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+/*
+ * Copyright (c) 2010, Andrea Mazzoleni. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+ * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+ * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+ * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+ * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+ * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+ * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/** \file
+ * Chain of nodes.
+ * A chain of nodes is an abstraction used to implements complex list operations
+ * like sorting.
+ *
+ * Do not use this directly. Use lists instead.
+ */
+
+#ifndef __TOMMYCHAIN_H
+#define __TOMMYCHAIN_H
+
+#include "tommytypes.h"
+
+/******************************************************************************/
+/* chain */
+
+/**
+ * Chain of nodes.
+ * A chain of nodes is a sequence of nodes with the following properties:
+ * - It contains at least one node. A chains of zero nodes cannot exist.
+ * - The next field of the tail is of *undefined* value.
+ * - The prev field of the head is of *undefined* value.
+ * - All the other inner prev and next fields are correctly set.
+ */
+typedef struct tommy_chain_struct {
+ tommy_node* head; /**< Pointer to the head of the chain. */
+ tommy_node* tail; /**< Pointer to the tail of the chain. */
+} tommy_chain;
+
+/**
+ * Splices a chain in the middle of another chain.
+ */
+tommy_inline void tommy_chain_splice(tommy_node* first_before, tommy_node* first_after, tommy_node* second_head, tommy_node* second_tail)
+{
+ /* set the prev list */
+ first_after->prev = second_tail;
+ second_head->prev = first_before;
+
+ /* set the next list */
+ first_before->next = second_head;
+ second_tail->next = first_after;
+}
+
+/**
+ * Concats two chains.
+ */
+tommy_inline void tommy_chain_concat(tommy_node* first_tail, tommy_node* second_head)
+{
+ /* set the prev list */
+ second_head->prev = first_tail;
+
+ /* set the next list */
+ first_tail->next = second_head;
+}
+
+/**
+ * Merges two chains.
+ */
+tommy_inline void tommy_chain_merge(tommy_chain* first, tommy_chain* second, tommy_compare_func* cmp)
+{
+ tommy_node* first_i = first->head;
+ tommy_node* second_i = second->head;
+
+ /* merge */
+ while (1) {
+ if (cmp(first_i->data, second_i->data) > 0) {
+ tommy_node* next = second_i->next;
+ if (first_i == first->head) {
+ tommy_chain_concat(second_i, first_i);
+ first->head = second_i;
+ } else {
+ tommy_chain_splice(first_i->prev, first_i, second_i, second_i);
+ }
+ if (second_i == second->tail)
+ break;
+ second_i = next;
+ } else {
+ if (first_i == first->tail) {
+ tommy_chain_concat(first_i, second_i);
+ first->tail = second->tail;
+ break;
+ }
+ first_i = first_i->next;
+ }
+ }
+}
+
+/**
+ * Merges two chains managing special degenerated cases.
+ * It's funtionally equivalent at tommy_chain_merge() but faster with already ordered chains.
+ */
+tommy_inline void tommy_chain_merge_degenerated(tommy_chain* first, tommy_chain* second, tommy_compare_func* cmp)
+{
+ /* identify the condition first <= second */
+ if (cmp(first->tail->data, second->head->data) <= 0) {
+ tommy_chain_concat(first->tail, second->head);
+ first->tail = second->tail;
+ return;
+ }
+
+ /* identify the condition second < first */
+ /* here we must be strict on comparison to keep the sort stable */
+ if (cmp(second->tail->data, first->head->data) < 0) {
+ tommy_chain_concat(second->tail, first->head);
+ first->head = second->head;
+ return;
+ }
+
+ tommy_chain_merge(first, second, cmp);
+}
+
+/**
+ * Max number of elements as a power of 2.
+ */
+#define TOMMY_CHAIN_BIT_MAX 32
+
+/**
+ * Sorts a chain.
+ * It's a stable merge sort using power of 2 buckets, with O(N*log(N)) complexity,
+ * similar at the one used in the SGI STL libraries and in the Linux Kernel,
+ * but faster on degenerated cases like already ordered lists.
+ *
+ * SGI STL stl_list.h
+ * http://www.sgi.com/tech/stl/stl_list.h
+ *
+ * Linux Kernel lib/list_sort.c
+ * http://lxr.linux.no/#linux+v2.6.36/lib/list_sort.c
+ */
+tommy_inline void tommy_chain_mergesort(tommy_chain* chain, tommy_compare_func* cmp)
+{
+ /*
+ * Bit buckets of chains.
+ * Each bucket contains 2^i nodes or it's empty.
+ * The chain at address TOMMY_CHAIN_BIT_MAX is an independet variable operating as "carry".
+ * We keep it in the same "bit" vector to avoid reports from the valgrind tool sgcheck.
+ */
+ tommy_chain bit[TOMMY_CHAIN_BIT_MAX + 1];
+
+ /**
+ * Value stored inside the bit bucket.
+ * It's used to know which bucket is empty of full.
+ */
+ tommy_count_t counter;
+ tommy_node* node = chain->head;
+ tommy_node* tail = chain->tail;
+ tommy_count_t mask;
+ tommy_count_t i;
+
+ counter = 0;
+ while (1) {
+ tommy_node* next;
+ tommy_chain* last;
+
+ /* carry bit to add */
+ last = &bit[TOMMY_CHAIN_BIT_MAX];
+ bit[TOMMY_CHAIN_BIT_MAX].head = node;
+ bit[TOMMY_CHAIN_BIT_MAX].tail = node;
+ next = node->next;
+
+ /* add the bit, propagating the carry */
+ i = 0;
+ mask = counter;
+ while ((mask & 1) != 0) {
+ tommy_chain_merge_degenerated(&bit[i], last, cmp);
+ mask >>= 1;
+ last = &bit[i];
+ ++i;
+ }
+
+ /* copy the carry in the first empty bit */
+ bit[i] = *last;
+
+ /* add the carry in the counter */
+ ++counter;
+
+ if (node == tail)
+ break;
+ node = next;
+ }
+
+ /* merge the buckets */
+ i = tommy_ctz_u32(counter);
+ mask = counter >> i;
+ while (mask != 1) {
+ mask >>= 1;
+ if (mask & 1)
+ tommy_chain_merge_degenerated(&bit[i + 1], &bit[i], cmp);
+ else
+ bit[i + 1] = bit[i];
+ ++i;
+ }
+
+ *chain = bit[i];
+}
+
+#endif
+