Modular Arithmetic

A PHP libarary to support modular arithmetic, aka clock arithmetic.

Requirement

• PHP ^8.4

Installation

composer install marcoconsiglio/modular-arithmetic

Usage

Construct a modular integer with its modulus.

use Marcoconsiglio\ModularArithmetic\ModularInteger;

$hour_on_a_clock = 12;
$current_hour = new ModularInteger(15, $hour_on_a_clock);
echo "The current hour is $current_hour->value o'clock.";

The current hour is 3 o'clock.

Modular Arithmetic

Addition

You can add two ModularInteger: the sum will be a ModularInteger instance.

use Marcoconsiglio\ModularArithmetic\ModularInteger;

$hour_on_a_clock = 12;
$work_start = new ModularInteger(9, $hour_on_a_clock);
$working_time = new ModularInteger(9, $hour_on_a_clock);
$work_end = $work_start->add($working_time);
echo "I'm going to start to work at {$work_start->value} o'clock a.m.\n";
echo "I'll work for {$working_time->value} hours.\n";
echo "I'll finish to work at {$work_end->value} o'clock p.m.";

I'm going to start to work at 9 o'clock a.m.
I'll work for 9 hours.
I'll finish to work at 6 o'clock p.m.

Multiplication

You can multiply two ModularInteger: the product will be a ModularInteger instance.

use Marcoconsiglio\ModularArithmetic\ModularInteger;

$hours_in_a_day = 24;
$start_shift = new ModularInteger(0, $hours_in_a_day); /* midnight */
$shift_duration = new ModularInteger(3, $hours_in_a_day);
$my_shift = new ModularInteger(5, $hours_in_a_day); /* 5th turn */
$time_to_wait = $shift_duration->multiply($my_shift);
$my_shift_start = $start_shift->add($time_to_wait);
echo "There is a new guard shift every {$shift_duration->value} hours.\n";
echo "My shift, starts at {$my_shift_start->value} o'clock.";

There is a new guard shift every 3 hours.
My shift, the 5th, starts at 15 o'clock.

Exponentiation

You can raise to power $k$ a ModularInteger: the result will be a ModularInteger instance.

use Marcoconsiglio\ModularArithmetic\ModularInteger;

$alphabet_lenght = 26;
$alphabet_set = range('A', 'Z');
$message = ['H', 'E', 'L', 'L', 'O'];
$encrypted_message = [];
$cypher_key = 3;
echo "Encrypting the message:\n";
echo implode("", $message)."\n";
foreach ($message as $char) {
    $unencrypted_index = new ModularInteger(
        array_search($char, $alphabet_set),
        $alphabet_lenght
    );
    $encrypted_index = $unencrypted_index->power($cypher_key);
    $encrypted_message[] = $alphabet_set[$encrypted_index->value];
}
echo "Encrypted message:\n";
echo implode("", array: $encrypted_message);

Encrypting the message:
HELLO
Encrypted message:
FMFFO

Error Exceptions

DifferentModulusError

This error is thrown when you try to perform an arithmetic operation using two ModularInteger with different modulus.

use Marcoconsiglio\ModularArithmetic\ModularInteger;

$a = new ModularInteger(3, 7);
$b = new ModularInteger(5, 12);
$sum = $a->add($b); // Throws DifferentModulusError

Marcoconsiglio\ModularArithmetic\Exceptions\DifferentModulusError: Different modules cannot be used (7 and 12).

IntegerOverflowError

This error is thrown when the value of a ModularInteger cannot be stored in a int type variable because it's too large.

use Marcoconsiglio\ModularArithmetic\ModularInteger;

$a = new ModularInteger(100, 1000);
$sum = $a->power(100); // Throws IntegerOverflowError

Marcoconsiglio\ModularArithmetic\Exceptions\IntegerOverflowError: The number 1.0E+200 exceeds the max integer value of 9223372036854775807 on this system.