scholarly journals A Mechanically Checked Proof of IEEE Compliance of the Floating Point Multiplication, Division and Square Root Algorithms of the AMD-K7™ Processor

1998 ◽  
Vol 1 ◽  
pp. 148-200 ◽  
Author(s):  
David M. Russinoff
Keyword(s):  
Register Transfer Level ◽  
The Other ◽  
Floating Point ◽  
Square Root ◽  
Rigorous Proof ◽  
Point Multiplication ◽  
Logical Operations ◽  
Other Hand ◽  
Ieee Standard ◽  
Proof Of Correctness

AbstractWe describe a mechanically verified proof of correctness of the floating point multiplication, division, and square root instructions of the AMD-K7 microprocessor. The instructions are implemented in hardware and represented here by register-transfer level specifications, the primitives of which are logical operations on bit vectors. On the other hand, the statements of correctness, derived from IEEE Standard 754, are arithmetic in nature and considerably more abstract. Therefore, we begin by developing a theory of bit vectors and their role in floating point representations and rounding. We then present the hardware model and a rigorous proof of its correctness. All of our definitions, lemmas and theorems have been formally encoded in the ACL2 logic, and every step in the proof has been mechanically checked with the ACL2 prover.

scholarly journals FPGA-Based Synthesis of High-Speed Hybrid Carry Select Adders

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
V. Kokilavani ◽  
K. Preethi ◽  
P. Balasubramanian
Keyword(s):  
High Speed ◽  
Boolean Logic ◽  
The Other ◽  
Square Root ◽  
Verilog Hdl ◽  
Other Hand ◽  
Carry Select Adder

Carry select adder is a square-root time high-speed adder. In this paper, FPGA-based synthesis of conventional and hybrid carry select adders are described with a focus on high speed. Conventionally, carry select adders are realized using the following: (i) full adders and 2 : 1 multiplexers, (ii) full adders, binary to excess 1 code converters, and 2 : 1 multiplexers, and (iii) sharing of common Boolean logic. On the other hand, hybrid carry select adders involve a combination of carry select and carry lookahead adders with/without the use of binary to excess 1 code converters. In this work, two new hybrid carry select adders are proposed involving the carry select and section-carry based carry lookahead subadders with/without binary to excess 1 converters. Seven different carry select adders were implemented in Verilog HDL and their performances were analyzed under two scenarios, dual-operand addition and multioperand addition, where individual operands are of sizes 32 and 64-bits. In the case of dual-operand additions, the hybrid carry select adder comprising the proposed carry select and section-carry based carry lookahead configurations is the fastest. With respect to multioperand additions, the hybrid carry select adder containing the carry select and conventional carry lookahead or section-carry based carry lookahead structures produce similar optimized performance.

scholarly journals An invariant of finitary codes with finite expected square root coding length

2010 ◽  
Vol 31 (1) ◽  
pp. 77-90 ◽  
Author(s):  
NATE HARVEY ◽  
YUVAL PERES
Keyword(s):  
Markov Chains ◽  
Marginal Distribution ◽  
Bernoulli Shift ◽  
The Other ◽  
Square Root ◽  
Other Hand ◽  
Lower Moment

AbstractLet p and q be probability vectors with the same entropy h. Denote by B(p) the Bernoulli shift indexed by ℤ with marginal distribution p. Suppose that φ is a measure-preserving homomorphism from B(p) to B(q). We prove that if the coding length of φ has a finite 1/2 moment, then σ2p=σ2q, where σ2p=∑ ipi(−log  pi−h)2 is the informational variance of p. In this result, the 1/2 moment cannot be replaced by a lower moment. On the other hand, for any θ<1, we exhibit probability vectors p and q that are not permutations of each other, such that there exists a finitary isomorphism Φ from B(p) to B(q) where the coding lengths of Φ and of its inverse have a finite θ moment. We also present an extension to ergodic Markov chains.

scholarly journals NOVEL DIGITAL LOCK SYSTEM

2012 ◽  
pp. 102-105
Author(s):  
N. BHUVANESH ◽  
M. GAUTHAMAN
Keyword(s):  
Embedded System ◽  
Low Cost ◽  
Dc Motor ◽  
The Other ◽  
Logical Operations ◽  
Other Hand ◽  
Recent Increase ◽  
The Common ◽  
Common Man ◽  
Stated Problem

In this paper we have proposed a new digital lock model which is primarily designed for low cost intermediate security purpose. Even though there are digital locks available this one is designed keeping the common man in mind. It will be the first digital locking system that would be available at a price less than 700 rupees. The recent increase in burglary levels proves the fact that the lever locking system is no more reliable and effective, but on the other hand the present digital locks are around 3000 rupees making it over priced. So this clearly shows the need for an intermediate effective digital locking system. Our novel digital locking system is aimed exactly to solve the above stated problem. Our model is an outcome of embedded system and can works using an 8051 microcontroller interfaced with a 16*2 lcd to perform logical operations. The input is given by the user using 3*3 matrixes key padded system. The locking system consist of a power lock which is widely used in automobiles, it primarily consist of an dc motor which on rotating moves the lever back and forth depending on the direction of rotation. The interrupt pins are used to clear the buzzer which is connected to port 3 pins which thereby notifies the user immediately in case of theft or burglary.

scholarly journals TOWARDS A MATHEMATICAL LIBRARY FOR UNUMs, AN ALTERNATIVE TO IEEE 754 FLOATING POINT NUMBERS

2017 ◽  
Author(s):  
Thomas Risse
Keyword(s):  
Analytic Functions ◽  
Numerical Results ◽  
The Other ◽  
Floating Point ◽  
Other Hand ◽  
Is Development ◽  
The One ◽  
Floating Point Numbers

The 1985 IEEE 754 standard for the representation of and the arithmetic with floating point numbers has been reconsidered. On the one hand today, its technological assumptions are by no means longer valid. On the other hand, the irritating numerical phenomena which have been collected cast a doubt as to whether this much uncertainty in numerical results is fate. Fortunately, around 2015, Gustafson proposed UNUMs, a modification of the IEEE 754 standard with the potential to heal the said shortcomings. Till now, there are some attempts to implement his ideas, both in software and in hardware. With these activities well under way, the other necessity is development of a mathematical library for UNUMs when one wants UNUMs to become the new floating point standard. This paper presented the ideas leading to UNUMs, gave some hints on floating point units for UNUMs and illustrated the difficulties in developing the said mathematical library by the example of approximating zeroes of analytic functions.  

Transport of fluorescein in trichomes of Lycopersicon esculentum

1982 ◽  
Vol 60 (4) ◽  
pp. 397-402 ◽  
Author(s):  
Gregor F. Barclay ◽  
Carol A. Peterson ◽  
Melvin T. Tyree
Keyword(s):  
Lycopersicon Esculentum ◽  
Cytoplasmic Streaming ◽  
Cytochalasin B ◽  
The Other ◽  
Square Root ◽  
Inhibiting Effect ◽  
Rate Limiting Step ◽  
Limiting Step ◽  
Other Hand ◽  
Rate Limiting

Translocation of the dye disodium fluorescein (uranin) in trichomes of Lycopersicon esculentum (tomato) was nonpolar and proportional to the square root of time. Inhibition of cytoplasmic streaming by cytochalasin B had no effect on the rate of dye movement. On the other hand, disruption of plasmodesmatal connections between adjacent cells by plasmolysis strongly diminished the rate of fluorescein translocation. Subsequent deplasmolysis of the cells did not remove the inhibiting effect of plasmolysis. The data are consistent with the interpretation that dye movement proceeds by diffusion, the rate-limiting step being transport through plasmodesmatal connections.

A study of cometary eruptions through OH radio-lines

1999 ◽  
Vol 173 ◽  
pp. 249-254
Author(s):  
A.M. Silva ◽  
R.D. Miró
Keyword(s):  
Short Duration ◽  
Growth Curves ◽  
The Other ◽  
Initial Mass ◽  
Radio Lines ◽  
Other Hand ◽  
Sudden Rise

AbstractWe have developed a model for theH2OandOHevolution in a comet outburst, assuming that together with the gas, a distribution of icy grains is ejected. With an initial mass of icy grains of 108kg released, theH2OandOHproductions are increased up to a factor two, and the growth curves change drastically in the first two days. The model is applied to eruptions detected in theOHradio monitorings and fits well with the slow variations in the flux. On the other hand, several events of short duration appear, consisting of a sudden rise ofOHflux, followed by a sudden decay on the second day. These apparent short bursts are frequently found as precursors of a more durable eruption. We suggest that both of them are part of a unique eruption, and that the sudden decay is due to collisions that de-excite theOHmaser, when it reaches the Cometopause region located at 1.35 × 105kmfrom the nucleus.

Closing the GAP—A 5Å Scanning Microscope

1969 ◽  
Vol 27 ◽  
pp. 6-7
Author(s):  
A. V. Crewe
Keyword(s):  
Normal Form ◽  
The Other ◽  
Resolving Power ◽  
Scanning Microscope ◽  
Conventional Microscope ◽  
Other Hand ◽  
Closing The Gap ◽  
Thermal Sources ◽  
Better Than ◽  
Transmission Microscope

We have become accustomed to differentiating between the scanning microscope and the conventional transmission microscope according to the resolving power which the two instruments offer. The conventional microscope is capable of a point resolution of a few angstroms and line resolutions of periodic objects of about 1Å. On the other hand, the scanning microscope, in its normal form, is not ordinarily capable of a point resolution better than 100Å. Upon examining reasons for the 100Å limitation, it becomes clear that this is based more on tradition than reason, and in particular, it is a condition imposed upon the microscope by adherence to thermal sources of electrons.

Life Beyond 1MeV

1980 ◽  
Vol 38 ◽  
pp. 30-33
Author(s):  
K.H. Westmacott
Keyword(s):  
Electron Microscopy ◽  
Past Experience ◽  
The Other ◽  
Good Case ◽  
Other Hand ◽  
The U.S

Life beyond 1MeV – like life after 40 – is not too different unless one takes advantage of past experience and is receptive to new opportunities. At first glance, the returns on performing electron microscopy at voltages greater than 1MeV diminish rather rapidly as the curves which describe the well-known advantages of HVEM often tend towards saturation. However, in a country with a significant HVEM capability, a good case can be made for investing in instruments with a range of maximum accelerating voltages. In this regard, the 1.5MeV KRATOS HVEM being installed in Berkeley will complement the other 650KeV, 1MeV, and 1.2MeV instruments currently operating in the U.S. One other consideration suggests that 1.5MeV is an optimum voltage machine – Its additional advantages may be purchased for not much more than a 1MeV instrument. On the other hand, the 3MeV HVEM's which seem to be operated at 2MeV maximum, are much more expensive.

Can the Academic Self-Concept be Positive and Realistic?

2005 ◽  
Vol 19 (3) ◽  
pp. 129-132 ◽  
Author(s):  
Reimer Kornmann
Keyword(s):  
Academic Performance ◽  
Opposite Effect ◽  
Self Esteem ◽  
Point Of View ◽  
The Other ◽  
Self Concept ◽  
High Ability ◽  
Self Image ◽  
Other Hand

Summary: My comment is basically restricted to the situation in which less-able students find themselves and refers only to literature in German. From this point of view I am basically able to confirm Marsh's results. It must, however, be said that with less-able pupils the opposite effect can be found: Levels of self-esteem in these pupils are raised, at least temporarily, by separate instruction, academic performance however drops; combined instruction, on the other hand, leads to improved academic performance, while levels of self-esteem drop. Apparently, the positive self-image of less-able pupils who receive separate instruction does not bring about the potential enhancement of academic performance one might expect from high-ability pupils receiving separate instruction. To resolve the dilemma, it is proposed that individual progress in learning be accentuated, and that comparisons with others be dispensed with. This fosters a self-image that can in equal measure be realistic and optimistic.

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