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Some characterizations of functions computable in online arithmetic
 I.E.E.E. Trans. on Computers
, 1994
"... AbsfmctAfter a short introduction to online computing, we prove that the functions computable in online by a finite automaton are piecewise afthe functions whose coefikients are rational numbers (i.e., the fnnctions f(s) = UP + b, or f(z, y) = nx + by + c where a. b, and c are rational). A con ..."
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AbsfmctAfter a short introduction to online computing, we prove that the functions computable in online by a finite automaton are piecewise afthe functions whose coefikients are rational numbers (i.e., the fnnctions f(s) = UP + b, or f(z, y) = nx + by + c where a. b, and c are rational). A consequence of this study is that multiplication, division, and elementary functions of operands of arbitrarily long length cannot be performed using boundedshe operators. Index Zhts4omputer arithmetic, finite automata, online arithmetic. I.
An IEEE compliant floatingpoint adder that conforms with the pipelined packetforwarding paradigm
, 2000
"... This paper presents a floating point addition algorithm and adder pipeline design employing a packet forwarding pipeline paradigm. The packet forwarding format and the proposed algorithms constitute a new paradigm for handling data hazards in deeply pipelined oating point pipelines. The addition and ..."
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Cited by 6 (0 self)
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This paper presents a floating point addition algorithm and adder pipeline design employing a packet forwarding pipeline paradigm. The packet forwarding format and the proposed algorithms constitute a new paradigm for handling data hazards in deeply pipelined oating point pipelines. The addition and rounding algorithms employ a four stage execution phase pipeline with each stage suitable for implementation in a short clock period, assuming about fteen logic levels per cycle. The first two cycles are related to addition proper and are the focus of this paper. The last two cycles perform the rounding and have been covered in a paper by Nielsen and Matula [8]. The addition algorithm accepts one operand in a standard binary oating point format at the start of cycle one. The second operand is represented in the packet forwarding oating point format, namely, it is divided into four parts: the sign bit, the exponent string, the principal part of the significand, and the carryround packet. T...
A Systolic ONLINE Nonrestoring Division Scheme
 In Proceedings of 27th Hawaii International Conference on System Sciences
, 1994
"... A new improved version of the classic binary nonrestoring division algorithm is presented. It is implemented on a systolic ONLINE architecture, targeted at use in digital signal processing applications. The overall goal is to implement DSP algorithms using redundant data representations throughout ..."
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Cited by 3 (2 self)
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A new improved version of the classic binary nonrestoring division algorithm is presented. It is implemented on a systolic ONLINE architecture, targeted at use in digital signal processing applications. The overall goal is to implement DSP algorithms using redundant data representations throughout the algorithm, and to obtain a balanced architecture according to the specifications of the application. The improved algorithm is based on calculating the absolute value rather than obtaining the sign of the remainders. The use of absolute value is based on a paper introducing absolute value in the operations of a CORDIC unit [DM92]. Compared to the original work, the algorithmic contributions of this paper is a mathematical deduction of the algorithm applied to division. The new algorithm maintains the advantages of the nonrestoring division compared to SRT: No normalization or scaling of the divisor is required, and the output quotient is produced in a nonredundant number representatio...
Number systems and Digit Serial Arithmetic
, 1997
"... this paper. By introducing an extra termination symbol, which signals that an operand was merely terminated due to its length exceeding some bound, operands can be kept as intervals, representing an imprecise operand. Operands terminated in the ordinary way can be taken to represent exact numbers. T ..."
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Cited by 1 (1 self)
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this paper. By introducing an extra termination symbol, which signals that an operand was merely terminated due to its length exceeding some bound, operands can be kept as intervals, representing an imprecise operand. Operands terminated in the ordinary way can be taken to represent exact numbers. The cube modeling a function of two variables, can be generalized to a hypercube modeling a polyhomographic function of n variables. For n = 3 the function is defined as:
Practical And Educational Aspects Of OnLine Arithmetic
 IN 5TH EUROCHIP WORKSHOP ON VLSI DESIGN TRAINING
, 1994
"... This paper describes how a basic set of arithmetic operators can be implemented using bit serial computations with most significant digit first. Area, throughput and latency are given for each operator. Simple composition rules for mapping from algorithm to architecture are demonstrated. Practical e ..."
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This paper describes how a basic set of arithmetic operators can be implemented using bit serial computations with most significant digit first. Area, throughput and latency are given for each operator. Simple composition rules for mapping from algorithm to architecture are demonstrated. Practical examples has shown, that complex operators (i.e. CORDIC) and applications (FSK demodulator) can be built using these basic cells and composition rules.
VariablePrecision Arithmetic for Vector Quantization
, 1994
"... This research proposes and investigates a method for the storage and computation in Vector Quantization (VQ)  a promising technique for image/speech compression. The improvement is in the representation and arithmetic algorithm; the idea is independent of the technology and accommodates different ..."
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This research proposes and investigates a method for the storage and computation in Vector Quantization (VQ)  a promising technique for image/speech compression. The improvement is in the representation and arithmetic algorithm; the idea is independent of the technology and accommodates different search algorithms. Specifically, with simple lossless compression, the codebook storage in tree searched VQ is reduced more than 20%. For large codebooks, the simulations predict that the compression would be more than 40%. The compression of codevectors is achieved with VariablePrecision Representation (VPR), where we eliminate the sign extension bits. By categorizing vectors, VPR uses nonstationary nature of codevectors. Entropy measure shows that VPR compresses at least 75% as well as Huffman coding of vector elements. In conjunction