（超快速计算素数个数）10的11次方内素数个数

#include 
#include 
#include 
#include 
#include 

#define COMP 4
#define MASKN(n)  (1 << ((n >> 1) & 7))
#define min(a, b) (a) < (b) ? (a) : (b)
#define MULTI_THREAD
#define THRED_NUMS 4
typedef unsigned int uint;
#ifdef _WIN32
typedef  __int64 int64;
#else
typedef long long int64;
#endif

int *Prime;
int *PI;

int64 MAXN = (int64)1e11;
int pt[130000];   // MAXN < 1e11, size = np

int *phiTable;
int *minfactor;

int x23, x12, x13, x14, y;
int64 x;

int ST = 7, Q = 1, phiQ = 1;
//Q    = 2*3*5*7*11*13 = 30030
//phiQ = 1*2*4*6*10*12 = 5760

int phi(int x, int a)
{
    if (a == ST)
        return (x / Q) * phiQ + phiTable[x % Q];
    else if (a == 0)
        return x;
    else if (x < Prime[a])
        return 1;
    else
        return phi(x, a - 1) - phi(x / Prime[a], a - 1);
}

#ifdef MULTI_THREAD
struct ThreadInfo{
    int pindex;
    int theadnums;
    int64 pnums;
}Threadparam[2 * THRED_NUMS + 2];

#ifdef _WIN32
#include 
DWORD WINAPI WIN32ThreadFun(LPVOID pinfo)
#else
#include 
void* POSIXThreadFun(void *pinfo)
#endif
{
    ThreadInfo *pThreadInfo = (ThreadInfo *) (pinfo);
    int addstep = pThreadInfo->theadnums * 2;

    for (int i = pThreadInfo->pindex; pt[i] != 0; i += addstep){
        if (pt[i] > 0)
            pThreadInfo->pnums -= phi(pt[i], pt[i + 1]);
        else
            pThreadInfo->pnums += phi(-pt[i], pt[i + 1]);
    }
    //    printf("ThreadID = %4d, phi(%d) = %d\n", GetCurrentThreadId(), pThreadInfo->pindex, pThreadInfo->pnums);
    //    printf("ThreadID = %4d, phi(%d) = %d\n", pthread_self(), pThreadInfo->pindex, pThreadInfo->pnums);
    return 0;
}

int64 multiThread(int theadnums)
{
    int i;
    int64 pnums = 0;

 assert(theadnums < 2 * THRED_NUMS);

    for (i = 0; i < theadnums; i++){
        Threadparam[i].pindex = 2 * i + 1;
        Threadparam[i].theadnums = theadnums;
        Threadparam[i].pnums  = 0;
    }

#ifdef _WIN32
    HANDLE tHand[THRED_NUMS * 2];
    DWORD threadID[THRED_NUMS * 2];
    for (i = 0; i < theadnums; i++){
        tHand[i] = CreateThread(NULL, 0, (LPTHREAD_START_ROUTINE)WIN32ThreadFun, (LPVOID)(&Threadparam[i]), 0, &threadID[i]);
        if (tHand[i] == NULL)
            printf("create Win32 thread error\n");
    }
    WaitForMultipleObjects(theadnums, tHand, true, INFINITE);
    for (i = 0; i < theadnums; i++){
        pnums += Threadparam[i].pnums;
        CloseHandle(tHand[i]);
    }
#else
    pthread_t tid[THRED_NUMS];
    for (i = 0; i < theadnums; i++){
        int    error = pthread_create(&tid[i], NULL, POSIXThreadFun, &Threadparam[i]);
        if ( error != 0 )

    }
    for (i = 0; i < theadnums; i++){
        pthread_join(tid[i], NULL);
        pnums += Threadparam[i].pnums;
    }
#endif
    return pnums;
}
#endif

int freememory(int alloc)
{
    int memsize = (x / y) + 100;
    if (alloc == 0){
        int psize = (int) (memsize / log(memsize));
        //printf("psize = %d memeszie = %d\n", psize, (int)(psize * 1.2) );
        PI = new int [memsize + 100];
        Prime = new int[(int)(psize * 1.2) + 100];
        assert(PI && Prime);
    }else{
        delete phiTable;
        delete minfactor;
        delete Prime;
        delete PI;
    }
    return alloc;
}

void init_phiTable( )
{
    clock_t start = clock();

    int p, i, j;

    if (x < 1e10)
        ST = 6;
    if (ST > PI[y])
        ST = PI[y];

    for (i = 1; i <= ST; ++i){
        Q *= Prime[i];
        phiQ *= Prime[i] - 1;
    }

    phiTable = new int[Q + 10];
    for (i = 0; i < Q; ++i)
        phiTable[i] = i;

    for (i = 1; i <= ST; ++i){
        p = Prime[i];
        for (j = Q - 1; j >= 0; --j)
            phiTable[j] -= phiTable[j / p];
    }


}

void init_minFactor( )
{
    clock_t start = clock();

    int i, j, maxy = y + 10;
    int sqrty = (int)sqrt(maxy) + 1;

    minfactor = new int[maxy + 10];
    for (i = 0; i < maxy; i++)
        minfactor[i] = i;

    for (i = 1; Prime[i] <= maxy; i++){
        for (j = Prime[i]; j <= maxy; j += Prime[i]){
            if (minfactor[j] == -j || minfactor[j] == j)
                minfactor[j] = -Prime[i];
            else
                minfactor[j] = -minfactor[j];
        }
    }

    for (i = 1; Prime[i] <= sqrty; i++){
        int powp = Prime[i] * Prime[i];
        for (j = powp; j <= maxy; j += powp)
            minfactor[j] = 0;
    }

}

int sieve( )
{
    clock_t start = clock();

    int primes = 1;
    int maxp = (x / y) + 10;
    Prime[1] = 2;

    unsigned char *bitMask = (unsigned char *) PI;
    memset(bitMask, 0, (maxp + 64) >> COMP);

    for (int p = 3; p < maxp; p += 2){
        if ( !(bitMask[p >> COMP] & MASKN(p)) ){
            Prime[++primes] = p;
            if (p > maxp / p)
                continue;
            for (int j = p * p; j < maxp; j += p << 1)
                bitMask[j >> COMP] |= MASKN(j);
        }
    }

    Prime[0] = primes;
    Prime[primes] = 0;

    return primes;
}

void init_x( )
{
   // x = (int64)MAXN;
    x23 = (int)(pow(x, 2.0 / 3) + 0.01);
    x12 = (int)(pow(x, 1.0 / 2) + 0.01);
    x13 = (int)(pow(x, 1.0 / 3) + 0.01);
    x14 = (int)(pow(x, 1.0 / 4) + 0.01);

    assert((int64)x12 * x12 <= x);
    assert((int64)x13 * x13 * x13 <= x);
    assert((int64)x14 * x14 * x14 * x14 <= x);

    y = x13;



    freememory(0);
}

int64 cal_S0( )
{
    int64 S0 = x;
    for (int j = 2; j <= y; j++){
        if (minfactor[j] > 0)
            S0 += x / j;
        else if (minfactor[j] < 0)
            S0 -= x / j;
    }


    return S0;
}

// so bad performance in this function
int64 cal_S3( )
{
    clock_t start = clock();

    int i, p, a;
    int np = 1;
    int64 S3 = 0;

    for (i = 1; i <= PI[x14]; i++){
        p = Prime[i];
        a = PI[p] - 1;
#ifdef PRINT_DEBUG
        assert(p <= x14 && a >= 0);
#endif
        for (int m = y / p + 1; m <= y; m++){
            int xx = x / (int64)(m * p);
#ifndef MULTI_THREAD
            if (minfactor[m] > p)
                S3 -= phi(xx, a);
            else if (minfactor[m] < -p)
                S3 += phi(xx, a);
#else
            if (minfactor[m] > p){
                pt[np++] = xx;
                pt[np++] = a;
            }
            else if (minfactor[m] < -p){
                pt[np++] = -xx;
                pt[np++] = a;
            }
#endif
        }
    }

#ifdef MULTI_THREAD

 if (np < 100)
  S3 = multiThread(1);
 else
  S3 = multiThread(THRED_NUMS);
#endif


    return S3;
}

void init_PI( )
{
    clock_t start = clock();

    int Px = 1;
    PI[0] = PI[1] = 0;
    for (int i = 1; Prime[i]; i++, Px++){
        for (int j = Prime[i]; j <= Prime[i + 1]; j++)
            PI[j] = Px;
    }

    //printf("        Px = %d, primes = %d\n", Px, Prime[0]);

}

int64 cal_P2xa( )
{
    int64 phi2 = (int64)PI[y] * (PI[y] - 1) / 2 - (int64)PI[x12] * (PI[x12] - 1) / 2;

    for (int i = PI[y] + 1; i <= PI[x12] + 0; i++){
        int p = Prime[i];
#ifdef PRINT_DEBUG
        assert(p > y && p <= x12);
#endif
        phi2 += PI[x / p];
    }


    return phi2;
}

int64 cal_S1( )
{
    int64 temp = PI[y] - PI[x13];
    int64 S1 = temp * (temp - 1) / 2;


    return S1;
}

int64 cal_U( )
{
    int64 p, U = 0;
    int sqrt_xdivy = (int)sqrt(x / y);
    for (int i = PI[sqrt_xdivy] + 1; i <= PI[x13]; i++){
        p = Prime[i];
        U += PI[y] - PI[x / (p * p)];
    }



    return U;
}

int64 cal_V1( )
{
    int64 V1 = 0;
    int MINq, p;
    for (int i = PI[x14] + 1; i <= PI[x13]; i++){
        p = Prime[i];
        MINq = min((uint)y, x / ((int64)p * p));
#ifdef PRINT_DEBUG
        assert(p > x14 && p <= x13 && MINq >= p);
#endif
        V1 += (int64)(2 - PI[p]) * (PI[MINq] - PI[p]); //!!!!!!
    }



    return V1;
}

int64 cal_V2( )
{
    int64 V2 = 0;
    int i, sqrt_xdivy  = (int)sqrt(x / y);
    //    int sqrt_xdivy2 = (int)sqrt(x / (y * y));
    //    int sqrt_xdivp  = (int)sqrt(x / 1);
    int xdivy2 = x / (y * y);

#if 0
    uint p, q;
    uint W[6] = {0};
    //W1
    for (p = x14 + 1; p <= xdivy2; p++)
        for (q = p + 1; q <= y; q++)
            W[1] += PI[x / (p * q)];

    //W2
    for (p = xdivy2 + 1; p <= sqrt_xdivy; p++){
        sqrt_xdivp = (uint)sqrt(x / p);
        for (q = p + 1;  q <= sqrt_xdivp; q++)
            W[2] += PI[x / (p * q)];
    }

    //W3
    for (p = xdivy2 + 1; p <= sqrt_xdivy; p++)
        for (q = sqrt(x / p) + 1;  q <= y; q++)
            W[3] += PI[x / (p * q)];

    //W4
    for (p = sqrt_xdivy + 1; p <= x13; p++){
        sqrt_xdivp = (uint)sqrt(x / p);
        for (q = p; q <= sqrt_xdivp; q++)
            W[4] += PI[x / (p * q)];
    }

    //W5
    for (p = sqrt_xdivy + 1; p <= x13; p++)
        for (q = sqrt(x / p) + 1; q <= xdivy2; q++)
            W[5] += PI[x / (p * q)];
    V2 = W[1] + W[2] + W[3] + W[4] + W[5];

#else

    for (i = PI[x14] + 1; i <= PI[sqrt_xdivy]; i++){
        int64 p = Prime[i];
#ifdef PRINT_DEBUG
        assert(p > x14 && p <= sqrt_xdivy);
#endif
        for (int j = PI[p] + 1; j <= PI[y]; j++){
            int q = Prime[j];
#ifdef PRINT_DEBUG
            assert(q > p && q <= y);
#endif
            V2 += PI[x / (p * q)];
        }
    }

    for (i = PI[sqrt_xdivy] + 1; i <= PI[x13]; i++){
        int64 p = Prime[i];
#ifdef PRINT_DEBUG
        assert(p > sqrt_xdivy && p <= x13);
#endif
        xdivy2 = x / (p * p);
        for (int j = PI[p] + 1; j <= PI[xdivy2]; j++){
            int q = Prime[j];
            V2 += PI[x / (p * q)];
        }
    }

#endif



    return V2;
}

int main(int argc, char* argv[])
{
    
 int ans[17]={0,0,1,2,2,2,3,3,4,4,4,4,5,5,6,6};
 if (argc > 1)
  MAXN = atoll(argv[1]); //mingw
    while(scanf("%lld",&x)!=EOF)
    {
    if(x<=15){printf("%d\n",ans[x]);continue;}
    init_x( );
    sieve( );
    init_PI( );
    init_minFactor( );
    init_phiTable( );
    int64 pix = PI[y] - 1;
    pix += cal_S3( ); //mul thread
    pix -= cal_P2xa( );
    pix += cal_S0( );
    if (y != x13){
        pix += cal_S1( );
        pix += cal_U( );
    }
    pix += cal_V2( );
    pix += cal_V1( );
    printf("%I64d\n",pix);
    }
freememory(1);
    return 0;
}