efficient AVL? help me improve it! - WIP

avl.h

#ifndef AVL_H
#define AVL_H

/* creates a mask that can be applied each time we need to invert
 * a value depending on the boolean that was provided
 * to new_bool_inv_mask(bool) aka bool?value:-value, this
 * is done to prevent forking. Am i right to do it like so? */
#include <stdbool.h>
__inline__
static signed char
new_bool_inv_mask(bool value) {
		return (signed char) ~( ((int)value) * 0xff );
}

/* applies a mask created with new_bool_inv_mask() */
__inline__
static signed char
apply_mask(register signed char balance, register signed char mask)
{
	return (signed char)
		( ((int)(balance^mask)) + (mask&1) );
}

#endif

#ifndef LOGFILE
#define LOGFILE stderr
#endif

#ifdef LOG
#include <stdio.h>
#endif

#define AVL_NODE struct AVL_NODE_##TYPE

AVL_NODE {
	signed char balance;
	AVL_NODE *left, *right, *parent;
	TYPE data;
};

/* We use this to measure the height of the subtree rooted at c. See:
 *
 * https://upload.wikimedia.org/wikipedia/commons/c/c4/The_Rebalancing.gif
 *
 * We then infer the heights of the children d, b and a, respectively,
 * in order to calculate node balances afterwards, something implemented
 * for the performance benefits of it vs calculating or storing heights. */
#define GET_HEIGHT GET_HEIGHT_##TYPE
#include <stddef.h>
__inline__ static size_t
GET_HEIGHT(register AVL_NODE *curr) {
	register size_t h = 0;

	while (curr) {
		h++;
		curr = *( &curr->left + (curr->balance > 0) );
	}

	return h;
}

/* refer to:
 * https://upload.wikimedia.org/wikipedia/commons/c/c4/The_Rebalancing.gif */
#define REBALANCE REBALANCE_##TYPE
static AVL_NODE* REBALANCE(AVL_NODE *n, bool n_rheavy, signed char n_balance) {
	AVL_NODE **ns_heaviest_ref = &n->left + n_rheavy,
					 *f = *ns_heaviest_ref;

	signed char f_balance = f->balance;

	/* FIXME !f_balance is here just for some delete situations.. how to optimize? */
	bool same_dir = n_balance == (f_balance<<1) || !f_balance,
			 /* is f's tallest subtree to the right? */
			 f_rheavy = same_dir == n_rheavy;

	AVL_NODE **fs_left_child_ref = &f->left,
					 **fs_heaviest_ref = fs_left_child_ref + f_rheavy,
					 *l = *fs_heaviest_ref,
					 **ls_left_child_ref = &l->left,
					 **ls_c_ref = ls_left_child_ref + !f_rheavy,
					 *c = *ls_c_ref,
					 **ns_parent_ref = &n->parent,
					 *ns_parent = *ns_parent_ref;

	signed char imask_n_rheavy = new_bool_inv_mask(n_rheavy),
							imask_f_rheavy = new_bool_inv_mask(f_rheavy),
							l_balance = l->balance;

	size_t c_height = GET_HEIGHT(c),
				 d_height = ( size_t ) ( (long long int)c_height +
						 apply_mask(l_balance, imask_f_rheavy) ),
				 l_height = (c_height>d_height?c_height:d_height) + 1,
				 b_height = ( size_t ) ( (long long int)l_height -
						 apply_mask(f_balance, imask_f_rheavy) ),
				 a_height = ( size_t ) ( (long long int)l_height + 1 -
						 apply_mask(n_balance, imask_n_rheavy) );
	/* fprintf(LOGFILE, "{dh:%zu, lh:%zu, bh:%zu, ah:%zu}", */
	/* 		d_height, l_height, b_height, a_height); */

#ifdef LOG
	fputs(n_rheavy?">":"<", LOGFILE);
	fputs((same_dir == n_rheavy)?">":"<", LOGFILE);
#endif

	if (same_dir) { /* one rotation */
		n->balance = apply_mask((signed char)
				b_height - a_height, imask_n_rheavy);
		f->balance = apply_mask((signed char) /* FIXME problem is here */
				l_height - ((b_height>a_height?b_height:a_height) + 1),
				imask_n_rheavy);
		/* fprintf(LOGFILE, "{nb:%d, fb:%d}", n->balance, f->balance); */

		*ns_parent_ref = f;
		{
			AVL_NODE **fs_lightest_ref = fs_left_child_ref + !f_rheavy,
							 *b = *fs_lightest_ref;

			if (b) b->parent = n;
			f->parent = ns_parent;
			if (ns_parent) *(&ns_parent->left + (n == ns_parent->right)) = f;

			*fs_lightest_ref = n;
			*ns_heaviest_ref = b;
		}

		return f;
	}

	/* two */
	n->balance = apply_mask((signed char) 
			(d_height - a_height), imask_n_rheavy);
	f->balance = apply_mask((signed char)
			(b_height - c_height), imask_n_rheavy);
	l->balance = apply_mask((signed char)
			( (b_height>c_height?b_height:c_height) -
				(d_height>a_height?d_height:a_height)
			), imask_n_rheavy);

	*ns_parent_ref = l;
	f->parent = l;

	{
		register AVL_NODE **ls_d_ref = ls_left_child_ref + f_rheavy,
						 *d = *ls_d_ref;

		if (d) d->parent = n;
		if (c) c->parent = f;
		l->parent = ns_parent;
		if (ns_parent) *(&ns_parent->left + (n == ns_parent->right)) = l;

		*fs_heaviest_ref = c;
		*ls_c_ref = f;
		*ns_heaviest_ref = d;
		*ls_d_ref = n;
	}
	return l;
}

#include <stdlib.h>
#define AVL_INSERT AVL_INSERT_##TYPE
AVL_NODE * AVL_INSERT(AVL_NODE *root, TYPE data) {
	AVL_NODE *l = (AVL_NODE*) malloc(sizeof(AVL_NODE));
	l->left = l->right = NULL;
	l->balance = 0;
	l->data = data;

	if (root) {
		register AVL_NODE **n_r = &root, *n;
		register int side;
		register bool bside;

		do {
			n = *n_r;
			side = CMP(n->data, data);
			bside = side>0;
			n_r = &n->left + bside;
#ifdef LOG
			fputs(bside?"r":"l", LOGFILE);
#endif
		} while (*n_r);

#ifdef LOG
	LOG(data);
#endif

		l->parent = n;
		*n_r = l;

		{
			register AVL_NODE *p;

avl_insert_go_up:
			{
				signed char *n_balance_r = &n->balance,
										n_balance = (*n_balance_r + (bside<<1) - 1);

				if (n_balance) {
					if ((n_balance&3) == 2) {
						n = REBALANCE(n, bside, n_balance);
					} else {
						*n_balance_r = n_balance;
						if ((p = n->parent)) {
							bside = n == p->right;
							n = p;
							goto avl_insert_go_up;
						}
						return root;
					}
				} else *n_balance_r = 0;
			}

			if (!(p = n->parent)) return n;
			return root;
		}
	}

#ifdef LOG
	LOG(data);
#endif

	l->parent = NULL;
	return l;
}

#define AVL_FIND AVL_FIND_##TYPE
AVL_NODE *AVL_FIND(AVL_NODE *root, TYPE data) {
	if (root) {
		register AVL_NODE **parent_ref = &root, *parent;
		register int side;

		do {
			parent = *parent_ref;
			side = CMP(parent->data, data);
			if (!side) return parent;
			parent_ref = &parent->left + (side>0);
		} while (*parent_ref);
	}

	return NULL;
}

#define REBALANCE_DEL REBALANCE_DEL_##TYPE
static AVL_NODE *
REBALANCE_DEL(AVL_NODE *root, register AVL_NODE *n, register bool lside) {
	do {
		signed char *n_balance_r = &n->balance;
		register signed char n_balance = *n_balance_r + 1 - (lside<<1);
		register AVL_NODE *p;

		if ((n_balance&3) == 2)
			n = REBALANCE(n, !lside, n_balance);
		else
			*n_balance_r = n_balance;

		p = n->parent;
		if (!p) return n;
		if (n->balance) return root;

		lside = n == p->right;
		n = p;
	} while (true);
}

#define _AVL_REMOVE _AVL_REMOVE_##TYPE
static AVL_NODE * _AVL_REMOVE(AVL_NODE* root, AVL_NODE* n) {

#ifdef LOG
  fputs("x", LOGFILE);
	LOG(n->data);
#endif

  if (n->left) {
    AVL_NODE *l = n->left, *nl = l, **lp_r, *lp;
    bool lside;

    while (l->right) l = l->right;

		lp_r = &l->parent;
    lp = *lp_r;
    lside = l == lp->right;
    l->balance = n->balance;

		{
			register AVL_NODE *np = n->parent;
			if ((*lp_r = np))
				*(&np->left + (n == np->right)) = l;
		}

    if (lp != n) {

			{
				register AVL_NODE *ll = l->left;
				if ((lp->right = ll))
					ll->parent = lp;
			}

			l->left = nl;
			nl->parent = l;
			{
				register AVL_NODE *nr = n->right;
				if ((l->right = nr))
					nr->parent = l;
			}

      return REBALANCE_DEL(n == root ? l : root, lp, lside);
    } else {
			register AVL_NODE *nr = n->right;
			l->right = nr;
			if (nr) nr->parent = l;
			return REBALANCE_DEL(n == root ? l : root, l, l == nr);
		}
  } else {
    AVL_NODE *p = n->parent, *nr = n->right;

    if (nr) nr->parent = p;

    if (p) {
      bool side = n == p->right;

			*(&p->left + side) = nr;
      return REBALANCE_DEL(root, p, side);
    }

    return nr;
  }
}

#define AVL_REMOVE AVL_REMOVE_##TYPE
AVL_NODE *AVL_REMOVE(AVL_NODE *root, AVL_NODE *n) {
	AVL_NODE *new_root = _AVL_REMOVE(root, n);
  free(n);
	return new_root;
}

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    C avl tree implementation
    Copyright (C) 2016 Paulo André Azevedo Quirino

    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU Affero General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
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Makefile

.PHONY: all test debug

all: debug

debug: test.c avl.h
	$(CC) -g $< -o debug

fast: test.c avl.h
	$(CC) $< -O -o fast

test: fast
	./test.sh

test.c

#define TYPE int
#define CMP(a, b) (b-a)
#define LOG(a) fprintf(LOGFILE, "%d", a)
#include "avl.h"
#include <time.h>
#include <stdlib.h>
#include <stdio.h>

int main() {
	size_t N = 200, hN = N>>1;
	int a[hN];
	long long seed = time(NULL);
	/* long long seed = 1478578044; */
	AVL_NODE *n = NULL;

	fprintf(stderr, "%ld\n", seed);
	srand(seed);

	/* insert elements to be removed */
	for (size_t i = 0; i<hN; i++) {
		a[i] = rand()%N - hN;
		n = AVL_INSERT(n, a[i]);
	}

	/* insert more elements */
	for (size_t i = 0; i < hN; i++)
		n = AVL_INSERT(n, rand()%N - hN);

	/* test removal */
	for (size_t i = 0; i < hN; i++)
		n = AVL_REMOVE(n, AVL_FIND(n, a[i]));

	return 0;
}

test.sh

#!/bin/sh
echo -ne "\033[s"
c=0
while ./fast 2>test; do
	let c=c+1
	echo -ne "\033[u\033[K$c"
done && cat test && rm test && echo

Looks pretty nice but my system is missing some headers such as linux/mmzone.h and gfp.h
Any idea where can I get them?

@Silkerdax sorry about that gfp.h is just a file with some typedefs of what i called "generic function pointers", like so:

typedef int (*compare_gfp_t)(void *, void*)

I've uploaded it.

But since then, I've made improvements as i get used to pointers, and there is a new version (avl.c & avl.h) and a c++ goodie to allow in-order-traversals through a lambda call (i.e for_each).

The new version avoids recursion a little better (there was a huge mistake in the other one) and is a bit more efficient. The problem is it doesn't have remove yet. but i will implement it too, and some more functions if you think they would be nice to have.

You will also notice the new version doesn't have those ugly LEFT and RIGHT macros

In regards to linux/mmzone.h, i don't know... I'm on linux but i thought i was just including standard libraries, but i'm not sure what version of the code you are on.. fifo.h was deprecated, and bool.h but it's just a typedef i'm probably using for noob reasons, but i'll upload on a different gist if you want. This one is getting kind of bloated.

Edit: Thanks for saying it looks nice ^w^

@Silkerdax Hi again. I have just updated this, it doesn't use those weird gfp things now, also no bool_t, implemented delete and fixed some errors. Tested 140000+ AVLs with 2000 random int item inserts, 1000 deletes, no segfaults or memory errors. Cheers

Moved to its own git repo.

@quirinpa Hi, I cannot find the repo you mentioned. Did you delete it? Is this Gist the most recent version?

@quirinpa I've just found this gist again today and realized I never thanked you properly. So here it is, better late than never! Was quite helpful back when I was first studying data structures.

Hi @wangkuiyi, sorry I seem to have deleted the repo. I have the following code locally: avl.

However, I have not continued to use this implementation so I am pretty sure it must have some errors. Nowadays, I use libdb. I really recommend it as it is really useful for both BTREE and HASH type databases / data structures. I found it a great skill to learn and it is very well documented here.

@andrecarini I'm very glad it was helpful to you back then! :) Thanks!

So sorry it took me such a long time to respond.