TRURL RPN Engine

TRURL Reverse Polish Notation for Object Pascal RPN Engine Lazarus and Free Pascal Edition Version 1.2 Document version 1.2.0 2025-10-20 Johannes W. Dietrich 2 TRURL RPN engine The TRURL RPN engine is a library of Object Pascal types, classes and procedures that can be used as a foundation for virtual calculators using Reverse Polish Notation (RPN). The unit “rpnengine.pas” is the basis of the library. It is necessary for all projects using the RPN engine and sufficient for both command-line and text-mode user interfaces. For applications based on a graphical user interface (GUI), the optional unit “rpnwidgets.pas” provides additional functionality that facilitates linking to predefined interface elements. About Reverse Polish Notation Reverse Polish Notation, abbreviated RPN, also known as Polish postfix notation or postfix notation, is a mathematical notation in which operators follow their operands. It dates back to the older Polish Notation, which was proposed in 1924 by the philosopher, mathematician, and logician Jan Łukasiewicz. For programming computers and calculators, RPN has many advantages over the more common algebraic notation, since it makes parentheses unnecessary and saves time and keystrokes. Additionally, it facilitates the detection and correction of errors. These reasons motivated producers of advanced scientific calculators, including Hewlett-Packard (HP), Elektronika, Semico, SwissMicros and others to base their models on RPN logic. RPN is also used by some well-known software packages, including dc, xcalc, RPL and Calc in Emacs, and by stack-oriented programming languages, e.g. Forth and PostScript. More information on RPN is available from: https://www.calculator.org/articles/Reverse_Polish_Notation.html http://www.hp-prime.de/files/composite_file/file/192-hp_rpn_en.pdf https://www.hpmuseum.org/rpn.htm https://en.wikipedia.org/wiki/Reverse_Polish_notation TRURL RPN engine 3 Unit rpnengine.pas The basic unit rpnengine.pas is required for every project, regardless of whether or not it uses a graphical user interface (GUI). It provides the following constants, types, data structures, classes and functions: Basic types TBinOperator = (PlusOp, MinusOp, MultOp, DivOp, PowerOp); TUniOperator = (PlusMinusOp, InvertOp, SinOp, CosOp, TanOp, ASinOp, ACosOp, ATanOp, sqrOp, sqrtOp); TAngleMode = (Degree, Radian, Turn, Grad); These global types are necessary for the engine, but also usable by your code. TUniOperator and TBinOperator represent unary and binary operators, respectively, which are used by TEngine.rpn. TAngleMode determines the mode by which angles are encoded. Global constants Version information: RPNEngine_major = 1; RPNEngine_minor = 2; RPNEngine_release = 0; RPNEngine_patch = 0; RPNEngine_fullversion = ((RPNEngine_major * 100 + RPNEngine_minor) * 103 + RPNEngine_release) * 100 + RPNEngine_patch; RPNEngine_version = '1.2.0.103; RPNEngine_internalversion = 'Gimel'; 4 TRURL RPN engine TStack TStack = class private {private fields} protected {protected fields and methods} public constructor create; destructor destroy; override; procedure Clear; procedure RollDown; procedure DropDown; procedure RollUp; procedure Push(operand: extended); function Pop: extended; procedure Error(msg: String); public property x: extended read fx write fx; property y: extended read fy; property z: extended read fz; property t: extended read ft; property lastx: extended read fl; end; TStack implements a virtual stack with four registers (x, y, z and t) and a special lastx register, which holds the content of the x register as it was before execution of certain operations. T 7.89 Z 4.56 Y 3.14 X 1.23 (Shown in the display by most calculators) L 1.23 TStack.Clear clears the virtual stack. This method sets all registers to 0. T 0.00 Z 0.00 Y 0.00 X 0.00 L 0.00 TRURL RPN engine 5 TStack.Rolldown rolls the registers in the virtual stack down and recycles the contents of the x register in the t register. T 7.89 ↓↑# ➡ T 1.23 Z 4.56 Z 7.89 Y 3.14 Y 4.56 X 1.23 X 3.14 L 1.23 L 1.23 TStack.DropDown drops the registers in the virtual stack down. It does not recycle contents, so that the t register receives the value 0. T 7.89 ⤓ ➡ T 0.00 Z 4.56 Z 7.89 Y 3.14 Y 4.56 X 1.23 X 3.14 L 1.23 L 1.23 TStack.Rollup rolls the registers in the virtual stack up. This method copies the contents of the x register to the y register. T 7.89 ↑# ➡ T 4.56 Z 4.56 Z 3.14 Y 3.14 Y 1.23 X 1.23 X 1.23 L 1.23 L 1.23 TStack.Push pushes the content of an operand to the stack, i.e. the x register gets the value of the operand and the stack is lifted. T 7.89 ↑# ➡ T 4.56 Z 4.56 Z 3.14 Y 3.14 Y 1.23 Operand: 2.72 ➡ X 1.23 X 2.72 L 1.23 L 1.23 6 TRURL RPN engine TStack.Pop delivers the contents of the x register and drops down the stack. T 7.89 ⤓# ➡ T 0.00 Z 4.56 Z 7.89 Y 3.14 Y 4.56 Result: 1.23 ⬅ X 1.23 X 3.14 L 1.23 L 1.23 TStack.Error is predominantly employed by the engine itself for reporting error conditions, but also usable by your code. TEngine TEngine = class public Stack: TStack; AngleMode: TAngleMode; constructor create; destructor destroy; override; procedure Add; procedure Sub; procedure Times; procedure Divide; procedure CHS; procedure Inv; procedure PWR; procedure Sinus; procedure Cosinus; procedure Tangens; procedure ArcSinus; procedure ArcCosinus; procedure ArcTangens; procedure sqr; procedure sqroot; function rpn(operand1, operand2: extended; binOp: TBinOperator): extended; function rpn(operand: extended; uniOp: TUniOperator): extended; end; TEngine is a class, which implements a virtual calculation engine. It provides the following variables and methods: TRURL RPN engine 7 TEngine.Stack refers to the engine’s stack object (of type TStack). It is automatically created by the create method of TEngine and cleared if the engine object is destroyed. TEngine.AngleMode is a global variable, which holds the mode of encoding angles. Its default value is Degree. TEngine.Add adds the two numbers in the x and y registers and stores the result in the x register. The lastx register is supported. TEngine.Sub subtracts the two numbers in the y and x registers and stores the result in the x register. The lastx register is supported. TEngine.Times multiplies the two numbers in the x and y registers and stores the result in the x register. The lastx register is supported. TEngine.Divide divides the two numbers in the y and x registers and stores the result in the x register. The lastx register is supported. TEngine.CHS toggles the sign of the number in the x register. TEngine.Inv inverts the number in the x register. The lastx register is supported. TEngine.PWR raises the number in the y register to that in the x register and stores the result in the x register. TEngine.Sinus calculates the sine of the number in the x register. The result depends on the value in the TEngine.AngleMode variable. The lastx register is supported. TEngine.Cosinus calculates the cosine of the number in the x register. The result depends on the value in the TEngine.AngleMode variable. The lastx register is supported. TEngine.Tangens calculates the tangent value of the number in the x register. The result depends on the value in the TEngine.AngleMode variable. The lastx register is supported. TEngine.ArcSinus calculates the inverse sine of the number in the x register. The result depends on the value in the TEngine.AngleMode variable. The lastx register is supported. TEngine.ArcCosinus calculates the inverse cosine of the number in the x register. The result depends on the value in the TEngine.AngleMode variable. The lastx register is supported. TEngine.ArcTangens calculates the inverse tangent value of the number in the x register. The result depends on the value in the TEngine.AngleMode variable. The lastx register is supported. 8 TRURL RPN engine TEngine.sqr delivers the square of the number in the x register. The lastx register is supported. TEngine.sqroot calculates the square root of the number in the x register. The lastx register is supported. The function TEngine.rpn is a polymorphic function, which accepts operands and operators, and calculates the result, which is returned as a floating point number of type extended. The two variants TEngine.rpn(operand1, operand2: extended; binOp: TBinOperator) and TEngine.rpn(operand: extended; uniOp: TUniOperator) use the following binary and unary operators: PlusOp: returns the sum of operand1 and operand2. MinusOp: calculates the difference of operand1 and operand2. MultOp: returns the product of operand1 and operand2. DivOp: calculates the ratio of operand1 and operand2. PowerOp: returns operand1 raised to the power of operand2. PlusMinusOp: toggles the sign of operand. InvertOp: inverts operand. SinOp: returns the sine of operand. CosOp: calculates the cosine of operand. TanOp: delivers the tangent of operand. ASinOp: returns the inverse sine of operand. ACosOp: calculates the inverse cosine of operand. ATanOp: delivers the inverse tangent of operand. sqrOp: returns the square of operand. sqrtOp: calculates the square root of operand. TRURL RPN engine 9 Unit rnpwidgets.pas The unit rpnwidgets.pas helps to create a GUI-based virtual calculator: Types TEntryMode = (PostOper, PostEnter, Number); TFrame TFrame = class private {private fields} public Engine: TEngine; TRegDisplay, ZRegDisplay, YRegDisplay, XRegDisplay: TControl; EntryMode: TEntryMode; ReplaceXAfterRollDown: boolean; constructor create; destructor destroy; override; procedure HandleEnter; procedure HandleClear; procedure HandleInv; procedure HandleAdd; procedure HandleSub; procedure HandleTimes; procedure HandleDiv; procedure HandleCHS; procedure HandlePWR; procedure HandleSin; procedure HandleCos; procedure HandleTan; procedure HandleASin; procedure HandleACos; procedure HandleATan; procedure HandleSqr; procedure HandleSqrt; procedure HandleRollDown; procedure DisplayRegisters; procedure AppendChar(ch: char); procedure InsertString(theString: String); procedure CheckEngine; procedure Error(msg: String); end; TFrame provides an object-oriented approach for creating a GUI-based calculator with the following objects and methods: