation. Also, tests were devised for finding open and short-circuited wires which connect VLSI chips on the boards and through the backplane.

Onyszchuk, I. M.↗

Spectral dispersion and fringe detection in IOTA

Pupil plane beam combination, spectral dispersion, detection, and fringe tracking are discussed for the IOTA interferometer. A new spectrometer design is presented in which the angular dispersion with respect to wavenumber is nearly constant. The dispersing element is a type of grism, a series combination of grating and prism, in which the constant parts of the dispersion add, but the slopes cancel. This grism is optimized for the display of channelled spectra. The dispersed fringes can be tracked by a matched-filter photon-counting correlator algorithm. This algorithm requires very few arithmetic operations per detected photon, making it well-suited for real-time fringe tracking. The algorithm is able to adapt to different stellar spectral types, intensity levels, and atmospheric time constants. The results of numerical experiments are reported.

Traub, W. A.↗

32 bit digital optical computer - A hardware update

Such state-of-the-art devices as multielement linear laser diode arrays, multichannel acoustooptic modulators, optical relays, and avalanche photodiode arrays, are presently applied to the implementation of a 32-bit supercomputer's general-purpose optical central processing architecture. Shannon's theorem, Morozov's control operator method (in conjunction with combinatorial arithmetic), and DeMorgan's law have been used to design an architecture whose 100 MHz clock renders it fully competitive with emerging planar-semiconductor technology. Attention is given to the architecture's multichannel Bragg cells, thermal design and RF crosstalk considerations, and the first and second anamorphic relay legs.

Guilfoyle, Peter S.↗

High-speed pitch angle sorter

A high-speed method was developed to compress the two-dimensional angular distribution of space particles gathered by space plasma instrumentation into the angle distribution, where the pitch angle is polar angle with respect to the ambient magnetic field. The pitch angle sorter can handle rates of up to 2 MHz and it is designed to accommodate high angular resolution plasma analyzers that are placed on a rotating spacecraft. This compression is achieved by relying on digitally encoded lookup tables to eliminate all arithmetic operations while applying the high symmetry of this compression to reduce the amount of digital memory.

Keller, John W.↗

Fault tolerant, radiation hard, high performance digital signal processor

An architecture has been developed for a high-performance VLSI digital signal processor that is highly reliable, fault-tolerant, and radiation-hard. The signal processor, part of a spacecraft receiver designed to support uplink radio science experiments at the outer planets, organizes the connections between redundant arithmetic resources, register files, and memory through a shuffle exchange communication network. The configuration of the network and the state of the processor resources are all under microprogram control, which both maps the resources according to algorithmic needs and reconfigures the processing should a failure occur. In addition, the microprogram is reloadable through the uplink to accommodate changes in the science objectives throughout the course of the mission. The processor will be implemented with silicon compiler tools, and its design will be verified through silicon compilation simulation at all levels from the resources to full functionality. By blending reconfiguration with redundancy the processor implementation is fault-tolerant and reliable, and possesses the long expected lifetime needed for a spacecraft mission to the outer planets.

Holmann, Edgar↗

Robust Assignment Of Eigensystems For Flexible Structures

Improved method for placement of eigenvalues and eigenvectors of closed-loop control system by use of either state or output feedback. Applied to reduced-order finite-element mathematical model of NASA's MAST truss beam structure. Model represents deployer/retractor assembly, inertial properties of Space Shuttle, and rigid platforms for allocation of sensors and actuators. Algorithm formulated in real arithmetic for efficient implementation. Choice of open-loop eigenvector matrix and its closest unitary matrix believed suitable for generating well-conditioned eigensystem with small control gains. Implication of this approach is that element of iterative search for "optimal" unitary matrix appears unnecessary in practice for many test problems.

Juang, Jer-Nan↗

Relationships between topographic roughness and aeolian processes

The interaction between winds and desert surfaces has important implications for sediment transport on Earth, Mars, and Venus, and for understanding the relationships between radar backscatter and aerodynamic roughness as part of the NASA Shuttle Imaging radar (SIR-C) Mission. Here, researchers report results from measurements of boundary layer wind profiles and surface roughness at sites in Death Valley and discuss their implications. The sites included a flat to undulating gravel and sand reg, alluvial fans, and a playa. Estimates of average particle size composition of Death Valley sites and arithmetic mean values of aerodynamic roughness are given in tabular form.

Greeley, Ronald↗

An O(log sup 2 N) parallel algorithm for computing the eigenvalues of a symmetric tridiagonal matrix

An O(log sup 2 N) parallel algorithm is presented for computing the eigenvalues of a symmetric tridiagonal matrix using a parallel algorithm for computing the zeros of the characteristic polynomial. The method is based on a quadratic recurrence in which the characteristic polynomial is constructed on a binary tree from polynomials whose degree doubles at each level. Intervals that contain exactly one zero are determined by the zeros of polynomials at the previous level which ensures that different processors compute different zeros. The exact behavior of the polynomials at the interval endpoints is used to eliminate the usual problems induced by finite precision arithmetic.

Swarztrauber, Paul N.↗

A Pacific Ocean general circulation model for satellite data assimilation

A tropical Pacific Ocean General Circulation Model (OGCM) to be used in satellite data assimilation studies is described. The transfer of the OGCM from a CYBER-205 at NOAA's Geophysical Fluid Dynamics Laboratory to a CRAY-2 at NASA's Ames Research Center is documented. Two 3-year model integrations from identical initial conditions but performed on those two computers are compared. The model simulations are very similar to each other, as expected, but the simulations performed with the higher-precision CRAY-2 is smoother than that with the lower-precision CYBER-205. The CYBER-205 and CRAY-2 use 32 and 64-bit mantissa arithmetic, respectively. The major features of the oceanic circulation in the tropical Pacific, namely the North Equatorial Current, the North Equatorial Countercurrent, the South Equatorial Current, and the Equatorial Undercurrent, are realistically produced and their seasonal cycles are described. The OGCM provides a powerful tool for study of tropical oceans and for the assimilation of satellite altimetry data.

Chao, Y.↗

Recognition of 3-D symmetric objects from range images in automated assembly tasks

A new technique is presented for the three dimensional recognition of symmetric objects from range images. Beginning from the implicit representation of quadrics, a set of ten coefficients is determined for symmetric objects like spheres, cones, cylinders, ellipsoids, and parallelepipeds. Instead of using these ten coefficients trying to fit them to smooth surfaces (patches) based on the traditional way of determining curvatures, a new approach based on two dimensional geometry is used. For each symmetric object, a unique set of two dimensional curves is obtained from the various angles at which the object is intersected with a plane. Using the same ten coefficients obtained earlier and based on the discriminant method, each of these curves is classified as a parabola, circle, ellipse, or hyperbola. Each symmetric object is found to possess a unique set of these two dimensional curves whereby it can be differentiated from the others. It is shown that instead of using the three dimensional discriminant which involves evaluation of the rank of its matrix, it is sufficient to use the two dimensional discriminant which only requires three arithmetic operations.

Alvertos, Nicolas↗

Sparse distributed memory and related models

Described here is sparse distributed memory (SDM) as a neural-net associative memory. It is characterized by two weight matrices and by a large internal dimension - the number of hidden units is much larger than the number of input or output units. The first matrix, A, is fixed and possibly random, and the second matrix, C, is modifiable. The SDM is compared and contrasted to (1) computer memory, (2) correlation-matrix memory, (3) feet-forward artificial neural network, (4) cortex of the cerebellum, (5) Marr and Albus models of the cerebellum, and (6) Albus' cerebellar model arithmetic computer (CMAC). Several variations of the basic SDM design are discussed: the selected-coordinate and hyperplane designs of Jaeckel, the pseudorandom associative neural memory of Hassoun, and SDM with real-valued input variables by Prager and Fallside. SDM research conducted mainly at the Research Institute for Advanced Computer Science (RIACS) in 1986-1991 is highlighted.

Kanerva, Pentti↗

Boundary implications for frequency response of interval FIR and IIR filters

It is shown that vertex implication results in parameter space apply to interval trigonometric polynomials. Subsequently, it is shown that the frequency responses of both interval FIR and IIR filters are bounded by the frequency responses of certain extreme filters. The results apply directly in the evaluation of properties of designed filters, especially because it is more realistic to bound the filter coefficients from above and below instead of determining those with infinite precision because of finite arithmetic effects. Illustrative examples are provided to show how the extreme filters might be easily derived in any specific interval FIR or IIR filter design problem.

Bose, N. K.↗

Y-MP floating point and Cholesky factorization

The floating point arithmetics implemented in the Cray 2 and Cray Y-MP computer systems are nearly identical, but large scale computations performed on the two systems have exhibited significant differences in accuracy. The difference in accuracy is analyzed for Cholesky factorization algorithm, and it is found that the source of the difference is the subtract magnitude operation of the Cray Y-MP. The results from numerical experiments for a range of problem sizes are presented, and an efficient method for improving the accuracy of the factorization obtained on the Y-MP is presented.

Carter, Russell↗

The algebraic decoding of the (41, 21, 9) quadratic residue code

A new algebraic approach for decoding the quadratic residue (QR) codes, in particular the (41, 21, 9) QR code is presented. The key ideas behind this decoding technique are a systematic application of the Sylvester resultant method to the Newton identities associated with the code syndromes to find the error-locator polynomial, and next a method for determining error locations by solving certain quadratic, cubic and quartic equations over GF(2 exp m) in a new way which uses Zech's logarithms for the arithmetic. The algorithms developed here are suitable for implementation in a programmable microprocessor or special-purpose VLSI chip. It is expected that the algebraic methods developed here can apply generally to other codes such as the BCH and Reed-Solomon codes.

Reed, Irving S.↗

Add/Compare/Select Circuit For Rapid Decoding

Prototype decoding system operates at 200 Mb/s. ACS (add/compare/select) gate array is highly integrated emitter-coupled-logic circuit implementing arithmetic operations essential to Viterbi decoding of convolutionally encoded data signals. Principal advantage of circuit is speed. Operates as single unit performing eight additions and finds minimum of eight sums, or operates as two independent units, each performing four additions and finding minimum of four sums. Flexibility enables application to variety of different codes. Includes built-in self-testing circuitry, enabling unit to be tested at full speed with help of only simple test fixture.

Budinger, James M.↗

Implementation details of the coupled QMR algorithm

The original quasi-minimal residual method (QMR) relies on the three-term look-ahead Lanczos process, to generate basis vectors for the underlying Krylov subspaces. However, empirical observations indicate that, in finite precision arithmetic, three-term vector recurrences are less robust than mathematically equivalent coupled two-term recurrences. Therefore, we recently proposed a new implementation of the QMR method based on a coupled two-term look-ahead Lanczos procedure. In this paper, we describe implementation details of this coupled QMR algorithm, and we present results of numerical experiments.

Freund, Roland W.↗

Image coding by way of wavelets

The application of two wavelet transforms to image compression is discussed. It is noted that the Haar transform, with proper bit allocation, has performance that is visually superior to an algorithm based on a Daubechies filter and to the discrete cosine transform based Joint Photographic Experts Group (JPEG) algorithm at compression ratios exceeding 20:1. In terms of the root-mean-square error, the performance of the Haar transform method is basically comparable to that of the JPEG algorithm. The implementation of the Haar transform can be achieved in integer arithmetic, making it very suitable for applications requiring real-time performance.

Shahshahani, M.↗

Using a Cray Y-MP as an array processor for a RISC Workstation

As microprocessors increase in power, the economics of centralized computing has changed dramatically. At the beginning of the 1980's, mainframes and super computers were often considered to be cost-effective machines for scalar computing. Today, microprocessor-based RISC (reduced-instruction-set computer) systems have displaced many uses of mainframes and supercomputers. Supercomputers are still cost competitive when processing jobs that require both large memory size and high memory bandwidth. One such application is array processing. Certain numerical operations are appropriate to use in a Remote Procedure Call (RPC)-based environment. Matrix multiplication is an example of an operation that can have a sufficient number of arithmetic operations to amortize the cost of an RPC call. An experiment which demonstrates that matrix multiplication can be executed remotely on a large system to speed the execution over that experienced on a workstation is described.

Lamaster, Hugh↗