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On programming of arithmetic operations

A. P. Ershov
1958 Communications of the ACM  
ON PROGRAMMING OF ARITHMETIC OPERATIONS A. P. ERSHOV Doklady, AN USSR, vol. 118, No. 3, 1958, pp. 427-430 Translated by Morris D.  ...  Programming algorithms of arithmetic operations (AO) consist of three parts. The first part Al successively generates the commands of the AO program.  ... 
doi:10.1145/368892.368907 fatcat:pjtpis6z2zhwdjxpovn4f63doe

Optimal scheduling of arithmetic operations in parallel with memory access (preliminary version)

David Bernstein, Ron Y. Pinter, Michael Rodeh
1985 Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages - POPL '85  
We propose a new machine model in which load operations can be performed in parallel with arithmetic operations by two separate functional units.  ...  If the arithmetic operations have at most two arguments, the com.plexity goes down to O(nlogn).  ...  We would like to thank Jeff Jaffe for numerous suggestions that improved (and sometimes corrected) the presentation of our results.  ... 
doi:10.1145/318593.318662 dblp:conf/popl/BernsteinPR85 fatcat:zyksyk577zflhkwva556smstsy

A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem

Rajendran Vidhya, Rajkumar Irene Hepzibah
2017 International Journal of Applied Mathematics and Computer Science  
This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers (IVIFNs) to solve the interval valued intuitionistic fuzzy multi-objective linear programming  ...  range of IFNs unstable from the most pessimistic evaluation to the most optimistic one.  ...  Based on MATLAB simulations, extended modified interval arithmetic operations are better than extended interval arithmetic operations.  ... 
doi:10.1515/amcs-2017-0040 fatcat:rx7i2dbaefgtjhqbochi3vv2nu

Genetic programming with smooth operators for arithmetic expressions: diviplication and subdition

R.K. Ursem, T. Krink
Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600)  
This paper introduces the smooth operators for arithmetic expressions as an approach to smoothening the search space in Genetic Programming (GP).  ...  Smooth operator GP interpolates between arithmetic operators such as * and /, thereby allowing a gradual adaptation to the problem.  ...  Acknowledgements The authors would like to thank Bogdan Filipič (Dept. of Intelligent Systems, Jošef Stefan Institute, Ljubljana, Slovenia) for valuable comments and discussion.  ... 
doi:10.1109/cec.2002.1004443 fatcat:twoeigqapvctjklic6ldlry3sy

Interval operations involving NaNs

Evgenija D. Popova
1996 Reliable Computing  
0 and a set of special values called NaNs (Not-a-Number). Arithmetic operations include operations on numeric, non-numeric or mixed operands in four rounding modes.  ...  Since there is no meaning of the arithmetic operations on intervals involving NaNs their implementation is up to the implementor's option.  ...  0 and a set of special values called NaNs (Not-a-Number). Arithmetic operations include operations on numeric, non-numeric or mixed operands in four rounding modes.  ... 
doi:10.1007/bf02425919 fatcat:7k2wpjpyizhcdghwhs3mjdbble

Arithmetic Flags and Instructions [chapter]

Sivarama P. Dandamudi
1998 Introduction to Assembly Language Programming  
Multiword ArithmeticArithmetic operations (add, sub, mul, and div) work on 8-, 16-, or 32-bit operands • Arithmetic on larger operands require multiword arithmetic software routines • Addition/subtraction  ...  * This two instruction sequence is better than initializing CX to zero and executing • Carry Flag * Records the fact that the result of an arithmetic operation on unsigned numbers is out of range * The  ...  one bit position -P := P+B » else -left shift P:A by one bit position -P := P−B  ... 
doi:10.1007/978-1-4757-2858-3_6 fatcat:r5kmxcfamneofeszo6yzgtvfv4

Limiting semantics of numerical programs

D.N Hoover
1997 Theoretical Computer Science  
types of limiting program semantics.  ...  These three kinds of program semantics are based on domains that are similar to those commonly used in denotational semantics, but are continuous rather than algebraic, a slightly weaker property.  ...  By [ 121, Lemma 2.2 and Theorems 4.4 and 5.3, the order on operations and the order on arithmetics both induce c.b.c. domains, the Scott topology of the order on operations being the topology of pointwise  ... 
doi:10.1016/s0304-3975(96)00050-3 fatcat:4z6kcdxmgrgwphxr6jnga45aay

An introduction to the scientific computing language Pascal-SC

L.B. Rall
1987 Computers and Mathematics with Applications  
Its most important features are: (i) accurate floating-point arithmetic for real, complex, and interval numbers, vectors, and matrices, with controlled rounding if desired; (ii) the convenience of operator  ...  notation for numerical data types and the ability to accept user-defined operators for nonstandard data types to make programs easier to write, read, and document; and (iii) compatibility with ordinary  ...  Corliss for reading the manuscript carefully, and a large number of valuable suggestions. Example (20) was provided by Professor Dr Ulrich Kulisch. Sponsored by the U.S. Army under Contract No.  ... 
doi:10.1016/0898-1221(87)90181-7 fatcat:5kaukwfwybalho2o27zqi6mwei

Transmathematical Basis of Infinitely Scalable Pipeline Machines

James A.D.W. Anderson
2015 Procedia Computer Science  
We describe infinitely scalable pipeline machines with perfect parallelism, in the sense that every instruction of an inline program is executed, on successive data, on every clock tick.  ...  Our pipeline machines exploit the totality of transreal arithmetic and the known waiting time of statically compiled programs to deliver the interesting property that they need no hardware or software  ...  The class of pipeline machines we consider, above, operate on programs for which the waiting time to completion is known. In this case no software exception handling is needed.  ... 
doi:10.1016/j.procs.2015.05.408 fatcat:p23366xt3rfgxj2ddnq7eggifq

Page 739 of Mathematical Reviews Vol. , Issue 83b [page]

1983 Mathematical Reviews  
[On the transformation of general programs into convergent programs] Z. Angew. Math. Mech. 6@ (1980), no. 7, T282—T283.  ...  In this way all operations can be composed of the basic operations +,-,+*,/, and scalar products. All of these operations have to be computed with only one single rounding error.  ... 

Analysis of the GCR method with mixed precision arithmetic using QuPAT

Tsubasa Saito, Emiko Ishiwata, Hidehiko Hasegawa
2012 Journal of Computational Science  
; (ii) to enable the use of both double and quadruple precision arithmetic at the same time; (iii) to be independent of any hardware and operating systems.  ...  Hence, we designed the quadruple precision arithmetic environment QuPAT on Scilab to satisfy the following requirements: (i) to enable programs to be written simply using quadruple precision arithmetic  ...  In addition, we were able to use all of double, quadruple and mixed precision arithmetic in the same program with the same operators (+, −, * , /).  ... 
doi:10.1016/j.jocs.2011.05.001 fatcat:s6ff5kwfbzeazhjr6fodv4fdce

Page 116 of The Arithmetic Teacher Vol. 8, Issue 3 [page]

1961 The Arithmetic Teacher  
The program is in its second year of operation at Sierra School, and it was adopted on a district-wide basis at the beginning of the current school year.  ...  Arithmetic Program: I.  ... 

Synthesis and Implementation of Reconfigurable PLC on FPGA Platform

Adam Milik, Edward Hrynkiewicz
2012 International Journal of Electronics and Telecommunications  
An example of logic functions, PID controller and mixed arithmetic and logic programming examples are considered.  ...  Synthesis and Implementation of Reconfigurable PLC on FPGA Platform The paper presents a set of algorithms dedicated for synthesis of reconfigurable logic controllers implemented on FPGA platform and programmed  ...  This method of mapping executes/assigns one arithmetic operation into the calculation cycle.  ... 
doi:10.2478/v10177-012-0012-8 fatcat:xrkjmmmwxjaynithlqqcekzfnq

The clinical biochemistry laboratory computer system as a simple calculator: a program in MUMPS

T. G. Pellar, N. Rawal, A. R. Henderson
1985 Journal of Automatic Chemistry  
This present program provides only the four common arithmetical operators, as these are, by far, the ones most needed.  ...  On program line CAL + 1,^CO UNTER is a global variable used to count the number of accesses to this program; it is updated (the count is indexed by 1) on calling the program.  ... 
doi:10.1155/s1463924685000086 pmid:18925066 pmcid:PMC2547597 fatcat:2scy6apkw5f7zoevjm3igj2b74

An FPGA Implementation for a Flexible-Length-Arithmetic Processor Employing the FDFM Processor Core Approach

Tatsuya KAWAMOTO, Xin ZHOU, Jacir L. BORDIM, Yasuaki ITO, Koji NAKANO
2016 IEICE transactions on information and systems  
To reduce the burden of implementing algorithm directly on the FPGA, applications requiring multiple-length arithmetic operations are written in a C-like language and translated into a machine program.  ...  The main contribution of this work is to present a flexible-lengtharithmetic processor based on FDFM (Few DSP slices and Few Memory blocks) approach that supports arithmetic operations on multiple-length  ...  require multiple-length-arithmetic operations to be executed on FP-GAs devices.  ... 
doi:10.1587/transinf.2016pap0029 fatcat:swvoab4pxjejply5xy5zwoe5ou
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