Primitive-Collections/src/builder/resources/speiger/assets/collections/templates/utils/Arrays.template

package speiger.src.collections.PACKAGE.utils;

import java.util.Arrays;
import java.util.Random;
import java.util.concurrent.RecursiveAction;
#if !TYPE_OBJECT

import speiger.src.collections.PACKAGE.functions.COMPARATOR;
#else
import java.util.Comparator;

#endif
import speiger.src.collections.utils.SanityChecks;

/**
 * A Helper class for Arrays
 */
public class ARRAYS
{
	public static final int BASE_THRESHOLD = 16;
	public static final int PARALLEL_THRESHOLD = 8192;
	
#if !TYPE_OBJECT
	public static final KEY_TYPE[] EMPTY_ARRAY = new KEY_TYPE[0];
	
	/**
	 * A Helper function to convert a Primitive Array to a CLASS_TYPE Array.
	 * @param a the array that should be converted
	 * @return a CLASS_TYPE Array of the input array.
	 */
	public static CLASS_TYPE[] wrap(KEY_TYPE[] a) {
		return wrap(a, 0, a.length);
	}
	
	/**
	 * A Helper function to convert a Primitive Array to a CLASS_TYPE Array.
	 * @param a the array that should be converted
	 * @param length the maximum length that should be coverted
	 * @return a CLASS_TYPE Array of the input array.
	 */
	public static CLASS_TYPE[] wrap(KEY_TYPE[] a, int length) {
		return wrap(a, 0, length);
	}
	
	/**
	 * A Helper function to convert a Primitive Array to a CLASS_TYPE Array.
	 * @param a the array that should be converted
	 * @param offset the starting offset of the inputarray
	 * @param length the maximum length that should be coverted
	 * @return a CLASS_TYPE Array of the input array.
	 */
	public static CLASS_TYPE[] wrap(KEY_TYPE[] a, int offset, int length) {
		SanityChecks.checkArrayCapacity(a.length, offset, length);
		CLASS_TYPE[] result = new CLASS_TYPE[length];
		for(int i = offset;i<length;i++)
			result[i] = KEY_TO_OBJ(a[i]);
		return result;
	}
	
	/**
	 * A Helper function to convert a CLASS_TYPE Array to a KEY_TYPE Array.
	 * @param a the array that should be converted
	 * @return a KEY_TYPE Array of the input array.
	 */
	public static KEY_TYPE[] unwrap(CLASS_TYPE[] a) {
		return unwrap(a, 0, a.length);
	}
	
	/**
	 * A Helper function to convert a CLASS_TYPE Array to a KEY_TYPE Array.
	 * @param a the array that should be converted
	 * @param length the maximum length that should be coverted
	 * @return a KEY_TYPE Array of the input array.
	 */
	public static KEY_TYPE[] unwrap(CLASS_TYPE[] a, int length) {
		return unwrap(a, 0, length);
	}
	
	/**
	 * A Helper function to convert a CLASS_TYPE Array to a KEY_TYPE Array.
	 * @param a the array that should be converted
	 * @param offset the starting offset of the inputarray
	 * @param length the maximum length that should be coverted
	 * @return a KEY_TYPE Array of the input array.
	 */
	public static KEY_TYPE[] unwrap(CLASS_TYPE[] a, int offset, int length) {
		SanityChecks.checkArrayCapacity(a.length, offset, length);
		KEY_TYPE[] result = new KEY_TYPE[length];
		for(int i = offset;i<length;i++)
			result[i] = OBJ_TO_KEY(a[i]);
		return result;
	}
	
#else
	public static final Object[] EMPTY_ARRAY = new Object[0];
	
	/**
	 * Function to create a new Array of a given size
	 * @param clz the class type of array that is requested
	 * @param length the lenght the array should be.
	 * @return a Array with the requested type and length
	 */
	public static GENERIC_KEY_BRACES KEY_TYPE[] newArray(Class<KEY_TYPE> clz, int length) {
		if(clz == Object.class) return (KEY_TYPE[])new Object[length];
		return (KEY_TYPE[]) java.lang.reflect.Array.newInstance(clz, length);
	}
	
#endif
	public static GENERIC_KEY_BRACES int shiftDown(KEY_TYPE[] data, int size, int index, COMPARATOR KEY_SUPER_GENERIC_TYPE comp) {
		int half = size >>> 1;
		KEY_TYPE value = data[index];
		if(comp != null) {
			while(index < half) {
				int child = (index << 1) + 1;
				KEY_TYPE childValue = data[child];
				int right = child+1;
				if(right < size && comp.compare(data[right], childValue) < 0) childValue = data[child = right];
				if(comp.compare(value, childValue) <= 0) break;
				data[index] = childValue;
				index = child;
			}
		}
		else {
			while(index < half) {
				int child = (index << 1) + 1;
				KEY_TYPE childValue = data[child];
				int right = child+1;
				if(right < size && COMPAREABLE_TO_KEY(data[right], childValue) < 0) childValue = data[child = right];
				if(COMPAREABLE_TO_KEY(value, childValue) <= 0) break;
				data[index] = childValue;
				index = child;
			}
		}
		data[index] = value;
		return index;
	}
	
	public static GENERIC_KEY_BRACES int shiftUp(KEY_TYPE[] data, int index, COMPARATOR KEY_SUPER_GENERIC_TYPE comp) {
		KEY_TYPE value = data[index];
		if(comp != null) {
			while(index > 0) {
				int parent = (index - 1) >>> 1;
				KEY_TYPE parentValue = data[parent];
				if(comp.compare(value, parentValue) >= 0) break;
				data[index] = parentValue;
				index = parent;
			}
		}
		else {
			while(index > 0) {
				int parent = (index - 1) >>> 1;
				KEY_TYPE parentValue = data[parent];
				if(COMPAREABLE_TO_KEY(value, parentValue) >= 0) break;
				data[index] = parentValue;
				index = parent;
			}
		}
		data[index] = value;
		return index;
	}
	
	public static GENERIC_KEY_BRACES KEY_TYPE[] heapify(KEY_TYPE[] data, int size, COMPARATOR KEY_SUPER_GENERIC_TYPE comp) {
		for(int i = (size >>> 1) - 1;i>=0;shiftDown(data, size, i--, comp));
		return data;
	}
	
	public static GENERIC_KEY_BRACES KEY_TYPE[] shuffle(KEY_TYPE[] array) {
		return shuffle(array, SanityChecks.getRandom());
	}
	
	public static GENERIC_KEY_BRACES KEY_TYPE[] shuffle(KEY_TYPE[] array, Random random) {
		for(int i = array.length-1; i>=0;i--) {
			int p = random.nextInt(i + 1);
			KEY_TYPE t = array[i];
			array[i] = array[p];
			array[p] = t;
		}
		return array;
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator,
	 * potentially dynamically choosing an appropriate algorithm given the type and size of the array.
	 * Stable sort referres to Mergesort or Insertionsort
	 * @param array the array that needs to be sorted
	 * @param comp the Comparator that decides the sorting order
	 */
	public static GENERIC_KEY_BRACES void stableSort(KEY_TYPE[] array, COMPARATOR KEY_GENERIC_TYPE comp) {
		stableSort(array, 0, array.length, comp);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator,
	 * potentially dynamically choosing an appropriate algorithm given the type and size of the array.
	 * Stable sort referres to Mergesort or Insertionsort
	 * @param array the array that needs to be sorted
	 * @param length the maxmium size of the array to be sorted
	 * @param comp the Comparator that decides the sorting order
	 */
	public static GENERIC_KEY_BRACES void stableSort(KEY_TYPE[] array, int length, COMPARATOR KEY_GENERIC_TYPE comp) {
		stableSort(array, 0, length, comp);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator,
	 * potentially dynamically choosing an appropriate algorithm given the type and size of the array.
	 * Stable sort referres to Mergesort or Insertionsort
	 * @param array the array that needs to be sorted
	 * @param from where the array should be sorted from
	 * @param to where the array should be sorted to
	 * @param comp the Comparator that decides the sorting order
	 */
	public static GENERIC_KEY_BRACES void stableSort(KEY_TYPE[] array, int from, int to, COMPARATOR KEY_GENERIC_TYPE comp) {
		mergeSort(array, null, from, to, comp);
	}
	
	/**
	 * Sorts an array according to the natural ascending order, 
	 * potentially dynamically choosing an appropriate algorithm given the type and size of the array.
	 * Stable sort referres to Mergesort or Insertionsort
	 * @param array the array that needs to be sorted
	 */
	public static COMPAREABLE_KEY_BRACES void stableSort(KEY_TYPE[] array) {
		stableSort(array, 0, array.length);
	}
	
	/**
	 * Sorts an array according to the natural ascending order, 
	 * potentially dynamically choosing an appropriate algorithm given the type and size of the array.
	 * Stable sort referres to Mergesort or Insertionsort
	 * @param array the array that needs to be sorted
	 * @param length the maxmium size of the array to be sorted
	 */
	public static COMPAREABLE_KEY_BRACES void stableSort(KEY_TYPE[] array, int length) {
		stableSort(array, 0, length);
	}
	
	/**
	 * Sorts an array according to the natural ascending order, 
	 * potentially dynamically choosing an appropriate algorithm given the type and size of the array.
	 * Stable sort referres to Mergesort or Insertionsort
	 * @param array the array that needs to be sorted
	 * @param from where the array should be sorted from
	 * @param to where the array should be sorted to
	 */
	public static COMPAREABLE_KEY_BRACES void stableSort(KEY_TYPE[] array, int from, int to) {
		mergeSort(array, null, from, to);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator,
	 * potentially dynamically choosing an appropriate algorithm given the type and size of the array.
	 * Unstable sort referres to QuickSort or SelectionSort
	 * @param array the array that needs to be sorted
	 * @param comp the Comparator that decides the sorting order
	 */
	public static GENERIC_KEY_BRACES void unstableSort(KEY_TYPE[] array, COMPARATOR KEY_GENERIC_TYPE comp) {
		unstableSort(array, 0, array.length, comp);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator,
	 * potentially dynamically choosing an appropriate algorithm given the type and size of the array.
	 * Unstable sort referres to QuickSort or SelectionSort
	 * @param array the array that needs to be sorted
	 * @param length the maxmium size of the array to be sorted
	 * @param comp the Comparator that decides the sorting order
	 */
	public static GENERIC_KEY_BRACES void unstableSort(KEY_TYPE[] array, int length, COMPARATOR KEY_GENERIC_TYPE comp) {
		unstableSort(array, 0, length, comp);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator,
	 * potentially dynamically choosing an appropriate algorithm given the type and size of the array.
	 * Unstable sort referres to QuickSort or SelectionSort
	 * @param array the array that needs to be sorted
	 * @param from where the array should be sorted from
	 * @param to where the array should be sorted to
	 * @param comp the Comparator that decides the sorting order
	 */
	public static GENERIC_KEY_BRACES void unstableSort(KEY_TYPE[] array, int from, int to, COMPARATOR KEY_GENERIC_TYPE comp) {
		quickSort(array, from, to, comp);
	}
	
	/**
	 * Sorts an array according to the natural ascending order, 
	 * potentially dynamically choosing an appropriate algorithm given the type and size of the array.
	 * Unstable sort referres to QuickSort or SelectionSort
	 * @param array the array that needs to be sorted
	 */
	public static COMPAREABLE_KEY_BRACES void unstableSort(KEY_TYPE[] array) {
		unstableSort(array, 0, array.length);
	}
	
	/**
	 * Sorts an array according to the natural ascending order, 
	 * potentially dynamically choosing an appropriate algorithm given the type and size of the array.
	 * Unstable sort referres to QuickSort or SelectionSort
	 * @param array the array that needs to be sorted
	 * @param length the maxmium size of the array to be sorted
	 */
	public static COMPAREABLE_KEY_BRACES void unstableSort(KEY_TYPE[] array, int length) {
		unstableSort(array, 0, length);
	}
	
	/**
	 * Sorts an array according to the natural ascending order, 
	 * potentially dynamically choosing an appropriate algorithm given the type and size of the array.
	 * Unstable sort referres to QuickSort or SelectionSort
	 * @param array the array that needs to be sorted
	 * @param from where the array should be sorted from
	 * @param to where the array should be sorted to
	 */
	public static COMPAREABLE_KEY_BRACES void unstableSort(KEY_TYPE[] array, int from, int to) {
		quickSort(array, from, to);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Insertion Sort,
	 * @param array the array that needs to be sorted
	 * @param comp the Comparator that decides the sorting order
	 */
	public static GENERIC_KEY_BRACES void insertionSort(KEY_TYPE[] array, COMPARATOR KEY_GENERIC_TYPE comp) {
		insertionSort(array, 0, array.length, comp);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Insertion Sort,
	 * @param array the array that needs to be sorted
	 * @param length the maxmium size of the array to be sorted
	 * @param comp the Comparator that decides the sorting order
	 */
	public static GENERIC_KEY_BRACES void insertionSort(KEY_TYPE[] array, int length, COMPARATOR KEY_GENERIC_TYPE comp) {
		insertionSort(array, 0, length, comp);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Insertion Sort,
	 * @param array the array that needs to be sorted
	 * @param from where the array should be sorted from
	 * @param to where the array should be sorted to
	 * @param comp the Comparator that decides the sorting order
	 */
	public static GENERIC_KEY_BRACES void insertionSort(KEY_TYPE[] array, int from, int to, COMPARATOR KEY_GENERIC_TYPE comp) {
		for (int i = from+1;i<to; i++) {
			KEY_TYPE current = array[i];
    		int j = i - 1;
    		while(j >= from && comp.compare(current, array[j]) < 0) {
    			array[j+1] = array[j--];
    		}
    		array[j+1] = current;
		}
	}
	
	/**
	 * Sorts an array according to the natural ascending order using InsertionSort, 
	 * @param array the array that needs to be sorted
	 */
	public static COMPAREABLE_KEY_BRACES void insertionSort(KEY_TYPE[] array) {
		insertionSort(array, 0, array.length);
	}
	
	/**
	 * Sorts an array according to the natural ascending order using InsertionSort,
	 * @param array the array that needs to be sorted
	 * @param length the maxmium size of the array to be sorted
	 */
	public static COMPAREABLE_KEY_BRACES void insertionSort(KEY_TYPE[] array, int length) {
		insertionSort(array, 0, length);
	}
	
	/**
	 * Sorts an array according to the natural ascending order using InsertionSort,
	 * @param array the array that needs to be sorted
	 * @param from where the array should be sorted from
	 */
	public static COMPAREABLE_KEY_BRACES void insertionSort(KEY_TYPE[] array, int from, int to) {
		for (int i = from+1;i<to; i++) {
			KEY_TYPE current = array[i];
    		int j = i - 1;
    		while(j >= from && COMPAREABLE_TO_KEY(current, array[j]) < 0) {
    			array[j+1] = array[j--];
    		}
    		array[j+1] = current;
		}
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Selection Sort,
	 * @param array the array that needs to be sorted
	 * @param comp the Comparator that decides the sorting order
	 */
	public static GENERIC_KEY_BRACES void selectionSort(KEY_TYPE[] array, COMPARATOR KEY_GENERIC_TYPE comp) {
		selectionSort(array, 0, array.length, comp);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Selection Sort,
	 * @param array the array that needs to be sorted
	 * @param length the maxmium size of the array to be sorted
	 * @param comp the Comparator that decides the sorting order
	 */
	public static GENERIC_KEY_BRACES void selectionSort(KEY_TYPE[] array, int length, COMPARATOR KEY_GENERIC_TYPE comp) {
		selectionSort(array, 0, length, comp);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Selection Sort,
	 * @param array the array that needs to be sorted
	 * @param from where the array should be sorted from
	 * @param to where the array should be sorted to
	 * @param comp the Comparator that decides the sorting order
	 */
	public static GENERIC_KEY_BRACES void selectionSort(KEY_TYPE[] array, int from, int to, COMPARATOR KEY_GENERIC_TYPE comp) {
    	for (int i = from; i < to; i++) {
    		KEY_TYPE min = array[i];
        	int minId = i;
        	for(int j = i+1; j < to; j++) {
            	if(comp.compare(array[j], min) < 0) {
                	min = array[j];
                	minId = j;
            	}
        	}
        	KEY_TYPE temp = array[i];
        	array[i] = min;
        	array[minId] = temp;
    	}
	}
	
	/**
	 * Sorts an array according to the natural ascending order using Selection Sort, 
	 * @param array the array that needs to be sorted
	 */
	public static COMPAREABLE_KEY_BRACES void selectionSort(KEY_TYPE[] array) {
		selectionSort(array, 0, array.length);
	}
	
	/**
	 * Sorts an array according to the natural ascending order using Selection Sort,
	 * @param array the array that needs to be sorted
	 * @param length the maxmium size of the array to be sorted
	 */
	public static COMPAREABLE_KEY_BRACES void selectionSort(KEY_TYPE[] array, int length) {
		selectionSort(array, 0, length);
	}
	
	/**
	 * Sorts an array according to the natural ascending order using Selection Sort,
	 * @param array the array that needs to be sorted
	 * @param from where the array should be sorted from
	 */
	public static COMPAREABLE_KEY_BRACES void selectionSort(KEY_TYPE[] array, int from, int to) {
    	for (int i = from; i < to; i++) {
    		KEY_TYPE min = array[i];
        	int minId = i;
        	for(int j = i+1; j < to; j++) {
            	if(COMPAREABLE_TO_KEY(array[j], min) < 0) {
                	min = array[j];
                	minId = j;
            	}
        	}
        	KEY_TYPE temp = array[i];
        	array[i] = min;
        	array[minId] = temp;
    	}
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Merge Sort,
	 * This implementation was copied from <a href="https://github.com/vigna/fastutil">FastUtil</a> with a couple custom optimizations
	 * @param array the array that needs to be sorted
	 * @param comp the Comparator that decides the sorting order
	 */
	public static GENERIC_KEY_BRACES void mergeSort(KEY_TYPE[] array, COMPARATOR KEY_GENERIC_TYPE comp) {
		mergeSort(array, null, 0, array.length, comp);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Merge Sort,
	 * This implementation was copied from <a href="https://github.com/vigna/fastutil">FastUtil</a> with a couple custom optimizations
	 * @param array the array that needs to be sorted
	 * @param length the maxmium size of the array to be sorted
	 * @param comp the Comparator that decides the sorting order
	 */
	public static GENERIC_KEY_BRACES void mergeSort(KEY_TYPE[] array, int length, COMPARATOR KEY_GENERIC_TYPE comp) {
		mergeSort(array, null, 0, length, comp);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Merge Sort,
	 * This implementation was copied from <a href="https://github.com/vigna/fastutil">FastUtil</a> with a couple custom optimizations
	 * @param array the array that needs to be sorted
	 * @param from where the array should be sorted from
	 * @param to where the array should be sorted to
	 * @param comp the Comparator that decides the sorting order
	 */
	public static GENERIC_KEY_BRACES void mergeSort(KEY_TYPE[] array, KEY_TYPE[] supp, int from, int to, COMPARATOR KEY_GENERIC_TYPE comp) {
		if(to - from < BASE_THRESHOLD) {
			insertionSort(array, from, to, comp);
			return;
		}
		if(supp == null) supp = Arrays.copyOf(array, to);
		int mid = (from + to) >>> 1;
		mergeSort(supp, array, from, mid, comp);
		mergeSort(supp, array, mid, to, comp);
		if(comp.compare(supp[mid - 1], supp[mid]) <= 0)
		{
			System.arraycopy(supp, from, array, from, to - from);
			return;
		}
		for(int p = from, q = mid;from < to;from++) {
			if(q >= to || p < mid && comp.compare(supp[p], supp[q]) < 0) array[from] = supp[p++];
			else array[from] = supp[q++];
		}
	}
	
	/**
	 * Sorts an array according to the natural ascending order using Merge Sort, 
	 * This implementation was copied from <a href="https://github.com/vigna/fastutil">FastUtil</a> with a couple custom optimizations
	 * @param array the array that needs to be sorted
	 */
	public static COMPAREABLE_KEY_BRACES void mergeSort(KEY_TYPE[] array) {
		mergeSort(array, null, 0, array.length);
	}
	
	/**
	 * Sorts an array according to the natural ascending order using Merge Sort,
	 * This implementation was copied from <a href="https://github.com/vigna/fastutil">FastUtil</a> with a couple custom optimizations
	 * @param array the array that needs to be sorted
	 * @param length the maxmium size of the array to be sorted
	 */
	public static COMPAREABLE_KEY_BRACES void mergeSort(KEY_TYPE[] array, int length) {
		mergeSort(array, null, 0, length);
	}
	
	/**
	 * Sorts an array according to the natural ascending order using Merge Sort,
	 * This implementation was copied from <a href="https://github.com/vigna/fastutil">FastUtil</a> with a couple custom optimizations
	 * @param array the array that needs to be sorted
	 * @param from where the array should be sorted from
	 * @param to where the array should be sorted to
	 */
	public static COMPAREABLE_KEY_BRACES void mergeSort(KEY_TYPE[] array, KEY_TYPE[] supp, int from, int to) {
		if(to - from < BASE_THRESHOLD) {
			insertionSort(array, from, to);
			return;
		}
		if(supp == null) supp = Arrays.copyOf(array, to);
		int mid = (from + to) >>> 1;
		mergeSort(supp, array, from, mid);
		mergeSort(supp, array, mid, to);
		if(COMPAREABLE_TO_KEY(supp[mid - 1], supp[mid]) <= 0)
		{
			System.arraycopy(supp, from, array, from, to - from);
			return;
		}
		for(int p = from, q = mid;from < to;from++) {
			if(q >= to || p < mid && COMPAREABLE_TO_KEY(supp[p], supp[q]) < 0) array[from] = supp[p++];
			else array[from] = supp[q++];
		}
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using a Parallel Merge Sort,
	 * This implementation was copied from <a href="https://github.com/vigna/fastutil">FastUtil</a> with a couple custom optimizations
	 * @param array the array that needs to be sorted
	 * @param comp the Comparator that decides the sorting order
	 * @Note This parallelization is invoked through {@link SanityChecks#invokeTask} which the threadpool can be changed as needed
	 */
	public static GENERIC_KEY_BRACES void parallelMergeSort(KEY_TYPE[] array, COMPARATOR KEY_GENERIC_TYPE comp) {
		parallelMergeSort(array, null, 0, array.length, comp);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Parallel Merge Sort,
	 * This implementation was copied from <a href="https://github.com/vigna/fastutil">FastUtil</a> with a couple custom optimizations
	 * @param array the array that needs to be sorted
	 * @param length the maxmium size of the array to be sorted
	 * @param comp the Comparator that decides the sorting order
	 * @Note This parallelization is invoked through {@link SanityChecks#invokeTask} which the threadpool can be changed as needed
	 */
	public static GENERIC_KEY_BRACES void parallelMergeSort(KEY_TYPE[] array, int length, COMPARATOR KEY_GENERIC_TYPE comp) {
		parallelMergeSort(array, null, 0, length, comp);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Parallel Merge Sort,
	 * This implementation was copied from <a href="https://github.com/vigna/fastutil">FastUtil</a> with a couple custom optimizations
	 * @param array the array that needs to be sorted
	 * @param from where the array should be sorted from
	 * @param to where the array should be sorted to
	 * @param comp the Comparator that decides the sorting order
	 * @Note This parallelization is invoked through {@link SanityChecks#invokeTask} which the threadpool can be changed as needed
	 */
	public static GENERIC_KEY_BRACES void parallelMergeSort(KEY_TYPE[] array, KEY_TYPE[] supp, int from, int to, COMPARATOR KEY_GENERIC_TYPE comp) {
		if(SanityChecks.canParallelTask() && to - from >= PARALLEL_THRESHOLD) {
			SanityChecks.invokeTask(new MergeSortActionCompBRACES(array, supp, from, to, comp));
			return;
		}
		mergeSort(array, supp, from, to, comp);
	}
	
	/**
	 * Sorts an array according to the natural ascending order using Parallel Merge Sort, 
	 * This implementation was copied from <a href="https://github.com/vigna/fastutil">FastUtil</a> with a couple custom optimizations
	 * @param array the array that needs to be sorted
	 * @Note This parallelization is invoked through {@link SanityChecks#invokeTask} which the threadpool can be changed as needed
	 */
	public static COMPAREABLE_KEY_BRACES void parallelMergeSort(KEY_TYPE[] array) {
		parallelMergeSort(array, null, 0, array.length);
	}
	
	/**
	 * Sorts an array according to the natural ascending order using Parallel Merge Sort,
	 * This implementation was copied from <a href="https://github.com/vigna/fastutil">FastUtil</a> with a couple custom optimizations
	 * @param array the array that needs to be sorted
	 * @param length the maxmium size of the array to be sorted
	 * @Note This parallelization is invoked through {@link SanityChecks#invokeTask} which the threadpool can be changed as needed
	 */
	public static COMPAREABLE_KEY_BRACES void parallelMergeSort(KEY_TYPE[] array, int length) {
		parallelMergeSort(array, null, 0, length);
	}
	
	/**
	 * Sorts an array according to the natural ascending order using Parallel Merge Sort,
	 * This implementation was copied from <a href="https://github.com/vigna/fastutil">FastUtil</a> with a couple custom optimizations
	 * @param array the array that needs to be sorted
	 * @param from where the array should be sorted from
	 * @param to where the array should be sorted to
	 * @Note This parallelization is invoked through {@link SanityChecks#invokeTask} which the threadpool can be changed as needed
	 */
	public static COMPAREABLE_KEY_BRACES void parallelMergeSort(KEY_TYPE[] array, KEY_TYPE[] supp, int from, int to) {
		if(SanityChecks.canParallelTask() && to - from >= PARALLEL_THRESHOLD) {
			SanityChecks.invokeTask(new MergeSortActionBRACES(array, supp, from, to));
			return;
		}
		mergeSort(array, supp, from, to);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Memory Free Merge Sort,
	 * This implementation is inspired by <a href="https://github.com/vigna/fastutil">FastUtil</a> original merge sort, but without the need to allocate a copy of the original Array. It is in Very Unsorted Instances 50% slower then Mergesort, otherwise it as fast.
	 * @param array the array that needs to be sorted
	 * @param comp the Comparator that decides the sorting order
	 */
	public static GENERIC_KEY_BRACES void memFreeMergeSort(KEY_TYPE[] array, COMPARATOR KEY_GENERIC_TYPE comp) {
		memFreeMergeSort(array, 0, array.length, comp);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Memory Free Merge Sort,
	 * This implementation is inspired by <a href="https://github.com/vigna/fastutil">FastUtil</a> original merge sort, but without the need to allocate a copy of the original Array. It is in Very Unsorted Instances 50% slower then Mergesort, otherwise it as fast.
	 * @param array the array that needs to be sorted
	 * @param length the maxmium size of the array to be sorted
	 * @param comp the Comparator that decides the sorting order
	 */
	public static GENERIC_KEY_BRACES void memFreeMergeSort(KEY_TYPE[] array, int length, COMPARATOR KEY_GENERIC_TYPE comp) {
		memFreeMergeSort(array, 0, length, comp);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Memory Free Merge Sort,
	 * This implementation is inspired by <a href="https://github.com/vigna/fastutil">FastUtil</a> original merge sort, but without the need to allocate a copy of the original Array. It is in Very Unsorted Instances 50% slower then Mergesort, otherwise it as fast.
	 * @param array the array that needs to be sorted
	 * @param from where the array should be sorted from
	 * @param to where the array should be sorted to
	 * @param comp the Comparator that decides the sorting order
	 */
	public static GENERIC_KEY_BRACES void memFreeMergeSort(KEY_TYPE[] array, int from, int to, COMPARATOR KEY_GENERIC_TYPE comp) {
		if(to - from < BASE_THRESHOLD) {
			insertionSort(array, from, to, comp);
			return;
		}
		int mid = (from + to) >>> 1;
		memFreeMergeSort(array, from, mid, comp);
		memFreeMergeSort(array, mid, to, comp);
		if(comp.compare(array[mid - 1], array[mid]) <= 0)
			return;
		for(int i = from, j = mid, compare;i < j && j < to;) {
			if((compare = comp.compare(array[i], array[j])) < 0)
				i++;
			else if(compare == 0) swap(array, ++i, j);
			else {
				int k = j;
				for(;k < to - 1 && comp.compare(array[i], array[k + 1]) > 0;k++);
				if(j == k) {
					swap(array, i++, j);
					continue;
				}
				else if(j + 1 == k) {
					KEY_TYPE value = array[j];
					System.arraycopy(array, i, array, i+1, j - i);
					array[i] = value;
					i++;
					j++;
					continue;
				}
				KEY_TYPE[] data = NEW_KEY_ARRAY(k - j);
				System.arraycopy(array, j, data, 0, data.length);
				System.arraycopy(array, i, array, i+data.length, j - i);
				System.arraycopy(data, 0, array, i, data.length);
				i+=data.length;
				j+=data.length;
			}
		}
	}
	
	/**
	 * Sorts an array according to the natural ascending order using Memory Free Merge Sort, 
	 * This implementation is inspired by <a href="https://github.com/vigna/fastutil">FastUtil</a> original merge sort, but without the need to allocate a copy of the original Array.
	 * It is depending on the size and the unsorted level of the input array slower or almost as fast as normal merge sort. Depending on the test size i can be 0.5x slower (5000 elements) or 4x slower (50000 elements) under the assumtion that the array is in its worst case scenario.
	 * It does stack allocate tiny amounts of data for shifting around elements.
	 * @author Speiger
	 * @param array the array that needs to be sorted
	 */
	public static COMPAREABLE_KEY_BRACES void memFreeMergeSort(KEY_TYPE[] array) {
		memFreeMergeSort(array, 0, array.length);
	}
	
	/**
	 * Sorts an array according to the natural ascending order using Memory Free Merge Sort, 
	 * This implementation is inspired by <a href="https://github.com/vigna/fastutil">FastUtil</a> original merge sort, but without the need to allocate a copy of the original Array.
	 * It is depending on the size and the unsorted level of the input array slower or almost as fast as normal merge sort. Depending on the test size i can be 0.5x slower (5000 elements) or 4x slower (50000 elements) under the assumtion that the array is in its worst case scenario.
	 * It does stack allocate tiny amounts of data for shifting around elements.
	 * @author Speiger
	 * @param array the array that needs to be sorted
	 * @param length the maxmium size of the array to be sorted
	 */
	public static COMPAREABLE_KEY_BRACES void memFreeMergeSort(KEY_TYPE[] array, int length) {
		memFreeMergeSort(array, 0, length);
	}
	
	/**
	 * Sorts an array according to the natural ascending order using Memory Free Merge Sort, 
	 * This implementation is inspired by <a href="https://github.com/vigna/fastutil">FastUtil</a> original merge sort, but without the need to allocate a copy of the original Array.
	 * It is depending on the size and the unsorted level of the input array slower or almost as fast as normal merge sort. Depending on the test size i can be 0.5x slower (5000 elements) or 4x slower (50000 elements) under the assumtion that the array is in its worst case scenario.
	 * It does stack allocate tiny amounts of data for shifting around elements.
	 * @author Speiger
	 * @param array the array that needs to be sorted
	 * @param from where the array should be sorted from
	 * @param to where the array should be sorted to
	 */
	public static COMPAREABLE_KEY_BRACES void memFreeMergeSort(KEY_TYPE[] array, int from, int to) {
		if(to - from < BASE_THRESHOLD) {
			insertionSort(array, from, to);
			return;
		}
		int mid = (from + to) >>> 1;
		memFreeMergeSort(array, from, mid);
		memFreeMergeSort(array, mid, to);
		if(COMPAREABLE_TO_KEY(array[mid - 1], array[mid]) <= 0)
			return;
		for(int i = from, j = mid, comp;i < j && j < to;) {
			if((comp = COMPAREABLE_TO_KEY(array[i], array[j])) < 0)
				i++;
			else if(comp == 0) swap(array, ++i, j);
			else {
				int k = j;
				for(;k < to - 1 && COMPAREABLE_TO_KEY(array[i], array[k + 1]) > 0;k++);
				if(j == k) {
					swap(array, i++, j);
					continue;
				}
				else if(j + 1 == k) {
					KEY_TYPE value = array[j];
					System.arraycopy(array, i, array, i+1, j - i);
					array[i] = value;
					i++;
					j++;
					continue;
				}
				KEY_TYPE[] data = NEW_KEY_ARRAY(k - j);
				System.arraycopy(array, j, data, 0, data.length);
				System.arraycopy(array, i, array, i+data.length, j - i);
				System.arraycopy(data, 0, array, i, data.length);
				i+=data.length;
				j+=data.length;
			}
		}
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Parallel Memory Free Merge Sort,
	 * This implementation is inspired by <a href="https://github.com/vigna/fastutil">FastUtil</a> original merge sort, but without the need to allocate a copy of the original Array.
	 * It is depending on the size and the unsorted level of the input array slower or almost as fast as normal merge sort. Depending on the test size i can be 0.5x slower (5000 elements) or 4x slower (50000 elements) under the assumtion that the array is in its worst case scenario.
	 * It does stack allocate tiny amounts of data for shifting around elements.
	 * @author Speiger
	 * @param array the array that needs to be sorted
	 * @param comp the Comparator that decides the sorting order
	 * @Note This parallelization is invoked through {@link SanityChecks#invokeTask} which the threadpool can be changed as needed
	 */
	public static GENERIC_KEY_BRACES void parallelMemFreeMergeSort(KEY_TYPE[] array, COMPARATOR KEY_GENERIC_TYPE comp) {
		parallelMemFreeMergeSort(array, 0, array.length, comp);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Parallel Memory Free Merge Sort,
	 * This implementation is inspired by <a href="https://github.com/vigna/fastutil">FastUtil</a> original merge sort, but without the need to allocate a copy of the original Array.
	 * It is depending on the size and the unsorted level of the input array slower or almost as fast as normal merge sort. Depending on the test size i can be 0.5x slower (5000 elements) or 4x slower (50000 elements) under the assumtion that the array is in its worst case scenario.
	 * It does stack allocate tiny amounts of data for shifting around elements.
	 * @author Speiger
	 * @param array the array that needs to be sorted
	 * @param length the maxmium size of the array to be sorted
	 * @param comp the Comparator that decides the sorting order
	 * @Note This parallelization is invoked through {@link SanityChecks#invokeTask} which the threadpool can be changed as needed
	 */
	public static GENERIC_KEY_BRACES void parallelMemFreeMergeSort(KEY_TYPE[] array, int length, COMPARATOR KEY_GENERIC_TYPE comp) {
		parallelMemFreeMergeSort(array, 0, length, comp);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Parallel Memory Free Merge Sort,
	 * This implementation is inspired by <a href="https://github.com/vigna/fastutil">FastUtil</a> original merge sort, but without the need to allocate a copy of the original Array.
	 * It is depending on the size and the unsorted level of the input array slower or almost as fast as normal merge sort. Depending on the test size i can be 0.5x slower (5000 elements) or 4x slower (50000 elements) under the assumtion that the array is in its worst case scenario.
	 * It does stack allocate tiny amounts of data for shifting around elements.
	 * @author Speiger
	 * @param array the array that needs to be sorted
	 * @param from where the array should be sorted from
	 * @param to where the array should be sorted to
	 * @param comp the Comparator that decides the sorting order
	 * @Note This parallelization is invoked through {@link SanityChecks#invokeTask} which the threadpool can be changed as needed
	 */
	public static GENERIC_KEY_BRACES void parallelMemFreeMergeSort(KEY_TYPE[] array, int from, int to, COMPARATOR KEY_GENERIC_TYPE comp) {
		if(SanityChecks.canParallelTask() && to - from >= PARALLEL_THRESHOLD) {
			SanityChecks.invokeTask(new MemFreeMergeSortActionCompBRACES(array, from, to, comp));
			return;
		}
		memFreeMergeSort(array, from, to, comp);
	}
	
	/**
	 * Sorts an array according to the natural ascending order using Parallel Memory Free Merge Sort, 
	 * This implementation is inspired by <a href="https://github.com/vigna/fastutil">FastUtil</a> original merge sort, but without the need to allocate a copy of the original Array.
	 * It is depending on the size and the unsorted level of the input array slower or almost as fast as normal merge sort. Depending on the test size i can be 0.5x slower (5000 elements) or 4x slower (50000 elements) under the assumtion that the array is in its worst case scenario.
	 * It does stack allocate tiny amounts of data for shifting around elements.
	 * @author Speiger
	 * @param array the array that needs to be sorted
	 * @Note This parallelization is invoked through {@link SanityChecks#invokeTask} which the threadpool can be changed as needed
	 */
	public static COMPAREABLE_KEY_BRACES void parallelMemFreeMergeSort(KEY_TYPE[] array) {
		parallelMemFreeMergeSort(array, 0, array.length);
	}
	
	/**
	 * Sorts an array according to the natural ascending order using Parallel Memory Free Merge Sort,
	 * This implementation is inspired by <a href="https://github.com/vigna/fastutil">FastUtil</a> original merge sort, but without the need to allocate a copy of the original Array.
	 * It is depending on the size and the unsorted level of the input array slower or almost as fast as normal merge sort. Depending on the test size i can be 0.5x slower (5000 elements) or 4x slower (50000 elements) under the assumtion that the array is in its worst case scenario.
	 * It does stack allocate tiny amounts of data for shifting around elements.
	 * @author Speiger
	 * @param array the array that needs to be sorted
	 * @param length the maxmium size of the array to be sorted
	 * @Note This parallelization is invoked through {@link SanityChecks#invokeTask} which the threadpool can be changed as needed
	 */
	public static COMPAREABLE_KEY_BRACES void parallelMemFreeMergeSort(KEY_TYPE[] array, int length) {
		parallelMemFreeMergeSort(array, 0, length);
	}
	
	/**
	 * Sorts an array according to the natural ascending order using Parallel Memory Free Merge Sort,
	 * This implementation is inspired by <a href="https://github.com/vigna/fastutil">FastUtil</a> original merge sort, but without the need to allocate a copy of the original Array.
	 * It is depending on the size and the unsorted level of the input array slower or almost as fast as normal merge sort. Depending on the test size i can be 0.5x slower (5000 elements) or 4x slower (50000 elements) under the assumtion that the array is in its worst case scenario.
	 * It does stack allocate tiny amounts of data for shifting around elements.
	 * @author Speiger
	 * @param array the array that needs to be sorted
	 * @param from where the array should be sorted from
	 * @param to where the array should be sorted to
	 * @Note This parallelization is invoked through {@link SanityChecks#invokeTask} which the threadpool can be changed as needed
	 */
	public static COMPAREABLE_KEY_BRACES void parallelMemFreeMergeSort(KEY_TYPE[] array, int from, int to) {
		if(SanityChecks.canParallelTask() && to - from >= PARALLEL_THRESHOLD) {
			SanityChecks.invokeTask(new MemFreeMergeSortActionBRACES(array, from, to));
			return;
		}
		memFreeMergeSort(array, from, to);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Quick Sort,
	 * This implementation is a custom of <a href="https://github.com/vigna/fastutil">FastUtil</a> quicksort but with a different code structure,
	 * and that sorting Algorithm is based on the tuned quicksort adapted from Jon L. Bentley and M. DouglasMcIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages1249−1265, 1993. 
	 * @param array the array that needs to be sorted
	 * @param comp the Comparator that decides the sorting order
	 */
	public static GENERIC_KEY_BRACES void quickSort(KEY_TYPE[] array, COMPARATOR KEY_GENERIC_TYPE comp) {
		quickSort(array, 0, array.length, comp);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Quick Sort,
	 * This implementation is a custom of <a href="https://github.com/vigna/fastutil">FastUtil</a> quicksort but with a different code structure,
	 * and that sorting Algorithm is based on the tuned quicksort adapted from Jon L. Bentley and M. DouglasMcIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages1249−1265, 1993. 
	 * @param array the array that needs to be sorted
	 * @param length the maxmium size of the array to be sorted
	 * @param comp the Comparator that decides the sorting order
	 */
	public static GENERIC_KEY_BRACES void quickSort(KEY_TYPE[] array, int length, COMPARATOR KEY_GENERIC_TYPE comp) {
		quickSort(array, 0, length, comp);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Quick Sort,
	 * This implementation is a custom of <a href="https://github.com/vigna/fastutil">FastUtil</a> quicksort but with a different code structure,
	 * and that sorting Algorithm is based on the tuned quicksort adapted from Jon L. Bentley and M. DouglasMcIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages1249−1265, 1993. 
	 * @param array the array that needs to be sorted
	 * @param from where the array should be sorted from
	 * @param to where the array should be sorted to
	 * @param comp the Comparator that decides the sorting order
	 */
	public static GENERIC_KEY_BRACES void quickSort(KEY_TYPE[] array, int from, int to, COMPARATOR KEY_GENERIC_TYPE comp) {
		int length = to - from;
		if(length <= 0) return;
		if(length < BASE_THRESHOLD) {
			selectionSort(array, from, to, comp);
			return;			
		}
		KEY_TYPE pivot = array[length > 128 ? subMedium(array, from, from + (length / 2), to - 1, length / 8, comp) : medium(array, from, from + (length / 2), to - 1, comp)];
		int a = from, b = a, c = to - 1, d = c;
		for(int compare;;swap(array, b++, c--)) {
			for(;b<=c && (compare = comp.compare(array[b], pivot)) <= 0;b++) {
				if(compare == 0) swap(array, a++, b);
			}
			for(;c>=b && (compare = comp.compare(array[c], pivot)) >= 0;c--) {
				if(compare == 0) swap(array, c, d--);
			}
			if(b>c) break;
		}
		swap(array, from, b, Math.min(a - from, b - a)); 
		swap(array, b, to, Math.min(d - c, to - d - 1));
		if((length = b - a) > 1) quickSort(array, from, from + length, comp);
		if((length = d - c) > 1) quickSort(array, to - length, to, comp);
	}
	
	/**
	 * Sorts an array according to the natural ascending order using Quick Sort, 
	 * This implementation is a custom of <a href="https://github.com/vigna/fastutil">FastUtil</a> quicksort but with a different code structure,
	 * and that sorting Algorithm is based on the tuned quicksort adapted from Jon L. Bentley and M. DouglasMcIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages1249−1265, 1993. 
	 * @param array the array that needs to be sorted
	 */
	public static COMPAREABLE_KEY_BRACES void quickSort(KEY_TYPE[] array) {
		quickSort(array, 0, array.length);
	}
	
	/**
	 * Sorts an array according to the natural ascending order using Quick Sort,
	 * This implementation is a custom of <a href="https://github.com/vigna/fastutil">FastUtil</a> quicksort but with a different code structure,
	 * and that sorting Algorithm is based on the tuned quicksort adapted from Jon L. Bentley and M. DouglasMcIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages1249−1265, 1993. 
	 * @param array the array that needs to be sorted
	 * @param length the maxmium size of the array to be sorted
	 */
	public static COMPAREABLE_KEY_BRACES void quickSort(KEY_TYPE[] array, int length) {
		quickSort(array, 0, length);
	}
	
	/**
	 * Sorts an array according to the natural ascending order using Quick Sort,
	 * This implementation is a custom of <a href="https://github.com/vigna/fastutil">FastUtil</a> quicksort but with a different code structure,
	 * and that sorting Algorithm is based on the tuned quicksort adapted from Jon L. Bentley and M. DouglasMcIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages1249−1265, 1993. 
	 * @param array the array that needs to be sorted
	 * @param from where the array should be sorted from
	 * @param to where the array should be sorted to
	 */
	public static COMPAREABLE_KEY_BRACES void quickSort(KEY_TYPE[] array, int from, int to) {
		int length = to - from;
		if(length <= 0) return;
		if(length < BASE_THRESHOLD) {
			selectionSort(array, from, to);
			return;			
		}
		KEY_TYPE pivot = array[length > 128 ? subMedium(array, from, from + (length / 2), to - 1, length / 8) : medium(array, from, from + (length / 2), to - 1)];
		int a = from, b = a, c = to - 1, d = c;
		for(int comp = 0;;swap(array, b++, c--)) {
			for(;b<=c && (comp = COMPAREABLE_TO_KEY(array[b], pivot)) <= 0;b++) {
				if(comp == 0) swap(array, a++, b);
			}
			for(;c>=b && (comp = COMPAREABLE_TO_KEY(array[c], pivot)) >= 0;c--) {
				if(comp == 0) swap(array, c, d--);
			}
			if(b>c) break;
		}
		swap(array, from, b, Math.min(a - from, b - a)); 
		swap(array, b, to, Math.min(d - c, to - d - 1));
		if((length = b - a) > 1) quickSort(array, from, from + length);
		if((length = d - c) > 1) quickSort(array, to - length, to);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Parallel Quick Sort,
	 * This implementation is a custom of <a href="https://github.com/vigna/fastutil">FastUtil</a> quicksort but with a different code structure,
	 * and that sorting Algorithm is based on the tuned quicksort adapted from Jon L. Bentley and M. DouglasMcIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages1249−1265, 1993. 
	 * @param array the array that needs to be sorted
	 * @param comp the Comparator that decides the sorting order
	 * @Note This parallelization is invoked through {@link SanityChecks#invokeTask} which the threadpool can be changed as needed
	 */
	public static GENERIC_KEY_BRACES void parallelQuickSort(KEY_TYPE[] array, COMPARATOR KEY_GENERIC_TYPE comp) {
		parallelQuickSort(array, 0, array.length, comp);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Parallel Quick Sort,
	 * This implementation is a custom of <a href="https://github.com/vigna/fastutil">FastUtil</a> quicksort but with a different code structure,
	 * and that sorting Algorithm is based on the tuned quicksort adapted from Jon L. Bentley and M. DouglasMcIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages1249−1265, 1993. 
	 * @param array the array that needs to be sorted
	 * @param length the maxmium size of the array to be sorted
	 * @param comp the Comparator that decides the sorting order
	 * @Note This parallelization is invoked through {@link SanityChecks#invokeTask} which the threadpool can be changed as needed
	 */
	public static GENERIC_KEY_BRACES void parallelQuickSort(KEY_TYPE[] array, int length, COMPARATOR KEY_GENERIC_TYPE comp) {
		parallelQuickSort(array, 0, length, comp);
	}
	
	/**
	 * Sorts the specified range of elements according to the order induced by the specified comparator using Parallel Quick Sort,
	 * This implementation is a custom of <a href="https://github.com/vigna/fastutil">FastUtil</a> quicksort but with a different code structure,
	 * and that sorting Algorithm is based on the tuned quicksort adapted from Jon L. Bentley and M. DouglasMcIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages1249−1265, 1993. 
	 * @param array the array that needs to be sorted
	 * @param from where the array should be sorted from
	 * @param to where the array should be sorted to
	 * @param comp the Comparator that decides the sorting order
	 * @Note This parallelization is invoked through {@link SanityChecks#invokeTask} which the threadpool can be changed as needed
	 */
	public static GENERIC_KEY_BRACES void parallelQuickSort(KEY_TYPE[] array, int from, int to, COMPARATOR KEY_GENERIC_TYPE comp) {
		if(SanityChecks.canParallelTask() && to - from >= PARALLEL_THRESHOLD) {
			SanityChecks.invokeTask(new QuickSortActionCompBRACES(array, from, to, comp));
			return;
		}
		quickSort(array, from, to, comp);
	}
	
	/**
	 * Sorts an array according to the natural ascending order using Parallel Quick Sort, 
	 * This implementation is a custom of <a href="https://github.com/vigna/fastutil">FastUtil</a> quicksort but with a different code structure,
	 * and that sorting Algorithm is based on the tuned quicksort adapted from Jon L. Bentley and M. DouglasMcIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages1249−1265, 1993. 
	 * @param array the array that needs to be sorted
	 * @Note This parallelization is invoked through {@link SanityChecks#invokeTask} which the threadpool can be changed as needed
	 */
	public static COMPAREABLE_KEY_BRACES void parallelQuickSort(KEY_TYPE[] array) {
		parallelQuickSort(array, 0, array.length);
	}
	
	/**
	 * Sorts an array according to the natural ascending order using Parallel Quick Sort,
	 * This implementation is a custom of <a href="https://github.com/vigna/fastutil">FastUtil</a> quicksort but with a different code structure,
	 * and that sorting Algorithm is based on the tuned quicksort adapted from Jon L. Bentley and M. DouglasMcIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages1249−1265, 1993. 
	 * @param array the array that needs to be sorted
	 * @param length the maxmium size of the array to be sorted
	 * @Note This parallelization is invoked through {@link SanityChecks#invokeTask} which the threadpool can be changed as needed
	 */
	public static COMPAREABLE_KEY_BRACES void parallelQuickSort(KEY_TYPE[] array, int length) {
		parallelQuickSort(array, 0, length);
	}
	
	/**
	 * Sorts an array according to the natural ascending order using Parallel Quick Sort,
	 * This implementation is a custom of <a href="https://github.com/vigna/fastutil">FastUtil</a> quicksort but with a different code structure,
	 * and that sorting Algorithm is based on the tuned quicksort adapted from Jon L. Bentley and M. DouglasMcIlroy, “Engineering a Sort Function”, Software: Practice and Experience, 23(11), pages1249−1265, 1993. 
	 * @param array the array that needs to be sorted
	 * @param from where the array should be sorted from
	 * @param to where the array should be sorted to
	 * @Note This parallelization is invoked through {@link SanityChecks#invokeTask} which the threadpool can be changed as needed
	 */
	public static COMPAREABLE_KEY_BRACES void parallelQuickSort(KEY_TYPE[] array, int from, int to) {
		if(SanityChecks.canParallelTask() && to - from >= PARALLEL_THRESHOLD) {
			SanityChecks.invokeTask(new QuickSortActionBRACES(array, from, to));
			return;
		}
		quickSort(array, from, to);
	}
	
	static GENERIC_KEY_BRACES void swap(KEY_TYPE[] a, int from, int to) {
		KEY_TYPE t = a[from];
		a[from] = a[to];
		a[to] = t;
	}
	
	static GENERIC_KEY_BRACES void swap(KEY_TYPE[] a, int from, int to, int length) {
		to -= length;
		for(int i = 0;i<length;i++,swap(a, from++, to++));
	}
	
	static GENERIC_KEY_BRACES int subMedium(KEY_TYPE[] data, int a, int b, int c, int length, COMPARATOR KEY_GENERIC_TYPE comp) {
		return medium(data, medium(data, a, a + length, a + (length * 2), comp), medium(data, b - length, b, b + length, comp), medium(data, c - (length * 2), c - length, c, comp), comp);
	}
	
	static GENERIC_KEY_BRACES int medium(KEY_TYPE[] data, int a, int b, int c, COMPARATOR KEY_GENERIC_TYPE comp) {
		return comp.compare(data[a], data[b]) < 0 ? (comp.compare(data[b], data[c]) < 0 ? b : comp.compare(data[a], data[c]) < 0 ? c : a) : (comp.compare(data[b], data[c]) > 0 ? b : comp.compare(data[a], data[c]) > 0 ? c : a);
	}
	
	static COMPAREABLE_KEY_BRACES int subMedium(KEY_TYPE[] data, int a, int b, int c, int length) {
		return medium(data, medium(data, a, a + length, a + (length * 2)), medium(data, b - length, b, b + length), medium(data, c - (length * 2), c - length, c));
	}
	
	static COMPAREABLE_KEY_BRACES int medium(KEY_TYPE[] data, int a, int b, int c) {
		return COMPAREABLE_TO_KEY(data[a], data[b]) < 0 ? (COMPAREABLE_TO_KEY(data[b], data[c]) < 0 ? b : COMPAREABLE_TO_KEY(data[a], data[c]) < 0 ? c : a) : (COMPAREABLE_TO_KEY(data[b], data[c]) > 0 ? b : COMPAREABLE_TO_KEY(data[a], data[c]) > 0 ? c : a);
	}
	
	static class QuickSortAction KEY_COMPAREABLE_TYPE extends RecursiveAction {
		private static final long serialVersionUID = 0L;
		KEY_TYPE[] array;
		int from;
		int to;
		
		QuickSortAction(KEY_TYPE[] array, int from, int to)
		{
			this.array = array;
			this.from = from;
			this.to = to;
		}
		
		@Override
		protected void compute()
		{
			int length = to - from;
			if(length <= 0) return;
			if(length < BASE_THRESHOLD) {
				selectionSort(array, from, to);
				return;			
			}
			KEY_TYPE pivot = array[length > 128 ? subMedium(array, from, from + (length / 2), to - 1, length / 8) : medium(array, from, from + (length / 2), to - 1)];
			int a = from, b = a, c = to - 1, d = c;
			for(int comp = 0;;swap(array, b++, c--)) {
				for(;b<=c && (comp = COMPAREABLE_TO_KEY(array[b], pivot)) <= 0;b++) {
					if(comp == 0) swap(array, a++, b);
				}
				for(;c>=b && (comp = COMPAREABLE_TO_KEY(array[c], pivot)) >= 0;c--) {
					if(comp == 0) swap(array, c, d--);
				}
				if(b>c) break;
			}
			swap(array, from, b, Math.min(a - from, b - a)); 
			swap(array, b, to, Math.min(d - c, to - d - 1));
			if(b - a > 1 && d - c > 1) invokeAll(new QuickSortActionBRACES(array, from, from + (b - a)), new QuickSortActionBRACES(array, to - (d - c), to));
			else if(b - a > 1) new QuickSortActionBRACES(array, from, from + (b - a)).invoke();
			else if(d - c > 1) new QuickSortActionBRACES(array, to - (d - c), to).invoke();
		}
	}
	
	static class QuickSortActionComp KEY_GENERIC_TYPE extends RecursiveAction {
		private static final long serialVersionUID = 0L;
		KEY_TYPE[] array;
		int from;
		int to;
		COMPARATOR KEY_GENERIC_TYPE comp;
		
		QuickSortActionComp(KEY_TYPE[] array, int from, int to, COMPARATOR KEY_GENERIC_TYPE comp)
		{
			this.array = array;
			this.from = from;
			this.to = to;
			this.comp = comp;
		}
		
		@Override
		protected void compute()
		{
			int length = to - from;
			if(length <= 0) return;
			if(length < BASE_THRESHOLD) {
				selectionSort(array, from, to, comp);
				return;			
			}
			KEY_TYPE pivot = array[length > 128 ? subMedium(array, from, from + (length / 2), to - 1, length / 8, comp) : medium(array, from, from + (length / 2), to - 1, comp)];
			int a = from, b = a, c = to - 1, d = c;
			for(int compare;;swap(array, b++, c--)) {
				for(;b<=c && (compare = comp.compare(array[b], pivot)) <= 0;b++) {
					if(compare == 0) swap(array, a++, b);
				}
				for(;c>=b && (compare = comp.compare(array[c], pivot)) >= 0;c--) {
					if(compare == 0) swap(array, c, d--);
				}
				if(b>c) break;
			}
			swap(array, from, b, Math.min(a - from, b - a)); 
			swap(array, b, to, Math.min(d - c, to - d - 1));
			if(b - a > 1 && d - c > 1) invokeAll(new QuickSortActionCompBRACES(array, from, from + (b - a), comp), new QuickSortActionCompBRACES(array, to - (d - c), to, comp));
			else if(b - a > 1) new QuickSortActionCompBRACES(array, from, from + (b - a), comp).invoke();
			else if(d - c > 1) new QuickSortActionCompBRACES(array, to - (d - c), to, comp).invoke();
		}
	}
	
	static class MergeSortAction KEY_COMPAREABLE_TYPE extends RecursiveAction {
		private static final long serialVersionUID = 0L;
		KEY_TYPE[] array;
		KEY_TYPE[] supp;
		int from;
		int to;
		
		MergeSortAction(KEY_TYPE[] array, KEY_TYPE[] supp, int from, int to)
		{
			this.array = array;
			this.supp = supp;
			this.from = from;
			this.to = to;
		}
		
		@Override
		protected void compute()
		{
			if(to - from < BASE_THRESHOLD) {
				insertionSort(array, from, to);
				return;
			}
			if(supp == null) supp = Arrays.copyOf(array, to);
			int mid = (from + to) >>> 1;
            invokeAll(new MergeSortActionBRACES(supp, array, from, mid), new MergeSortActionBRACES(supp, array, mid, to));
			if(COMPAREABLE_TO_KEY(supp[mid - 1], supp[mid]) <= 0)
			{
				System.arraycopy(supp, from, array, from, to - from);
				return;
			}
			for(int p = from, q = mid;from < to;from++) {
				if(q >= to || p < mid && COMPAREABLE_TO_KEY(supp[p], supp[q]) < 0) array[from] = supp[p++];
				else array[from] = supp[q++];
			}
		}
	}
	
	static class MergeSortActionComp KEY_GENERIC_TYPE extends RecursiveAction {
		private static final long serialVersionUID = 0L;
		KEY_TYPE[] array;
		KEY_TYPE[] supp;
		int from;
		int to;
		COMPARATOR KEY_GENERIC_TYPE comp;
		
		MergeSortActionComp(KEY_TYPE[] array, KEY_TYPE[] supp, int from, int to, COMPARATOR KEY_GENERIC_TYPE comp)
		{
			this.array = array;
			this.supp = supp;
			this.from = from;
			this.to = to;
			this.comp = comp;
		}
		
		@Override
		protected void compute()
		{
			if(to - from < BASE_THRESHOLD) {
				insertionSort(array, from, to, comp);
				return;
			}
			if(supp == null) supp = Arrays.copyOf(array, to);
			int mid = (from + to) >>> 1;
            invokeAll(new MergeSortActionCompBRACES(supp, array, from, mid, comp), new MergeSortActionCompBRACES(supp, array, mid, to, comp));
			if(comp.compare(supp[mid - 1], supp[mid]) <= 0)
			{
				System.arraycopy(supp, from, array, from, to - from);
				return;
			}
			for(int p = from, q = mid;from < to;from++) {
				if(q >= to || p < mid && comp.compare(supp[p], supp[q]) < 0) array[from] = supp[p++];
				else array[from] = supp[q++];
			}
		}
	}
	
	static class MemFreeMergeSortAction KEY_COMPAREABLE_TYPE extends RecursiveAction {
		private static final long serialVersionUID = 0L;
		KEY_TYPE[] array;
		int from;
		int to;
		
		MemFreeMergeSortAction(KEY_TYPE[] array, int from, int to)
		{
			this.array = array;
			this.from = from;
			this.to = to;
		}
		
		@Override
		protected void compute()
		{
			if(to - from < BASE_THRESHOLD) {
				insertionSort(array, from, to);
				return;
			}
			int mid = (from + to) >>> 1;
			invokeAll(new MemFreeMergeSortActionBRACES(array, from, mid), new MemFreeMergeSortActionBRACES(array, mid, to));
			if(COMPAREABLE_TO_KEY(array[mid - 1], array[mid]) <= 0)
				return;
			for(int i = from, j = mid, comp;i < j && j < to;) {
				if((comp = COMPAREABLE_TO_KEY(array[i], array[j])) < 0)
					i++;
				else if(comp == 0) swap(array, ++i, j);
				else {
					int k = j;
					for(;k < to - 1 && COMPAREABLE_TO_KEY(array[i], array[k + 1]) > 0;k++);
					if(j == k) {
						swap(array, i++, j);
						continue;
					}
					else if(j + 1 == k) {
						KEY_TYPE value = array[j];
						System.arraycopy(array, i, array, i+1, j - i);
						array[i] = value;
						i++;
						j++;
						continue;
					}
					KEY_TYPE[] data = NEW_KEY_ARRAY(k - j);
					System.arraycopy(array, j, data, 0, data.length);
					System.arraycopy(array, i, array, i+data.length, j - i);
					System.arraycopy(data, 0, array, i, data.length);
					i+=data.length;
					j+=data.length;
				}
			}
		}
	}
	
	static class MemFreeMergeSortActionComp KEY_GENERIC_TYPE extends RecursiveAction {
		private static final long serialVersionUID = 0L;
		KEY_TYPE[] array;
		int from;
		int to;
		COMPARATOR KEY_GENERIC_TYPE comp;
		
		MemFreeMergeSortActionComp(KEY_TYPE[] array, int from, int to, COMPARATOR KEY_GENERIC_TYPE comp)
		{
			this.array = array;
			this.from = from;
			this.to = to;
			this.comp = comp;
		}
		
		@Override
		protected void compute()
		{
			if(to - from < BASE_THRESHOLD) {
				insertionSort(array, from, to, comp);
				return;
			}
			int mid = (from + to) >>> 1;
			invokeAll(new MemFreeMergeSortActionCompBRACES(array, from, mid, comp), new MemFreeMergeSortActionCompBRACES(array, mid, to, comp));

			if(comp.compare(array[mid - 1], array[mid]) <= 0)
				return;
			for(int i = from, j = mid, compare;i < j && j < to;) {
				if((compare = comp.compare(array[i], array[j])) < 0)
					i++;
				else if(compare == 0) swap(array, ++i, j);
				else {
					int k = j;
					for(;k < to - 1 && comp.compare(array[i], array[k + 1]) > 0;k++);
					if(j == k) {
						swap(array, i++, j);
						continue;
					}
					else if(j + 1 == k) {
						KEY_TYPE value = array[j];
						System.arraycopy(array, i, array, i+1, j - i);
						array[i] = value;
						i++;
						j++;
						continue;
					}
					KEY_TYPE[] data = NEW_KEY_ARRAY(k - j);
					System.arraycopy(array, j, data, 0, data.length);
					System.arraycopy(array, i, array, i+data.length, j - i);
					System.arraycopy(data, 0, array, i, data.length);
					i+=data.length;
					j+=data.length;
				}
			}
		}
	}
}