Infix notation
40-547: The HP-42S RPN Scientific is a programmable RPN Scientific hand held calculator introduced by Hewlett-Packard in 1988.It is a popular calculator designed for science and engineering students. Perhaps the HP-42S was to be released as a replacement for the aging HP-41 series as it is designed to be compatible with all programs written for the HP-41. Since it lacked expandability, and lacked any real I/O ability, both key features of
80-434: 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
120-479: 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
160-435: 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
200-533: 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
240-448: A projectivity when b ⊼ c . {\displaystyle b\ \barwedge \ c.} Infix notation is more difficult to parse by computers than prefix notation (e.g. + 2 2) or postfix notation (e.g. 2 2 + ). However many programming languages use it due to its familiarity. It is more used in arithmetic, e.g. 5 × 6. Infix notation may also be distinguished from function notation, where
280-432: A reverse Polish notation variant later referred to as three-level RPN . This calculator popularized reverse Polish notation among the scientific and engineering communities. 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,
320-562: Is also based on reverse Polish notation. 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 Enter ↑ key and top register copies on pops, but switchable between
360-426: 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
400-422: Is in a subroutine in which case it returns to the caller). Keystrokes (of functions) are enclosed between LBL and RTN or .END . In a running program, a GTO label causes program execution to branch to the specified label and continue running at that line.Executing a GTO instruction from the keyboard moves the program pointer to the corresponding label. No program lines are executed. XEQ
440-449: Is sometimes known as entry 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,
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#1733094044363480-467: 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 (3 + 4) × (5 + 6) becomes 3 4 + 5 6 + × in reverse Polish notation. Reverse Polish notation has been compared to how one had to work through problems with
520-461: Is used in much the same way with one important difference: after an XEQ instruction has transferred execution to the specified label, the next RTN (return) or END instruction causes the program to branch back to the instruction that immediately follows the XEQ instruction.Programs/Subroutines can also be executed with the help XEQ label (Execute) key. Important Difference is that XEQ executes
560-526: The Enter ↑ 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
600-487: The Enter ↑ 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
640-647: 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
680-494: 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,
720-763: 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. 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
760-564: The Minuteman *6 (MM6) without an Enter ↑ key and the Minuteman *6X (MM6X) with an Enter ↑ 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 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
800-501: 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
840-455: The nationality of logician Jan Łukasiewicz , who invented Polish notation in 1924. The first computer to use postfix notation, though it long remained essentially unknown outside of Germany, was Konrad Zuse 's Z3 in 1941 as well as his Z4 in 1945. The reverse Polish scheme was again proposed in 1954 by Arthur Burks , Don Warren, and Jesse Wright and was independently reinvented by Friedrich L. Bauer and Edsger W. Dijkstra in
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#1733094044363880-524: The plus sign in 2 + 2 . Binary relations are often denoted by an infix symbol such as set membership a ∈ A when the set A has a for an element. In geometry , perpendicular lines a and b are denoted a ⊥ b , {\displaystyle a\perp b\ ,} and in projective geometry two points b and c are in perspective when b ⩞ c {\displaystyle b\ \doublebarwedge \ c} while they are connected by
920-438: The 2020s. In computer science , reverse Polish notation is used in stack-oriented programming languages such as Forth , dc , Factor , STOIC , PostScript , RPL , and Joy . 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 4 − 5 + in reverse Polish notation: 4
960-653: The 42S ended in 1995. The HP-42S is keystroke-programmable , meaning that it can remember and later execute sequences of keystrokes to solve particular problems of interest to the user. The HP-42S uses a superset of the HP-41CX FOCAL language. All programs are stored in one continuous program space, and may be created and edited by switching to programming mode, using the PRGM key. Subroutines are enclosed in LBL /Label (name of subroutine) and RTN /Return ( halts execution unless it
1000-1088: 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
1040-464: The HP-41 series, it was marketed as an HP-15C replacement. The 42S, however, has a much smaller form factor than the 41, and features many more built-in functions, such as a matrix editor, complex number support, an equation solver , user-defined menus, and basic graphing capabilities (the 42S can draw graphs only by programs). Additionally, it features a two-line dot matrix display, which made stack manipulation easier to understand. Production of
1080-446: The calculator models 12C, 12C Platinum, 17bII+ , 20b , 30b , 33s , 35s , 48gII (RPL) and 50g (RPL) which support reverse Polish notation. 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 Enter ↑ key behaves as in RPL. This latter variant
1120-459: 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
1160-748: 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. 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"),
1200-401: 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. 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
1240-516: 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. 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
HP-42S - Misplaced Pages Continue
1280-468: The label and returns to previous subroutine and continues execution from the line following XEQ ,whereas GOTO branches to the label specificied and doesn't return back. GTO . . packs the current subroutines and moves to new program space. GTO . nnnn can be used to reach a particular line of program. A simple program to calculate circumference of circle Program instructions like STOP , PROMPT , INPUT halt
1320-483: 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. In Britain, Clive Sinclair 's Sinclair Scientific (1974) and Scientific Programmable (1975) models used reverse Polish notation. In 1974, Commodore produced
1360-487: 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. 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
1400-432: The name of a function suggests a particular operation, and its arguments are the operands. An example of such a function notation would be S (1, 3) in which the function S denotes addition ("sum"): S(1, 3) = 1 + 3 = 4 . In infix notation, unlike in prefix or postfix notations, parentheses surrounding groups of operands and operators are necessary to indicate the intended order in which operations are to be performed. In
1440-434: The program execution,which can be continued by pressing R/S . VIEW is used to view contents of a register,For example R in the above example. It is necessary to write a program or subroutine that evaluates f(x) for the function which needs to be solved or integrated. Variables used in program should be declared using MVAR Here is a sample program to solve the equation °F = (9/5×°C) + 32 After, accessing
1480-433: The solver using Shift 7 ( SOLVER ),Select program TEMP . In a similar way,expressions can be integrated.After selecting the variable of integration,enter the lower limit and then press on LLIM , similarly input ULIM (upper limit) and ACC (accuracy). HP 42s can be accessed through Android Emulators like Emu42 and Free42 . WP 34S project uses a modern HP financial calculator HP 30b as
1520-400: 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 Enter ↑ 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
1560-636: The starting point to create an advanced scientific RPN calculator. It is a more powerful scientific (non-graphing) calculator compared to the original HP 42s. Functionality Programmability Reverse Polish Notation Infix notation 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
1600-466: Was incorporated as a selectable function into the DM42 since firmware DMCP-3.21 / DM42-3.18. Software calculators: Existing implementations using reverse Polish notation include: Infix notation Infix notation is the notation commonly used in arithmetical and logical formulae and statements. It is characterized by the placement of operators between operands —"infixed operators"—such as
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