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At least 109 records · Page 6

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NASA NTRS1972

Extended precision software packages

A description of three extended precision packages is presented along with three small conversion subroutines which can be used in conjunction with the extended precision packages. These extended packages represent software packages written in FORTRAN 4. They contain normalized or unnormalized floating point arithmetic with symmetric rounding and arbitrary mantissa lengths, and normalized floating point interval arithmetic with appropriate rounding. The purpose of an extended precision package is to enable the user to use and manipulate numbers with large decimal places as well as those with small decimal places where precision beyond double precision is required.

Phillips, E. J.↗

NASA NTRS1973

Low-cost coding techniques for digital fault diagnosis

Published report discusses fault location properties of arithmetic codes. Criterion for effectiveness of given code is detection probability of local fault by application of checking algorithm to results of entire set of algorithms of processor. Report also presents analysis of arithmetic codes with low-cost check algorithm which possesses partial fault-location properties.

Avizienis, A. A.↗

NASA NTRS1973

Some observed seasonal changes in extratropical general circulation: A study in terms of vorticity

Extratropical eddy distributions in four months typical of the four seasons are treated in terms of temporal mean and temporal r.m.s. values of the geostrophic relative vorticity. The geographical distributions of these parameters at the 300 mb level show that the arithmetic mean fields are highly biased representatives of the extratropical eddy distributions. The zonal arithmetic means of these parameters are also presented. These show that the zonal-and-time mean relative vorticity is but a small fraction of the zonal mean of the temporal r.m.s. relative vorticity, K. The reasons for considering the r.m.s. values as the temporal normal values of vorticity in the extratropics are given in considerable detail. The parameter K is shown to be of considerable importance in locating the extratropical frontal jet streams (EFJ) in time-and-zonal average distributions. The study leads to an understanding of the seasonal migrations of the EFJ which have not been explored until now.

Srivatsangam, S.↗

NASA NTRS1976

Architecture and data processing alternatives for the TSE computer. Volume 2: Extraction of topological information from an image by the Tse computer

A simple programmable Tse processor organization and arithmetic operations necessary for extraction of the desired topological information are described. Hardware additions to this organization are discussed along with trade-offs peculiar to the tse computing concept. An improved organization is presented along with the complementary software for the various arithmetic operations. The performance of the two organizations is compared in terms of speed, power, and cost. Software routines developed to extract the desired information from an image are included.

Jones, J. R.↗

NASA NTRS1976

Applications of satellite technology for regional organizations (Project ASTRO)

The direct arithmetic processing of adaptive delta modulation (ADM) encoded signals, conversion from ADM encoded signals to pulse code modulation (PCM) encoded signals, and conversion from PCM to ADM encoded signals are discussed. It is shown that signals which are ADM encoded can be arithmetically processed directly, without first decoding. Operating on the DM bit stream, and employing only standard digital hardware, the sum, difference and product can be obtained in PCM and ADM format.

Schilling, D. L.↗

NASA NTRS1978

Suggested architecture for a specialized fluid dynamics computer

Future flow simulations in 3-D will require computers with extremely large main memories and an advantageous ratio between computer cost and arithmetic speed. Since random access memories are very expensive, a pipeline design is proposed which allows the use of much cheaper sequential devices without any sacrifice in speed for vector references (even with arbitrary spacing between successive elements). Also scalar arithmetic can be performed efficiently. The comparatively low speed of the proposed machine (about 10 to the 7th power operations per second) would be offset by a very low price per unit, making mass production possible.

Fornberg, B.↗

NASA NTRS1978

Preliminary study of the use of the STAR-100 computer for transonic flow calculations

A description is presented for a new explicit algorithm for solving the transonic small-disturbance potential equation on the STAR-100 computer. The STAR computer has a 'pipeline' type of processor which is very efficient in doing arithmetic operations on long vectors. Unfortunately, the successive line over-relaxation method, which represents the best method for solving the considered equation, is not suitable for vector-arithmetic procedures. The described algorithm, however, can be vectorized to make an employment of the STAR-100 possible. It is found that a use of the new algorithm for solving the equation on the STAR-100 computer can almost halve the computer time required for this type of computation when compared to successive line over-relaxation on the CYBER 175 computer.

Keller, J. D.↗

NASA NTRS1978

Incomplete nested dissection for solving n by n grid problems

Nested dissection orderings are known to be very effective for solving sparse positive definite linear systems which arise from n by n grid problems. In this paper we consider incomplete nested dissection, an ordering which corresponds to the premature termination of nested dissection. Analyses of the arithmetic and storage requirements for incomplete nested dissection are given and the ordering is shown to be competitive with nested dissection with regard to arithmetic operations and superior to that ordering in storage requirements.

George, A.↗

NASA NTRS1984

Optical residue addition and storage units using a Hughes liquid crystal light valve

Optical addition and storage units are described in this paper. These units are implemented using the Hughes Liquid Crystal Light Valve (LCLV) as a spatial light modulator using residue arithmetic for a numerical representation. The main hardware components of the design, besides the light valve, include an array of single-mode optical fibers that provide input information, a polarizing prism in combination with quarter-wave and half-wave retarders for residue arithmetic implementation in the adder, and a holographic array for spatial stability in the storage unit.

Habiby, S. F.↗

NASA NTRS1986

Multiplier Architecture for Coding Circuits

Multipliers based on new algorithm for Galois-field (GF) arithmetic regular and expandable. Pipeline structures used for computing both multiplications and inverses. Designs suitable for implementation in very-large-scale integrated (VLSI) circuits. This general type of inverter and multiplier architecture especially useful in performing finite-field arithmetic of Reed-Solomon error-correcting codes and of some cryptographic algorithms.

Wang, C. C.↗

NASA NTRS1984

Formal verification of mathematical software

Methods are investigated for formally specifying and verifying the correctness of mathematical software (software which uses floating point numbers and arithmetic). Previous work in the field was reviewed. A new model of floating point arithmetic called the asymptotic paradigm was developed and formalized. Two different conceptual approaches to program verification, the classical Verification Condition approach and the more recently developed Programming Logic approach, were adapted to use the asymptotic paradigm. These approaches were then used to verify several programs; the programs chosen were simplified versions of actual mathematical software.

Sutherland, D.↗

NASA NTRS1985

Geologic analysis of averaged magnetic satellite anomalies

To investigate relative advantages and limitations for quantitative geologic analysis of magnetic satellite scalar anomalies derived from arithmetic averaging of orbital profiles within equal-angle or equal-area parallelograms, the anomaly averaging process was simulated by orbital profiles computed from spherical-earth crustal magnetic anomaly modeling experiments using Gauss-Legendre quadrature integration. The results indicate that averaging can provide reasonable values at satellite elevations, where contributing error factors within a given parallelogram include the elevation distribution of the data, and orbital noise and geomagnetic field attributes. Various inversion schemes including the use of equivalent point dipoles are also investigated as an alternative to arithmetic averaging. Although inversion can provide improved spherical grid anomaly estimates, these procedures are problematic in practice where computer scaling difficulties frequently arise due to a combination of factors including large source-to-observation distances ( 400 km), high geographic latitudes, and low geomagnetic field inclinations.

Goyal, H. K.↗

NASA NTRS1985

Hardware math for the 6502 microprocessor

A floating-point arithmetic unit is described which is being used in the Ground Facility of Large Space Structures Control Verification (GF/LSSCV). The experiment uses two complete inertial measurement units and a set of three gimbal torquers in a closed loop to control the structural vibrations in a flexible test article (beam). A 6502 (8-bit) microprocessor controls four AMD 9511A floating-point arithmetic units to do all the computation in 20 milliseconds.

Kissel, R.↗

NASA NTRS1988

Comparison of UNL laser imaging and sizing system and a phase/Doppler system for analyzing sprays from a NASA nozzle

Aerosol spray characterization was done using a P/DPA and a laser imaging/video processing system on a NASA MOD-1 air-assist nozzle being evaluated for use in aircraft icing research. Benchmark tests were performed on monodispersed particles and on the NASA MOD-1 nozzle under identical laboratory operating conditions. The laser imaging/video processing system and the P/DPA showed agreement on calibration tests in monodispersed aerosol sprays of + or - 2.6 microns with a standard deviation of + or - 2.6 microns. Tests were performed on the NASA MOD-1 nozzle on the centerline and radially at one-half inch increments to the outer edge of the spray plume at a distance two feet (0.61 m) downstream from the exit of the nozzle. Comparative results at two operating conditions of the nozzle are presented for the two instruments. For the first case, the deviation in arithmetic mean diameters determined by the two instruments was in a range of 0.1 to 2.8 microns, and the deviation in Sauter mean diameters varied from 0 to 2.2 microns. Operating conditions in the second case were more severe which resulted in the arithmetic mean diameter deviating from 1.4 to 7.1 microns and the deviation in the Sauter mean diameters ranging from 0.4 to 6.7 microns.

Alexander, Dennis R.↗

NASA NTRS1988

Real time pipelined system for forming the sum of products in the processing of video data

A 3-by-3 convolver utilizes 9 binary arithmetic units connected in cascade for multiplying 12-bit binary pixel values P sub i which are positive or two's complement binary numbers by 5-bit magnitide (plus sign) weights W sub i which may be positive or negative. The weights are stored in registers including the sign bits. For a negative weight, the one's complement of the pixel value to be multiplied is formed at each unit by a bank of 17 exclusive or gates G sub i under control of the sign of the corresponding weight W sub i, and a correction is made by adding the sum of the absolute values of all the negative weights for each 3-by-3 kernel. Since this correction value remains constant as long as the weights are constant, it can be precomputed and stored in a register as a value to be added to the product PW of the first arithmetic unit.

Wilcox, Brian↗

NASA NTRS1988

A sparse matrix algorithm on the Boolean vector machine

VLSI technology is being used to implement a prototype Boolean Vector Machine (BVM), which is a large network of very small processors with equally small memories that operate in SIMD mode; these use bit-serial arithmetic, and communicate via cube-connected cycles network. The BVM's bit-serial arithmetic and the small memories of individual processors are noted to compromise the system's effectiveness in large numerical problem applications. Attention is presently given to the implementation of a basic matrix-vector iteration algorithm for space matrices of the BVM, in order to generate over 1 billion useful floating-point operations/sec for this iteration algorithm. The algorithm is expressed in a novel language designated 'BVM'.

Wagner, Robert A.↗

NASA NTRS1986

Paranoia.Ada: Sample output reports

Paranoia.Ada is a program to diagnose floating point arithmetic in the context of the Ada programming language. The program evaluates the quality of a floating point arithmetic implementation with respect to the proposed IEEE Standards P754 and P854. Paranoia.Ada is derived from the original BASIC programming language version of Paranoia. The Paranoia.Ada replicates in Ada the test algorithms originally implemented in BASIC and adheres to the evaluation criteria established by W. M. Kahan. Paranoia.Ada incorporates a major structural redesign and employs applicable Ada architectural and stylistic features.

Source record↗

NASA NTRS1988

Parallel algorithms for interactive manipulation of digital terrain models

Interactive three-dimensional graphics applications, such as terrain data representation and manipulation, require extensive arithmetic processing. Massively parallel machines are attractive for this application since they offer high computational rates, and grid connected architectures provide a natural mapping for grid based terrain models. Presented here are algorithms for data movement on the massive parallel processor (MPP) in support of pan and zoom functions over large data grids. It is an extension of earlier work that demonstrated real-time performance of graphics functions on grids that were equal in size to the physical dimensions of the MPP. When the dimensions of a data grid exceed the processing array size, data is packed in the array memory. Windows of the total data grid are interactively selected for processing. Movement of packed data is needed to distribute items across the array for efficient parallel processing. Execution time for data movement was found to exceed that for arithmetic aspects of graphics functions. Performance figures are given for routines written in MPP Pascal.

Davis, E. W.↗