本節簡單介紹了PostgreSQL在執行插入過程中與儲存相關的函式RecordAndGetPageWithFreeSpace->fsm_search,該函式搜尋FSM,找到有足夠空閒空間(min_cat)的堆page.

### 一、資料結構
**宏定義**
包括FSM頁面的葉子節點數/非葉子節點數/FSM樹深度等等.
```

#define MaxFSMRequestSize   MaxHeapTupleSize
#define MaxHeapTupleSize   (BLCKSZ - MAXALIGN(SizeOfPageHeaderData + sizeof(ItemIdData)))
#define FSM_CAT_STEP   (BLCKSZ / FSM_CATEGORIES)
#define FSM_CATEGORIES   256
//塊大小為8K則FSM_CAT_STEP = 32

#define SlotsPerFSMPage   LeafNodesPerPage
#define LeafNodesPerPage   (NodesPerPage - NonLeafNodesPerPage) = 8156 - 4095 = 4061
#define NodesPerPage (BLCKSZ - MAXALIGN(SizeOfPageHeaderData) - \
                 offsetof(FSMPageData, fp_nodes)) = 8192 - 32 - 4 = 8156
#define NonLeafNodesPerPage (BLCKSZ / 2 - 1) = 4095

/*
 * Depth of the on-disk tree. We need to be able to address 2^32-1 blocks,
 * and 1626 is the smallest number that satisfies X^3 >= 2^32-1. Likewise,
 * 216 is the smallest number that satisfies X^4 >= 2^32-1. In practice,
 * this means that 4096 bytes is the smallest BLCKSZ that we can get away
 * with a 3-level tree, and 512 is the smallest we support.
 * 儲存在磁碟上的樹深度.
 * 我們需要為2^32 - 1個塊定位定址,1626是可以滿足X^3 >= 2^32 - 1的最小數字.
 * 另外,216是可以滿足X^4 >= 2^32 - 1的最小數字.
 * 在實踐中,這意味著4096位元組是三層數可以支撐的最小BLCKSZ,512是最小可支援的.
 */
#define FSM_TREE_DEPTH  ((SlotsPerFSMPage >= 1626) ? 3 : 4)

```

**FSMAddress**
內部的FSM處理過程以邏輯地址scheme的方式工作,樹的每一個層次都可以認為是一個獨立的地址檔案.
```
/*
 * The internal FSM routines work on a logical addressing scheme. Each
 * level of the tree can be thought of as a separately addressable file.
 * 內部的FSM處理過程工作在一個邏輯地址scheme上.
 * 樹的每一個層次都可以認為是一個獨立的地址檔案.
 */
typedef struct
{
    //層次
    int         level;          /* level */
    //該層次內的頁編號
    int         logpageno;      /* page number within the level */
} FSMAddress;

/* Address of the root page. */
//根頁地址
static const FSMAddress FSM_ROOT_ADDRESS = {FSM_ROOT_LEVEL, 0};

```

**FSMPage**
 FSM page資料結構.詳細可參看src/backend/storage/freespace/README.
```
/*
 * Structure of a FSM page. See src/backend/storage/freespace/README for
 * details.
 * FSM page資料結構.詳細可參看src/backend/storage/freespace/README.
 */
typedef struct
{
    /*
     * fsm_search_avail() tries to spread the load of multiple backends by
     * returning different pages to different backends in a round-robin
     * fashion. fp_next_slot points to the next slot to be returned (assuming
     * there's enough space on it for the request). It's defined as an int,
     * because it's updated without an exclusive lock. uint16 would be more
     * appropriate, but int is more likely to be atomically
     * fetchable/storable.
     * fsm_search_avail()函式嘗試透過在一輪迴圈中返回不同的頁面到不同的後臺程式,
     *   從而分散在後臺程式上分散負載.
     * 該欄位因為無需獨佔鎖,因此定義為整型.
     * unit16可能會更合適,但整型看起來更適合於原子提取和儲存.
     */
    int         fp_next_slot;

/*
     * fp_nodes contains the binary tree, stored in array. The first
     * NonLeafNodesPerPage elements are upper nodes, and the following
     * LeafNodesPerPage elements are leaf nodes. Unused nodes are zero.
     * fp_nodes以陣列的形式儲存二叉樹.
     * 第一個NonLeafNodesPerPage元素是上一層的節點,接下來的LeafNodesPerPage元素是葉子節點.
     * 未使用的節點為0.
     */
    uint8       fp_nodes[FLEXIBLE_ARRAY_MEMBER];
} FSMPageData;

typedef FSMPageData *FSMPage;

```

**FSMLocalMap**
對於小表,不需要建立FSM來儲存空間資訊,使用本地的記憶體對映資訊.
```

/* Either already tried, or beyond the end of the relation */
//已嘗試或者已在表的末尾之後
#define FSM_LOCAL_NOT_AVAIL 0x00

/* Available to try */
//可用於嘗試
#define FSM_LOCAL_AVAIL     0x01

/*
 * For small relations, we don't create FSM to save space, instead we use
 * local in-memory map of pages to try.  To locate free space, we simply try
 * pages directly without knowing ahead of time how much free space they have.
 * 對於小表,不需要建立FSM來儲存空間資訊,使用本地的記憶體對映資訊.
 * 為了定位空閒空間,我們不需要知道他們有多少空閒空間而是直接簡單的對page進行嘗試.
 *
 * Note that this map is used to the find the block with required free space
 * for any given relation.  We clear this map when we have found a block with
 * enough free space, when we extend the relation, or on transaction abort.
 * See src/backend/storage/freespace/README for further details.
 * 注意這個map用於搜尋給定表的請求空閒空間.
 * 在找到有足夠空閒空間的block/擴充套件了relation/在事務回滾時,則清除這個map的資訊.
 * 詳細可檢視src/backend/storage/freespace/README.
 */
typedef struct
{
    BlockNumber nblocks;//塊數
    uint8       map[HEAP_FSM_CREATION_THRESHOLD];//陣列
}           FSMLocalMap;

static FSMLocalMap fsm_local_map =
{
    0,
    {
        FSM_LOCAL_NOT_AVAIL
    }
};

#define FSM_LOCAL_MAP_EXISTS (fsm_local_map.nblocks > 0)

```

**通用例程**
包括獲取左子節點/右子節點/父節點等
```

/* Macros to navigate the tree within a page. Root has index zero. */
//在page中遍歷樹.Root編號為0
#define leftchild(x)    (2 * (x) + 1)
#define rightchild(x)   (2 * (x) + 2)
#define parentof(x)     (((x) - 1) / 2)

/*
 * Find right neighbor of x, wrapping around within the level
 * 搜尋x右邊的鄰居,如需要在同一個層次上需回捲
 */
static int
rightneighbor(int x)
{
    /*
     * Move right. This might wrap around, stepping to the leftmost node at
     * the next level.
     * 移到右邊.這可能會引起回捲,調到下一個層次最左邊的節點上.
     */
    x++;

/*
     * Check if we stepped to the leftmost node at next level, and correct if
     * so. The leftmost nodes at each level are numbered x = 2^level - 1, so
     * check if (x + 1) is a power of two, using a standard
     * twos-complement-arithmetic trick.
     * 檢查是否跳轉到下一個層次最左邊的節點上,如是則修正x.
     * 每一個層次上最左邊的節點編號為x = 2^level - 1,
     *   因此檢查(x+1)是否為2的冪,使用標準的twos-complement-arithmetic技巧即可.
     */
    if (((x + 1) & x) == 0)//有符號整型,全1為0
        x = parentof(x);

return x;
}

/*
 * Returns the physical block number of a FSM page
 * 返回FSM page的物理塊號
 */
/*
計算公式:
To find the physical block # corresponding to leaf page n, we need to
count the number of leaf and upper-level pages preceding page n.
This turns out to be

y = n + (n / F + 1) + (n / F^2 + 1) + ... + 1

where F is the fanout . The first term n is the number
of preceding leaf pages, the second term is the number of pages at level 1,
and so forth.
*/
static BlockNumber
fsm_logical_to_physical(FSMAddress addr)
{
    BlockNumber pages;//塊號
    int         leafno;//頁號
    int         l;//臨時變數

/*
     * Calculate the logical page number of the first leaf page below the
     * given page.
     * 在給定的page下,計算第一個葉子頁面的邏輯頁號
     */
    leafno = addr.logpageno;
    for (l = 0; l < addr.level; l++)
        leafno *= SlotsPerFSMPage;

/* Count upper level nodes required to address the leaf page */
    //統計用於定位葉子頁面的上層節點數
    pages = 0;
    for (l = 0; l < FSM_TREE_DEPTH; l++)
    {
        pages += leafno + 1;
        leafno /= SlotsPerFSMPage;
    }

/*
     * If the page we were asked for wasn't at the bottom level, subtract the
     * additional lower level pages we counted above.
     * 如果請求的頁面不在底層,減去上面技術的額外的底層頁面數.
     */
    pages -= addr.level;
 
     /* Turn the page count into 0-based block number */
     //計數從0開始(減一)
     return pages - 1;
}

/*
 * Return the FSM location corresponding to given heap block.
 * 返回給定堆block的FSM位置.
 */
//addr = fsm_get_location(oldPage, &slot);
static FSMAddress
fsm_get_location(BlockNumber heapblk, uint16 *slot)
{
    FSMAddress  addr;

addr.level = FSM_BOTTOM_LEVEL;
    //#define SlotsPerFSMPage   LeafNodesPerPage
    //#define LeafNodesPerPage   (NodesPerPage - NonLeafNodesPerPage) = 8156 - 4095 = 4061
    //#define NodesPerPage (BLCKSZ - MAXALIGN(SizeOfPageHeaderData) - \
                       offsetof(FSMPageData, fp_nodes)) = 8192 - 32 - 4 = 8156
    //#define NonLeafNodesPerPage (BLCKSZ / 2 - 1) = 4095
    addr.logpageno = heapblk / SlotsPerFSMPage;
    *slot = heapblk % SlotsPerFSMPage;

return addr;
}

```

### 二、原始碼解讀
fsm_search函式搜尋FSM,找到有足夠空閒空間(min_cat)的堆page.
```

/*
 * Search the tree for a heap page with at least min_cat of free space
 * 搜尋FSM,找到有足夠空閒空間(min_cat)的堆page
 */
//return fsm_search(rel, search_cat);
static BlockNumber
fsm_search(Relation rel, uint8 min_cat)
{
    int         restarts = 0;
    FSMAddress  addr = FSM_ROOT_ADDRESS;

for (;;)
    {
        //--------- 迴圈
        int         slot;
        Buffer      buf;
        uint8       max_avail = 0;

/* Read the FSM page. */
        //讀取FSM page
        buf = fsm_readbuf(rel, addr, false);

/* Search within the page */
        //頁內搜尋
        if (BufferIsValid(buf))
        {
            LockBuffer(buf, BUFFER_LOCK_SHARE);
            //搜尋可用的slot
            slot = fsm_search_avail(buf, min_cat,
                                    (addr.level == FSM_BOTTOM_LEVEL),
                                    false);
            if (slot == -1)
                //獲取最大可用空間
                max_avail = fsm_get_max_avail(BufferGetPage(buf));
            UnlockReleaseBuffer(buf);
        }
        else
            //buffer無效,則設定為-1
            slot = -1;

if (slot != -1)
        {
            /*
             * Descend the tree, or return the found block if we're at the
             * bottom.
             * 如在樹的底部,則返回找到的塊.
             */
            if (addr.level == FSM_BOTTOM_LEVEL)
                return fsm_get_heap_blk(addr, slot);

addr = fsm_get_child(addr, slot);
        }
        else if (addr.level == FSM_ROOT_LEVEL)
        {
            /*
             * At the root, failure means there's no page with enough free
             * space in the FSM. Give up.
             * 處於根節點,失敗意味著FSM中沒有足夠空閒空間的頁面存在,放棄.
             */
            return InvalidBlockNumber;
        }
        else
        {
            uint16      parentslot;
            FSMAddress  parent;

/*
             * At lower level, failure can happen if the value in the upper-
             * level node didn't reflect the value on the lower page. Update
             * the upper node, to avoid falling into the same trap again, and
             * start over.
             * 在低層上,如果上層節點沒有反映更低層頁面的值則會出現失敗.
             * 更新高層節點,避免重複掉入同一個陷阱,重新開始.
             *
             * There's a race condition here, if another backend updates this
             * page right after we release it, and gets the lock on the parent
             * page before us. We'll then update the parent page with the now
             * stale information we had. It's OK, because it should happen
             * rarely, and will be fixed by the next vacuum.
             * 在我們釋放後,另外的後臺程式更新這個頁面同時在我們之前鎖定了父節點的話,會存在條件競爭.
             * 然後我們使用現有已知穩定的資訊更新父頁面.
             * 如OK,因為這種很少出現,那麼會在下一個vacuum中修復此問題.
             */
            parent = fsm_get_parent(addr, &parentslot);
            fsm_set_and_search(rel, parent, parentslot, max_avail, 0);

/*
             * If the upper pages are badly out of date, we might need to loop
             * quite a few times, updating them as we go. Any inconsistencies
             * should eventually be corrected and the loop should end. Looping
             * indefinitely is nevertheless scary, so provide an emergency
             * valve.
             * 如果上層頁面過舊,可能需要迴圈很多次,更新上層頁面資訊.
             * 不一致性會被週期性的糾正,迴圈會停止.
             * 但無限迴圈是很可怕的,因此設定閾值,超過此閾值則退出迴圈.
             */
            if (restarts++ > 10000)
                return InvalidBlockNumber;

/* Start search all over from the root */
            //從root開始搜尋
            addr = FSM_ROOT_ADDRESS;
        }
    }
}

```

### 三、跟蹤分析
N/A

### 四、參考資料
[PG Source Code](https://doxygen.postgresql.org)
[Database Cluster, Databases, and Tables](http://www.interdb.jp/pg/pgsql01.html)
[free space map README](https://github.com/postgres/postgres/tree/master/src/backend/storage/freespace)

PostgreSQL 原始碼解讀（147）- Storage Manager#3（fsm_search函式）

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