RPX: RPN eXtended Calculator

Table of Contents

1. Installation
2. Introduction
3. Basic Concepts
4. Modes of Operation
5. Input Format
6. Operators and Functions
7. Special Features
8. Commands
9. Examples
10. Error Handling
11. Advanced Topics

Installation

$ sudo make install

Introduction

RPX (RPN eXtended) is a powerful calculator that uses Reverse Polish Notation (RPN). It supports real, complex, and matrix calculations, offering a wide range of mathematical operations and functions.

Basic Concepts

• Uses Reverse Polish Notation (RPN)
• No parallel processing
• No GUI
• Low keystrokes

Modes of Operation

RPX offers four modes of operation:

1. Real Number Mode (default)
   • Supports floating-point operations and transcendental functions
2. Complex Number Mode
   • Toggle with :tc command
   • Supports complex number operations
   • Supports matrix operations

Input Format

• Use spaces to separate numbers and operators
• Negative numbers: Use 'm' operator (e.g., 5 m for -5)
• Decimal numbers are supported
• Complex numbers: Use 'i' operator (e.g., 3m 4 i + for -3+4i)
• Polar coordinates: Use 'p' operator (e.g., 1(\P2/)p for 1i)
• Matrices: Use [columns elements,] format (e.g., [2 1,2,3,4,] for a 2x2 matrix)
• Spaces are required only to delimit numbers (e.g., 5 3m4i+ for 5-3+4i)

Operators and Functions

Basic Arithmetic Operators

• + (addition), - (subtraction), * (multiplication), / (division)
• % (modulo), ^ (exponentiation)

Unary Functions

• A (absolute value)
• m (negate)
• i (multiply by i, for complex mode)

Trigonometric Functions

• s (sin), c (cos), t (tan)
• as (asin), ac (acos), at (atan)

Hyperbolic Functions

• hs (sinh), hc (cosh), ht (tanh)

Logarithmic Functions

• l2 (log2), lc (log10), le (ln)
• L (custom base log)

Rounding Functions

• C (ceil), F (floor), R (round)

Angle Conversion Functions

• r (degree to radian), d (radian to degree)

Matrix Operation Functions

• ~ (Inverse Matrix)

Special Features

Constants

• \E: Euler's number
• \P: Pi

Variable Operations

• $ followed by a letter (a-z) for variable operations
• u to update variables (e.g., 3 5 + $x u for $x=3+5)

Random Number

• $R: Random number (0 to 1)

Function Operations

• ! followed by a letter (a-z) for function call

Builtin Operations (can be dangerous)

• @a: Reference to previous result (ANS)
• @h: Access to result history (e.g., 5 @h for 5 previous history)
• @p: Duplicate the top stack value
• @s: Access specific stack value (e.g., 5 @h for 5 previous stack value)

Other

• ( ): Specify the valid range of the operator
• ;: Start of a comment (ignored until end of line)

Commands

• :d[a-z(name)][1-9(argc)]: Define function
• :tc: Toggle between real and complex number mode
• :tp: Toggle between explicit and implicit function in plot
• :o: Optimize expression (e.g., remove unnecessary spaces)
• :p: Plot graph (argument is $1)

CommandLine Options

• -h: Show help
• -r: Evaluate following argument as expression
• -q: Quit Arguments whose first letter is not '-' are interpreted as file name.

Examples

1. Basic arithmetic: 3 4 + 2 * -> 14.000000
2. Using constants: \P 2 / s -> 1.000000 (sin(Pi/2))
3. Complex expression: 2 3 ^ (4 5 *) + (6 7 /) - -> 27.142857
4. Using previous result: 5 @a + -> Adds 5 to previous result
5. Complex mode: 3 4i + -> 3.000000 + 4.000000i
6. Matrix addition: [2 1,2,3,4,][2,4,5,6,7,]+ -> [2 5,7,9,11,]
7. Matrix inverse: [3 1,1,1m,2m,0,1,0,2,1,]~ -> [3 -0.5,-0.75,0.25,0.5,0.25,0.25,-1,-0.5,0.5,]
8. Plot fn: :p $1s -> Graph of sin(x)
9. Plot implicit fn: :p $12^($22^)+1- -> Circle of radius 1
10. Display help and exit: rpx -h -q
11. One-shot calculator: rpx -r "1 1 +" -q
12. One-shot graph plottor: rpx -r ":spr\\P,\\Pm,1,1m" -r ":p $1s" -q
13. Run script files: rpx sample1.rpx sample2.rpx sample3.rpx

Error Handling

• Unknown operators or functions result in an error message
• Division by zero and other mathematical errors are not explicitly handled
• NaN results are not displayed

Advanced Topics

Matrix Input Details

• First element is the number of columns
• Elements separated by commas
• End matrix with ,]
• Example: [2 1,2,3,4,] creates a 2x2 matrix [1 2; 3 4]