English | 简体中文

---

Arbitrary Precision Rational Arithmetic Calculator

📖 Introduction

A GUI calculator built with C++17 and Qt6 that supports arbitrary-precision rational number arithmetic. It utilizes a custom BigInt class (linked-list-based arbitrary precision integer) and a Rational class built on top of it for exact fraction arithmetic with no precision loss.

✨ Key Features

• Arbitrary-precision integer: Linked list (DigitNode) storage, theoretically limited only by memory
• Exact rational arithmetic: Always stored and computed as fractions, automatically reduced
• Multiple input formats: Integers, decimals, fractions (a/b), and scientific notation
• Dual display: Results shown as both fractions and decimals
• Modern Qt GUI: Fusion style, clean layout, friendly interaction

---

📁 Project Structure

├── main.cpp                # Entry point
├── CalculatorWidget.h      # Calculator UI header
├── CalculatorWidget.cpp    # Calculator UI implementation
├── Storage.h               # Linked list node + BigInteger/BigRational (reference)
├── BigInt.h                # Arbitrary-precision integer (header-only)
├── Rational.h              # Rational number class (header-only)
├── CMakeLists.txt          # CMake build configuration
└── PLAN.md                 # Development plan

---

🔧 Build & Run

Dependencies

• CMake ≥ 3.16
• C++17 compatible compiler (GCC, Clang, MSVC)
• Qt 6 (Core + Widgets modules)

Build Steps

cd ArbitraryRationalCalculator
mkdir build && cd build
cmake ..
cmake --build .
./ArbitraryRationalCalculator

Windows Users: Make sure Qt6 is in your system PATH, or use Visual Studio's CMake integration.

macOS Users: If Qt6 is installed via Homebrew, use cmake .. -DCMAKE_PREFIX_PATH=$(brew --prefix qt6).

---

⌨️ Input Formats

Format	Example	Description
Integer	12345678901234567890	Arbitrary length integer
Decimal	3.14159265358979323846	Arbitrary precision decimal, auto-converted to fraction
Fraction	1/2	Numerator/Denominator, auto-reduced
Scientific	1.23e-5	Supports positive and negative exponents

Notes: Denominator must not be zero; divisor must not be zero for division; whitespace is automatically ignored.

---

⚙️ Technical Implementation

BigInt (Arbitrary-Precision Integer)

The BigInt class uses a little-endian linked list to store each digit (0–9). Each DigitNode holds one digit and a pointer to the next higher digit.

• Base unit: BASE = 1e9 (stores 9 decimal digits per element in to_vec())
• Core algorithms:
  • Addition / Subtraction: column addition/subtraction on vector representation
  • Multiplication: double loop column multiplication
  • Division: binary search trial quotient method
  • normalize(): auto-reduction using Euclidean algorithm (GCD)
• Operator overloads: Full set of comparison, arithmetic, and compound assignment operators

Rational

The Rational class builds upon BigInt to represent rational numbers exactly as numerator/denominator fractions. Automatically reduced on construction, results always simplified, supports decimal conversion via toDecimalString(int precision).

GUI (Qt Widgets)

Two QLineEdit widgets for operands, QComboBox for operator selection, results displayed as both fraction and decimal, custom stylesheet.

---

🎯 Use Cases

• Applications requiring exact large integer and fraction arithmetic
• Educational demonstrations of big number algorithms, fraction arithmetic, and Qt GUI programming
• Any calculation exceeding the limits of native C++ integer types (e.g., int64_t)