Min Heap API¶

Introduction¶

The Min Heap API provides a set of functions and macros for managing min-heaps in the Linux kernel. A min-heap is a binary tree structure where the value of each node is less than or equal to the values of its children, ensuring that the smallest element is always at the root.

This document provides a guide to the Min Heap API, detailing how to define and use min-heaps. Users should not directly call functions with __min_heap_*() prefixes, but should instead use the provided macro wrappers.

In addition to the standard version of the functions, the API also includes a set of inline versions for performance-critical scenarios. These inline functions have the same names as their non-inline counterparts but include an _inline suffix. For example, __min_heap_init_inline and its corresponding macro wrapper min_heap_init_inline. The inline versions allow custom comparison and swap functions to be called directly, rather than through indirect function calls. This can significantly reduce overhead, especially when CONFIG_MITIGATION_RETPOLINE is enabled, as indirect function calls become more expensive. As with the non-inline versions, it is important to use the macro wrappers for inline functions instead of directly calling the functions themselves.

Data Structures¶

Min-Heap Definition¶

The core data structure for representing a min-heap is defined using the MIN_HEAP_PREALLOCATED and DEFINE_MIN_HEAP macros. These macros allow you to define a min-heap with a preallocated buffer or dynamically allocated memory.

Example:

#define MIN_HEAP_PREALLOCATED(_type, _name, _nr)
struct _name {
    int nr;         /* Number of elements in the heap */
    int size;       /* Maximum number of elements that can be held */
    _type *data;    /* Pointer to the heap data */
    _type preallocated[_nr];  /* Static preallocated array */
}

#define DEFINE_MIN_HEAP(_type, _name) MIN_HEAP_PREALLOCATED(_type, _name, 0)

A typical heap structure will include a counter for the number of elements (nr), the maximum capacity of the heap (size), and a pointer to an array of elements (data). Optionally, you can specify a static array for preallocated heap storage using MIN_HEAP_PREALLOCATED.

Min Heap Callbacks¶

The struct min_heap_callbacks provides customization options for ordering elements in the heap and swapping them. It contains two function pointers:

struct min_heap_callbacks {
    bool (*less)(const void *lhs, const void *rhs, void *args);
    void (*swp)(void *lhs, void *rhs, void *args);
};

less is the comparison function used to establish the order of elements.
swp is a function for swapping elements in the heap. If swp is set to NULL, the default swap function will be used, which swaps the elements based on their size

Macro Wrappers¶

The following macro wrappers are provided for interacting with the heap in a user-friendly manner. Each macro corresponds to a function that operates on the heap, and they abstract away direct calls to internal functions.

Each macro accepts various parameters that are detailed below.

Heap Initialization¶

min_heap_init(heap, data, size);

heap: A pointer to the min-heap structure to be initialized.
data: A pointer to the buffer where the heap elements will be stored. If NULL, the preallocated buffer within the heap structure will be used.
size: The maximum number of elements the heap can hold.

This macro initializes the heap, setting its initial state. If data is NULL, the preallocated memory inside the heap structure will be used for storage. Otherwise, the user-provided buffer is used. The operation is O(1).

Inline Version: min_heap_init_inline(heap, data, size)

Accessing the Top Element¶

element = min_heap_peek(heap);

heap: A pointer to the min-heap from which to retrieve the smallest element.

This macro returns a pointer to the smallest element (the root) of the heap, or NULL if the heap is empty. The operation is O(1).

Inline Version: min_heap_peek_inline(heap)

Heap Insertion¶

success = min_heap_push(heap, element, callbacks, args);

heap: A pointer to the min-heap into which the element should be inserted.
element: A pointer to the element to be inserted into the heap.
callbacks: A pointer to a struct min_heap_callbacks providing the less and swp functions.
args: Optional arguments passed to the less and swp functions.

This macro inserts an element into the heap. It returns true if the insertion was successful and false if the heap is full. The operation is O(log n).

Inline Version: min_heap_push_inline(heap, element, callbacks, args)

Heap Removal¶

success = min_heap_pop(heap, callbacks, args);

heap: A pointer to the min-heap from which to remove the smallest element.
callbacks: A pointer to a struct min_heap_callbacks providing the less and swp functions.
args: Optional arguments passed to the less and swp functions.

This macro removes the smallest element (the root) from the heap. It returns true if the element was successfully removed, or false if the heap is empty. The operation is O(log n).

Inline Version: min_heap_pop_inline(heap, callbacks, args)

Heap Maintenance¶

You can use the following macros to maintain the heap’s structure:

min_heap_sift_down(heap, pos, callbacks, args);

heap: A pointer to the min-heap.
pos: The index from which to start sifting down.
callbacks: A pointer to a struct min_heap_callbacks providing the less and swp functions.
args: Optional arguments passed to the less and swp functions.

This macro restores the heap property by moving the element at the specified index (pos) down the heap until it is in the correct position. The operation is O(log n).

Inline Version: min_heap_sift_down_inline(heap, pos, callbacks, args)

min_heap_sift_up(heap, idx, callbacks, args);

heap: A pointer to the min-heap.
idx: The index of the element to sift up.
callbacks: A pointer to a struct min_heap_callbacks providing the less and swp functions.
args: Optional arguments passed to the less and swp functions.

This macro restores the heap property by moving the element at the specified index (idx) up the heap. The operation is O(log n).

Inline Version: min_heap_sift_up_inline(heap, idx, callbacks, args)

min_heapify_all(heap, callbacks, args);

heap: A pointer to the min-heap.
callbacks: A pointer to a struct min_heap_callbacks providing the less and swp functions.
args: Optional arguments passed to the less and swp functions.

This macro ensures that the entire heap satisfies the heap property. It is called when the heap is built from scratch or after many modifications. The operation is O(n).

Inline Version: min_heapify_all_inline(heap, callbacks, args)

Removing Specific Elements¶

success = min_heap_del(heap, idx, callbacks, args);

heap: A pointer to the min-heap.
idx: The index of the element to delete.
callbacks: A pointer to a struct min_heap_callbacks providing the less and swp functions.
args: Optional arguments passed to the less and swp functions.

This macro removes an element at the specified index (idx) from the heap and restores the heap property. The operation is O(log n).

Inline Version: min_heap_del_inline(heap, idx, callbacks, args)

Other Utilities¶

min_heap_full(heap): Checks whether the heap is full. Complexity: O(1).

bool full = min_heap_full(heap);

heap: A pointer to the min-heap to check.

This macro returns true if the heap is full, otherwise false.

Inline Version: min_heap_full_inline(heap)

min_heap_empty(heap): Checks whether the heap is empty. Complexity: O(1).

bool empty = min_heap_empty(heap);

heap: A pointer to the min-heap to check.

This macro returns true if the heap is empty, otherwise false.

Inline Version: min_heap_empty_inline(heap)

Example Usage¶

An example usage of the min-heap API would involve defining a heap structure, initializing it, and inserting and removing elements as needed.

#include <linux/min_heap.h>

int my_less_function(const void *lhs, const void *rhs, void *args) {
    return (*(int *)lhs < *(int *)rhs);
}

struct min_heap_callbacks heap_cb = {
    .less = my_less_function,    /* Comparison function for heap order */
    .swp  = NULL,                /* Use default swap function */
};

void example_usage(void) {
    /* Pre-populate the buffer with elements */
    int buffer[5] = {5, 2, 8, 1, 3};
    /* Declare a min-heap */
    DEFINE_MIN_HEAP(int, my_heap);

    /* Initialize the heap with preallocated buffer and size */
    min_heap_init(&my_heap, buffer, 5);

    /* Build the heap using min_heapify_all */
    my_heap.nr = 5;  /* Set the number of elements in the heap */
    min_heapify_all(&my_heap, &heap_cb, NULL);

    /* Peek at the top element (should be 1 in this case) */
    int *top = min_heap_peek(&my_heap);
    pr_info("Top element: %d\n", *top);

    /* Pop the top element (1) and get the new top (2) */
    min_heap_pop(&my_heap, &heap_cb, NULL);
    top = min_heap_peek(&my_heap);
    pr_info("New top element: %d\n", *top);

    /* Insert a new element (0) and recheck the top */
    int new_element = 0;
    min_heap_push(&my_heap, &new_element, &heap_cb, NULL);
    top = min_heap_peek(&my_heap);
    pr_info("Top element after insertion: %d\n", *top);
}