Floating-point arithmetic: Difference between revisions

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[[File:Quevedo 1917.jpg|thumb|upright=0.7|[[Leonardo Torres Quevedo]], in 1914, published an analysis of floating point based on the [[analytical engine]].]]
In 1914, the Spanish engineer [[Leonardo Torres Quevedo]] published ''Essays on Automatics'',<ref>Torres Quevedo, Leonardo. [https://quickclick.es/rop/pdf/publico/1914/1914_tomoI_2043_01.pdf Automática: Complemento de la Teoría de las Máquinas, (pdf)], pp. 575–583, Revista de Obras Públicas, 19 November 1914.</ref> where he designed a special-purpose electromechanical calculator based on [[Charles Babbage]]'s [[analytical engine]] and described a way to store floating-point numbers in a consistent manner. He stated that numbers will be stored in exponential format as ''n'' x× 10<math>^m</math>, and offered three rules by which consistent manipulation of floating-point numbers by machines could be implemented. For Torres, "''n'' will always be the same number of [[Numerical digit|digits]] (e.g. six), the first digit of ''n'' will be of order of tenths, the second of hundredths, etc, and one will write each quantity in the form: ''n''; ''m''." The format he proposed shows the need for a fixed-sized significand as is presently used for floating-point data, fixing the ___location of the decimal point in the significand so that each representation was unique, and how to format such numbers by specifying a syntax to be used that could be entered through a [[typewriter]], as was the case of his [[Leonardo Torres y Quevedo#Analytical machines|Electromechanical Arithmometer]] in 1920.<ref>Ronald T. Kneusel. ''[https://books.google.com/books?id=eq4ZDgAAQBAJ&dq=leonardo+torres+quevedo++electromechanical+machine+essays&pg=PA84 Numbers and Computers],'' Springer, pp. 84–85, 2017. {{ISBN|978-3319505084}}</ref>{{Sfn|Randell|1982|pp=6, 11–13}}<ref>Randell, Brian. [https://dl.acm.org/doi/pdf/10.5555/1074100.1074334 Digital Computers, History of Origins, (pdf)], p. 545, Digital Computers: Origins, Encyclopedia of Computer Science, January 2003.</ref>
 
[[File:Konrad Zuse (1992).jpg|thumb|upright=0.7|right|[[Konrad Zuse]], architect of the [[Z3 (computer)|Z3]] computer, which uses a 22-bit binary floating-point representation]]