Reverse Polish notation

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File:Typing the calculation for "8 times 6" into a pocket calculator HP-32SII which uses RPN logic.webm
Video: Keys pressed for calculating eight times six on a HP-32SII (employing RPN) from 1991

Reverse Polish notation (RPN), also known as reverse Łukasiewicz notation, Polish postfix notation or simply postfix notation, is a mathematical notation in which operators follow their operands, in contrast to prefix or Polish notation (PN), in which operators precede their operands. The notation does not need any parentheses for as long as each operator has a fixed number of operands.

The term postfix notation describes the general scheme in mathematics and computer sciences, whereas the term reverse Polish notation typically refers specifically to the method used to enter calculations into hardware or software calculators, which often have additional side effects and implications depending on the actual implementation involving a stack. The description "Polish" refers to the nationality of logician Jan Łukasiewicz,[1][2] who invented Polish notation in 1924.[3][4][5][6]

The first computer to use postfix notation, though it long remained essentially unknown outside of Germany, was Konrad Zuse's Z3 in 1941[7][8] as well as his Z4 in 1945. The reverse Polish scheme was again proposed in 1954 by Arthur Burks, Don Warren, and Jesse Wright[9] and was independently reinvented by Friedrich L. Bauer and Edsger W. Dijkstra in the early 1960s to reduce computer memory access and use the stack to evaluate expressions. The algorithms and notation for this scheme were extended by the philosopher and computer scientist Charles L. Hamblin in the mid-1950s.[10][11][12][13][14][15]Template:Excessive citations inline

During the 1970s and 1980s, Hewlett-Packard used RPN in all of their desktop and hand-held calculators, and has continued to use it in some models into the 2020s.[16][17] In computer science, reverse Polish notation is used in stack-oriented programming languages such as Forth, dc, Factor, STOIC, PostScript, RPL, and Joy.

Explanation

In reverse Polish notation, the operators follow their operands. For example, to add 3 and 4 together, the expression is 3 4 + rather than 3 + 4. The conventional notation expression 3 − 4 + 5 becomes 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 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 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 or pulled.

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 (3 + 4) × (5 + 6) becomes 3 4 + 5 6 + × in reverse Polish notation.

Practical implications

Reverse Polish notation has been compared to how one had to work through problems with a slide rule.[18]

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.[19][20] 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.[21] However, anecdotal evidence suggests that reverse Polish notation is more difficult for users who previously learned algebraic notation.[20]

Converting from infix notation

Script error: No such module "Labelled list hatnote". 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.

Implementations

Hardware calculators

Early history

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.[22][23][24][25] In dialog mode, it allowed operators to enter two operands followed by the desired operation.Template:Refn It was destroyed on 21 December 1943 in a bombing raid.[23] With Zuse's help a first replica was built in 1961.[23] The 1945 Z4 also added a 2-level stack.[26][27]

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,[28] 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),[10][11][13][29][30][27] an autocode programming system written for a DEUCE computer installed at the University of Sydney, Australia, in 1957.[10][11][13][28]

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,[31][32][33] where he found a reference to Polish notation,[33] which made him read the works of Jan Łukasiewicz as well,[33] 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,[34] supporting a four-level stack[5] in June 1963.[35] The successor EC-132 added a square root function in April 1965.[36] Around 1966, the Monroe Epic calculator supported an unnamed input scheme resembling RPN as well.[5]

Script error: No such module "anchor".Hewlett-Packard

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File:Hewlett-Packard No Equals hat.jpg
A promotional Hewlett-Packard "No Equals" hat from the 1980s – both a boast and a reference to RPN

Script error: No such module "anchor".Hewlett-Packard engineers designed the 9100A Desktop Calculator in 1968 with reverse Polish notation[16] with only three stack levels with working registers X ("keyboard"), Y ("accumulate") and visible storage register Z ("temporary"),[37][38] a reverse Polish notation variant later referred to as three-level RPN.[39] This calculator popularized reverse Polish notation among the scientific and engineering communities. Script error: No such module "anchor".The HP-35, the world's first handheld scientific calculator,[16] introduced the classical four-level RPN with its specific ruleset of the so-called operational (memory) stack[40][nb 1] (later also called automatic memory stack[41][42][nb 1]) in 1972.[43] In this scheme, the Template:Key press 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.[42] 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.

Script error: No such module "anchor".In 1986,[44][45] 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.[46] 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 Template:Key press 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.[47]

Script error: No such module "anchor".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 Template:Key press key behaves as in RPL. This latter variant is sometimes known as entry RPN.[48]

Script error: No such module "anchor".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.[46] 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 HP 15C Collector's Edition, and the Prime remain active models supporting RPN. Script error: No such module "Labelled list hatnote".

Sinclair Radionics

In Britain, Clive Sinclair's Sinclair Scientific (1974) and Scientific Programmable (1975) models used reverse Polish notation.[49][50]

Script error: No such module "anchor".Commodore

In 1974, Commodore produced the Minuteman *6 (MM6) without an Template:Key press key and the Minuteman *6X (MM6X) with an Template:Key press 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 Template:Key press 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.[51]

Prinztronic

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[52] Programmable Scientific Calculator which featured reverse Polish notation.

Script error: No such module "anchor".Heathkit

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

Soviet Union / Semico

Soviet programmable calculators (MK-52, MK-61, B3-34 and earlier B3-21[53] models) used reverse Polish notation for both automatic mode and programming. Modern Russian calculators MK-161[54] and MK-152,[55] designed and manufactured in Novosibirsk since 2007 and offered by Semico,[56] are backwards compatible with them. Their extended architecture is also based on reverse Polish notation.

Others

Script error: No such module "anchor".Community-developed hardware-based calculators

Script error: No such module "Labelled list hatnote". An eight-level stack was suggested by John A. Ball in 1978.[5]

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 Template:Key press 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 Template:Key press key, a feature often requested by the community.[61] 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.[62][63]

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.[64][65]

Software calculators

Software calculators:

Programming languages

Existing implementations using reverse Polish notation include:

See also

Notes

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References

Template:Reflist

Further reading

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External links

  1. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Łukasiewicz_1951
  2. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Łukasiewicz_1957
  3. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Łukasiewicz_1929
  4. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Hamblin_1962
  5. ↑ a b c d Cite error: Invalid <ref> tag; no text was provided for refs named Ball_1978
  6. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Kennedy_1982
  7. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Ceruzzi_1980
  8. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Rojas_1997
  9. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Burks_1954
  10. ↑ a b c Cite error: Invalid <ref> tag; no text was provided for refs named Hamblin_1957_1
  11. ↑ a b c Cite error: Invalid <ref> tag; no text was provided for refs named Hamblin_1957_2
  12. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Hamblin_1957_3
  13. ↑ a b c Cite error: Invalid <ref> tag; no text was provided for refs named Hamblin_1958
  14. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named McBurney_2008_2
  15. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named McBurney_2008_1
  16. ↑ a b c Cite error: Invalid <ref> tag; no text was provided for refs named Osborne_1994
  17. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Peterson_2011
  18. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Williams_2023
  19. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Kasprzyk-Drury-Bialas_1979
  20. ↑ a b Cite error: Invalid <ref> tag; no text was provided for refs named Agate_1980
  21. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Hoffman_1994
  22. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named parTU_2000
  23. ↑ a b c Cite error: Invalid <ref> tag; no text was provided for refs named Zuse_2008
  24. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named DHM_2013
  25. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Bundesmann_2016
  26. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Blaauw-Brooks_1997
  27. ↑ a b Cite error: Invalid <ref> tag; no text was provided for refs named LaForest_2007
  28. ↑ a b Cite error: Invalid <ref> tag; no text was provided for refs named Beard_1997
  29. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Duncan_1977
  30. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Allen_1985
  31. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named NewApproach
  32. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named B5000_1985
  33. ↑ a b c Cite error: Invalid <ref> tag; no text was provided for refs named Galler-Rosin_1985
  34. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Ragen_2012
  35. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Friden_EC-130
  36. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Friden_EC-132
  37. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Monnier_1968
  38. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named HP9100A_1968
  39. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named HP9100A_1998
  40. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named HP35_UM
  41. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named HP42_OM
  42. ↑ a b Cite error: Invalid <ref> tag; no text was provided for refs named HP15C_2011
  43. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Laporte_2014
  44. ↑ a b Cite error: Invalid <ref> tag; no text was provided for refs named Wickes_1987
  45. ↑ a b Cite error: Invalid <ref> tag; no text was provided for refs named RPLMAN
  46. ↑ a b Cite error: Invalid <ref> tag; no text was provided for refs named Wessman_2016
  47. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named HP_Calc
  48. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named HP_Evolves
  49. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Shirriff_2013
  50. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Sharwood_2013
  51. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Commodore_SR4921R
  52. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Prinztronic
  53. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Elektronika_B3-21
  54. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Elektronika_MK-161
  55. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Elektronika_MK-61
  56. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named SEMICO
  57. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named RE_1972
  58. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Berger_1973
  59. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named MITS7400
  60. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named TKE_1976
  61. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Paul_2015
  62. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Bit_2014
  63. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Bit_2015
  64. ↑ https://forum.swissmicros.com/viewtopic.php?f=16&t=2939
  65. ↑ https://forum.swissmicros.com/viewtopic.php?f=15&t=2845
  66. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Adobe_1986_PLTC
  67. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Adobe_PLRM3
  68. ↑ Script error: No such module "citation/CS1".
  69. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Born_2001_WKS
  70. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Born_2001_WK3
  71. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Feichtinger_1987
  72. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Wostrack_1989
  73. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Dietrich_2019


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