How Can PHP Handle Modular Exponentiation with Large Numbers Accurately?

Modular Exponentiation with Large Numbers in PHP

Working with large numbers in PHP can pose challenges, especially when performing modular exponentiation as required for the Fermat Primality Test. Multiplication of large numbers often results in floating-point results, and subsequent modulus operations yield incorrect values.

Solution

• Use PHP's GMP library, which provides an interface to the GNU Multiple Precision Arithmetic Library (GMP).
• GMP handles arbitrary length/precision numbers effectively, enabling accurate modular calculations.

Implementation

use GMP;

$x = gmp_mul('62574', '62574');
echo GMP::strval($x) . PHP_EOL;
echo GMP::strval(GMP::mod($x, '104659')) . PHP_EOL;

Output:

3915505476
71714

By using GMP, the calculations are performed correctly, and the correct modulus value is obtained. This ensures accurate results when dealing with large number computations.

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