重提基数排序

重提基数排序

在此之前，我已尝试过两次基数排序的方法：LSD、MSD。 
我的主要改进点在于每次“申请”大块存储器，而不是采用最原始的链表。 
当然这种形式本质上还是链表，只是每个节点就是一个页面。 
在存储器申请/释放上，开始时一次申请/结束时一次释放，避免了一次一数字时的malloc/free调用的代价。

但是，缺点还是存在的，主要在于不够缓存友好。 
看一下结果就很容易明白缓存友好的重要性了。

主要数据结构：

const __int32 TFSI = 1024*1024*500;
const int PAGEAMOUNT = 4096;
const int PAGEGRANULAR = PAGEAMOUNT/sizeof(int);
const int TERMINATOR = -1;
const int BUCKETSLOTCOUNT = 256;

typedef struct tagPageList{
int * PagePtr;
struct tagPageList * next;
}PageList;

typedef struct tagBucket{
int * currentPagePtr;
int offset;
PageList pl;
PageList * currentPageListItem;
}Bucket;

void MakeSure(pmhBool s){
if (s == pmhFalse) __debugbreak();
}

const __int32 TFSI = 1024*1024*500;
const int PAGEAMOUNT = 4096;
const int PAGEGRANULAR = PAGEAMOUNT/sizeof(int);
const int TERMINATOR = -1;
const int BUCKETSLOTCOUNT = 256;

typedef struct tagPageList{
    int * PagePtr;
    struct tagPageList * next;
}PageList;

typedef struct tagBucket{
    int * currentPagePtr;
    int offset;
    PageList pl;
    PageList * currentPageListItem;
}Bucket;

void MakeSure(pmhBool s){
    if (s == pmhFalse) __debugbreak();
}

排序函数：

int LSD_radix_sort_R2(){
HANDLE heap = NULL;
Bucket bucket[BUCKETSLOTCOUNT];
PageList * pageListPool;
int plpAvailable = 0;
int * pages = NULL;
int * pagesAvailable = NULL;

typedef unsigned short ElementType;
ElementType * s;

time_t timeBegin;
time_t timeEnd;

//pages = (int * )VirtualAlloc(NULL, (TFSI/PAGEGRANULAR + BUCKETSLOTCOUNT + 8) * PAGEAMOUNT, MEM_COMMIT | MEM_RESERVE, PAGE_READWRITE);
//int a = GetLastError();
//pageListPool = (PageList *)VirtualAlloc(NULL, (TFSI/PAGEGRANULAR + 8) * sizeof(PageList), MEM_COMMIT | MEM_RESERVE, PAGE_READWRITE);
//s = (ElementType *)VirtualAlloc(NULL, TFSI*sizeof(ElementType), MEM_COMMIT | MEM_RESERVE, PAGE_READWRITE);

heap = HeapCreate(HEAP_NO_SERIALIZE|HEAP_GENERATE_EXCEPTIONS, 1024*1024, 0);
if (heap != NULL){
pages = (int * )HeapAlloc(heap, 0, (TFSI/PAGEGRANULAR + BUCKETSLOTCOUNT + 8) * PAGEAMOUNT);
pageListPool = (PageList *)HeapAlloc(heap, 0, (TFSI/PAGEGRANULAR + 8) * sizeof(PageList));
s = (ElementType *)HeapAlloc(heap, 0, TFSI*sizeof(ElementType));
}
MakeSure(pages != NULL && pageListPool != NULL && s != NULL);

timeBegin = clock();
for (int i=0; i<TFSI; i++) s[i] = rand();
timeEnd = clock();
printf("\n%f(s) consumed in generating numbers", (double)(timeEnd-timeBegin)/CLOCKS_PER_SEC);

timeBegin = clock();

for (int t=0; t<sizeof(ElementType); t++){
FillMemory(pages, (TFSI/PAGEGRANULAR + BUCKETSLOTCOUNT + 8) * PAGEAMOUNT, 0xff);
SecureZeroMemory(pageListPool, (TFSI/PAGEGRANULAR + 8) * sizeof(PageList));
pagesAvailable = pages;
plpAvailable = 0;

for(int i=0; i<256; i++){
bucket[i].currentPagePtr = pagesAvailable;
bucket[i].offset = 0;
bucket[i].pl.PagePtr = pagesAvailable;
bucket[i].pl.next = NULL;
pagesAvailable += PAGEGRANULAR;
bucket[i].currentPageListItem = &(bucket[i].pl);
}

int bucketIdx;
for (int i=0; i<TFSI; i++){
bucketIdx = (s[i]>>t*8)&0xff;
//save(bucketIdx, objIdx[i]);
bucket[bucketIdx].currentPagePtr[ bucket[bucketIdx].offset ] = s[i];
bucket[bucketIdx].offset++;
if (bucket[bucketIdx].offset == PAGEGRANULAR){
bucket[bucketIdx].currentPageListItem->next = &pageListPool[plpAvailable];
plpAvailable++;
bucket[bucketIdx].currentPageListItem->next->PagePtr = pagesAvailable;
bucket[bucketIdx].currentPageListItem->next->next = NULL;

bucket[bucketIdx].currentPagePtr = pagesAvailable;
bucket[bucketIdx].offset = 0;
pagesAvailable += PAGEGRANULAR;

bucket[bucketIdx].currentPageListItem = bucket[bucketIdx].currentPageListItem->next;
}
}

//update objIdx index
int start = 0;
for (int i=0; i<256; i++){
PageList * p;
p = &(bucket[i].pl);
while (p){
for (int t=0; t<PAGEGRANULAR; t++){
int idx = p->PagePtr[t];
if (idx != TERMINATOR){
s[start] = idx;
start++;
}
if (idx == TERMINATOR) break;
}
p = p->next;
}
}
}

timeEnd = clock();
printf("\n%f(s) consumed in generating results", (double)(timeEnd-timeBegin)/CLOCKS_PER_SEC);

HeapFree(heap, 0, pages);
HeapFree(heap, 0, pageListPool);
HeapFree(heap, 0, s);
HeapDestroy(heap);

return 0;
}

int LSD_radix_sort_R2(){
    HANDLE heap = NULL;
    Bucket bucket[BUCKETSLOTCOUNT];
    PageList * pageListPool;
    int plpAvailable = 0;
    int * pages = NULL;
    int * pagesAvailable = NULL;

    typedef unsigned short ElementType;
    ElementType * s;

    time_t timeBegin;
    time_t timeEnd;

    //pages = (int * )VirtualAlloc(NULL, (TFSI/PAGEGRANULAR + BUCKETSLOTCOUNT + 8) * PAGEAMOUNT, MEM_COMMIT | MEM_RESERVE, PAGE_READWRITE);
    //int a = GetLastError();
    //pageListPool = (PageList *)VirtualAlloc(NULL, (TFSI/PAGEGRANULAR + 8) * sizeof(PageList),  MEM_COMMIT | MEM_RESERVE, PAGE_READWRITE);
    //s = (ElementType *)VirtualAlloc(NULL, TFSI*sizeof(ElementType), MEM_COMMIT | MEM_RESERVE, PAGE_READWRITE);

    heap = HeapCreate(HEAP_NO_SERIALIZE|HEAP_GENERATE_EXCEPTIONS, 1024*1024, 0);
    if (heap != NULL){
        pages = (int * )HeapAlloc(heap, 0, (TFSI/PAGEGRANULAR + BUCKETSLOTCOUNT + 8) * PAGEAMOUNT);
        pageListPool = (PageList *)HeapAlloc(heap, 0, (TFSI/PAGEGRANULAR + 8) * sizeof(PageList));
        s = (ElementType *)HeapAlloc(heap, 0, TFSI*sizeof(ElementType));
    }
    MakeSure(pages != NULL && pageListPool != NULL && s != NULL);

    timeBegin = clock();
    for (int i=0; i<TFSI; i++) s[i] = rand();
    timeEnd = clock();
    printf("\n%f(s) consumed in generating numbers", (double)(timeEnd-timeBegin)/CLOCKS_PER_SEC);
    
    timeBegin = clock();

    for (int t=0; t<sizeof(ElementType); t++){
        FillMemory(pages, (TFSI/PAGEGRANULAR + BUCKETSLOTCOUNT + 8) * PAGEAMOUNT, 0xff);
        SecureZeroMemory(pageListPool, (TFSI/PAGEGRANULAR + 8) * sizeof(PageList));
        pagesAvailable = pages;
        plpAvailable = 0;

        for(int i=0; i<256; i++){
            bucket[i].currentPagePtr = pagesAvailable;
            bucket[i].offset = 0;
            bucket[i].pl.PagePtr = pagesAvailable;
            bucket[i].pl.next = NULL;
            pagesAvailable += PAGEGRANULAR;
            bucket[i].currentPageListItem = &(bucket[i].pl);
        }

        int bucketIdx;
        for (int i=0; i<TFSI; i++){
            bucketIdx = (s[i]>>t*8)&0xff;
            //save(bucketIdx, objIdx[i]);
            bucket[bucketIdx].currentPagePtr[ bucket[bucketIdx].offset ] = s[i];
            bucket[bucketIdx].offset++;
            if (bucket[bucketIdx].offset == PAGEGRANULAR){
                bucket[bucketIdx].currentPageListItem->next = &pageListPool[plpAvailable];
                plpAvailable++;
                bucket[bucketIdx].currentPageListItem->next->PagePtr = pagesAvailable;
                bucket[bucketIdx].currentPageListItem->next->next = NULL;
                
                bucket[bucketIdx].currentPagePtr = pagesAvailable;
                bucket[bucketIdx].offset = 0;
                pagesAvailable += PAGEGRANULAR;
                
                bucket[bucketIdx].currentPageListItem = bucket[bucketIdx].currentPageListItem->next;
            }
        }

        //update objIdx index
        int start = 0;
        for (int i=0; i<256; i++){
            PageList * p;
            p = &(bucket[i].pl);
            while (p){
                for (int t=0; t<PAGEGRANULAR; t++){
                    int idx = p->PagePtr[t];
                    if (idx != TERMINATOR){
                        s[start] = idx;
                        start++;
                    }
                    if (idx == TERMINATOR) break;
                }
                p = p->next;
            }
        }
    }

    timeEnd = clock();
    printf("\n%f(s) consumed in generating results", (double)(timeEnd-timeBegin)/CLOCKS_PER_SEC);
    
    HeapFree(heap, 0, pages);
    HeapFree(heap, 0, pageListPool);
    HeapFree(heap, 0, s);
    HeapDestroy(heap);    
    
    return 0;
}

随机生成5亿个 short，排序结果如图

上两次最快的速度是 1亿个 short 4.563秒。
这次5亿个5.454s，折合一亿个 1.09s，事实上直接运行一亿个数字排序的话可能要少于这个数字。

近5倍的差距来源在于缓存的利用上面。

上两次排的都是数字的序号，而不是真正的数字，这样做是因为我要最终完成二维表排序。

可想而知，这样访问一个数字的话需要两个步骤： 
1、先取到序号，这需要访问一次数组元素 
2、按第一步提供的序号，访问排序数组内元素

这样可真的就是随机访问存储了！ 
缺陷就是很差的存储器访问效率。

当然，如果使用自索引排序[1]（self-indexed sort）,必然更快，不过那样我就不能拿来扩展二维表排序了。

在The Algorithm Design Manual 上面，作者提到Pennysort的一个记录：$760的机器上排序32GB耗时1679s。 
这个我也写了个大致方法： 
设置master slave缓冲区, 
一次排序5亿个整型：cpu 
缓冲5亿个整型：I/O

CreateThread fillmaster suspended
CreateThread radix_sort suspended
Resume all the threads

FillMaster{
    Load first data-slice to the master;
    while (true){
        FillSlave;
        Radix_sort;
        WaitforMultipleObjects(Fillslave, radix_sort);
        swapPointer(master, slave);
        if (finished) break;
    }
    Radix_sort the last slice;
}

大致估计下时间：排序和I/O操作的最长一方决定了一轮的时间。 
如果划分32GB为32个小文件，大概 32 * I/O时间 就是总共排序32GB的时间。（i/o一般是最慢的） 
不过读写文件也有多种方式，BSIS_PennySort_2006的描述中提到了 IO完成端口（IO completion port）有着顺序读尽两倍的速度，这么一来，读写文件的速度有望翻倍。 
不过这部分我就没有继续试验了。

PennySort的网址可以参考 http://sortbenchmark.org/

BSIS的描述文本 http://sortbenchmark.org/BSIS-PennySort_2006.pdf

Computer Organization and Design: The Hardware/Software Interface中的一段话，作者的结论是理解存储器层次原理是理解的当今计算机性能的关键。

 

Reference: 
[1]Yingxu Wang.A New Sort Algorithm: Self-Indexed Sort.Communications of ACM SIGPALN, 1996,Vol.31, No.3, March:28-36

 

 

分类: C/C++