<?php

namespace alveolata\math;


/**
 * modulo operator
 * 
 * @author Christian Fraß <frass@greenscale.de>
 */
function mod(
	int $number,
	int $modulus
) : int
{
	// return (x - (div(x, y) * y));
	if ($modulus <= 0) {
		throw (new \Exception('invalid divisor'));
	}
	else {
		return (
			($number >= 0)
			? ($number%$modulus)
			: (($modulus-((-$number)%$modulus))%$modulus)
		);
	}
}


/**
 * computes the power of a number in a residue class ring via square and multiply
 * 
 * @author Christian Fraß <frass@greenscale.de>
 */
function modpow(
	int $base,
	int $exponent,
	int $modulus
) : int
{
	if ($exponent === 0) {
		return 1;
	}
	else {
		$a = modpow($base, $exponent >> 1, $modulus);
		$a = mod(($a * $a), $modulus);
		if (($exponent & 1) != 0) {
			$a = mod(($a * $base), $modulus);
		}
		return $a;
	}
}


/**
 * @template TypeElement
 * @param \Closure {function<pair<type_element,type_element>,boolean>}
 * @param array $set1 {list<type_element>}
 * @param array $set2 {list<type_element>}
 * @return array {list<type_element>}
 * @author Christian Fraß <frass@greenscale.de>
 */
function set_sub/*<type_element>*/(
	\Closure $collation,
	array $set1,
	array $set2
) : bool
{
	foreach ($set1 as $element1) {
		$present = false;
		foreach ($set2 as $element2) {
			if ($collation($element1, $element2)) {
				$present = true;
				break;
			}
		}
		if (! $present) {
			return false;
			break;
		}
	}
	return true;
}


/**
 * @param \Closure function<pair<type_element,type_element>,boolean>
 * @param array $set1 {list<type_element>}
 * @param array $set2 {list<type_element>}
 * @return array {list<type_element>}
 * @author Christian Fraß <frass@greenscale.de>
 */
function set_union/*<type_element>*/(
	\Closure $collation,
	array $set1,
	array $set2
) : array
{
	$set3 = [];
	foreach ([$set1, $set2] as $source) {
		foreach ($source as $element) {
			$add = true;
			foreach ($set3 as $element_) {
				if ($collation($element, $element_)) {
					$add = false;
					break;
				}
			}
			if ($add) {
				array_push($set3, $element);
			}
		}
	}
	return $set3;
}


/**
 * @param \Closure function<pair<type_element,type_element>,boolean>
 * @param array $set1 {list<type_element>}
 * @param array $set2 {list<type_element>}
 * @return array {list<type_element>}
 * @author Christian Fraß <frass@greenscale.de>
 */
function set_intersection/*<type_element>*/(
	\Closure $collation,
	array $set1,
	array $set2
) : array
{
	$set3 = [];
	foreach ($set1 as $element1) {
		$add = false;
		foreach ($set2 as $element2) {
			if ($collation($element1, $element2)) {
				$add = true;
				break;
			}
		}
		if ($add) {
			array_push($set3, $element1);
		}
	}
	return $set3;
}


/**
 * @param \Closure function<pair<type_element,type_element>,boolean>
 * @param array $set1 {list<type_element>}
 * @param array $set2 {list<type_element>}
 * @return array {list<type_element>}
 * @author Christian Fraß <frass@greenscale.de>
 */
function set_difference/*<type_element>*/(
	\Closure $collation,
	array $set1,
	array $set2
) : array
{
	$set3 = [];
	foreach ($set1 as $element1) {
		$add = true;
		foreach ($set2 as $element2) {
			if ($collation($element1, $element2)) {
				$add = false;
				break;
			}
		}
		if ($add) {
			array_push($set3, $element1);
		}
	}
	return $set3;
}


/**
 * applies the lexicographic order
 * 
 * @template type_element
 * @param order Closure {function<type_element,type_element,boolean>}
 * @param array $list1 {list<type_element>}
 * @param array $list2 {list<type_element>}
 * @return boolean
 * @author Christian Fraß <frass@greenscale.de>
 */
function order_lexicographic(
	\Closure $order,
	array $list1,
	array $list2
) : bool
{
	if (empty($list1)) {
		if (empty($list2)) {
			return true;
		}
		else {
			return true;
		}
	}
	else {
		if (empty($list2)) {
			return false;
		}
		else {
			$le = $order($list1[0], $list2[0]);
			$ge = $order($list2[0], $list1[0]);
			if (! $le) {
				if (! $ge) {
					// impossible: badly defined order
				}
				else {
					return false;
				}
			}
			else {
				if (! $ge) {
					return true;
				}
				else {
					return order_lexicographic(
						$order,
						array_slice($list1, 1),
						array_slice($list2, 1)
					);
				}
			}
		}
	}
}

 ?>