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The Interval Logarithmic Number System
 Proceedings of the 9th IEEE Symposium on Computer Arithmetic
, 1989
"... System (ILNS), in which the Logarithmic Number System (LNS) is used as the underlying number system for interval arithmetic. The basic operations in ILNS are introduced and an efficient method for performing ILNS addition and subtraction is presented. The paper compares ILNS to Interval Floating Poi ..."
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Cited by 2 (1 self)
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System (ILNS), in which the Logarithmic Number System (LNS) is used as the underlying number system for interval arithmetic. The basic operations in ILNS are introduced and an efficient method for performing ILNS addition and subtraction is presented. The paper compares ILNS to Interval Floating
The Denormal Logarithmic Number System
, 2013
"... Abstract—Economical hardware often uses a FiXedpoint Number System (FXNS), whose constant absolute precision is acceptable for many signalprocessing algorithms. The almostconstant relative precision of the more expensive FloatingPoint (FP) number system simplifies design, for example, by eliminat ..."
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Cited by 1 (0 self)
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, by eliminating worries about FXNS overflow because the range of FP is much larger than FXNS for the same wordsize; however, primitive FP introduces another problem: underflow. The conventional Signed Logarithmic Number System (SLNS) offers similar range and precision as FP with much better performance (in terms
GeometricMean Interpolation for Logarithmic Number Systems
 In Proc. of the International Symposium on Circuits and Systems
, 2004
"... A new hardware implementation of linearLagrange interpolation is proposed where the interpolation line is approximated as the geometric mean of the slopes at the endpoints of the interpolation interval. The geometric mean is easy to compute using the Logarithmic Number System (LNS). ..."
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A new hardware implementation of linearLagrange interpolation is proposed where the interpolation line is approximated as the geometric mean of the slopes at the endpoints of the interpolation interval. The geometric mean is easy to compute using the Logarithmic Number System (LNS).
GEOMETRICMEAN INTERPOLATION FOR LOGARITHMIC NUMBER SYSTEMS
"... A new hardware implementation of linearLagrange interpolation is proposed where the interpolation line is approximated as the geometric mean of the slopes at the endpoints of the interpolation interval. The geometric mean is easy to compute using the Logarithmic Number System (LNS). 1. ..."
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A new hardware implementation of linearLagrange interpolation is proposed where the interpolation line is approximated as the geometric mean of the slopes at the endpoints of the interpolation interval. The geometric mean is easy to compute using the Logarithmic Number System (LNS). 1.
A Serial Logarithmic Number System ALU
"... Serial arithmetic uses less hardware than parallel arithmetic. Serial floating point (FP) is slower than parallel FP. The Logarithmic Number System (LNS) simplifies operations, but a fast serial implementation of LNS has never been proposed previously. This paper presents a fast bitserial LNS that c ..."
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Serial arithmetic uses less hardware than parallel arithmetic. Serial floating point (FP) is slower than parallel FP. The Logarithmic Number System (LNS) simplifies operations, but a fast serial implementation of LNS has never been proposed previously. This paper presents a fast bitserial LNS
Bipartite Implementation of the Residue Logarithmic Number System
"... The Logarithmic Number System (LNS) has area and power advantages over fixedpoint and floatingpoint number systems in some applications that tolerate moderate precision. LNS multiplication/division require only addition/subtraction of logarithms. Normally, LNS is implemented with ripplecarry bina ..."
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Cited by 2 (1 self)
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The Logarithmic Number System (LNS) has area and power advantages over fixedpoint and floatingpoint number systems in some applications that tolerate moderate precision. LNS multiplication/division require only addition/subtraction of logarithms. Normally, LNS is implemented with ripple
Digital Filtering Using the Multidimensional Logarithmic Number System
"... We introduce the use of multidimensional logarithmic number system (MDLNS) as a generalization of the classical 1D logarithmic number system (LNS) and analyze its use in DSP applications. The major drawback of the LNS is the requirement to use very large ROM arrays in implementing the additions and ..."
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We introduce the use of multidimensional logarithmic number system (MDLNS) as a generalization of the classical 1D logarithmic number system (LNS) and analyze its use in DSP applications. The major drawback of the LNS is the requirement to use very large ROM arrays in implementing the additions
Algorithms for Quantum Computation: Discrete Logarithms and Factoring
, 1994
"... A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a cost in computation time of at most a polynomial factol: It is not clear whether this is still true when quantum mechanics is taken into consider ..."
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Cited by 1111 (5 self)
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into consideration. Several researchers, starting with David Deutsch, have developed models for quantum mechanical computers and have investigated their computational properties. This paper gives Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number
An algorithm for finding best matches in logarithmic expected time
 ACM Transactions on Mathematical Software
, 1977
"... An algorithm and data structure are presented for searching a file containing N records, each described by k real valued keys, for the m closest matches or nearest neighbors to a given query record. The computation required to organize the file is proportional to kNlogN. The expected number of recor ..."
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Cited by 764 (2 self)
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An algorithm and data structure are presented for searching a file containing N records, each described by k real valued keys, for the m closest matches or nearest neighbors to a given query record. The computation required to organize the file is proportional to kNlogN. The expected number
A GPU Implementation of the Complex Logarithmic Number System
"... Abstract — In this paper we present a technique to implement the Complex Logarithmic Number System (CLNS) on a Graphics Processing Unit (GPU). Although CLNS multiplication is a simple FP addition, CLNS addition involves evaluations of transcendental functions, which can be carried out in a few diffe ..."
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Abstract — In this paper we present a technique to implement the Complex Logarithmic Number System (CLNS) on a Graphics Processing Unit (GPU). Although CLNS multiplication is a simple FP addition, CLNS addition involves evaluations of transcendental functions, which can be carried out in a few
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