Arithmetic Compiler

An Arithmetic Compiler built in Rust, utilizing Recursive Descent Parsing for AST creation and Postfix Notation for evaluation.

This project is designed for parsing, evaluating, and visualizing arithmetic expressions. It supports features like variable management, root finding, and plotting, making it a comprehensive tool for mathematical expression handling.

Table of Contents

• Features
• Getting Started
• Supported Tokens
• Usage Examples
  • Lexer
  • Parser and AST
  • Evaluation
  • Postfix Representation
  • Finding Roots
  • Plot
• Contributing

Features

• Lexical Analysis: Tokenizes arithmetic expressions for parsing.
• Parser: Constructs an Abstract Syntax Tree (AST) using Recursive Descent Parsing.
• AST Representation: Represents expressions hierarchically for evaluation.
• Evaluator: Computes the result of the AST using Postfix Notation and a stack-based approach.
• Variable Manager: Enables the use of variables by storing and retrieving their values.
• Root Finding: Calculates roots of functions within a given range using the Bisection Method.
• Plotting: Visualizes functions over a specified range using the custom evaluator.
• Error Handling: Provides detailed feedback for syntax, evaluation, and runtime errors.

Getting Started

Follow these steps to set up and run the project:

1. Clone the Repository

   git clone <repository-url>
   cd arithmetic

2. Run the Project

cargo run

Note: Make sure to have rust installed.

Supported Tokens

This compiler supports a variety of tokens for processing mathematical expressions. Below is a comprehensive list:

Literals:

• Numbers:
  • Integers (i64)
  • Floats (f64)

Identifiers:

• Variables: e.g., x, y

Operators:

• Arithmetic Operators:

  • + (Addition)
  • - (Subtraction)
  • * (Multiplication)
  • / (Division)
  • ^ (Exponentiation)

• Integer Division and Modulus:

  • div (Integer Division)
  • mod (Modulus)

Separators:

• Parentheses:

  • ( (Left Parenthesis)
  • ) (Right Parenthesis)

Mathematical Functions:

• Trigonometric Functions:
  • sin, cos, tan, cotan
• Inverse Trigonometric Functions:
  • arcsin, arccos, arctan, arccotan
• Logarithmic and Exponential Functions:
  • ln Natural Logarithm
  • log Logarithm
  • exp Exponential Function
• Square and Square Root:
  • sqrt Square Root
  • sqr Square

Constants:

• Mathematical Constants:
  • e Euler’s Number
  • π Pi

Special Tokens:

• Eof: End of input.

Usage Examples

Lexer

The input is tokenized by the lexer.

Sample Input:

2 + 3^2 + cos(x)

Sample Output:

Lexer Output. Token Stream:
Token: Number(Integer(2))
  Span: TextSpan { start: 0, end: 1, literal: "2", line: 1, column: 0 }

Token: Plus
  Span: TextSpan { start: 2, end: 3, literal: "+", line: 1, column: 2 }

Token: Number(Integer(3))
  Span: TextSpan { start: 4, end: 5, literal: "3", line: 1, column: 4 }

Token: Power
  Span: TextSpan { start: 5, end: 6, literal: "^", line: 1, column: 5 }

Token: Number(Integer(2))
  Span: TextSpan { start: 6, end: 7, literal: "2", line: 1, column: 6 }

Token: Plus
  Span: TextSpan { start: 8, end: 9, literal: "+", line: 1, column: 8 }

Token: Cos
  Span: TextSpan { start: 10, end: 13, literal: "cos", line: 1, column: 10 }

Token: LeftParen
  Span: TextSpan { start: 13, end: 14, literal: "(", line: 1, column: 13 }

Token: Identifier("x")
  Span: TextSpan { start: 14, end: 15, literal: "x", line: 1, column: 14 }

Token: RightParen
  Span: TextSpan { start: 15, end: 16, literal: ")", line: 1, column: 15 }

Parser and AST

The parser constructs an Abstract Syntax Tree (AST) using Recursive Descent Parsing (RDP).

Sample Input:

2 + 3^2 + cos(x)

Sample Output:

└── +
    ├── +
    │   ├── 2
    │   └── ^
    │       ├── 3
    │       └── 2
    └── cos
        └── x

Evaluation

Evaluates the expression using a variable manager and Postfix Notation.

Sample Input:

2 + 3^2 + cos(x)

Prompt:

Please Enter the value for x:
> 180

Sample Output:

Evaluation result: 10

Postfix representation

Generates the Postfix Notation String from the AST.

Sample Input:

2 + 3^2 + cos(x)

Sample Output:

2 3 2 ^ + x cos + 

Finding roots

Determines the roots of a function within a specified range using the Bisection Method.

Sample Input:

sin(x)

Prompt:

Please Enter the value for a:
> -180

Please Enter the value for b:
> 180

Sample Output:

Roots: -180.000, 0.000, 180.000

Plot

Plots the function within the specified range.

Sample Input:

sin(x)

Prompt

Please Enter the value for a:
> -180

Please Enter the value for b:
> 180

Sample Output:

A plot image is generated and saved in the plot directory.

contributors

• Amirhossein Edadi
• Amin Owrang Pour
• Amin Sheikh Azimi