Reverse Polish notation#Automatic Memory Stack

In reverse Polish notation, the operators follow their operands. For example, to add 3 and 4 together, the expression is {{nowrap|3 4 +}} rather than {{nowrap|3 + 4}}. The conventional notation expression {{nowrap|3 − 4 + 5}} becomes {{nowrap|3 (enter) 4 − 5 +}} in reverse Polish notation: 4 is first subtracted from 3, then 5 is added to it.

The concept of a stack, a last-in/first-out construct, is integral to the left-to-right evaluation of RPN. In the example {{nowrap|3 4 −}}, first the 3 is put onto the stack, then the 4; the 4 is now on top and the 3 below it. The subtraction operator removes the top two items from the stack, performs {{nowrap|3 − 4}}, and puts the result of −1 onto the stack.

The common terminology is that added items are pushed on the stack and removed items are popped.

The advantage of reverse Polish notation is that it removes the need for order of operations and parentheses that are required by infix notation and can be evaluated linearly, left-to-right. For example, the infix expression {{nowrap|(3 + 4) × (5 + 6)}} becomes {{nowrap|3 4 + 5 6 + ×}} in reverse Polish notation.

Reverse Polish notation has been compared to how one had to work through problems with a slide rule.

In comparison, testing of reverse Polish notation with algebraic notation, reverse Polish has been found to lead to faster calculations, for two reasons. The first reason is that reverse Polish calculators do not need expressions to be parenthesized, so fewer operations need to be entered to perform typical calculations. Additionally, users of reverse Polish calculators made fewer mistakes than for other types of calculators. Later research clarified that the increased speed from reverse Polish notation may be attributed to the smaller number of keystrokes needed to enter this notation, rather than to a smaller cognitive load on its users. However, anecdotal evidence suggests that reverse Polish notation is more difficult for users who previously learned algebraic notation.

{{main|Shunting-yard algorithm}}

Edsger W. Dijkstra invented the shunting-yard algorithm to convert infix expressions to postfix expressions (reverse Polish notation), so named because its operation resembles that of a railroad shunting yard.

There are other ways of producing postfix expressions from infix expressions. Most operator-precedence parsers can be modified to produce postfix expressions; in particular, once an abstract syntax tree has been constructed, the corresponding postfix expression is given by a simple post-order traversal of that tree.

The first computer implementing a form of reverse Polish notation (but without the name and also without a stack), was Konrad Zuse's Z3, which he started to construct in 1938 and demonstrated publicly on 12 May 1941. In dialog mode, it allowed operators to enter two operands followed by the desired operation.{{refn|group=z3|In reference to "In dialog mode, it allowed operators to enter two operands followed by the desired operation" for the Z3 computer, the following citations are relevant :}} It was destroyed on 21 December 1943 in a bombing raid. With Zuse's help a first replica was built in 1961. The 1945 Z4 also added a 2-level stack.

Other early computers to implement architectures enabling reverse Polish notation were the English Electric Company's KDF9 machine, which was announced in 1960 and commercially available in 1963, and the Burroughs B5000, announced in 1961 and also delivered in 1963:

Presumably, the KDF9 designers drew ideas from Hamblin's GEORGE (General Order Generator), an autocode programming system written for a DEUCE computer installed at the University of Sydney, Australia, in 1957.

One of the designers of the B5000, Robert S. Barton, later wrote that he developed reverse Polish notation independently of Hamblin sometime in 1958 after reading a 1954 textbook on symbolic logic by Irving Copi, where he found a reference to Polish notation, which made him read the works of Jan Łukasiewicz as well, and before he was aware of Hamblin's work.

Friden introduced reverse Polish notation to the desktop calculator market with the EC-130, designed by Robert "Bob" Appleby Ragen, supporting a four-level stack in June 1963. The successor EC-132 added a square root function in April 1965. Around 1966, the Monroe Epic calculator supported an unnamed input scheme resembling RPN as well.

{{main|HP calculators}}

File:Hewlett-Packard No Equals hat.jpg

{{anchor|Three-level RPN}}Hewlett-Packard engineers designed the 9100A Desktop Calculator in 1968 with reverse Polish notation with only three stack levels with working registers X ("keyboard"), Y ("accumulate") and visible storage register Z ("temporary"), a reverse Polish notation variant later referred to as three-level RPN. This calculator popularized reverse Polish notation among the scientific and engineering communities.

{{anchor|Four-level RPN|Classical RPN|Automatic Memory Stack}}The HP-35, the world's first handheld scientific calculator, introduced the classical four-level RPN with its specific ruleset of the so-called operational (memory) stack (later also called automatic memory stack) in 1972. In this scheme, the {{key press|Enter {{larger|↑}}}} key duplicates values into Y under certain conditions (automatic stack lift with temporary stack lift disable), and the top register T ("top") gets duplicated on drops (top copy on pop aka top stack level repetition) in order to ease some calculations and to save keystrokes. HP used reverse Polish notation on every handheld calculator it sold, whether scientific, financial, or programmable, until it introduced the HP-10 adding machine calculator in 1977. By this time, HP was the leading manufacturer of calculators for professionals, including engineers and accountants.

Later calculators with LCDs in the early 1980s, such as the HP-10C, HP-11C, HP-15C, HP-16C, and the financial HP-12C calculator also used reverse Polish notation. In 1988, Hewlett-Packard introduced a business calculator, the HP-19B, without reverse Polish notation, but its 1990 successor, the HP-19BII, gave users the option of using algebraic or reverse Polish notation again.

{{anchor|Dynamic stack}}In 1986, HP introduced RPL, an object-oriented successor to reverse Polish notation. It deviates from classical reverse Polish notation by using a dynamic stack only limited by the amount of available memory (instead of three or four fixed levels) and which could hold all kinds of data objects (including symbols, strings, lists, matrices, graphics, programs, etc.) instead of just numbers. The system would display an error message when running out of memory instead of just dropping values off the stack on overflow as with fixed-sized stacks. It also changed the behaviour of the stack to no longer duplicate the top register on drops (since in an unlimited stack there is no longer a top register) and the behaviour of the {{key press|Enter {{larger|↑}}}} key so that it no longer duplicated values into Y, which had shown to sometimes cause confusion among users not familiar with the specific properties of the automatic memory stack. From 1990 to 2003, HP manufactured the HP-48 series of graphing RPL calculators, followed by the HP-49 series between 1999 and 2008. The last RPL calculator was named HP 50g, introduced in 2006 and discontinued in 2015. However, there are several community efforts like newRPL or DB48X to recreate RPL on modern calculators.

As of 2011, Hewlett-Packard was offering the calculator models 12C, 12C Platinum, 17bII+, 20b, 30b, 33s, 35s, 48gII (RPL) and 50g (RPL) which support reverse Polish notation.

{{anchor|Entry RPN}}While calculators emulating classical models continued to support classical reverse Polish notation, new reverse Polish notation models feature a variant of reverse Polish notation, where the {{key press|Enter {{larger|↑}}}} key behaves as in RPL. This latter variant is sometimes known as entry RPN.

{{anchor|128-level RPN|Advanced RPN}}In 2013, the HP Prime introduced a 128-level form of entry RPN called advanced RPN. In contrast to RPL with its dynamic stack, it just drops values off the stack on overflow like other fixed-sized stacks do. However, like RPL, it does not emulate the behaviour of a classical operational RPN stack to duplicate the top register on drops.

In late 2017, the list of active models supporting reverse Polish notation included only the 12C, 12C Platinum, 17bii+, 35s, and Prime. By July 2023, only the 12C, 12C Platinum, the freshly released HP 15C Collector's Edition, and the Prime remain active models supporting RPN.

{{See also|#Community-developed hardware-based calculators{{!}}HP-related community-developed calculators}}

In Britain, Clive Sinclair's Sinclair Scientific (1974) and Scientific Programmable (1975) models used reverse Polish notation.

In 1974, Commodore produced the Minuteman *6 (MM6) without an {{key press|Enter {{larger|↑}}}} key and the Minuteman *6X (MM6X) with an {{key press|Enter {{larger|↑}}}} key, both implementing a form of two-level RPN. The SR4921 RPN came with a variant of four-level RPN with stack levels named X, Y, Z, and W (rather than T) and an {{key press|Ent}} key (for "entry"). In contrast to Hewlett-Packard's reverse Polish notation implementation, W filled with 0 instead of its contents being duplicated on stack drops.

Prinz and Prinztronic were own-brand trade names of the British Dixons photographic and electronic goods stores retail chain, later rebranded as Currys Digital stores, and became part of DSG International. A variety of calculator models was sold in the 1970s under the Prinztronic brand, all made for them by other companies.

Among these was the PROGRAM Programmable Scientific Calculator which featured reverse Polish notation.

The Aircraft Navigation Computer Heathkit OC-1401/OCW-1401 used five-level RPN in 1978.

Soviet programmable calculators (MK-52, MK-61, B3-34 and earlier B3-21 models) used reverse Polish notation for both automatic mode and programming. Modern Russian calculators MK-161 and MK-152, designed and manufactured in Novosibirsk since 2007 and offered by Semico, are backwards compatible with them. Their extended architecture is also based on reverse Polish notation.

• {{anchor|7-level RPN}}A seven-level stack had been implemented in the MITS 7400C scientific desktop calculator in 1972
• National Semiconductor 4615 and 4640
• Novus 650 Mathbox, 3500 Sliderule, 4510 Mathematician, 4515 Mathematician PRO/RG, 4520 Scientist and 4525 Scientist PR
• Some APF calculators like the Mark 55 (1976)
• SwissMicros (originally firming as RPN-Calc) calculators including the DM-10CC (2012), DM-11CC (2012), DM-12CC (2012), DM-15CC (2012), DM-16CC (2012), DM10 (2013), DM11 (2013), DM12 (2013), DM15 (2013), DM16 (2013), DM10L Collector's Edition (2020), DM11L (2016), DM12L (2016), DM15L (2015), DM16L (2015), DM41 (2015), DM41L (2015), DM41X (2020), DM42 (2017) and DM32 (2023).

{{See also|#Hewlett-Packard{{!}}Hewlett-Packard RPN calculators}}

An eight-level stack was suggested by John A. Ball in 1978.

The community-developed calculators WP 34S (2011), WP 31S (2014) and WP 34C (2015), which are based on the HP 20b/HP 30b hardware platform, support classical Hewlett-Packard-style reverse Polish notation supporting automatic stack lift behaviour of the {{key press|Enter {{larger|↑}}}} key and top register copies on pops, but switchable between a four- and an eight-level operational stack.

In addition to the optional support for an eight-level stack, the newer SwissMicros DM42-based WP 43S as well as the WP 43C (2019) / C43 (2022) / C47 (2023) derivatives support data types for stack objects (real numbers, infinite integers, finite integers, complex numbers, strings, matrices, dates and times). The latter three variants can also be switched between classical and entry RPN behaviour of the {{key press|Enter {{larger|↑}}}} key, a feature often requested by the community. They also support a rarely seen significant figures mode, which had already been available as a compile-time option for the WP 34S and WP 31S.

Since 2021, the HP-42S simulator Free42 version 3 can be enabled to support a dynamic RPN stack only limited by the amount of available memory instead of the classical 4-level stack. This feature was incorporated as a selectable function into the DM42 since firmware DMCP-3.21 / DM42-3.18.https://forum.swissmicros.com/viewtopic.php?f=16&t=2939https://forum.swissmicros.com/viewtopic.php?f=15&t=2845

Software calculators:

• Atari Calculator
• Mac OS X Calculator
• Several Apple iPhone applications e.g. "reverse polish notation calculator"
• Several Android applications e.g. "RealCalc"
• Several Windows 10 Mobile applications e.g. "RPN9"
• Unix system calculator program dc
• Emacs lisp library package calc
• Xorg calculator (xcalc)
• ARPCalc, a powerful scientific/engineering RPN calculator for Windows, Linux and Android that also has a web-browser based version
• {{Proper name|grpn}} scientific/engineering calculator using the GIMP Toolkit (GTK+)
• F-Correlatives in MultiValue dictionary items
• RRDtool, a widely used tabulating and graphing software
• {{Proper name|grdmath}}, a program for algebraic operations on NetCDF grids, part of Generic Mapping Tools (GMT) suite
• {{Proper name|galculator}}, a GTK desktop calculator
• Mouseless Stack-Calculator scientific/engineering calculator including complex numbers
• {{Proper name|rpCalc}}, a simple reverse polish notation calculator written in Python for Linux and MS Windows and published under the GNU GPLv2 license
• orpie, RPN calculator for the terminal for real or complex numbers or matrices
• Qalculate!, a powerful and versatile cross-platform desktop calculator
• WRPN Calculator

Existing implementations using reverse Polish notation include:

• Stack-oriented programming languages such as:
• Forth
• dc
• STOIC
• Factor
• PostScript page description language
• BibTeX style files{{citation

| last1 = Dagnat | first1 = Fabien

| last2 = Keryell | first2 = Ronan

| last3 = Aoun | first3 = Youssef

| last4 = Sastre | first4 = Laura Barrero

| last5 = de Rosière | first5 = Emmanuel Donin

| last6 = Torneri | first6 = Nicolas

| department = Proceedings of EuroTeX 2003

| issue = 3

| journal = TUGboat

| pages = 472–488

| title = BibTeX++: Toward Higher-order BibTeXing

| url = https://www.tug.org/TUGboat/Articles/tb24-3/keryell.pdf

| volume = 24

| year = 2003}}

• Befunge
• Joy
• IPTSCRAE
• Lotus 1-2-3 and Lotus Symphony formulas
• RPL (aka Reverse Polish Language), a programming language for the Commodore PET around 1979/1981
• RPL (aka Reverse Polish Lisp), a programming language for Hewlett-Packard calculators between 1986 and 2015
• RPNL (Reverse Polish Notation Language)
• Class libraries
• TRURL, a class library for the construction of RPN calculators in Object Pascal

• Calculator input methods
• FOCAL keystroke programming
• Stack machine
• Head-directionality parameter
• Scrambling (linguistics)
• Subject object verb and Object subject verb

{{reflist|group="nb"|refs=

Hewlett-Packard, in the 1970s, called their special RPN stack implementation an operational (memory) stack or automatic memory stack. Interestingly, Klaus Samelson and Friedrich L. Bauer, the inventors of the stack principle, called their stack {{lang|de|Operationskeller}} (Engl. "operational cellar") in 1955, and parallel discoverer {{ill|Wilhelm Kämmerer|de}} called his stack concept {{lang|de|Automatisches Gedächtnis}} (Engl. "automatic memory") in 1958.

}}

{{reflist|group="z3"}}

{{reflist|refs=

{{cite book |title=An Addressless Coding Scheme based on Mathematical Notation |author-first=Charles Leonard |author-last=Hamblin |author-link=Charles Leonard Hamblin |publisher=New South Wales University of Technology |date=May 1957 |type=Typescript}}

{{cite journal |title=An addressless coding scheme based on mathematical notation |author-first=Charles Leonard |author-last=Hamblin |author-link=Charles Leonard Hamblin |date=June 1957 |journal=Proceedings of the First Australian Conference on Computing and Data Processing |location=Salisbury, South Australia |publisher=Weapons Research Establishment}}

{{cite journal |title=Computer Languages |author-first=Charles Leonard |author-last=Hamblin |author-link=Charles Leonard Hamblin |date=1957 |journal=The Australian Journal of Science |number=20? |pages=135–139 |postscript=;}} {{cite journal |title=Computer Languages |author-first=Charles Leonard |author-last=Hamblin |author-link=Charles Leonard Hamblin |date=November 1985 |journal=The Australian Computer Journal |volume=17 |issue=4 |pages=195–198 |type=Reprint}}

{{cite book |author-first=Charles Leonard |author-last=Hamblin |author-link=Charles Leonard Hamblin |title=GEORGE IA and II: A semi-translation programming scheme for DEUCE: Programming and Operation Manual |publisher=School of Humanities, University of New South Wales, Kensington, New South Wales |date=1958 |url=http://members.iinet.net.au/~dgreen/deuce/GEORGEProgrammingManual.pdf |access-date=2020-07-27 |url-status=live |archive-url=https://web.archive.org/web/20200404093021/http://members.iinet.net.au/~dgreen/deuce/GEORGEProgrammingManual.pdf |archive-date=2020-04-04}}

{{cite magazine |magazine=Resurrection - The Bulletin of the Computer Conservation Society |issn=0958-7403 |publisher=Computer Conservation Society (CCS) |number=18 |date=Autumn 1997 |orig-date=1996-10-01 |title=The KDF9 Computer — 30 Years On |author-first=Bob |author-last=Beard |pages=7–15 |url=http://www.cs.man.ac.uk/CCS/Archive/Resurrection/pdf/res18.pdf |access-date=2020-07-27 |url-status=live |archive-url=https://web.archive.org/web/20200727140754/http://www.cs.man.ac.uk/CCS/Archive/Resurrection/pdf/res18.pdf |archive-date=2020-07-27 |quote-page=8 |quote=[…] The KDF9 is remarkable because it is the believed to be the first zero-address instruction format computer to have been announced (in 1960). It was first delivered at about the same time (early 1963) as the other famous zero-address computer, the Burroughs B5000 in America. Like many modern pocket calculators, a zero-address machine allows the use of Reverse Polish arithmetic; this offers certain advantages to compiler writers. It is believed that the attention of the English Electric team was first drawn to the zero-address concept through contact with George (General Order Generator), an autocode programming system written for a Deuce computer by the University of Sydney, Australia, in the latter half of the 1950s. George used Reversed Polish, and the KDF9 team were attracted to this convention for the pragmatic reason of wishing to enhance performance by minimising accesses to main store. This may be contrasted with the more "theoretical" line taken independently by Burroughs. Besides a hardware nesting store or stack - the basic mechanism of a zero-address computer - the KDF9 had other groups of central registers for improving performance which gave it an interesting internal structure. […]}} [https://web.archive.org/web/20200427075718/http://www.cs.man.ac.uk/CCS/res/res18.htm#c] (NB. This is an edited version of a talk given to North West Group of the Society at the Museum of Science and Industry, Manchester, UK on 1996-10-01.)

{{cite book |title=Elementy logiki matematycznej |language=pl |author-last=Łukasiewicz |author-first=Jan |author-link=Jan Łukasiewicz |location=Warsaw, Poland |edition=1 |publisher=Państwowe Wydawnictwo Naukowe |date=February 1929 |postscript=none}}; {{cite book |title=Elements of mathematical logic |author-last=Łukasiewicz |author-first=Jan |author-link=Jan Łukasiewicz |translator-first=Olgierd Adrian |translator-last=Wojtasiewicz |translator-link=:pl:Olgierd Adrian Wojtasiewicz |date=1963 |publication-place=New York, USA |publisher=The MacMillan Company |page=24}}

{{cite book |title=Aristotle's Syllogistic from the Standpoint of Modern Formal Logic |author-last=Łukasiewicz |author-first=Jan |author-link=Jan Łukasiewicz |date=1951 |edition=1 |chapter=Chapter IV. Aristotle's System in Symbolic Form (section on "Explanation of the Symbolism") |page=78}}

{{cite book |title=Aristotle's Syllogistic from the Standpoint of Modern Formal Logic |author-last=Łukasiewicz |author-first=Jan |author-link=Jan Łukasiewicz |publisher=Oxford University Press |date=1957 |edition=2}} (Reprinted by Garland Publishing in 1987 {{isbn|0-8240-6924-2}}.)

{{cite journal |title=RPN Perspective |author-first=John |author-last=Kennedy |location=Mathematics Department, Santa Monica College, Santa Monica, California, USA |journal=PPC Calculator Journal |volume=9 |number=5 |date=August 1982 |pages=26–29 |citeseerx=10.1.1.90.6448 |url=http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.90.6448&rep=rep1&type=pdf |access-date=2022-07-02 |url-status=live |archive-url=https://web.archive.org/web/20220701223543/http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.90.6448&rep=rep1&type=pdf |archive-date=2022-07-01}} (12 pages)

{{cite book |title=Algorithms for RPN calculators |url=https://archive.org/details/algorithmsforrpn0000ball |url-access=registration |author-first=John A. |author-last=Ball |date=1978 |edition=1 |publisher=Wiley-Interscience, John Wiley & Sons, Inc. |location=Cambridge, Massachusetts, USA |isbn=0-471-03070-8 |lccn=77-14977 |quote-page=2 |quote=[…] In their advertisements and also in a letter to me, Hewlett-Packard Company (HP), the best known manufacturer of RPN calculators, says that RPN is based on a suggestion by Jan Łukasiewicz (1878–1956), and that RPN was invented and is patented by HP. Aside from the apparent contradiction in these two statements, I do not think that either of them is quite true. My first experience with RPN involved a nice old Friden EC-130 desktop electronic calculator, circa 1964. The EC-130 has RPN with a push-down stack of four registers, all visible simultaneously on a cathode ray tube display. Furthermore, they are shown upside down, that is, the last-in-first-out register is at the bottom. […] Around 1966, the Monroe Epic calculator offered RPN with a stack of four, a printer, and either 14 or 42 step programmability. The instruction booklets with these two calculators make no mention of RPN or Jan Łukasiewicz. […]}}

{{cite news |url=https://www.wsj.com/articles/SB10001424052748703841904576257440326458056 |url-access=subscription |title=Wall Street's Cult Calculator Turns 30 |author-first=Kristina |author-last=Peterson |date=2011-05-04 |work=The Wall Street Journal |access-date=6 December 2015 |archive-url=https://web.archive.org/web/20150316030830/https://www.wsj.com/articles/SB10001424052748703841904576257440326458056 |archive-date=2015-03-16}}

{{cite journal |title=Electronic calculators: which notation is the better? |journal=Applied Ergonomics |issn=0003-6870 |eissn=1872-9126 |volume=11 |issue=1 |date=March 1980 |pages=2–6 |author-first1=Seb J. |author-last1=Agate |author-first2=Colin G. |author-last2=Drury |location=Department of Industrial Engineering, University at Buffalo, State University of New York, USA |doi=10.1016/0003-6870(80)90114-3 |pmid=15676368 |id=0003-6870/80/01 0002-05 |publisher=IPC Business Press |url=https://www.keesvandersanden.nl/calculators/downloads/Electronic-calculators-which-notation-is-the-better.pdf |access-date=2018-09-22 |url-status=live |archive-url=https://web.archive.org/web/20230923063402/https://www.keesvandersanden.nl/calculators/downloads/Electronic-calculators-which-notation-is-the-better.pdf |archive-date=2023-09-23 |quote-page=6 |quote=In terms of practical choice between calculators, it would appear that RPN is faster and more accurate overall but particularly for more complex problems.}} (5 pages)

{{cite web |title=Oral History: Burroughs B5000 Conference |editor-first1=Bernard A. |editor-last1=Galler |editor-first2=Robert F. |editor-last2=Rosin |date=1985-09-06 |id=OH 98 |publisher=AFIPS / Burroughs Corporation |location=Marina del Rey, California, USA, archived by the Charles Babbage Institute, University of Minnesota, Minneapolis |url=https://conservancy.umn.edu/bitstream/handle/11299/107105/oh098b5c.pdf?sequence=1&isAllowed=y |hdl=11299/107105 |access-date=2023-09-23 |url-status=live |archive-url=https://web.archive.org/web/20230923064139/https://conservancy.umn.edu/bitstream/handle/11299/107105/oh098b5c.pdf?sequence=1&isAllowed=y |archive-date=2023-09-23}}

{{cite web |title=1928–2012 Obituary Condolences Robert (Bob) Ragen |website=Legacy.com |date=2012-07-23 |url=http://www.legacy.com/obituaries/insidebayarea/obituary.aspx?n=robert-ragen-bob&pid=158717663 |access-date=2016-01-01 |url-status=live |archive-url=https://web.archive.org/web/20171218233505/http://www.legacy.com/obituaries/name/robert-ragen-obituary?pid=1000000158717663 |archive-date=2017-12-18 |quote=[…] Bob holds over 80 patents awarded during his work as Director of RD for Friden, and Singer and as Senior Project Engineer at Xerox. He retired from Xerox RD in 1990. He is responsible for the development of the first commercial electronic calculator, the Friden 130, which has been displayed at the Smithsonian. […]}}

{{cite web |title=Tom Osborne's Story in His Own Words |author-first=Thomas E. |author-last=Osborne |author-link=Tom Osborne (engineer) |orig-date=1994 |date=2010 |publisher=Steve Leibson |url=http://www.hp9825.com/html/osborne_s_story.html |access-date=2016-01-01 |url-status=live |archive-url=https://web.archive.org/web/20220404222610/http://www.hp9825.com/html/osborne_s_story.html |archive-date=2022-04-04 |quote=[…] I changed the architecture to use RPN (Reverse Polish Notation), which is the ideal notation for programming environment in which coding efficiency is critical. In the beginning, that change was not well received... […]}}

{{cite journal |author-first=Richard E. |author-last=Monnier |title=A New Electronic Calculator with Computerlike Capabilities |journal=Hewlett-Packard Journal |publisher=Hewlett-Packard |location=Palo Alto, California, USA |date=September 1968 |volume=20 |issue=1 |pages=3–9 |url=http://www.hparchive.com/Journals/HPJ-1968-09.pdf |access-date=2016-01-03 |url-status=live |archive-url=https://web.archive.org/web/20221020175450/http://www.hparchive.com/Journals/HPJ-1968-09.pdf |archive-date=2022-10-20}}

{{cite web |title=The slide rule killer: a milestone in computer history |author-first=Jacques |author-last=Laporte |date=2014-05-22 |url=http://www.jacques-laporte.org/HP%2035%20Saga.htm |url-status=dead |archive-url=https://web.archive.org/web/20150211194800/http://jacques-laporte.org/HP%2035%20Saga.htm |archive-date=2015-02-11 |access-date=2016-01-01}}

{{cite book |title=HP-42S RPN Scientific Calculator – Owner's Manual |date=June 1988 |edition=1 |id=00042-90001 |location=Corvallis, Oregon, USA |publisher=Hewlett-Packard Co. |page=3 |url=http://www.hp41.net/forum/fileshp41net/manuel-hp42s-us.pdf |access-date=2017-09-17 |url-status=live |archive-url=https://web.archive.org/web/20170917215457/http://www.hp41.net/forum/fileshp41net/manuel-hp42s-us.pdf |archive-date=2017-09-17}}

{{cite book |title=HP35 User's Manual |publisher=Hewlett-Packard |page=i |quote-page=i |quote=[…] The operational stack and reverse Polish (Łukasiewicz) notation used in the HP-35 are the most efficient way known to computer science for evaluating mathematical expressions. […]}}

{{cite web |title=Reversing Sinclair's amazing 1974 calculator hack – half the ROM of the HP-35 |author-last=Shirriff |author-first=Ken |url=http://files.righto.com/calculator/sinclair_scientific_simulator.html |access-date=2013-12-09 |url-status=live |archive-url=https://web.archive.org/web/20220826223841/http://files.righto.com/calculator/sinclair_scientific_simulator.html |archive-date=2022-08-26}}

{{cite web |title=Google chap reverse engineers Sinclair Scientific Calculator |work=The Register |author-last=Sharwood |author-first=Simon |date=2013-09-02 |url=https://www.theregister.co.uk/2013/09/02/google_chap_reverse_engineers_sinclair_scientific_calculator/ |access-date=2013-12-09 |url-status=live |archive-url=https://web.archive.org/web/20221020172550/https://www.theregister.com/2013/09/02/google_chap_reverse_engineers_sinclair_scientific_calculator/ |archive-date=2022-10-20}}

{{cite book |title=PostScript Language Tutorial and Cookbook |author=Adobe Systems Incorporated |author-link=Adobe Systems Incorporated |publisher=Addison Wesley Publishing Company |date=1986 |orig-date=1985 |isbn=0-201-10179-3 |id=9-780201-101799 |edition=27th printing, August 1998, 1st |contribution=Preface |contributor-first=Charles |contributor-last=Geschke |contributor-link=Charles Geschke |url-access=registration |url=https://archive.org/details/postscriptlangua00adobrich}} (NB. This book is informally called "blue book" due to its blue cover.)

{{cite book |title=PostScript Language Reference Manual |edition=1st printing, 3rd |date=February 1999 |orig-date=1985 |isbn=0-201-37922-8 |author=Adobe Systems Incorporated |author-link=Adobe Systems Incorporated |publisher=Addison-Wesley Publishing Company |url=https://www.adobe.com/products/postscript/pdfs/PLRM.pdf |access-date=2017-02-18 |url-status=live |archive-url=https://web.archive.org/web/20170218093716/https://www.adobe.com/products/postscript/pdfs/PLRM.pdf |archive-date=2017-02-18}} (NB. This book is informally called "red book" due to its red cover.)

{{cite book |title=Dateiformate – Eine Referenz – Tabellenkalkulation, Text, Grafik, Multimedia, Sound und Internet |language=de |trans-title=File formats – a reference – spreadsheets, text, graphics, multimedia, sound and internet |author-first=Günter |author-last=Born |author-link=:de:Günter Born |date=December 2000 |publisher=Galileo Computing |chapter=Kapitel 1. LOTUS 1-2-3-Format (WKS/WK1) |trans-chapter=Chapter 1. Lotus 1-2-3 WKS/WK1 format |location=Bonn, Germany |isbn=3-934358-83-7 |url=http://www.aboutvb.de/bas/formate/pdf/wks.pdf |access-date=2016-11-28 |url-status=live |archive-url=https://web.archive.org/web/20161129191803/http://www.aboutvb.de/bas/formate/pdf/wks.pdf |archive-date=2016-11-29}}

{{cite book |title=Dateiformate – Eine Referenz – Tabellenkalkulation, Text, Grafik, Multimedia, Sound und Internet |language=de |trans-title=File formats – a reference – spreadsheets, text, graphics, multimedia, sound and internet |author-first=Günter |author-last=Born |author-link=:de:Günter Born |date=December 2000 |publisher=Galileo Computing |chapter=Kapitel 2. LOTUS 1-2-3-Format (WK3) |trans-chapter=Chapter 2. Lotus 1-2-3 WK3 format |location=Bonn, Germany |isbn=3-934358-83-7 |url=http://www.aboutvb.de/bas/formate/pdf/wk3.pdf |access-date=2016-11-28 |url-status=live |archive-url=https://web.archive.org/web/20161129183043/http://www.aboutvb.de/bas/formate/pdf/wk3.pdf |archive-date=2016-11-29}}

{{cite book |author-first=Herwig |author-last=Feichtinger |title=Arbeitsbuch Mikrocomputer |language=de |location=Munich, Germany |publisher=Franzis-Verlag GmbH |isbn=3-7723-8022-0 |date=1987 |edition=2 |pages=427–428}} (NB. According to this book, a 4 KB compiler was available from Lifeboat Software for CP/M.)

{{cite book |title=RPNL. Eine FORTH ähnliche Sprache mit strukturunterstützenden Sprachkonstrukten |language=de |author-first=Gustav |author-last=Wostrack |publisher=Wolf-Detlef Luther, Gens |date=January 1989 |isbn=978-3-88707022-9}}

{{cite journal |author-first=Charles Leonard |author-last=Hamblin |author-link=Charles Leonard Hamblin |date=1962-11-01 |title=Translation to and from Polish notation |journal=Computer Journal |volume=5 |issue=3 |pages=210–213 |doi=10.1093/comjnl/5.3.210 |doi-access=free |url=https://watermark.silverchair.com/5-3-210.pdf?token=AQECAHi208BE49Ooan9kkhW_Ercy7Dm3ZL_9Cf3qfKAc485ysgAAAsYwggLCBgkqhkiG9w0BBwagggKzMIICrwIBADCCAqgGCSqGSIb3DQEHATAeBglghkgBZQMEAS4wEQQMqgrWehLt3Q-vndNgAgEQgIICeS9dAMLeq1AKBwrDN5TQY4gNgYDbjJ5TgZIWaINiDgof7kP40GMNOaOAJKG_fk3O3n0hphWohj0964P0lCTTGaBHL8qeej_r1vwugGCx8J0jiQbGpEMX0ujPrsUo_AKgFkE4sUk_9MWZ2gobDpNP1kZ-akNB0R_87g5zmCRSwFnUgjRC6t45kCf4zsq4xPTYkL1QCQNXdePk3WmarvEwgeCzvP8onePqPBlKtDZK5ZC6XUq6Q4T3IIikvJoEUwyxn7OW2s-_h3C6CKGxztBiTMy9au1PeH1aKV7t5V_LWhGqP9Xe2LzhZ2hTMA5iCcoMkbMWhZiOq65FOSajlzw3_1ivADCs5zMCzD_SXhKtDCQQuRFJmnXBGPzA89QcUcHhtdZlFkaA16p7dWv7SJ0Wkg0_mwxyGoL3jwZNQmtTiV2Uzv_aC2fmFpI6gPiDnBMwgpslWy8UHU4bhT7mTzbBPwGbHZcuIzN7bApBRAZbu6yWWuftwgDZiKU9XUciDucNnNiCWd8bhVW9i_g-rS6SEAHtfsQ9A-ghgTOCPXEN2f7dZT9HD9BSuhvKWPKoYeFYx67Xn1CbMDpKZnOb2qPgssbSZDoGhVVjTrirBakr8TKjEJMrDz53Sf5qRlPLOARYwbzTD48hk5YDJX4dPPoO3lJ2Uepe5-GlMmCv5rAyHwaA9DzxQ7_7fidTQU6EfqXGwgehQwBQsaU2T0zKOikANeFIZ2pEskKqffFftVgy345S0j_p7z60_39YZHEiX7wA-hssZq_BUaE8rDXWuU8y6MQ4DATET83QkyKa7e7rupJ6zZ-hOLLPmyN7GCfUovWBqOcjrR_a_GJozQ |url-status=dead |archive-url=https://web.archive.org/web/20221020172114/https://watermark.silverchair.com/5-3-210.pdf?token=AQECAHi208BE49Ooan9kkhW_Ercy7Dm3ZL_9Cf3qfKAc485ysgAAAsYwggLCBgkqhkiG9w0BBwagggKzMIICrwIBADCCAqgGCSqGSIb3DQEHATAeBglghkgBZQMEAS4wEQQMqgrWehLt3Q-vndNgAgEQgIICeS9dAMLeq1AKBwrDN5TQY4gNgYDbjJ5TgZIWaINiDgof7kP40GMNOaOAJKG_fk3O3n0hphWohj0964P0lCTTGaBHL8qeej_r1vwugGCx8J0jiQbGpEMX0ujPrsUo_AKgFkE4sUk_9MWZ2gobDpNP1kZ-akNB0R_87g5zmCRSwFnUgjRC6t45kCf4zsq4xPTYkL1QCQNXdePk3WmarvEwgeCzvP8onePqPBlKtDZK5ZC6XUq6Q4T3IIikvJoEUwyxn7OW2s-_h3C6CKGxztBiTMy9au1PeH1aKV7t5V_LWhGqP9Xe2LzhZ2hTMA5iCcoMkbMWhZiOq65FOSajlzw3_1ivADCs5zMCzD_SXhKtDCQQuRFJmnXBGPzA89QcUcHhtdZlFkaA16p7dWv7SJ0Wkg0_mwxyGoL3jwZNQmtTiV2Uzv_aC2fmFpI6gPiDnBMwgpslWy8UHU4bhT7mTzbBPwGbHZcuIzN7bApBRAZbu6yWWuftwgDZiKU9XUciDucNnNiCWd8bhVW9i_g-rS6SEAHtfsQ9A-ghgTOCPXEN2f7dZT9HD9BSuhvKWPKoYeFYx67Xn1CbMDpKZnOb2qPgssbSZDoGhVVjTrirBakr8TKjEJMrDz53Sf5qRlPLOARYwbzTD48hk5YDJX4dPPoO3lJ2Uepe5-GlMmCv5rAyHwaA9DzxQ7_7fidTQU6EfqXGwgehQwBQsaU2T0zKOikANeFIZ2pEskKqffFftVgy345S0j_p7z60_39YZHEiX7wA-hssZq_BUaE8rDXWuU8y6MQ4DATET83QkyKa7e7rupJ6zZ-hOLLPmyN7GCfUovWBqOcjrR_a_GJozQ |archive-date=2022-10-20}} (4 pages)

{{cite journal |doi=10.2307/2001990 |jstor=2001990 |title=An Analysis of a Logical Machine Using Parenthesis-Free Notation |journal=Mathematical Tables and Other Aids to Computation |volume=8 |issue=46 |pages=53–57 |date=1954 |author-last1=Burks |author-first1=Arthur Walter |author-link1=Arthur Walter Burks |author-last2=Warren |author-first2=Don W. |author-last3=Wright |author-first3=Jesse B.}}

{{cite web |title=Charles L. Hamblin: Computer Pioneer |author-first=Peter |author-last=McBurney |date=2008-07-27 |url=http://www.csc.liv.ac.uk/~peter/this-month/this-month-3-030303.html |url-status=dead |archive-url=https://web.archive.org/web/20081207005233/http://www.csc.liv.ac.uk/~peter/this-month/this-month-3-030303.html |archive-date=2008-12-07 |quote=[…] Hamblin soon became aware of the problems of (a) computing mathematical formulae containing brackets, and (b) the memory overhead in having dealing with memory stores each of which had its own name. One solution to the first problem was Jan Łukasiewicz's Polish notation, which enables a writer of mathematical notation to instruct a reader the order in which to execute the operations (e.g. addition, multiplication, etc) without using brackets. Polish notation achieves this by having an operator (+, ×, etc) precede the operands to which it applies, e.g., +ab, instead of the usual, a+b. Hamblin, with his training in formal logic, knew of Lukasiewicz's work. […]}}

{{cite web |title=Charles L. Hamblin and his work |date=2008-12-06 |author-first=Peter |author-last=McBurney |url=http://www.csc.liv.ac.uk/~peter/hamblin.html |url-status=dead |archive-url=https://web.archive.org/web/20081206093044/http://www.csc.liv.ac.uk/~peter/hamblin.html |archive-date=2008-12-06}}

{{cite journal |title=Human behaviour and performance in calculator use with Algebraic and Reverse Polish Notation |author-first1=Dennis Michael |author-last1=Kasprzyk |author-first2=Colin G. |author-last2=Drury |author-first3=Wayne F. |author-last3=Bialas |location=Department of Industrial Engineering, State University of New York at Buffalo, Amherst, New York, USA |journal=Ergonomics |issn=0014-0139 |eissn=1366-5847 |publisher=Taylor & Francis |volume=22 |issue=9 |date=1979 |orig-date=1978-09-25 |doi=10.1080/00140137908924675 |s2cid=62692402 |pages=1011–1019}} (9 pages)

{{cite journal |title=Calculator logic: when and why is RPN superior to algebraic? |author-first1=Errol |author-last1=Hoffman |author-first2=Patrick |author-last2=Ma |author-first3=Jason |author-last3=See |author-first4=Chee Kee |author-last4=Yong |author-first5=Jason |author-last5=Brand |author-first6=Matthew |author-last6=Poulton |journal=Applied Ergonomics |issn=0003-6870 |eissn=1872-9126 |volume=25 |issue=5 |date=1994 |publisher=Elsevier Science Ltd. |doi=10.1016/0003-6870(94)90048-5 |pages=327–333}}

{{cite conference |title=The Burroughs B 5000 Conference - OH 98 |editor-first1=Bernard A. |editor-last1=Galler |editor-first2=Robert F. |editor-last2=Rosin |date=1986 |orig-date=1985-09-06 |location=Marina Del Ray Hotel, Marina Del Ray, California, USA |publisher=Charles Babbage Institute, The Center for the History of Information Processing, University of Minnesota, Minneapolis, USA |url=http://conservancy.umn.edu/bitstream/107105/1/oh098b5c.pdf |access-date=2013-02-27 |url-status=dead |archive-url=https://web.archive.org/web/20120422070048/http://conservancy.umn.edu/bitstream/107105/1/oh098b5c.pdf |archive-date=2012-04-22}} A New Approach to the Design of a Digital Computer (1961)

{{cite web |title=The Burroughs B5000 Conference (1985) |date=17 June 2023 |page=49 |url=http://special.lib.umn.edu/cbi/oh/pdf.phtml?id=21}}

{{cite web |title=Friden EC-130 Electronic Calculator |date=2020-08-09 |website=www.oldcalculatormuseum.com |url=http://www.oldcalculatormuseum.com/friden130.html |access-date=2018-03-21 |url-status=live |archive-url=https://web.archive.org/web/20221020175311/https://www.oldcalculatormuseum.com/friden130.html |archive-date=2022-10-20}}

{{cite web |title=Friden EC-132 Electronic Calculator |date=2022-07-15 |website=www.oldcalculatormuseum.com |url=http://www.oldcalculatormuseum.com/friden132.html |access-date=2018-03-21 |url-status=live |archive-url=https://web.archive.org/web/20221020175254/https://www.oldcalculatormuseum.com/friden132.html |archive-date=2022-10-20}}

{{cite web |title=HP Calculators |url=http://www8.hp.com/us/en/products/calculators/index.html}}

{{cite journal |title=HP RPN Evolves |author-first=Richard J. |author-last=Nelson |journal=HP Solve |publisher=Hewlett-Packard Development Company, L.P. |date=April 2012 |number=27 |pages=42–45 |url=http://h20331.www2.hp.com/hpsub/downloads/S07%20HP%20RPN%20Evolves%20V5b.pdf |access-date=2022-10-20 |url-status=live |archive-url=https://web.archive.org/web/20221020173134/http://h20331.www2.hp.com/hpsub/downloads/S07%20HP%20RPN%20Evolves%20V5b.pdf |archive-date=2022-10-20}} [http://h20331.www2.hp.com/hpsub/downloads/HP_Calculator_eNL_04_April_2012%2520(2).pdf] (4 of 56 pages)

{{cite magazine |title=A new standard!... The 7400 scientific & engineering calculator |type=Advertisement |magazine=Radio-Electronics - For men with ideas in electronics |date=December 1972 |volume=43 |issue=12 |publisher=Gernsback Publications, Inc. |publication-place=New York, USA |page=17 |url=https://worldradiohistory.com/Archive-Radio-Electronics/70s/1972/Radio-Electronics-1972-12.pdf |access-date=2022-12-28 |url-status=live |archive-url=https://web.archive.org/web/20221228161558/https://worldradiohistory.com/Archive-Radio-Electronics/70s/1972/Radio-Electronics-1972-12.pdf |archive-date=2022-12-28 |quote-page=17 |quote=DATA STORAGE: 2 Auxiliary Storage Registers plus up to 7 push-up Stack Registers. […] 7400A 3 Registers Kit $299.95 Assembled $379.95 […] 7400B 5 Registers Kit $319.95 Assembled $399.95 […] 7400C 7 Registers Kit $339.95 Assembled $419.95}}

{{cite journal |title=New calculator kits: From pocket minis to versatile desk models |author-first=Ivan |author-last=Berger |journal=Popular Mechanics |publisher=Hearst Magazines |date=May 1973 |page=152 |url=https://books.google.com/books?id=htQDAAAAMBAJ&pg=PA151 |access-date=2017-04-29}}

{{cite web |title=MITS 7400 Scientific/Engineering Calculator |url=http://www.oldcalculatormuseum.com/w-mits7400.html |access-date=2017-04-30 |url-status=live |archive-url=https://web.archive.org/web/20170430004710/http://www.oldcalculatormuseum.com/w-mits7400.jpg |archive-date=2017-04-30}} (NB. Shows a photo of the MITS 7400, but the text erroneously refers to the later algebraic 7440 model instead of the 7400A/B/C models.)

{{cite book |title=SR4921 RPN Reverse Notation Scientific Calculator Instruction Manual |publisher=Commodore Business Machines, Inc. |date= |location=Palo Alto, California, USA |url=http://www.wass.net/manuals/Commodore%20SR4921R.pdf |access-date=2022-10-16 |url-status=live |archive-url=https://web.archive.org/web/20170625231745/http://www.wass.net/manuals/Commodore%20SR4921R.pdf |archive-date=2017-06-25}}

{{cite web |title=Prinztronic Program |website=www.vintagecalculators.com |url=http://www.vintagecalculators.com/html/program.html |access-date=21 March 2018}}

[http://www.rskey.org/detail.asp?manufacturer=Elektronika&model=B3-21 Elektronika B3-21] page on RSkey.org

[http://www.rskey.org/detail.asp?manufacturer=Elektronika&model=MK-161 Elektronika MK-161] page on RSkey.org

{{cite web |url=http://arbinada.com/pmk/node/56 |title=Elektronika MK-61/52 and 152/161: small tech review (En) - Кон-Тики |website=arbinada.com |access-date=2018-03-21}}

{{cite web |url=http://mk.semico.ru/ |title=НПП СЕМИКО - вычислительная техника и устройства автоматизации |website=mk.semico.ru |access-date=2018-03-21}}

{{cite web |url=http://lashwhip.com/grpn.html |title=Katharina & Paul Wilkins' Home Page |website=lashwhip.com |access-date=2018-03-21}}

{{cite web |url=http://galculator.mnim.org/ |title=galculator - a GTK 2 / GTK 3 algebraic and RPN calculator |website=galculator.mnim.org |access-date=2024-01-05}}

{{cite web |url=https://rpcalc.bellz.org/ |title=rpCalc |website=rpcalc.bellz.org |access-date=2024-01-05}}

{{cite web |url=http://www.stack-calculator.com/ |title=Home - mouseless Stack-Calculator |first=Frans |last=Schrijver |website=www.stack-calculator.com |access-date=2018-03-21}}

{{cite web |title=hp 9100A Calculator |type=marketing brochure |date=1968 |publisher=Hewlett-Packard |pages=8–10 |url=http://archive.computerhistory.org/resources/text/HP/HP.9100A.1968.102646164.pdf |access-date=2013-01-26 |url-status=live |archive-url=https://web.archive.org/web/20211022222725/http://archive.computerhistory.org/resources/text/HP/HP.9100A.1968.102646164.pdf |archive-date=2021-10-22}}

{{cite book |title=Hewlett-Packard HP-15C Owner's Handbook |chapter=Section 3: The Automatic Memory Stack, LAST X, and Data Storage |publisher=Hewlett-Packard Development Company, LP. |date=September 2011 |version=2.4 |id=00015-90001 |pages=32–46 |url=http://www.hp.com/ctg/Manual/c03030589.pdf |access-date=2015-12-05 |url-status=live |archive-url=https://web.archive.org/web/20170917224935/http://www.hp.com/ctg/Manual/c03030589.pdf |archive-date=2017-09-17}}

{{cite journal |title=1941 RPN Computer? |author-first=Paul E. |author-last=Ceruzzi |author-link=Paul E. Ceruzzi |journal=PPC Calculator Journal |date=April 1980 |volume=7 |number=3 |page=25 |url=https://www.hpcalc.org/hp48/docs/columns/1941rpn.html |access-date=2022-07-01 |url-status=live |archive-url=https://web.archive.org/web/20220701172806/https://www.hpcalc.org/hp48/docs/columns/1941rpn.html |archive-date=2022-07-01 |quote-page=25 |quote=The interesting aspect of the programming of the Z-3 was that this code was very similar to that of, say, an HP-25. To perform an operation on two numbers, commands would first be given to recall the numbers from appropriate locations in the memory, followed by the command for the operation. Numbers were automatically positioned in registers in the Arithmetic Unit of the machine so that operations like division and subtraction would proceed in the right order. Results were left in a register in the AU so that long sequences of operations could be carried out. Thus, the Z-3 used a version of RPN that was nearly identical to that used by HP! I have obtained copies of early programs that Zuse had written for the evaluation of a 5 × 5 determinant, and it is possible to run these programs on an HP-41C with almost no modification whatsoever (once the numbers have been placed in the storage registers beforehand). The AU of the Z-3 contained 3 registers, although Zuse never referred to them as a stack, of course. These registers were labelled "f", "a", and "b". All entrance and exit to and from the AU was through the "f" register. This is sort of like the display register of the 41C, which is distinct from the stack. Arithmetic operations were performed on numbers in the a and b registers, so these may be thought of as corresponding to the x and y registers of HP's. Unlike modern computer practice, the actual numbers themselves were moved around the registers, not just a pointer.}}

{{cite book |title=Reckoners - The prehistory of the digital computer, from relays to the stored program concept, 1935–1945 |author-first=Paul E. |author-last=Ceruzzi |author-link=Paul E. Ceruzzi |series=Contributions to the study of computer science |issn=0734-757X |volume=1 |date=1983 |lccn=82-20980 |isbn=0-313-23382-9 |publisher=Greenwood Press, Congressional Information Service, Inc. |publication-place=Westport, Connecticut, USA |edition=1 |page=0010 |chapter=2. Computers in Germany |url=http://ed-thelen.org/comp-hist/Reckoners.html#TOC |chapter-url=http://ed-thelen.org/comp-hist/Reckoners-ch-2.html |access-date=2022-07-02 |url-status=live |archive-url=https://web.archive.org/web/20220701223948/http://ed-thelen.org/comp-hist/Reckoners-ch-2.html |archive-date=2022-07-01}}

{{cite magazine |title=Rechenhilfe für Ingenieure |language=de |publisher=Technische Universität Berlin |magazine=Alumni-Magazin der Technischen Universität Berlin |volume=2 |number=3 |date=December 2000 |url=http://www2.tu-berlin.de/alumni/parTU/00dez/zuse.htm |url-status=dead |archive-url=https://web.archive.org/web/20090213222711/http://www2.tu-berlin.de/alumni/parTU/00dez/zuse.htm |archive-date=2009-02-13}}

{{cite conference |conference=INFORMATIK 2005 Informatik LIVE! Band 1, Beiträge der 35. Jahrestagung der Gesellschaft für Informatik e.V. (GI), 19. bis 22. September 2005 in Bonn |title=Die ergonomischen Erfindungen der Zuse-Maschinen |language=de |chapter=2. Dialogfähigkeit der Maschine Z3 |series=Lecture Notes in Informatics |author-first=Horst |author-last=Zuse |author-link=Horst Zuse |editor-first1=Armin B. |editor-last1=Cremers |editor-first2=Rainer |editor-last2=Manthey |editor-first3=Peter |editor-last3=Martini |editor-first4=Volker |editor-last4=Steinhage |location=Berlin, Germany |publisher=Gesellschaft für Informatik (GI) |publication-place=Bonn, Germany |pages=200–204 [200–201] |url=https://subs.emis.de/LNI/Proceedings/Proceedings67/GI-Proceedings.67-42.pdf |access-date=2022-07-02 |url-status=live |archive-url=https://web.archive.org/web/20220701225356/https://subs.emis.de/LNI/Proceedings/Proceedings67/GI-Proceedings.67-42.pdf |archive-date=2022-07-01 |quote-page=201 |quote=Dazu stehen die beiden Register R1 und R2 als Kurzspeicher für die Operanden der arithmetischen Operationen zur Verfügung. Gerechnet wird in der umgekehrten polnischen Notation, wie z.B. beim Taschenrechner HP 45 (1972) oder HP11 (1998).}} (5 pages)

{{cite web |title=Z3 im Detail |language=de |trans-title=Z3 in details |editor-first=Horst |editor-last=Zuse |editor-link=Horst Zuse |date=2008-02-22 |work=Professor Dr.-Ing. habil. Horst Zuse |url=http://www.horst-zuse.homepage.t-online.de/z3-detail.html |access-date=2022-07-01 |url-status=live |archive-url=https://web.archive.org/web/20220701173220/http://www.horst-zuse.homepage.t-online.de/z3-detail.html |archive-date=2022-07-01 |quote=Die Z3 konnte in zwei Betriebsmodi betrieben werden, und zwar in dem Programm- und Dialogmodus. Das Rechnen im Dialog erfolgt wie mit einem Taschenrechner in der umgekehrten polnischen Notation.}} [https://web.archive.org/web/20220701173354/http://www.horst-zuse.homepage.t-online.de/foto-scout-zuse-internet-html/fsz-readme-1.pdf]

{{cite web |title=Fast Calculators: Konrad Zuse's Z1 and Z3 |author-first=Jo H. M. |author-last=Bonten |location=Geldrop, Netherlands |date=2009-05-28 |orig-date=2009-03-08 |url=http://home.kpn.nl/jhm.bonten/computers/bitsandbytes/wordsizes/crayzuse.htm |access-date=2022-07-02 |url-status=live |archive-url=https://web.archive.org/web/20220701230722/http://home.kpn.nl/jhm.bonten/computers/bitsandbytes/wordsizes/crayzuse.htm |archive-date=2022-07-01 |quote=The computer can be used as a simple hand-held calculator. In this mode besides entering the numeric values the user must enter the instructions and the addresses by pressing their keys. He has to enter the numbers and operators in the reverse Polish notation.}}

{{cite web |title=An einem 12. Mai |language=de |publisher=Deutsches Historisches Museum (German Historical Museum) |url=http://www.dhm.de/gaeste/luise/tagesfakten/tf05/0512.htm |url-status=dead |archive-url=https://web.archive.org/web/20130530040033/http://www.dhm.de/gaeste/luise/tagesfakten/tf05/0512.htm |archive-date=2013-05-30}}

{{cite magazine |title=Zum 75. Geburtstag von Konrad Zuses Z3: Ratterkasten |author-first=Jan |author-last=Bundesmann |language=de |magazine=iX |publisher=Heise Verlag |issue=6 |volume=2016 |date=June 2016 |department=Report / Jubiläum |page=94 |url=https://www.heise.de/select/ix/2016/6/1464579381888967#literaturverzeichnis |access-date=2022-07-01 |url-status=live |archive-url=https://web.archive.org/web/20220701174549/https://www.heise.de/select/ix/2016/6/1464579381888967#literaturverzeichnis |archive-date=2022-07-01 |quote-page=94 |quote=Zum Eingeben der Zahlen stand eine Tastatur bereit (Dezimalzahlen, Gleitkommadarstellung). Anweisungen gaben Nutzer in umgekehrter polnischer Notation: zuerst die Argumente, um Register zu befüllen, dann der auszuführende Operator.}}

{{cite magazine |title=Die Computerwelt von Konrad Zuse - Auf den Spuren eines EDV-Genies |language=de |magazine={{ill|Welt der Fertigung|de}} |issn=2194-9239 |department=Die Welt der technischen Museen |volume=2018 |number=2 |date=2018 |pages=32–35 |url=https://www.weltderfertigung.de/assets/konrad-zuse-museum.pdf |access-date=2022-07-02 |url-status=live |archive-url=https://web.archive.org/web/20191017185004/http://weltderfertigung.de/assets/konrad-zuse-museum.pdf |archive-date=2019-10-17 |quote-pages=32–33 |quote=Er hat wohl auch als erster die vom polnischen Mathematiker Jan Lukasiewicz entwickelte ›polnische Notation‹ weiterentwickelt und daraus die ›umgekehrte polnische Notation‹ (UPN) ersonnen, da diese in seinen Rechnern verwendet wird: zunächst werden die Werte eingegeben, danach die gewünschte Rechenoperation ausgelöst. Klammern werden auf diese Weise vermieden.}} (4 pages)

{{cite magazine |title=Computergeschichte: Zuse Z3 "im Test" |date=2021-11-21 |magazine=c't magazin |publisher=Heise Verlag |author-first=Sylvester |author-last=Tremmel |page= |url=https://www.heise.de/tests/Comnputergeschichte-Zuse-Z3-im-Test-6275272.html |access-date=2022-07-01 |url-status=live |archive-url=https://web.archive.org/web/20220301130344/https://www.heise.de/tests/Comnputergeschichte-Zuse-Z3-im-Test-6275272.html |archive-date=2022-03-01 |quote-page= |quote=Über die I/O-Einheit kann man die Z3 als reine Rechenmaschine einsetzen, Operationen nimmt sie dann in der praktischen – wenn auch gewöhnungsbedürftigen – umgekehrten polnischen Notation entgegen. Werte im Speicher ablegen (oder von dort laden) kann man so allerdings nicht.}}

{{cite journal |author-last=Dietrich |author-first=Johannes W. |title=TRURL RPN Engine |journal=Zenodo |date=2019-07-24 |doi=10.5281/zenodo.3257689 |url=https://zenodo.org/record/3350851 |access-date=2022-07-02}}

{{cite book |title=Computer architecture: Concepts and evolution |author-first1=Gerrit Anne |author-last1=Blaauw |author-link1=Gerrit Anne Blaauw |author-first2=Frederick Phillips |author-last2=Brooks, Jr. |author-link2=Frederick Phillips Brooks |publisher=Addison-Wesley Longman Publishing Co., Inc. |publication-place=Boston, Massachusetts, USA |date=1997}}

{{cite magazine |title=Stack Machine Development: Australia, Great Britain, and Europe |author-first=Fraser George |author-last=Duncan |location=University of Bristol, Bristol, Virginia, USA |magazine=Computer |id={{CODEN|CPTRB4}} |s2cid=17013010 |doi=10.1109/MC.1977.315873 |issn=0018-9162 |eissn=1558-0814 |publisher= |volume=10 |date=1977-05-01 |issue=5 |pages=50–52 |url=https://csdl-downloads.ieeecomputer.org/mags/co/1977/05/01646485.pdf?Expires=1697369097&Policy=eyJTdGF0ZW1lbnQiOlt7IlJlc291cmNlIjoiaHR0cHM6Ly9jc2RsLWRvd25sb2Fkcy5pZWVlY29tcHV0ZXIub3JnL21hZ3MvY28vMTk3Ny8wNS8wMTY0NjQ4NS5wZGYiLCJDb25kaXRpb24iOnsiRGF0ZUxlc3NUaGFuIjp7IkFXUzpFcG9jaFRpbWUiOjE2OTczNjkwOTd9fX1dfQ__&Signature=xUP0yvim4Anf0nWqRYKhw7EINRBgqttNgyV0fOBmg4jGQU~Uo1eP91Mw2CL34gK18qbzYjWRKwqifo7aVUL2hgxz~ZplAiqNXRqbLpbB4bYfoPiJNJ3x0AJmfERxcIG058YoTI8~uiEhmUNgjJkrfSMbqHwUoqit~4p7xFLfFBqiPau56WqdEngihf8OXuDeUxkMvCPgo2tGnN5GCoGY9-ALYc99IxqY8-ltGpsyauyASyerp42tY7E6r7T~6x75q8mjilSfo~tTpJMTdX2DpGepaobjf9D7MAXWv7iko038yLn8Kp8WxQceX6VX8fM85pPPYapXGK4HrPNnUIGeiw__&Key-Pair-Id=K12PMWTCQBDMDT |access-date=2023-10-15 |url-status=dead |archive-url=https://web.archive.org/web/20231015112418/https://csdl-downloads.ieeecomputer.org/mags/co/1977/05/01646485.pdf?Expires=1697369097&Policy=eyJTdGF0ZW1lbnQiOlt7IlJlc291cmNlIjoiaHR0cHM6Ly9jc2RsLWRvd25sb2Fkcy5pZWVlY29tcHV0ZXIub3JnL21hZ3MvY28vMTk3Ny8wNS8wMTY0NjQ4NS5wZGYiLCJDb25kaXRpb24iOnsiRGF0ZUxlc3NUaGFuIjp7IkFXUzpFcG9jaFRpbWUiOjE2OTczNjkwOTd9fX1dfQ__&Signature=xUP0yvim4Anf0nWqRYKhw7EINRBgqttNgyV0fOBmg4jGQU~Uo1eP91Mw2CL34gK18qbzYjWRKwqifo7aVUL2hgxz~ZplAiqNXRqbLpbB4bYfoPiJNJ3x0AJmfERxcIG058YoTI8~uiEhmUNgjJkrfSMbqHwUoqit~4p7xFLfFBqiPau56WqdEngihf8OXuDeUxkMvCPgo2tGnN5GCoGY9-ALYc99IxqY8-ltGpsyauyASyerp42tY7E6r7T~6x75q8mjilSfo~tTpJMTdX2DpGepaobjf9D7MAXWv7iko038yLn8Kp8WxQceX6VX8fM85pPPYapXGK4HrPNnUIGeiw__&Key-Pair-Id=K12PMWTCQBDMDT |archive-date=2023-10-15}} (3 pages)

{{cite journal |title=Charles Hamblin (1922–1985) |author-first=Murray W. |author-last=Allen |journal=Australian Computer Journal |publisher=Australian Computer Society, Inc. |publication-place=Darlinghurst, Australia |issn=0004-8917 |volume=17 |date=1985-11-01 |issue=4 |pages=194–195 |url=https://dl.acm.org/doi/10.5555/7385.7391 |access-date=2023-10-15}} (2 pages)

{{cite book |title=Second-Generation Stack Computer Architecture |chapter=2.1 Lukasiewicz and the First Generation: 2.1.2 Germany: Konrad Zuse (1910–1995); 2.2 The First Generation of Stack Computers: 2.2.1 Zuse Z4 |author-first=Charles Eric |author-last=LaForest |type=thesis |publisher=University of Waterloo |location=Waterloo, Canada |date=April 2007 |pages=8, 11 |url=http://fpgacpu.ca/publications/Second-Generation_Stack_Computer_Architecture.pdf |access-date=2022-07-02 |url-status=live |archive-url=https://web.archive.org/web/20220120155616/http://fpgacpu.ca/publications/Second-Generation_Stack_Computer_Architecture.pdf |archive-date=2022-01-20}} (178 pages)

{{cite journal |title=Konrad Zuse's Legacy: The Architecture of the Z1 and Z3 |author-last=Rojas |author-first=Raúl |author-link=Raúl Rojas |journal=IEEE Annals of the History of Computing |volume=19 |number=2 |date=April–June 1997 |pages=5–16 [7–8] |doi=10.1109/85.586067 |url=http://ed-thelen.org/comp-hist/Zuse_Z1_and_Z3.pdf |access-date=2022-07-03 |url-status=live |archive-url=https://web.archive.org/web/20220703082408/http://ed-thelen.org/comp-hist/Zuse_Z1_and_Z3.pdf |archive-date=2022-07-03}} (12 pages)

{{cite web |title=RPLMan from Goodies Disk 4 |author=Hewlett-Packard |author-link=Hewlett-Packard |format=RPLMAN.ZIP |url=http://www.hpcalc.org/details.php?id=1743 |access-date=2015-09-12}}

{{cite journal |title=The HP-28C: An Insider's Perspective |author-first=William C. |author-last=Wickes |journal=HPX Exchange |volume=1 |number=1 |date=January–February 1987 |pages= |url=}} [https://web.archive.org/web/20231006184209/https://www.hpmuseum.org/forum/thread-1140.html]

{{cite web |title=In Praise Of RPN (with Python Or C) |author-first=Al |author-last=Williams |date=2023-06-21 |work=Hackaday |url=https://hackaday.com/2023/06/21/in-praise-of-rpn-with-python-or-c/ |access-date=2023-09-23 |url-status=live |archive-url=https://web.archive.org/web/20230923090403/https://hackaday.com/2023/06/21/in-praise-of-rpn-with-python-or-c/ |archive-date=2023-09-23}}

{{cite web |title=HP 9100A/B |date=1998 |work=MoHPC - The Museum of HP Calculators |url=https://www.hpmuseum.org/hp9100.htm |access-date=2023-09-23 |url-status=live |archive-url=https://web.archive.org/web/20230923125424/https://www.hpmuseum.org/hp9100.htm |archive-date=2023-09-23}}

{{cite web |title=What to do with stack overflow OBJ->/LIST->? |author-first=Timothy "Tim" James |author-last=Wessman |date=2016-06-21 |orig-date=2016-06-20 |work=MoHPC - The Museum of HP Calculators |url=https://www.hpmuseum.org/forum/printthread.php?tid=6436 |access-date=2023-09-24 |url-status=live |archive-url=https://web.archive.org/web/20230924101041/https://www.hpmuseum.org/forum/printthread.php?tid=6436 |archive-date=2023-09-24}}

{{cite web |title=[34S] Proposal for Entry RPN mode with dynamic stack |author-first=Matthias R. |author-last=Paul |date=2015-02-18 |orig-date=2015-02-15 |work=MoHPC - The Museum of HP Calculators |url=https://www.hpmuseum.org/forum/thread-3108.html |access-date=2023-09-24 |url-status=live |archive-url=https://web.archive.org/web/20230923202314/https://www.hpmuseum.org/forum/thread-3108.html |archive-date=2023-09-23}}

{{cite web |title=Bit's WP 34S and 31S patches and custom binaries (version: r3802 20150805-1) |author=Bit |date=2014-11-15 |work=MoHPC - The Museum of HP Calculators |url=https://www.hpmuseum.org/forum/thread-2433.html |access-date=2023-09-24 |url-status=live |archive-url=https://web.archive.org/web/20230924153615/https://www.hpmuseum.org/forum/thread-2433.html |archive-date=2023-09-24}}

{{cite web |title=[34S & 31S] Unique display mode: significant figures |author=Bit |date=2015-02-07 |work=MoHPC - The Museum of HP Calculators |url=https://www.hpmuseum.org/forum/thread-3029.html |access-date=2023-09-24 |url-status=live |archive-url=https://web.archive.org/web/20230924153537/https://www.hpmuseum.org/forum/thread-3029.html |archive-date=2023-09-24}}

{{cite web |title=Everything you've always wanted to know about RPN but were afraid to pursue – Comprehensive manual for scientific calculators – Corvus 500 – APF Mark 55 – OMRON 12-SR and others |publisher=T. K. Enterprises |date=1976 |url=http://www.wass.net/manuals/Everything%20RPN.pdf |access-date=2017-06-24 |url-status=live |archive-url=https://web.archive.org/web/20170624162722/http://www.wass.net/manuals/Everything%20RPN.pdf |archive-date=2017-06-24}} (NB. The book's cover title contains a typographical error reading "APS Mark 55" instead of the correct "APF Mark 55".)

{{cite web | url=https://www.cgtk.co.uk/software/arpcalc | title=CGTK - ARPCalc - Al's Reverse Polish Calculator }}

}}

• {{cite web |author-last=Brown |author-first=Bob |date=2015-06-05 |orig-date=April 2001 |title=Postfix Notation Mini-Lecture |publisher=Information Technology Department, College of Computing and Software Engineering, Kennesaw State University|url=http://bbrown.kennesaw.edu/web_lectures/postfix/ |access-date=2015-09-12 |url-status=live |archive-url=https://web.archive.org/web/20170624164922/http://ksuweb.kennesaw.edu/faculty/rbrow211/web_lectures/postfix/ |archive-date=2017-06-24}}
• {{cite web |title=Advanced Calculator Logic HP RPN/Algebraic: A Comparative Analysis |url=http://archive.computerhistory.org/resources/access/text/2016/05/102651973-05-01-acc.pdf |access-date=2022-12-26 |url-status=live |archive-url=https://web.archive.org/web/20221226175054/http://archive.computerhistory.org/resources/access/text/2016/05/102651973-05-01-acc.pdf |archive-date=2022-12-26 |publisher=Hewlett-Packard Corporation |date=1979 |location=Corvallis, Oregon, USA |id=5953-1930}} (13 pages)
• {{cite web |author-last=Hicks |author-first=David G. |date=2013 |orig-date=1995 |title=What is RPN? |publisher=The Museum of HP Calculators (MoHPC) |url=http://hpmuseum.org/rpn.htm |access-date=2015-09-12 |url-status=live |archive-url=https://web.archive.org/web/20170624165003/http://hpmuseum.org/rpn.htm |archive-date=2017-06-24}}
• {{cite web |author-last=Klaver |author-first=Hans |date=2023-08-14 |orig-date=2014 |title=RPN Tutorial, incl. some things HP did not tell |url=https://klaverscholten.nl/rpn/index.html |location=Netherlands |access-date=2015-09-12 |url-status=live |archive-url=https://web.archive.org/web/20230923125928/https://klaverscholten.nl/rpn/index.html |archive-date=2023-09-23}}
• {{cite journal |author-last=Kreifeldt |author-first=John G. |date=October 1981 |title=Hand Calculator Performance Under Interrupted Operation |location=Department of Engineering Design, Tufts University, Medford, Massachusetts, USA |journal=Proceedings of the Human Factors Society Annual Meeting |volume=25 |number=1 |doi=10.1177/107118138102500187 |pages=329–332|s2cid=106904297 }} (4 pages)
• {{cite conference |author-last1=Kreifeldt |author-first1=John G. |author-last2=McCarthy |author-first2=Mary E. |date=1981-10-15 |orig-date=1981-06-16/18 |title=Interruption as a test of the user-computer interface |location=Department of Engineering Design, Tufts University, Medford, Massachusetts, USA |conference=Proceedings of the Seventeenth Annual Conference on Manual Control |publication-place=University of California, Los Angeles, California, USA |publisher=Jet Propulsion Laboratory / Office of Naval Research / NASA |id=02155, N82-13721, 82N13721, 19820005848, JPL 81-95 |pages=655–667 |url=https://ntrs.nasa.gov/api/citations/19820005848/downloads/19820005848.pdf |access-date=2018-09-22 |url-status=live |archive-url=https://web.archive.org/web/20220130063534/https://ntrs.nasa.gov/api/citations/19820005848/downloads/19820005848.pdf |archive-date=2022-01-30}} [https://books.google.com/books?id=dHZKAQAAMAAJ] (13 of 702 pages)
• {{cite web |author-last=Redin |author-first=James |date=2005-02-12 |orig-date=1997-10-05 |title=RPN or DAL? A brief analysis of Reverse Polish Notation against Direct Algebraic Logic |url=http://www.xnumber.com/xnumber/rpn_or_adl.htm |access-date=2015-09-12 |url-status=live |archive-url=https://web.archive.org/web/20170624164945/http://www.xnumber.com/xnumber/rpn_or_adl.htm |archive-date=2017-06-24}}
• {{cite book |author-last=Vanderbeek |author-first=Greg |date=July 2007 |title=Order of Operations and RPN |type=Expository paper |series=Master of Arts in Teaching (MAT) Exam Expository Papers |id=Paper 46 |publisher=University of Nebraska |location=Lincoln, USA |url=https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1045&context=mathmidexppap |access-date=2020-06-14 |url-status=live |archive-url=https://web.archive.org/web/20200614191608/https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1045&context=mathmidexppap |archive-date=2020-06-14}}
• {{cite web |author-last=Wirth |author-first=Niklaus |author-link=Niklaus Wirth |date=2005-06-15 |orig-date=2005-02-02 |title=Good Ideas, Through the Looking Glass |location=Zürich, Switzerland |url=http://www.inf.ethz.ch/~wirth/Articles/GoodIdeas_origFig.pdf |access-date=2015-09-12 |url-status=live |archive-url=https://web.archive.org/web/20170624164254/https://www.inf.ethz.ch/personal/wirth/Articles/GoodIdeas_origFig.pdf |archive-date=2017-06-24}}

• [http://rosettacode.org/wiki/Parsing/RPN_calculator_algorithm Rosettacode.org] providing many implementations in several programming languages.
• http://rpn.codeplex.com/ Implementation of RPN with custom functions support and flexible list of operators.
• https://xrjunque.nom.es/ConvertAlg2RPN_RPL.aspx Free online Algebraic expression to RPN Converter

{{DEFAULTSORT:Reverse Polish Notation}}

Category:Calculators

Category:Mathematical notation

Category:Science and technology in Poland

Category:Operators (programming)