Integer Magnitude Upper Bound Calculator

This project implements a numerical algorithm in C that determines the Magnitude Upper Bound of a given integer. It calculates the largest possible integer value that shares the same number of digits as the input.

🧮 Mathematical Concept

For any integer $x$, let $d$ be the number of digits (magnitude). The algorithm constructs the maximum value $M$ such that:

$$M = \sum_{i=0}^{d-1} 9 \times 10^i = 10^d - 1$$

This represents the "ceiling" value for that specific digit class (e.g., for any 3-digit number, the ceiling is 999).

⚙️ Algorithm Logic

1. Input Normalization: Handles negative inputs by converting them to absolute values (abs).
2. Digit Analysis:
   • Checks edge case $0$ (1 digit).
   • Uses a logarithmic approach (iterative division by 10) to count digits: $d = \lfloor \log_{10}|x| \rfloor + 1$.
3. Output Generation:
   • Instead of using pow() functions (which can be computationally expensive), it uses a linear loop to print the character '9', $d$ times.

🚀 Usage Example

Input:  1253  (4 digits)
Logic:  Capacity = 4 -> Generate '9' x 4
Output: 9999

Input:  -50   (2 digits)
Logic:  Capacity = 2 -> Generate '9' x 2
Output: 99