Comments on “Fast architecture for decimal digit multiplication”

2016 ◽  
Vol 47 ◽  
pp. 441-444 ◽  
Author(s):  
E. Castillo ◽  
A. Lloris ◽  
A. García ◽  
L. Parrilla ◽  
D.P. Morales
Keyword(s):  
2021 ◽  
Vol 25 (1) ◽  
pp. 20-30
Author(s):  
Srikant Kumar Beura ◽  
◽  
Rekib Uddin Ahmed ◽  
Bishnulatpam Pushpa Devi ◽  
Prabir Saha ◽  
...  

Decimal digit number computation, through bit compression methodology, offers space and time saving, which can be incurred by the Chen-Ho and Densely Packed Decimal (DPD) coding techniques. Such coding techniques have a property of bit compression, like, three decimal digits can be represented by 10 bits instead of 12 bits in binary coded decimal (BCD) format. The compression has been obtained through the elimination of the redundant 0’s from BCD representation. This manuscript reports the pros and cons of the techniques mentioned above. The logic level functionalities have been examined through MATLAB, whereas circuit simulation has been erified through Cadence Spectre. Performance parameters (such as delay, power consumption) have been evaluated through CMOS gpdk45 nm technology. Furthermore, the best design has been chosen from them, and the decimal adder design technique has been incorporated in this paper.


2016 ◽  
Author(s):  
Charles S. Zender

Abstract. Lossy compression schemes can help reduce the space required to store the false precision (i.e, scientifically meaningless data bits) that geoscientific models and measurements generate. We introduce, implement, and characterize a new lossy compression scheme suitable for IEEE floating-point data. Our new Bit Grooming algorithm alternately shaves (to zero) and sets (to one) the least significant bits of consecutive values to preserve a desired precision. This is a symmetric, two-sided variant of an algorithm sometimes called Bit Shaving which quantizes values solely by zeroing bits. Our variation eliminates the artificial low-bias produced by always zeroing bits, and makes Bit Grooming more suitable for arrays and multi-dimensional fields whose mean statistics are important. Bit Grooming relies on standard lossless compression schemes to achieve the actual reduction in storage space, so we tested Bit Grooming by applying the DEFLATE compression algorithm to bit-groomed and full-precision climate data stored in netCDF3, netCDF4, HDF4, and HDF5 formats. Bit Grooming reduces the storage space required by uncompressed and compressed climate data by up to 50 % and 20 %, respectively, for single-precision data (the most common case for climate data). When used aggressively (i.e., preserving only 1–3 decimal digits of precision), Bit Grooming produces storage reductions comparable to other quantization techniques such as linear packing. Unlike linear packing, Bit Grooming works on the full representable range of floating-point data. Bit Grooming reduces the volume of single-precision compressed data by roughly 10 % per decimal digit quantized (or "groomed") after the third such digit, up to a maximum reduction of about 50 %. The potential reduction is greater for double-precision datasets. Data quantization by Bit Grooming is irreversible (i.e., lossy) yet transparent, meaning that no extra processing is required by data users/readers. Hence Bit Grooming can easily reduce data storage volume without sacrificing scientific precision or imposing extra burdens on users.


2003 ◽  
Vol 10 (6) ◽  
pp. 599-614 ◽  
Author(s):  
V. P. Lukomsky ◽  
I. S. Gandzha

Abstract. In the framework of the canonical model of hydrodynamics, where fluid is assumed to be ideal and incompressible, waves are potential, two-dimensional, and symmetric, the authors have recently reported the existence of a new type of gravity waves on deep water besides well studied Stokes waves (Lukomsky et al., 2002b). The distinctive feature of these waves is that horizontal water velocities in the wave crests exceed the speed of the crests themselves. Such waves were found to describe irregular flows with stagnation point inside the flow domain and discontinuous streamlines near the wave crests. In the present work, a new highly efficient method for computing steady potential gravity waves on deep water is proposed to examine the character of singularity of irregular flows in more detail. The method is based on the truncated fractional approximations for the velocity potential in terms of the basis functions 1/(1 - exp(y0 - y -  ix))n, y0 being a free parameter. The non-linear transformation of the horizontal scale x = c - g sin c, 0  < g  <  1,  is additionally applied to concentrate a numerical emphasis on the crest region of a wave for accelerating the convergence of the series. For lesser computational time, the advantage in accuracy over ordinary Fourier expansions in terms of the basis functions exp(n(y + ix))  was found to be from one to ten decimal orders for steep Stokes waves and up to one decimal digit for irregular flows. The data obtained supports the following conjecture: irregular waves to all appearance represent a family of sharp-crested waves like the limiting Stokes wave but of lesser amplitude.


2007 ◽  
Vol 1 (4) ◽  
pp. 377 ◽  
Author(s):  
G. Jaberipur ◽  
A. Kaivani
Keyword(s):  

Author(s):  
Arno Berger ◽  
Theodore P. Hill

This introductory chapter provides an overview of Benford' law. Benford's law, also known as the First-digit or Significant-digit law, is the empirical gem of statistical folklore that in many naturally occurring tables of numerical data, the significant digits are not uniformly distributed as might be expected, but instead follow a particular logarithmic distribution. In its most common formulation, the special case of the first significant (i.e., first non-zero) decimal digit, Benford's law asserts that the leading digit is not equally likely to be any one of the nine possible digits 1, 2, … , 9, but is 1 more than 30 percent of the time, and is 9 less than 5 percent of the time, with the probabilities decreasing monotonically in between. The remainder of the chapter covers the history of Benford' law, empirical evidence, early explanations and mathematical framework of Benford' law.


Author(s):  
Michele Giunta ◽  
W. Hänsel ◽  
M. Lezius ◽  
M. Fischer ◽  
Thomas Udem ◽  
...  

1996 ◽  
Vol 11 (3) ◽  
pp. 253-258 ◽  
Author(s):  
Norberto Masciocchi ◽  
Gilberto Artioli

A well-crystallized sample of powdered KCl has been distributed among several laboratories in order to test the reproducibility of the lattice parameter measurement on different X-ray powder diffraction instruments. The precision of the determined unit-cell dimension is in the 10−5 Å range, while the discrepancies among the results from different laboratories using the same numerical analysis are at least one order of magnitude higher. It is shown that if different numerical analyses, including full pattern refinement, are used, values differing in the third decimal digit are obtained for the same data set.


1959 ◽  
Vol 37 (9) ◽  
pp. 983-988 ◽  
Author(s):  
J. F. Hart ◽  
Beatrice H. Worsley

The FERUT program previously described for calculating Hartree–Fock wave functions by the method of the self-consistent field has been adapted to the configuration Pb+++. Although the exchange factors were omitted, the program was extended beyond its original scope in other respects, and an assessment of the difficulties so encountered is made. It might be noted, however, that, except in the case of the 4ƒ wave function, it was possible to begin all the integrations at a common point. Initial estimates were made from the Douglas, Hartree, and Runciman results for thallium. The estimates for the core functions were not assumed to be satisfactory. The errors in the final wave functions are considered to be no more than one or two units in the second decimal digit.


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