| 1 | |
| 2 | #include <linux/compiler.h>
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| 3 | #include <linux/export.h>
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| 4 | #include <linux/list_sort.h>
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| 5 | #include <linux/list.h>
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| 6 |
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| 7 | |
| 8 | * Returns a list organized in an intermediate format suited
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| 9 | * to chaining of merge() calls: null-terminated, no reserved or
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| 10 | * sentinel head node, "prev" links not maintained.
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| 11 |
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| 12 | __attribute__((nonnull(2,3,4)))
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| 13 | static struct list_head *merge(void *priv, list_cmp_func_t cmp,
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| 14 | struct list_head *a, struct list_head *b)
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| 15 | {
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| 16 | struct list_head *head, **tail = &head;
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| 17 |
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| 18 | for (;;) {
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| 19 |
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| 20 | if (cmp(priv, a, b) <= 0) {
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| 21 | *tail = a;
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| 22 | tail = &a->next;
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| 23 | a = a->next;
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| 24 | if (!a) {
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| 25 | *tail = b;
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| 26 | break;
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| 27 | }
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| 28 | } else {
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| 29 | *tail = b;
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| 30 | tail = &b->next;
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| 31 | b = b->next;
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| 32 | if (!b) {
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| 33 | *tail = a;
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| 34 | break;
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| 35 | }
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| 36 | }
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| 37 | }
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| 38 | return head;
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| 39 | }
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| 40 |
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| 41 | |
| 42 | * Combine final list merge with restoration of standard doubly-linked
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| 43 | * list structure. This approach duplicates code from merge(), but
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| 44 | * runs faster than the tidier alternatives of either a separate final
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| 45 | * prev-link restoration pass, or maintaining the prev links
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| 46 | * throughout.
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| 47 |
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| 48 | __attribute__((nonnull(2,3,4,5)))
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| 49 | static void merge_final(void *priv, list_cmp_func_t cmp, struct list_head *head,
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| 50 | struct list_head *a, struct list_head *b)
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| 51 | {
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| 52 | struct list_head *tail = head;
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| 53 |
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| 54 | for (;;) {
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| 55 |
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| 56 | if (cmp(priv, a, b) <= 0) {
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| 57 | tail->next = a;
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| 58 | a->prev = tail;
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| 59 | tail = a;
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| 60 | a = a->next;
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| 61 | if (!a)
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| 62 | break;
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| 63 | } else {
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| 64 | tail->next = b;
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| 65 | b->prev = tail;
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| 66 | tail = b;
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| 67 | b = b->next;
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| 68 | if (!b) {
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| 69 | b = a;
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| 70 | break;
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| 71 | }
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| 72 | }
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| 73 | }
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| 74 |
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| 75 |
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| 76 | tail->next = b;
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| 77 | do {
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| 78 | b->prev = tail;
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| 79 | tail = b;
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| 80 | b = b->next;
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| 81 | } while (b);
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| 82 |
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| 83 |
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| 84 | tail->next = head;
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| 85 | head->prev = tail;
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| 86 | }
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| 87 |
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| 88 | |
| 89 | * list_sort - sort a list
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| 90 | * @priv: private data, opaque to list_sort(), passed to @cmp
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| 91 | * @head: the list to sort
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| 92 | * @cmp: the elements comparison function
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| 93 | *
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| 94 | * The comparison function @cmp must return > 0 if @a should sort after
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| 95 | * @b ("@a > @b" if you want an ascending sort), and <= 0 if @a should
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| 96 | * sort before @b *or* their original order should be preserved. It is
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| 97 | * always called with the element that came first in the input in @a,
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| 98 | * and list_sort is a stable sort, so it is not necessary to distinguish
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| 99 | * the @a < @b and @a == @b cases.
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| 100 | *
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| 101 | * The comparison function must adhere to specific mathematical properties
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| 102 | * to ensure correct and stable sorting:
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| 103 | * - Antisymmetry: cmp(@a, @b) must return the opposite sign of
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| 104 | * cmp(@b, @a).
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| 105 | * - Transitivity: if cmp(@a, @b) <= 0 and cmp(@b, @c) <= 0, then
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| 106 | * cmp(@a, @c) <= 0.
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| 107 | *
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| 108 | * This is compatible with two styles of @cmp function:
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| 109 | * - The traditional style which returns <0 / =0 / >0, or
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| 110 | * - Returning a boolean 0/1.
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| 111 | * The latter offers a chance to save a few cycles in the comparison
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| 112 | * (which is used by e.g. plug_ctx_cmp() in block/blk-mq.c).
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| 113 | *
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| 114 | * A good way to write a multi-word comparison is::
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| 115 | *
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| 116 | * if (a->high != b->high)
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| 117 | * return a->high > b->high;
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| 118 | * if (a->middle != b->middle)
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| 119 | * return a->middle > b->middle;
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| 120 | * return a->low > b->low;
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| 121 | *
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| 122 | *
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| 123 | * This mergesort is as eager as possible while always performing at least
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| 124 | * 2:1 balanced merges. Given two pending sublists of size 2^k, they are
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| 125 | * merged to a size-2^(k+1) list as soon as we have 2^k following elements.
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| 126 | *
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| 127 | * Thus, it will avoid cache thrashing as long as 3*2^k elements can
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| 128 | * fit into the cache. Not quite as good as a fully-eager bottom-up
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| 129 | * mergesort, but it does use 0.2*n fewer comparisons, so is faster in
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| 130 | * the common case that everything fits into L1.
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| 131 | *
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| 132 | *
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| 133 | * The merging is controlled by "count", the number of elements in the
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| 134 | * pending lists. This is beautifully simple code, but rather subtle.
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| 135 | *
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| 136 | * Each time we increment "count", we set one bit (bit k) and clear
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| 137 | * bits k-1 .. 0. Each time this happens (except the very first time
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| 138 | * for each bit, when count increments to 2^k), we merge two lists of
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| 139 | * size 2^k into one list of size 2^(k+1).
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| 140 | *
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| 141 | * This merge happens exactly when the count reaches an odd multiple of
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| 142 | * 2^k, which is when we have 2^k elements pending in smaller lists,
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| 143 | * so it's safe to merge away two lists of size 2^k.
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| 144 | *
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| 145 | * After this happens twice, we have created two lists of size 2^(k+1),
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| 146 | * which will be merged into a list of size 2^(k+2) before we create
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| 147 | * a third list of size 2^(k+1), so there are never more than two pending.
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| 148 | *
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| 149 | * The number of pending lists of size 2^k is determined by the
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| 150 | * state of bit k of "count" plus two extra pieces of information:
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| 151 | *
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| 152 | * - The state of bit k-1 (when k == 0, consider bit -1 always set), and
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| 153 | * - Whether the higher-order bits are zero or non-zero (i.e.
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| 154 | * is count >= 2^(k+1)).
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| 155 | *
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| 156 | * There are six states we distinguish. "x" represents some arbitrary
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| 157 | * bits, and "y" represents some arbitrary non-zero bits:
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| 158 | * 0: 00x: 0 pending of size 2^k; x pending of sizes < 2^k
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| 159 | * 1: 01x: 0 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
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| 160 | * 2: x10x: 0 pending of size 2^k; 2^k + x pending of sizes < 2^k
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| 161 | * 3: x11x: 1 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
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| 162 | * 4: y00x: 1 pending of size 2^k; 2^k + x pending of sizes < 2^k
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| 163 | * 5: y01x: 2 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
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| 164 | * (merge and loop back to state 2)
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| 165 | *
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| 166 | * We gain lists of size 2^k in the 2->3 and 4->5 transitions (because
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| 167 | * bit k-1 is set while the more significant bits are non-zero) and
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| 168 | * merge them away in the 5->2 transition. Note in particular that just
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| 169 | * before the 5->2 transition, all lower-order bits are 11 (state 3),
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| 170 | * so there is one list of each smaller size.
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| 171 | *
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| 172 | * When we reach the end of the input, we merge all the pending
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| 173 | * lists, from smallest to largest. If you work through cases 2 to
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| 174 | * 5 above, you can see that the number of elements we merge with a list
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| 175 | * of size 2^k varies from 2^(k-1) (cases 3 and 5 when x == 0) to
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| 176 | * 2^(k+1) - 1 (second merge of case 5 when x == 2^(k-1) - 1).
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| 177 |
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| 178 | __attribute__((nonnull(2,3)))
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| 179 | void list_sort(void *priv, struct list_head *head, list_cmp_func_t cmp)
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| 180 | {
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| 181 | struct list_head *list = head->next, *pending = NULL;
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| 182 | size_t count = 0;
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| 183 |
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| 184 | if (list == head->prev)
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| 185 | return;
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| 186 |
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| 187 |
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| 188 | head->prev->next = NULL;
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| 189 |
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| 190 | |
| 191 | * Data structure invariants:
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| 192 | * - All lists are singly linked and null-terminated; prev
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| 193 | * pointers are not maintained.
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| 194 | * - pending is a prev-linked "list of lists" of sorted
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| 195 | * sublists awaiting further merging.
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| 196 | * - Each of the sorted sublists is power-of-two in size.
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| 197 | * - Sublists are sorted by size and age, smallest & newest at front.
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| 198 | * - There are zero to two sublists of each size.
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| 199 | * - A pair of pending sublists are merged as soon as the number
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| 200 | * of following pending elements equals their size (i.e.
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| 201 | * each time count reaches an odd multiple of that size).
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| 202 | * That ensures each later final merge will be at worst 2:1.
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| 203 | * - Each round consists of:
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| 204 | * - Merging the two sublists selected by the highest bit
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| 205 | * which flips when count is incremented, and
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| 206 | * - Adding an element from the input as a size-1 sublist.
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| 207 |
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| 208 | do {
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| 209 | size_t bits;
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| 210 | struct list_head **tail = &pending;
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| 211 |
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| 212 |
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| 213 | for (bits = count; bits & 1; bits >>= 1)
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| 214 | tail = &(*tail)->prev;
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| 215 |
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| 216 | if (likely(bits)) {
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| 217 | struct list_head *a = *tail, *b = a->prev;
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| 218 |
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| 219 | a = merge(priv, cmp, b, a);
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| 220 |
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| 221 | a->prev = b->prev;
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| 222 | *tail = a;
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| 223 | }
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| 224 |
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| 225 |
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| 226 | list->prev = pending;
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| 227 | pending = list;
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| 228 | list = list->next;
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| 229 | pending->next = NULL;
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| 230 | count++;
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| 231 | } while (list);
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| 232 |
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| 233 |
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| 234 | list = pending;
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| 235 | pending = pending->prev;
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| 236 | for (;;) {
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| 237 | struct list_head *next = pending->prev;
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| 238 |
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| 239 | if (!next)
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| 240 | break;
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| 241 | list = merge(priv, cmp, pending, list);
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| 242 | pending = next;
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| 243 | }
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| 244 |
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| 245 | merge_final(priv, cmp, head, pending, list);
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| 246 | }
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| 247 | EXPORT_SYMBOL(list_sort);
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