# strtab

key: ack-jr
filename: fparith.bib
value:
Jon Rokne, Department of Computer Science, The University of Calgary, 2500 University Drive N.W., Calgary, Alberta T2N 1N4, Canada

entry:
@String{ack-jr =       "Jon Rokne,
                     Department of Computer Science,
                     The University of Calgary,
                     2500 University Drive N.W.,
                     Calgary, Alberta T2N 1N4,
                     Canada"}


key: ack-kr
filename: fparith.bib
value:
Karin Remington, National Institute of Standards and Technology, Building 820, Room 365, Gaithersburg, MD 20899, USA, Tel: +1 301 975-5119, FAX: +1 301 990-4127, e-mail: path |karin@cam.nist.gov|

entry:
@String{ack-kr =    "Karin Remington,
                  National Institute of Standards and Technology,
                  Building 820, Room 365,
                  Gaithersburg, MD 20899, USA,
                  Tel: +1 301 975-5119,
                  FAX: +1 301 990-4127,
                  e-mail: \path|karin@cam.nist.gov|"}


key: ack-mfc
filename: fparith.bib
value:
Michael F. Cowlishaw, IBM UK (MP5), PO Box 31, Birmingham Road, Warwick, CV34 5JL, UK, e-mail: path |mfc@uk.ibm.com|, URL: path |http://www2.hursley.ibm.com/decimal|

entry:
@String{ack-mfc = "Michael F. Cowlishaw,
                   IBM UK (MP5),
                   PO Box 31,
                   Birmingham Road,
                   Warwick, CV34 5JL,
                   UK,
                   e-mail: \path|mfc@uk.ibm.com|,
                   URL: \path|http://www2.hursley.ibm.com/decimal|"}


key: ack-nhfb
filename: fparith.bib
value:
Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, e-mail: path |beebe@math.utah.edu|, path |beebe@acm.org|, path |beebe@computer.org| (Internet), URL: path |https://www.math.utah.edu/~beebe/|

entry:
@String{ack-nhfb = "Nelson H. F. Beebe,
                    University of Utah,
                    Department of Mathematics, 110 LCB,
                    155 S 1400 E RM 233,
                    Salt Lake City, UT 84112-0090, USA,
                    Tel: +1 801 581 5254,
                    FAX: +1 801 581 4148,
                    e-mail: \path|beebe@math.utah.edu|,
                            \path|beebe@acm.org|,
                            \path|beebe@computer.org| (Internet),
                    URL: \path|https://www.math.utah.edu/~beebe/|"}


key: ack-nj
value: Norbert Juffa, 2445 Mission College Blvd. Santa Clara, CA 95054 USA email: path =norbert@iit.com=
filename: fparith.bib
entry:
@String{ack-nj =    "Norbert Juffa,
                  2445 Mission College Blvd.
                  Santa Clara, CA 95054
                  USA
                  email: \path=norbert@iit.com="}


key: ack-pb
filename: fparith.bib
value:
Preston Briggs, Tera Computer Company, 2815 Eastlake East, Seattle, WA 98102, USA, Tel: +1 206 325-0800, e-mail: path |preston@tera.com|

entry:
@String{ack-pb =      "Preston Briggs,
                     Tera Computer Company,
                     2815 Eastlake East,
                     Seattle, WA 98102,
                     USA,
                     Tel: +1 206 325-0800,
                     e-mail: \path|preston@tera.com|"}


key: ack-rfb
filename: fparith.bib
value:
Ronald F. Boisvert, Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA, Tel: +1 301 975 3812, e-mail: path =boisvert@cam.nist.gov=

entry:
@String{ack-rfb = "Ronald F. Boisvert,
                  Applied and Computational Mathematics Division,
                  National Institute of Standards and Technology,
                  Gaithersburg, MD 20899, USA,
                  Tel: +1 301 975 3812,
                  e-mail: \path=boisvert@cam.nist.gov="}


key: inst-ANL:adr
value: 9700 South Cass Avenue, Argonne, IL 60439-4801, USA
filename: fparith.bib
entry:
@String{inst-ANL:adr            = "9700 South Cass Avenue, Argonne, IL
                                  60439-4801, USA"}


key: inst-BERKELEY-CPAM
value: Center for Pure and Applied Mathematics, University of California
filename: fparith.bib
entry:
@String{inst-BERKELEY-CPAM      = "Center for Pure and Applied Mathematics,
                                  University of California"}


key: inst-BERKELEY-CS
value: Department of Computer Science, University of California
filename: fparith.bib
entry:
@String{inst-BERKELEY-CS        = "Department of Computer Science, University
                                  of California"}


key: inst-BERKELEY-EECS
value: Department of Electrical Engineering and Computer Science, University of California, Berkeley
filename: fparith.bib
entry:
@String{inst-BERKELEY-EECS      = "Department of Electrical Engineering and
                                  Computer Science, University of California,
                                  Berkeley"}


key: inst-CS-PURDUE
value: Department of Computer Science, Purdue University
filename: fparith.bib
entry:
@String{inst-CS-PURDUE          = "Department of Computer Science, Purdue
                                  University"}


key: inst-CSC
value: Center for Scientific Computing, Department of Mathematics, University of Utah
filename: fparith.bib
entry:
@String{inst-CSC                = "Center for Scientific Computing,
                                  Department of Mathematics, University of
                                  Utah"}


key: inst-LORIA-INRIA-LORRAINE:adr
filename: fparith.bib
value:
Batiment A, Technopole de Nancy-Brabois, 615 rue du jardin botanique, F-54602 Villers-les-Nancy Cedex, France

entry:
@String{inst-LORIA-INRIA-LORRAINE:adr = "B{\^a}timent A, Technop{\^o}le de
                                  Nancy-Brabois, 615 rue du jardin
                                  botanique, F-54602
                                  Villers-l{\`e}s-Nancy Cedex, France"}


key: inst-MATHWORKS:adr
value: 3 Apple Hill Drive, Natick, MA 01760-2098, USA
filename: fparith.bib
entry:
@String{inst-MATHWORKS:adr      = "3 Apple Hill Drive, Natick, MA 01760-2098,
                                  USA"}


key: inst-MRC-WISCONSIN
value: Mathematics Research Center, University of Wisconsin, Madison
filename: fparith.bib
entry:
@String{inst-MRC-WISCONSIN      = "Mathematics Research Center, University of
                                  Wisconsin, Madison"}


key: inst-STAN-CS
value: Stanford University, Department of Computer Science
filename: fparith.bib
entry:
@String{inst-STAN-CS            = "Stanford University, Department of
                                  Computer Science"}


key: inst-UT-CS
value: Department of Computer Science, University of Tennessee, Knoxville
filename: fparith.bib
entry:
@String{inst-UT-CS              = "Department of Computer Science,
                                  University of Tennessee, Knoxville"}


key: j-ADV-SOFT-SCI-TECH
value: Advances in software science and technology
filename: fparith.bib
entry:
@String{j-ADV-SOFT-SCI-TECH     = "Advances in software science and
                                  technology"}


key: j-APPL-ALGEBRA-ENG-COMMUN-COMPUT
value: Applicable algebra in engineering, communication and computing
filename: fparith.bib
entry:
@String{j-APPL-ALGEBRA-ENG-COMMUN-COMPUT = "Applicable algebra in engineering,
                                  communication and computing"}


key: j-BIT
value: BIT (Nordisk tidskrift for informationsbehandling)
filename: fparith.bib
entry:
@String{j-BIT                   = "BIT (Nordisk tidskrift for
                                  informationsbehandling)"}


key: j-BRITISH-J-HIST-MATH
value: British Journal for the History of Mathematics
filename: fparith.bib
entry:
@String{j-BRITISH-J-HIST-MATH   = "British Journal for the History of
                                  Mathematics"}


key: j-BULL-AMS
value: Bulletin of the American Mathematical Society
filename: fparith.bib
entry:
@String{j-BULL-AMS              = "Bulletin of the American Mathematical
                                  Society"}


key: j-C-R-ACAD-BULGARE-SCI
value: Comptes rendus de l'Academie bulgare des sciences
filename: fparith.bib
entry:
@String{j-C-R-ACAD-BULGARE-SCI  = "Comptes rendus de l'Acad{\'e}mie bulgare
                                  des sciences"}


key: j-C-R-ACAD-SCI-PARIS-SER-I-MATH
value: Comptes Rendus des Seances de l'Academie des Sciences. Serie I. Mathematique
filename: fparith.bib
entry:
@String{j-C-R-ACAD-SCI-PARIS-SER-I-MATH = "Comptes Rendus des S{\'e}ances de
                                  l'Acad{\'e}mie des Sciences. S{\'e}rie I.
                                  Math{\'e}matique"}


key: j-CACM
value: Communications of the Association for Computing Machinery
filename: fparith.bib
entry:
@String{j-CACM                  = "Communications of the Association for
                                  Computing Machinery"}


key: j-CCPE
value: Concurrency and Computation: Practice and Experience
filename: fparith.bib
entry:
@String{j-CCPE                  = "Concurrency and Computation: Prac\-tice and
                                   Experience"}


key: j-COMMUN-STAT-SIMUL-COMPUT
value: Communications in Statistics: Simulation and Computation
filename: fparith.bib
entry:
@String{j-COMMUN-STAT-SIMUL-COMPUT = "Communications in Statistics: Simulation
                                  and Computation"}


key: j-COMMUN-STAT-THEORY-METH
value: Communications in Statistics: Theory and Methods
filename: fparith.bib
entry:
@String{j-COMMUN-STAT-THEORY-METH = "Communications in Statistics: Theory and
                                  Methods"}


key: j-COMP-GEOM
value: Computational Geometry. Theory and Applications
filename: fparith.bib
entry:
@String{j-COMP-GEOM             = "Computational Geometry. Theory and
                                  Applications"}


key: j-COMPUTING
value: Computing: Archiv fur informatik und numerik
filename: fparith.bib
entry:
@String{j-COMPUTING             = "Computing: Archiv fur informatik und
                                  numerik"}


key: j-DTRAP
value: Digital Threats: Research and Practice (DTRAP)
filename: fparith.bib
entry:
@String{j-DTRAP                 = "Digital Threats: Research and Practice
                                  (DTRAP)"}


key: j-ELECT-COMM-JAPAN-3-FUND-ELECT-SCI
value: Electronics and communications in Japan. Part 3, Fundamental electronic science
filename: fparith.bib
entry:
@String{j-ELECT-COMM-JAPAN-3-FUND-ELECT-SCI = "Electronics and communications in
                                  Japan. Part 3, Fundamental electronic
                                  science"}


key: j-ELECT-NOTES-THEOR-COMP-SCI
value: Electronic Notes in Theoretical Computer Science
filename: fparith.bib
entry:
@String{j-ELECT-NOTES-THEOR-COMP-SCI = "Electronic Notes in Theoretical
                                  Computer Science"}


key: j-ELECTR-ENG
value: Electrical Engineering (American Institute of Electrical Engineers)
filename: fparith.bib
entry:
@String{j-ELECTR-ENG            = "Electrical Engineering (American Institute of
                                  Electrical Engineers)"}


key: j-EURASIP-J-ADV-SIGNAL-PROCESS
value: EURASIP Journal on Advances in Signal Processing
filename: fparith.bib
entry:
@String{j-EURASIP-J-ADV-SIGNAL-PROCESS = "EURASIP Journal on Advances in Signal
                                Processing"}


key: j-GAMM-MIT
value: Mitteilungen der Gesellschaft fur Angewandte Mathematik und Mechanik
filename: fparith.bib
entry:
@String{j-GAMM-MIT              = "Mitteilungen der Gesellschaft f{\\\"u}r
                                  Angewandte Mathematik und Mechanik"}


key: j-HIST-SCI-2
filename: fparith.bib
value:
Historia Scientiarum. Second Series. International Journal of the History of Science Society of Japan

entry:
@String{j-HIST-SCI-2            = "Historia Scientiarum. Second Series.
                                  International Journal of the History
                                  of Science Society of Japan"}


key: j-IEE-PROC-COMPUT-DIGIT-TECH
value: IEE Proceedings. Computers and Digital Techniques
filename: fparith.bib
entry:
@String{j-IEE-PROC-COMPUT-DIGIT-TECH = "IEE Proceedings. Computers and Digital
                                  Techniques"}


key: j-IEE-PROC-E
value: IEE proceedings, E: Computers and digital techniques
filename: fparith.bib
entry:
@String{j-IEE-PROC-E            = "IEE proceedings, E: Computers and digital
                                  techniques"}


key: j-IEEE-INT-CONF-ALG-ARCH-PAR-PROC
value: IEEE International Conference on Algorithms and Architectures for Parallel Processing
filename: fparith.bib
entry:
@String{j-IEEE-INT-CONF-ALG-ARCH-PAR-PROC = "IEEE International Conference on
                                  Algorithms and Architectures for Parallel
                                  Processing"}


key: j-IEEE-J-EMERG-SEL-TOP-CIRCUITS-SYST
value: IEEE Journal on Emerging and Selected Topics in Circuits and Systems
filename: fparith.bib
entry:
@String{j-IEEE-J-EMERG-SEL-TOP-CIRCUITS-SYST = "IEEE Journal on Emerging and
                                  Selected Topics in Circuits and Systems"}


key: j-IEEE-J-SEL-AREAS-COMMUN
value: IEEE Journal on Selected Areas in Communications
filename: fparith.bib
entry:
@String{j-IEEE-J-SEL-AREAS-COMMUN = "IEEE Journal on Selected Areas in
                                  Communications"}


key: j-IEEE-TRANS-ACOUST-SPEECH
value: IEEE Transactions on Acoustics, Speech, and Signal Processing
filename: fparith.bib
entry:
@String{j-IEEE-TRANS-ACOUST-SPEECH = "IEEE Transactions on Acoustics, Speech,
                                  and Signal Processing"}


key: j-IEEE-TRANS-AEROSP-ELECTRON-SYST
value: IEEE Transactions on Aerospace and Electronic Systems
filename: fparith.bib
entry:
@String{j-IEEE-TRANS-AEROSP-ELECTRON-SYST = "IEEE Transactions on Aerospace
                                  and Electronic Systems"}


key: j-IEEE-TRANS-APPL-SUPERCOND
value: IEEE Transactions on Applied Superconductivity
filename: fparith.bib
entry:
@String{j-IEEE-TRANS-APPL-SUPERCOND = "IEEE Transactions on Applied
                                  Superconductivity"}


key: j-IEEE-TRANS-AUDIO-ELECTROACOUST
value: IEEE Transactions on Audio and Electroacoustics
filename: fparith.bib
entry:
@String{j-IEEE-TRANS-AUDIO-ELECTROACOUST = "IEEE Transactions on Audio and
                                  Electroacoustics"}


key: j-IEEE-TRANS-BIOMED-ENG
value: IEEE Transactions on Biomedical Engineering
filename: fparith.bib
entry:
@String{j-IEEE-TRANS-BIOMED-ENG = "IEEE Transactions on Biomedical
                                  Engineering"}


key: j-IEEE-TRANS-CAD-ICS
value: IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
filename: fparith.bib
entry:
@String{j-IEEE-TRANS-CAD-ICS    = "IEEE Transactions on Computer-Aided Design
                                  of Integrated Circuits and Systems"}


key: j-IEEE-TRANS-CIRCUITS-SYST
value: IEEE Transactions on Circuits and Systems
filename: fparith.bib
entry:
@String{j-IEEE-TRANS-CIRCUITS-SYST = "IEEE Transactions on Circuits and
                                  Systems"}


key: j-IEEE-TRANS-CIRCUITS-SYST-1
value: IEEE Transactions on Circuits and Systems I: Regular Papers
filename: fparith.bib
entry:
@String{j-IEEE-TRANS-CIRCUITS-SYST-1 = "IEEE Transactions on Circuits and
                                  Systems I: Regular Papers"}


key: j-IEEE-TRANS-CIRCUITS-SYST-I-FUNDAM-THEORY-APPL
value: IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
filename: fparith.bib
entry:
@String{j-IEEE-TRANS-CIRCUITS-SYST-I-FUNDAM-THEORY-APPL = "IEEE Transactions on
                                Circuits and Systems I: Fundamental
                                Theory and Applications"}


key: j-IEEE-TRANS-CIRCUITS-SYST-2
value: IEEE transactions on circuits and systems. 2, Analog and digital signal processing
filename: fparith.bib
entry:
@String{j-IEEE-TRANS-CIRCUITS-SYST-2 = "IEEE transactions on circuits and
                                  systems. 2, Analog and digital signal
                                  processing"}


key: j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS
value: IEEE Transactions on Circuits and Systems II: Express Briefs
filename: fparith.bib
entry:
@String{j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS = "IEEE Transactions on
                                  Circuits and Systems II: Express Briefs"}


key: j-IEEE-TRANS-CIRCUITS-SYST-VIDEO-TECH
value: IEEE Transactions on Circuits and Systems for Video Technology
filename: fparith.bib
entry:
@String{j-IEEE-TRANS-CIRCUITS-SYST-VIDEO-TECH = "IEEE Transactions on Circuits
                                  and Systems for Video Technology"}


key: j-IEEE-TRANS-CONSUMER-ELECTRONICS
value: IEEE Transactions on Consumer Electronics
filename: fparith.bib
entry:
@String{j-IEEE-TRANS-CONSUMER-ELECTRONICS = "IEEE Transactions on Consumer
                                  Electronics"}


key: j-IEEE-TRANS-CONTROL-SYST-TECHNOL
value: IEEE Transactions on Control Systems Technology
filename: fparith.bib
entry:
@String{j-IEEE-TRANS-CONTROL-SYST-TECHNOL = "IEEE Transactions on Control
                                  Systems Technology"}


key: j-IEEE-TRANS-EMERG-TOP-COMPUT
value: IEEE Transactions on Emerging Topics in Computing
filename: fparith.bib
entry:
@String{j-IEEE-TRANS-EMERG-TOP-COMPUT = "IEEE Transactions on Emerging Topics in
                                  Computing"}


key: j-IEEE-TRANS-IND-ELECTRON
value: IEEE Transactions on Industrial Electronics
filename: fparith.bib
entry:
@String{j-IEEE-TRANS-IND-ELECTRON = "IEEE Transactions on Industrial
                                  Electronics"}


key: j-IEEE-TRANS-INSTRUM-MEAS
value: IEEE Transactions on Instrumentation and Measurement
filename: fparith.bib
entry:
@String{j-IEEE-TRANS-INSTRUM-MEAS = "IEEE Transactions on Instrumentation and
                                  Measurement"}


key: j-IEEE-TRANS-PAR-DIST-SYS
value: IEEE Transactions on Parallel and Distributed Systems
filename: fparith.bib
entry:
@String{j-IEEE-TRANS-PAR-DIST-SYS = "IEEE Transactions on Parallel and
                                    Distributed Systems"}


key: j-IEEE-TRANS-PROF-COMMUN
value: IEEE Transactions on Professional Communication
filename: fparith.bib
entry:
@String{j-IEEE-TRANS-PROF-COMMUN = "IEEE Transactions on Professional
                                  Communication"}


key: j-IEEE-TRANS-VIS-COMPUT-GRAPH
value: IEEE Transactions on Visualization and Computer Graphics
filename: fparith.bib
entry:
@String{j-IEEE-TRANS-VIS-COMPUT-GRAPH = "IEEE Transactions on Visualization and
                                  Computer Graphics"}


key: j-IEEE-TRANS-VLSI-SYST
value: IEEE Transactions on Very Large Scale Integration (VLSI) Systems
filename: fparith.bib
entry:
@String{j-IEEE-TRANS-VLSI-SYST  = "IEEE Transactions on Very Large Scale
                                  Integration (VLSI) Systems"}


key: j-IFIP-TRANS-A
value: IFIP Transactions. A. Computer Science and Technology
filename: fparith.bib
entry:
@String{j-IFIP-TRANS-A          = "IFIP Transactions. A. Computer Science and
                                  Technology"}


key: j-IJSA
value: The International Journal of Supercomputer Applications
filename: fparith.bib
entry:
@String{j-IJSA                  = "The International Journal of Supercomputer
                                  Applications"}


key: j-IJHPCA
value: The International Journal of High Performance Computing Applications
filename: fparith.bib
entry:
@String{j-IJHPCA                = "The International Journal of High Performance
                                  Computing Applications"}


key: j-INFO-PROC
value: Journal of Information Processing (of Japan??)
filename: fparith.bib
entry:
@String{j-INFO-PROC             = "Journal of Information Processing (of
                                  Japan??)"}


key: j-INFORM-THEOR-APPL
value: RAIRO. Informatique theorique et applications := Theoretical informatics and applications
filename: fparith.bib
entry:
@String{j-INFORM-THEOR-APPL     = "RAIRO. Informatique th{\'e}orique et
                                  applications := Theoretical
                                  informatics and applications"}


key: j-INT-J-COMPUT-GEOM-APPL
value: International Journal of Computational Geometry and Applications (IJCGA)
filename: fparith.bib
entry:
@String{j-INT-J-COMPUT-GEOM-APPL = "International Journal of
                                   Computational Geometry and Applications
                                   (IJCGA)"}


key: j-INT-J-ELECTRON
value: International Journal of Electronics Theoretical & Experimental
filename: fparith.bib
entry:
@String{j-INT-J-ELECTRON        = "International Journal of Electronics
                                  Theoretical \& Experimental"}


key: j-INT-J-FOUND-COMP-SCI
value: International Journal of Foundations of Computer Science
filename: fparith.bib
entry:
@String{j-INT-J-FOUND-COMP-SCI  = "International Journal of Foundations of
                                  Computer Science"}


key: j-INT-J-INFO-SEC
value: International Journal of Information Security
filename: fparith.bib
entry:
@String{j-INT-J-INFO-SEC        = "International Journal of Information
                                  Security"}


key: j-INT-J-HIGH-SPEED-COMPUTING
value: International Journal of High Speed Computing
filename: fparith.bib
entry:
@String{j-INT-J-HIGH-SPEED-COMPUTING = "International Journal of High Speed
                                  Computing"}


key: j-INT-J-MINI-MICROCOMPUTERS
value: International Journal of Mini and Microcomputers
filename: fparith.bib
entry:
@String{j-INT-J-MINI-MICROCOMPUTERS = "International Journal of Mini and
                                  Microcomputers"}


key: j-INT-J-PAR-EMER-DIST-SYS
value: International Journal of Parallel, Emergent and Distributed Systems: IJPEDS
filename: fparith.bib
entry:
@String{j-INT-J-PAR-EMER-DIST-SYS = "International Journal of Parallel, Emergent
                                  and Distributed Systems: IJPEDS"}


key: j-INT-J-PARALLEL-PROG
value: International Journal of Parallel Programming
filename: fparith.bib
entry:
@String{j-INT-J-PARALLEL-PROG   = "International Journal of Parallel
                                   Programming"}


key: j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER
value: International Journal on Software Tools for Technology Transfer: STTT
filename: fparith.bib
entry:
@String{j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER = "International Journal on
                                  Software Tools for Technology Transfer:
                                  STTT"}


key: j-INTERVAL-COMP
value: Interval Computations = Interval'nye vychisleniia
filename: fparith.bib
entry:
@String{j-INTERVAL-COMP         = "Interval Computations = Interval'nye
                                  vychisleniia"}


key: j-J-ACM
value: Journal of the Association for Computing Machinery
filename: fparith.bib
entry:
@String{j-J-ACM                 = "Journal of the Association for Computing
                                  Machinery"}


key: j-J-ACOUST-SOC-AM
value: Journal of the Acoustical Society of America
filename: fparith.bib
entry:
@String{j-J-ACOUST-SOC-AM       = "Journal of the Acoustical Society of
                                  America"}


key: j-J-ADV-MODEL-EARTH-SYST
value: Journal of Advances in Modeling Earth Systems
filename: fparith.bib
entry:
@String{j-J-ADV-MODEL-EARTH-SYST = "Journal of Advances in Modeling Earth
                                  Systems"}


key: j-J-AM-STAT-ASSOC
value: Journal of the American Statistical Association
filename: fparith.bib
entry:
@String{j-J-AM-STAT-ASSOC       = "Journal of the American Statistical
                                  Association"}


key: j-J-AUSTRALIAN-MATH-SOC
value: Journal of the Australian Mathematical Society
filename: fparith.bib
entry:
@String{j-J-AUSTRALIAN-MATH-SOC = "Journal of the Australian Mathematical
                                  Society"}


key: j-J-CHINESE-INST-ENG
value: Journal of the Chinese Institute of Engineers = Chung-kuo kung ch'eng hsueh kan
filename: fparith.bib
entry:
@String{j-J-CHINESE-INST-ENG    = "Journal of the Chinese Institute of Engineers
                                  = Chung-kuo kung ch'eng hsueh kan"}


key: j-J-COMPUT-APPL-MATH
value: Journal of Computational and Applied Mathematics
filename: fparith.bib
entry:
@String{j-J-COMPUT-APPL-MATH    = "Journal of Computational and Applied
                                  Mathematics"}


key: j-J-CRYPTOLOGY
value: Journal of Cryptology: the journal of the International Association for Cryptologic Research
filename: fparith.bib
entry:
@String{j-J-CRYPTOLOGY          = "Journal of Cryptology: the journal of the
                                  International Association for Cryptologic
                                  Research"}


key: j-J-INFO-PROC-CYBERNETICS-EIK
value: Journal of Information Processing and Cybernetics: EIK
filename: fparith.bib
entry:
@String{j-J-INFO-PROC-CYBERNETICS-EIK = "Journal of Information Processing and
                                  Cybernetics: EIK"}


key: j-J-INST-MATH-APPL
value: Journal of the Institute of Mathematics and its Applications
filename: fparith.bib
entry:
@String{j-J-INST-MATH-APPL      = "Journal of the Institute of Mathematics and
                                  its Applications"}


key: j-J-KOREA-INFO-SCI-SOCIETY
value: Journal of the Korea Information Science Society = Chongbo Kwahakhoe nonmunji
filename: fparith.bib
entry:
@String{j-J-KOREA-INFO-SCI-SOCIETY = "Journal of the Korea Information Science
                                  Society = Chongbo Kwahakhoe nonmunji"}


key: j-MONTHLY-NOT-ROY-ASTRON-SOC
value: Monthly Notices of the Royal Astronomical Society
filename: fparith.bib
entry:
@String{j-MONTHLY-NOT-ROY-ASTRON-SOC = "Monthly Notices of the Royal
                                  Astronomical Society"}


key: j-J-NETW-COMPUT-APPL
value: Journal of Network and Computer Applications
filename: fparith.bib
entry:
@String{j-J-NETW-COMPUT-APPL    = "Journal of Network and Computer
                                  Applications"}


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# namtab

filename: fparith.bib
name:
IEEE Computer Society Standards Committee.Working group of the Microprocessor Standards Subcommittee


# bibtab

bibtype: article
filename: fparith.bib
label: Leibniz:1703:EAB
author: G.-W. Leibniz
title: Explication de l'Arithmetique Binaire. (French) [Explanation of binary arithmetic]
journal: Memoires de mathematique et de physique de l Academie royale des sciences
pages: 85--89
year: 1703
bibdate: Fri Mar 17 08:48:17 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.03.17 08:48:17 ???
URL: https://hal.archives-ouvertes.fr/ads-00104781/document
language: French
acknowledgement: ack-nhfb
rawauthor: G.-W. Leibniz
rawtitle: Explication de {l'Arithm{\'e}tique} Binaire. ({French}) [{Explanation} of binary arithmetic]
note:
Leibniz is often credited with the invention of the binary number system, but there is other work from his era, and detailed analysis of Leibniz's use of binary numbers. See cite Greve:1966:HLR,Glaser:1969:HMN,Glaser:1971:HBO,Lautz:1979:JLD,Glaser:1981:HBO,Esmay:2017:HNS,Strickland:2022:LBI,Zlatopolski:2023:PAV

rawnote:
Leibniz is often credited with the invention of the binary number system, but there is other work from his era, and detailed analysis of Leibniz's use of binary numbers. See \cite{Greve:1966:HLR,Glaser:1969:HMN,Glaser:1971:HBO,Lautz:1979:JLD,Glaser:1981:HBO,Esmay:2017:HNS,Strickland:2022:LBI,Zlatopolski:2023:PAV}

entry:
@Article{Leibniz:1703:EAB,
  author =       "G.-W. Leibniz",
  title =        "Explication de {l'Arithm{\'e}tique} Binaire.
                 ({French}) [{Explanation} of binary arithmetic]",
  journal =      "M{\'e}moires de math{\'e}matique et de physique de l
                 Acad{\'e}mie royale des sciences",
  volume =       "??",
  number =       "??",
  pages =        "85--89",
  month =        "????",
  year =         "1703",
  bibdate =      "Fri Mar 17 08:48:17 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Leibniz is often credited with the invention of the
                 binary number system, but there is other work from his
                 era, and detailed analysis of Leibniz's use of binary
                 numbers. See
                 \cite{Greve:1966:HLR,Glaser:1969:HMN,Glaser:1971:HBO,Lautz:1979:JLD,Glaser:1981:HBO,Esmay:2017:HNS,Strickland:2022:LBI,Zlatopolski:2023:PAV}",
  URL =          "https://hal.archives-ouvertes.fr/ads-00104781/document",
  acknowledgement = ack-nhfb,
  language =     "French",
}


bibtype: book
filename: fparith.bib
label: Pelicano:1712:APQ
author: Wenceslao Josepho Pelicano
address: Prague, Czechoslovakia
year: 1712
bibdate: Fri Mar 17 08:56:14 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.03.17 08:56:14 ???
URL: https://play.google.com/books/reader?id=cNxdAAAAcAAJ
acknowledgement: ack-nhfb
rawauthor: Wenceslao Josepho Pelicano
title:
Arithmeticus Perfectus Qui tria numerare nescit, ldots . (Latin) [A Perfect Arithmetic for who does not know how to count to three]

rawtitle:
Arithmeticus Perfectus Qui tria numerare nescit, \ldots{}. ({Latin}) [{A} Perfect Arithmetic for who does not know how to count to three]

entry:
@Book{Pelicano:1712:APQ,
  author =       "Wenceslao Josepho Pelicano",
  title =        "Arithmeticus Perfectus Qui tria numerare nescit,
                 \ldots{}. ({Latin}) [{A} Perfect Arithmetic for who
                 does not know how to count to three]",
  publisher =    "????",
  address =      "Prague, Czechoslovakia",
  pages =        "????",
  year =         "1712",
  bibdate =      "Fri Mar 17 08:56:14 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://play.google.com/books/reader?id=cNxdAAAAcAAJ",
  acknowledgement = ack-nhfb,
  longtitle =    "Arithmeticus Perfectus Qui tria numerare nescit, sen
                 Arithmetica dualis in qua Numerando non proceditur,
                 nisi ad duo, \& tamen omnes questiones Arithmetic{\ae}
                 negoti{\^o} facile enodar possunt ad perilsturem equite
                 Mathematic{\ae}. ({Latin}) [{A} Perfect Arithmetic for
                 who does not know how to count to three, is a dual
                 arithmetic in which he does not proceed to numbering
                 except to two, and yet all the questions of arithmetic
                 business can easily be entangled to the peril of the
                 mathematician]",
}


bibtype: article
filename: fparith.bib
label: Colson:1726:SAN
author: John Colson, F.R.S.
title: A Short Account of Negativo-Affirmative Arithmetick
journal: j-PHILOS-TRANS-R-SOC-LOND
volume: 34
number: 392--398
pages: 161--173
year: 1726
CODEN: PTRSAV
DOI: https://doi.org/10.1098/rstl.1726.0032
ISSN: 0370-2316 (print), 2053-9207 (electronic) OR 03702316 (print), 20539207 (electronic)
bibdate: Tue Jul 28 14:21:05 2015
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2015.07.28 14:21:05 ???
URL: http://arith22.gforge.inria.fr/slides/s2-ercegovac.pdf
fjournal: Philosophical transactions of the Royal Society of London
acknowledgement: ack-nhfb
journalURL: http://rsta.royalsocietypublishing.org/
rawauthor: John {Colson, F.R.S.}
rawtitle: A Short Account of Negativo-Affirmative Arithmetick
remark:
Early work on signed-digit arithmetic, reported by Milos Ercegovac in a talk at the ARITH'22 conference, Lyon, France, June 2015.

entry:
@Article{Colson:1726:SAN,
  author =       "John {Colson, F.R.S.}",
  title =        "A Short Account of Negativo-Affirmative Arithmetick",
  journal =      j-PHILOS-TRANS-R-SOC-LOND,
  volume =       "34",
  number =       "392--398",
  pages =        "161--173",
  month =        "????",
  year =         "1726",
  CODEN =        "PTRSAV",
  DOI =          "https://doi.org/10.1098/rstl.1726.0032",
  ISSN =         "0370-2316 (print), 2053-9207 (electronic)",
  bibdate =      "Tue Jul 28 14:21:05 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith22.gforge.inria.fr/slides/s2-ercegovac.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Philosophical transactions of the Royal Society of
                 London",
  journal-URL =  "http://rsta.royalsocietypublishing.org/",
  remark =       "Early work on signed-digit arithmetic, reported by
                 Milo{\v{s}} Ercegovac in a talk at the ARITH'22
                 conference, Lyon, France, June 2015.",
}


bibtype: unpublished
filename: fparith.bib
label: Babbage:1837:MPC
author: Charles Babbage
title: On the mathematical powers of the calculating engine
pages: 161--173
month: dec
monthnumber: 12
year: 1837
bibdate: Wed Oct 13 11:09:59 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:09:59 ???
acknowledgement: ack-nhfb
rawauthor: Charles Babbage
rawtitle: On the mathematical powers of the calculating engine
note:
Manuscript held by Museum of the History of Science, Oxford, UK. Reprinted in cite [ 2.1]Randell:1982:ODC.

rawnote:
Manuscript held by Museum of the History of Science, Oxford, UK. Reprinted in \cite[\S 2.1]{Randell:1982:ODC}.

entry:
@Unpublished{Babbage:1837:MPC,
  author =       "Charles Babbage",
  title =        "On the mathematical powers of the calculating engine",
  month =        dec,
  year =         "1837",
  bibdate =      "Wed Oct 13 11:09:59 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Manuscript held by Museum of the History of Science,
                 Oxford, UK. Reprinted in \cite[\S
                 2.1]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Nystrom:1862:PNS
author: John W. (John William) Nystrom
publisher: J. B. Lippincott and Co.
address: Philadelphia, PA, USA
pages: 106
year: 1862
LCCN: QC96 .N95
bibdate: Sat Oct 29 10:28:27 MDT 2016
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2016.10.29 10:28:27 MDT
subject: Weights and measures; Numeration; base-16 arithmetic; hexadecimal arithmetic
acknowledgement: ack-nhfb
authordates: Johan Vilhelm Nystrom (1824--1885)
rawauthor: John W. (John William) Nystrom
title:
Project of a new system of arithmetic, weight, measure and coins, proposed to be called the tonal system, with sixteen to the base

URL:
http://unifoundry.com/tonal/; https://catalog.hathitrust.org/Record/011602816; https://lccn.loc.gov/04025433

remark:
Thanks to Paul Hardy of Unifoundry in San Diego, CA, USA, for information about Nystrom's promotion of hexadecimal arithmetic, and for creating a Web site about Nystrom's tonal system, as well as developing Unicode-compatible fonts to represent the additional digits needed by the system.

rawtitle:
Project of a new system of arithmetic, weight, measure and coins, proposed to be called the tonal system, with sixteen to the base

entry:
@Book{Nystrom:1862:PNS,
  author =       "John W. (John William) Nystrom",
  title =        "Project of a new system of arithmetic, weight, measure
                 and coins, proposed to be called the tonal system, with
                 sixteen to the base",
  publisher =    "J. B. Lippincott and Co.",
  address =      "Philadelphia, PA, USA",
  pages =        "106",
  year =         "1862",
  LCCN =         "QC96 .N95",
  bibdate =      "Sat Oct 29 10:28:27 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://unifoundry.com/tonal/;
                 https://catalog.hathitrust.org/Record/011602816;
                 https://lccn.loc.gov/04025433",
  acknowledgement = ack-nhfb,
  author-dates = "Johan Vilhelm Nystr{\"o}m (1824--1885)",
  remark =       "Thanks to Paul Hardy of Unifoundry in San Diego, CA,
                 USA, for information about Nystrom's promotion of
                 hexadecimal arithmetic, and for creating a Web site
                 about Nystrom's tonal system, as well as developing
                 Unicode-compatible fonts to represent the additional
                 digits needed by the system.",
  subject =      "Weights and measures; Numeration; base-16 arithmetic;
                 hexadecimal arithmetic",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1875:AOM
author: Anonymous
title: The Arithmetical Operations of Multiplication and Division
journal: j-SCI-AMER
volume: 32
number: 3
pages: 41--42
day: 16
month: jan
monthnumber: 1
year: 1875
CODEN: SCAMAC
DOI: https://doi.org/10.1038/scientificamerican01161875-41
ISSN: 0036-8733 (print), 1946-7087 (electronic) OR 00368733 (print), 19467087 (electronic)
ISSNL: 0036-8733 OR 00368733
bibdate: Fri May 17 10:29:24 MDT 2013
bibtimestamp: 2013.05.17 10:29:24 MDT
URL: http://www.nature.com/scientificamerican/journal/v32/n3/pdf/scientificamerican01161875-41.pdf
fjournal: Scientific American
acknowledgement: ack-nhfb
journalURL: http://www.nature.com/scientificamerican
rawauthor: Anonymous
rawtitle: The Arithmetical Operations of Multiplication and Division
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sciam1870.bib

entry:
@Article{Anonymous:1875:AOM,
  author =       "Anonymous",
  title =        "The Arithmetical Operations of Multiplication and
                 Division",
  journal =      j-SCI-AMER,
  volume =       "32",
  number =       "3",
  pages =        "41--42",
  day =          "16",
  month =        jan,
  year =         "1875",
  CODEN =        "SCAMAC",
  DOI =          "https://doi.org/10.1038/scientificamerican01161875-41",
  ISSN =         "0036-8733 (print), 1946-7087 (electronic)",
  ISSN-L =       "0036-8733",
  bibdate =      "Fri May 17 10:29:24 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sciam1870.bib",
  URL =          "http://www.nature.com/scientificamerican/journal/v32/n3/pdf/scientificamerican01161875-41.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific American",
  journal-URL =  "http://www.nature.com/scientificamerican",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1879:TRA
author: Anonymous
title: Three Rules for Abbreviating Multiplication
journal: j-SCI-AMER
volume: 41
number: 12
pages: 184--184
day: 20
month: sep
monthnumber: 9
year: 1879
CODEN: SCAMAC
DOI: https://doi.org/10.1038/scientificamerican09201879-184
ISSN: 0036-8733 (print), 1946-7087 (electronic) OR 00368733 (print), 19467087 (electronic)
ISSNL: 0036-8733 OR 00368733
bibdate: Fri May 17 10:36:54 MDT 2013
bibtimestamp: 2013.05.17 10:36:54 MDT
URL: http://www.nature.com/scientificamerican/journal/v41/n12/pdf/scientificamerican09201879-184.pdf
fjournal: Scientific American
acknowledgement: ack-nhfb
journalURL: http://www.nature.com/scientificamerican
rawauthor: Anonymous
rawtitle: Three Rules for Abbreviating Multiplication
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sciam1870.bib

entry:
@Article{Anonymous:1879:TRA,
  author =       "Anonymous",
  title =        "Three Rules for Abbreviating Multiplication",
  journal =      j-SCI-AMER,
  volume =       "41",
  number =       "12",
  pages =        "184--184",
  day =          "20",
  month =        sep,
  year =         "1879",
  CODEN =        "SCAMAC",
  DOI =          "https://doi.org/10.1038/scientificamerican09201879-184",
  ISSN =         "0036-8733 (print), 1946-7087 (electronic)",
  ISSN-L =       "0036-8733",
  bibdate =      "Fri May 17 10:36:54 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sciam1870.bib",
  URL =          "http://www.nature.com/scientificamerican/journal/v41/n12/pdf/scientificamerican09201879-184.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific American",
  journal-URL =  "http://www.nature.com/scientificamerican",
}


bibtype: article
filename: fparith.bib
label: Newcomb:1881:NFU
author: Simon Newcomb
title: Note on the frequency of use of the different digits in natural numbers
journal: j-AM-J-MATH
volume: 4
number: 1/4
pages: 39--40
year: 1881
CODEN: AJMAAN
ISSN: 0002-9327 (print), 1080-6377 (electronic) OR 00029327 (print), 10806377 (electronic)
ISSNL: 0002-9327 OR 00029327
bibdate: Thu Feb 15 16:35:24 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.02.15 16:35:24 ???
URL: http://links.jstor.org/sici?sici=0002-9327%281881%294%3A1%2F4%3C39%3ANOTFOU%3E2.0.CO%3B2-K
fjournal: American Journal of Mathematics
keywords: Benford's Law; Law of Anomalous Numbers; Zipf's Law
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journal/amerjmath
rawauthor: Simon Newcomb
rawtitle: Note on the frequency of use of the different digits in natural numbers
abstract:
That the ten digits do not occur with equal frequency must be evident to any one making much use of logarithmic tables, and noticing how much faster the first pages wear out than the last ones. The first significant figure is oftener 1 than any other digit, and the frequency diminishes up to 9.

remark:
From p. 40: ``The law of probability of the occurrence of numbers is such that all mantissas of their logarithms are equally probable.''

rawabstract:
That the ten digits do not occur with equal frequency must be evident to any one making much use of logarithmic tables, and noticing how much faster the first pages wear out than the last ones. The first significant figure is oftener 1 than any other digit, and the frequency diminishes up to 9.

entry:
@Article{Newcomb:1881:NFU,
  author =       "Simon Newcomb",
  title =        "Note on the frequency of use of the different digits
                 in natural numbers",
  journal =      j-AM-J-MATH,
  volume =       "4",
  number =       "1/4",
  pages =        "39--40",
  year =         "1881",
  CODEN =        "AJMAAN",
  ISSN =         "0002-9327 (print), 1080-6377 (electronic)",
  ISSN-L =       "0002-9327",
  bibdate =      "Thu Feb 15 16:35:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://links.jstor.org/sici?sici=0002-9327%281881%294%3A1%2F4%3C39%3ANOTFOU%3E2.0.CO%3B2-K",
  abstract =     "That the ten digits do not occur with equal frequency
                 must be evident to any one making much use of
                 logarithmic tables, and noticing how much faster the
                 first pages wear out than the last ones. The first
                 significant figure is oftener 1 than any other digit,
                 and the frequency diminishes up to 9.",
  acknowledgement = ack-nhfb,
  fjournal =     "American Journal of Mathematics",
  journal-URL =  "https://www.jstor.org/journal/amerjmath",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "From p. 40: ``The law of probability of the occurrence
                 of numbers is such that all mantissas of their
                 logarithms are equally probable.''",
}


bibtype: article
filename: fparith.bib
label: Holman:1888:DPM
author: Silas W. Holman
title: Discussion of the precision of measurement
journal: Technol. Q.
volume: 1
pages: 194--207
year: 1888
bibdate: Mon May 21 17:12:03 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2018.05.21 17:12:03 ???
remark: Cited in cite [ref. 14]Carter:2013:ESF.
acknowledgement: ack-nhfb
rawauthor: Silas W. Holman
rawtitle: Discussion of the precision of measurement
entry:
@Article{Holman:1888:DPM,
  author =       "Silas W. Holman",
  title =        "Discussion of the precision of measurement",
  journal =      "Technol. Q.",
  volume =       "1",
  number =       "??",
  pages =        "194--207",
  month =        "????",
  year =         "1888",
  bibdate =      "Mon May 21 17:12:03 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite[ref. 14]{Carter:2013:ESF}.",
}


bibtype: book
filename: fparith.bib
label: Holman:1892:DPM
author: Silas W. Holman
publisher: Ferris Brothers Printers
address: New York, NY, USA
year: 1892
bibdate: Mon May 21 17:14:39 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2018.05.21 17:14:39 ???
remark: Cited in cite [ref. 15]Carter:2013:ESF.
acknowledgement: ack-nhfb
rawauthor: Silas W. Holman
title:
Discussion of the Precision of Measurements: With Examples Taken Mainly From Physics And Electrical Engineering

rawtitle:
Discussion of the Precision of Measurements: With Examples Taken Mainly From Physics And Electrical Engineering

entry:
@Book{Holman:1892:DPM,
  author =       "Silas W. Holman",
  title =        "Discussion of the Precision of Measurements: With
                 Examples Taken Mainly From Physics And Electrical
                 Engineering",
  publisher =    "Ferris Brothers Printers",
  address =      "New York, NY, USA",
  pages =        "????",
  year =         "1892",
  bibdate =      "Mon May 21 17:14:39 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite[ref. 15]{Carter:2013:ESF}.",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1893:IDb
author: Anonymous
title: The Instantaneous Divider
journal: j-SCI-AMER
volume: 68
number: 21
pages: 325--325
day: 27
month: may
monthnumber: 5
year: 1893
CODEN: SCAMAC
DOI: https://doi.org/10.1038/scientificamerican05271893-325a
ISSN: 0036-8733 (print), 1946-7087 (electronic) OR 00368733 (print), 19467087 (electronic)
ISSNL: 0036-8733 OR 00368733
bibdate: Wed May 22 19:04:00 MDT 2013
bibtimestamp: 2013.05.22 19:04:00 MDT
URL: http://www.nature.com/scientificamerican/journal/v68/n21/pdf/scientificamerican05271893-325a.pdf
fjournal: Scientific American
acknowledgement: ack-nhfb
journalURL: http://www.nature.com/scientificamerican
rawauthor: Anonymous
rawtitle: The Instantaneous Divider
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sciam1890.bib

entry:
@Article{Anonymous:1893:IDb,
  author =       "Anonymous",
  title =        "The Instantaneous Divider",
  journal =      j-SCI-AMER,
  volume =       "68",
  number =       "21",
  pages =        "325--325",
  day =          "27",
  month =        may,
  year =         "1893",
  CODEN =        "SCAMAC",
  DOI =          "https://doi.org/10.1038/scientificamerican05271893-325a",
  ISSN =         "0036-8733 (print), 1946-7087 (electronic)",
  ISSN-L =       "0036-8733",
  bibdate =      "Wed May 22 19:04:00 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sciam1890.bib",
  URL =          "http://www.nature.com/scientificamerican/journal/v68/n21/pdf/scientificamerican05271893-325a.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific American",
  journal-URL =  "http://www.nature.com/scientificamerican",
}


bibtype: article
filename: fparith.bib
label: Felt:1893:MA
author: Dorr E. Felt
title: Mechanical Arithmetic
journal: j-SCI-AMER
volume: 69
number: 20
pages: 309--310
day: 11
month: nov
monthnumber: 11
year: 1893
CODEN: SCAMAC
DOI: https://doi.org/10.1038/scientificamerican11111893-309b
ISSN: 0036-8733 (print), 1946-7087 (electronic) OR 00368733 (print), 19467087 (electronic)
ISSNL: 0036-8733 OR 00368733
bibdate: Wed May 22 19:04:25 MDT 2013
bibtimestamp: 2013.05.22 19:04:25 MDT
URL: http://www.nature.com/scientificamerican/journal/v69/n20/pdf/scientificamerican11111893-309b.pdf
fjournal: Scientific American
acknowledgement: ack-nhfb
journalURL: http://www.nature.com/scientificamerican
rawauthor: Dorr E. Felt
rawtitle: Mechanical Arithmetic
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sciam1890.bib

entry:
@Article{Felt:1893:MA,
  author =       "Dorr E. Felt",
  title =        "Mechanical Arithmetic",
  journal =      j-SCI-AMER,
  volume =       "69",
  number =       "20",
  pages =        "309--310",
  day =          "11",
  month =        nov,
  year =         "1893",
  CODEN =        "SCAMAC",
  DOI =          "https://doi.org/10.1038/scientificamerican11111893-309b",
  ISSN =         "0036-8733 (print), 1946-7087 (electronic)",
  ISSN-L =       "0036-8733",
  bibdate =      "Wed May 22 19:04:25 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sciam1890.bib",
  URL =          "http://www.nature.com/scientificamerican/journal/v69/n20/pdf/scientificamerican11111893-309b.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific American",
  journal-URL =  "http://www.nature.com/scientificamerican",
}


bibtype: article
filename: fparith.bib
label: Aley:1897:DES
author: Robert J. Aley
title: A Device for Extracting the Square Root of Certain Surd Quantities
journal: j-AMER-MATH-MONTHLY
volume: 4
number: 8/9
pages: 204--208
month: aug
monthnumber: 8
year: 1897
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Jun 28 12:37:08 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1999.06.28 12:37:08 MDT
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: Robert J. Aley
rawtitle: A Device for Extracting the Square Root of Certain Surd Quantities
entry:
@Article{Aley:1897:DES,
  author =       "Robert J. Aley",
  title =        "A Device for Extracting the Square Root of Certain
                 Surd Quantities",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "4",
  number =       "8/9",
  pages =        "204--208",
  month =        aug # "\slash " # sep,
  year =         "1897",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:37:08 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: article
filename: fparith.bib
label: Anonymous:1898:OFA
author: Anonymous
title: Our Fingers as an Aid in Multiplication
journal: j-SCI-AMER
volume: 79
number: 17
pages: 265--266
day: 22
month: oct
monthnumber: 10
year: 1898
CODEN: SCAMAC
DOI: https://doi.org/10.1038/scientificamerican10221898-265
ISSN: 0036-8733 (print), 1946-7087 (electronic) OR 00368733 (print), 19467087 (electronic)
ISSNL: 0036-8733 OR 00368733
bibdate: Wed May 22 19:08:57 MDT 2013
bibtimestamp: 2013.05.22 19:08:57 MDT
URL: http://www.nature.com/scientificamerican/journal/v79/n17/pdf/scientificamerican10221898-265.pdf
fjournal: Scientific American
acknowledgement: ack-nhfb
journalURL: http://www.nature.com/scientificamerican
rawauthor: Anonymous
rawtitle: Our Fingers as an Aid in Multiplication
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sciam1890.bib

entry:
@Article{Anonymous:1898:OFA,
  author =       "Anonymous",
  title =        "Our Fingers as an Aid in Multiplication",
  journal =      j-SCI-AMER,
  volume =       "79",
  number =       "17",
  pages =        "265--266",
  day =          "22",
  month =        oct,
  year =         "1898",
  CODEN =        "SCAMAC",
  DOI =          "https://doi.org/10.1038/scientificamerican10221898-265",
  ISSN =         "0036-8733 (print), 1946-7087 (electronic)",
  ISSN-L =       "0036-8733",
  bibdate =      "Wed May 22 19:08:57 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sciam1890.bib",
  URL =          "http://www.nature.com/scientificamerican/journal/v79/n17/pdf/scientificamerican10221898-265.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific American",
  journal-URL =  "http://www.nature.com/scientificamerican",
}


bibtype: article
filename: fparith.bib
label: Ludgate:1909:PAM
author: P. E. Ludgate
title: On a proposed analytical machine
journal: j-SCI-PROC-ROY-DUBLIN-SOC
volume: 12
number: 9
pages: 77--91
year: 1909
CODEN: SPRDAP
ISSN: 0371-2303 OR 03712303
bibdate: Wed Oct 13 11:14:08 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:14:08 ???
note: Reprinted in cite [ 2.4]Randell:1982:ODC.
fjournal: Scientific proceedings of the Royal Dublin Society
acknowledgement: ack-nhfb
rawauthor: P. E. Ludgate
rawnote: Reprinted in \cite[\S 2.4]{Randell:1982:ODC}.
rawtitle: On a proposed analytical machine
entry:
@Article{Ludgate:1909:PAM,
  author =       "P. E. Ludgate",
  title =        "On a proposed analytical machine",
  journal =      j-SCI-PROC-ROY-DUBLIN-SOC,
  volume =       "12",
  number =       "9",
  pages =        "77--91",
  year =         "1909",
  CODEN =        "SPRDAP",
  ISSN =         "0371-2303",
  bibdate =      "Wed Oct 13 11:14:08 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 2.4]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific proceedings of the Royal Dublin Society",
}


bibtype: article
filename: fparith.bib
label: Babbage:1910:BBA
author: H. P. Babbage
title: Babbage: Babbage's analytical engine
journal: j-MONTHLY-NOT-ROY-ASTRON-SOC
volume: 70
pages: 517--526, 645
year: 1910
CODEN: MNRAA4
ISSN: 0035-8711 (print), 1365-2966 (electronic) OR 00358711 (print), 13652966 (electronic)
ISSNL: 0035-8711 OR 00358711
bibdate: Wed Oct 13 11:12:08 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:12:08 ???
note: Reprinted in cite [ 2.3]Randell:1982:ODC.
fjournal: Monthly Notices of the Royal Astronomical Society
acknowledgement: ack-nhfb
journalURL: https://academic.oup.com/mnras
rawauthor: H. P. Babbage
rawnote: Reprinted in \cite[\S 2.3]{Randell:1982:ODC}.
rawtitle: {Babbage}: {Babbage}'s analytical engine
entry:
@Article{Babbage:1910:BBA,
  author =       "H. P. Babbage",
  title =        "{Babbage}: {Babbage}'s analytical engine",
  journal =      j-MONTHLY-NOT-ROY-ASTRON-SOC,
  volume =       "70",
  number =       "??",
  pages =        "517--526, 645",
  year =         "1910",
  CODEN =        "MNRAA4",
  ISSN =         "0035-8711 (print), 1365-2966 (electronic)",
  ISSN-L =       "0035-8711",
  bibdate =      "Wed Oct 13 11:12:08 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 2.3]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Monthly Notices of the Royal Astronomical Society",
  journal-URL =  "https://academic.oup.com/mnras",
}


bibtype: article
filename: fparith.bib
label: TorresyQuevedo:1915:EAS
author: L. Torres y Quevedo
journal: j-REV-GEN-SCI-PURES-APPL
pages: 601--611
day: 15
month: nov
monthnumber: 11
year: 1915
ISSN: 0370-7431 OR 03707431
bibdate: Wed Oct 13 11:15:08 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:15:08 ???
note: Reprinted in cite [ 2.5]Randell:1982:ODC. Translated by Mr. R. Basu.
fjournal: Revue Generale des Sciences Pures et Appliquees
language: French
acknowledgement: ack-nhfb
rawauthor: L. {Torres y Quevedo}
rawnote: Reprinted in \cite[\S 2.5]{Randell:1982:ODC}. Translated by Mr. R. Basu.
title:
Essais sur l'automatique. Sa definition. Etendue theorique de ses applications (French) [Essays on automation. Its definition. Theoretical extent of its applications]

rawtitle:
Essais sur l'automatique. Sa definition. {{\'E}}tendue th{\'e}orique de ses applications ({French}) [{Essays} on automation. {Its} definition. {Theoretical} extent of its applications]

entry:
@Article{TorresyQuevedo:1915:EAS,
  author =       "L. {Torres y Quevedo}",
  title =        "Essais sur l'automatique. Sa definition. {{\'E}}tendue
                 th{\'e}orique de ses applications ({French}) [{Essays}
                 on automation. {Its} definition. {Theoretical} extent
                 of its applications]",
  journal =      j-REV-GEN-SCI-PURES-APPL,
  volume =       "??",
  number =       "??",
  pages =        "601--611",
  day =          "15",
  month =        nov,
  year =         "1915",
  ISSN =         "0370-7431",
  bibdate =      "Wed Oct 13 11:15:08 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 2.5]{Randell:1982:ODC}.
                 Translated by Mr. R. Basu.",
  acknowledgement = ack-nhfb,
  fjournal =     "Revue G{\'e}n{\'e}rale des Sciences Pures et
                 Appliqu{\'e}es",
  language =     "French",
}


bibtype: article
filename: fparith.bib
label: Barrow:1924:QDD
author: D. F. Barrow
title: Questions and Discussions: Discussions: On Taking Square Roots of Integers
journal: j-AMER-MATH-MONTHLY
volume: 31
number: 10
pages: 482--484
month: dec
monthnumber: 12
year: 1924
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Jun 28 12:37:29 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1999.06.28 12:37:29 MDT
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: D. F. Barrow
rawtitle: Questions and Discussions: Discussions: On Taking Square Roots of Integers
entry:
@Article{Barrow:1924:QDD,
  author =       "D. F. Barrow",
  title =        "Questions and Discussions: Discussions: On Taking
                 Square Roots of Integers",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "31",
  number =       "10",
  pages =        "482--484",
  month =        dec,
  year =         "1924",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:37:29 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: article
filename: fparith.bib
label: Smith:1924:FPA
author: David Eugene Smith
title: The First Printed Arithmetic (Treviso, 1478)
journal: j-ISIS
volume: 6
number: 3
pages: 311--331
year: 1924
CODEN: ISISA4
ISSN: 0021-1753 (print), 1545-6994 (electronic) OR 00211753 (print), 15456994 (electronic)
ISSNL: 0021-1753 OR 00211753
bibdate: Tue Jul 30 21:57:26 MDT 2013
bibtimestamp: 2013.07.30 21:57:26 MDT
URL: http://www.jstor.org/stable/224315
fjournal: Isis
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journal/isis
rawauthor: David Eugene Smith
rawtitle: The First Printed Arithmetic ({Treviso}, 1478)
bibsource:
http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i211087; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/isis1920.bib

entry:
@Article{Smith:1924:FPA,
  author =       "David Eugene Smith",
  title =        "The First Printed Arithmetic ({Treviso}, 1478)",
  journal =      j-ISIS,
  volume =       "6",
  number =       "3",
  pages =        "311--331",
  month =        "????",
  year =         "1924",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:57:26 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i211087;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1920.bib",
  URL =          "http://www.jstor.org/stable/224315",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}


bibtype: book
filename: fparith.bib
label: Karpinski:1925:HA
author: Louis Charles Karpinski
title: The History of Arithmetic
publisher: Rand McNally & Company
address: New York, NY, USA
pages: xi + 200
year: 1925
bibdate: Fri Nov 28 18:09:05 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 18:09:05 ???
acknowledgement: ack-mfc
rawauthor: Louis Charles Karpinski
rawtitle: The History of Arithmetic
entry:
@Book{Karpinski:1925:HA,
  author =       "Louis Charles Karpinski",
  title =        "The History of Arithmetic",
  publisher =    "Rand McNally \& Company",
  address =      "New York, NY, USA",
  pages =        "xi + 200",
  year =         "1925",
  bibdate =      "Fri Nov 28 18:09:05 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Cajori:1926:BRB
author: Florian Cajori
title: Book Review: booktitle The History of Arithmetic by Louis Charles Karpinski
journal: j-ISIS
volume: 8
number: 1
pages: 231--232
month: feb
monthnumber: 2
year: 1926
CODEN: ISISA4
ISSN: 0021-1753 (print), 1545-6994 (electronic) OR 00211753 (print), 15456994 (electronic)
ISSNL: 0021-1753 OR 00211753
bibdate: Tue Jul 30 21:57:36 MDT 2013
bibtimestamp: 2013.07.30 21:57:36 MDT
URL: http://www.jstor.org/stable/223706
fjournal: Isis
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journal/isis
rawauthor: Florian Cajori
rawtitle: Book Review: {{\booktitle{The History of Arithmetic}} by Louis Charles Karpinski}
bibsource:
http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i211094; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/isis1920.bib

entry:
@Article{Cajori:1926:BRB,
  author =       "Florian Cajori",
  title =        "Book Review: {{\booktitle{The History of Arithmetic}}
                 by Louis Charles Karpinski}",
  journal =      j-ISIS,
  volume =       "8",
  number =       "1",
  pages =        "231--232",
  month =        feb,
  year =         "1926",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:57:36 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i211094;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1920.bib",
  URL =          "http://www.jstor.org/stable/223706",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}


bibtype: article
filename: fparith.bib
label: Smith:1926:FGC
author: David Eugene Smith
title: The First Great Commercial Arithmetic
journal: j-ISIS
volume: 8
number: 1
pages: 41--49
month: feb
monthnumber: 2
year: 1926
CODEN: ISISA4
ISSN: 0021-1753 (print), 1545-6994 (electronic) OR 00211753 (print), 15456994 (electronic)
ISSNL: 0021-1753 OR 00211753
bibdate: Tue Jul 30 21:57:36 MDT 2013
bibtimestamp: 2013.07.30 21:57:36 MDT
URL: http://www.jstor.org/stable/223673
fjournal: Isis
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journal/isis
rawauthor: David Eugene Smith
rawtitle: The First Great Commercial Arithmetic
bibsource:
http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i211094; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/isis1920.bib

entry:
@Article{Smith:1926:FGC,
  author =       "David Eugene Smith",
  title =        "The First Great Commercial Arithmetic",
  journal =      j-ISIS,
  volume =       "8",
  number =       "1",
  pages =        "41--49",
  month =        feb,
  year =         "1926",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:57:36 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i211094;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1920.bib",
  URL =          "http://www.jstor.org/stable/223673",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}


bibtype: article
filename: fparith.bib
label: Cajori:1927:EAP
author: Florian Cajori
title: The Earliest Arithmetic Published in America
journal: j-ISIS
volume: 9
number: 3
pages: 391--401
month: dec
monthnumber: 12
year: 1927
CODEN: ISISA4
ISSN: 0021-1753 (print), 1545-6994 (electronic) OR 00211753 (print), 15456994 (electronic)
ISSNL: 0021-1753 OR 00211753
bibdate: Tue Jul 30 21:57:45 MDT 2013
bibtimestamp: 2013.07.30 21:57:45 MDT
URL: http://www.jstor.org/stable/330806
fjournal: Isis
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journal/isis
rawauthor: Florian Cajori
rawtitle: The Earliest Arithmetic Published in {America}
bibsource:
http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i214411; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/isis1920.bib

entry:
@Article{Cajori:1927:EAP,
  author =       "Florian Cajori",
  title =        "The Earliest Arithmetic Published in {America}",
  journal =      j-ISIS,
  volume =       "9",
  number =       "3",
  pages =        "391--401",
  month =        dec,
  year =         "1927",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:57:45 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
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  URL =          "http://www.jstor.org/stable/330806",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}


bibtype: article
filename: fparith.bib
label: J:1930:RPRb
author: R. A. J.
title: Recent Publications: Reviews: em Standard Table of Square Roots, by L. M. Milne-Thomson
journal: j-AMER-MATH-MONTHLY
volume: 37
number: 6
pages: 314--314
month: jun
monthnumber: 6
year: 1930
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Jun 28 12:35:55 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1999.06.28 12:35:55 MDT
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: R. A. J.
rawtitle: Recent Publications: Reviews: {{\em Standard Table of Square Roots}}, by {L. M. Milne-Thomson}
entry:
@Article{J:1930:RPRb,
  author =       "R. A. J.",
  title =        "Recent Publications: Reviews: {{\em Standard Table of
                 Square Roots}}, by {L. M. Milne-Thomson}",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "37",
  number =       "6",
  pages =        "314--314",
  month =        jun # "\slash " # jul,
  year =         "1930",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:35:55 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: article
filename: fparith.bib
label: Laughlin:1930:LND
author: Harry H. Laughlin
title: Large-Number Division by Calculating Machine
journal: j-AMER-MATH-MONTHLY
volume: 37
number: 6
pages: 287--293
month: jun
monthnumber: 6
year: 1930
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Jun 28 12:35:55 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1999.06.28 12:35:55 MDT
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: Harry H. Laughlin
rawtitle: Large-Number Division by Calculating Machine
entry:
@Article{Laughlin:1930:LND,
  author =       "Harry H. Laughlin",
  title =        "Large-Number Division by Calculating Machine",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "37",
  number =       "6",
  pages =        "287--293",
  month =        jun # "\slash " # jul,
  year =         "1930",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:35:55 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: article
filename: fparith.bib
label: Garver:1932:QDNb
author: Raymond Garver
title: Questions, Discussions, and Notes: a Square Root Method and Continued Fractions
journal: j-AMER-MATH-MONTHLY
volume: 39
number: 9
pages: 533--535
month: nov
monthnumber: 11
year: 1932
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Jun 28 12:36:47 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1999.06.28 12:36:47 MDT
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: Raymond Garver
rawtitle: Questions, Discussions, and Notes: a Square Root Method and Continued Fractions
entry:
@Article{Garver:1932:QDNb,
  author =       "Raymond Garver",
  title =        "Questions, Discussions, and Notes: a Square Root
                 Method and Continued Fractions",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "39",
  number =       "9",
  pages =        "533--535",
  month =        nov,
  year =         "1932",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:36:47 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: article
filename: fparith.bib
label: Polachek:1932:MMU
author: H. Polachek
title: A method of multiplication used by Saadia Gaon in the 10th century
journal: j-SCRIPTA-MATH
volume: 1
pages: 245--246
year: 1932
ISSN: 0036-9713 OR 00369713
bibdate: Thu Oct 26 11:15:25 2023
bibtimestamp: 2023.10.26 11:15:25 ???
acknowledgement: ack-nhfb
ajournal: Scripta Math.
rawauthor: H. Polachek
rawtitle: A method of multiplication used by {Saadia Gaon} in the 10th century
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/scripta-math.bib

fjournal:
Scripta Mathematica: A Quarterly Journal Devoted to the Philosophy, History, and Expository Treatment of Mathematics

entry:
@Article{Polachek:1932:MMU,
  author =       "H. Polachek",
  title =        "A method of multiplication used by {Saadia Gaon} in
                 the 10th century",
  journal =      j-SCRIPTA-MATH,
  volume =       "1",
  number =       "??",
  pages =        "245--246",
  month =        "????",
  year =         "1932",
  ISSN =         "0036-9713",
  bibdate =      "Thu Oct 26 11:15:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Scripta Math.",
  fjournal =     "Scripta Mathematica: A Quarterly Journal Devoted to
                 the Philosophy, History, and Expository Treatment of
                 Mathematics",
  jfm =          "59.0019.03",
  ZBmath =       "2542288",
}


bibtype: article
filename: fparith.bib
label: Simons:1932:IGA
author: T. E. Simons
title: Isaac Greenwood's arithmetic
journal: j-SCRIPTA-MATH
volume: 1
pages: 262--264
year: 1932
ISSN: 0036-9713 OR 00369713
bibdate: Thu Oct 26 11:15:25 2023
bibtimestamp: 2023.10.26 11:15:25 ???
acknowledgement: ack-nhfb
ajournal: Scripta Math.
rawauthor: T. E. Simons
rawtitle: {Isaac Greenwood}'s arithmetic
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/scripta-math.bib

fjournal:
Scripta Mathematica: A Quarterly Journal Devoted to the Philosophy, History, and Expository Treatment of Mathematics

entry:
@Article{Simons:1932:IGA,
  author =       "T. E. Simons",
  title =        "{Isaac Greenwood}'s arithmetic",
  journal =      j-SCRIPTA-MATH,
  volume =       "1",
  number =       "??",
  pages =        "262--264",
  month =        "????",
  year =         "1932",
  ISSN =         "0036-9713",
  bibdate =      "Thu Oct 26 11:15:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Scripta Math.",
  fjournal =     "Scripta Mathematica: A Quarterly Journal Devoted to
                 the Philosophy, History, and Expository Treatment of
                 Mathematics",
  jfm =          "59.0026.02",
  ZBmath =       "2542316",
}


bibtype: book
filename: fparith.bib
label: Couffignal:1933:MCL
author: L. Couffignal
publisher: Gauthier-Villars
address: Paris, France
pages: 262--264
year: 1933
bibdate: Wed Oct 13 11:19:11 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:19:11 ???
note: Extracts reprinted in cite [ 3.2]Randell:1982:ODC. Translated by Mr. R. Basu.
language: French
acknowledgement: ack-nhfb
rawauthor: L. Couffignal
rawnote: Extracts reprinted in \cite[\S 3.2]{Randell:1982:ODC}. Translated by Mr. R. Basu.
title:
Les machines a calculer, leurs principes, leur evolution. (French) [Calculating machines, their principles, their evolution]

rawtitle:
Les machines {\`a} calculer, leurs principes, leur {\'e}volution. ({French}) [{Calculating} machines, their principles, their evolution]

entry:
@Book{Couffignal:1933:MCL,
  author =       "L. Couffignal",
  title =        "Les machines {\`a} calculer, leurs principes, leur
                 {\'e}volution. ({French}) [{Calculating} machines,
                 their principles, their evolution]",
  publisher =    "Gauthier-Villars",
  address =      "Paris, France",
  year =         "1933",
  bibdate =      "Wed Oct 13 11:19:11 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Extracts reprinted in \cite[\S 3.2]{Randell:1982:ODC}.
                 Translated by Mr. R. Basu.",
  acknowledgement = ack-nhfb,
  language =     "French",
}


bibtype: article
filename: fparith.bib
label: Kalbfell:1934:QDN
author: D. C. Kalbfell
title: Questions, Discussions and Notes: On a Method for Calculating Square Roots
journal: j-AMER-MATH-MONTHLY
volume: 41
number: 8
pages: 504--506
month: oct
monthnumber: 10
year: 1934
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Jun 28 12:37:31 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1999.06.28 12:37:31 MDT
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: D. C. Kalbfell
rawtitle: Questions, Discussions and Notes: On a Method for Calculating Square Roots
entry:
@Article{Kalbfell:1934:QDN,
  author =       "D. C. Kalbfell",
  title =        "Questions, Discussions and Notes: On a Method for
                 Calculating Square Roots",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "41",
  number =       "8",
  pages =        "504--506",
  month =        oct,
  year =         "1934",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:37:31 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: article
filename: fparith.bib
label: Simons:1935:EEC
author: L. G. Simons
title: An early eighteenth century American readyreckoner
journal: j-SCRIPTA-MATH
volume: 3
pages: 94--96
year: 1935
ISSN: 0036-9713 OR 00369713
bibdate: Thu Oct 26 11:15:25 2023
bibtimestamp: 2023.10.26 11:15:25 ???
acknowledgement: ack-nhfb
ajournal: Scripta Math.
rawauthor: L. G. Simons
rawtitle: An early eighteenth century {American} readyreckoner
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/scripta-math.bib

fjournal:
Scripta Mathematica: A Quarterly Journal Devoted to the Philosophy, History, and Expository Treatment of Mathematics

entry:
@Article{Simons:1935:EEC,
  author =       "L. G. Simons",
  title =        "An early eighteenth century {American} readyreckoner",
  journal =      j-SCRIPTA-MATH,
  volume =       "3",
  number =       "??",
  pages =        "94--96",
  month =        "????",
  year =         "1935",
  ISSN =         "0036-9713",
  bibdate =      "Thu Oct 26 11:15:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Scripta Math.",
  fjournal =     "Scripta Mathematica: A Quarterly Journal Devoted to
                 the Philosophy, History, and Expository Treatment of
                 Mathematics",
  jfm =          "61.0020.03",
  ZBmath =       "2531128",
}


bibtype: article
filename: fparith.bib
label: Calvert:1936:DDS
author: H. R. Calvert
title: Decimal Division of Scales before the Metric System
journal: j-ISIS
volume: 25
number: 2
pages: 433--436
month: sep
monthnumber: 9
year: 1936
CODEN: ISISA4
ISSN: 0021-1753 (print), 1545-6994 (electronic) OR 00211753 (print), 15456994 (electronic)
ISSNL: 0021-1753 OR 00211753
bibdate: Tue Jul 30 21:21:25 MDT 2013
bibtimestamp: 2013.07.30 21:21:25 MDT
URL: http://www.jstor.org/stable/225380
fjournal: Isis
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journal/isis
rawauthor: H. R. Calvert
rawtitle: Decimal Division of Scales before the Metric System
bibsource:
http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i211115; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/isis1930.bib

entry:
@Article{Calvert:1936:DDS,
  author =       "H. R. Calvert",
  title =        "Decimal Division of Scales before the Metric System",
  journal =      j-ISIS,
  volume =       "25",
  number =       "2",
  pages =        "433--436",
  month =        sep,
  year =         "1936",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:21:25 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i211115;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1930.bib",
  URL =          "http://www.jstor.org/stable/225380",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}


bibtype: book
filename: fparith.bib
label: LeVita:1936:ALI
author: Maurice H. Le Vita
title: An Arithmetic of Life Insurance
publisher: Life Office Management Association
address: New York
pages: xii + 132
year: 1936
LCCN: HG8781 .L43
bibdate: Sat Aug 12 14:42:20 MDT 2023
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.08.12 14:42:20 MDT
acknowledgement: ack-nhfb
rawauthor: Maurice H. {Le Vita}
rawtitle: An Arithmetic of Life Insurance
URL:
http://hdl.handle.net/2027/mdp.39015017290688; https://babel.hathitrust.org/cgi/pt?id=mdp.39015017290688

abstract:
We have determined this item to be in the public domain according to US copyright law through information in the bibliographic record and/or US copyright renewal records. The digital version is available for all educational uses worldwide. Please contact HathiTrust staff at hathitrust-help <at> umich.edu with any questions about this item. Life insurance--Mathematics. (LCCN)36034103. (OCoLC)ocm03161649. HG8781 .L43. HG 8781 .L66. Http://hdl.handle.net/2027/mdp.39015017290688.

remark:
While not about computer arithmetic, this book is about practical applications of arithmetic in the life insurance industry. It considers compound interest calculations, present values of financial instruments, mortality tables, insurance premiums, bond returns, and so on. In Table 1, which shows the growth of an investment at 3 percent over 10 years, the author [amusingly] comments ``Mathematicians have already worked out the multiplications and have incorporated them into a table. With the use of this table, the result can be obtained by a single multiplication.''. Although the MARC record indicates the book is in the public domain, the URL only permits download of a single page at a time, although it is possible to page through the book.

TOC:
Preface / vii Index to Tables / xi Notes on the Solution of Problems / xii I. Interest and Discount / 1 Interest Discount Examples Observations Problems II. The Mortality Table and Easy Problems in Rate Calculation at Age 90 / 6 Natural or Net One-Year Term Premium Net One-Year Pure Endowment Net Single Premium Whole Life Fundamental Principle Observations Problems III. Single Premium Contracts --- Age 35 / 14 Mortality Table (Net) Single Premium 10-Year Term (Net) Single Premium 10-Year Pure Endowment (Net) Single Premium 10-Year Endowment (Net) Single Premium Whole Life (Net) Single Premium 10-Year Temporary Annuity (Net) Single Premium Life Annuity IV. Development of Net Annual Premiums / 22 Extension of Use of Discount (Net) Annual Premium, Whole Life Policy (Net) Annual Premium, 10-Payment Life (Net) Annual Premium, 10-Year Term (Net) Annual Premium, 10-Year Endowment The ``Practical' and `More Exact' Premium Alternative Method of Obtaining Net Annual Premiums Problems V. More About Premiums / 30 The Yearly Renewable Term Policy Loading the Premium Partial or Instalment Premiums Problems VI. Net Level Premium Reserves / 34 10-Year Term Policy 10-Year Endowment Policy Whole Life Policy 10-Payment Life Policy Yearly Renewable Term Problems VII. Reserve Fund, Mortality Fund and Cost of Insurance / 44 Reserve Credit Payment of Death Claims The Reserve Fund and Mortality Fund Cost of Insurance Problems VIII. Full Preliminary Term Valuation Gross Level Annual Premiums Preliminary Term Terminal Reserves Policy P Full Preliminary Term Valuation Modified Preliminary Term Problems IX. Initial, Mean, and Calendar Year Reserves Initial Reserve Mean Reserve Calendar Year Reserve Initial and Mean Reserves, F.P.T. Basis Problems X. Non-Foreiture Options; Cash VALUE; Paid-Up and Extended Insurance; Loan Value / 61 The Cash Value What Happens When Policy is Surrendered Non-Forfeiture Options (Option 1, Option 2, and Option 3) Cash Values under F.P.T. Basis of Valuation Loan Values Problems XI. Profits to a Life Insurance Company / 67 Actual and Expected Mortality Actual and Expected Expenses Actual and Expected Interest Gain and Loss for the Year Arithmetical Statement of Financial Status Problems XII. Distribution of Surplus --- Dividend Options / 73 Allocating Surplus to Policyholders Share of Gain from Mortality, Loading and Interest Dividend Formula Variations in Dividend Formula Dividend Options (Options 1 to 6) Withdrawing the Dividend or Surrendering the Dividend Credit Problems XIII. Further Problems in Interest and Discount / 79 Fundamental Principle Annuity Certain (Present Value of) Annuity Certain (Amount of) Interest Compounded Oftener than Once a Year Value of a Bond Problems XIV. Deferred Annuity --- Certain and Continuous Annuity --- Optional Modes of Settlement / 91 Deferred Life Annuity ``Combination'' Annuity Contract Optional Modes of Settlement Problems XV. Mortality Rates and Mortality Tables / 94 Rate of Mortality Building the Table Changing Number at Initial Age Selection and Select Tables Indicating the Age (for Mortality Analysis) Select Table Ultimate Tables and Select and Ultimate Tables Problems XVI. More About Reserves / 103 Fundamental Principle Amended Corollary to Amended Principle Prospective and Retrospective Method of Obtaining the Reserve Reserves on Single Premium Policies Reserves on Substandard Policies Percentage Mortality Rating Table Problems. XVII. Modified Preliminary Term Valuation / 109 M.P.T. Basis of Valuation Method A: M.P.T. Whole Life Basis Method B: M.P.T. 20-Payment Life Basis Method C: M.P.T. Original Plan Basis Illinois Standard System of Valuation Ohio Standard System of Valuation New Jersey Standard System of Valuation Problems Appendices: I. Miscellaneous Examples / 118 II. Chart 3B --- Single Premium Life Insurance (Age 35) / 121 III. Chart 5B -- Single Premium Life Annuity (Age 35) / 122 IV. Answers to Problems and Miscellaneous Examples 123 Index / 127

rawabstract:
We have determined this item to be in the public domain according to US copyright law through information in the bibliographic record and/or US copyright renewal records. The digital version is available for all educational uses worldwide. Please contact HathiTrust staff at hathitrust-help <at> umich.edu with any questions about this item. Life insurance--Mathematics. (LCCN)36034103. (OCoLC)ocm03161649. HG8781 .L43. HG 8781 .L66. Http://hdl.handle.net/2027/mdp.39015017290688.

rawTOC:
Preface / vii \\ Index to Tables / xi \\ Notes on the Solution of Problems / xii \\ \\ I. Interest and Discount / 1 \\ Interest \\ Discount \\ Examples \\ Observations \\ Problems \\ \\ II. The Mortality Table and Easy Problems in Rate Calculation at Age 90 / 6 \\ Natural or Net One-Year Term Premium \\ Net One-Year Pure Endowment \\ Net Single Premium Whole Life \\ Fundamental Principle \\ Observations \\ Problems \\ \\ III. Single Premium Contracts --- Age 35 / 14 \\ Mortality Table \\ (Net) Single Premium 10-Year Term \\ (Net) Single Premium 10-Year Pure Endowment \\ (Net) Single Premium 10-Year Endowment \\ (Net) Single Premium Whole Life \\ (Net) Single Premium 10-Year Temporary Annuity \\ (Net) Single Premium Life Annuity \\ \\ IV. Development of Net Annual Premiums / 22 \\ Extension of Use of Discount \\ (Net) Annual Premium, Whole Life Policy \\ (Net) Annual Premium, 10-Payment Life \\ (Net) Annual Premium, 10-Year Term \\ (Net) Annual Premium, 10-Year Endowment \\ The ``Practical' and `More Exact' Premium \\ Alternative Method of Obtaining Net Annual Premiums \\ Problems \\ \\ V. More About Premiums / 30 \\ The Yearly Renewable Term Policy \\ Loading the Premium \\ Partial or Instalment Premiums \\ Problems \\ \\ VI. Net Level Premium Reserves / 34 \\ 10-Year Term Policy \\ 10-Year Endowment Policy \\ Whole Life Policy \\ 10-Payment Life Policy \\ Yearly Renewable Term \\ Problems \\ \\ VII. Reserve Fund, Mortality Fund and Cost of Insurance / 44 \\ Reserve Credit \\ Payment of Death Claims \\ The Reserve Fund and Mortality Fund \\ Cost of Insurance \\ Problems \\ \\ VIII. Full Preliminary Term Valuation \\ Gross Level Annual Premiums \\ Preliminary Term \\ Terminal Reserves Policy P \\ Full Preliminary Term Valuation \\ Modified Preliminary Term \\ Problems \\ \\ IX. Initial, Mean, and Calendar Year Reserves \\ \\ Initial Reserve \\ Mean Reserve \\ Calendar Year Reserve \\ Initial and Mean Reserves, F.P.T. Basis \\ Problems \\ \\ X. Non-Foreiture Options; Cash VALUE; Paid-Up and Extended Insurance; Loan Value / 61 \\ The Cash Value \\ What Happens When Policy is Surrendered \\ Non-Forfeiture Options (Option 1, Option 2, and Option 3) \\ Cash Values under F.P.T. Basis of Valuation \\ Loan Values \\ Problems \\ \\ XI. Profits to a Life Insurance Company / 67 \\ Actual and Expected Mortality \\ Actual and Expected Expenses \\ Actual and Expected Interest \\ Gain and Loss for the Year \\ Arithmetical Statement of Financial Status \\ Problems \\ \\ XII. Distribution of Surplus --- Dividend Options / 73 \\ Allocating Surplus to Policyholders \\ Share of Gain from Mortality, Loading and Interest \\ Dividend Formula \\ Variations in Dividend Formula \\ Dividend Options (Options 1 to 6) \\ Withdrawing the Dividend or Surrendering the Dividend Credit \\ Problems \\ \\ XIII. Further Problems in Interest and Discount / 79 \\ Fundamental Principle \\ Annuity Certain (Present Value of) \\ Annuity Certain (Amount of) \\ Interest Compounded Oftener than Once a Year \\ Value of a Bond \\ Problems \\ \\ XIV. Deferred Annuity --- Certain and Continuous Annuity --- Optional Modes of Settlement / 91 \\ Deferred Life Annuity \\ ``Combination'' Annuity Contract \\ Optional Modes of Settlement \\ Problems \\ \\ XV. Mortality Rates and Mortality Tables / 94 \\ Rate of Mortality \\ Building the Table \\ Changing Number at Initial Age \\ Selection and Select Tables \\ Indicating the Age (for Mortality Analysis) \\ Select Table \\ Ultimate Tables and Select and Ultimate Tables \\ Problems \\ \\ XVI. More About Reserves / 103 \\ Fundamental Principle Amended \\ Corollary to Amended Principle \\ Prospective and Retrospective Method of Obtaining the Reserve \\ Reserves on Single Premium Policies \\ Reserves on Substandard Policies \\ Percentage Mortality Rating Table \\ Problems. \\ \\ XVII. Modified Preliminary Term Valuation / 109 \\ M.P.T. Basis of Valuation \\ Method A: M.P.T. Whole Life Basis \\ Method B: M.P.T. 20-Payment Life Basis \\ Method C: M.P.T. Original Plan Basis \\ Illinois Standard System of Valuation \\ Ohio Standard System of Valuation \\ New Jersey Standard System of Valuation \\ Problems \\ \\ Appendices: \\ I. Miscellaneous Examples / 118 \\ II. Chart 3B --- Single Premium Life Insurance (Age 35) / 121 \\ III. Chart 5B -- Single Premium Life Annuity (Age 35) / 122 \\ IV. Answers to Problems and Miscellaneous Examples 123 \\ Index / 127

entry:
@Book{LeVita:1936:ALI,
  author =       "Maurice H. {Le Vita}",
  title =        "An Arithmetic of Life Insurance",
  publisher =    "Life Office Management Association",
  address =      "New York",
  pages =        "xii + 132",
  year =         "1936",
  LCCN =         "HG8781 .L43",
  bibdate =      "Sat Aug 12 14:42:20 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://hdl.handle.net/2027/mdp.39015017290688;
                 https://babel.hathitrust.org/cgi/pt?id=mdp.39015017290688",
  abstract =     "We have determined this item to be in the public
                 domain according to US copyright law through
                 information in the bibliographic record and/or US
                 copyright renewal records. The digital version is
                 available for all educational uses worldwide. Please
                 contact HathiTrust staff at hathitrust-help <at>
                 umich.edu with any questions about this item. Life
                 insurance--Mathematics. (LCCN)36034103.
                 (OCoLC)ocm03161649. HG8781 .L43. HG 8781 .L66.
                 Http://hdl.handle.net/2027/mdp.39015017290688.",
  acknowledgement = ack-nhfb,
  remark =       "While not about computer arithmetic, this book is
                 about practical applications of arithmetic in the life
                 insurance industry. It considers compound interest
                 calculations, present values of financial instruments,
                 mortality tables, insurance premiums, bond returns, and
                 so on. In Table 1, which shows the growth of an
                 investment at 3 percent over 10 years, the author
                 [amusingly] comments ``Mathematicians have already
                 worked out the multiplications and have incorporated
                 them into a table. With the use of this table, the
                 result can be obtained by a single multiplication.''.
                 Although the MARC record indicates the book is in the
                 public domain, the URL only permits download of a
                 single page at a time, although it is possible to page
                 through the book.",
  tableofcontents = "Preface / vii \\
                 Index to Tables / xi \\
                 Notes on the Solution of Problems / xii \\
                 \\
                 I. Interest and Discount / 1 \\
                 Interest \\
                 Discount \\
                 Examples \\
                 Observations \\
                 Problems \\
                 \\
                 II. The Mortality Table and Easy Problems in Rate
                 Calculation at Age 90 / 6 \\
                 Natural or Net One-Year Term Premium \\
                 Net One-Year Pure Endowment \\
                 Net Single Premium Whole Life \\
                 Fundamental Principle \\
                 Observations \\
                 Problems \\
                 \\
                 III. Single Premium Contracts --- Age 35 / 14 \\
                 Mortality Table \\
                 (Net) Single Premium 10-Year Term \\
                 (Net) Single Premium 10-Year Pure Endowment \\
                 (Net) Single Premium 10-Year Endowment \\
                 (Net) Single Premium Whole Life \\
                 (Net) Single Premium 10-Year Temporary Annuity \\
                 (Net) Single Premium Life Annuity \\
                 \\
                 IV. Development of Net Annual Premiums / 22 \\
                 Extension of Use of Discount \\
                 (Net) Annual Premium, Whole Life Policy \\
                 (Net) Annual Premium, 10-Payment Life \\
                 (Net) Annual Premium, 10-Year Term \\
                 (Net) Annual Premium, 10-Year Endowment \\
                 The ``Practical' and `More Exact' Premium \\
                 Alternative Method of Obtaining Net Annual Premiums \\
                 Problems \\
                 \\
                 V. More About Premiums / 30 \\
                 The Yearly Renewable Term Policy \\
                 Loading the Premium \\
                 Partial or Instalment Premiums \\
                 Problems \\
                 \\
                 VI. Net Level Premium Reserves / 34 \\
                 10-Year Term Policy \\
                 10-Year Endowment Policy \\
                 Whole Life Policy \\
                 10-Payment Life Policy \\
                 Yearly Renewable Term \\
                 Problems \\
                 \\
                 VII. Reserve Fund, Mortality Fund and Cost of Insurance
                 / 44 \\
                 Reserve Credit \\
                 Payment of Death Claims \\
                 The Reserve Fund and Mortality Fund \\
                 Cost of Insurance \\
                 Problems \\
                 \\
                 VIII. Full Preliminary Term Valuation \\
                 Gross Level Annual Premiums \\
                 Preliminary Term \\
                 Terminal Reserves Policy P \\
                 Full Preliminary Term Valuation \\
                 Modified Preliminary Term \\
                 Problems \\
                 \\
                 IX. Initial, Mean, and Calendar Year Reserves \\
                 \\
                 Initial Reserve \\
                 Mean Reserve \\
                 Calendar Year Reserve \\
                 Initial and Mean Reserves, F.P.T. Basis \\
                 Problems \\
                 \\
                 X. Non-Foreiture Options; Cash VALUE; Paid-Up and
                 Extended Insurance; Loan Value / 61 \\
                 The Cash Value \\
                 What Happens When Policy is Surrendered \\
                 Non-Forfeiture Options (Option 1, Option 2, and Option
                 3) \\
                 Cash Values under F.P.T. Basis of Valuation \\
                 Loan Values \\
                 Problems \\
                 \\
                 XI. Profits to a Life Insurance Company / 67 \\
                 Actual and Expected Mortality \\
                 Actual and Expected Expenses \\
                 Actual and Expected Interest \\
                 Gain and Loss for the Year \\
                 Arithmetical Statement of Financial Status \\
                 Problems \\
                 \\
                 XII. Distribution of Surplus --- Dividend Options / 73
                 \\
                 Allocating Surplus to Policyholders \\
                 Share of Gain from Mortality, Loading and Interest \\
                 Dividend Formula \\
                 Variations in Dividend Formula \\
                 Dividend Options (Options 1 to 6) \\
                 Withdrawing the Dividend or Surrendering the Dividend
                 Credit \\
                 Problems \\
                 \\
                 XIII. Further Problems in Interest and Discount / 79
                 \\
                 Fundamental Principle \\
                 Annuity Certain (Present Value of) \\
                 Annuity Certain (Amount of) \\
                 Interest Compounded Oftener than Once a Year \\
                 Value of a Bond \\
                 Problems \\
                 \\
                 XIV. Deferred Annuity --- Certain and Continuous
                 Annuity --- Optional Modes of Settlement / 91 \\
                 Deferred Life Annuity \\
                 ``Combination'' Annuity Contract \\
                 Optional Modes of Settlement \\
                 Problems \\
                 \\
                 XV. Mortality Rates and Mortality Tables / 94 \\
                 Rate of Mortality \\
                 Building the Table \\
                 Changing Number at Initial Age \\
                 Selection and Select Tables \\
                 Indicating the Age (for Mortality Analysis) \\
                 Select Table \\
                 Ultimate Tables and Select and Ultimate Tables \\
                 Problems \\
                 \\
                 XVI. More About Reserves / 103 \\
                 Fundamental Principle Amended \\
                 Corollary to Amended Principle \\
                 Prospective and Retrospective Method of Obtaining the
                 Reserve \\
                 Reserves on Single Premium Policies \\
                 Reserves on Substandard Policies \\
                 Percentage Mortality Rating Table \\
                 Problems. \\
                 \\
                 XVII. Modified Preliminary Term Valuation / 109 \\
                 M.P.T. Basis of Valuation \\
                 Method A: M.P.T. Whole Life Basis \\
                 Method B: M.P.T. 20-Payment Life Basis \\
                 Method C: M.P.T. Original Plan Basis \\
                 Illinois Standard System of Valuation \\
                 Ohio Standard System of Valuation \\
                 New Jersey Standard System of Valuation \\
                 Problems \\
                 \\
                 Appendices: \\
                 I. Miscellaneous Examples / 118 \\
                 II. Chart 3B --- Single Premium Life Insurance (Age 35)
                 / 121 \\
                 III. Chart 5B -- Single Premium Life Annuity (Age 35) /
                 122 \\
                 IV. Answers to Problems and Miscellaneous Examples 123
                 \\
                 Index / 127",
  usmarc540 =    "[US Library of Congress record]: We have determined
                 this item to be in the public domain according to US
                 copyright law through information in the bibliographic
                 record and/or US copyright renewal records. The digital
                 version is available for all educational uses
                 worldwide.",
}


bibtype: article
filename: fparith.bib
label: Phillips:1936:BC
author: E. W. Phillips
title: Binary calculation
journal: j-J-INST-ACTUARIES
volume: 67
pages: 187--221
year: 1936
ISSN: 0020-2681 OR 00202681
bibdate: Wed Oct 13 11:33:16 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:33:16 ???
note: Reprinted in cite [ 7.1]Randell:1982:ODC.
fjournal: Journal of the Institute of Actuaries
acknowledgement: ack-nhfb
rawauthor: E. W. Phillips
rawnote: Reprinted in \cite[\S 7.1]{Randell:1982:ODC}.
rawtitle: Binary calculation
entry:
@Article{Phillips:1936:BC,
  author =       "E. W. Phillips",
  title =        "Binary calculation",
  journal =      j-J-INST-ACTUARIES,
  volume =       "67",
  number =       "??",
  pages =        "187--221",
  year =         "1936",
  ISSN =         "0020-2681",
  bibdate =      "Wed Oct 13 11:33:16 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 7.1]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Institute of Actuaries",
}


bibtype: misc
filename: fparith.bib
label: Zuse:1936:VSD
author: K. Zuse
pages: 187--221
day: 11
month: apr
monthnumber: 4
year: 1936
bibdate: Wed Oct 13 11:22:03 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:22:03 ???
note: Reprinted in cite [ 4.1]Randell:1982:ODC.
language: German
acknowledgement: ack-nhfb
howpublished: German patent application Z23624.
rawauthor: K. Zuse
rawnote: Reprinted in \cite[\S 4.1]{Randell:1982:ODC}.
title:
Verfahren zur selbsttatigen Durchfuhrung von Rechnungen mit Hilfe von Rechenmaschinen. (German) [Procedure for automatic execution of calculations by calculating machines]

rawtitle:
{Verfahren zur selbstt{\"a}tigen Durchfuhrung von Rechnungen mit Hilfe von Rechenmaschinen}. ({German}) [{Procedure} for automatic execution of calculations by calculating machines]

entry:
@Misc{Zuse:1936:VSD,
  author =       "K. Zuse",
  title =        "{Verfahren zur selbstt{\"a}tigen Durchfuhrung von
                 Rechnungen mit Hilfe von Rechenmaschinen}. ({German})
                 [{Procedure} for automatic execution of calculations by
                 calculating machines]",
  howpublished = "German patent application Z23624.",
  day =          "11",
  month =        apr,
  year =         "1936",
  bibdate =      "Wed Oct 13 11:22:03 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 4.1]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  language =     "German",
}


bibtype: article
filename: fparith.bib
label: Escott:1937:QDN
author: E. B. Escott
title: Questions, Discussions, and Notes: Rapid Method for Extracting a Square Root
journal: j-AMER-MATH-MONTHLY
volume: 44
number: 10
pages: 644--646
month: dec
monthnumber: 12
year: 1937
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Jun 28 12:38:44 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1999.06.28 12:38:44 MDT
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: E. B. Escott
rawtitle: Questions, Discussions, and Notes: Rapid Method for Extracting a Square Root
entry:
@Article{Escott:1937:QDN,
  author =       "E. B. Escott",
  title =        "Questions, Discussions, and Notes: Rapid Method for
                 Extracting a Square Root",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "44",
  number =       "10",
  pages =        "644--646",
  month =        dec,
  year =         "1937",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:38:44 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: book
filename: fparith.bib
label: Millikan:1937:MMP
author: Robert A. Millikan and Duane E. Roller and Earnest C. Watson
title: Mechanics, Molecular Physics, Heat, and Sound
publisher: pub-MIT
address: pub-MIT:adr
year: 1937
bibdate: Mon May 21 17:16:04 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2018.05.21 17:16:04 ???
note: See Appendix: Significant Figures and Notations by Powers of Ten.
remark: Cited in cite [ref. 22]Carter:2013:ESF.
acknowledgement: ack-nhfb
rawauthor: Robert A. Millikan and Duane E. Roller and Earnest C. Watson
rawnote: See Appendix: Significant Figures and Notations by Powers of Ten.
rawtitle: Mechanics, Molecular Physics, Heat, and Sound
entry:
@Book{Millikan:1937:MMP,
  author =       "Robert A. Millikan and Duane E. Roller and Earnest C.
                 Watson",
  title =        "Mechanics, Molecular Physics, Heat, and Sound",
  publisher =    pub-MIT,
  address =      pub-MIT:adr,
  pages =        "????",
  year =         "1937",
  bibdate =      "Mon May 21 17:16:04 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See Appendix: Significant Figures and Notations by
                 Powers of Ten.",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite[ref. 22]{Carter:2013:ESF}.",
}


bibtype: mastersthesis
filename: fparith.bib
label: Shannon:1937:SAR
author: Claude Elwood Shannon
title: A Symbolic Analysis of Relay and Switching Circuits
type: Master of Science
school: Department of Electrical Engineering, MIT
address: Cambridge, MA, USA
pages: 72
day: 10
month: aug
monthnumber: 8
year: 1937
bibdate: Thu Nov 18 10:35:20 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.11.18 10:35:20 ???
note: Not submitted until 1940
URL: http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425.pdf
acknowledgement: ack-nhfb
authordates: April 30, 1916--February 24, 2001
rawauthor: Claude Elwood Shannon
rawnote: Not submitted until 1940
rawtitle: A Symbolic Analysis of Relay and Switching Circuits
remark:
Smiley cite [p. 91]Smiley:2010:MWI claims: ``He [Shannon] also had the insight, like Atanasoff, that the binary arithmetic that relay switches represented would simplify information systems. His master's thesis, written when he as twenty-one and published when he was twenty-two, is considered to be one of the most important, if not the most important, master's thesis of the twentieth century.''par Pages 59--61 of the thesis are a section called ``Electric Adder to the Base Two'', and pages 62--68, ``A Factor Table Machine'', describe a machine that will print a table of factors and primes of all the integers from 1 to 100,000,000. Shannon notes on page 68: ``As to the practicality of such a device, it might be said that J. P. Kulik spent 20 years in constructing a table of primes up to 100,000,000 and when finished it was found to contain so many errors that it was not worth publishing. The machine described here could probably be made to handle 5 numbers per second so that the table would require only about 2 months to construct.''

entry:
@MastersThesis{Shannon:1937:SAR,
  author =       "Claude Elwood Shannon",
  title =        "A Symbolic Analysis of Relay and Switching Circuits",
  type =         "{Master of Science}",
  school =       "Department of Electrical Engineering, MIT",
  address =      "Cambridge, MA, USA",
  pages =        "72",
  day =          "10",
  month =        aug,
  year =         "1937",
  bibdate =      "Thu Nov 18 10:35:20 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Not submitted until 1940",
  URL =          "http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "April 30, 1916--February 24, 2001",
  remark =       "Smiley \cite[p. 91]{Smiley:2010:MWI} claims: ``He
                 [Shannon] also had the insight, like Atanasoff, that
                 the binary arithmetic that relay switches represented
                 would simplify information systems. His master's
                 thesis, written when he as twenty-one and published
                 when he was twenty-two, is considered to be one of the
                 most important, if not the most important, master's
                 thesis of the twentieth century.''\par

                 Pages 59--61 of the thesis are a section called
                 ``Electric Adder to the Base Two'', and pages 62--68,
                 ``A Factor Table Machine'', describe a machine that
                 will print a table of factors and primes of all the
                 integers from 1 to 100,000,000. Shannon notes on page
                 68: ``As to the practicality of such a device, it might
                 be said that J. P. Kulik spent 20 years in constructing
                 a table of primes up to 100,000,000 and when finished
                 it was found to contain so many errors that it was not
                 worth publishing. The machine described here could
                 probably be made to handle 5 numbers per second so that
                 the table would require only about 2 months to
                 construct.''",
}


bibtype: article
filename: fparith.bib
label: Benford:1938:LAN
author: Frank Benford
title: The Law of Anomalous Numbers
journal: j-PROC-AMER-PHIL-SOC
volume: 78
number: 4
pages: 551--572
month: mar
monthnumber: 3
year: 1938
CODEN: PAPCAA
ISSN: 0003-049X (print), 2326-9243 (electronic) OR 0003049X (print), 23269243 (electronic)
ISSNL: 0003-049X OR 0003049X
bibdate: Thu Feb 15 16:28:28 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.02.15 16:28:28 ???
URL: http://links.jstor.org/sici?sici=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-G
keywords: Benford's Law; Law of Anomalous Numbers; Zipf's Law
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journal/procamerphilsoci
rawauthor: Frank Benford
rawtitle: The Law of Anomalous Numbers
abstract:
It has been observed that the first pages of a table of common logarithms show more wear than do the last pages, indicating that more used numbers begin with the digit 1 than with the digit 9. A compilation of some 20,000 first digits taken from widely divergent sources shows that there is a logarithmic distribution of first digits when the numbers are composed of four or more digits. An analysis of the numbers from different sources shows that the numbers taken from unrelated subjects, such as a group of newspaper items, show a much better agreement with a logarithmic distribution than do numbers from mathematical tabulations or other formal data. There is here the peculiar fact that numbers that individually are without relationship are, when considered in large groups, in good agreement with a distribution law---hence the name ``Anomalous Numbers.''par A further analysis of the data shows a strong tendency for bodies of numerical data to fall into geometric series. If the series is made up of numbers containing three or more digits the first digits form a logarithmic series. If the numbers contain only single digits the geometric relation still holds but the simple logarithmic relation no longer applies.par An equation is given showing the frequencies of first digits in the different orders of numbers 1 to 10, 10 to 100, etc.par The equation also gives the frequency of digits in the second, third + place of a multi-digit number, and it is shown that the same law applies to reciprocals.par There are many instances showing that the geometric series, or the logarithmic law, has long been recognized as a common phenomenon in factual literature and in the ordinary affairs of life. The wire gauge and drill gauge of the mechanic, the magnitude scale of the astronomer and the sensory response curves of the psychologist are all particular examples of a relationship that seems to extend to all human affairs. The Law of Anomalous Numbers is thus a general probability law of widespread application.

fjournal:
Proceedings of the American Philosophical Society held at Philadelphia for promoting useful knowledge

remark:
From cite Logan:1978:FDP: ``Benford's paper was published in 1938 in a journal of rather limited circulation and not usually read by mathematicians. It so happened that it was immediately followed in the same issue by a physics paper which became of some importance for secret nuclear work during World War II [H. A. Bethe, M. E. Rose, and L. P. Smith, `The Multiple Scattering of Electrons', Proc. Amer. Phil. Soc. 78(4), 573--585 (1938)]. That is why Benford's paper caught the attention of physicists in the early 1940's and was much discussed. This led to the notes in Nature by Goudsmit and Furry [3] and Furry and Hurwitz [4] containing an effort to explain Benford's law. We considered it at that time merely a welcome diversion and did not expect that over thirty papers would be devoted to this subject in subsequent years.'' The 2006 bibliography cite Hurlimann:2006:BLB cites 325 publications about Benford's Law.

rawabstract:
It has been observed that the first pages of a table of common logarithms show more wear than do the last pages, indicating that more used numbers begin with the digit 1 than with the digit 9. A compilation of some 20,000 first digits taken from widely divergent sources shows that there is a logarithmic distribution of first digits when the numbers are composed of four or more digits. An analysis of the numbers from different sources shows that the numbers taken from unrelated subjects, such as a group of newspaper items, show a much better agreement with a logarithmic distribution than do numbers from mathematical tabulations or other formal data. There is here the peculiar fact that numbers that individually are without relationship are, when considered in large groups, in good agreement with a distribution law---hence the name ``Anomalous Numbers.''\par A further analysis of the data shows a strong tendency for bodies of numerical data to fall into geometric series. If the series is made up of numbers containing three or more digits the first digits form a logarithmic series. If the numbers contain only single digits the geometric relation still holds but the simple logarithmic relation no longer applies.\par An equation is given showing the frequencies of first digits in the different orders of numbers 1 to 10, 10 to 100, etc.\par The equation also gives the frequency of digits in the second, third + place of a multi-digit number, and it is shown that the same law applies to reciprocals.\par There are many instances showing that the geometric series, or the logarithmic law, has long been recognized as a common phenomenon in factual literature and in the ordinary affairs of life. The wire gauge and drill gauge of the mechanic, the magnitude scale of the astronomer and the sensory response curves of the psychologist are all particular examples of a relationship that seems to extend to all human affairs. The Law of Anomalous Numbers is thus a general probability law of widespread application.

entry:
@Article{Benford:1938:LAN,
  author =       "Frank Benford",
  title =        "The Law of Anomalous Numbers",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "78",
  number =       "4",
  pages =        "551--572",
  month =        mar,
  year =         "1938",
  CODEN =        "PAPCAA",
  ISSN =         "0003-049X (print), 2326-9243 (electronic)",
  ISSN-L =       "0003-049X",
  bibdate =      "Thu Feb 15 16:28:28 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://links.jstor.org/sici?sici=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-G",
  abstract =     "It has been observed that the first pages of a table
                 of common logarithms show more wear than do the last
                 pages, indicating that more used numbers begin with the
                 digit 1 than with the digit 9. A compilation of some
                 20,000 first digits taken from widely divergent sources
                 shows that there is a logarithmic distribution of first
                 digits when the numbers are composed of four or more
                 digits. An analysis of the numbers from different
                 sources shows that the numbers taken from unrelated
                 subjects, such as a group of newspaper items, show a
                 much better agreement with a logarithmic distribution
                 than do numbers from mathematical tabulations or other
                 formal data. There is here the peculiar fact that
                 numbers that individually are without relationship are,
                 when considered in large groups, in good agreement with
                 a distribution law---hence the name ``Anomalous
                 Numbers.''\par

                 A further analysis of the data shows a strong tendency
                 for bodies of numerical data to fall into geometric
                 series. If the series is made up of numbers containing
                 three or more digits the first digits form a
                 logarithmic series. If the numbers contain only single
                 digits the geometric relation still holds but the
                 simple logarithmic relation no longer applies.\par

                 An equation is given showing the frequencies of first
                 digits in the different orders of numbers 1 to 10, 10
                 to 100, etc.\par

                 The equation also gives the frequency of digits in the
                 second, third + place of a multi-digit number, and it
                 is shown that the same law applies to
                 reciprocals.\par

                 There are many instances showing that the geometric
                 series, or the logarithmic law, has long been
                 recognized as a common phenomenon in factual literature
                 and in the ordinary affairs of life. The wire gauge and
                 drill gauge of the mechanic, the magnitude scale of the
                 astronomer and the sensory response curves of the
                 psychologist are all particular examples of a
                 relationship that seems to extend to all human affairs.
                 The Law of Anomalous Numbers is thus a general
                 probability law of widespread application.",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the {American Philosophical Society}
                 held at {Philadelphia} for promoting useful knowledge",
  journal-URL =  "http://www.jstor.org/journal/procamerphilsoci",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "From \cite{Logan:1978:FDP}: ``Benford's paper was
                 published in 1938 in a journal of rather limited
                 circulation and not usually read by mathematicians. It
                 so happened that it was immediately followed in the
                 same issue by a physics paper which became of some
                 importance for secret nuclear work during World War II
                 [H. A. Bethe, M. E. Rose, and L. P. Smith, `The
                 Multiple Scattering of Electrons', Proc. Amer. Phil.
                 Soc. 78(4), 573--585 (1938)]. That is why Benford's
                 paper caught the attention of physicists in the early
                 1940's and was much discussed. This led to the notes in
                 Nature by Goudsmit and Furry [3] and Furry and Hurwitz
                 [4] containing an effort to explain Benford's law. We
                 considered it at that time merely a welcome diversion
                 and did not expect that over thirty papers would be
                 devoted to this subject in subsequent years.'' The 2006
                 bibliography \cite{Hurlimann:2006:BLB} cites 325
                 publications about Benford's Law.",
}


bibtype: phdthesis
filename: fparith.bib
label: Couffignal:1938:AMA
author: L. Couffignal
publisher: Gauthier-Villars
school: Faculte des Sciences de Paris
address: Paris, France
pages: 551--572
year: 1938
bibdate: Wed Oct 13 11:17:22 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:17:22 ???
note: Extracts reprinted in cite [ 2.7]Randell:1982:ODC. Translated by Mr. R. Basu.
language: French
acknowledgement: ack-nhfb
rawauthor: L. Couffignal
rawnote: Extracts reprinted in \cite[\S 2.7]{Randell:1982:ODC}. Translated by Mr. R. Basu.
title:
Sur l'analyse mecanique. Application aux machines a calculer et aux calculs de la mecanique celeste. (French) [On mechanical analysis. Application to calculating machines and to calculation in celestial mechanics]

rawtitle:
Sur l'analyse m{\'e}canique. Application aux machines {\`a} calculer et aux calculs de la m{\'e}canique c{\'e}leste. ({French}) [{On} mechanical analysis. Application to calculating machines and to calculation in celestial mechanics]

entry:
@PhdThesis{Couffignal:1938:AMA,
  author =       "L. Couffignal",
  title =        "Sur l'analyse m{\'e}canique. Application aux machines
                 {\`a} calculer et aux calculs de la m{\'e}canique
                 c{\'e}leste. ({French}) [{On} mechanical analysis.
                 Application to calculating machines and to calculation
                 in celestial mechanics]",
  publisher =    "Gauthier-Villars",
  school =       "Facult{\'e} des Sciences de Paris",
  address =      "Paris, France",
  year =         "1938",
  bibdate =      "Wed Oct 13 11:17:22 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Extracts reprinted in \cite[\S 2.7]{Randell:1982:ODC}.
                 Translated by Mr. R. Basu.",
  acknowledgement = ack-nhfb,
  language =     "French",
}


bibtype: book
filename: fparith.bib
label: Hardy:1938:ITN
author: G. H. (Godfrey Harold) Hardy and E. M. (Edward Maitland) Wright
title: An Introduction to the Theory of Numbers
publisher: pub-OXFORD
address: pub-OXFORD:adr
pages: xvi + 403
year: 1938
LCCN: QA241 .H28
bibdate: Fri Nov 30 06:49:15 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.30 06:49:15 ???
acknowledgement: ack-nhfb
rawauthor: G. H. (Godfrey Harold) Hardy and E. M. (Edward Maitland) Wright
rawtitle: An Introduction to the Theory of Numbers
entry:
@Book{Hardy:1938:ITN,
  author =       "G. H. (Godfrey Harold) Hardy and E. M. (Edward
                 Maitland) Wright",
  title =        "An Introduction to the Theory of Numbers",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xvi + 403",
  year =         "1938",
  LCCN =         "QA241 .H28",
  bibdate =      "Fri Nov 30 06:49:15 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Shannon:1938:SAR
author: Claude E. Shannon
title: A Symbolic Analysis of Relay and Switching Circuits
journal: j-TRANS-AMER-INST-ELEC-ENG
volume: 57
pages: 713--723
month: dec
monthnumber: 12
year: 1938
CODEN: TAEEA5
ISSN: 0096-3860 OR 00963860
bibdate: Sat Nov 20 08:54:12 2010
bibtimestamp: 2010.11.20 08:54:12 ???
fjournal: Transactions of the American Institute of Electrical Engineers
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714
rawauthor: Claude E. Shannon
rawtitle: A Symbolic Analysis of Relay and Switching Circuits
bibsource:
http://www2.research.att.com/~njas/doc/shannonbio.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib

remark:
This is Shannon's first published paper (his Master's thesis). In 1940, it received the Alfred Noble Prize of the combined engineering societies of the United States, an award given each year to a person not over thirty for a paper published in one of the journals of the participating societies. H. H. Goldstine cite Goldstine:1972:CPN called this work ``one of the most important master's theses ever written ldots a landmark in that it helped to change digital circuit design from an art to a science.''

entry:
@Article{Shannon:1938:SAR,
  author =       "Claude E. Shannon",
  title =        "A Symbolic Analysis of Relay and Switching Circuits",
  journal =      j-TRANS-AMER-INST-ELEC-ENG,
  volume =       "57",
  number =       "??",
  pages =        "713--723",
  month =        dec,
  year =         "1938",
  CODEN =        "TAEEA5",
  ISSN =         "0096-3860",
  bibdate =      "Sat Nov 20 08:54:12 2010",
  bibsource =    "http://www2.research.att.com/~njas/doc/shannonbio.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Transactions of the American Institute of Electrical
                 Engineers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714",
  remark =       "This is Shannon's first published paper (his Master's
                 thesis). In 1940, it received the Alfred Noble Prize of
                 the combined engineering societies of the United
                 States, an award given each year to a person not over
                 thirty for a paper published in one of the journals of
                 the participating societies. H. H. Goldstine
                 \cite{Goldstine:1972:CPN} called this work ``one of the
                 most important master's theses ever written \ldots{} a
                 landmark in that it helped to change digital circuit
                 design from an art to a science.''",
}


bibtype: article
filename: fparith.bib
label: Jager:1939:AAD
author: Robert Jager and Boyd C. Patterson
title: The Artificial Arithmetick in Decimals of Robert Jager (London, 1651)
journal: j-ISIS
volume: 31
number: 1
pages: 25--31
month: nov
monthnumber: 11
year: 1939
CODEN: ISISA4
ISSN: 0021-1753 (print), 1545-6994 (electronic) OR 00211753 (print), 15456994 (electronic)
ISSNL: 0021-1753 OR 00211753
bibdate: Tue Jul 30 21:26:49 MDT 2013
bibtimestamp: 2013.07.30 21:26:49 MDT
URL: http://www.jstor.org/stable/226014
fjournal: Isis
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journal/isis
rawauthor: Robert Jager and Boyd C. Patterson
rawtitle: The Artificial Arithmetick in Decimals of {Robert Jager} ({London}, 1651)
bibsource:
http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i302217; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/isis1930.bib

entry:
@Article{Jager:1939:AAD,
  author =       "Robert Jager and Boyd C. Patterson",
  title =        "The Artificial Arithmetick in Decimals of {Robert
                 Jager} ({London}, 1651)",
  journal =      j-ISIS,
  volume =       "31",
  number =       "1",
  pages =        "25--31",
  month =        nov,
  year =         "1939",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:26:49 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i302217;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1930.bib",
  URL =          "http://www.jstor.org/stable/226014",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}


bibtype: article
filename: fparith.bib
label: K:1939:BRBd
author: M. G. K.
title: Book Review: booktitle Duodecimal Arithmetic, by George S. Terry
journal: j-J-R-STAT-SOC
volume: 102
number: 2
pages: 299--300
year: 1939
DOI: https://doi.org/10.2307/2980013
ISSN: 0952-8385 OR 09528385
bibdate: Sat Jan 24 11:18:08 MST 2015
bibtimestamp: 2015.01.24 11:18:08 MST
URL: http://www.jstor.org/stable/2980013
fjournal: Journal of the Royal Statistical Society
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/09528385.html
rawauthor: M. G. K.
rawtitle: Book Review: {{\booktitle{Duodecimal Arithmetic}}, by George S. Terry}
bibsource:
http://www.jstor.org/stable/i349540; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jrss-a-1930.bib

entry:
@Article{K:1939:BRBd,
  author =       "M. G. K.",
  title =        "Book Review: {{\booktitle{Duodecimal Arithmetic}}, by
                 George S. Terry}",
  journal =      j-J-R-STAT-SOC,
  volume =       "102",
  number =       "2",
  pages =        "299--300",
  month =        "????",
  year =         "1939",
  DOI =          "https://doi.org/10.2307/2980013",
  ISSN =         "0952-8385",
  bibdate =      "Sat Jan 24 11:18:08 MST 2015",
  bibsource =    "http://www.jstor.org/stable/i349540;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jrss-a-1930.bib",
  URL =          "http://www.jstor.org/stable/2980013",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society",
  journal-URL =  "http://www.jstor.org/journals/09528385.html",
}


bibtype: techreport
filename: fparith.bib
label: Atanasoff:1940:CMS
author: J. V. Atanasoff
title: Computing machine for the solution of large systems of linear algebraic equations
type: Unpublished memorandum
institution: Iowa State College
address: Ames, IA, USA
pages: 299--300
month: aug
monthnumber: 8
year: 1940
bibdate: Wed Oct 13 11:36:11 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:36:11 ???
note: Reprinted in cite [ 7.2]Randell:1982:ODC.
acknowledgement: ack-nhfb
rawauthor: J. V. Atanasoff
rawnote: Reprinted in \cite[\S 7.2]{Randell:1982:ODC}.
rawtitle: Computing machine for the solution of large systems of linear algebraic equations
entry:
@TechReport{Atanasoff:1940:CMS,
  author =       "J. V. Atanasoff",
  title =        "Computing machine for the solution of large systems of
                 linear algebraic equations",
  type =         "Unpublished memorandum",
  institution =  "Iowa State College",
  address =      "Ames, IA, USA",
  month =        aug,
  year =         "1940",
  bibdate =      "Wed Oct 13 11:36:11 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 7.2]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Bush:1940:AM
author: V. Bush
title: Arithmetical Machine
pages: 299--300
year: 1940
bibdate: Wed Oct 13 11:37:32 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:37:32 ???
acknowledgement: ack-nhfb
howpublished: Vannevar Bush Papers, Container 18, Folder: Caldwell, Samuel, 1939--1940
rawauthor: V. Bush
rawtitle: Arithmetical Machine
note:
Reprinted in cite [ 7.3]Randell:1982:ODC. Copyright interest in the unpublished writings of Vannevar Bush has been dedicated to the public.

rawnote:
Reprinted in \cite[\S 7.3]{Randell:1982:ODC}. Copyright interest in the unpublished writings of Vannevar Bush has been dedicated to the public.

entry:
@Misc{Bush:1940:AM,
  author =       "V. Bush",
  title =        "Arithmetical Machine",
  howpublished = "Vannevar Bush Papers, Container 18, Folder: Caldwell,
                 Samuel, 1939--1940",
  year =         "1940",
  bibdate =      "Wed Oct 13 11:37:32 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 7.3]{Randell:1982:ODC}.
                 Copyright interest in the unpublished writings of
                 Vannevar Bush has been dedicated to the public.",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Stibitz:1940:C
author: G. R. Stibitz
title: Computer
type: Unpublished memorandum
institution: Bell Telephone Laboratories
address: New York, NY, USA
pages: 299--300
year: 1940
bibdate: Wed Oct 13 11:30:38 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:30:38 ???
note: Reprinted in cite [ 6.1]Randell:1982:ODC.
acknowledgement: ack-nhfb
rawauthor: G. R. Stibitz
rawnote: Reprinted in \cite[\S 6.1]{Randell:1982:ODC}.
rawtitle: Computer
entry:
@TechReport{Stibitz:1940:C,
  author =       "G. R. Stibitz",
  title =        "Computer",
  type =         "Unpublished memorandum",
  institution =  "Bell Telephone Laboratories",
  address =      "New York, NY, USA",
  year =         "1940",
  bibdate =      "Wed Oct 13 11:30:38 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 6.1]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
}


bibtype: mastersthesis
filename: fparith.bib
label: Berry:1941:DED
author: Clifford Edward Berry
title: Design of electrical data recording and reading mechanism
type: M.S. thesis
school: Iowa State College
address: Ames, IA, USA
pages: 32
year: 1941
bibdate: Thu Nov 18 11:18:18 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.11.18 11:18:18 ???
acknowledgement: ack-nhfb
authordates: 1918--1963
rawauthor: Clifford Edward Berry
rawtitle: Design of electrical data recording and reading mechanism
remark:
This thesis may be one of the earliest surviving records of the ABC computer built by John Atanasoff and Clifford Berry in the late 1930s. The one-of-a-kind ABC was destroyed in 1948, and most of its parts were lost. Also cited in ``Charles W. Bradley Collection on the ENIAC Trial, 1930--1966'', (found in http://discover.lib.umn.edu/): CWB as an attorney for the group retained by Honeywell in the Honeywell v. Sperry Rand ENIAC trial. The ABC had a 50-bit word.

entry:
@MastersThesis{Berry:1941:DED,
  author =       "Clifford Edward Berry",
  title =        "Design of electrical data recording and reading
                 mechanism",
  type =         "{M.S.} thesis",
  school =       "Iowa State College",
  address =      "Ames, IA, USA",
  pages =        "32",
  year =         "1941",
  bibdate =      "Thu Nov 18 11:18:18 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1918--1963",
  historical-note = "From
                 http://www.lib.iastate.edu/arch/rgrp/5-2-1-1.html:

                 ``John Vincent Atanasoff received his M.S. (1926) in
                 Mathematics from Iowa State College (University) and
                 received his Ph.D. (1930) in Theoretical Physics from
                 the University of Wisconsin-Madison. He returned to
                 Iowa State in 1930 as Assistant Professor in
                 mathematics and physics and was promoted to Associate
                 Professor (1936). Atanasoff began developing concepts
                 for an electronic computing machine in 1937. It was
                 shortly thereafter that he, along with graduate student
                 Clifford Berry, started work on the world's first
                 electronic digital computer. The computer would later
                 be named the Atanasoff-Berry Computer (ABC).

                 Work on the machine stopped at the start of World War
                 II in 1941 and the ABC was never patented. Atanasoff
                 and Berry were both called to support the war effort
                 and left Iowa State. By the end of the decade, the ABC
                 was removed from the basement of Physics Hall and
                 dismantled.

                 Atanasoff and the ABC were part of a major court case
                 between Honeywell, Inc. and Sperry Rand Corporation
                 which occurred 1967-1973. The case involved the ENIAC
                 patent which covered basic ownership rights to the
                 design of electronic digital computers. During the
                 trial, the judge concluded that the invention of the
                 ENIAC was derived from the work of John Vincent
                 Atanasoff at Iowa State University.

                 A replica of the Atanasoff-Berry Computer was completed
                 and unveiled to the public in 1996. The ABC replica was
                 constructed by a team of Iowa State scientists at the
                 Ames Laboratory and was exhibited at museums throughout
                 the country over the next several years.''",
  remark =       "This thesis may be one of the earliest surviving
                 records of the ABC computer built by John Atanasoff and
                 Clifford Berry in the late 1930s. The one-of-a-kind ABC
                 was destroyed in 1948, and most of its parts were lost.
                 Also cited in ``Charles W. Bradley Collection on the
                 ENIAC Trial, 1930--1966'', (found in
                 http://discover.lib.umn.edu/): CWB as an attorney for
                 the group retained by Honeywell in the Honeywell v.
                 Sperry Rand ENIAC trial. The ABC had a 50-bit word.",
}


bibtype: article
filename: fparith.bib
label: Lancaster:1942:MME
author: Otis E. Lancaster
title: Machine Method for the Extraction of Cube Root
journal: j-J-AM-STAT-ASSOC
volume: 37
number: 217
pages: 112--115
month: mar
monthnumber: 3
year: 1942
CODEN: JSTNAL
ISSN: 0162-1459 (print), 1537-274X (electronic) OR 01621459 (print), 1537274X (electronic)
ISSNL: 0162-1459 OR 01621459
bibdate: Wed Jan 25 08:05:24 MST 2012
bibtimestamp: 2012.01.25 08:05:24 MST
URL: http://www.jstor.org/stable/2279437
fjournal: Journal of the American Statistical Association
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/uasa20
rawauthor: Otis E. Lancaster
rawtitle: Machine Method for the Extraction of Cube Root
bibsource:
http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314096; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib

entry:
@Article{Lancaster:1942:MME,
  author =       "Otis E. Lancaster",
  title =        "Machine Method for the Extraction of Cube Root",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "37",
  number =       "217",
  pages =        "112--115",
  month =        mar,
  year =         "1942",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Jan 25 08:05:24 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314096;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
  URL =          "http://www.jstor.org/stable/2279437",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}


bibtype: techreport
filename: fparith.bib
label: Mauchly:1942:UHS
author: J. W. Mauchly
title: The use of high speed vacuum tube devices for calculating
type: Privately circulated memorandum
institution: Moore School of Electrical Engineering, University of Pennsylvania
address: Philadelphia, PA, USA
pages: 112--115
month: aug
monthnumber: 8
year: 1942
bibdate: Wed Oct 13 11:52:54 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:52:54 ???
note: Reprinted in cite [ 7.6]Randell:1982:ODC.
acknowledgement: ack-nhfb
rawauthor: J. W. Mauchly
rawnote: Reprinted in \cite[\S 7.6]{Randell:1982:ODC}.
rawtitle: The use of high speed vacuum tube devices for calculating
entry:
@TechReport{Mauchly:1942:UHS,
  author =       "J. W. Mauchly",
  title =        "The use of high speed vacuum tube devices for
                 calculating",
  type =         "Privately circulated memorandum",
  institution =  "Moore School of Electrical Engineering, University of
                 Pennsylvania",
  address =      "Philadelphia, PA, USA",
  month =        aug,
  year =         "1942",
  bibdate =      "Wed Oct 13 11:52:54 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 7.6]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Rajchman:1942:REP
author: J. A. Rajchman and G. A. Morton and A. W. Vance
title: Report on Electronic Predictors for Anti-Aircraft Fire Control
institution: Research Laboratories, R.C.A. Manufacturing Company, Inc.
address: Camden, NJ, USA
pages: 112--115
month: apr
monthnumber: 4
year: 1942
bibdate: Sat Feb 8 10:28:55 2020
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2020.02.08 10:28:55 ???
note: Reprinted in cite [ 7.4]Randell:1982:ODC.
acknowledgement: ack-nhfb
rawauthor: J. A. Rajchman and G. A. Morton and A. W. Vance
rawnote: Reprinted in \cite[\S 7.4]{Randell:1982:ODC}.
rawtitle: Report on Electronic Predictors for Anti-Aircraft Fire Control
entry:
@TechReport{Rajchman:1942:REP,
  author =       "J. A. Rajchman and G. A. Morton and A. W. Vance",
  title =        "Report on Electronic Predictors for Anti-Aircraft Fire
                 Control",
  institution =  "Research Laboratories, R.C.A. Manufacturing Company,
                 Inc.",
  address =      "Camden, NJ, USA",
  month =        apr,
  year =         "1942",
  bibdate =      "Sat Feb 8 10:28:55 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 7.4]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Crawford:1943:DNS
author: W. S. H. Crawford
title: Discussions and Notes: Square Roots from a Table of Cosines
journal: j-AMER-MATH-MONTHLY
volume: 50
number: 3
pages: 190--191
month: mar
monthnumber: 3
year: 1943
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Jun 28 12:36:57 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1999.06.28 12:36:57 MDT
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: W. S. H. Crawford
rawtitle: Discussions and Notes: Square Roots from a Table of Cosines
entry:
@Article{Crawford:1943:DNS,
  author =       "W. S. H. Crawford",
  title =        "Discussions and Notes: Square Roots from a Table of
                 Cosines",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "50",
  number =       "3",
  pages =        "190--191",
  month =        mar,
  year =         "1943",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:36:57 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: techreport
filename: fparith.bib
label: Rademacher:1943:MTI
author: Hans Rademacher
type: PX Report
number: 14
institution: Moore School of Electrical Engineering, Office of the Director Records, University of Pennsylvania
address: Philadelphia, PA, USA
pages: 190--191
day: 30
month: nov
monthnumber: 11
year: 1943
bibdate: Fri Jun 15 17:39:28 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2018.06.15 17:39:28 ???
acknowledgement: ack-nhfb
rawauthor: Hans Rademacher
title:
Mathematical Topics of Interest in PX, Part Two: Summary of Articles Dealing with Rounding off Errors

remark:
Cited on page 34 of Haigh, Priestley, and Rope, booktitle ENIAC in Action (2016) (ISBN 0-262-03398-4) as an annotated bibliography of rounding errors.

rawtitle:
Mathematical Topics of Interest in {PX}, Part Two: Summary of Articles Dealing with Rounding off Errors

entry:
@TechReport{Rademacher:1943:MTI,
  author =       "Hans Rademacher",
  title =        "Mathematical Topics of Interest in {PX}, Part Two:
                 Summary of Articles Dealing with Rounding off Errors",
  type =         "{PX} Report",
  number =       "14",
  institution =  "Moore School of Electrical Engineering, Office of the
                 Director Records, University of Pennsylvania",
  address =      "Philadelphia, PA, USA",
  day =          "30",
  month =        nov,
  year =         "1943",
  bibdate =      "Fri Jun 15 17:39:28 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited on page 34 of Haigh, Priestley, and Rope,
                 \booktitle{ENIAC in Action} (2016) (ISBN 0-262-03398-4)
                 as an annotated bibliography of rounding errors.",
}


bibtype: article
filename: fparith.bib
label: Goudsmit:1944:SFN
author: S. A. Goudsmit and W. H. Furry
title: Significant Figures of Numbers in Statistical Tables
journal: j-NATURE
volume: 154
number: 3921
pages: 800--801
day: 23
month: dec
monthnumber: 12
year: 1944
CODEN: NATUAS
DOI: https://doi.org/10.1038/154800a0
ISSN: 0028-0836 (print), 1476-4687 (electronic) OR 00280836 (print), 14764687 (electronic)
ISSNL: 0028-0836 OR 00280836
bibdate: Sun Sep 18 11:57:19 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2011.09.18 11:57:19 ???
URL: http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf
fjournal: Nature
keywords: Benford's Law; Law of Anomalous Numbers; Zipf's Law
acknowledgement: ack-nhfb
journalURL: http://www.nature.com/nature/archive/
rawauthor: S. A. Goudsmit and W. H. Furry
rawtitle: Significant Figures of Numbers in Statistical Tables
abstract:
A rough qualitative explanation of this fact can easily be given. If we consider tables in which the entries become rarer the larger they are, we can draw the obvious conclusion that in any interval, say, between 10 and 99, or 10,000 and 99,999, there are more entries on the small side than on the large side.

rawabstract:
A rough qualitative explanation of this fact can easily be given. If we consider tables in which the entries become rarer the larger they are, we can draw the obvious conclusion that in any interval, say, between 10 and 99, or 10,000 and 99,999, there are more entries on the small side than on the large side.

entry:
@Article{Goudsmit:1944:SFN,
  author =       "S. A. Goudsmit and W. H. Furry",
  title =        "Significant Figures of Numbers in Statistical Tables",
  journal =      j-NATURE,
  volume =       "154",
  number =       "3921",
  pages =        "800--801",
  day =          "23",
  month =        dec,
  year =         "1944",
  CODEN =        "NATUAS",
  DOI =          "https://doi.org/10.1038/154800a0",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Sun Sep 18 11:57:19 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf",
  abstract =     "A rough qualitative explanation of this fact can
                 easily be given. If we consider tables in which the
                 entries become rarer the larger they are, we can draw
                 the obvious conclusion that in any interval, say,
                 between 10 and 99, or 10,000 and 99,999, there are more
                 entries on the small side than on the large side.",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}


bibtype: article
filename: fparith.bib
label: Furry:1945:DND
author: W. H. Furry and Henry Hurwitz
title: Distribution of Numbers and Distribution of Significant Figures
journal: j-NATURE
volume: 155
number: 3924
pages: 52--53
day: 13
month: jan
monthnumber: 1
year: 1945
CODEN: NATUAS
DOI: https://doi.org/10.1038/155052a0
ISSN: 0028-0836 (print), 1476-4687 (electronic) OR 00280836 (print), 14764687 (electronic)
ISSNL: 0028-0836 OR 00280836
bibdate: Sun Sep 18 11:51:37 2011
bibtimestamp: 2011.09.18 11:51:37 ???
URL: http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf
fjournal: Nature
keywords: Benford's Law; Law of Anomalous Numbers; Zipf's Law
acknowledgement: ack-nhfb
journalURL: http://www.nature.com/nature/archive/
rawauthor: W. H. Furry and Henry Hurwitz
rawtitle: Distribution of Numbers and Distribution of Significant Figures
bibsource:
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Furry:1945:DND,
  author =       "W. H. Furry and Henry Hurwitz",
  title =        "Distribution of Numbers and Distribution of
                 Significant Figures",
  journal =      j-NATURE,
  volume =       "155",
  number =       "3924",
  pages =        "52--53",
  day =          "13",
  month =        jan,
  year =         "1945",
  CODEN =        "NATUAS",
  DOI =          "https://doi.org/10.1038/155052a0",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Sun Sep 18 11:51:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}


bibtype: techreport
filename: fparith.bib
label: vonNeumann:1945:FDR
author: John von Neumann
title: First Draft of a Report on the EDVAC
institution: University of Pennsylvania
pages: 52--53
day: 30
month: jun
monthnumber: 6
year: 1945
bibdate: Mon Jun 06 19:17:03 2005
bibtimestamp: 2005.06.06 19:17:03 ???
note: Reprinted in cite [ 8.2]Randell:1982:ODC.
acknowledgement: ack-nhfb
rawauthor: John von Neumann
rawnote: Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.
rawtitle: First Draft of a Report on the {EDVAC}
bibsource:
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

remark:
This is the report that got von Neumann's name associated with the serial, stored-program, general purpose, digital architecture upon which 99.99% of all computers today are based.

entry:
@TechReport{vonNeumann:1945:FDR,
  author =       "John von Neumann",
  title =        "First Draft of a Report on the {EDVAC}",
  institution =  "University of Pennsylvania",
  day =          "30",
  month =        jun,
  year =         "1945",
  bibdate =      "Mon Jun 06 19:17:03 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  remark =       "This is the report that got von Neumann's name
                 associated with the serial, stored-program, general
                 purpose, digital architecture upon which 99.99\% of all
                 computers today are based.",
  xxnote =       "Report prepared for U.S. Army Ordinance Department
                 under Contract W-670-ORD-4926. Reprinted in
                 \cite[pp.~177--246]{Stern:1981:EUA},
                 \cite[pp.~399--413]{Randell:1982:ODC},
                 \cite{vonNeumann:1993:FDR}, and
                 \cite{Laplante:1996:GPC}.",
}


bibtype: article
filename: fparith.bib
label: Aiken:1946:ASC
author: H. H. Aiken and G. M. Hopper
title: The Automatic Sequence Controlled Calculator
journal: j-ELECTR-ENG
volume: 65
pages: 384--391, 449--454, 522--528
year: 1946
CODEN: ELENAC
ISSN: 0095-9197 OR 00959197
bibdate: Wed Oct 13 11:26:29 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:26:29 ???
note: Reprinted in cite [ 5.2]Randell:1982:ODC.
fjournal: Electrical Engineering (American Institute of Electrical Engineers)
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714
rawauthor: H. H. Aiken and G. M. Hopper
rawnote: Reprinted in \cite[\S 5.2]{Randell:1982:ODC}.
rawtitle: The {Automatic Sequence Controlled Calculator}
entry:
@Article{Aiken:1946:ASC,
  author =       "H. H. Aiken and G. M. Hopper",
  title =        "The {Automatic Sequence Controlled Calculator}",
  journal =      j-ELECTR-ENG,
  volume =       "65",
  number =       "??",
  pages =        "384--391, 449--454, 522--528",
  year =         "1946",
  CODEN =        "ELENAC",
  ISSN =         "0095-9197",
  bibdate =      "Wed Oct 13 11:26:29 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 5.2]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Electrical Engineering (American Institute of
                 Electrical Engineers)",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714",
}


bibtype: techreport
filename: fparith.bib
label: Burks:1946:PDL
author: Arthur W. Burks and Herman H. Goldstine and John von Neumann
title: Preliminary discussion of the logical design of an electronic computing instrument
institution: inst-INST-ADV-STUDY
address: inst-INST-ADV-STUDY:adr
pages: 42
day: 28
month: jun
monthnumber: 6
year: 1946
MRnumber: MR22442
bibdate: Wed Oct 13 08:17:48 2004
bibtimestamp: 2004.10.13 08:17:48 ???
acknowledgement: ack-nhfb
authordates: John von Neumann (28 December 1903--8 February 1957)
rawauthor: Arthur W. Burks and Herman H. Goldstine and John von Neumann
rawtitle: Preliminary discussion of the logical design of an electronic computing instrument
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

note:
Report to the U.S. Army Ordnance Department under contract W-36-034-OKD-7481. Reprinted in cite [Paper 2]Taub:1963:JNCa, cite Bell:1971:CSR, cite [pp. 221--259]Swartzlander:1976:CDD and cite [pp. 97--146]Aspray:1987:PJN

URL:
https://deepblue.lib.umich.edu/handle/2027.42/3972; https://grch.com.ar/docs/p1/Apuntes/eng/Logical%20Design%20of%20an%20Electronic%20Computing%20Instrument.pdf

remark:
Discusses floating-point versus fixed-point computation, and concludes that floating-point is probably not justifiable. They wrote:par ``There appear to be two major purposes in a `floating' decimal point system both of which arise from the fact that the number of digits in a word is a constant fixed by design considerations for each particular machine. The first of these purposes is to retain in a sum or product as many significant digits as possible and the second of these is to free the human operator from the burden of estimating and inserting into a problem `scale factors' --- multiplicative constants which serve to keep numbers within the limits of the machine.par There is, of course, no denying the fact that human time is consumed in arranging for the introduction of suitable scale factors. We only argue that the time so consumed is a very small percentage of the total time we will spend in preparing an interesting problem for our machine. The first advantage of the floating point is, we feel, somewhat illusory. In order to have such a floating point, one must waste memory capacity which could otherwise be used for carrying more digits per word. It would therefore seem to us not at all clear whether the modest advantages of a floating binary point offset the loss of memory capacity and the increased complexity of the arithmetic and control circuits.''

rawnote:
Report to the U.S. Army Ordnance Department under contract W-36-034-OKD-7481. Reprinted in \cite[Paper 2]{Taub:1963:JNCa}, \cite{Bell:1971:CSR}, \cite[pp. 221--259]{Swartzlander:1976:CDD} and \cite[pp. 97--146]{Aspray:1987:PJN}

entry:
@TechReport{Burks:1946:PDL,
  author =       "Arthur W. Burks and Herman H. Goldstine and John von
                 Neumann",
  title =        "Preliminary discussion of the logical design of an
                 electronic computing instrument",
  institution =  inst-INST-ADV-STUDY,
  address =      inst-INST-ADV-STUDY:adr,
  pages =        "42",
  day =          "28",
  month =        jun,
  year =         "1946",
  MRnumber =     "MR22442",
  bibdate =      "Wed Oct 13 08:17:48 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Report to the U.S. Army Ordnance Department under
                 contract W-36-034-OKD-7481. Reprinted in \cite[Paper
                 2]{Taub:1963:JNCa}, \cite{Bell:1971:CSR}, \cite[pp.
                 221--259]{Swartzlander:1976:CDD} and \cite[pp.
                 97--146]{Aspray:1987:PJN}",
  URL =          "https://deepblue.lib.umich.edu/handle/2027.42/3972;
                 https://grch.com.ar/docs/p1/Apuntes/eng/Logical%20Design%20of%20an%20Electronic%20Computing%20Instrument.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "John von Neumann (28 December 1903--8 February 1957)",
  remark =       "Discusses floating-point versus fixed-point
                 computation, and concludes that floating-point is
                 probably not justifiable. They wrote:\par

                 ``There appear to be two major purposes in a `floating'
                 decimal point system both of which arise from the fact
                 that the number of digits in a word is a constant fixed
                 by design considerations for each particular machine.
                 The first of these purposes is to retain in a sum or
                 product as many significant digits as possible and the
                 second of these is to free the human operator from the
                 burden of estimating and inserting into a problem
                 `scale factors' --- multiplicative constants which
                 serve to keep numbers within the limits of the
                 machine.\par

                 There is, of course, no denying the fact that human
                 time is consumed in arranging for the introduction of
                 suitable scale factors. We only argue that the time so
                 consumed is a very small percentage of the total time
                 we will spend in preparing an interesting problem for
                 our machine. The first advantage of the floating point
                 is, we feel, somewhat illusory. In order to have such a
                 floating point, one must waste memory capacity which
                 could otherwise be used for carrying more digits per
                 word. It would therefore seem to us not at all clear
                 whether the modest advantages of a floating binary
                 point offset the loss of memory capacity and the
                 increased complexity of the arithmetic and control
                 circuits.''",
}


bibtype: article
filename: fparith.bib
label: Cesareo:1946:RI
author: O. Cesareo
title: The Relay Interpolator
journal: j-BELL-LABS-RECORD
volume: 23
pages: 457--460
year: 1946
CODEN: BLRCAB
ISSN: 0005-8564 OR 00058564
bibdate: Wed Oct 13 11:31:47 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:31:47 ???
note: Reprinted in cite [ 6.2]Randell:1982:ODC.
fjournal: Bell Laboratories Record
acknowledgement: ack-nhfb
rawauthor: O. Cesareo
rawnote: Reprinted in \cite[\S 6.2]{Randell:1982:ODC}.
rawtitle: The Relay Interpolator
entry:
@Article{Cesareo:1946:RI,
  author =       "O. Cesareo",
  title =        "The Relay Interpolator",
  journal =      j-BELL-LABS-RECORD,
  volume =       "23",
  number =       "??",
  pages =        "457--460",
  year =         "1946",
  CODEN =        "BLRCAB",
  ISSN =         "0005-8564",
  bibdate =      "Wed Oct 13 11:31:47 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 6.2]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Bell Laboratories Record",
}


bibtype: article
filename: fparith.bib
label: Comrie:1946:BDC
author: L. J. Comrie
title: Babbage's Dream Come True
journal: j-NATURE
volume: 158
number: 4017
pages: 567--568
day: 26
month: oct
monthnumber: 10
year: 1946
CODEN: NATUAS
DOI: https://doi.org/10.1038/158567a0
ISSN: 0028-0836 (print), 1476-4687 (electronic) OR 00280836 (print), 14764687 (electronic)
ISSNL: 0028-0836 OR 00280836
bibdate: Wed Aug 9 07:30:09 2023
bibtimestamp: 2023.08.09 07:30:09 ???
fjournal: Nature
acknowledgement: ack-nhfb
journalURL: http://www.nature.com/nature/archive/
rawauthor: L. J. Comrie
rawtitle: {Babbage}'s Dream Come True
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
The black mark earned by the government of the day more than a hundred years ago for its failure to see Charles Babbage's difference engine brought to a successful conclusion has still to be wiped out. It is not too much to say that it cost Britain the leading place in the art of mechanical computing. Babbage then conceived and worked on his `analytical engine', designed to store numbers and operate on them according to a sequence of processes conveyed to the machine by cards similar to those used in the Jacquard loom. This, however, was never completed.

remark:
The title in the Nature archive index is completely wrong: it says ``A Manual of Operation for the Automatic Sequence Controlled Calculator''. After the critical introduction [see the abstract], the article goes on to describe IBM's gift to Harvard of the Automatic Sequence Controlled Calculator. It reports about the ASCC: ``The machine contains seventy-two storage counters, capable of holding twenty-three digits and a sign. ldots When working to the full 23-figure capacity of the machine, multiplication takes about six seconds, and division twice as long; additions and subtractions are done at the rate of three a second, whatever their length.'' It then describes the computation of logarithms via the Taylor series expansion of $ log (1 + x) $, and reports that it can do exponential, trigonometric, and hyperbolic functions as well.

rawabstract:
The black mark earned by the government of the day more than a hundred years ago for its failure to see Charles Babbage's difference engine brought to a successful conclusion has still to be wiped out. It is not too much to say that it cost Britain the leading place in the art of mechanical computing. Babbage then conceived and worked on his `analytical engine', designed to store numbers and operate on them according to a sequence of processes conveyed to the machine by cards similar to those used in the Jacquard loom. This, however, was never completed.

entry:
@Article{Comrie:1946:BDC,
  author =       "L. J. Comrie",
  title =        "{Babbage}'s Dream Come True",
  journal =      j-NATURE,
  volume =       "158",
  number =       "4017",
  pages =        "567--568",
  day =          "26",
  month =        oct,
  year =         "1946",
  CODEN =        "NATUAS",
  DOI =          "https://doi.org/10.1038/158567a0",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Wed Aug 9 07:30:09 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The black mark earned by the government of the day
                 more than a hundred years ago for its failure to see
                 Charles Babbage's difference engine brought to a
                 successful conclusion has still to be wiped out. It is
                 not too much to say that it cost Britain the leading
                 place in the art of mechanical computing. Babbage then
                 conceived and worked on his `analytical engine',
                 designed to store numbers and operate on them according
                 to a sequence of processes conveyed to the machine by
                 cards similar to those used in the Jacquard loom. This,
                 however, was never completed.",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  remark =       "The title in the Nature archive index is completely
                 wrong: it says ``A Manual of Operation for the
                 Automatic Sequence Controlled Calculator''. After the
                 critical introduction [see the abstract], the article
                 goes on to describe IBM's gift to Harvard of the
                 Automatic Sequence Controlled Calculator. It reports
                 about the ASCC: ``The machine contains seventy-two
                 storage counters, capable of holding twenty-three
                 digits and a sign. \ldots{} When working to the full
                 23-figure capacity of the machine, multiplication takes
                 about six seconds, and division twice as long;
                 additions and subtractions are done at the rate of
                 three a second, whatever their length.'' It then
                 describes the computation of logarithms via the Taylor
                 series expansion of $ \log (1 + x) $, and reports that
                 it can do exponential, trigonometric, and hyperbolic
                 functions as well.",
}


bibtype: techreport
filename: fparith.bib
label: Dreyer:1946:REM
author: H.-J. Dreyer and A. Walther
type: Bericht
number: A3
institution: Institut fur Praktische Mathematik, Technische Hochschule
address: Darmstadt, West Germany
pages: 567--568
day: 19
month: aug
monthnumber: 8
year: 1946
bibdate: Wed Oct 13 11:20:15 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:20:15 ???
note: Reprinted in cite [ 3.3]Randell:1982:ODC. Translated by Mr. and Mrs. P. Jones
language: German
acknowledgement: ack-nhfb
rawauthor: H.-J. Dreyer and A. Walther
rawnote: Reprinted in \cite[\S 3.3]{Randell:1982:ODC}. Translated by Mr. and Mrs. P. Jones
title:
Der Rechenautomat Ipm. Entwicklung Mathematischer Instrumente in Deutschland 1939 bis 1945. (German) [The Ipm Calculator. The development of mathematical instruments in Germany 1939--1945]

rawtitle:
{Der Rechenautomat Ipm. Entwicklung Mathematischer Instrumente in Deutschland 1939 bis 1945}. ({German}) [{The} {Ipm} Calculator. {The} development of mathematical instruments in {Germany} 1939--1945]

entry:
@TechReport{Dreyer:1946:REM,
  author =       "H.-J. Dreyer and A. Walther",
  title =        "{Der Rechenautomat Ipm. Entwicklung Mathematischer
                 Instrumente in Deutschland 1939 bis 1945}. ({German})
                 [{The} {Ipm} Calculator. {The} development of
                 mathematical instruments in {Germany} 1939--1945]",
  type =         "{Bericht}",
  number =       "A3",
  institution =  "Institut f{\"u}r Praktische Mathematik, Technische
                 Hochschule",
  address =      "Darmstadt, West Germany",
  day =          "19",
  month =        aug,
  year =         "1946",
  bibdate =      "Wed Oct 13 11:20:15 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 3.3]{Randell:1982:ODC}.
                 Translated by Mr. and Mrs. P. Jones",
  acknowledgement = ack-nhfb,
  language =     "German",
}


bibtype: article
filename: fparith.bib
label: Goldstine:1946:ENI
author: H. H. Goldstine and Adele Goldstine
title: The Electronic Numerical Integrator and Computer (ENIAC)
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 2
number: 15
pages: 97--110
month: jul
monthnumber: 7
year: 1946
CODEN: MTTCAS
ISSN: 0891-6837 OR 08916837
bibdate: Tue Oct 13 08:44:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1998.10.13 08:44:19 MDT
note: Reprinted in cite [ 7.7]Randell:1982:ODC.
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
ajournal: Math. Tables Other Aids Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: H. H. Goldstine and Adele Goldstine
rawnote: Reprinted in \cite[\S 7.7]{Randell:1982:ODC}.
rawtitle: The {Electronic Numerical Integrator and Computer (ENIAC)}
entry:
@Article{Goldstine:1946:ENI,
  author =       "H. H. Goldstine and Adele Goldstine",
  title =        "The {Electronic Numerical Integrator and Computer
                 (ENIAC)}",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "2",
  number =       "15",
  pages =        "97--110",
  month =        jul,
  year =         "1946",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibdate =      "Tue Oct 13 08:44:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  note =         "Reprinted in \cite[\S 7.7]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Tables Other Aids Comput.",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: techreport
filename: fparith.bib
label: Goldstine:1947:PCPa
author: Herman H. Goldstine and John von Neumann
title: Planning and coding of problems for an electronic computing instrument. Part 1, Vol. 1
type: Technical report
institution: inst-INST-ADV-STUDY
address: inst-INST-ADV-STUDY:adr
year: 1947
bibdate: Fri Nov 16 16:35:14 2012
bibtimestamp: 2012.11.16 16:35:14 ???
acknowledgement: ack-nhfb
rawauthor: Herman H. Goldstine and John von Neumann
rawtitle: Planning and coding of problems for an electronic computing instrument. {Part 1}, Vol. 1
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@TechReport{Goldstine:1947:PCPa,
  author =       "Herman H. Goldstine and John von Neumann",
  title =        "Planning and coding of problems for an electronic
                 computing instrument. {Part 1}, Vol. 1",
  type =         "Technical report",
  institution =  inst-INST-ADV-STUDY,
  address =      inst-INST-ADV-STUDY:adr,
  pages =        "??",
  month =        "????",
  year =         "1947",
  bibdate =      "Fri Nov 16 16:35:14 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Goldstine:1947:PCPb
author: Herman H. Goldstine and John von Neumann
title: Planning and coding of problems for an electronic computing instrument. Part 2, Vol. 1
type: Technical report
number: 1
institution: inst-INST-ADV-STUDY
address: inst-INST-ADV-STUDY:adr
pages: 69
day: 1
month: apr
monthnumber: 4
year: 1947
MRnumber: MR22443
bibdate: Wed Jun 01 17:41:33 2005
bibtimestamp: 2005.06.01 17:41:33 ???
acknowledgement: ack-nhfb
rawauthor: Herman H. Goldstine and John von Neumann
rawtitle: Planning and coding of problems for an electronic computing instrument. {Part 2}, Vol. 1
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

note:
Report prepared for U.S. Army Ordnance Department under contract W-36-034-OKD-7481. Reprinted in cite [80--151]Taub:1963:JNCa. Knuth cite [p. 278]Knuth:1998:SA cites pp. 142--151 of this report as the first published treatment of double-precision arithmetic on digital computers.

rawnote:
Report prepared for U.S. Army Ordnance Department under contract W-36-034-OKD-7481. Reprinted in \cite[80--151]{Taub:1963:JNCa}. Knuth \cite[p. 278]{Knuth:1998:SA} cites pp. 142--151 of this report as the first published treatment of double-precision arithmetic on digital computers.

entry:
@TechReport{Goldstine:1947:PCPb,
  author =       "Herman H. Goldstine and John von Neumann",
  title =        "Planning and coding of problems for an electronic
                 computing instrument. {Part 2}, Vol. 1",
  type =         "Technical report",
  number =       "1",
  institution =  inst-INST-ADV-STUDY,
  address =      inst-INST-ADV-STUDY:adr,
  pages =        "69",
  day =          "1",
  month =        apr,
  year =         "1947",
  MRnumber =     "MR22443",
  bibdate =      "Wed Jun 01 17:41:33 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Report prepared for U.S. Army Ordnance Department
                 under contract W-36-034-OKD-7481. Reprinted in
                 \cite[80--151]{Taub:1963:JNCa}. Knuth \cite[p.
                 278]{Knuth:1998:SA} cites pp. 142--151 of this report
                 as the first published treatment of double-precision
                 arithmetic on digital computers.",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Goldstine:1947:PCPc
author: Herman H. Goldstine and John von Neumann
title: Planning and coding of problems for an electronic computing instrument. Part 1, Vol. 2
type: Technical report
institution: inst-INST-ADV-STUDY
address: inst-INST-ADV-STUDY:adr
year: 1947
bibdate: Fri Nov 16 16:35:14 2012
bibtimestamp: 2012.11.16 16:35:14 ???
acknowledgement: ack-nhfb
rawauthor: Herman H. Goldstine and John von Neumann
rawtitle: Planning and coding of problems for an electronic computing instrument. {Part 1}, Vol. 2
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@TechReport{Goldstine:1947:PCPc,
  author =       "Herman H. Goldstine and John von Neumann",
  title =        "Planning and coding of problems for an electronic
                 computing instrument. {Part 1}, Vol. 2",
  type =         "Technical report",
  institution =  inst-INST-ADV-STUDY,
  address =      inst-INST-ADV-STUDY:adr,
  pages =        "??",
  month =        "????",
  year =         "1947",
  bibdate =      "Fri Nov 16 16:35:14 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Goldstine:1947:PCPd
author: Herman H. Goldstine and John von Neumann
title: Planning and coding of problems for an electronic computing instrument. Part 2, Vol. 2
type: Technical report
institution: inst-INST-ADV-STUDY
address: inst-INST-ADV-STUDY:adr
year: 1947
bibdate: Fri Nov 16 16:35:14 2012
bibtimestamp: 2012.11.16 16:35:14 ???
acknowledgement: ack-nhfb
rawauthor: Herman H. Goldstine and John von Neumann
rawtitle: Planning and coding of problems for an electronic computing instrument. {Part 2}, Vol. 2
entry:
@TechReport{Goldstine:1947:PCPd,
  author =       "Herman H. Goldstine and John von Neumann",
  title =        "Planning and coding of problems for an electronic
                 computing instrument. {Part 2}, Vol. 2",
  type =         "Technical report",
  institution =  inst-INST-ADV-STUDY,
  address =      inst-INST-ADV-STUDY:adr,
  pages =        "??",
  month =        "????",
  year =         "1947",
  bibdate =      "Fri Nov 16 16:35:14 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Goldstine:1947:PCPe
author: Herman H. Goldstine and John von Neumann
title: Planning and coding of problems for an electronic computing instrument. Part 1, Vol. 3
type: Technical report
institution: inst-INST-ADV-STUDY
address: inst-INST-ADV-STUDY:adr
year: 1947
bibdate: Fri Nov 16 16:35:14 2012
bibtimestamp: 2012.11.16 16:35:14 ???
acknowledgement: ack-nhfb
rawauthor: Herman H. Goldstine and John von Neumann
rawtitle: Planning and coding of problems for an electronic computing instrument. {Part 1}, Vol. 3
entry:
@TechReport{Goldstine:1947:PCPe,
  author =       "Herman H. Goldstine and John von Neumann",
  title =        "Planning and coding of problems for an electronic
                 computing instrument. {Part 1}, Vol. 3",
  type =         "Technical report",
  institution =  inst-INST-ADV-STUDY,
  address =      inst-INST-ADV-STUDY:adr,
  pages =        "??",
  month =        "????",
  year =         "1947",
  bibdate =      "Fri Nov 16 16:35:14 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: fparith.bib
label: Goldstine:1947:PCPf
author: Herman H. Goldstine and John von Neumann
title: Planning and coding of problems for an electronic computing instrument. Part 2, Vol. 3
type: Technical report
institution: inst-INST-ADV-STUDY
address: inst-INST-ADV-STUDY:adr
year: 1947
bibdate: Fri Nov 16 16:35:14 2012
bibtimestamp: 2012.11.16 16:35:14 ???
acknowledgement: ack-nhfb
rawauthor: Herman H. Goldstine and John von Neumann
rawtitle: Planning and coding of problems for an electronic computing instrument. {Part 2}, Vol. 3
entry:
@TechReport{Goldstine:1947:PCPf,
  author =       "Herman H. Goldstine and John von Neumann",
  title =        "Planning and coding of problems for an electronic
                 computing instrument. {Part 2}, Vol. 3",
  type =         "Technical report",
  institution =  inst-INST-ADV-STUDY,
  address =      inst-INST-ADV-STUDY:adr,
  pages =        "??",
  month =        "????",
  year =         "1947",
  bibdate =      "Fri Nov 16 16:35:14 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: HUCL:1946:MOA
author: Harvard University. Computation Laboratory
title: A Manual of Operation for the Automatic Sequence Controlled Calculator
publisher: pub-HARVARD
address: pub-HARVARD:adr
pages: 561
year: 1946
LCCN: QA3 .H3 v.1
bibdate: Mon Nov 4 07:46:57 MST 2002
bibtimestamp: 2002.11.04 07:46:57 MST
series: Its Annals v. 1
keywords: electronic digital computers; mathematics --- bibliography
acknowledgement: ack-nhfb
rawauthor: {Harvard University. Computation Laboratory}
rawtitle: A Manual of Operation for the {Automatic Sequence Controlled Calculator}
bibsource:
https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Book{HUCL:1946:MOA,
  author =       "{Harvard University. Computation Laboratory}",
  title =        "A Manual of Operation for the {Automatic Sequence
                 Controlled Calculator}",
  publisher =    pub-HARVARD,
  address =      pub-HARVARD:adr,
  pages =        "561",
  year =         "1946",
  LCCN =         "QA3 .H3 v.1",
  bibdate =      "Mon Nov 4 07:46:57 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Its Annals v. 1",
  acknowledgement = ack-nhfb,
  keywords =     "electronic digital computers; mathematics ---
                 bibliography",
}


bibtype: techreport
filename: fparith.bib
label: Turing:1946:PEC
author: A. M. Turing
title: Proposed Electronic Calculator
type: Report
number: E882
institution: inst-NPL
address: inst-NPL:adr
pages: 48
year: 1946
bibdate: Fri Nov 25 16:22:27 2005
bibtimestamp: 2005.11.25 16:22:27 ???
URL: http://www.emula3.com/docs/Turing_Report_on_ACE.pdf
acknowledgement: ack-nhfb
authordates: Alan Mathison Turing (23 June 1912--7 June 1954)
rawauthor: A. M. Turing
rawtitle: Proposed Electronic Calculator
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@TechReport{Turing:1946:PEC,
  author =       "A. M. Turing",
  title =        "Proposed Electronic Calculator",
  type =         "Report",
  number =       "E882",
  institution =  inst-NPL,
  address =      inst-NPL:adr,
  pages =        "48",
  year =         "1946",
  bibdate =      "Fri Nov 25 16:22:27 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.emula3.com/docs/Turing_Report_on_ACE.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Alan Mathison Turing (23 June 1912--7 June 1954)",
  xxnote =       "Reprinted in \cite{Turing:1972:MTO}.",
}


bibtype: article
filename: fparith.bib
label: Juley:1947:BC
author: J. Juley
title: The Ballistic Computer
journal: j-BELL-LABS-RECORD
volume: 24
pages: 5--9
year: 1947
CODEN: BLRCAB
ISSN: 0005-8564 OR 00058564
bibdate: Wed Oct 13 11:32:38 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:32:38 ???
note: Reprinted in cite [ 6.3]Randell:1982:ODC.
fjournal: Bell Laboratories Record
acknowledgement: ack-nhfb
rawauthor: J. Juley
rawnote: Reprinted in \cite[\S 6.3]{Randell:1982:ODC}.
rawtitle: The Ballistic Computer
entry:
@Article{Juley:1947:BC,
  author =       "J. Juley",
  title =        "The Ballistic Computer",
  journal =      j-BELL-LABS-RECORD,
  volume =       "24",
  number =       "??",
  pages =        "5--9",
  year =         "1947",
  CODEN =        "BLRCAB",
  ISSN =         "0005-8564",
  bibdate =      "Wed Oct 13 11:32:38 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 6.3]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Bell Laboratories Record",
}


bibtype: inproceedings
filename: fparith.bib
label: Mauchly:1947:PPE
author: J. W. Mauchly
booktitle: Proceedings of a Symposium on Large Scale Digital Calculating Machinery, 7--10 January 1947
title: Preparation of problems for EDVAC-type machines
publisher: Harvard University Press
address: Cambridge, MA, USA
pages: 5--9
year: 1947
bibdate: Wed Oct 13 11:55:58 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:55:58 ???
acknowledgement: ack-nhfb
rawauthor: J. W. Mauchly
rawbooktitle: {Proceedings of a Symposium on Large Scale Digital Calculating Machinery, 7--10 January 1947}
rawtitle: Preparation of problems for {EDVAC}-type machines
note:
Reprinted in em Annals of the Computation Laboratory of Harvard University, bf 16, 203--207 (1948). Reprinted in cite [ 8.2]Randell:1982:ODC.

rawnote:
Reprinted in {\em Annals of the Computation Laboratory of Harvard University}, {\bf 16}, 203--207 (1948). Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.

entry:
@InProceedings{Mauchly:1947:PPE,
  author =       "J. W. Mauchly",
  booktitle =    "{Proceedings of a Symposium on Large Scale Digital
                 Calculating Machinery, 7--10 January 1947}",
  title =        "Preparation of problems for {EDVAC}-type machines",
  publisher =    "Harvard University Press",
  address =      "Cambridge, MA, USA",
  year =         "1947",
  bibdate =      "Wed Oct 13 11:55:58 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in {\em Annals of the Computation Laboratory
                 of Harvard University}, {\bf 16}, 203--207 (1948).
                 Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Richeson:1947:FAP
author: A. W. Richeson
title: The First Arithmetic Printed in English
journal: j-ISIS
volume: 37
number: 1--2
pages: 47--56
month: may
monthnumber: 5
year: 1947
CODEN: ISISA4
ISSN: 0021-1753 (print), 1545-6994 (electronic) OR 00211753 (print), 15456994 (electronic)
ISSNL: 0021-1753 OR 00211753
bibdate: Tue Jul 30 21:27:09 MDT 2013
bibtimestamp: 2013.07.30 21:27:09 MDT
URL: http://www.jstor.org/stable/226161
fjournal: Isis
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journal/isis
rawauthor: A. W. Richeson
rawtitle: The First Arithmetic Printed in {English}
bibsource:
http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i302230; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/isis1940.bib

remark:
From the second paragraph: ``The earliest printed work in English to discuss arithmetic, booktitle The Myrrour of the World, came from the press of William Caxton in 1481. This work, however, contained only one page devoted entirely to arithmetic. It is not until 1537 that we find another book printed in English devoted entirely to arithmetic and dealing with the Hindu--Arabic system of numbers. This is an anonymous publication, from a press located at St. Albans, with the title booktitle An Introduction for to Lerne to Recken with the Pen, or with the Counters,'' This book went through eight editions between 1537 and 1629. The article quotes book sections on integer division.

entry:
@Article{Richeson:1947:FAP,
  author =       "A. W. Richeson",
  title =        "The First Arithmetic Printed in {English}",
  journal =      j-ISIS,
  volume =       "37",
  number =       "1--2",
  pages =        "47--56",
  month =        may,
  year =         "1947",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:27:09 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i302230;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1940.bib",
  URL =          "http://www.jstor.org/stable/226161",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
  remark =       "From the second paragraph: ``The earliest printed work
                 in English to discuss arithmetic, \booktitle{The
                 Myrrour of the World}, came from the press of William
                 Caxton in 1481. This work, however, contained only one
                 page devoted entirely to arithmetic. It is not until
                 1537 that we find another book printed in English
                 devoted entirely to arithmetic and dealing with the
                 Hindu--Arabic system of numbers. This is an anonymous
                 publication, from a press located at St. Albans, with
                 the title \booktitle{An Introduction for to Lerne to
                 Recken with the Pen, or with the Counters},'' This book
                 went through eight editions between 1537 and 1629. The
                 article quotes book sections on integer division.",
}


bibtype: article
filename: fparith.bib
label: vonNeumann:1947:NIM
author: John von Neumann and Herman H. Goldstine
title: Numerical Inverting of Matrices of High Order
journal: j-BULL-AMS
volume: 53
number: 11
pages: 1021--1099
month: nov
monthnumber: 11
year: 1947
CODEN: BAMOAD
ISSN: 0002-9904 (print), 1936-881X (electronic) OR 00029904 (print), 1936881X (electronic)
ISSNL: 0002-9904 OR 00029904
MRclass: 65.0X
MRnumber: MR0024235 (9,471b)
MRreviewer: E. Bodewig
bibdate: Thu Nov 8 14:49:36 2007
bibtimestamp: 2007.11.08 14:49:36 ???
note: See cite Goldstine:1951:NIM for Part II. Reprinted in cite [vol. 5, pp. 479--557]Taub:1961:JNCa.
URL: http://projecteuclid.org/euclid.bams/1183511222
fjournal: Bulletin of the American Mathematical Society
ZMnumber: 0031.31402
acknowledgement: ack-nhfb
authordates: John von Neumann (28 December 1903--8 February 1957)
journalURL: http://www.ams.org/journals/bull/all_issues.html
rawauthor: John von Neumann and Herman H. Goldstine
rawtitle: Numerical Inverting of Matrices of High Order
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/auto.diff.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.1.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/Matrix.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/sparse.linear.systems.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

remark:
This may be the first journal publication about the use of double-precision arithmetic on computers, used for the accumulation of inner products and matrix products. On pp. 1035--1038, the authors show that when the sum of $m$ products of two $s$-digit numbers is accumulated in precision $ 2 s $, with rounding to $s$ digits only after the final sum is complete, then the rounding error is essentially one unit in the last place, instead of $m$ times that value. Cited in cite Sterbenz:1974:FPC.

rawnote:
See \cite{Goldstine:1951:NIM} for Part II. Reprinted in \cite[vol. 5, pp. 479--557]{Taub:1961:JNCa}.

entry:
@Article{vonNeumann:1947:NIM,
  author =       "John von Neumann and Herman H. Goldstine",
  title =        "Numerical Inverting of Matrices of High Order",
  journal =      j-BULL-AMS,
  volume =       "53",
  number =       "11",
  pages =        "1021--1099",
  month =        nov,
  year =         "1947",
  CODEN =        "BAMOAD",
  ISSN =         "0002-9904 (print), 1936-881X (electronic)",
  ISSN-L =       "0002-9904",
  MRclass =      "65.0X",
  MRnumber =     "MR0024235 (9,471b)",
  MRreviewer =   "E. Bodewig",
  bibdate =      "Thu Nov 8 14:49:36 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/auto.diff.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.1.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/Matrix.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/sparse.linear.systems.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Goldstine:1951:NIM} for Part II. Reprinted
                 in \cite[vol. 5, pp. 479--557]{Taub:1961:JNCa}.",
  URL =          "http://projecteuclid.org/euclid.bams/1183511222",
  ZMnumber =     "0031.31402",
  acknowledgement = ack-nhfb # " and " # ack-jg,
  author-dates = "John von Neumann (28 December 1903--8 February 1957)",
  fjournal =     "Bulletin of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/bull/all_issues.html",
  kwds =         "nla, linear system, rounding error",
  referred =     "[Markov1999a].",
  remark =       "This may be the first journal publication about the
                 use of double-precision arithmetic on computers, used
                 for the accumulation of inner products and matrix
                 products. On pp. 1035--1038, the authors show that when
                 the sum of $m$ products of two $s$-digit numbers is
                 accumulated in precision $ 2 s $, with rounding to $s$
                 digits only after the final sum is complete, then the
                 rounding error is essentially one unit in the last
                 place, instead of $m$ times that value. Cited in
                 \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Alt:1948:BTLa
author: Franz L. Alt
title: A Bell Telephone Laboratories' Computing Machine---I
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 3
number: 21
pages: 1--13
month: jan
monthnumber: 1
year: 1948
CODEN: MTTCAS
ISSN: 0891-6837 OR 08916837
bibdate: Tue Oct 13 08:44:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1998.10.13 08:44:19 MDT
note: Reprinted in cite [ 6.4]Randell:1982:ODC.
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
ajournal: Math. Tables Other Aids Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: Franz L. Alt
rawnote: Reprinted in \cite[\S 6.4]{Randell:1982:ODC}.
rawtitle: A {Bell Telephone Laboratories}' Computing Machine---{I}
entry:
@Article{Alt:1948:BTLa,
  author =       "Franz L. Alt",
  title =        "A {Bell Telephone Laboratories}' Computing
                 Machine---{I}",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "3",
  number =       "21",
  pages =        "1--13",
  month =        jan,
  year =         "1948",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibdate =      "Tue Oct 13 08:44:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  note =         "Reprinted in \cite[\S 6.4]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Tables Other Aids Comput.",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: fparith.bib
label: Eckert:1948:EC
author: W. J. Eckert
title: Electrons and computation
journal: j-SCI-MONTHLY
volume: 67
number: 5
pages: 315--323
month: nov
monthnumber: 11
year: 1948
CODEN: SCMOAA
ISSN: 0096-3771 (print), 2327-7513 (electronic) OR 00963771 (print), 23277513 (electronic)
bibdate: Wed Oct 13 11:27:40 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:27:40 ???
note: Reprinted in cite [ 5.3]Randell:1982:ODC.
fjournal: The Scientific Monthly
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journal/sciemont
rawauthor: W. J. Eckert
rawnote: Reprinted in \cite[\S 5.3]{Randell:1982:ODC}.
rawtitle: Electrons and computation
entry:
@Article{Eckert:1948:EC,
  author =       "W. J. Eckert",
  title =        "Electrons and computation",
  journal =      j-SCI-MONTHLY,
  volume =       "67",
  number =       "5",
  pages =        "315--323",
  month =        nov,
  year =         "1948",
  CODEN =        "SCMOAA",
  ISSN =         "0096-3771 (print), 2327-7513 (electronic)",
  bibdate =      "Wed Oct 13 11:27:40 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 5.3]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "The Scientific Monthly",
  journal-URL =  "http://www.jstor.org/journal/sciemont",
}


bibtype: inproceedings
filename: fparith.bib
label: Rademacher:1948:AEP
author: Hans A. Rademacher
title: On the Accumulation of Errors in Processes of Integration on High-Speed Calculating Machines
crossref: Anonymous:1948:PSL
pages: 176--187
year: 1948
bibdate: Mon Jun 18 11:03:56 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2018.06.18 11:03:56 ???
acknowledgement: ack-nhfb
rawauthor: Hans A. Rademacher
rawtitle: On the Accumulation of Errors in Processes of Integration on High-Speed Calculating Machines
remark:
From page 186, remark by John W. Mauchly: ``I just wanted to remark that this paper is probably one of the first to appear as a result of the interaction between computing machines and mathematics. I think many of us have been looking forward with certainty to the day when the advent of computing machines would influence the course of mathematics, and there are still many directions in which we can look forward to further such impacts. This reaction is not, of course, one way. Mathematics should also influence the computing machine.''

entry:
@InProceedings{Rademacher:1948:AEP,
  author =       "Hans A. Rademacher",
  title =        "On the Accumulation of Errors in Processes of
                 Integration on High-Speed Calculating Machines",
  crossref =     "Anonymous:1948:PSL",
  pages =        "176--187",
  year =         "1948",
  bibdate =      "Mon Jun 18 11:03:56 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "From page 186, remark by John W. Mauchly: ``I just
                 wanted to remark that this paper is probably one of the
                 first to appear as a result of the interaction between
                 computing machines and mathematics. I think many of us
                 have been looking forward with certainty to the day
                 when the advent of computing machines would influence
                 the course of mathematics, and there are still many
                 directions in which we can look forward to further such
                 impacts. This reaction is not, of course, one way.
                 Mathematics should also influence the computing
                 machine.''",
}


bibtype: techreport
filename: fparith.bib
label: Tukey:1948:NSR
author: John W. Tukey
title: A note on the square-root iteration
type: SRG Memorandum report
number: 10
institution: inst-PRINCETON
address: inst-PRINCETON:adr
pages: 18
year: 1948
bibdate: Tue May 15 08:00:09 2012
bibtimestamp: 2012.05.15 08:00:09 ???
acknowledgement: ack-nhfb
rawauthor: John W. Tukey
rawtitle: A note on the square-root iteration
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@TechReport{Tukey:1948:NSR,
  author =       "John W. Tukey",
  title =        "A note on the square-root iteration",
  type =         "SRG Memorandum report",
  number =       "10",
  institution =  inst-PRINCETON,
  address =      inst-PRINCETON:adr,
  pages =        "18",
  year =         "1948",
  bibdate =      "Tue May 15 08:00:09 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Turing:1948:REM
author: A. M. Turing
title: Rounding-Off Errors in Matrix Processes
journal: j-QUART-J-MECH-APPLIED-MATH
volume: 1
pages: 287--308
month: sep
monthnumber: 9
year: 1948
CODEN: QJMMAV
ISSN: 0033-5614 (print), 1464-3855 (electronic) OR 00335614 (print), 14643855 (electronic)
ISSNL: 0033-5614 OR 00335614
MRclass: 65.0X
MRnumber: MR0028100 (10,405c)
MRreviewer: E. Bodewig
bibdate: Sat Nov 19 12:09:58 2005
bibtimestamp: 2005.11.19 12:09:58 ???
note: Reprinted in cite Turing:1992:PM with summary and notes (including corrections)
URL: http://turing.ecs.soton.ac.uk/browse.php/B/18
fjournal: Quarterly Journal of Mechanics and Applied Mathematics
ZMnumber: 0033.28501
acknowledgement: ack-nhfb
journalURL: http://qjmam.oxfordjournals.org/content/by/year
rawauthor: A. M. Turing
rawnote: Reprinted in \cite{Turing:1992:PM} with summary and notes (including corrections)
rawtitle: Rounding-Off Errors in Matrix Processes
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/a/turing-alan-mathison.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Turing:1948:REM,
  author =       "A. M. Turing",
  title =        "Rounding-Off Errors in Matrix Processes",
  journal =      j-QUART-J-MECH-APPLIED-MATH,
  volume =       "1",
  pages =        "287--308",
  month =        sep,
  year =         "1948",
  CODEN =        "QJMMAV",
  ISSN =         "0033-5614 (print), 1464-3855 (electronic)",
  ISSN-L =       "0033-5614",
  MRclass =      "65.0X",
  MRnumber =     "MR0028100 (10,405c)",
  MRreviewer =   "E. Bodewig",
  bibdate =      "Sat Nov 19 12:09:58 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/a/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite{Turing:1992:PM} with summary and
                 notes (including corrections)",
  URL =          "http://turing.ecs.soton.ac.uk/browse.php/B/18",
  ZMnumber =     "0033.28501",
  acknowledgement = ack-nhfb,
  fjournal =     "Quarterly Journal of Mechanics and Applied
                 Mathematics",
  journal-URL =  "http://qjmam.oxfordjournals.org/content/by/year",
  mynote =       "The notes are not very good. They mainly correct
                 errors and fill in the gaps of derivations. Much better
                 would have been higher level comments from a numerical
                 analyst, e.g. on where Turing's ideas/predictions were
                 wrong.",
}


bibtype: article
filename: fparith.bib
label: Williams:1948:EDC
author: F. C. Williams and T. Kilburn
title: Electronic digital computers
journal: j-NATURE
volume: 162
number: 4117
pages: 487--487
day: 25
month: sep
monthnumber: 9
year: 1948
CODEN: NATUAS
DOI: https://doi.org/10.1038/162487a0
ISSN: 0028-0836 (print), 1476-4687 (electronic) OR 00280836 (print), 14764687 (electronic)
ISSNL: 0028-0836 OR 00280836
bibdate: Wed Oct 13 12:00:02 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 12:00:02 ???
note: Reprinted in cite [ 8.4]Randell:1982:ODC.
fjournal: Nature
acknowledgement: ack-nhfb
journalURL: http://www.nature.com/nature/archive/
rawauthor: F. C. Williams and T. Kilburn
rawnote: Reprinted in \cite[\S 8.4]{Randell:1982:ODC}.
rawtitle: Electronic digital computers
remark:
Letter submitted 3 August 1948. Describes a small prototype digital computer with 32 31-bit words for instructions, data, and working storage.

entry:
@Article{Williams:1948:EDC,
  author =       "F. C. Williams and T. Kilburn",
  title =        "Electronic digital computers",
  journal =      j-NATURE,
  volume =       "162",
  number =       "4117",
  pages =        "487--487",
  day =          "25",
  month =        sep,
  year =         "1948",
  CODEN =        "NATUAS",
  DOI =          "https://doi.org/10.1038/162487a0",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Wed Oct 13 12:00:02 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 8.4]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  remark =       "Letter submitted 3 August 1948. Describes a small
                 prototype digital computer with 32 31-bit words for
                 instructions, data, and working storage.",
}


bibtype: article
filename: fparith.bib
label: Davis:1949:MM
author: Harry M. Davis
title: Mathematical Machines
journal: j-SCI-AMER
volume: 180
number: 4
pages: 28--39
month: apr
monthnumber: 4
year: 1949
CODEN: SCAMAC
DOI: https://doi.org/10.1038/scientificamerican0449-28
ISSN: 0036-8733 (print), 1946-7087 (electronic) OR 00368733 (print), 19467087 (electronic)
ISSNL: 0036-8733 OR 00368733
bibdate: Sat May 18 16:12:10 MDT 2013
bibtimestamp: 2013.05.18 16:12:10 MDT
fjournal: Scientific American
remark: Description of counting devices before 1950, including an introduction to the binary number system.
acknowledgement: ack-nhfb
journalURL: http://www.nature.com/scientificamerican
rawauthor: Harry M. Davis
rawtitle: Mathematical Machines
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sciam1940.bib

URL:
http://www.jstor.org/stable/24967160; http://www.nature.com/scientificamerican/journal/v180/n4/pdf/scientificamerican0449-28.pdf

entry:
@Article{Davis:1949:MM,
  author =       "Harry M. Davis",
  title =        "Mathematical Machines",
  journal =      j-SCI-AMER,
  volume =       "180",
  number =       "4",
  pages =        "28--39",
  month =        apr,
  year =         "1949",
  CODEN =        "SCAMAC",
  DOI =          "https://doi.org/10.1038/scientificamerican0449-28",
  ISSN =         "0036-8733 (print), 1946-7087 (electronic)",
  ISSN-L =       "0036-8733",
  bibdate =      "Sat May 18 16:12:10 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sciam1940.bib",
  URL =          "http://www.jstor.org/stable/24967160;
                 http://www.nature.com/scientificamerican/journal/v180/n4/pdf/scientificamerican0449-28.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific American",
  journal-URL =  "http://www.nature.com/scientificamerican",
  remark =       "Description of counting devices before 1950, including
                 an introduction to the binary number system.",
}


bibtype: article
filename: fparith.bib
label: Hartree:1949:NSR
author: Douglas R. (Douglas Rayner) Hartree
title: Note On Systematic Roundoff Errors in Numerical Integration
journal: Journal of Research of the National Bureau of Standards
volume: 42
pages: 62--??
year: 1949
bibdate: Wed Feb 14 19:07:37 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.02.14 19:07:37 ???
acknowledgement: ack-nhfb
rawauthor: Douglas R. (Douglas Rayner) Hartree
rawtitle: Note On Systematic Roundoff Errors in Numerical Integration
entry:
@Article{Hartree:1949:NSR,
  author =       "Douglas R. (Douglas Rayner) Hartree",
  title =        "Note On Systematic Roundoff Errors in Numerical
                 Integration",
  journal =      "Journal of Research of the National Bureau of
                 Standards",
  volume =       "42",
  number =       "??",
  pages =        "62--??",
  month =        "????",
  year =         "1949",
  bibdate =      "Wed Feb 14 19:07:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Huskey:1949:PCP
author: H. D. Huskey
title: On the Precision of a Certain Procedure of Numerical Integration
journal: j-J-RES-NATL-BUR-STAND
volume: 42
number: 1
pages: 57--62
month: jan
monthnumber: 1
year: 1949
CODEN: JRNBAG
DOI: https://doi.org/10.6028/jres.042.005
ISSN: 0091-0635 (print), 2376-5305 (electronic) OR 00910635 (print), 23765305 (electronic)
ISSNL: 0091-0635 OR 00910635
bibdate: Fri Aug 20 09:32:34 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.08.20 09:32:34 ???
note: With an appendix by Douglas R. Hartree.
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
journalURL: https://www.nist.gov/nist-research-library/journal-research-nist/past-papers
rawauthor: H. D. Huskey
rawnote: With an appendix by Douglas R. Hartree.
rawtitle: On the Precision of a Certain Procedure of Numerical Integration
abstract:
An example of numerical integration is given that shows very systematic effects in the less significant digits. This lack of randomness gives rounding-off errors that exceed the predicted standard deviation by a factor of three. The example considered in this paper shows that systematic rounding-off errors can occur in numerical in integration, irrespective of the number of digits kept in the contributions to the integral. In the appendix this phenomenon is examined, and criteria are set up to detect the cases in which it may arise to a serious extent.

rawabstract:
An example of numerical integration is given that shows very systematic effects in the less significant digits. This lack of randomness gives rounding-off errors that exceed the predicted standard deviation by a factor of three. The example considered in this paper shows that systematic rounding-off errors can occur in numerical in integration, irrespective of the number of digits kept in the contributions to the integral. In the appendix this phenomenon is examined, and criteria are set up to detect the cases in which it may arise to a serious extent.

entry:
@Article{Huskey:1949:PCP,
  author =       "H. D. Huskey",
  title =        "On the Precision of a Certain Procedure of Numerical
                 Integration",
  journal =      j-J-RES-NATL-BUR-STAND,
  volume =       "42",
  number =       "1",
  pages =        "57--62",
  month =        jan,
  year =         "1949",
  CODEN =        "JRNBAG",
  DOI =          "https://doi.org/10.6028/jres.042.005",
  ISSN =         "0091-0635 (print), 2376-5305 (electronic)",
  ISSN-L =       "0091-0635",
  bibdate =      "Fri Aug 20 09:32:34 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "With an appendix by Douglas R. Hartree.",
  abstract =     "An example of numerical integration is given that
                 shows very systematic effects in the less significant
                 digits. This lack of randomness gives rounding-off
                 errors that exceed the predicted standard deviation by
                 a factor of three. The example considered in this paper
                 shows that systematic rounding-off errors can occur in
                 numerical in integration, irrespective of the number of
                 digits kept in the contributions to the integral. In
                 the appendix this phenomenon is examined, and criteria
                 are set up to detect the cases in which it may arise to
                 a serious extent.",
  acknowledgement = ack-nhfb,
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: techreport
filename: fparith.bib
label: Tukey:1949:TRA
author: John W. Tukey and M. F. Freeman
title: Transformation related to the angular and the square-root
type: SRG Memorandum report
number: 24
institution: inst-PRINCETON
address: inst-PRINCETON:adr
year: 1949
bibdate: Tue May 15 08:00:09 2012
bibtimestamp: 2012.05.15 08:00:09 ???
acknowledgement: ack-nhfb
rawauthor: John W. Tukey and M. F. Freeman
rawtitle: Transformation related to the angular and the square-root
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@TechReport{Tukey:1949:TRA,
  author =       "John W. Tukey and M. F. Freeman",
  title =        "Transformation related to the angular and the
                 square-root",
  type =         "SRG Memorandum report",
  number =       "24",
  institution =  inst-PRINCETON,
  address =      inst-PRINCETON:adr,
  pages =        "??",
  year =         "1949",
  bibdate =      "Tue May 15 08:00:09 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Stifler:1950:HSC
editor: W. W. Stifler, Jr.
title: High-speed computing devices
publisher: pub-MCGRAW-HILL
address: pub-MCGRAW-HILL:adr
pages: xiii + 451
year: 1950
LCCN: QA75 .E5
bibdate: Fri Aug 20 10:18:44 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.08.20 10:18:44 MDT
subject: computers
acknowledgement: ack-nhfb
raweditor: W. W. {Stifler, Jr.}
rawtitle: High-speed computing devices
remark:
Supervised by Charles Brown Tompkins and C. H. Wakelin, Engineering Research Associates. The contents of this volume were first assembled in the form of a report to the Office of Naval Research, prepared under a provision of contract N6-ONR-240, Task 1. Cited in cite Sterbenz:1974:FPC.

entry:
@Book{Stifler:1950:HSC,
  editor =       "W. W. {Stifler, Jr.}",
  title =        "High-speed computing devices",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xiii + 451",
  year =         "1950",
  LCCN =         "QA75 .E5",
  bibdate =      "Fri Aug 20 10:18:44 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "Supervised by Charles Brown Tompkins and C. H.
                 Wakelin, Engineering Research Associates. The contents
                 of this volume were first assembled in the form of a
                 report to the Office of Naval Research, prepared under
                 a provision of contract N6-ONR-240, Task 1. Cited in
                 \cite{Sterbenz:1974:FPC}.",
  subject =      "computers",
}


bibtype: article
filename: fparith.bib
label: Harrison:1950:BDC
author: J. O. Harrison, Jr.
title: Binary--Decimal Conversion on a Desk Calculator (in Automatic Computing Machinery; Discussions)
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 4
number: 32
pages: 231--234
month: oct
monthnumber: 10
year: 1950
CODEN: MTTCAS
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
URL: http://www.jstor.org/stable/2002500
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
ajournal: Math. Tables Other Aids Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: J. O. {Harrison, Jr.}
rawtitle: Binary--Decimal Conversion on a Desk Calculator (in Automatic Computing Machinery; Discussions)
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib; JSTOR database

entry:
@Article{Harrison:1950:BDC,
  author =       "J. O. {Harrison, Jr.}",
  title =        "Binary--Decimal Conversion on a Desk Calculator (in
                 Automatic Computing Machinery; Discussions)",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "4",
  number =       "32",
  pages =        "231--234",
  month =        oct,
  year =         "1950",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2002500",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Tables Other Aids Comput.",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: inproceedings
filename: fparith.bib
label: Wilkes:1950:E
author: M. V. Wilkes and W. Renwick
booktitle: Report of a Conference on High Speed Automatic Calculating Machines, 22--25 June 1949
title: The EDSAC
publisher: University Mathematical Laboratory
address: Cambridge, UK
pages: 9--11
month: jan
monthnumber: 1
year: 1950
bibdate: Wed Oct 13 12:00:41 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 12:00:41 ???
note: Reprinted in cite [ 8.5]Randell:1982:ODC.
acknowledgement: ack-nhfb
rawauthor: M. V. Wilkes and W. Renwick
rawbooktitle: {Report of a Conference on High Speed Automatic Calculating Machines, 22--25 June 1949}
rawnote: Reprinted in \cite[\S 8.5]{Randell:1982:ODC}.
rawtitle: The {EDSAC}
entry:
@InProceedings{Wilkes:1950:E,
  author =       "M. V. Wilkes and W. Renwick",
  booktitle =    "{Report of a Conference on High Speed Automatic
                 Calculating Machines, 22--25 June 1949}",
  title =        "The {EDSAC}",
  publisher =    "University Mathematical Laboratory",
  address =      "Cambridge, UK",
  pages =        "9--11",
  month =        jan,
  year =         "1950",
  bibdate =      "Wed Oct 13 12:00:41 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 8.5]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Worsley:1950:ED
author: B. H. Worsley
booktitle: Report of a Conference on High Speed Automatic Calculating Machines, 22--25 June 1949
title: The EDSAC demonstration
publisher: University Mathematical Laboratory
address: Cambridge, UK
pages: 12--16
month: jan
monthnumber: 1
year: 1950
bibdate: Wed Oct 13 11:39:09 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:39:09 ???
note: Reprinted in cite [ 8.6]Randell:1982:ODC.
acknowledgement: ack-nhfb
rawauthor: B. H. Worsley
rawbooktitle: Report of a Conference on High Speed Automatic Calculating Machines, {22--25 June 1949}
rawnote: Reprinted in \cite[\S 8.6]{Randell:1982:ODC}.
rawtitle: The {EDSAC} demonstration
entry:
@InProceedings{Worsley:1950:ED,
  author =       "B. H. Worsley",
  booktitle =    "Report of a Conference on High Speed Automatic
                 Calculating Machines, {22--25 June 1949}",
  title =        "The {EDSAC} demonstration",
  publisher =    "University Mathematical Laboratory",
  address =      "Cambridge, UK",
  pages =        "12--16",
  month =        jan,
  year =         "1950",
  bibdate =      "Wed Oct 13 11:39:09 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 8.6]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Anonymous:1951:R
author: Anonymous
title: RECIPROOT
pages: 12--16
day: 9
month: jul
monthnumber: 7
year: 1951
bibdate: Sat Aug 19 09:57:33 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.08.19 09:57:33 ???
note: To calculate square roots and reciprocal square roots.
URL: https://0x5f37642f.com/documents/ManchesterRecipRoot.pdf
remark: Code used on Ferranti Mark I.
acknowledgement: ack-nhfb
howpublished: Manchester University Electronic Computer Web document.
rawauthor: Anonymous
rawnote: To calculate square roots and reciprocal square roots.
rawtitle: {RECIPROOT}
entry:
@Misc{Anonymous:1951:R,
  author =       "Anonymous",
  title =        "{RECIPROOT}",
  howpublished = "Manchester University Electronic Computer Web
                 document.",
  day =          "9",
  month =        jul,
  year =         "1951",
  bibdate =      "Sat Aug 19 09:57:33 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "To calculate square roots and reciprocal square
                 roots.",
  URL =          "https://0x5f37642f.com/documents/ManchesterRecipRoot.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Code used on Ferranti Mark I.",
}


bibtype: article
filename: fparith.bib
label: Booth:1951:SBM
author: A. D. Booth
title: A signed binary multiplication technique
journal: j-QUART-J-MECH-APPLIED-MATH
volume: 4
number: 2
pages: 236--240
year: 1951
CODEN: QJMMAV
ISSN: 0033-5614 (print), 1464-3855 (electronic) OR 00335614 (print), 14643855 (electronic)
ISSNL: 0033-5614 OR 00335614
bibdate: Thu Apr 2 08:38:35 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.02 08:38:35 ???
fjournal: Quarterly Journal of Mechanics and Applied Mathematics
acknowledgement: ack-sfo
journalURL: http://qjmam.oxfordjournals.org/content/by/year
rawauthor: A. D. Booth
rawtitle: A signed binary multiplication technique
entry:
@Article{Booth:1951:SBM,
  author =       "A. D. Booth",
  title =        "A signed binary multiplication technique",
  journal =      j-QUART-J-MECH-APPLIED-MATH,
  volume =       "4",
  number =       "2",
  pages =        "236--240",
  month =        "????",
  year =         "1951",
  CODEN =        "QJMMAV",
  ISSN =         "0033-5614 (print), 1464-3855 (electronic)",
  ISSN-L =       "0033-5614",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "Quarterly Journal of Mechanics and Applied
                 Mathematics",
  journal-URL =  "http://qjmam.oxfordjournals.org/content/by/year",
}


bibtype: incollection
filename: fparith.bib
label: Brown:1951:HRR
author: G. W. Brown
title: History of RAND's random digits
crossref: Householder:1951:MCM
pages: 31--32
year: 1951
bibdate: Sun Sep 18 12:02:43 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2011.09.18 12:02:43 ???
URL: http://www.rand.org/pubs/papers/2008/P113.pdf
acknowledgement: ack-nhfb
rawauthor: G. W. Brown
rawtitle: History of {RAND}'s random digits
entry:
@InCollection{Brown:1951:HRR,
  author =       "G. W. Brown",
  title =        "History of {RAND}'s random digits",
  crossref =     "Householder:1951:MCM",
  pages =        "31--32",
  year =         "1951",
  bibdate =      "Sun Sep 18 12:02:43 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.rand.org/pubs/papers/2008/P113.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Gill:1951:PSS
author: S. Gill
journal: j-PROC-CAMBRIDGE-PHIL-SOC
volume: 47
pages: 96--108
year: 1951
CODEN: PCPSA4
ISSN: 0008-1981 OR 00081981
bibdate: Tue Aug 28 05:54:12 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.08.28 05:54:12 ???
fjournal: Proceedings of the Cambridge Philosophical Society. Mathematical and physical sciences
keywords: accurate floating-point summation; floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: http://journals.cambridge.org/action/displayJournal?jid=PSP
rawauthor: S. Gill
title:
A process for the step-by-step integration of differential equations in an automatic digital computing machine

remark:
Higham cite Higham:1993:AFP comments ``In 1951 Gill [8] noticed that the rounding error in the sum of two numbers could be estimated by subtracting one of the numbers from the sum, and he made use of this estimate in a Runge--Kutta code in a program library for the EDSAC computer.''

rawtitle:
A process for the step-by-step integration of differential equations in an automatic digital computing machine

entry:
@Article{Gill:1951:PSS,
  author =       "S. Gill",
  title =        "A process for the step-by-step integration of
                 differential equations in an automatic digital
                 computing machine",
  journal =      j-PROC-CAMBRIDGE-PHIL-SOC,
  volume =       "47",
  pages =        "96--108",
  year =         "1951",
  CODEN =        "PCPSA4",
  ISSN =         "0008-1981",
  bibdate =      "Tue Aug 28 05:54:12 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Cambridge Philosophical Society.
                 Mathematical and physical sciences",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=PSP",
  keywords =     "accurate floating-point summation; floating-point
                 arithmetic; rounding errors",
  remark =       "Higham \cite{Higham:1993:AFP} comments ``In 1951 Gill
                 [8] noticed that the rounding error in the sum of two
                 numbers could be estimated by subtracting one of the
                 numbers from the sum, and he made use of this estimate
                 in a Runge--Kutta code in a program library for the
                 EDSAC computer.''",
}


bibtype: article
filename: fparith.bib
label: Goldstine:1951:NIM
author: Herman H. Goldstine and John von Neumann
title: Numerical Inverting of Matrices of High Order. II
journal: j-PROC-AM-MATH-SOC
volume: 2
pages: 188--202
year: 1951
CODEN: PAMYAR
ISSN: 0002-9939 (print), 1088-6826 (electronic) OR 00029939 (print), 10886826 (electronic)
ISSNL: 0002-9939 OR 00029939
MRclass: 65.0X
MRnumber: MR0041539 (12,861b)
MRreviewer: F. J. Murray
bibdate: Thu Nov 8 14:49:46 2007
bibtimestamp: 2007.11.08 14:49:46 ???
note: See cite vonNeumann:1947:NIM for Part I. Reprinted in cite [Paper 15, pp. 558--572]Taub:1963:JNCa.
URL: http://www.jstor.org/view/00029939/di970628/97p0185x/0
fjournal: Proceedings of the American Mathematical Society
ZMnumber: 043.12301
acknowledgement: ack-nhfb
authordates: John von Neumann (28 December 1903--8 February 1957)
journalURL: http://www.ams.org/journals/proc
rawauthor: Herman H. Goldstine and John von Neumann
rawtitle: Numerical Inverting of Matrices of High Order. {II}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawnote:
See \cite{vonNeumann:1947:NIM} for Part I. Reprinted in \cite[Paper 15, pp. 558--572]{Taub:1963:JNCa}.

entry:
@Article{Goldstine:1951:NIM,
  author =       "Herman H. Goldstine and John von Neumann",
  title =        "Numerical Inverting of Matrices of High Order. {II}",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "2",
  pages =        "188--202",
  year =         "1951",
  CODEN =        "PAMYAR",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "65.0X",
  MRnumber =     "MR0041539 (12,861b)",
  MRreviewer =   "F. J. Murray",
  bibdate =      "Thu Nov 8 14:49:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{vonNeumann:1947:NIM} for Part I. Reprinted
                 in \cite[Paper 15, pp. 558--572]{Taub:1963:JNCa}.",
  URL =          "http://www.jstor.org/view/00029939/di970628/97p0185x/0",
  ZMnumber =     "043.12301",
  acknowledgement = ack-nhfb,
  author-dates = "John von Neumann (28 December 1903--8 February 1957)",
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
}


bibtype: article
filename: fparith.bib
label: MacMillan:1951:FDC
author: Donald B. MacMillan and Richard H. Stark
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 5
number: 34
pages: 86--92
month: apr
monthnumber: 4
year: 1951
CODEN: MTTCAS
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
ajournal: Math. Tables Other Aids Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: Donald B. MacMillan and Richard H. Stark
title:
``Floating Decimal'' Calculation on the IBM Card Programmed Electronic Calculator (in Automatic Computing Machinery; Discussions)

bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib; JSTOR database

rawtitle:
``Floating Decimal'' Calculation on the {IBM} Card Programmed Electronic Calculator (in Automatic Computing Machinery; Discussions)

entry:
@Article{MacMillan:1951:FDC,
  author =       "Donald B. MacMillan and Richard H. Stark",
  title =        "``Floating Decimal'' Calculation on the {IBM} Card
                 Programmed Electronic Calculator (in Automatic
                 Computing Machinery; Discussions)",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "5",
  number =       "34",
  pages =        "86--92",
  month =        apr,
  year =         "1951",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Tables Other Aids Comput.",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: inproceedings
filename: fparith.bib
label: Rademacher:1951:AEP
author: Hans Rademacher
booktitle: Proceedings of a Symposium on Large-scale Digital Calculating Machinery
title: On the accumulation of errors in processes of integration on high-speed calculating machines
publisher: pub-HARVARD
address: pub-HARVARD:adr
pages: 176--185
year: 1951
bibdate: Mon Jun 18 06:50:41 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2018.06.18 06:50:41 ???
acknowledgement: ack-nhfb
rawauthor: Hans Rademacher
rawbooktitle: Proceedings of a Symposium on Large-scale Digital Calculating Machinery
rawtitle: On the accumulation of errors in processes of integration on high-speed calculating machines
entry:
@InProceedings{Rademacher:1951:AEP,
  author =       "Hans Rademacher",
  booktitle =    "Proceedings of a Symposium on Large-scale Digital
                 Calculating Machinery",
  title =        "On the accumulation of errors in processes of
                 integration on high-speed calculating machines",
  publisher =    pub-HARVARD,
  address =      pub-HARVARD:adr,
  pages =        "176--185",
  year =         "1951",
  bibdate =      "Mon Jun 18 06:50:41 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Shirley:1951:BNB
author: John W. Shirley
title: Binary Numeration before Leibniz
journal: j-AMER-J-PHYSICS
volume: 19
number: 8
pages: 452--454
month: nov
monthnumber: 11
year: 1951
CODEN: AJPIAS
DOI: https://doi.org/10.1119/1.1933042
ISSN: 0002-9505 (print), 1943-2909 (electronic) OR 00029505 (print), 19432909 (electronic)
ISSNL: 0002-9505 OR 00029505
bibdate: Sat Feb 8 10:29:20 2020
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2020.02.08 10:29:20 ???
URL: http://scitation.aip.org/content/aapt/journal/ajp/19/8/10.1119/1.1933042
fjournal: American Journal of Physics
remark: Submitted 14 November 1950.
acknowledgement: ack-nhfb
journalURL: http://scitation.aip.org/content/aapt/journal/ajp
rawauthor: John W. Shirley
rawtitle: Binary Numeration before {Leibniz}
abstract:
Though it is frequently stated that binary numeration was first formally proposed by Leibniz as an illustration of his dualistic philosophy, the mathematical papers of Thomas Hariot (1560--1621) show clearly that Hariot not only experimented with number systems, but also understood clearly the theory and practice of binary numeration nearly a century before Leibniz's time.

rawabstract:
Though it is frequently stated that binary numeration was first formally proposed by Leibniz as an illustration of his dualistic philosophy, the mathematical papers of Thomas Hariot (1560--1621) show clearly that Hariot not only experimented with number systems, but also understood clearly the theory and practice of binary numeration nearly a century before Leibniz's time.

entry:
@Article{Shirley:1951:BNB,
  author =       "John W. Shirley",
  title =        "Binary Numeration before {Leibniz}",
  journal =      j-AMER-J-PHYSICS,
  volume =       "19",
  number =       "8",
  pages =        "452--454",
  month =        nov,
  year =         "1951",
  CODEN =        "AJPIAS",
  DOI =          "https://doi.org/10.1119/1.1933042",
  ISSN =         "0002-9505 (print), 1943-2909 (electronic)",
  ISSN-L =       "0002-9505",
  bibdate =      "Sat Feb 8 10:29:20 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://scitation.aip.org/content/aapt/journal/ajp/19/8/10.1119/1.1933042",
  abstract =     "Though it is frequently stated that binary numeration
                 was first formally proposed by Leibniz as an
                 illustration of his dualistic philosophy, the
                 mathematical papers of Thomas Hariot (1560--1621) show
                 clearly that Hariot not only experimented with number
                 systems, but also understood clearly the theory and
                 practice of binary numeration nearly a century before
                 Leibniz's time.",
  acknowledgement = ack-nhfb,
  fjournal =     "American Journal of Physics",
  journal-URL =  "http://scitation.aip.org/content/aapt/journal/ajp",
  remark =       "Submitted 14 November 1950.",
}


bibtype: book
filename: fparith.bib
label: Wilkes:1951:PPE
author: Maurice V. Wilkes and David J. Wheeler and Stanley Gill
title: The Preparation of Programs for an Electronic Digital Computer
publisher: pub-AW
address: pub-AW:adr
pages: 167
year: 1951
LCCN: QA76.5 .W55 1951
bibdate: Mon Feb 10 09:42:47 2020
bibtimestamp: 2020.02.10 09:42:47 ???
note: See also second edition cite Wilkes:1957:PPE, and reprint cite Wilkes:1982:PPE.
acknowledgement: ack-nhfb
rawauthor: Maurice V. Wilkes and David J. Wheeler and Stanley Gill
rawnote: See also second edition \cite{Wilkes:1957:PPE}, and reprint \cite{Wilkes:1982:PPE}.
rawtitle: The Preparation of Programs for an Electronic Digital Computer
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

TOC:
Part I Chapter 1. The Design of Programs for Electronic Computing Machines / 1 1-1 Introduction / 1 1-2 Types of automatic computing machines / 2 1-3 Description of the EDSAC / 3 1-4 The EDSAC order code / 5 1-5 Notes on the order code / 6 1-6 The use of conditional orders / 7 1-7 Modification of orders by the program / 8 1-8 Multiaddress codes / 11 1-9 Binary--decimal conversion / 12 1-10 Checking facilities / 14 Chapter 2. Input of Orders / 15 2-1 Initial orders / 15 2-2 Pseudo-orders / 17 2-3 Examples / 17 2-4 Control combinations / 17 2-5 Starting the program / 18 2-6 Use of code letters / 19 2-7 Constants / 20 2-8 Notation / 20 Chapter 3. Subroutines and Parameters / 22 3-1 Open subroutines / 22 3-2 closed subroutines / 22 3-3 preset parameters / 23 3-4 program parameters / 23 Chapter 4. Library Subroutines and their Use in Constructing Programs / 25 4-1 Library catalog / 25 4-2 Input and output subroutines / 25 4-3 Division subroutines / 27 4-4 Trigonometrical and other functions / 27 4-5 Quadrature / 27 4-6 Assembly subroutines / 27 4-7 Integration of differential equations / 32 4-8 Processes, Interpretive subroutines / 34 Chapter 5. Pitfalls / 38 5-1 Proofreading of programs, points to be checked / 38 5-2 Location of mistakes in a program / 39 5-3 Counting operations / 41 Chapter 6. Use of the EDSAC & Its Associated Equipment / 42 6-1 Tape Punching & editing facilities / 42 6-2 Storage of library subroutines / 43 6-3 EDSAC organization / 43 6-4 EDSAC controls / 43 Chapter 7. Examples / 45 7-1 Example 1. Calculation of $exp (-sin x)$ / 45 7-2 Example 2. Calculation of $pi $ by evaluation of definite integral / 48 7-3 Alternative method for Example 2 / 52 7-4 Example 2, with extra print orders for checking / 53 7-5 Application of checking subroutine C11 to Example 2 / 54 7-6 Example of integration of an ordinary differential equation / 46 7-7 Evaluation of a definite integral / 61 7-8 Program to facilitate the solution of algebraic equation / 66 Part II. Specifications of Library Subroutines / 72 A. Subroutines to carry out floating point arithmetic / 73 B. Subroutines to carry out arithmetical operations on complex numbers / 78 C. Checking subroutines / 79 D. Division subroutines / 82 E. Exponential subroutines / 83 F. General routines relating to functions / 84 G. Subroutines for integration of ordinary differential equations / 86 J. Subroutines for calculating special functions [Legendre polynomials] / 88 K. Subroutines for the summation of power series / 88 L. Subroutines for evaluating logarithms / 91 M. Miscellaneous subroutines / 91 P. Print subroutines / 92 Q. Quadrature subroutines / 95 R. Input subroutines / 96 S. Subroutines for evaluation of fractional powers / 98 T. Subroutines for calculating trigonometrical functions / 99 U. Subroutines for counting operations / 101 V1. Multiplication of vector by symmetric matrix / 102 V2. Addition and subtraction of $n$ dimensional vectors / 103 Part III. Programs of Selected Library Subroutines / 104 Appendix A. Keyboard perforator code, etc. / 158 Appendix B. The initial orders / 159 Appendix C. Control combinations / 161 Appendix D. Interpretive subroutines: example of packing of orders / 162 Appendix E. Methods of counting in a simple cycle / 164 Index

rawTOC:
Part I \\ Chapter 1. The Design of Programs for Electronic Computing Machines / 1 \\ 1-1 Introduction / 1 \\ 1-2 Types of automatic computing machines / 2 \\ 1-3 Description of the EDSAC / 3 \\ 1-4 The EDSAC order code / 5 \\ 1-5 Notes on the order code / 6 \\ 1-6 The use of conditional orders / 7 \\ 1-7 Modification of orders by the program / 8 \\ 1-8 Multiaddress codes / 11 \\ 1-9 Binary--decimal conversion / 12 \\ 1-10 Checking facilities / 14 \\ Chapter 2. Input of Orders / 15 \\ 2-1 Initial orders / 15 \\ 2-2 Pseudo-orders / 17 \\ 2-3 Examples / 17 \\ 2-4 Control combinations / 17 \\ 2-5 Starting the program / 18 \\ 2-6 Use of code letters / 19 \\ 2-7 Constants / 20 \\ 2-8 Notation / 20 \\ Chapter 3. Subroutines and Parameters / 22 \\ 3-1 Open subroutines / 22 \\ 3-2 closed subroutines / 22 \\ 3-3 preset parameters / 23 \\ 3-4 program parameters / 23 \\ Chapter 4. Library Subroutines and their Use in Constructing Programs / 25 \\ 4-1 Library catalog / 25 \\ 4-2 Input and output subroutines / 25 \\ 4-3 Division subroutines / 27 \\ 4-4 Trigonometrical and other functions / 27 \\ 4-5 Quadrature / 27 \\ 4-6 Assembly subroutines / 27 \\ 4-7 Integration of differential equations / 32 \\ 4-8 Processes, Interpretive subroutines / 34 \\ Chapter 5. Pitfalls / 38 \\ 5-1 Proofreading of programs, points to be checked / 38 \\ 5-2 Location of mistakes in a program / 39 \\ 5-3 Counting operations / 41 \\ Chapter 6. Use of the EDSAC \& Its Associated Equipment / 42 \\ 6-1 Tape Punching \& editing facilities / 42 \\ 6-2 Storage of library subroutines / 43 \\ 6-3 EDSAC organization / 43 \\ 6-4 EDSAC controls / 43 \\ Chapter 7. Examples / 45 \\ 7-1 Example 1. Calculation of $\exp(-\sin x)$ / 45 \\ 7-2 Example 2. Calculation of $\pi$ by evaluation of definite integral / 48 \\ 7-3 Alternative method for Example 2 / 52 \\ 7-4 Example 2, with extra print orders for checking / 53 \\ 7-5 Application of checking subroutine C11 to Example 2 / 54 \\ 7-6 Example of integration of an ordinary differential equation / 46 \\ 7-7 Evaluation of a definite integral / 61 \\ 7-8 Program to facilitate the solution of algebraic equation / 66 \\ Part II. Specifications of Library Subroutines / 72 \\ A. Subroutines to carry out floating point arithmetic / 73 \\ B. Subroutines to carry out arithmetical operations on complex numbers / 78 \\ C. Checking subroutines / 79 \\ D. Division subroutines / 82 \\ E. Exponential subroutines / 83 \\ F. General routines relating to functions / 84 \\ G. Subroutines for integration of ordinary differential equations / 86 \\ J. Subroutines for calculating special functions [Legendre polynomials] / 88 \\ K. Subroutines for the summation of power series / 88 \\ L. Subroutines for evaluating logarithms / 91 \\ M. Miscellaneous subroutines / 91 \\ P. Print subroutines / 92 \\ Q. Quadrature subroutines / 95 \\ R. Input subroutines / 96 \\ S. Subroutines for evaluation of fractional powers / 98 \\ T. Subroutines for calculating trigonometrical functions / 99 \\ U. Subroutines for counting operations / 101 \\ V1. Multiplication of vector by symmetric matrix / 102 \\ V2. Addition and subtraction of $n$ dimensional vectors / 103 \\ Part III. Programs of Selected Library Subroutines / 104 \\ Appendix A. Keyboard perforator code, etc. / 158 \\ Appendix B. The initial orders / 159 \\ Appendix C. Control combinations / 161 \\ Appendix D. Interpretive subroutines: example of packing of orders / 162 \\ Appendix E. Methods of counting in a simple cycle / 164 \\ Index

entry:
@Book{Wilkes:1951:PPE,
  author =       "Maurice V. Wilkes and David J. Wheeler and Stanley
                 Gill",
  title =        "The Preparation of Programs for an Electronic Digital
                 Computer",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "167",
  year =         "1951",
  LCCN =         "QA76.5 .W55 1951",
  bibdate =      "Mon Feb 10 09:42:47 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also second edition \cite{Wilkes:1957:PPE}, and
                 reprint \cite{Wilkes:1982:PPE}.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Part I \\
                 Chapter 1. The Design of Programs for Electronic
                 Computing Machines / 1 \\
                 1-1 Introduction / 1 \\
                 1-2 Types of automatic computing machines / 2 \\
                 1-3 Description of the EDSAC / 3 \\
                 1-4 The EDSAC order code / 5 \\
                 1-5 Notes on the order code / 6 \\
                 1-6 The use of conditional orders / 7 \\
                 1-7 Modification of orders by the program / 8 \\
                 1-8 Multiaddress codes / 11 \\
                 1-9 Binary--decimal conversion / 12 \\
                 1-10 Checking facilities / 14 \\
                 Chapter 2. Input of Orders / 15 \\
                 2-1 Initial orders / 15 \\
                 2-2 Pseudo-orders / 17 \\
                 2-3 Examples / 17 \\
                 2-4 Control combinations / 17 \\
                 2-5 Starting the program / 18 \\
                 2-6 Use of code letters / 19 \\
                 2-7 Constants / 20 \\
                 2-8 Notation / 20 \\
                 Chapter 3. Subroutines and Parameters / 22 \\
                 3-1 Open subroutines / 22 \\
                 3-2 closed subroutines / 22 \\
                 3-3 preset parameters / 23 \\
                 3-4 program parameters / 23 \\
                 Chapter 4. Library Subroutines and their Use in
                 Constructing Programs / 25 \\
                 4-1 Library catalog / 25 \\
                 4-2 Input and output subroutines / 25 \\
                 4-3 Division subroutines / 27 \\
                 4-4 Trigonometrical and other functions / 27 \\
                 4-5 Quadrature / 27 \\
                 4-6 Assembly subroutines / 27 \\
                 4-7 Integration of differential equations / 32 \\
                 4-8 Processes, Interpretive subroutines / 34 \\
                 Chapter 5. Pitfalls / 38 \\
                 5-1 Proofreading of programs, points to be checked / 38
                 \\
                 5-2 Location of mistakes in a program / 39 \\
                 5-3 Counting operations / 41 \\
                 Chapter 6. Use of the EDSAC \& Its Associated Equipment
                 / 42 \\
                 6-1 Tape Punching \& editing facilities / 42 \\
                 6-2 Storage of library subroutines / 43 \\
                 6-3 EDSAC organization / 43 \\
                 6-4 EDSAC controls / 43 \\
                 Chapter 7. Examples / 45 \\
                 7-1 Example 1. Calculation of $\exp(-\sin x)$ / 45 \\
                 7-2 Example 2. Calculation of $\pi$ by evaluation of
                 definite integral / 48 \\
                 7-3 Alternative method for Example 2 / 52 \\
                 7-4 Example 2, with extra print orders for checking /
                 53 \\
                 7-5 Application of checking subroutine C11 to Example 2
                 / 54 \\
                 7-6 Example of integration of an ordinary differential
                 equation / 46 \\
                 7-7 Evaluation of a definite integral / 61 \\
                 7-8 Program to facilitate the solution of algebraic
                 equation / 66 \\
                 Part II. Specifications of Library Subroutines / 72 \\
                 A. Subroutines to carry out floating point arithmetic /
                 73 \\
                 B. Subroutines to carry out arithmetical operations on
                 complex numbers / 78 \\
                 C. Checking subroutines / 79 \\
                 D. Division subroutines / 82 \\
                 E. Exponential subroutines / 83 \\
                 F. General routines relating to functions / 84 \\
                 G. Subroutines for integration of ordinary differential
                 equations / 86 \\
                 J. Subroutines for calculating special functions
                 [Legendre polynomials] / 88 \\
                 K. Subroutines for the summation of power series / 88
                 \\
                 L. Subroutines for evaluating logarithms / 91 \\
                 M. Miscellaneous subroutines / 91 \\
                 P. Print subroutines / 92 \\
                 Q. Quadrature subroutines / 95 \\
                 R. Input subroutines / 96 \\
                 S. Subroutines for evaluation of fractional powers / 98
                 \\
                 T. Subroutines for calculating trigonometrical
                 functions / 99 \\
                 U. Subroutines for counting operations / 101 \\
                 V1. Multiplication of vector by symmetric matrix / 102
                 \\
                 V2. Addition and subtraction of $n$ dimensional vectors
                 / 103 \\
                 Part III. Programs of Selected Library Subroutines /
                 104 \\
                 Appendix A. Keyboard perforator code, etc. / 158 \\
                 Appendix B. The initial orders / 159 \\
                 Appendix C. Control combinations / 161 \\
                 Appendix D. Interpretive subroutines: example of
                 packing of orders / 162 \\
                 Appendix E. Methods of counting in a simple cycle / 164
                 \\
                 Index",
}


bibtype: inproceedings
filename: fparith.bib
label: Andrews:1952:RBL
author: E. G. Andrews
editor: J. C. McPherson
title: A review of the Bell Laboratories' digital computer developments
publisher: pub-ACM
address: pub-ACM:adr
pages: 101--105
year: 1952
DOI: https://doi.org/10.1145/1434770.1434787
bibdate: Fri Dec 03 09:17:58 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.12.03 09:17:58 ???
acknowledgement: ack-nhfb
bookpages: vi + 114
rawauthor: E. G. Andrews
raweditor: J. C. McPherson
rawtitle: A review of the {Bell Laboratories}' digital computer developments
booktitle:
Proceedings of the AIEE-IRE '51: Papers and discussions presented at the December 10--12, 1951, joint AIEE-IRE computer conference, Philadelphia, PA: Review of electronic digital computers

keywords:
Bell Laboratories Model 1--5 relay computers; complex fixed-point decimal arithmetic; complex floating-point decimal arithmetic

rawbooktitle:
Proceedings of the {AIEE-IRE '51}: Papers and discussions presented at the December 10--12, 1951, joint {AIEE-IRE} computer conference, Philadelphia, {PA}: Review of electronic digital computers

entry:
@InProceedings{Andrews:1952:RBL,
  author =       "E. G. Andrews",
  editor =       "J. C. McPherson",
  booktitle =    "Proceedings of the {AIEE-IRE '51}: Papers and
                 discussions presented at the December 10--12, 1951,
                 joint {AIEE-IRE} computer conference, Philadelphia,
                 {PA}: Review of electronic digital computers",
  title =        "A review of the {Bell Laboratories}' digital computer
                 developments",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  bookpages =    "vi + 114",
  pages =        "101--105",
  year =         "1952",
  DOI =          "https://doi.org/10.1145/1434770.1434787",
  LCCN =         "????",
  bibdate =      "Fri Dec 03 09:17:58 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Bell Laboratories Model 1--5 relay computers; complex
                 fixed-point decimal arithmetic; complex floating-point
                 decimal arithmetic",
}


bibtype: article
filename: fparith.bib
label: Davis:1952:ARS
author: K. Davis and R. Biddulph and S. Balashek
title: Automatic Recognition of Spoken Digits
journal: j-J-ACOUST-SOC-AM
volume: 24
number: 6
pages: 637--642
month: nov
monthnumber: 11
year: 1952
CODEN: JASMAN
ISSN: 0001-4966 OR 00014966
ISSNL: 0001-4966 OR 00014966
bibdate: Fri Nov 28 16:38:51 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 16:38:51 ???
fjournal: Journal of the Acoustical Society of America
acknowledgement: ack-mfc
journalURL: http://scitation.aip.org/content/asa/journal/jasa
rawauthor: K. Davis and R. Biddulph and S. Balashek
rawtitle: Automatic Recognition of Spoken Digits
entry:
@Article{Davis:1952:ARS,
  author =       "K. Davis and R. Biddulph and S. Balashek",
  title =        "Automatic Recognition of Spoken Digits",
  journal =      j-J-ACOUST-SOC-AM,
  volume =       "24",
  number =       "6",
  pages =        "637--642",
  month =        nov,
  year =         "1952",
  CODEN =        "JASMAN",
  ISSN =         "0001-4966",
  ISSN-L =       "0001-4966",
  bibdate =      "Fri Nov 28 16:38:51 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "Journal of the Acoustical Society of America",
  journal-URL =  "http://scitation.aip.org/content/asa/journal/jasa",
}


bibtype: article
filename: fparith.bib
label: Hammersley:1952:CSS
author: J. M. Hammersley
title: The computation of sums of squares and products on a desk calculator
journal: j-BIOMETRICS
volume: 8
pages: 156--168
year: 1952
CODEN: BIOMB6
DOI: https://doi.org/10.2307/3001930
ISSN: 0006-341X (print), 1541-0420 (electronic) OR 0006341X (print), 15410420 (electronic)
ISSNL: 0006-341X OR 0006341X
MRclass: 65.0X
MRnumber: 48908
MRreviewer: E. Lukacs
bibdate: Thu Jun 25 17:01:03 2020
bibtimestamp: 2020.06.25 17:01:03 ???
fjournal: Biometrics
acknowledgement: ack-nhfb
ajournal: Biometrics
journalURL: http://www.jstor.org/journal/biometrics
rawauthor: J. M. Hammersley
rawtitle: The computation of sums of squares and products on a desk calculator
bibsource:
https://www.math.utah.edu/pub/tex/bib/biometrics1950.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Hammersley:1952:CSS,
  author =       "J. M. Hammersley",
  title =        "The computation of sums of squares and products on a
                 desk calculator",
  journal =      j-BIOMETRICS,
  volume =       "8",
  number =       "??",
  pages =        "156--168",
  year =         "1952",
  CODEN =        "BIOMB6",
  DOI =          "https://doi.org/10.2307/3001930",
  ISSN =         "0006-341X (print), 1541-0420 (electronic)",
  ISSN-L =       "0006-341X",
  MRclass =      "65.0X",
  MRnumber =     "48908",
  MRreviewer =   "E. Lukacs",
  bibdate =      "Thu Jun 25 17:01:03 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/biometrics1950.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Biometrics",
  fjournal =     "Biometrics",
  journal-URL =  "http://www.jstor.org/journal/biometrics",
}


bibtype: article
filename: fparith.bib
label: Irani:1952:SMT
author: Rida A. K. Irani
title: A sexagesimal multiplication table in the Arabic alphabetical system
journal: j-SCRIPTA-MATH
volume: 18
pages: 92--93
year: 1952
ISSN: 0036-9713 OR 00369713
ISSNL: 0036-9713 OR 00369713
MRclass: 01.0X
MRnumber: 49109
bibdate: Thu Oct 26 11:15:25 2023
bibtimestamp: 2023.10.26 11:15:25 ???
ZMnumber: 0046.00102
acknowledgement: ack-nhfb
ajournal: Scripta Math.
rawauthor: Rida A. K. Irani
rawtitle: A sexagesimal multiplication table in the {Arabic} alphabetical system
entry:
@Article{Irani:1952:SMT,
  author =       "Rida A. K. Irani",
  title =        "A sexagesimal multiplication table in the {Arabic}
                 alphabetical system",
  journal =      j-SCRIPTA-MATH,
  volume =       "18",
  number =       "??",
  pages =        "92--93",
  month =        "????",
  year =         "1952",
  ISSN =         "0036-9713",
  ISSN-L =       "0036-9713",
  MRclass =      "01.0X",
  MRnumber =     "49109",
  bibdate =      "Thu Oct 26 11:15:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
  ZMnumber =     "0046.00102",
  acknowledgement = ack-nhfb,
  ajournal =     "Scripta Math.",
  fjournal =     "Scripta Mathematica: A Quarterly Journal Devoted to
                 the Philosophy, History, and Expository Treatment of
                 Mathematics",
  ZBmath =       "3070983",
}


bibtype: article
filename: fparith.bib
label: Michaelson:1952:BA
author: R. L. Michaelson
title: Binary Arithmetic
journal: j-INC-STAT
volume: 3
number: 1
pages: 35--40
month: feb
monthnumber: 2
year: 1952
DOI: https://doi.org/10.2307/2986591
ISSN: 1466-9404 OR 14669404
ISSNL: 1466-9404 OR 14669404
bibdate: Thu Jan 22 18:10:18 MST 2015
bibtimestamp: 2015.01.22 18:10:18 MST
URL: http://www.jstor.org/stable/2986591
fjournal: The Incorporated Statistician
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/14669404.html
rawauthor: R. L. Michaelson
rawtitle: Binary Arithmetic
bibsource:
http://www.jstor.org/stable/i349863; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jrss-d-1950.bib

entry:
@Article{Michaelson:1952:BA,
  author =       "R. L. Michaelson",
  title =        "Binary Arithmetic",
  journal =      j-INC-STAT,
  volume =       "3",
  number =       "1",
  pages =        "35--40",
  month =        feb,
  year =         "1952",
  CODEN =        "????",
  DOI =          "https://doi.org/10.2307/2986591",
  ISSN =         "1466-9404",
  ISSN-L =       "1466-9404",
  bibdate =      "Thu Jan 22 18:10:18 MST 2015",
  bibsource =    "http://www.jstor.org/stable/i349863;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jrss-d-1950.bib",
  URL =          "http://www.jstor.org/stable/2986591",
  acknowledgement = ack-nhfb,
  fjournal =     "The Incorporated Statistician",
  journal-URL =  "http://www.jstor.org/journals/14669404.html",
}


bibtype: article
filename: fparith.bib
label: Morrill:1952:SEM
author: C. D. Morrill and R. V. Baum
title: A Stabilized Electronic Multiplier
journal: j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT
volume: EC-1
pages: 52--59
month: dec
monthnumber: 12
year: 1952
bibdate: Fri Jul 15 15:20:53 2011
bibtimestamp: 2011.07.15 15:20:53 ???
fjournal: Transactions of the I.R.E. Professional Group on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: C. D. Morrill and R. V. Baum
rawtitle: A Stabilized Electronic Multiplier
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib

entry:
@Article{Morrill:1952:SEM,
  author =       "C. D. Morrill and R. V. Baum",
  title =        "A Stabilized Electronic Multiplier",
  journal =      j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT,
  volume =       "EC-1",
  number =       "??",
  pages =        "52--59",
  month =        dec,
  year =         "1952",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Fri Jul 15 15:20:53 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Transactions of the I.R.E. Professional Group on
                 Electronic Computers",
}


bibtype: inproceedings
filename: fparith.bib
label: Sheldon:1952:ICP
author: J. W. Sheldon and L. Tatum
booktitle: Review of Electronic Digital Computers. Joint AIEE--IRE Computer Conference. 10--12 December 1951
title: The IBM card-programmed electronic calculator
publisher: American Institute of Electrical Engineers
address: New York, NY, USA
pages: 30--36
year: 1952
bibdate: Wed Oct 13 11:28:45 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:28:45 ???
note: Reprinted in cite [ 5.4]Randell:1982:ODC.
acknowledgement: ack-nhfb
rawauthor: J. W. Sheldon and L. Tatum
rawbooktitle: Review of Electronic Digital Computers. {Joint AIEE--IRE Computer Conference. 10--12 December 1951}
rawnote: Reprinted in \cite[\S 5.4]{Randell:1982:ODC}.
rawtitle: The {IBM} card-programmed electronic calculator
entry:
@InProceedings{Sheldon:1952:ICP,
  author =       "J. W. Sheldon and L. Tatum",
  booktitle =    "Review of Electronic Digital Computers. {Joint
                 AIEE--IRE Computer Conference. 10--12 December 1951}",
  title =        "The {IBM} card-programmed electronic calculator",
  publisher =    "American Institute of Electrical Engineers",
  address =      "New York, NY, USA",
  pages =        "30--36",
  year =         "1952",
  bibdate =      "Wed Oct 13 11:28:45 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 5.4]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Brooker:1953:FOE
author: R. A. Brooker and D. J. Wheeler
title: Floating Operations on the EDSAC (in Automatic Computing Machinery; Discussions)
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 7
number: 41
pages: 37--47
month: jan
monthnumber: 1
year: 1953
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-1953-0052901-3
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematical Tables and Other Aids to Computation
keywords: floating-point decimal arithmetic
acknowledgement: ack-nhfb
ajournal: Math. Tables Other Aids Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: R. A. Brooker and D. J. Wheeler
rawtitle: Floating Operations on the {EDSAC} (in Automatic Computing Machinery; Discussions)
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib; JSTOR database

abstract:
The difficulties which arise when programming calculations for large automatic calculating machines which have a fixed decimal point are discussed. This leads to a consideration of the possibility of using floating decimal arithmetic for certain kinds of calculations. A method by which floating decimal arithmetic can be carried out with any fixed decimal-point machine is outlined and the scheme adopted for use with the EDSAC is described in detail.

rawabstract:
The difficulties which arise when programming calculations for large automatic calculating machines which have a fixed decimal point are discussed. This leads to a consideration of the possibility of using floating decimal arithmetic for certain kinds of calculations. A method by which floating decimal arithmetic can be carried out with any fixed decimal-point machine is outlined and the scheme adopted for use with the EDSAC is described in detail.

entry:
@Article{Brooker:1953:FOE,
  author =       "R. A. Brooker and D. J. Wheeler",
  title =        "Floating Operations on the {EDSAC} (in Automatic
                 Computing Machinery; Discussions)",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "7",
  number =       "41",
  pages =        "37--47",
  month =        jan,
  year =         "1953",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1953-0052901-3",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 JSTOR database",
  abstract =     "The difficulties which arise when programming
                 calculations for large automatic calculating machines
                 which have a fixed decimal point are discussed. This
                 leads to a consideration of the possibility of using
                 floating decimal arithmetic for certain kinds of
                 calculations. A method by which floating decimal
                 arithmetic can be carried out with any fixed
                 decimal-point machine is outlined and the scheme
                 adopted for use with the EDSAC is described in
                 detail.",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Tables Other Aids Comput.",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "floating-point decimal arithmetic",
  remark-01 =    "From page 38: ``The problem [of programmer-controlled
                 numeric scaling] does not arise with machines designed
                 to operate directly with numbers expressed in the
                 floating radix form. Numbers in this form are
                 represented by $a \cdot r^p$. The first machine of this
                 kind was the Bell Telephone Laboratories Relay Computer
                 Model V(1). This is a decimal machine (that is, $r =
                 10$) in which $1 > |a| > 0.1$, $19 > p > -19$ and $a$
                 is expressed to an accuracy of seven significant
                 figures. Since this was completed all important relay
                 machines have been equipped with similar facilities. No
                 electronic machine of this kind has yet been built but
                 we would remark that in our opinion an electronic
                 machine provided with a floating point arithmetical
                 unit would be a powerful computing instrument even if
                 it had a relatively slow store, a magnetic drum, for
                 example.''",
  remark-02 =    "From page 39: ``Two long and two short storage
                 locations are set aside to form a kind of `arithmetical
                 unit.' One long location holds the numerical part of a
                 number and one short location holds the exponent.
                 Together they form the {\em floating decimal
                 accumulator}. In a similar fashion the other long
                 location and the other short location form the {\em
                 floating decimal register}.''",
  remark-03 =    "From page 40: ``the floating decimal accumulator is
                 then `cleared' by replacing the number held in it by
                 zero, that is, by the special number $010^{-63}$.''",
  remark-04 =    "From page 40: `The use of two separate storage
                 locations for the floating decimal accumulator allows
                 the range and accuracy of numbers held therein to be
                 greater than those held in a single storage location
                 elsewhere. This enables products to be accumulated
                 without loss of accuracy due to intermediate
                 rounding-off errors.''",
  remark-05 =    "From the conclusion on page 46: ``From a direct
                 comparison it would seem that the floating 'orders,'
                 other than those used for reading and writing, are
                 about 60 times as slow as the machine orders and hence
                 that a programme using the interpretive subroutine
                 would be slower by the same factor. This is not
                 altogether true because in such a programme fewer
                 orders' are needed than would otherwise be necessary as
                 there are no scale factors to deal with and the
                 techniques for counting and for the modification of
                 orders' have been streamlined. Moreover, the time taken
                 by the C auxiliaries is about the same as that taken by
                 the corresponding subroutine in fixed decimal-point
                 working. These factors vary from problem to problem but
                 our experience has shown that the reduction in speed
                 varies from about 20 to 1 to about 4 to 1. The
                 reduction of the time taken to code a problem has to be
                 experienced to be believed!''",
}


bibtype: book
filename: fparith.bib
label: IBM:1953:POT
author: IBM Corporation
title: Principles of Operation: Type 701 and Associated Equipment
publisher: pub-IBM
address: pub-IBM:adr
pages: 103
year: 1953
bibdate: Wed Sep 14 23:17:49 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.14 23:17:49 ???
acknowledgement: ack-nhfb
rawauthor: {IBM Corporation}
rawtitle: Principles of Operation: Type 701 and Associated Equipment
entry:
@Book{IBM:1953:POT,
  author =       "{IBM Corporation}",
  title =        "Principles of Operation: Type 701 and Associated
                 Equipment",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  pages =        "103",
  year =         "1953",
  bibdate =      "Wed Sep 14 23:17:49 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Samelson:1953:ORR
author: Klaus Samelson and Friedrich L. Bauer
journal: j-Z-ANGE-MATH-PHYS
volume: 4
number: 4
pages: 312--316
month: jul
monthnumber: 7
year: 1953
CODEN: ZAMPDB
DOI: https://doi.org/10.1007/bf02074638
ISSN: 0044-2275 (print), 1420-9039 (electronic) OR 00442275 (print), 14209039 (electronic)
ISSNL: 0044-2275 OR 00442275
bibdate: Sun Aug 16 18:04:35 2020
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2020.08.16 18:04:35 ???
fjournal: Zeitschrift fur Angewandte Mathematik und Physik = Journal of Applied Mathematics and Physics
keywords: number base conversion
language: German
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/33
rawauthor: Klaus Samelson and Friedrich L. Bauer
title:
Optimale Rechengenauigkeit bei Rechenanlagen mit gleitendem Komma. (German) [Optimal calculation accuracy for calculators with a floating point]

abstract:
Digital automatic computing machines with floating binary point are investigated with respect to their accuracy. It is concluded that special devices can be designed without difficulty, which guarantee the highest accuracy obtainable with a fixed number of digits. For binary computers, a modification of the usual conversion routine is necessary, which is discussed in detail.

rawabstract:
Digital automatic computing machines with floating binary point are investigated with respect to their accuracy. It is concluded that special devices can be designed without difficulty, which guarantee the highest accuracy obtainable with a fixed number of digits. For binary computers, a modification of the usual conversion routine is necessary, which is discussed in detail.

rawtitle:
{Optimale Rechengenauigkeit bei Rechenanlagen mit gleitendem Komma}. ({German}) [{Optimal} calculation accuracy for calculators with a floating point]

entry:
@Article{Samelson:1953:ORR,
  author =       "Klaus Samelson and Friedrich L. Bauer",
  title =        "{Optimale Rechengenauigkeit bei Rechenanlagen mit
                 gleitendem Komma}. ({German}) [{Optimal} calculation
                 accuracy for calculators with a floating point]",
  journal =      j-Z-ANGE-MATH-PHYS,
  volume =       "4",
  number =       "4",
  pages =        "312--316",
  month =        jul,
  year =         "1953",
  CODEN =        "ZAMPDB",
  DOI =          "https://doi.org/10.1007/bf02074638",
  ISSN =         "0044-2275 (print), 1420-9039 (electronic)",
  ISSN-L =       "0044-2275",
  bibdate =      "Sun Aug 16 18:04:35 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Digital automatic computing machines with floating
                 binary point are investigated with respect to their
                 accuracy. It is concluded that special devices can be
                 designed without difficulty, which guarantee the
                 highest accuracy obtainable with a fixed number of
                 digits. For binary computers, a modification of the
                 usual conversion routine is necessary, which is
                 discussed in detail.",
  acknowledgement = ack-nhfb,
  fjournal =     "{Zeitschrift f{\"u}r Angewandte Mathematik und Physik
                 = Journal of Applied Mathematics and Physics}",
  journal-URL =  "http://link.springer.com/journal/33",
  keywords =     "number base conversion",
  language =     "German",
}


bibtype: incollection
filename: fparith.bib
label: Stiefel:1953:MCA
author: E. Stiefel
booktitle: Les machines a calculer et la pensee humaine
publisher: Centre National de la Recherche Scientifique
address: Paris, France
pages: 33--40
year: 1953
MRclass: 65.0X
MRnumber: 0066093
bibdate: Wed Sep 2 16:23:13 2020
bibtimestamp: 2020.09.02 16:23:13 ???
series: Colloques internationaux du Centre National de la Recherche Scientifique, no 37
language: French
acknowledgement: ack-nhfb
authordates: Eduard Stiefel (21 April 1909--25 November 1978)
rawauthor: E. Stiefel
rawbooktitle: Les machines {\`a} calculer et la pens{\'e}e humaine
title:
La machine a calculer arithmetique ``Z4'' de l'Ecole Polytechnique Federale a Zurich (Suisse) et son application a la resolution d'une equation aux derivees partielles de type elliptique. (French) [The arithmetic calculator ``Z4'' of the Swiss Federal Polytechnical University in Zurich (Switzerland) and its application to the solution of an elliptical type partial derivative equation]

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
La machine {\`a} calculer arithm{\'e}tique ``{Z4}'' de l'{Ecole} {Polytechnique} {F}{\'e}d{\'e}rale {\`a} {Zurich} ({Suisse}) et son application {\`a} la r{\'e}solution d'une {\'e}quation aux d{\'e}riv{\'e}es partielles de type elliptique. ({French}) [{The} arithmetic calculator ``{Z4}'' of the {Swiss Federal Polytechnical University in Zurich (Switzerland)} and its application to the solution of an elliptical type partial derivative equation]

entry:
@InCollection{Stiefel:1953:MCA,
  author =       "E. Stiefel",
  booktitle =    "Les machines {\`a} calculer et la pens{\'e}e humaine",
  title =        "La machine {\`a} calculer arithm{\'e}tique ``{Z4}'' de
                 l'{Ecole} {Polytechnique} {F}{\'e}d{\'e}rale {\`a}
                 {Zurich} ({Suisse}) et son application {\`a} la
                 r{\'e}solution d'une {\'e}quation aux d{\'e}riv{\'e}es
                 partielles de type elliptique. ({French}) [{The}
                 arithmetic calculator ``{Z4}'' of the {Swiss Federal
                 Polytechnical University in Zurich (Switzerland)} and
                 its application to the solution of an elliptical type
                 partial derivative equation]",
  publisher =    "Centre National de la Recherche Scientifique",
  address =      "Paris, France",
  pages =        "33--40",
  year =         "1953",
  MRclass =      "65.0X",
  MRnumber =     "0066093",
  bibdate =      "Wed Sep 2 16:23:13 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Colloques internationaux du Centre National de la
                 Recherche Scientifique, no 37",
  acknowledgement = ack-nhfb,
  author-dates = "Eduard Stiefel (21 April 1909--25 November 1978)",
  language =     "French",
}


bibtype: article
filename: fparith.bib
label: Backus:1954:ISS
author: J. W. Backus
title: The IBM 701 Speedcoding System
journal: j-J-ACM
volume: 1
number: 1
pages: 4--6
month: jan
monthnumber: 1
year: 1954
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Fri Nov 04 00:18:27 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.11.04 00:18:27 ???
URL: http://community.computerhistory.org/scc/projects/FORTRAN/paper/p4-backus.pdf
fjournal: Journal of the ACM
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
rawauthor: J. W. Backus
rawtitle: The {IBM 701 Speedcoding} System
abstract:
The IBM 701 Speedcoding System is a set of instructions which causes the 701 to behave like a three-address floating point calculator. Let us call this the Speedcoding calculator. In addition to operating in floating point, this Speedcoding calculator has extremely convenient means for getting information into the machine and for printing results; it has an extensive set of operations to make the job of programming as easy as possible. Speedcoding also provides automatic address modification, flexible tracing, convenient use of auxiliary storage, and built-in checking.

rawabstract:
The IBM 701 Speedcoding System is a set of instructions which causes the 701 to behave like a three-address floating point calculator. Let us call this the Speedcoding calculator. In addition to operating in floating point, this Speedcoding calculator has extremely convenient means for getting information into the machine and for printing results; it has an extensive set of operations to make the job of programming as easy as possible. Speedcoding also provides automatic address modification, flexible tracing, convenient use of auxiliary storage, and built-in checking.

entry:
@Article{Backus:1954:ISS,
  author =       "J. W. Backus",
  title =        "The {IBM 701 Speedcoding} System",
  journal =      j-J-ACM,
  volume =       "1",
  number =       "1",
  pages =        "4--6",
  month =        jan,
  year =         "1954",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Fri Nov 04 00:18:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://community.computerhistory.org/scc/projects/FORTRAN/paper/p4-backus.pdf",
  abstract =     "The IBM 701 Speedcoding System is a set of
                 instructions which causes the 701 to behave like a
                 three-address floating point calculator. Let us call
                 this the Speedcoding calculator. In addition to
                 operating in floating point, this Speedcoding
                 calculator has extremely convenient means for getting
                 information into the machine and for printing results;
                 it has an extensive set of operations to make the job
                 of programming as easy as possible. Speedcoding also
                 provides automatic address modification, flexible
                 tracing, convenient use of auxiliary storage, and
                 built-in checking.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}


bibtype: manual
filename: fparith.bib
label: Burroughs:1954:DH
author: Burroughs Corporation.ElectroData
title: Datatron handbooks
organization: The Division
address: Pasadena, CA, USA
pages: 4--6
year: 1954
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
note: 12 volumes in 1.
keywords: Datatron (Computer)
acknowledgement: ack-nhfb
rawauthor: {Burroughs Corporation.ElectroData}
rawnote: 12 volumes in 1.
rawtitle: Datatron handbooks
remark:
Datatron programming and coding manual --- Datatron operation manual --- Central computer handbook --- Paper tape system handbook --- Card converter Model 500 handbook --- Magnetic tape system handbook --- Cardatron system handbook --- Model 560 DATAFILE handbook --- Control console and consolette handbook --- Floating point control unit handbook --- External switching unit handbook --- Tape preparation unit handbook.

entry:
@Manual{Burroughs:1954:DH,
  author =       "{Burroughs Corporation.ElectroData}",
  title =        "Datatron handbooks",
  organization = "The Division",
  address =      "Pasadena, CA, USA",
  year =         "1954",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "12 volumes in 1.",
  acknowledgement = ack-nhfb,
  keywords =     "Datatron (Computer)",
  remark =       "Datatron programming and coding manual --- Datatron
                 operation manual --- Central computer handbook ---
                 Paper tape system handbook --- Card converter Model 500
                 handbook --- Magnetic tape system handbook ---
                 Cardatron system handbook --- Model 560 DATAFILE
                 handbook --- Control console and consolette handbook
                 --- Floating point control unit handbook --- External
                 switching unit handbook --- Tape preparation unit
                 handbook.",
}


bibtype: article
filename: fparith.bib
label: Freeman:1954:TSA
author: H. Freeman and E. Parsons
title: Time-Sharing Analog Multiplier (TSAM)
journal: j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT
volume: EC-3
number: 1
pages: 11--17
month: mar
monthnumber: 3
year: 1954
bibdate: Fri Jul 15 15:20:53 2011
bibtimestamp: 2011.07.15 15:20:53 ???
fjournal: Transactions of the I.R.E. Professional Group on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: H. Freeman and E. Parsons
rawtitle: Time-Sharing Analog Multiplier ({TSAM})
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib

remark:
Cited in US Patent 3,043,516 (10 July 1962): Time Summing Device for Division, Multiplication, Root Taking and Interpolation, by Harold W. Abbott and Vernon P. Mathis.

entry:
@Article{Freeman:1954:TSA,
  author =       "H. Freeman and E. Parsons",
  title =        "Time-Sharing Analog Multiplier ({TSAM})",
  journal =      j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT,
  volume =       "EC-3",
  number =       "1",
  pages =        "11--17",
  month =        mar,
  year =         "1954",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Fri Jul 15 15:20:53 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Transactions of the I.R.E. Professional Group on
                 Electronic Computers",
  remark =       "Cited in US Patent 3,043,516 (10 July 1962): Time
                 Summing Device for Division, Multiplication, Root
                 Taking and Interpolation, by Harold W. Abbott and
                 Vernon P. Mathis.",
}


bibtype: article
filename: fparith.bib
label: Gorn:1954:AAC
author: Saul Gorn
title: The Automatic Analysis and Control of Computing Errors
journal: j-J-SIAM
volume: 2
number: 2
pages: 69--81
month: jun
monthnumber: 6
year: 1954
CODEN: JSIMAV
ISSN: 0368-4245 (print), 1095-712X (electronic) OR 03684245 (print), 1095712X (electronic)
bibdate: Thu Oct 15 18:16:06 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1998.10.15 18:16:06 MDT
fjournal: Journal of the Society for Industrial and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/loi/smjmap.1
rawauthor: Saul Gorn
rawtitle: The Automatic Analysis and Control of Computing Errors
entry:
@Article{Gorn:1954:AAC,
  author =       "Saul Gorn",
  title =        "The Automatic Analysis and Control of Computing
                 Errors",
  journal =      j-J-SIAM,
  volume =       "2",
  number =       "2",
  pages =        "69--81",
  month =        jun,
  year =         "1954",
  CODEN =        "JSIMAV",
  ISSN =         "0368-4245 (print), 1095-712X (electronic)",
  bibdate =      "Thu Oct 15 18:16:06 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Society for Industrial and Applied
                 Mathematics",
  journal-URL =  "http://epubs.siam.org/loi/smjmap.1",
}


bibtype: article
filename: fparith.bib
label: Kovach:1954:AMU
author: L. D. Kovach and W. Comley
title: An Analog Multiplier Using Thyrite
journal: j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT
volume: EC-3
number: 2
pages: 42--45
month: jun
monthnumber: 6
year: 1954
bibdate: Sun Jul 17 09:57:13 2011
bibtimestamp: 2011.07.17 09:57:13 ???
fjournal: Transactions of the I.R.E. Professional Group on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: L. D. Kovach and W. Comley
rawtitle: An Analog Multiplier Using Thyrite
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib

entry:
@Article{Kovach:1954:AMU,
  author =       "L. D. Kovach and W. Comley",
  title =        "An Analog Multiplier Using Thyrite",
  journal =      j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT,
  volume =       "EC-3",
  number =       "2",
  pages =        "42--45",
  month =        jun,
  year =         "1954",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sun Jul 17 09:57:13 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Transactions of the I.R.E. Professional Group on
                 Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Mayer:1954:ODF
author: M. A. Mayer and B. M. Gordon and R. N. Nicola
title: An operational digital feedback divider
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-3
number: 1
pages: 17--20
month: mar
monthnumber: 3
year: 1954
CODEN: IRELAO
ISSN: 0367-9950 OR 03679950
bibdate: Sun Jul 17 09:52:58 2011
bibtimestamp: 2011.07.17 09:52:58 ???
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: M. A. Mayer and B. M. Gordon and R. N. Nicola
rawtitle: An operational digital feedback divider
entry:
@Article{Mayer:1954:ODF,
  author =       "M. A. Mayer and B. M. Gordon and R. N. Nicola",
  title =        "An operational digital feedback divider",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-3",
  number =       "1",
  pages =        "17--20",
  month =        mar,
  year =         "1954",
  CODEN =        "IRELAO",
  ISSN =         "0367-9950",
  bibdate =      "Sun Jul 17 09:52:58 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Moshman:1954:GPR
author: Jack Moshman
title: The Generation of Pseudo-Random Numbers on a Decimal Calculator
journal: j-J-ACM
volume: 1
number: 2
pages: 88--91
month: apr
monthnumber: 4
year: 1954
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Fri Nov 04 00:18:27 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.11.04 00:18:27 ???
fjournal: Journal of the ACM
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
rawauthor: Jack Moshman
rawtitle: The Generation of Pseudo-Random Numbers on a Decimal Calculator
entry:
@Article{Moshman:1954:GPR,
  author =       "Jack Moshman",
  title =        "The Generation of Pseudo-Random Numbers on a Decimal
                 Calculator",
  journal =      j-J-ACM,
  volume =       "1",
  number =       "2",
  pages =        "88--91",
  month =        apr,
  year =         "1954",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Fri Nov 04 00:18:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Clenshaw:1955:NSC
author: C. W. Clenshaw
title: A note on the summation of Chebyshev series
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 9
number: 51
pages: 118--120
year: 1955
CODEN: MTTCAS
DOI: https://doi.org/10.1090/S0025-5718-1955-0071856-0
ISSN: 0891-6837 (print), 2326-4853 (electronic) OR 08916837 (print), 23264853 (electronic)
ISSNL: 0891-6837 OR 08916837
MRclass: 65.0X
MRnumber: 0071856
bibdate: Thu Feb 08 16:17:25 2018
bibtimestamp: 2018.02.08 16:17:25 ???
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nhfb
ajournal: Math. Tables Other Aids Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: C. W. Clenshaw
rawtitle: A note on the summation of {Chebyshev} series
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib

remark:
Hidden inside cite Brenner:1955:TNS, but important in its own right for commentary on the recursive algorithm for summation of Chebyshev series, and a brief analysis of its accuracy.

entry:
@Article{Clenshaw:1955:NSC,
  author =       "C. W. Clenshaw",
  title =        "A note on the summation of {Chebyshev} series",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "9",
  number =       "51",
  pages =        "118--120",
  year =         "1955",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1955-0071856-0",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  MRclass =      "65.0X",
  MRnumber =     "0071856",
  bibdate =      "Thu Feb 08 16:17:25 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Tables Other Aids Comput.",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Hidden inside \cite{Brenner:1955:TNS}, but important
                 in its own right for commentary on the recursive
                 algorithm for summation of Chebyshev series, and a
                 brief analysis of its accuracy.",
}


bibtype: article
filename: fparith.bib
label: Crockett:1955:GMM
author: J. B. Crockett and H. Chernoff
title: Gradient Methods of Maximization
journal: j-PAC-J-MATH
volume: 5
pages: 33--50
year: 1955
CODEN: PJMAAI
ISSN: 0030-8730 (print), 1945-5844 (electronic) OR 00308730 (print), 19455844 (electronic)
ISSNL: 0030-8730 OR 00308730
bibdate: Fri Aug 20 08:54:24 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.08.20 08:54:24 ???
fjournal: Pacific Journal of Mathematics
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
journalURL: http://msp.org/pjm
rawauthor: J. B. Crockett and H. Chernoff
rawtitle: Gradient Methods of Maximization
entry:
@Article{Crockett:1955:GMM,
  author =       "J. B. Crockett and H. Chernoff",
  title =        "Gradient Methods of Maximization",
  journal =      j-PAC-J-MATH,
  volume =       "5",
  number =       "??",
  pages =        "33--50",
  year =         "1955",
  CODEN =        "PJMAAI",
  ISSN =         "0030-8730 (print), 1945-5844 (electronic)",
  ISSN-L =       "0030-8730",
  bibdate =      "Fri Aug 20 08:54:24 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Pacific Journal of Mathematics",
  journal-URL =  "http://msp.org/pjm",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: book
filename: fparith.bib
label: Eckert:1955:FFS
author: W. J. (Wallace John) Eckert and Rebecca Bradley Jones
title: Faster, faster; a simple description of a giant electronic calculator and the problems it solves
publisher: pub-IBM
address: pub-IBM:adr
pages: 160
year: 1955
LCCN: QA76 .E25
bibdate: Fri Aug 20 08:57:56 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.08.20 08:57:56 MDT
remark: Cited in cite Sterbenz:1974:FPC.
subject: Computers
acknowledgement: ack-nhfb
authordates: 1902--1971
rawauthor: W. J. (Wallace John) Eckert and Rebecca Bradley Jones
rawtitle: Faster, faster; a simple description of a giant electronic calculator and the problems it solves
entry:
@Book{Eckert:1955:FFS,
  author =       "W. J. (Wallace John) Eckert and Rebecca Bradley
                 Jones",
  title =        "Faster, faster; a simple description of a giant
                 electronic calculator and the problems it solves",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  pages =        "160",
  year =         "1955",
  LCCN =         "QA76 .E25",
  bibdate =      "Fri Aug 20 08:57:56 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1902--1971",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
  subject =      "Computers",
  xxaddress =    pub-MCGRAW-HILL:adr,
  xxpublisher =  pub-MCGRAW-HILL,
}


bibtype: book
filename: fparith.bib
label: Hastings:1955:ADC
author: Cecil B. Hastings, Jr. and Jeanne T. Hayward and James P. Wong, Jr.
title: Approximations for Digital Computers
publisher: pub-PRINCETON
address: pub-PRINCETON:adr
pages: viii + 201
year: 1955
LCCN: QA76 .H33
bibdate: Mon Sep 30 14:51:50 1996
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.09.30 14:51:50 ???
acknowledgement: ack-nj
rawauthor: Cecil B. {Hastings, Jr.} and Jeanne T. Hayward and James P. {Wong, Jr.}
rawtitle: Approximations for Digital Computers
entry:
@Book{Hastings:1955:ADC,
  author =       "Cecil B. {Hastings, Jr.} and Jeanne T. Hayward and
                 James P. {Wong, Jr.}",
  title =        "Approximations for Digital Computers",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  pages =        "viii + 201",
  year =         "1955",
  LCCN =         "QA76 .H33",
  bibdate =      "Mon Sep 30 14:51:50 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Lenaerts:1955:ASR
author: E. H. Lenaerts
title: Automatic Square Rooting
journal: j-ELECTRON-ENG
volume: 27
pages: 287--289
month: jul
monthnumber: 7
year: 1955
CODEN: ELEGAP
ISSN: 0013-4902 OR 00134902
bibdate: Thu Sep 1 10:15:41 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:41 ???
fjournal: Electronic Engineering
acknowledgement: ack-nj
rawauthor: E. H. Lenaerts
rawtitle: Automatic Square Rooting
entry:
@Article{Lenaerts:1955:ASR,
  author =       "E. H. Lenaerts",
  title =        "Automatic Square Rooting",
  journal =      j-ELECTRON-ENG,
  volume =       "27",
  number =       "??",
  pages =        "287--289",
  month =        jul,
  year =         "1955",
  CODEN =        "ELEGAP",
  ISSN =         "0013-4902",
  bibdate =      "Thu Sep 1 10:15:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronic Engineering",
}


bibtype: article
filename: fparith.bib
label: Parsons:1955:SDC
author: Frances L. Parsons
journal: j-J-ACM
volume: 2
number: 3
pages: 205--207
month: jul
monthnumber: 7
year: 1955
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Wed Nov 09 01:00:34 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.11.09 01:00:34 ???
fjournal: Journal of the ACM
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
rawauthor: Frances L. Parsons
title:
A Simple Desk-Calculator Method for Checking Binary Results of Digital Computer Arithmetic Operations

rawtitle:
A Simple Desk-Calculator Method for Checking Binary Results of Digital Computer Arithmetic Operations

entry:
@Article{Parsons:1955:SDC,
  author =       "Frances L. Parsons",
  title =        "A Simple Desk-Calculator Method for Checking Binary
                 Results of Digital Computer Arithmetic Operations",
  journal =      j-J-ACM,
  volume =       "2",
  number =       "3",
  pages =        "205--207",
  month =        jul,
  year =         "1955",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Wed Nov 09 01:00:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}


bibtype: book
filename: fparith.bib
label: Richards:1955:AOD
author: Richard Kohler Richards
title: Arithmetic Operations in Digital Computers
publisher: D. Van Nostrand
address: New York, NY, USA
pages: iv + 397
year: 1955
LCCN: QA75 .R5 1955
bibdate: Fri Nov 28 18:46:37 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 18:46:37 ???
acknowledgement: ack-nhfb
rawauthor: Richard Kohler Richards
rawtitle: Arithmetic Operations in Digital Computers
entry:
@Book{Richards:1955:AOD,
  author =       "Richard Kohler Richards",
  title =        "Arithmetic Operations in Digital Computers",
  publisher =    "D. Van Nostrand",
  address =      "New York, NY, USA",
  pages =        "iv + 397",
  year =         "1955",
  LCCN =         "QA75 .R5 1955",
  bibdate =      "Fri Nov 28 18:46:37 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Robertson:1955:TCM
author: J. E. Robertson
title: Two's Complement Multiplication in Binary Parallel Digital Computers
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-4
number: 3
pages: 118--119
month: sep
monthnumber: 9
year: 1955
CODEN: IRELAO
DOI: https://doi.org/10.1109/IRETELC.1955.5407911
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jun 30 15:10:39 MDT 2011
bibtimestamp: 2011.06.30 15:10:39 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5407911
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: J. E. Robertson
rawtitle: Two's Complement Multiplication in Binary Parallel Digital Computers
entry:
@Article{Robertson:1955:TCM,
  author =       "J. E. Robertson",
  title =        "Two's Complement Multiplication in Binary Parallel
                 Digital Computers",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-4",
  number =       "3",
  pages =        "118--119",
  month =        sep,
  year =         "1955",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/IRETELC.1955.5407911",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jun 30 15:10:39 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5407911",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: book
filename: fparith.bib
label: Stiefel:1955:RID
author: Eduard Stiefel
volume: 45
publisher: Westdeutscher Verlag
address: Cologne and Opladen, West Germany
pages: 29--45; Diskussion 47--65
year: 1955
MRclass: 68.0X
MRnumber: 0073311
MRreviewer: H. H. Goldstine
bibdate: Wed Sep 2 16:23:13 2020
bibtimestamp: 2020.09.02 16:23:13 ???
series: Arbeitsgemeinschaft fur Forschung des Landes Nordrhein-Westfalen. Heft
language: German
acknowledgement: ack-nhfb
authordates: Eduard Stiefel (21 April 1909--25 November 1978)
rawauthor: Eduard Stiefel
title:
Rechenautomaten im Dienste der Technik. Erfahrungen mit dem Zuse-Rechenautomaten Z4. (German) [Calculating machines in the service of technology. Experience with the Zuse-calculator Z4]

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
{Rechenautomaten im Dienste der Technik. Erfahrungen mit dem Zuse-Rechenautomaten Z4}. ({German}) [{Calculating} machines in the service of technology. {Experience} with the {Zuse}-calculator {Z4}]

entry:
@Book{Stiefel:1955:RID,
  author =       "Eduard Stiefel",
  title =        "{Rechenautomaten im Dienste der Technik. Erfahrungen
                 mit dem Zuse-Rechenautomaten Z4}. ({German})
                 [{Calculating} machines in the service of technology.
                 {Experience} with the {Zuse}-calculator {Z4}]",
  volume =       "45",
  publisher =    "Westdeutscher Verlag",
  address =      "Cologne and Opladen, West Germany",
  pages =        "29--45; Diskussion 47--65",
  year =         "1955",
  MRclass =      "68.0X",
  MRnumber =     "0073311",
  MRreviewer =   "H. H. Goldstine",
  bibdate =      "Wed Sep 2 16:23:13 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Arbeitsgemeinschaft f{\"{u}}r Forschung des Landes
                 Nordrhein-Westfalen. Heft",
  acknowledgement = ack-nhfb,
  author-dates = "Eduard Stiefel (21 April 1909--25 November 1978)",
  language =     "German",
}


bibtype: article
filename: fparith.bib
label: Estrin:1956:NHS
author: G. Estrin and B. Gilchrist and J. H. Pomerene
title: A Note on High-Speed Digital Multiplication
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-5
number: 3
pages: 140--140
month: sep
monthnumber: 9
year: 1956
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1956.5219936
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jun 30 15:46:27 MDT 2011
bibtimestamp: 2011.06.30 15:46:27 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219936
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: G. Estrin and B. Gilchrist and J. H. Pomerene
rawtitle: A Note on High-Speed Digital Multiplication
entry:
@Article{Estrin:1956:NHS,
  author =       "G. Estrin and B. Gilchrist and J. H. Pomerene",
  title =        "A Note on High-Speed Digital Multiplication",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-5",
  number =       "3",
  pages =        "140--140",
  month =        sep,
  year =         "1956",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1956.5219936",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jun 30 15:46:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219936",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: book
filename: fparith.bib
label: Hildebrand:1956:INA
author: Francis Begnaud Hildebrand
title: Introduction to Numerical Analysis
publisher: pub-MCGRAW-HILL
address: pub-MCGRAW-HILL:adr
pages: 511
year: 1956
LCCN: QA300 .H5
bibdate: Fri Aug 20 09:19:58 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.08.20 09:19:58 MDT
series: International series in pure and applied mathematics
remark: See also second edition cite Hildebrand:1974:INA,Hildebrand:1987:INA.
subject: Numerical analysis
acknowledgement: ack-nhfb
rawauthor: Francis Begnaud Hildebrand
rawtitle: Introduction to Numerical Analysis
TOC:
1. Introduction (significant figures, random errors, error bounds, etc.) 2. Interpolation with divided differences 3. Lagrangian methods 4. Finite-difference interpolation 5. Operations with finite differences 6. Numerical solution of ordinary differential equations 7. Least-squares polynomial approximation 8. Gaussian quadrature and related topics 9. Approximations of various types 10. Numerical solution of equations Appendix: Justification of the Crout reduction

rawTOC:
1. Introduction (significant figures, random errors, error bounds, etc.) \\ 2. Interpolation with divided differences \\ 3. Lagrangian methods \\ 4. Finite-difference interpolation \\ 5. Operations with finite differences \\ 6. Numerical solution of ordinary differential equations \\ 7. Least-squares polynomial approximation \\ 8. Gaussian quadrature and related topics \\ 9. Approximations of various types \\ 10. Numerical solution of equations \\ Appendix: Justification of the Crout reduction

entry:
@Book{Hildebrand:1956:INA,
  author =       "Francis Begnaud Hildebrand",
  title =        "Introduction to Numerical Analysis",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "511",
  year =         "1956",
  LCCN =         "QA300 .H5",
  bibdate =      "Fri Aug 20 09:19:58 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "International series in pure and applied mathematics",
  acknowledgement = ack-nhfb,
  remark =       "See also second edition
                 \cite{Hildebrand:1974:INA,Hildebrand:1987:INA}.",
  subject =      "Numerical analysis",
  tableofcontents = "1. Introduction (significant figures, random
                 errors, error bounds, etc.) \\
                 2. Interpolation with divided differences \\
                 3. Lagrangian methods \\
                 4. Finite-difference interpolation \\
                 5. Operations with finite differences \\
                 6. Numerical solution of ordinary differential
                 equations \\
                 7. Least-squares polynomial approximation \\
                 8. Gaussian quadrature and related topics \\
                 9. Approximations of various types \\
                 10. Numerical solution of equations \\
                 Appendix: Justification of the Crout reduction",
}


bibtype: techreport
filename: fparith.bib
label: Lazarus:1956:MI
title: MANIAC II
type: Report
number: LA-2083
institution: inst-LASL
address: inst-LASL:adr
pages: 54
day: 1
month: oct
monthnumber: 10
year: 1956
bibdate: Tue Mar 20 11:14:15 2007
bibtimestamp: 2007.03.20 11:14:15 ???
URL: https://sgp.fas.org/othergov/doe/lanl/lib-www/la-pubs/00320765.pdf
acknowledgement: ack-nhfb
rawtitle: {MANIAC II}
author:
R. B. Lazarus and N. Metropolis and W. Orvedahl and J. H. Richardson and W. Spack, Jr. and R. L. Bivins and J. V. Caulfield and I. Kral and A. F. Malmberg and G. T. McKinley and R. E. Williamson

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawauthor:
R. B. Lazarus and N. Metropolis and W. Orvedahl and J. H. Richardson and W. {Spack, Jr.} and R. L. Bivins and J. V. Caulfield and I. Kral and A. F. Malmberg and G. T. McKinley and R. E. Williamson

entry:
@TechReport{Lazarus:1956:MI,
  author =       "R. B. Lazarus and N. Metropolis and W. Orvedahl and J.
                 H. Richardson and W. {Spack, Jr.} and R. L. Bivins and
                 J. V. Caulfield and I. Kral and A. F. Malmberg and G.
                 T. McKinley and R. E. Williamson",
  title =        "{MANIAC II}",
  type =         "Report",
  number =       "LA-2083",
  institution =  inst-LASL,
  address =      inst-LASL:adr,
  pages =        "54",
  day =          "1",
  month =        oct,
  year =         "1956",
  bibdate =      "Tue Mar 20 11:14:15 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://sgp.fas.org/othergov/doe/lanl/lib-www/la-pubs/00320765.pdf",
  acknowledgement = ack-nhfb,
  remark-1 =     "OSTI ID: 4382471",
  remark-2 =     "From page 9: ``The Maniac II \ldots{} has 12,288
                 48-bit words. It is asynchronous and has no clock. Its
                 speed is that appropriate to (1) a memory cycle of 8
                 microseconds, (2) a basic add time of 6 microseconds,
                 and (3) a shift time of about 1.3 microseconds per
                 stage. The average multiply time is about 160
                 microseconds.''",
  remark-3 =     "From page 14, the 48-bit floating-point word consists
                 of a 1-bit sign, a 3-bit exponent-of-65536, a 1-bit
                 sign of the exponent, and a 43-bit fraction in [0,1).
                 The range of nonzero numbers is (0x1p-155, 0x1p112), or
                 roughly (2e-47, 5e33). The report notes: ``Although
                 such a large base implies of possibility of as many as
                 15 lead[ing] zeros, the large word size of 48 bits
                 guarantees adequate significance.''",
}


bibtype: article
filename: fparith.bib
label: Lilamand:1956:TDM
author: M. Lejet Lilamand
title: A Time-Division Multiplier
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-5
number: 1
pages: 26--34
month: mar
monthnumber: 3
year: 1956
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1956.5219789
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jun 30 15:46:18 MDT 2011
bibtimestamp: 2011.06.30 15:46:18 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219789
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: M. Lejet Lilamand
rawtitle: A Time-Division Multiplier
entry:
@Article{Lilamand:1956:TDM,
  author =       "M. Lejet Lilamand",
  title =        "A Time-Division Multiplier",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-5",
  number =       "1",
  pages =        "26--34",
  month =        mar,
  year =         "1956",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1956.5219789",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jun 30 15:46:18 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219789",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Perkins:1956:EPC
author: Robert Perkins
title: EASIAC, A Pseudo-Computer
journal: j-J-ACM
volume: 3
number: 2
pages: 65--72
month: apr
monthnumber: 4
year: 1956
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Fri Nov 04 23:46:26 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.11.04 23:46:26 ???
fjournal: Journal of the ACM
keywords: decimal floating-point arithmetic
remark: Early example of a decimal floating-point machine.
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
rawauthor: Robert Perkins
rawtitle: {EASIAC}, {A} Pseudo-Computer
abstract:
One of the primary functions of the MIDAC installation at the University of Michigan is the instruction of beginners in the various aspects of digital machine use including programming and coding. ldots In conducting these courses it was soon found to be extremely difficult, in five or six instruction periods, to bring a complete newcomer up to the point where he can code and check out on MIDAC anything more than a rather trivial routine. As might be expected the difficulty centers around problems of scaling, instruction modification and binary representation. ldots To alleviate these problems it was decided that a new computer was needed: one designed to make programming easier. At the cost of some of MIDAC's speed and capacity plus two or three man-months of programming time EASIAC, the EASy Instruction Automatic Computer, was realized as a translation-interpretation program in MIDAC.

rawabstract:
One of the primary functions of the MIDAC installation at the University of Michigan is the instruction of beginners in the various aspects of digital machine use including programming and coding. \ldots{} In conducting these courses it was soon found to be extremely difficult, in five or six instruction periods, to bring a complete newcomer up to the point where he can code and check out on MIDAC anything more than a rather trivial routine. As might be expected the difficulty centers around problems of scaling, instruction modification and binary representation. \ldots{} To alleviate these problems it was decided that a new computer was needed: one designed to make programming easier. At the cost of some of MIDAC's speed and capacity plus two or three man-months of programming time EASIAC, the EASy Instruction Automatic Computer, was realized as a translation-interpretation program in MIDAC.

entry:
@Article{Perkins:1956:EPC,
  author =       "Robert Perkins",
  title =        "{EASIAC}, {A} Pseudo-Computer",
  journal =      j-J-ACM,
  volume =       "3",
  number =       "2",
  pages =        "65--72",
  month =        apr,
  year =         "1956",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Fri Nov 04 23:46:26 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "One of the primary functions of the MIDAC installation
                 at the University of Michigan is the instruction of
                 beginners in the various aspects of digital machine use
                 including programming and coding. \ldots{} In
                 conducting these courses it was soon found to be
                 extremely difficult, in five or six instruction
                 periods, to bring a complete newcomer up to the point
                 where he can code and check out on MIDAC anything more
                 than a rather trivial routine. As might be expected the
                 difficulty centers around problems of scaling,
                 instruction modification and binary representation.
                 \ldots{} To alleviate these problems it was decided
                 that a new computer was needed: one designed to make
                 programming easier. At the cost of some of MIDAC's
                 speed and capacity plus two or three man-months of
                 programming time EASIAC, the EASy Instruction Automatic
                 Computer, was realized as a translation-interpretation
                 program in MIDAC.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  keywords =     "decimal floating-point arithmetic",
  remark =       "Early example of a decimal floating-point machine.",
}


bibtype: article
filename: fparith.bib
label: Robertson:1956:NCD
author: J. E. Robertson
title: A new class of digital division methods
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-5
pages: 65--73
month: jun
monthnumber: 6
year: 1956
CODEN: IRELAO
ISSN: 0367-9950 OR 03679950
bibdate: Fri Nov 09 19:14:45 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:14:45 ???
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: J. E. Robertson
rawtitle: A new class of digital division methods
entry:
@Article{Robertson:1956:NCD,
  author =       "J. E. Robertson",
  title =        "A new class of digital division methods",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-5",
  number =       "??",
  pages =        "65--73",
  month =        jun,
  year =         "1956",
  CODEN =        "IRELAO",
  ISSN =         "0367-9950",
  bibdate =      "Fri Nov 09 19:14:45 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Stegun:1956:PC
author: Irene A. Stegun and Milton Abramowitz
title: Pitfalls in computation
journal: Journal of the Society for Industrial and Applied Mathematics
volume: 4
pages: 207--219
year: 1956
bibdate: Tue Aug 28 06:16:28 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2001.08.28 06:16:28 ???
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
rawauthor: Irene A. Stegun and Milton Abramowitz
rawtitle: Pitfalls in computation
entry:
@Article{Stegun:1956:PC,
  author =       "Irene A. Stegun and Milton Abramowitz",
  title =        "Pitfalls in computation",
  journal =      "Journal of the Society for Industrial and Applied
                 Mathematics",
  volume =       "4",
  pages =        "207--219",
  year =         "1956",
  bibdate =      "Tue Aug 28 06:16:28 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Sydnor:1956:AMS
author: R. L. Sydnor and T. R. O'Meara and J. Strathman
title: Analog Multipliers and Squarers Using a Multigrid Modulator
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-5
number: 2
pages: 82--85
month: jun
monthnumber: 6
year: 1956
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1956.5219804
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jun 30 15:46:21 MDT 2011
bibtimestamp: 2011.06.30 15:46:21 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219804
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: R. L. Sydnor and T. R. O'Meara and J. Strathman
rawtitle: Analog Multipliers and Squarers Using a Multigrid Modulator
entry:
@Article{Sydnor:1956:AMS,
  author =       "R. L. Sydnor and T. R. O'Meara and J. Strathman",
  title =        "Analog Multipliers and Squarers Using a Multigrid
                 Modulator",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-5",
  number =       "2",
  pages =        "82--85",
  month =        jun,
  year =         "1956",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1956.5219804",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jun 30 15:46:21 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219804",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Weinberger:1956:OMA
author: A. Weinberger and J. L. Smith
title: A One-Microsecond Adder Using One-Megacycle Circuitry
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-5
pages: 65--73
month: jun
monthnumber: 6
year: 1956
CODEN: IRELAO
ISSN: 0367-9950 OR 03679950
bibdate: Fri Nov 09 19:38:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:38:57 ???
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: A. Weinberger and J. L. Smith
rawtitle: A One-Microsecond Adder Using One-Megacycle Circuitry
entry:
@Article{Weinberger:1956:OMA,
  author =       "A. Weinberger and J. L. Smith",
  title =        "A One-Microsecond Adder Using One-Megacycle
                 Circuitry",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-5",
  number =       "??",
  pages =        "65--73",
  month =        jun,
  year =         "1956",
  CODEN =        "IRELAO",
  ISSN =         "0367-9950",
  bibdate =      "Fri Nov 09 19:38:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Wolontis:1956:CFD
author: V. M. Wolontis
title: A Complete Floating-Decimal Interpretive System for the IBM 650 Magnetic Drum Calculator
journal: IBM Technical Newsletter
number: 11
pages: xxi + 63
month: mar
monthnumber: 3
year: 1956
bibdate: Mon Sep 04 13:55:28 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.09.04 13:55:28 ???
URL: https://babel.hathitrust.org/cgi/pt?id=coo.31924003945759&seq=7
acknowledgement: ack-nhfb
rawauthor: V. M. Wolontis
rawtitle: A Complete Floating-Decimal Interpretive System for the {IBM 650 Magnetic Drum Calculator}
entry:
@Article{Wolontis:1956:CFD,
  author =       "V. M. Wolontis",
  title =        "A Complete Floating-Decimal Interpretive System for
                 the {IBM 650 Magnetic Drum Calculator}",
  journal =      "IBM Technical Newsletter",
  volume =       "??",
  number =       "11",
  pages =        "xxi + 63",
  month =        mar,
  year =         "1956",
  bibdate =      "Mon Sep 04 13:55:28 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://babel.hathitrust.org/cgi/pt?id=coo.31924003945759&seq=7",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Alt:1957:EDC
editor: Franz L. Alt
title: Electronic Digital Computers: Their Use in Science and Engineering
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: x + 335
year: 1957
bibdate: Sun Jun 17 18:53:23 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2018.06.17 18:53:23 ???
remark: Section 2.3 discusses number representation and decimal versus binary arithmetic.
acknowledgement: ack-nhfb
raweditor: Franz L. Alt
rawtitle: Electronic Digital Computers: Their Use in Science and Engineering
entry:
@Book{Alt:1957:EDC,
  editor =       "Franz L. Alt",
  title =        "Electronic Digital Computers: Their Use in Science and
                 Engineering",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "x + 335",
  year =         "1957",
  bibdate =      "Sun Jun 17 18:53:23 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Section 2.3 discusses number representation and
                 decimal versus binary arithmetic.",
  xxnote =       "Check page count: incomplete view in Google books.
                 Price bibliography says 1958.",
}


bibtype: article
filename: fparith.bib
label: Ercoli:1957:EDO
author: Paolo Ercoli and Roberto Vacca
title: Errors Due to Overflow in Arithmetic Operations Particularly as Regards FINAC Electronic Computer
journal: j-J-ACM
volume: 4
number: 4
pages: 450--455
month: oct
monthnumber: 10
year: 1957
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Thu Dec 08 09:28:48 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.12.08 09:28:48 ???
note: See letter cite Ercoli:1960:LEE.
fjournal: Journal of the ACM
keywords: floating-point arithmetic; overflow
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
rawauthor: Paolo Ercoli and Roberto Vacca
rawnote: See letter \cite{Ercoli:1960:LEE}.
rawtitle: Errors Due to Overflow in Arithmetic Operations Particularly as Regards {FINAC} Electronic Computer
entry:
@Article{Ercoli:1957:EDO,
  author =       "Paolo Ercoli and Roberto Vacca",
  title =        "Errors Due to Overflow in Arithmetic Operations
                 Particularly as Regards {FINAC} Electronic Computer",
  journal =      j-J-ACM,
  volume =       "4",
  number =       "4",
  pages =        "450--455",
  month =        oct,
  year =         "1957",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Thu Dec 08 09:28:48 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See letter \cite{Ercoli:1960:LEE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  keywords =     "floating-point arithmetic; overflow",
}


bibtype: article
filename: fparith.bib
label: Gini:1957:SFD
author: Corrado Gini
journal: Bull. Inst. Internat. Stat.
volume: 35
pages: 57--76
year: 1957
bibdate: Sun Sep 18 11:54:25 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2011.09.18 11:54:25 ???
note: 29th session, 2nd delivery, Rio de Janerio.
keywords: Benford's Law; Law of Anomalous Numbers; Zipf's Law
language: Italian
acknowledgement: ack-nhfb
rawauthor: Corrado Gini
rawnote: 29th session, 2nd delivery, Rio de Janerio.
title:
Sulla frequenza delle cifre iniziali dei numeri osservati. (Italian) [On the frequency of initial digits of observed numbers]

rawtitle:
Sulla frequenza delle cifre iniziali dei numeri osservati. ({Italian}) [{On} the frequency of initial digits of observed numbers]

entry:
@Article{Gini:1957:SFD,
  author =       "Corrado Gini",
  title =        "Sulla frequenza delle cifre iniziali dei numeri
                 osservati. ({Italian}) [{On} the frequency of initial
                 digits of observed numbers]",
  journal =      "Bull. Inst. Internat. Stat.",
  volume =       "35",
  number =       "??",
  pages =        "57--76",
  year =         "1957",
  bibdate =      "Sun Sep 18 11:54:25 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "29th session, 2nd delivery, Rio de Janerio.",
  URL =          "",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  language =     "Italian",
}


bibtype: article
filename: fparith.bib
label: Herzel:1957:SDD
author: Amato Herzel
journal: Atti dell XV e XVII Riunione, Societa Italiana di Statistica
pages: ??--??
year: 1957
bibdate: Sun Sep 18 12:00:07 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2011.09.18 12:00:07 ???
keywords: Benford's Law; Law of Anomalous Numbers; Zipf's Law
language: Italian
acknowledgement: ack-nhfb
rawauthor: Amato Herzel
title:
Sulla distribuzione della cifre iniziali dei numeri statistici. (Italian) [On the frequency of initial digits of statistical numbers]

rawtitle:
Sulla distribuzione della cifre iniziali dei numeri statistici. ({Italian}) [{On} the frequency of initial digits of statistical numbers]

entry:
@Article{Herzel:1957:SDD,
  author =       "Amato Herzel",
  title =        "Sulla distribuzione della cifre iniziali dei numeri
                 statistici. ({Italian}) [{On} the frequency of initial
                 digits of statistical numbers]",
  journal =      "Atti dell XV e XVII Riunione, Societa Italiana di
                 Statistica",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  year =         "1957",
  bibdate =      "Sun Sep 18 12:00:07 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  language =     "Italian",
}


bibtype: article
filename: fparith.bib
label: Howe:1957:TRA
author: R. M. Howe and E. G. Gilbert
title: Trigonometric Resolution in Analog Computers by Means of Multiplier Elements
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-6
number: 2
pages: 86--92
month: jun
monthnumber: 6
year: 1957
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1957.5221576
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jun 30 16:07:27 MDT 2011
bibtimestamp: 2011.06.30 16:07:27 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221576
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: R. M. Howe and E. G. Gilbert
rawtitle: Trigonometric Resolution in Analog Computers by Means of Multiplier Elements
entry:
@Article{Howe:1957:TRA,
  author =       "R. M. Howe and E. G. Gilbert",
  title =        "Trigonometric Resolution in Analog Computers by Means
                 of Multiplier Elements",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-6",
  number =       "2",
  pages =        "86--92",
  month =        jun,
  year =         "1957",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1957.5221576",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jun 30 16:07:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221576",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Kalbfell:1957:EAM
author: David C. Kalbfell
title: An Electronic Analog Multiplier
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-6
number: 2
pages: 100--103
month: jun
monthnumber: 6
year: 1957
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1957.5221579
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jun 30 16:07:27 MDT 2011
bibtimestamp: 2011.06.30 16:07:27 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221579
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: David C. Kalbfell
rawtitle: An Electronic Analog Multiplier
entry:
@Article{Kalbfell:1957:EAM,
  author =       "David C. Kalbfell",
  title =        "An Electronic Analog Multiplier",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-6",
  number =       "2",
  pages =        "100--103",
  month =        jun,
  year =         "1957",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1957.5221579",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jun 30 16:07:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221579",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Kogbetliantz:1957:CEN
author: E. G. Kogbetliantz
title: Computation of $ e^n $ for $ - infty < n < + infty $ Using an Electronic Computer
journal: j-IBM-JRD
volume: 1
number: 2
pages: 110--115
month: apr
monthnumber: 4
year: 1957
CODEN: IBMJAE
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
bibdate: Tue Sep 06 18:04:49 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.06 18:04:49 ???
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nj
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
rawauthor: E. G. Kogbetliantz
rawtitle: Computation of $ e^n $ for $ - \infty < n < + \infty $ Using an Electronic Computer
entry:
@Article{Kogbetliantz:1957:CEN,
  author =       "E. G. Kogbetliantz",
  title =        "Computation of $ e^n $ for $ - \infty < n < + \infty $
                 Using an Electronic Computer",
  journal =      j-IBM-JRD,
  volume =       "1",
  number =       "2",
  pages =        "110--115",
  month =        apr,
  year =         "1957",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Sep 06 18:04:49 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}


bibtype: article
filename: fparith.bib
label: Lehman:1957:HSD
author: M. Lehman
title: High-Speed Digital Multiplication
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-6
number: 3
pages: 204--205
month: sep
monthnumber: 9
year: 1957
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1957.5222025
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jun 30 16:07:34 MDT 2011
bibtimestamp: 2011.06.30 16:07:34 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222025
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: M. Lehman
rawtitle: High-Speed Digital Multiplication
entry:
@Article{Lehman:1957:HSD,
  author =       "M. Lehman",
  title =        "High-Speed Digital Multiplication",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-6",
  number =       "3",
  pages =        "204--205",
  month =        sep,
  year =         "1957",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1957.5222025",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jun 30 16:07:34 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222025",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Luke:1957:CLZ
author: Y. L. Luke
title: On the Computation of $ log Z $ and $ arctan Z $
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 11
pages: 16--18
year: 1957
CODEN: MTTCAS
ISSN: 0891-6837 OR 08916837
bibdate: Thu Sep 1 10:16:09 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:09 ???
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nj
ajournal: Math. Tables Other Aids Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: Y. L. Luke
rawtitle: On the Computation of $ \log {Z} $ and $ \arctan {Z} $
entry:
@Article{Luke:1957:CLZ,
  author =       "Y. L. Luke",
  title =        "On the Computation of $ \log {Z} $ and $ \arctan {Z}
                 $",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "11",
  number =       "??",
  pages =        "16--18",
  month =        "????",
  year =         "1957",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibdate =      "Thu Sep 1 10:16:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  ajournal =     "Math. Tables Other Aids Comput.",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: techreport
filename: fparith.bib
label: Metze:1957:SPO
author: G. Metze
title: A Study of Parallel One's Complement Arithmetic Units with Separate Carry or Borrow Storage
type: Report
number: 81
institution: Digital Computer Laboratory, University of Illinois
address: Urbana, IL, USA
pages: 77
year: 1957
bibdate: Thu Nov 18 09:07:07 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.11.18 09:07:07 ???
acknowledgement: ack-nhfb
rawauthor: G. Metze
rawtitle: A Study of Parallel One's Complement Arithmetic Units with Separate Carry or Borrow Storage
remark:
Flores' book cite [p. 485]Flores:1963:LCA cites this report, and says that its conclusion is that the disadvantages of one's complement arithmetic outweigh the advantages.

entry:
@TechReport{Metze:1957:SPO,
  author =       "G. Metze",
  title =        "A Study of Parallel One's Complement Arithmetic Units
                 with Separate Carry or Borrow Storage",
  type =         "Report",
  number =       "81",
  institution =  "Digital Computer Laboratory, University of Illinois",
  address =      "Urbana, IL, USA",
  pages =        "77",
  year =         "1957",
  bibdate =      "Thu Nov 18 09:07:07 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Flores' book \cite[p. 485]{Flores:1963:LCA} cites this
                 report, and says that its conclusion is that the
                 disadvantages of one's complement arithmetic outweigh
                 the advantages.",
}


bibtype: article
filename: fparith.bib
label: Murphy:1957:PIA
author: R. W. Murphy
title: A Positive-Integer Arithmetic for Data Processing
journal: j-IBM-JRD
volume: 1
number: 2
pages: 158--170
month: apr
monthnumber: 4
year: 1957
CODEN: IBMJAE
DOI: https://doi.org/10.1147/rd.12.0158
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
MRclass: 68.0X
MRnumber: 18,939d
bibdate: Tue Sep 11 15:35:33 MDT 2012
bibtimestamp: 2012.09.11 15:35:33 MDT
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
bookURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
reviewer: C. C. Gotlieb
rawauthor: R. W. Murphy
rawtitle: A Positive-Integer Arithmetic for Data Processing
bibsource:
http://www.research.ibm.com/journal/; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib

URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392735; http://www.research.ibm.com/journal/rd/012/ibmrd0102G.pdf

abstract:
It is hypothesized that positive numbers suffice for the expression of quantities in accounting. New arithmetic operations are devised that yield non-negative results in computation, and the applicability of these operations to data processing is studied. These operations permit a wide variety of functions to be computed with fewer and less complex steps and imply the feasibility of constructing less complex data-processing machines.

rawabstract:
It is hypothesized that positive numbers suffice for the expression of quantities in accounting. New arithmetic operations are devised that yield non-negative results in computation, and the applicability of these operations to data processing is studied. These operations permit a wide variety of functions to be computed with fewer and less complex steps and imply the feasibility of constructing less complex data-processing machines.

entry:
@Article{Murphy:1957:PIA,
  author =       "R. W. Murphy",
  title =        "A Positive-Integer Arithmetic for Data Processing",
  journal =      j-IBM-JRD,
  volume =       "1",
  number =       "2",
  pages =        "158--170",
  month =        apr,
  year =         "1957",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.12.0158",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "68.0X",
  MRnumber =     "18,939d",
  bibdate =      "Tue Sep 11 15:35:33 MDT 2012",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392735;
                 http://www.research.ibm.com/journal/rd/012/ibmrd0102G.pdf",
  abstract =     "It is hypothesized that positive numbers suffice for
                 the expression of quantities in accounting. New
                 arithmetic operations are devised that yield
                 non-negative results in computation, and the
                 applicability of these operations to data processing is
                 studied. These operations permit a wide variety of
                 functions to be computed with fewer and less complex
                 steps and imply the feasibility of constructing less
                 complex data-processing machines.",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  reviewer =     "C. C. Gotlieb",
}


bibtype: article
filename: fparith.bib
label: Pawlak:1957:UEN
author: Z. Pawlak
title: Use of expansions with a negative basis in the arithmometer of a digital computer
journal: Bull. Acad. Pol. Sci., Ser. Sci. Tech.
volume: 5
pages: 232--236
year: 1957
bibdate: Thu Nov 06 05:56:32 2014
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2014.11.06 05:56:32 ???
keywords: negative base
acknowledgement: ack-nhfb
rawauthor: Z. Pawlak
rawtitle: Use of expansions with a negative basis in the arithmometer of a digital computer
entry:
@Article{Pawlak:1957:UEN,
  author =       "Z. Pawlak",
  title =        "Use of expansions with a negative basis in the
                 arithmometer of a digital computer",
  journal =      "Bull. Acad. Pol. Sci., Ser. Sci. Tech.",
  volume =       "5",
  number =       "??",
  pages =        "232--236",
  month =        "????",
  year =         "1957",
  bibdate =      "Thu Nov 06 05:56:32 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "negative base",
}


bibtype: techreport
filename: fparith.bib
label: Taylor:1957:CCA
author: W. Bruce Taylor
institution: Operations Research Office, Johns Hopkins University
address: Bethesda, MD, USA
pages: 43
year: 1957
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Military art and science --- Data processing.; Military research --- Data processing.
acknowledgement: ack-nhfb
rawauthor: W. Bruce Taylor
title:
COIN (Compile-Interpreter): an automatic programming, fixed and floating-point library of subroutines for the ERA 1103 computer

series:
Staff paper / Johns Hopkins University, Operations Research Office; ORO-SP-32 Staff paper (Johns Hopkins University. Operations Research Office); ORO-SP-32.

remark:
Cover title. ``Operating under contract with the Department of the Army.'' ``Project COMPLAB.'' ``October 1957.'' ORO-SP-32

rawtitle:
{COIN} (Compile-Interpreter): an automatic programming, fixed and floating-point library of subroutines for the {ERA} 1103 computer

entry:
@TechReport{Taylor:1957:CCA,
  author =       "W. Bruce Taylor",
  title =        "{COIN} (Compile-Interpreter): an automatic
                 programming, fixed and floating-point library of
                 subroutines for the {ERA} 1103 computer",
  institution =  "Operations Research Office, Johns Hopkins University",
  address =      "Bethesda, MD, USA",
  pages =        "43",
  year =         "1957",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Staff paper / Johns Hopkins University, Operations
                 Research Office; ORO-SP-32 Staff paper (Johns Hopkins
                 University. Operations Research Office); ORO-SP-32.",
  acknowledgement = ack-nhfb,
  keywords =     "Military art and science --- Data processing.;
                 Military research --- Data processing.",
  remark =       "Cover title. ``Operating under contract with the
                 Department of the Army.'' ``Project COMPLAB.''
                 ``October 1957.'' ORO-SP-32",
}


bibtype: article
filename: fparith.bib
label: Wadel:1957:NBN
author: L. B. Wadel
title: Negative base number systems
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-6
pages: 123--??
month: jun
monthnumber: 6
year: 1957
CODEN: IRELAO
ISSN: 0367-9950 OR 03679950
bibdate: Thu Nov 06 05:53:55 2014
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2014.11.06 05:53:55 ???
fjournal: IRE Transactions on Electronic Computers
keywords: negative base
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: L. B. Wadel
rawtitle: Negative base number systems
entry:
@Article{Wadel:1957:NBN,
  author =       "L. B. Wadel",
  title =        "Negative base number systems",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-6",
  number =       "??",
  pages =        "123--??",
  month =        jun,
  year =         "1957",
  CODEN =        "IRELAO",
  ISSN =         "0367-9950",
  bibdate =      "Thu Nov 06 05:53:55 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
  keywords =     "negative base",
}


bibtype: article
filename: fparith.bib
label: Walker:1957:EMA
author: R. M. Walker and D. E. Rosenheim and P. A. Lewis and A. G. Anderson
title: An Experimental 50-Megacycle Arithmetic Unit
journal: j-IBM-JRD
volume: 1
number: 3
pages: 257--278
month: jul
monthnumber: 7
year: 1957
CODEN: IBMJAE
DOI: https://doi.org/10.1147/rd.13.0257
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
bibdate: Tue Sep 11 15:35:35 MDT 2012
bibtimestamp: 2012.09.11 15:35:35 MDT
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
bookURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
rawauthor: R. M. Walker and D. E. Rosenheim and P. A. Lewis and A. G. Anderson
rawtitle: An Experimental 50-Megacycle Arithmetic Unit
bibsource:
http://www.research.ibm.com/journal/; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib

URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392687; http://www.research.ibm.com/journal/rd/013/ibmrd0103H.pdf

abstract:
An experimental 50-megacycle arithmetic unit has been built which performs a repetitive multiplication program and checks the results for errors. The unit uses pulse circuitry which has been developed to perform digital operations at a 50-megacycle pulse-repetition rate. This paper describes the arithmetic system and the circuits which perform the required functions. These circuits include a full binary adder, a phase-locked frequency divider which provides a 3.125-megacycle secondary timing source, a reshaping and retiming circuit using germanium diodes and capacitive storage, a high-speed shift register, a high-speed indicator register, and a binary word generator.par Various novel features of a digital system operating at these high speeds are described. These include the use of coaxial delay lines for the distribution of signals and as storage elements, and the use of secondary emission tubes in amplifier and multivibrator circuits.par In a 50-megacycle system the interdependence of the space and time dimensions is marked, and although this introduces problems which are not ordinarily encountered in computing systems, it may be used advantageously to provide features such as the variable-phase clock system used in the arithmetic unit.par The performance and reliability of the arithmetic unit are discussed as well as the reliability of the components and circuits which make up the system. Although the techniques and circuitry discussed here have been applied only to a relatively simple arithmetic unit, it is felt that they could be useful in a variety of high-speed computing and measurements applications.

rawabstract:
An experimental 50-megacycle arithmetic unit has been built which performs a repetitive multiplication program and checks the results for errors. The unit uses pulse circuitry which has been developed to perform digital operations at a 50-megacycle pulse-repetition rate. This paper describes the arithmetic system and the circuits which perform the required functions. These circuits include a full binary adder, a phase-locked frequency divider which provides a 3.125-megacycle secondary timing source, a reshaping and retiming circuit using germanium diodes and capacitive storage, a high-speed shift register, a high-speed indicator register, and a binary word generator.\par Various novel features of a digital system operating at these high speeds are described. These include the use of coaxial delay lines for the distribution of signals and as storage elements, and the use of secondary emission tubes in amplifier and multivibrator circuits.\par In a 50-megacycle system the interdependence of the space and time dimensions is marked, and although this introduces problems which are not ordinarily encountered in computing systems, it may be used advantageously to provide features such as the variable-phase clock system used in the arithmetic unit.\par The performance and reliability of the arithmetic unit are discussed as well as the reliability of the components and circuits which make up the system. Although the techniques and circuitry discussed here have been applied only to a relatively simple arithmetic unit, it is felt that they could be useful in a variety of high-speed computing and measurements applications.

entry:
@Article{Walker:1957:EMA,
  author =       "R. M. Walker and D. E. Rosenheim and P. A. Lewis and
                 A. G. Anderson",
  title =        "An Experimental 50-Megacycle Arithmetic Unit",
  journal =      j-IBM-JRD,
  volume =       "1",
  number =       "3",
  pages =        "257--278",
  month =        jul,
  year =         "1957",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.13.0257",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Sep 11 15:35:35 MDT 2012",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392687;
                 http://www.research.ibm.com/journal/rd/013/ibmrd0103H.pdf",
  abstract =     "An experimental 50-megacycle arithmetic unit has been
                 built which performs a repetitive multiplication
                 program and checks the results for errors. The unit
                 uses pulse circuitry which has been developed to
                 perform digital operations at a 50-megacycle
                 pulse-repetition rate. This paper describes the
                 arithmetic system and the circuits which perform the
                 required functions. These circuits include a full
                 binary adder, a phase-locked frequency divider which
                 provides a 3.125-megacycle secondary timing source, a
                 reshaping and retiming circuit using germanium diodes
                 and capacitive storage, a high-speed shift register, a
                 high-speed indicator register, and a binary word
                 generator.\par

                 Various novel features of a digital system operating at
                 these high speeds are described. These include the use
                 of coaxial delay lines for the distribution of signals
                 and as storage elements, and the use of secondary
                 emission tubes in amplifier and multivibrator
                 circuits.\par

                 In a 50-megacycle system the interdependence of the
                 space and time dimensions is marked, and although this
                 introduces problems which are not ordinarily
                 encountered in computing systems, it may be used
                 advantageously to provide features such as the
                 variable-phase clock system used in the arithmetic
                 unit.\par

                 The performance and reliability of the arithmetic unit
                 are discussed as well as the reliability of the
                 components and circuits which make up the system.
                 Although the techniques and circuitry discussed here
                 have been applied only to a relatively simple
                 arithmetic unit, it is felt that they could be useful
                 in a variety of high-speed computing and measurements
                 applications.",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}


bibtype: article
filename: fparith.bib
label: Weibel:1957:EAM
author: Erich S. Weibel
title: An Electronic Analog Multiplier Using Carriers
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-6
number: 1
pages: 30--34
month: mar
monthnumber: 3
year: 1957
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1957.5221558
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jun 30 16:07:23 MDT 2011
bibtimestamp: 2011.06.30 16:07:23 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221558
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: Erich S. Weibel
rawtitle: An Electronic Analog Multiplier Using Carriers
entry:
@Article{Weibel:1957:EAM,
  author =       "Erich S. Weibel",
  title =        "An Electronic Analog Multiplier Using Carriers",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-6",
  number =       "1",
  pages =        "30--34",
  month =        mar,
  year =         "1957",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1957.5221558",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jun 30 16:07:23 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221558",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: book
filename: fparith.bib
label: Wilkes:1957:PPE
author: Maurice V. Wilkes and David J. Wheeler and Stanley Gill
title: The Preparation of Programs for an Electronic Digital Computer
publisher: pub-AW
address: pub-AW:adr
edition: Second
pages: xiv + 238
year: 1957
LCCN: QA76.5 .W52 1957
bibdate: Mon Feb 10 09:42:47 2020
bibtimestamp: 2020.02.10 09:42:47 ???
note: See also first edition cite Wilkes:1951:PPE.
URL: https://b-ok.org/book/3668116/b363ff
acknowledgement: ack-nhfb
rawauthor: Maurice V. Wilkes and David J. Wheeler and Stanley Gill
rawnote: See also first edition \cite{Wilkes:1951:PPE}.
rawtitle: The Preparation of Programs for an Electronic Digital Computer
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

TOC:
CHAPTER 1. THE ELEMENTS OF PROGRAM DESIGN / 1 1-1 Introduction / 1 1-2 Types of automatic computing machine / 1 1-3 The EDSAC / 3 1-4 Store / 5 1-5 Arithmetical unit / 5 1-6 Form of numbers in the machine / 5 1-7 Form of orders in the machine / 6 1-8 Storage of orders / 6 1-9 Written form of orders / 7 1-10 Some simple examples / 7 Exercises A / 9 1-11 Jump orders / 9 Exercises B / 11 1-12 Repeated groups of orders / 11 1-13 The use of the B-register / 15 Exercises C / 18 1-14 Equivalence between orders and numbers; pseudo-orders / 18 1-15 Use of the arithmetical unit for constructing or modifying orders / 20 1-16 The mix order / 23 Exercises D / 24 CHAPTER 2. SUBROUTINES / 25 2-1 Introduction / 25 2-2 Relative numbering of addresses / 25 2-3 Internal and external forms of orders / 26 2-4 Reading of orders from the input tape / 28 2-5 Open and closed subroutines / 29 2-6 Entering and leaving a closed subroutine / 29 2-7 Closed B subroutines / 30 2-8 Closed A subroutines / 31 2-9 Use of library subroutines / 32 Exercises E / 33 2-10 Long numbers / 35 2-11 Some further orders in the order code / 36 2-12 Scale factors / 38 2-13 Control combinations / 39 Exercises F / 40 2-14 Relative addresses in control combinations / 41 2-15 Extension of the use of relative addresses / 41 2-16 Setting of the constants to be added by terminal code letters / 43 2-17 Complete table of terminal code letters / 44 2-18 Parameters / 45 2-19 Preset parameters / 46 2-20 Program parameters / 46 2-21 Standard procedure for setting preset parameters / 46 2-22 Interpretive subroutines / 47 Exercises G / 49 CHAPTER 3. PROGRAMMING FOR OTHER MACHINES / 51 3-1 Introduction / 51 3-2 Single-address codes / 52 3-3 Multi-address codes / 53 3-4 Multiplication and division / 56 3-5 Source-destination codes / 57 3-6 Representation of negative numbers / 59 3-7 Miscellaneous facilities / 60 3-8 Minimum-access coding / 61 3-9 The evaluation of an order code / 63 3-10 Use of an auxiliary store / 64 CHAPTER 4. INPUT AND OUTPUT / 66 4-1 Introduction / 66 4-2 Input of numbers / 66 4-3 Output of numbers / 67 4-4 Input of orders / 69 4-5 Recognition of the code letter S / 72 4-6 Economy of input and output time / 72 4-7 Some features of input systems used with other machines / 73 4-8 Punched tape / 73 4-9 Punched cards / 75 CHAPTER 5. THE LIBRARY OF SUBROUTINES / 80 5-1 Introduction / 80 5-2 Library catalog / 80 5-3 Input subroutines / 81 5-4 Output subroutines / 81 5-5 Division subroutines / 82 5-6 Trigonometric and other functions / 82 5-7 The economization of a power series by the use of Chebyshev polynomials / 83 5-8 Quadrature / 86 5-9 Integration of ordinary differential equations / 87 5-10 Library subroutines Gl2 and G13: Runge--Kutta processes / 88 5-11 The independent variable / 88 5-12 Definition of the Runge--Kutta--Gill process / 89 5-13 Taylor-series method / 90 5-14 Interpretive subroutines / 90 5-15 Floating-point subroutines / 90 CHAPTER 6. DIAGNOSIS OF ERRORS IN PROGRAM / 92 6-1 Introduction / 92 6-2 Proofreading of programs / 93 6-3 Punching / 93 6-4 Locating mistakes in a program- / 94 6-5 Subroutines for checking programs / 96 6-6 The development of a program / 97 CHAPTER 7. EXAMPLES OF COMPLETE PROGRAMS FOR THE EDSAC / 99 EXAMPLE 1 Calculation of $e^-sin x$ / 99 EXAMPLE 2 The evaluation of a definite integral / 102 EXAMPLE 3 Integration of an ordinary differential equation / 108 EXAMPLE 4 Evaluation of a Fourier transform / 113 EXAMPLE 5 Evaluation of a definite integral / 118 CHAPTER 8. AUTOMATIC PROGRAMMING / 126 8-1 Introduction / 126 8-2 Conversion versus interpretation / 127 8-3 Assembly of a program / 127 8-4 Floating addresses / 129 8-5 Formula recognition / 136 Part Two: SPECIFICATIONS OF EDSAC LIBRARY SUBROUTINES / 139 CATEGORY A. Subroutines to carry out floating-point arithmetic / 140 CATEGORY B. Subroutines to perform arithmetical operations on complex numbers / 142 CATEGORY C. Error-diagnosis subroutines / 144 CATEGORY D. Division subroutines / 146 CATEGORY E. Exponential subroutines / 148 CATEGORY F. General subroutines relating to functions / 148 CATEGORY G. Subroutines for the integration of differential equations / 150 CATEGORY L. Subroutines for evaluating logarithms / 153 CATEGORY M. Miscellaneous subroutines / 154 CATEGORY N. Operations on double-length numbers / 156 CATEGORY P. Print subroutines / 158 CATEGORY Q. Quadrature subroutines / 162 CATEGORY R. Input subroutines / 164 CATEGORY s. Subroutines for evaluating fractional powers / 168 CATEGORY T. Subroutines for calculating trigonometric functions / 169 CATEGORY Z. Post-mortem routines / 170 PART THREE: PROGRAMS OF SELECTED EDSAC LIBRARY SUBROUTINES / 173 APPENDIX 1. Input and output codes of the EDSAC / 212 APPENDIX 2. Order code and controls of the EDSAC / 214 APPENDIX 3. The initial input routine of the EDSAC / 218 APPENDIX 4. Control combinations / 221 APPENDIX 5. Specimen solutions to programming exercises / 223 BIBLIOGRAPHY / 233 INDEX / 237

rawTOC:
CHAPTER 1. THE ELEMENTS OF PROGRAM DESIGN / 1 \\ 1-1 Introduction / 1 \\ 1-2 Types of automatic computing machine / 1 \\ 1-3 The EDSAC / 3 \\ 1-4 Store / 5 \\ 1-5 Arithmetical unit / 5 \\ 1-6 Form of numbers in the machine / 5 \\ 1-7 Form of orders in the machine / 6 \\ 1-8 Storage of orders / 6 \\ 1-9 Written form of orders / 7 \\ 1-10 Some simple examples / 7 \\ Exercises A / 9 \\ 1-11 Jump orders / 9 \\ Exercises B / 11 \\ 1-12 Repeated groups of orders / 11 \\ 1-13 The use of the B-register / 15 \\ Exercises C / 18 \\ 1-14 Equivalence between orders and numbers; pseudo-orders / 18 \\ 1-15 Use of the arithmetical unit for constructing or modifying orders / 20 \\ 1-16 The mix order / 23 \\ Exercises D / 24 \\ CHAPTER 2. SUBROUTINES / 25 \\ 2-1 Introduction / 25 \\ 2-2 Relative numbering of addresses / 25 \\ 2-3 Internal and external forms of orders / 26 \\ 2-4 Reading of orders from the input tape / 28 \\ 2-5 Open and closed subroutines / 29 \\ 2-6 Entering and leaving a closed subroutine / 29 \\ 2-7 Closed B subroutines / 30 \\ 2-8 Closed A subroutines / 31 \\ 2-9 Use of library subroutines / 32 \\ Exercises E / 33 \\ 2-10 Long numbers / 35 \\ 2-11 Some further orders in the order code / 36 \\ 2-12 Scale factors / 38 \\ 2-13 Control combinations / 39 \\ Exercises F / 40 \\ 2-14 Relative addresses in control combinations / 41 \\ 2-15 Extension of the use of relative addresses / 41 \\ 2-16 Setting of the constants to be added by terminal code letters / 43 \\ 2-17 Complete table of terminal code letters / 44 \\ 2-18 Parameters / 45 \\ 2-19 Preset parameters / 46 \\ 2-20 Program parameters / 46 \\ 2-21 Standard procedure for setting preset parameters / 46 \\ 2-22 Interpretive subroutines / 47 \\ Exercises G / 49 \\ CHAPTER 3. PROGRAMMING FOR OTHER MACHINES / 51 \\ 3-1 Introduction / 51 \\ 3-2 Single-address codes / 52 \\ 3-3 Multi-address codes / 53 \\ 3-4 Multiplication and division / 56 \\ 3-5 Source-destination codes / 57 \\ 3-6 Representation of negative numbers / 59 \\ 3-7 Miscellaneous facilities / 60 \\ 3-8 Minimum-access coding / 61 \\ 3-9 The evaluation of an order code / 63 \\ 3-10 Use of an auxiliary store / 64 \\ CHAPTER 4. INPUT AND OUTPUT / 66 \\ 4-1 Introduction / 66 \\ 4-2 Input of numbers / 66 \\ 4-3 Output of numbers / 67 \\ 4-4 Input of orders / 69 \\ 4-5 Recognition of the code letter S / 72 \\ 4-6 Economy of input and output time / 72 \\ 4-7 Some features of input systems used with other machines / 73 \\ 4-8 Punched tape / 73 \\ 4-9 Punched cards / 75 \\ CHAPTER 5. THE LIBRARY OF SUBROUTINES / 80 \\ 5-1 Introduction / 80 \\ 5-2 Library catalog / 80 \\ 5-3 Input subroutines / 81 \\ 5-4 Output subroutines / 81 \\ 5-5 Division subroutines / 82 \\ 5-6 Trigonometric and other functions / 82 \\ 5-7 The economization of a power series by the use of Chebyshev polynomials / 83 \\ 5-8 Quadrature / 86 \\ 5-9 Integration of ordinary differential equations / 87 \\ 5-10 Library subroutines Gl2 and G13: Runge--Kutta processes / 88 \\ 5-11 The independent variable / 88 \\ 5-12 Definition of the Runge--Kutta--Gill process / 89 \\ 5-13 Taylor-series method / 90 \\ 5-14 Interpretive subroutines / 90 \\ 5-15 Floating-point subroutines / 90 \\ CHAPTER 6. DIAGNOSIS OF ERRORS IN PROGRAM / 92 \\ 6-1 Introduction / 92 \\ 6-2 Proofreading of programs / 93 \\ 6-3 Punching / 93 \\ 6-4 Locating mistakes in a program- / 94 \\ 6-5 Subroutines for checking programs / 96 \\ 6-6 The development of a program / 97 \\ CHAPTER 7. EXAMPLES OF COMPLETE PROGRAMS FOR THE EDSAC / 99 \\ EXAMPLE 1 Calculation of $e^{-\sin x}$ / 99 \\ EXAMPLE 2 The evaluation of a definite integral / 102 \\ EXAMPLE 3 Integration of an ordinary differential equation / 108 \\ EXAMPLE 4 Evaluation of a Fourier transform / 113 \\ EXAMPLE 5 Evaluation of a definite integral / 118 \\ CHAPTER 8. AUTOMATIC PROGRAMMING / 126 \\ 8-1 Introduction / 126 \\ 8-2 Conversion versus interpretation / 127 \\ 8-3 Assembly of a program / 127 \\ 8-4 Floating addresses / 129 \\ 8-5 Formula recognition / 136 \\ Part Two: SPECIFICATIONS OF EDSAC LIBRARY SUBROUTINES / 139 \\ CATEGORY A. Subroutines to carry out floating-point arithmetic / 140 \\ CATEGORY B. Subroutines to perform arithmetical operations on complex numbers / 142 \\ CATEGORY C. Error-diagnosis subroutines / 144 \\ CATEGORY D. Division subroutines / 146 \\ CATEGORY E. Exponential subroutines / 148 \\ CATEGORY F. General subroutines relating to functions / 148 \\ CATEGORY G. Subroutines for the integration of differential equations / 150 \\ CATEGORY L. Subroutines for evaluating logarithms / 153 \\ CATEGORY M. Miscellaneous subroutines / 154 \\ CATEGORY N. Operations on double-length numbers / 156 \\ CATEGORY P. Print subroutines / 158 \\ CATEGORY Q. Quadrature subroutines / 162 \\ CATEGORY R. Input subroutines / 164 \\ CATEGORY s. Subroutines for evaluating fractional powers / 168 \\ CATEGORY T. Subroutines for calculating trigonometric functions / 169 \\ CATEGORY Z. Post-mortem routines / 170 \\ PART THREE: PROGRAMS OF SELECTED EDSAC LIBRARY SUBROUTINES / 173 \\ APPENDIX 1. Input and output codes of the EDSAC / 212 \\ APPENDIX 2. Order code and controls of the EDSAC / 214 \\ APPENDIX 3. The initial input routine of the EDSAC / 218 \\ APPENDIX 4. Control combinations / 221 \\ APPENDIX 5. Specimen solutions to programming exercises / 223 \\ BIBLIOGRAPHY / 233 \\ INDEX / 237

entry:
@Book{Wilkes:1957:PPE,
  author =       "Maurice V. Wilkes and David J. Wheeler and Stanley
                 Gill",
  title =        "The Preparation of Programs for an Electronic Digital
                 Computer",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Second",
  pages =        "xiv + 238",
  year =         "1957",
  LCCN =         "QA76.5 .W52 1957",
  bibdate =      "Mon Feb 10 09:42:47 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also first edition \cite{Wilkes:1951:PPE}.",
  URL =          "https://b-ok.org/book/3668116/b363ff",
  acknowledgement = ack-nhfb,
  remark-1 =     "According to \cite{Anderson:2019:SAM}, this book
                 discusses the computation of integer population counts
                 on the Electronic Delay Storage Automatic Calculator
                 (EDSAC) computer using a recursive divide-and-conquer
                 algorithm. See also somewhat negative 1958 review by
                 Fernando J. Corbat{\'o}
                 \url{https://doi.org/10.1063/1.3062687}. Floating-point
                 arithmetic is discussed on pages 60, 90--91, and
                 135--137.",
  remark-2 =     "From page 5: ``Each storage location in the EDSAC
                 holds 17 binary digits. In words representing numbers,
                 the binary point is regarded as being to the right of
                 the extreme left-hand digit; this digit (the most
                 significant digit) is used as a sign indicator and is
                 referred to as the sign digit. \ldots{} the capacity of
                 the accumulator is 70 digits; there is, therefore,
                 plenty of room to hold the full 33-digit product of two
                 17-digit numbers. \ldots{} A negative number $-x$
                 (where $O < x \leq 1$) is represented by a $1$ in the
                 sign-digit position, followed by the digits of $(1 -
                 x)$; for example, $1.1100\ldots{}$ represents $-(1 -
                 3/4) = -1/4$. \ldots{} Another way of explaining the
                 representation of negative numbers is to regard the
                 sign digit as an ordinary numerical digit, and to say
                 that $-x$ is stored as the number $(2 - x)$. Note in
                 particular that $1.0000\ldots{}$ represents $-1$.''
                 [Page 59 calls this a {\em True complements}
                 representation, distinguished from one's complement.]",
  remark-3 =     "From page 35: ``The EDSAC has a facility which enables
                 an even-numbered storage location and the following
                 odd-numbered storage to be used as a single storage
                 location holding 35 binary digits.'' [This suggests the
                 word size in 18, not 17 as page 5 suggests. The
                 Wikipedia article on the EDSAC reports: ``The EDSAC's
                 main memory consisted of 1024 locations, though only
                 512 locations were initially installed. Each contained
                 18 bits, but the topmost bit was always unavailable due
                 to timing problems, so only 17 bits were used.'']",
  remark-4 =     "From page 36: ``The multiplier register of the
                 arithmetical unit is of sufficient capacity to hold a
                 long number, and the accumulator is of sufficient
                 capacity to hold the complete (69) binary digit
                 [including the sign bit] product of two long
                 numbers.''",
  remark-5 =     "From page 36: ``In some calculations, long numbers may
                 not provide sufficient precision. In such cases, the
                 programmer may make use of what is known as
                 double-length or double-precision working, in which two
                 long storage locations are used to hold the digits of a
                 single number.'' [this would be a quad-word number
                 holding 69 bits, including the sign bit.].",
  remark-6 =     "From page 60: ``\ldots{} two double-length numbers,
                 each stored in two locations, can be added and the
                 result put in two locations in the store, by means of
                 six orders''.",
  remark-7 =     "From page 90: ``Each number is expressed in the form
                 $a \cdot 10^p$, where $-10 \leq a \leq 10$ and $63 \leq
                 p < 63$ and is represented in the store by $a \cdot
                 2^{-11} + p \cdot 2^{-6}$.''",
  remark-8 =     "From page 91: ``Numbers are expressed in the form $a
                 \cdot 10^p$, where $a$ and $p$ are packed into a single
                 storage location. The number of digits defining $p$ may
                 be varied from 4 to 15 by means of a preset parameter,
                 so that a suitable value for the permissible range of
                 variation of numbers may be selected for a given
                 calculation.''",
  remark-9 =     "From page 91: ``Although the use of floating-point
                 operation can simplify the programmer's task by
                 relieving him of undue preoccupation with scaling, it
                 must not be thought that it solves all his
                 difficulties. In particular, the loss of significant
                 digits resulting from the subtraction of a number from
                 a nearly equal number can have serious consequences
                 unless proper precautions are taken.''",
  tableofcontents = "CHAPTER 1. THE ELEMENTS OF PROGRAM DESIGN / 1 \\
                 1-1 Introduction / 1 \\
                 1-2 Types of automatic computing machine / 1 \\
                 1-3 The EDSAC / 3 \\
                 1-4 Store / 5 \\
                 1-5 Arithmetical unit / 5 \\
                 1-6 Form of numbers in the machine / 5 \\
                 1-7 Form of orders in the machine / 6 \\
                 1-8 Storage of orders / 6 \\
                 1-9 Written form of orders / 7 \\
                 1-10 Some simple examples / 7 \\
                 Exercises A / 9 \\
                 1-11 Jump orders / 9 \\
                 Exercises B / 11 \\
                 1-12 Repeated groups of orders / 11 \\
                 1-13 The use of the B-register / 15 \\
                 Exercises C / 18 \\
                 1-14 Equivalence between orders and numbers;
                 pseudo-orders / 18 \\
                 1-15 Use of the arithmetical unit for constructing or
                 modifying orders / 20 \\
                 1-16 The mix order / 23 \\
                 Exercises D / 24 \\
                 CHAPTER 2. SUBROUTINES / 25 \\
                 2-1 Introduction / 25 \\
                 2-2 Relative numbering of addresses / 25 \\
                 2-3 Internal and external forms of orders / 26 \\
                 2-4 Reading of orders from the input tape / 28 \\
                 2-5 Open and closed subroutines / 29 \\
                 2-6 Entering and leaving a closed subroutine / 29 \\
                 2-7 Closed B subroutines / 30 \\
                 2-8 Closed A subroutines / 31 \\
                 2-9 Use of library subroutines / 32 \\
                 Exercises E / 33 \\
                 2-10 Long numbers / 35 \\
                 2-11 Some further orders in the order code / 36 \\
                 2-12 Scale factors / 38 \\
                 2-13 Control combinations / 39 \\
                 Exercises F / 40 \\
                 2-14 Relative addresses in control combinations / 41
                 \\
                 2-15 Extension of the use of relative addresses / 41
                 \\
                 2-16 Setting of the constants to be added by terminal
                 code letters / 43 \\
                 2-17 Complete table of terminal code letters / 44 \\
                 2-18 Parameters / 45 \\
                 2-19 Preset parameters / 46 \\
                 2-20 Program parameters / 46 \\
                 2-21 Standard procedure for setting preset parameters /
                 46 \\
                 2-22 Interpretive subroutines / 47 \\
                 Exercises G / 49 \\
                 CHAPTER 3. PROGRAMMING FOR OTHER MACHINES / 51 \\
                 3-1 Introduction / 51 \\
                 3-2 Single-address codes / 52 \\
                 3-3 Multi-address codes / 53 \\
                 3-4 Multiplication and division / 56 \\
                 3-5 Source-destination codes / 57 \\
                 3-6 Representation of negative numbers / 59 \\
                 3-7 Miscellaneous facilities / 60 \\
                 3-8 Minimum-access coding / 61 \\
                 3-9 The evaluation of an order code / 63 \\
                 3-10 Use of an auxiliary store / 64 \\
                 CHAPTER 4. INPUT AND OUTPUT / 66 \\
                 4-1 Introduction / 66 \\
                 4-2 Input of numbers / 66 \\
                 4-3 Output of numbers / 67 \\
                 4-4 Input of orders / 69 \\
                 4-5 Recognition of the code letter S / 72 \\
                 4-6 Economy of input and output time / 72 \\
                 4-7 Some features of input systems used with other
                 machines / 73 \\
                 4-8 Punched tape / 73 \\
                 4-9 Punched cards / 75 \\
                 CHAPTER 5. THE LIBRARY OF SUBROUTINES / 80 \\
                 5-1 Introduction / 80 \\
                 5-2 Library catalog / 80 \\
                 5-3 Input subroutines / 81 \\
                 5-4 Output subroutines / 81 \\
                 5-5 Division subroutines / 82 \\
                 5-6 Trigonometric and other functions / 82 \\
                 5-7 The economization of a power series by the use of
                 Chebyshev polynomials / 83 \\
                 5-8 Quadrature / 86 \\
                 5-9 Integration of ordinary differential equations / 87
                 \\
                 5-10 Library subroutines Gl2 and G13: Runge--Kutta
                 processes / 88 \\
                 5-11 The independent variable / 88 \\
                 5-12 Definition of the Runge--Kutta--Gill process / 89
                 \\
                 5-13 Taylor-series method / 90 \\
                 5-14 Interpretive subroutines / 90 \\
                 5-15 Floating-point subroutines / 90 \\
                 CHAPTER 6. DIAGNOSIS OF ERRORS IN PROGRAM / 92 \\
                 6-1 Introduction / 92 \\
                 6-2 Proofreading of programs / 93 \\
                 6-3 Punching / 93 \\
                 6-4 Locating mistakes in a program- / 94 \\
                 6-5 Subroutines for checking programs / 96 \\
                 6-6 The development of a program / 97 \\
                 CHAPTER 7. EXAMPLES OF COMPLETE PROGRAMS FOR THE EDSAC
                 / 99 \\
                 EXAMPLE 1 Calculation of $e^{-\sin x}$ / 99 \\
                 EXAMPLE 2 The evaluation of a definite integral / 102
                 \\
                 EXAMPLE 3 Integration of an ordinary differential
                 equation / 108 \\
                 EXAMPLE 4 Evaluation of a Fourier transform / 113 \\
                 EXAMPLE 5 Evaluation of a definite integral / 118 \\
                 CHAPTER 8. AUTOMATIC PROGRAMMING / 126 \\
                 8-1 Introduction / 126 \\
                 8-2 Conversion versus interpretation / 127 \\
                 8-3 Assembly of a program / 127 \\
                 8-4 Floating addresses / 129 \\
                 8-5 Formula recognition / 136 \\
                 Part Two: SPECIFICATIONS OF EDSAC LIBRARY SUBROUTINES /
                 139 \\
                 CATEGORY A. Subroutines to carry out floating-point
                 arithmetic / 140 \\
                 CATEGORY B. Subroutines to perform arithmetical
                 operations on complex numbers / 142 \\
                 CATEGORY C. Error-diagnosis subroutines / 144 \\
                 CATEGORY D. Division subroutines / 146 \\
                 CATEGORY E. Exponential subroutines / 148 \\
                 CATEGORY F. General subroutines relating to functions /
                 148 \\
                 CATEGORY G. Subroutines for the integration of
                 differential equations / 150 \\
                 CATEGORY L. Subroutines for evaluating logarithms / 153
                 \\
                 CATEGORY M. Miscellaneous subroutines / 154 \\
                 CATEGORY N. Operations on double-length numbers / 156
                 \\
                 CATEGORY P. Print subroutines / 158 \\
                 CATEGORY Q. Quadrature subroutines / 162 \\
                 CATEGORY R. Input subroutines / 164 \\
                 CATEGORY s. Subroutines for evaluating fractional
                 powers / 168 \\
                 CATEGORY T. Subroutines for calculating trigonometric
                 functions / 169 \\
                 CATEGORY Z. Post-mortem routines / 170 \\
                 PART THREE: PROGRAMS OF SELECTED EDSAC LIBRARY
                 SUBROUTINES / 173 \\
                 APPENDIX 1. Input and output codes of the EDSAC / 212
                 \\
                 APPENDIX 2. Order code and controls of the EDSAC / 214
                 \\
                 APPENDIX 3. The initial input routine of the EDSAC /
                 218 \\
                 APPENDIX 4. Control combinations / 221 \\
                 APPENDIX 5. Specimen solutions to programming exercises
                 / 223 \\
                 BIBLIOGRAPHY / 233 \\
                 INDEX / 237",
}


bibtype: techreport
filename: fparith.bib
label: Anonymous:1958:ARM
author: Anonymous
title: Analysis and research memorandum 294
type: AR Memo
number: 294 (AD 207929)
institution: Massachusetts Institute of Technology, Naval Supersonic Laboratory
address: Cambridge, MA, USA
pages: 7
day: 23
month: oct
monthnumber: 10
year: 1958
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Error functions.; Floating-point arithmetic.
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: Analysis and research memorandum 294
entry:
@TechReport{Anonymous:1958:ARM,
  author =       "Anonymous",
  title =        "Analysis and research memorandum 294",
  type =         "{AR} Memo",
  number =       "294 (AD 207929)",
  institution =  "Massachusetts Institute of Technology, Naval
                 Supersonic Laboratory",
  address =      "Cambridge, MA, USA",
  pages =        "7",
  day =          "23",
  month =        oct,
  year =         "1958",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Error functions.; Floating-point arithmetic.",
}


