Topic
Division (mathematics)
About: Division (mathematics) is a research topic. Over the lifetime, 12717 publications have been published within this topic receiving 87814 citations.
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TL;DR: It is shown that applying operand decomposition to the inputs as a preprocessing step to Mitchell's multiplication algorithm significantly improves the accuracy, and that the OD method yields further improvement when combined with the other correction methods proposed in the literature.
Abstract: Logarithmic number systems (LNS) offer a viable alternative in terms of area, delay, and power to binary number systems for implementing multiplication and division operations for applications in signal processing. The Mitchell algorithm (MA), proposed, reduces the complexity of finding the logarithms and the antilogarithms using piecewise straight line approximations of the logarithm and the antilogarithm curves. The approximations, however, result in some loss of accuracy. Thus, several methods have been proposed in the literature for improving the accuracy of Mitchell's algorithm. In this work, we investigate a new method based on operand decomposition (OD) to improve the accuracy of Mitchell's algorithm when applied to logarithmic multiplication. In the OD technique proposed, for reducing the amount of switching activity in binary multiplication, the two inputs to be multiplied are together decomposed into four binary operands and the product is expressed as the sum of the products of the decomposed numbers. We show that applying operand decomposition to the inputs as a preprocessing step to Mitchell's multiplication algorithm significantly improves the accuracy. Experimental results indicate that the proposed algorithm for logarithmic multiplication reduces the error percentage of Mitchell's algorithm by 44.7 percent on the average. It is also shown that the OD method yields further improvement when combined with the other correction methods proposed in the literature
73 citations
TL;DR: These algorithms avoid the need to multiply two high-precision numbers, speeding up the last iteration by as much as a factor of 10, and show how to produce the floating-point number closest to the exact result with relatively few additional operations.
Abstract: We present division and square root algorithm for calculations with more bits than are handled by the floating-point hardware. These algorithms avoid the need to multiply two high-precision numbers, speeding up the last iteration by as much as a factor of 10. We also show how to produce the floating-point number closest to the exact result with relatively few additional operations.
73 citations
Patent•
31 Mar 1988TL;DR: In this article, a high capacity metroplita area network (MAN) is described, where data traffic from users is connected to data concentrators at the edge of the network, and is transmitted over fiber optic data links to a hub where the data is switched.
Abstract: A high capacity metroplita, area network (MAN) is described. Data traffic from users is connected to data concentrators at the edge of the network, and is transmitted over fiber optic data links to a hub where the data is switched. The hub includes a plurality of data switching modules, each having a control means, and each connected to a distributed control space division switch. Advantageously, the data switching modules, whose inputs are connected to the concentrators, perform all checking and routing functions, while the 1024x1024 maximum size space division switch, whose outputs are connected to the concentrators, provides a large fan-out distribution network for reaching many concentrators from each data switching module. Distributed control of the space division switch permits several million connection and disconnection actions to be performed each second, while the pipelined and parallel operation within the control means permits each of the 256 switching modules to process at least 50,000 transactions per second. The data switching modules chain groups of incoming packets destined for a common outlet of the space division switch so that only one connection in that switch is required for transmitting each group of chained packets from a data switching module to a concentrator. Data streams from different inputs of the space division switch to a concentrator are synchronized to a clock by a circuit that detects the delay between a clock transition and an initial data signal transition and by a circuit for delaying the signal from the space division switch in accordance with the detected delay.
72 citations
Patent•
21 Jul 1941
TL;DR: In this article, an improved apparatus which responds to and measures the space gradient of a magnetic field is described. But this is not the case in this paper, as it is in the present paper.
Abstract: 1. This invention relates to improvements in apparatus for responding to magnetic fields and in particular it concerns improved apparatus which responds to and measures the space gradient of a magnetic field. The instant application is a division of my copending application, Ser. No. 403,455,...
72 citations
01 Jan 1997
TL;DR: This paper presented a moving-knife procedure, requiring only 11 cuts, that produces an envy-free allocation of a cake among four players and discuss possible extensions to five players, and discussed possible extensions for five players.
Abstract: We present a moving-knife procedure, requiring only 11 cuts, that produces an envy-free allocation of a cake among four players and discuss possible extensions to five players.
72 citations