| # Overflow-Safe Modular Multiplication | |
| ## Description | |
| Compute the signed modular product of two integers by repeated doubling without directly multiplying them. | |
| ## Input | |
| The function receives integers $a$, $b$, and a positive modulus. | |
| ## Output | |
| Return a representative congruent to $ab$ modulo the modulus. | |
| ## Constraints | |
| - $-modulus < a < modulus$. | |
| - `b` fits signed C `int`. | |
| - $0 < modulus$ and $2\,modulus \le \texttt{INT_MAX}$. | |
| ## Source | |
| Classical modular-arithmetic problem reconstructed from the verified C artifact. | |