Multiple precision computations on the IBM- 360 Interim technical report
Multiple precision subroutine source programs for IBM 360
Luke, Y. L.↗
SEARCH · Search NASA
Results for “multiple precision”
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.
Hardware /or software/ provisions for multiple precision floating-point arithmetic
Hardware-software provisions for multiple precision floating point arithmetic
Turner, L. R.↗
Binary/BCD-to-ASCII data converter
Converter inputs multiple precision binary words, converts data to multiple precision binary-coded decimal, and routes data back to computer. Converter base can be readily changed without need for new gate structure for each base changeover.
Miller, A. J.↗
A survey of the state of the art and focused research in range systems, task 2
Many communication, control, and information processing subsystems are modeled by linear systems incorporating tapped delay lines (TDL). Such optimized subsystems result in full precision multiplications in the TDL. In order to reduce complexity and cost in a microprocessor implementation, these multiplications can be replaced by single-shift instructions which are equivalent to powers of two multiplications. Since, in general, the obvious operation of rounding the infinite precision TDL coefficients to the nearest powers of two usually yield quite poor system performance, the optimum powers of two coefficient solution was considered. Detailed explanations on the use of branch-and-bound algorithms for finding the optimum powers of two solutions are given. Specific demonstration of this methodology to the design of a linear data equalizer and its implementation in assembly language on a 8080 microprocessor with a 12 bit A/D converter are reported. This simple microprocessor implementation with optimized TDL coefficients achieves a system performance comparable to the optimum linear equalization with full precision multiplications for an input data rate of 300 baud. The philosophy demonstrated in this implementation is dully applicable to many other microprocessor controlled information processing systems.
Yao, K.↗
A methodology based on reduced complexity algorithm for system applications using microprocessors
The paper considers a methodology on the analysis and design of a minimum mean-square error criterion linear system incorporating a tapped delay line (TDL) where all the full-precision multiplications in the TDL are constrained to be powers of two. A linear equalizer based on the dispersive and additive noise channel is presented. This microprocessor implementation with optimized power of two TDL coefficients achieves a system performance comparable to the optimum linear equalization with full-precision multiplications for an input data rate of 300 baud.
Yan, T. Y.↗
Unidentified galactic X-ray sources positioned with the HEAO-1 scanning modulation collimator
Observations made with the HEAO-1 scanning modulation collimator are used to determine the positions of 16 unidentified X-ray sources at low galactic latitudes. Positions were obtained to within 10-30 arcsec in one dimension from two four-grid collimator observations made at six-month intervals. Positions determined in addition for eight sources identified with optical objects verify the method employed. Of the unidentified sources, the positional uncertainties of ten are reduced by factors of two to eight, the precise X-ray positions (within 10 arcsec) obtained by lunar occultation experiments are confirmed for three and multiple precise positions (within 20 arcsec) which reduce the previous location uncertainties by factors of greater than 100 are obtained for the remaining three.
Reid, C. A.↗
Radio frequency performance predictions for the hoop/column point design
Preliminary antenna pattern tests were conducted to determine if catastrophic effects were produced by cables (conducting) in the aperture. This test consisted of an apex feed illuminating a 3 meter solid reflector. A hoop/column configuration was used in positioning the various wires and cables. Radiation patterns were measured at 7 GHz and 10 GHz. No catastrophic effects were observed for this configuration, but additional tests are required to determine the effects for more precision multiple beam applications. In order to better understand the scattering and blockage effects on multiple beam performance, a 35 GHz model was used to model somewhat a single quad aperture configuration. Experimental results using this models are presented in graphs.
Campbell, T. G.↗
A floating-point/multiple-precision processor for airborne applications
A compact input output (I/O) numerical processor capable of performing floating-point, multiple precision and other arithmetic functions at execution times which are at least 100 times faster than comparable software emulation is described. The I/O device is a microcomputer system containing a 16 bit microprocessor, a numerical coprocessor with eight 80 bit registers running at a 5 MHz clock rate, 18K random access memory (RAM) and 16K electrically programmable read only memory (EPROM). The processor acts as an intelligent slave to the host computer and can be programmed in high order languages such as FORTRAN and PL/M-86.
Yee, R.↗
Astrogam - A magnetic rigidity spectrometer for gamma-ray astronomy
A novel concept is presented for a high-energy gamma-ray telescope with an extended energy range and excellent energy and angular resolution. The characteristics of Astrogam, a wide-field camera which makes an all-sky survey, are enumerated. Consideration is given to the instrument's unique features: wide energy range (four orders of magnitude and energy, which will bridge the gap between satellite and ground-based observations); excellent source location precision (multiple scattering error dominating nuclear recoil and measurement error below 20 GeV); and excellent energy resolution (1-percent energy resolution). Astrogam will make observations in the GTE energy range possible and could resolve complex source regions like the Crab pulsar/Nebular system, the Galactic center, and the Geminga region as well as discover the true nature of the sources.
Adams, James H., Jr.↗
On the Rapid Computation of Various Polylogarithmic Constants
We give algorithms for the computation of the d-th digit of certain transcendental numbers in various bases. These algorithms can be easily implemented (multiple precision arithmetic is not needed), require virtually no memory, and feature run times that scale nearly linearly with the order of the digit desired. They make it feasible to compute, for example, the billionth binary digit of log(2) or pi on a modest workstation in a few hours run time. We demonstrate this technique by computing the ten billionth hexadecimal digit of pi, the billionth hexadecimal digits of pi-squared, log(2) and log-squared(2), and the ten billionth decimal digit of log(9/10). These calculations rest on the observation that very special types of identities exist for certain numbers like pi, pi-squared, log(2) and log-squared(2). These are essentially polylogarithmic ladders in an integer base. A number of these identities that we derive in this work appear to be new, for example a critical identity for pi.
Bailey, David H.↗
Finding New Math Identities by Computer
Recently a number of interesting new mathematical identities have been discovered by means of numerical searches on high performance computers, using some newly discovered algorithms. These include the following: pi = ((sup oo)(sub k=0))(Sigma) (1 / 16) (sup k) ((4 / 8k+1) - (2 / 8k+4) - (1 / 8k+5) - (1 / 8k+6)) and ((17 pi(exp 4)) / 360) = ((sup oo)(sub k=1))(Sigma) (1 + (1/2) + (1/3) + ... + (1/k))(exp 2) k(exp -2), zeta(3, 1, 3, 1, ..., 3, 1) = (2 pi(exp 4m) / (4m+2)! where m = number of (3,1) pairs. and where zeta(n1,n2,...,nr) = (sub k1 (is greater than) k2 (is greater than) ... (is greater than) kr)(Sigma) (1 / (k1 (sup n1) k2 (sup n2) ... kr (sup nr). The first identity is remarkable in that it permits one to compute the n-th binary or hexadecimal digit of pu directly, without computing any of the previous digits, and without using multiple precision arithmetic. Recently the ten billionth hexadecimal digit of pi was computed using this formula. The third identity has connections to quantum field theory. (The first and second of these been formally established; the third is affirmed by numerical evidence only.) The background and results of this work will be described, including an overview of the algorithms and computer techniques used in these studies.
Bailey, David H.↗
Progress on a Multichannel, Dual-Mixer Stability Analyzer
Several documents describe aspects of the continuing development of a multichannel, dual-mixer system for simultaneous characterization of the instabilities of multiple precise, low-noise oscillators. One of the oscillators would be deemed to be a reference oscillator, its frequency would be offset by an amount (100 Hz) much greater than the desired data rate, and each of the other oscillators would be compared with the frequency-offset signal by operation of a combination of hardware and software. A high-rate time-tag counter would collect zero-crossing times of the approximately equal 100-Hz beat notes. The system would effect a combination of interpolation and averaging to process the time tags into low-rate phase residuals at the desired grid times. Circuitry that has been developed since the cited prior article includes an eight-channel timer board to replace an obsolete commercial time-tag counter, plus a custom offset generator, cleanup loop, distribution amplifier, zero-crossing detector, and frequency divider.
Kirk, Albert↗
Precision targeting for multiple swingby interplanetary trajectories
Reference trajectory determination for multiple swingby interplanetary trajectories
Bayliss, S. S.↗
Relationship of paper speed to precision of pulse wave measurements - A multiple observer study of left ventricular ejection time.
Recording instrument paper speed effect on pulse wave measurements precision, discussing multiple observer studies of left ventricular ejection time
Flessas, A. P.↗
A modular multiple use system for precise time and frequency measurement and distribution
A modular CAMAC based system is described which was developed to meet a variety of precise time and frequency measurement and distribution needs. The system was based on a generalization of the dual mixer concept. By using a 16 channel 100 ns event clock, the system can intercompare the phase of 16 frequency standards with subpicosecond resolution. The system has a noise floor of 26 fs and a long term stability on the order of 1 ps or better. The system also used a digitally controlled crystal oscillator in a control loop to provide an offsettable 5 MHz output with subpicosecond phase tracking capability. A detailed description of the system is given including theory of operation and performance. A method to improve the performance of the dual mixer technique is discussed when phase balancing of the two input ports cannot be accomplished.
Reinhardt, V. S.↗
Isotopic Investigations of Nebular and Parent Body Processes with a High Sensitivity Ion Microprobe
NASA supported the development of the CAMECA ims 1270 ion microprobe at UCLA for applications in cosmochemistry. The primary investigations centered on measuring the microscopic distributions of key isotopic abundances in primitive meteoritic materials as a means of constraining the nature of important thermal and chemical processes in the solar nebula and the timescales associated with those processes. Our prior work on oxygen isotope anomalies in a wide variety of meteoritic materials had led us to a view of a spatially heterogeneous nebula, and in particular, a restricted region for CAI formation that is characterized by O-16-rich gas. Because of its production of CAIs in the energetic local environment near the protosun, the existence of a natural transport mechanism via bipolar outflows, and a general astrophysical plausibility, we were attracted to the fluctuating X-wind model which had been put forward by Frank Shu, Typhoon Lee, and colleagues. With our collaborators, we undertook a series of investigations to test the viability of this hypothesis; this work led directly to the discovery of live Be in CAIs and a clear demonstration of the existence of 160-rich condensates, which necessarily implies an O-16-rich gaseous reservoir in the nebula. Both of these observations fit well within the context of X-wind type models, i.e. formation of CAIs (or condensation of their precursors) in the reconnection ring sunward of the inner edge of the accretion disk, however much work remains to be done to test whether the physical parameters of the model can quantitatively predict not only the thermal histories of CAIs but also their radioactivity. The issue of spatial heterogeneity in the nebula, central to the X-wind model, is also at the heart of any chronology based on short-lived radioisotopes. In this work, we followed up on strong hints for presence of exireme:j: (53 day) short-lived Be-7, and have prepared a manuscript (in revision). We also measured A1-Mg systematics by a combined approach of high-precision multiple-collector SIMS analyses, traditional analyses on the UCLA ims 1270, and high-spatial resolution analyses using a NanoSIMS instrument. The data help to deconvolve effects due to partial resetting of the A1-Mg system by multiple thermal events. Finally, we initiated investigations related to nebular heterogeneity with a new initiative of in situ high-precision sulfur isotope analyses of sulfides from a wide variety of components of chondrites. The ultimate goal of all this work is to help develop a better understanding of the relationships between CAIs and chondrules, the astrophysical environments in which they formed, and the timescales of nebular processes. As detailed in Table 1, for the project period, 14 manuscripts were published and 17 abstracts were presented describing the work.
McKeegan, Kevin D.↗
Optical Measurement System for Strain Field Ahead of a Crack Tip for Lattice Structures
The aim of the ARAMADAS project is to automate the construction of cuboctahedral lattice structures. Lattice materials are appealing for aerospace applications due to their strength and stiffness at ultra-light densities. However, in order for any material to be realistically considered for such environments, it must also be damage tolerant. The ability of a material to absorb damage is characterized by its fracture toughness, which remains poorly characterized for lattice materials. Consequently, the objective of this research is to develop an optical measurement system to experimentally validate the strain field ahead of a crack tip in architecture lattice materials. Although the ability to predict the strain field ahead of a crack tip has been investigated for continuum materials, such behaviour of three-dimensional architectures is under-investigated. As such, we will use a custom optical measurement system to track deformation of the voxels in a side-cracked plate fracture specimen. The system shall use 3D pose estimation, stereo imaging, and possibly color tracking, in combination with optical flow algorithms, to compute information regarding the three-dimensional movement movement of the lattice nodes during mechanical testing. Bench top experiments will validate the optical measurement system and characterize precision. Additionally, the effect of multiple cameras on precision, as well as system scalability will be investigated. Final results will compare measured lattice deformation with finite element predictions.
Lennig, Miriam↗
Detectability of extrasolar planetary transits
Precise stellar photometry can be used to detect other planetary systems. However, the intrinsic variability of stellar luminosity imposes a fundamental limit on the sensitivity of this method. Based on recent precise solar observations made from the Solar Maximum Mission satellite, it appears that the detection of earth-sized planets will be marginal during periods of high stellar activity. However, with a suitable photometer larger planets should be readily detectable even in the presence of stellar activity equal to that of the sun at the peak of its sunspot cycle. The high precision, multiple-star photometric system required to detect planets in other stellar systems could be used to monitor flares, starspots, and global oscillations.
Borucki, W. J.↗