###### tags: `linux2022`
# [linux list sort](https://github.com/torvalds/linux/blob/master/lib/list_sort.c)
contributed by < `eric88525` >
| 函式 | 功能 |
| -------- | -------- |
| merge | merge two linked list |
| merge_final | 跟 merge 很像，但有特殊設計來讓 merge 在特定情況下加快，最後把忽略的 prev 連接回來 |
| list_sort | 主要函式，規劃 merge 流程和回傳結果 |
## 核心思想
概念源自於這篇論文 [ queue merge sort](https://reader.elsevier.com/reader/sd/pii/002001909390088Q?token=93BFACC6D1E9C0FB60C8B25BEC9955E81089605F952EF32B8D98D47A4DA70FFCBABF76BC3EA4E4929DE9A0BA0437FB54&originRegion=us-east-1&originCreation=20220301053808)，把 linked list 視為一個 queue。
每次的 merge 對象為 queue 中的最前面二個節點，merge 後放到 tail 並視為一個節點，重複步驟直到全部 merge 完成。
> 圖片取自論文
而 linux 的實做方式為用二進制來判斷哪時該 merge
| count | action | linked list state |
| -------- | -------- | -------- |
| 0b000 | add 1 | [==1==,1,1,1,1,1] |
| 0b001 | add 1 | [==1,1==,1,,1,1,1] |
| 0b010 | merge,add 1 | [==1==,1,1,1,2] |
| 0b011 | add 1 | [==1,1==,1,1,2] |
| 0b100 | merge | [1,1,2,2] |
| 0b101 | pend 已經有兩組 2^k節點，merge | [1,1,4] |
| after do..while | merge | [2,4] |
## 推演
+ 在推演中以 list = [4,2,1,3,5,6] 來展示
### count = 0b0
> line 187-194
+ 6 的 next 指向 null
```graphviz
digraph{
label = " count = 0b0";
rankdir=LR;
node [ shape=record]
// 4 2 1 3 5
head [label = "<data>head|{<prev>prev|<next>next}"]
4 [label = "<data>4|{<prev>prev|<next>next}"]
3 [label = "<data>3|{<prev>prev|<next>next}"]
5 [label = "<data>5|{<prev>prev|<next>next}"]
2 [label = "<data>2|{<prev>prev|<next>next}"]
1 [label = "<data>1|{<prev>prev|<next>next}"]
6 [label = "<data>6|{<prev>prev|<next>next}"]
list [shape = box,label = "*list" , style=filled, fillcolor=burlywood1]
pending [shape = box,label = "*pending" , style=filled, fillcolor=burlywood1]
{rank=same;pending list}
list->4:data:n;
head:next -> 4:data;
// node 4
4:next -> 2:data;
// node 4
2:next -> 1:data;
// node 4
1:next -> 3:data;
// node 4
3:next -> 5:data;
// node 4
5:next ->6:data:w;
}
```
> line 219-229: skip
這段不會執行 因為 count = 0
tail 指向 pending
```graphviz
digraph{
label = " count = 0b0";
rankdir=LR;
node [ shape=record]
// 4 2 1 3 5
head [label = "<data>head|{<prev>prev|<next>next}"]
4 [label = "<data>4|{<prev>prev|<next>next}"]
3 [label = "<data>3|{<prev>prev|<next>next}"]
5 [label = "<data>5|{<prev>prev|<next>next}"]
2 [label = "<data>2|{<prev>prev|<next>next}"]
1 [label = "<data>1|{<prev>prev|<next>next}"]
6 [label = "<data>6|{<prev>prev|<next>next}"]
list [shape = box,label = "*list" , style=filled, fillcolor=burlywood1]
pending [shape = box,label = "*pending" , style=filled, fillcolor=burlywood1]
tail [shape = box,label = "**tail" , style=filled, fillcolor=slateblue1]
// list
list->4:data:n;
// tail
tail->pending;
head:next -> 4:data;
// node 4
4:next -> 2:data;
// node 4
2:next -> 1:data;
// node 4
1:next -> 3:data;
// node 4
3:next -> 5:data;
// node 4
5:next ->6:data;
}
```
> line: 232-236
+ list->prev = pending，因此4->prev 會指向 null
+ list 往 next 移動
+ pending 接替 list 的前一個位置
+ count++
+ pending->next = null
```graphviz
digraph{
label = " count = 0b0";
rankdir=LR;
node [ shape=record]
// 4 2 1 3 5
head [label = "<data>head|{<prev>prev|<next>next}"]
4 [label = "<data>4|{<prev>prev|<next>next}"]
3 [label = "<data>3|{<prev>prev|<next>next}"]
5 [label = "<data>5|{<prev>prev|<next>next}"]
2 [label = "<data>2|{<prev>prev|<next>next}"]
1 [label = "<data>1|{<prev>prev|<next>next}"]
6 [label = "<data>6|{<prev>prev|<next>next}"]
list [shape = box,label = "*list" , style=filled, fillcolor=burlywood1]
pending [shape = box,label = "*pending" , style=filled, fillcolor=burlywood1]
tail [shape = box,label = "**tail" , style=filled, fillcolor=slateblue1]
// list
list->2:data:n;
//pending
pending->4:data:n;
// tail
tail->pending;
// head
head:next -> 4:data;
// node 4
4:next -> 2:data [style=invis];
//4:prev;
// node 4
2:next -> 1:data;
// node 4
1:next -> 3:data;
// node 4
3:next -> 5:data;
// node 4
5:next->6:data;
}
```
### count = 0b1
> line 219-229
tail 指向 `指向指標(pending)` 的 `prev`，line 222-229不執行
```graphviz
digraph{
label = "count = 0b1";
rankdir=LR;
node [ shape=record]
// 4 2 1 3 5
head [label = "<data>head|{<prev>prev|<next>next}"]
4 [label = "<data>4|{<prev>prev|<next>next}"]
3 [label = "<data>3|{<prev>prev|<next>next}"]
5 [label = "<data>5|{<prev>prev|<next>next}"]
2 [label = "<data>2|{<prev>prev|<next>next}"]
1 [label = "<data>1|{<prev>prev|<next>next}"]
6 [label = "<data>6|{<prev>prev|<next>next}"]
list [shape = box,label = "*list" , style=filled, fillcolor=burlywood1]
pending [shape = box,label = "*pending" , style=filled, fillcolor=burlywood1]
tail [shape = box,label = "**tail" , style=filled, fillcolor=slateblue1]
// list
list->2:data:n;
//pending
pending->4:data:n;
// tail
tail->4:prev;
// head
head:next -> 4:data;
// node 4
4:next -> 2:data [style=invis];
//4:prev;
// node 4
2:next -> 1:data;
// node 4
1:next -> 3:data;
// node 4
3:next -> 5:data;
// node 4
5:next->6:data;
}
```
> line 232-236
+ 做跟上輪一樣的事情
+ list(2)->prev = pending(4)
+ list 右移動
+ pending 接替位置
+ pending->next = null
```graphviz
digraph{
label = "count = 0b1";
rankdir=LR;
node [ shape=record]
// 4 2 1 3 5
head [label = "<data>head|{<prev>prev|<next>next}"]
4 [label = "<data>4|{<prev>prev|<next>next}"]
3 [label = "<data>3|{<prev>prev|<next>next}"]
5 [label = "<data>5|{<prev>prev|<next>next}"]
2 [label = "<data>2|{<prev>prev|<next>next}"]
1 [label = "<data>1|{<prev>prev|<next>next}"]
6 [label = "<data>6|{<prev>prev|<next>next}"]
list [shape = box,label = "*list" , style=filled, fillcolor=burlywood1]
pending [shape = box,label = "*pending" , style=filled, fillcolor=burlywood1]
tail [shape = box,label = "**tail" , style=filled, fillcolor=slateblue1]
// list
list->1:data:n;
//pending
pending->2:data:n;
// tail
tail->4:prev;
// head
head:next -> 4:data;
// node 4
4:next -> 2:data [style=invis];
//4:prev;
// node 4
2:next -> 1:data [style=invis];
2:prev->4:data [color=red];
// node 4
1:next -> 3:data;
// node 4
3:next -> 5:data;
// node 4
5:next->6:data;
}
```
### count = 0b10
> line 216
+ tail 指回 pending
```graphviz
digraph{
label = "count = 0b1";
rankdir=LR;
node [ shape=record]
// 4 2 1 3 5
head [label = "<data>head|{<prev>prev|<next>next}"]
4 [label = "<data>4|{<prev>prev|<next>next}"]
3 [label = "<data>3|{<prev>prev|<next>next}"]
5 [label = "<data>5|{<prev>prev|<next>next}"]
2 [label = "<data>2|{<prev>prev|<next>next}"]
1 [label = "<data>1|{<prev>prev|<next>next}"]
6 [label = "<data>6|{<prev>prev|<next>next}"]
list [shape = box,label = "*list" , style=filled, fillcolor=burlywood1]
pending [shape = box,label = "*pending" , style=filled, fillcolor=burlywood1]
tail [shape = box,label = "**tail" , style=filled, fillcolor=slateblue1]
// list
list->1:data:n;
//pending
pending->2:data:n;
// tail
tail->pending;
// head
head:next -> 4:data;
// node 4
4:next -> 2:data [style=invis];
//4:prev;
// node 4
2:next -> 1:data [style=invis];
2:prev->4:data [color=red];
// node 4
1:next -> 3:data;
// node 4
3:next -> 5:data;
// node 4
5:next->6:data;
}
```
> 219-220 skip
> 222-229
+ bits = 0b10 ，進入 if
+ a 指向 \*tail ， b指向 a->prev (這邊 a 會指向 2 ， b 指向 4)，傳入 `merge()`
```graphviz
digraph{
label = "count = 0b1";
rankdir=LR;
node [ shape=record]
// 4 2 1 3 5
head [label = "<data>head|{<prev>prev|<next>next}"]
4 [label = "<data>4|{<prev>prev|<next>next}"]
3 [label = "<data>3|{<prev>prev|<next>next}"]
5 [label = "<data>5|{<prev>prev|<next>next}"]
2 [label = "<data>2|{<prev>prev|<next>next}"]
1 [label = "<data>1|{<prev>prev|<next>next}"]
6 [label = "<data>6|{<prev>prev|<next>next}"]
list [shape = box,label = "*list" , style=filled, fillcolor=burlywood1]
pending [shape = box,label = "*pending" , style=filled, fillcolor=burlywood1]
tail [shape = box,label = "**tail" , style=filled, fillcolor=slateblue1]
a [shape = box,label = "*a" , style=filled, fillcolor=burlywood1]
b [shape = box,label = "*b" , style=filled, fillcolor=burlywood1]
//a
a->2:data
//b
b->4:data
// list
list->1:data:n;
//pending
pending->2:data:n;
// tail
tail->pending;
// head
head:next -> 4:data;
// node 4
4:next -> 2:data [style=invis];
//4:prev;
// node 4
2:next -> 1:data [style=invis];
2:prev->4:data [color=red];
// node 4
1:next -> 3:data;
// node 4
3:next -> 5:data;
// node 4
5:next->6:data;
}
```
> line 225-228
+ a 指向 merge 完成的 2和4節點
+ a->prev = b ->prev ， b->prev是 null，因此 a->prev = null
+ `*tail` (pending) = a
```graphviz
digraph{
label = "count = 0b1";
rankdir=LR;
node [ shape=record]
// 4 2 1 3 5
4 [label = "<data>4|{<prev>prev|<next>next}"]
3 [label = "<data>3|{<prev>prev|<next>next}"]
5 [label = "<data>5|{<prev>prev|<next>next}"]
2 [label = "<data>2|{<prev>prev|<next>next}"]
1 [label = "<data>1|{<prev>prev|<next>next}"]
6 [label = "<data>6|{<prev>prev|<next>next}"]
list [shape = box,label = "*list" , style=filled, fillcolor=burlywood1]
pending [shape = box,label = "*pending" , style=filled, fillcolor=burlywood1]
tail [shape = box,label = "**tail" , style=filled, fillcolor=slateblue1]
a [shape = box,label = "*a" , style=filled, fillcolor=burlywood1]
// b [shape = box,label = "*b" , style=filled, fillcolor=burlywood1]
{rank=same;list a}
list->1:data;
tail->pending;
pending->2:data;
a->2:data;
2:next->4:data;
1:next -> 3:data;
// node 4
3:next -> 5:data;
// node 4
5:next->6:data;
}
```
> line 232-236
```c=232
list->prev = pending;
pending = list;
list = list->next;
pending->next = NULL;
count++;
```
```graphviz
digraph{
label = "count = 0b1";
rankdir=LR;
node [ shape=record]
// 4 2 1 3 5
4 [label = "<data>4|{<prev>prev|<next>next}"]
3 [label = "<data>3|{<prev>prev|<next>next}"]
5 [label = "<data>5|{<prev>prev|<next>next}"]
2 [label = "<data>2|{<prev>prev|<next>next}"]
1 [label = "<data>1|{<prev>prev|<next>next}"]
6 [label = "<data>6|{<prev>prev|<next>next}"]
list [shape = box,label = "*list" , style=filled, fillcolor=burlywood1]
pending [shape = box,label = "*pending" , style=filled, fillcolor=burlywood1]
tail [shape = box,label = "**tail" , style=filled, fillcolor=slateblue1]
// a [shape = box,label = "*a" , style=filled, fillcolor=burlywood1]
// b [shape = box,label = "*b" , style=filled, fillcolor=burlywood1]
list->3:data;
tail->pending;
pending->1:data;
2:next->4:data;
1:next
1:prev->2:data[color=red];
// node 4
3:next -> 5:data;
// node 4
5:next->6:data;
}
```
### count = 0b11
> line 219-220
+ 執行2次
+ 第一次指向 1->prev
+ 第二次指向 2->prev
```graphviz
digraph{
label = " count = 0b11";
rankdir=LR;
node [ shape=record]
// 4 2 1 3 5
4 [label = "<data>4|{<prev>prev|<next>next}"]
3 [label = "<data>3|{<prev>prev|<next>next}"]
5 [label = "<data>5|{<prev>prev|<next>next}"]
2 [label = "<data>2|{<prev>prev|<next>next}"]
1 [label = "<data>1|{<prev>prev|<next>next}"]
6 [label = "<data>6|{<prev>prev|<next>next}"]
list [shape = box,label = "*list" , style=filled, fillcolor=burlywood1]
pending [shape = box,label = "*pending" , style=filled, fillcolor=burlywood1]
tail [shape = box,label = "**tail" , style=filled, fillcolor=slateblue1]
// a [shape = box,label = "*a" , style=filled, fillcolor=burlywood1]
// b [shape = box,label = "*b" , style=filled, fillcolor=burlywood1]
{rank=same;list pending}
list->3:data;
tail->2:prev;
pending->1:data;
2:next->4:data;
1:next
1:prev->2:data [color=red];
// node 4
3:next -> 5:data;
// node 4
5:next->6:data;
}
```
> line 232-236
```c=232
list->prev = pending;
pending = list;
list = list->next;
pending->next = NULL;
count++;
```
```graphviz
digraph{
label = " count = 0b11";
rankdir=LR;
node [ shape=record]
// 4 2 1 3 5
4 [label = "<data>4|{<prev>prev|<next>next}"]
3 [label = "<data>3|{<prev>prev|<next>next}"]
5 [label = "<data>5|{<prev>prev|<next>next}"]
2 [label = "<data>2|{<prev>prev|<next>next}"]
1 [label = "<data>1|{<prev>prev|<next>next}"]
6 [label = "<data>6|{<prev>prev|<next>next}"]
list [shape = box,label = "*list" , style=filled, fillcolor=burlywood1]
pending [shape = box,label = "*pending" , style=filled, fillcolor=burlywood1]
tail [shape = box,label = "**tail" , style=filled, fillcolor=slateblue1]
// a [shape = box,label = "*a" , style=filled, fillcolor=burlywood1]
// b [shape = box,label = "*b" , style=filled, fillcolor=burlywood1]
list->5:data;
tail->2:prev;
pending->3:data;
2:next->4:data;
1:next
1:prev->2:data [color=red];
// node 4
3:next -> 5:data[style=invis];
3:prev ->1:data:w [color=red];
// node 4
5:next->6:data;
}
```
### count = 0b100
```graphviz
digraph{
label = "count = 0b100";
rankdir=LR;
node [ shape=record]
// 4 2 1 3 5
4 [label = "<data>4|{<prev>prev|<next>next}"]
3 [label = "<data>3|{<prev>prev|<next>next}"]
5 [label = "<data>5|{<prev>prev|<next>next}"]
2 [label = "<data>2|{<prev>prev|<next>next}"]
1 [label = "<data>1|{<prev>prev|<next>next}"]
6 [label = "<data>6|{<prev>prev|<next>next}"]
list [shape = box,label = "*list" , style=filled, fillcolor=burlywood1]
pending [shape = box,label = "*pending" , style=filled, fillcolor=burlywood1]
tail [shape = box,label = "**tail" , style=filled, fillcolor=slateblue1]
// a [shape = box,label = "*a" , style=filled, fillcolor=burlywood1]
// b [shape = box,label = "*b" , style=filled, fillcolor=burlywood1]
list->5:data;
tail->pending;
pending->3:data;
2:next->4:data;
1:prev->2:data [color=red];
// node 4
3:next -> 5:data[style=invis];
3:prev ->1:data:w [color=red];
// node 4
5:next->6:data;
}
```
> line 222-229
```c=222
if (likely(bits)) {
struct list_head *a = *tail, *b = a->prev;
a = merge(priv, cmp, b, a);
/* Install the merged result in place of the inputs */
a->prev = b->prev;
*tail = a;
}
```
+ 進入 if
+ a 指向 tail ， b = a->prev，執行 `merge()`
```graphviz
digraph{
label = "count = 0b100";
rankdir=LR;
node [ shape=record]
// 4 2 1 3 5
4 [label = "<data>4|{<prev>prev|<next>next}"]
3 [label = "<data>3|{<prev>prev|<next>next}"]
5 [label = "<data>5|{<prev>prev|<next>next}"]
2 [label = "<data>2|{<prev>prev|<next>next}"]
1 [label = "<data>1|{<prev>prev|<next>next}"]
6 [label = "<data>6|{<prev>prev|<next>next}"]
list [shape = box,label = "*list" , style=filled, fillcolor=burlywood1]
pending [shape = box,label = "*pending" , style=filled, fillcolor=burlywood1]
tail [shape = box,label = "**tail" , style=filled, fillcolor=slateblue1]
a [shape = box,label = "*a" , style=filled, fillcolor=burlywood1]
b [shape = box,label = "*b" , style=filled, fillcolor=burlywood1]
a->3:data;
b->1:data;
list->5:data;
tail->pending;
pending->3:data;
2:next->4:data;
1:next
1:prev->2:data [color=red];
// node 4
3:next -> 5:data[style=invis];
3:prev ->1:data:w [color=red];
// node 4
5:next->6:data;
}
```
+ merge + 修正 prev 後的結果
```graphviz
digraph{
label = "count = 0b100";
rankdir=LR;
node [ shape=record]
// 4 2 1 3 5
4 [label = "<data>4|{<prev>prev|<next>next}"]
3 [label = "<data>3|{<prev>prev|<next>next}"]
5 [label = "<data>5|{<prev>prev|<next>next}"]
2 [label = "<data>2|{<prev>prev|<next>next}"]
1 [label = "<data>1|{<prev>prev|<next>next}"]
6 [label = "<data>6|{<prev>prev|<next>next}"]
list [shape = box,label = "*list" , style=filled, fillcolor=burlywood1]
pending [shape = box,label = "*pending" , style=filled, fillcolor=burlywood1]
tail [shape = box,label = "**tail" , style=filled, fillcolor=slateblue1]
a [shape = box,label = "*a" , style=filled, fillcolor=burlywood1]
//b [shape = box,label = "*b" , style=filled, fillcolor=burlywood1]
a->1:data
3:data;
// b->1:data;
list->5:data;
tail->pending;
pending->1:data;
2:next->4:data;
1:next->3:data;
1:prev->2:data [color=red];
// node 4
3:next -> 5:data[style=invis];
// node 4
5:next->6:data;
}
```
> line 232-236
此時候的狀態為 [2,2,2]
```graphviz
digraph{
label = "count = 0b100";
rankdir=LR;
node [ shape=record]
// 4 2 1 3 5
4 [label = "<data>4|{<prev>prev|<next>next}"]
3 [label = "<data>3|{<prev>prev|<next>next}"]
5 [label = "<data>5|{<prev>prev|<next>next}"]
2 [label = "<data>2|{<prev>prev|<next>next}"]
1 [label = "<data>1|{<prev>prev|<next>next}"]
6 [label = "<data>6|{<prev>prev|<next>next}"]
list [shape = box,label = "*list" , style=filled, fillcolor=burlywood1]
pending [shape = box,label = "*pending" , style=filled, fillcolor=burlywood1]
tail [shape = box,label = "**tail" , style=filled, fillcolor=slateblue1]
//a [shape = box,label = "*a" , style=filled, fillcolor=burlywood1]
//b [shape = box,label = "*b" , style=filled, fillcolor=burlywood1]
//a->1:data
3:data;
// b->1:data;
list->6:data:n;
tail->pending;
pending->5:data;
2:next->4:data;
1:next->3:data;
1:prev->2:data[color=red];
// node 4
3:next -> 5:data[style=invis];
// node 4
5:prev ->1:data:n [color=red];
5:next->6:data;
}
```
## count = 0b101
> 219-229
+ tail 指向 pending 的 `prev`
+ a = *tail (1) ， b = b->prev (2)，進行 merge
```graphviz
digraph{
label = "count = 0b101";
rankdir=LR;
node [ shape=record]
// 4 2 1 3 5
4 [label = "<data>4|{<prev>prev|<next>next}"]
3 [label = "<data>3|{<prev>prev|<next>next}"]
5 [label = "<data>5|{<prev>prev|<next>next}"]
2 [label = "<data>2|{<prev>prev|<next>next}"]
1 [label = "<data>1|{<prev>prev|<next>next}"]
6 [label = "<data>6|{<prev>prev|<next>next}"]
list [shape = box,label = "*list" , style=filled, fillcolor=burlywood1]
pending [shape = box,label = "*pending" , style=filled, fillcolor=burlywood1]
tail [shape = box,label = "**tail" , style=filled, fillcolor=slateblue1]
a [shape = box,label = "*a" , style=filled, fillcolor=burlywood1]
b [shape = box,label = "*b" , style=filled, fillcolor=burlywood1]
//a->1:data
3:data;
// b->1:data;
list->6:data:n;
pending->5:data;
2:next->4:data;
1:next->3:data;
1:prev->2:data[color=red];
// node 4
3:next -> 5:data[style=invis];
// node 4
5:prev ->1:data:n [color=red];
5:next->6:data;
a->1:data;
b->2:data;
{rank=same;a b pending tail}
tail->pending[style=invis];
tail -> 5:prev:w;
}
```
+ merge 後的結果
+ list = [2,4]
```graphviz
digraph{
label = "count = 0b101";
rankdir=LR;
node [ shape=record]
// 4 2 1 3 5
4 [label = "<data>4|{<prev>prev|<next>next}"]
3 [label = "<data>3|{<prev>prev|<next>next}"]
5 [label = "<data>5|{<prev>prev|<next>next}"]
2 [label = "<data>2|{<prev>prev|<next>next}"]
1 [label = "<data>1|{<prev>prev|<next>next}"]
6 [label = "<data>6|{<prev>prev|<next>next}"]
list [shape = box,label = "*list" , style=filled, fillcolor=burlywood1]
pending [shape = box,label = "*pending" , style=filled, fillcolor=burlywood1]
tail [shape = box,label = "**tail" , style=filled, fillcolor=slateblue1]
a [shape = box,label = "*a" , style=filled, fillcolor=burlywood1]
// b [shape = box,label = "*b" , style=filled, fillcolor=burlywood1]
//a->1:data
3:data;
// b->1:data;
list->6:data:n;
pending->5:data;
5:next->6:data;
tail->5:prev;
{rank=same;a pending}
5:prev->1:data:n [color=red];
1:next->2:data;
2:next->3:data;
3:next->4:data;
a->1:data;
}
```
> 232-236
執行完成後，跳出 do while 迴圈
```graphviz
digraph{
label = "count = 0b101";
rankdir=LR;
node [ shape=record]
// 4 2 1 3 5
4 [label = "<data>4|{<prev>prev|<next>next}"]
3 [label = "<data>3|{<prev>prev|<next>next}"]
5 [label = "<data>5|{<prev>prev|<next>next}"]
2 [label = "<data>2|{<prev>prev|<next>next}"]
1 [label = "<data>1|{<prev>prev|<next>next}"]
6 [label = "<data>6|{<prev>prev|<next>next}"]
//list [shape = box,label = "*list" , style=filled, fillcolor=burlywood1]
pending [shape = box,label = "*pending" , style=filled, fillcolor=burlywood1]
tail [shape = box,label = "**tail" , style=filled, fillcolor=slateblue1]
// a [shape = box,label = "*a" , style=filled, fillcolor=burlywood1]
// b [shape = box,label = "*b" , style=filled, fillcolor=burlywood1]
//a->1:data
3:data;
// b->1:data;
pending->6:data:n;
5:next->6:data;
6:prev->5:data[color=red];
tail->5:prev;
white[style=invis];
white->1[style=invis];
5:prev:s->1:data:w [color=red];
1:next->2:data;
2:next->3:data;
3:next->4:data;
}
```
+ 第一次的for(;;)
讓 pending 指回 5，list 指向6進行 `merge(pending,list)`
merge後的結果為 list 指向排序好的 `5->6`
```graphviz
digraph{
label = "count = 0b101";
rankdir=LR;
node [ shape=record]
// 4 2 1 3 5
4 [label = "<data>4|{<prev>prev|<next>next}"]
3 [label = "<data>3|{<prev>prev|<next>next}"]
5 [label = "<data>5|{<prev>prev|<next>next}"]
2 [label = "<data>2|{<prev>prev|<next>next}"]
1 [label = "<data>1|{<prev>prev|<next>next}"]
6 [label = "<data>6|{<prev>prev|<next>next}"]
list [shape = box,label = "*list" , style=filled, fillcolor=burlywood1]
pending [shape = box,label = "*pending" , style=filled, fillcolor=burlywood1]
//tail [shape = box,label = "**tail" , style=filled, fillcolor=slateblue1]
// a [shape = box,label = "*a" , style=filled, fillcolor=burlywood1]
// b [shape = box,label = "*b" , style=filled, fillcolor=burlywood1]
//a->1:data
3:data;
// b->1:data;
pending->1:data;
list->5:data:w;
5:next->6:data;
white[style=invis];
white->1[style=invis];
5:prev:s->1:data:w [color=red];
1:next->2:data;
2:next->3:data;
3:next->4:data;
}
```
+ 第二次的for(;;)
merge `5->6` 和 `1->2->3->4`完成排序
```graphviz
digraph{
label = "count = 0b101";
rankdir=LR;
node [ shape=record]
// 4 2 1 3 5
4 [label = "<data>4|{<prev>prev|<next>next}"]
3 [label = "<data>3|{<prev>prev|<next>next}"]
5 [label = "<data>5|{<prev>prev|<next>next}"]
2 [label = "<data>2|{<prev>prev|<next>next}"]
1 [label = "<data>1|{<prev>prev|<next>next}"]
6 [label = "<data>6|{<prev>prev|<next>next}"]
list [shape = box,label = "*list" , style=filled, fillcolor=burlywood1]
pending [shape = box,label = "*pending" , style=filled, fillcolor=burlywood1]
//tail [shape = box,label = "**tail" , style=filled, fillcolor=slateblue1]
// a [shape = box,label = "*a" , style=filled, fillcolor=burlywood1]
// b [shape = box,label = "*b" , style=filled, fillcolor=burlywood1]
//a->1:data
3:data;
// b->1:data;
list->1:data:w;
5:next->6:data;
white[style=invis];
white->1[style=invis];
1:next->2:data;
2:next->3:data;
3:next->4:data;
4:next->5:data;
}
```
把 merge 結果傳入 `merge_final()` 修正 prev 指標
```c=240
list = pending;
pending = pending->prev;
for (;;) {
struct list_head *next = pending->prev;
if (!next)
break;
list = merge(priv, cmp, pending, list);
pending = next;
}
/* The final merge, rebuilding prev links */
merge_final(priv, cmp, head, pending, list);
```
merge_final 會再一次 merge ，並把 prev 給修正
## code
```c=
// SPDX-License-Identifier: GPL-2.0
#include <linux/kernel.h>
#include <linux/bug.h>
#include <linux/compiler.h>
#include <linux/export.h>
#include <linux/string.h>
#include <linux/list_sort.h>
#include <linux/list.h>
/*
* Returns a list organized in an intermediate format suited
* to chaining of merge() calls: null-terminated, no reserved or
* sentinel head node, "prev" links not maintained.
*/
__attribute__((nonnull(2,3,4)))
static struct list_head *merge(void *priv, list_cmp_func_t cmp,
struct list_head *a, struct list_head *b)
{
struct list_head *head, **tail = &head;
for (;;) {
/* if equal, take 'a' -- important for sort stability */
if (cmp(priv, a, b) <= 0) {
*tail = a;
tail = &a->next;
a = a->next;
if (!a) {
*tail = b;
break;
}
} else {
*tail = b;
tail = &b->next;
b = b->next;
if (!b) {
*tail = a;
break;
}
}
}
return head;
}
/*
* Combine final list merge with restoration of standard doubly-linked
* list structure. This approach duplicates code from merge(), but
* runs faster than the tidier alternatives of either a separate final
* prev-link restoration pass, or maintaining the prev links
* throughout.
*/
__attribute__((nonnull(2,3,4,5)))
static void merge_final(void *priv, list_cmp_func_t cmp, struct list_head *head,
struct list_head *a, struct list_head *b)
{
struct list_head *tail = head;
u8 count = 0;
for (;;) {
/* if equal, take 'a' -- important for sort stability */
if (cmp(priv, a, b) <= 0) {
tail->next = a;
a->prev = tail;
tail = a;
a = a->next;
if (!a)
break;
} else {
tail->next = b;
b->prev = tail;
tail = b;
b = b->next;
if (!b) {
b = a;
break;
}
}
}
/* Finish linking remainder of list b on to tail */
tail->next = b;
do {
/*
* If the merge is highly unbalanced (e.g. the input is
* already sorted), this loop may run many iterations.
* Continue callbacks to the client even though no
* element comparison is needed, so the client's cmp()
* routine can invoke cond_resched() periodically.
*/
if (unlikely(!++count))
cmp(priv, b, b);
b->prev = tail;
tail = b;
b = b->next;
} while (b);
/* And the final links to make a circular doubly-linked list */
tail->next = head;
head->prev = tail;
}
/**
* list_sort - sort a list
* @priv: private data, opaque to list_sort(), passed to @cmp
* @head: the list to sort
* @cmp: the elements comparison function
*
* The comparison function @cmp must return > 0 if @a should sort after
* @b ("@a > @b" if you want an ascending sort), and <= 0 if @a should
* sort before @b *or* their original order should be preserved. It is
* always called with the element that came first in the input in @a,
* and list_sort is a stable sort, so it is not necessary to distinguish
* the @a < @b and @a == @b cases.
*
* This is compatible with two styles of @cmp function:
* - The traditional style which returns <0 / =0 / >0, or
* - Returning a boolean 0/1.
* The latter offers a chance to save a few cycles in the comparison
* (which is used by e.g. plug_ctx_cmp() in block/blk-mq.c).
*
* A good way to write a multi-word comparison is::
*
* if (a->high != b->high)
* return a->high > b->high;
* if (a->middle != b->middle)
* return a->middle > b->middle;
* return a->low > b->low;
*
*
* This mergesort is as eager as possible while always performing at least
* 2:1 balanced merges. Given two pending sublists of size 2^k, they are
* merged to a size-2^(k+1) list as soon as we have 2^k following elements.
*
* Thus, it will avoid cache thrashing as long as 3*2^k elements can
* fit into the cache. Not quite as good as a fully-eager bottom-up
* mergesort, but it does use 0.2*n fewer comparisons, so is faster in
* the common case that everything fits into L1.
*
*
* The merging is controlled by "count", the number of elements in the
* pending lists. This is beautifully simple code, but rather subtle.
*
* Each time we increment "count", we set one bit (bit k) and clear
* bits k-1 .. 0. Each time this happens (except the very first time
* for each bit, when count increments to 2^k), we merge two lists of
* size 2^k into one list of size 2^(k+1).
*
* This merge happens exactly when the count reaches an odd multiple of
* 2^k, which is when we have 2^k elements pending in smaller lists,
* so it's safe to merge away two lists of size 2^k.
*
* After this happens twice, we have created two lists of size 2^(k+1),
* which will be merged into a list of size 2^(k+2) before we create
* a third list of size 2^(k+1), so there are never more than two pending.
*
* The number of pending lists of size 2^k is determined by the
* state of bit k of "count" plus two extra pieces of information:
*
* - The state of bit k-1 (when k == 0, consider bit -1 always set), and
* - Whether the higher-order bits are zero or non-zero (i.e.
* is count >= 2^(k+1)).
*
* There are six states we distinguish. "x" represents some arbitrary
* bits, and "y" represents some arbitrary non-zero bits:
* 0: 00x: 0 pending of size 2^k; x pending of sizes < 2^k
* 1: 01x: 0 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
* 2: x10x: 0 pending of size 2^k; 2^k + x pending of sizes < 2^k
* 3: x11x: 1 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
* 4: y00x: 1 pending of size 2^k; 2^k + x pending of sizes < 2^k
* 5: y01x: 2 pending of size 2^k; 2^(k-1) + x pending of sizes < 2^k
* (merge and loop back to state 2)
*
* We gain lists of size 2^k in the 2->3 and 4->5 transitions (because
* bit k-1 is set while the more significant bits are non-zero) and
* merge them away in the 5->2 transition. Note in particular that just
* before the 5->2 transition, all lower-order bits are 11 (state 3),
* so there is one list of each smaller size.
*
* When we reach the end of the input, we merge all the pending
* lists, from smallest to largest. If you work through cases 2 to
* 5 above, you can see that the number of elements we merge with a list
* of size 2^k varies from 2^(k-1) (cases 3 and 5 when x == 0) to
* 2^(k+1) - 1 (second merge of case 5 when x == 2^(k-1) - 1).
*/
__attribute__((nonnull(2,3)))
void list_sort(void *priv, struct list_head *head, list_cmp_func_t cmp)
{
struct list_head *list = head->next, *pending = NULL;
size_t count = 0; /* Count of pending */
if (list == head->prev) /* Zero or one elements */
return;
/* Convert to a null-terminated singly-linked list. */
head->prev->next = NULL;
/*
* Data structure invariants:
* - All lists are singly linked and null-terminated; prev
* pointers are not maintained.
* - pending is a prev-linked "list of lists" of sorted
* sublists awaiting further merging.
* - Each of the sorted sublists is power-of-two in size.
* - Sublists are sorted by size and age, smallest & newest at front.
* - There are zero to two sublists of each size.
* - A pair of pending sublists are merged as soon as the number
* of following pending elements equals their size (i.e.
* each time count reaches an odd multiple of that size).
* That ensures each later final merge will be at worst 2:1.
* - Each round consists of:
* - Merging the two sublists selected by the highest bit
* which flips when count is incremented, and
* - Adding an element from the input as a size-1 sublist.
*/
do {
size_t bits;
struct list_head **tail = &pending;
/* Find the least-significant clear bit in count */
for (bits = count; bits & 1; bits >>= 1)
tail = &(*tail)->prev;
/* Do the indicated merge */
if (likely(bits)) {
struct list_head *a = *tail, *b = a->prev;
a = merge(priv, cmp, b, a);
/* Install the merged result in place of the inputs */
a->prev = b->prev;
*tail = a;
}
/* Move one element from input list to pending */
list->prev = pending;
pending = list;
list = list->next;
pending->next = NULL;
count++;
} while (list);
/* End of input; merge together all the pending lists. */
list = pending;
pending = pending->prev;
for (;;) {
struct list_head *next = pending->prev;
if (!next)
break;
list = merge(priv, cmp, pending, list);
pending = next;
}
/* The final merge, rebuilding prev links */
merge_final(priv, cmp, head, pending, list);
}
EXPORT_SYMBOL(list_sort);
```
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