Editing Analytical engine (section)

== Design ==
[[File:PunchedCardsAnalyticalEngine.jpg|thumb|Two types of [[punched card]]s used to program the machine. Foreground: 'operational cards', for inputting [[instruction set architecture|instructions]]; background: 'variable cards', for inputting [[data (computing)|data]]]]

Babbage's first attempt at a mechanical computing device, the [[difference engine]], was a special-purpose machine designed to tabulate [[logarithm]]s and [[trigonometric function]]s by evaluating [[finite difference]]s to create approximating [[polynomial]]s. Construction of this machine was never completed; Babbage had conflicts with his chief engineer, [[Joseph Clement]], and ultimately the British government withdrew its funding for the project.{{sfn|Collier|1970|p=chapter 3}}<ref>{{cite book|url=https://books.google.com/books?id=ocx4Jc12mkgC&pg=PA176 |title=International Biographical Dictionary of Computer Pioneers | first = John A.n | last = Lee |access-date=1 August 2012|isbn=9781884964473 |year=1995 |publisher=Taylor & Francis }}</ref><ref>{{cite book|url=https://archive.org/details/science100scient0000balc |url-access=registration |page=[https://archive.org/details/science100scient0000balc/page/105 105] |title=Science: 100 Scientists Who Changed the World |publisher=Enchanted Lion Books | first = Jon | last = Balchin |access-date=1 August 2012|isbn=9781592700172 |year=2003 }}</ref>

During this project, Babbage realised that a much more general design, the analytical engine, was possible.{{sfn|Collier|1970|p=chapter 3}} The work on the design of the analytical engine started around 1833.<ref>{{Cite book|url=https://books.google.com/books?id=gkWunaISTsgC&q=Analytical+Engine+1833&pg=PA197|title=The Mathematical Work of Charles Babbage|last1=Dubbey|first1=J. M.|last2=Dubbey|first2=John Michael|date=12 February 2004|publisher=Cambridge University Press|isbn=9780521524766|pages=197|language=en}}</ref>{{sfn|Bromley|1982|p=196}}

The input, consisting of programs ("formulae") and data,{{sfn|Menabrea|Lovelace|1843}}{{sfn|Collier|1970|p=chapter 3}} was to be provided to the machine via [[punched card]]s, a method being used at the time to direct mechanical [[loom]]s such as the [[Jacquard loom]].{{sfn|Bromley|1982|p=215}} For output, the machine would have a printer, a curve plotter, and a bell.{{sfn|Collier|1970|p=chapter 3}} The machine would also be able to punch numbers onto cards to be read in later. It employed ordinary [[base-10]] fixed-point arithmetic.{{sfn|Collier|1970|p=chapter 3}}

There was to be a store (that is, a memory) capable of holding 1,000 numbers of 40 decimal digits{{sfn|Bromley|1982|p=198}} each (ca. 16.6&nbsp;[[kilobyte|kB]]). An [[arithmetic logic unit|arithmetic unit]] (the "mill") would be able to perform all four [[arithmetic operations]], plus comparisons and optionally [[square root]]s.{{sfn|Bromley|1982|p=211}} Initially (1838) it was conceived as a [[difference engine]] curved back upon itself, in a generally circular layout, with the long store exiting off to one side.{{sfn|Bromley|1982|p=209}} Later drawings (1858) depict a regularised grid layout.<ref>{{cite web |url=https://cse.stanford.edu/classes/sophomore-college/projects-98/babbage/ana-mech.htm |title=Babbage's Analytical Engine: The First True Digital Computer |access-date=2008-08-21 |url-status=dead |archive-url=https://web.archive.org/web/20080821191451/http://cse.stanford.edu/classes/sophomore-college/projects-98/babbage/ana-mech.htm |archive-date=2008-08-21 |website=The Analytical Engine}}</ref><ref>{{cite web|url=https://projects.exeter.ac.uk/babbage/engines.html |title=The Babbage Pages: Calculating Engines |publisher=Projects.exeter.ac.uk |date=8 January 1997 |access-date=23 April 2024 |archive-date=2008-03-12 |archive-url=https://web.archive.org/web/20080312060230/http://www.projects.ex.ac.uk/babbage/engines.html |url-status=live }}</ref> Like the [[central processing unit]] (CPU) in a modern computer, the mill would rely upon its own internal procedures, roughly equivalent to [[microcode]] in modern CPUs, to be stored in the form of [[read-only memory|pegs inserted into rotating drums]] called "barrels", to carry out some of the more complex instructions the user's program might specify.<ref name="meccano">{{cite web |first=Tim |last=Robinson |url=https://www.meccano.us/analytical_engine/index.html |title=Difference Engines <!-- |chapter= --> – Analytical Engine |publisher=Meccano.us |date=28 May 2007 |access-date=1 August 2012 |archive-date=2020-10-05 |archive-url=https://web.archive.org/web/20201005153610/http://www.meccano.us/analytical_engine/index.html |url-status=live}}</ref>

The programming language to be employed by users was akin to modern day [[assembly language]]s. Loops and conditional branching were possible, and so the language as conceived would have been [[Turing-complete]] as later defined by [[Alan Turing]]. Three different types of punch cards were used: one for arithmetical operations, one for numerical constants, and one for load and store operations, transferring numbers from the store to the arithmetical unit or back. There were three separate readers for the three types of cards. Babbage developed some two dozen programs for the analytical engine between 1837 and 1840, and one program later.{{sfn|Bromley|1982|p=215}}{{sfn|Bromley|1990|p=89}} These programs treat polynomials, iterative formulas, [[Gaussian elimination]], and [[Bernoulli number]]s.{{sfn|Bromley|1982|p=215}}{{sfn|Bromley|2000|p=11}}

In 1842, the Italian mathematician [[Luigi Federico Menabrea]] published a description of the engine in French,<ref>{{Cite journal|last=Menabrea|first=Mr. L.-F.|year=1842|title=Notions sur la machine analytique de M. Charles Babbage|url=http://www.bibnum.education.fr/calcul-informatique/calcul/notions-sur-la-machine-analytique-de-m-charles-babbage|journal=[[Bibliothèque universelle de Genève]]|volume=41|pages=352–376|via=Bibnum}}</ref> based on lectures Babbage gave when he visited [[Turin]] in 1840.<ref>{{Cite magazine|last=Sterling|first=Bruce|date=14 May 2017|title=Charles Babbage left a computer program in Turin in 1840. Here it is.|language=en-US|magazine=Wired|url=https://www.wired.com/beyond-the-beyond/2017/05/charles-babbage-left-computer-program-turin-1840|access-date=2021-06-10|issn=1059-1028}}</ref> In 1843, the description was translated into English and extensively annotated by [[Ada Lovelace]], who had become interested in the engine eight years earlier.{{sfn|Menabrea|Lovelace|1843}} In recognition of her additions to Menabrea's paper, which included a way to calculate [[Bernoulli number]]s using the machine (widely considered to be the first complete computer program), she has been described by many as the first [[computer programmer]], although others have challenged this view.