#include <float.h>
#include <math.h>
#include <stddef.h>
#include <stdio.h>
#include <stdlib.h>
#include <sys/times.h>
#include <unistd.h>

void
initMatrix(size_t m, size_t n,
     double *A,
     ptrdiff_t incRow, ptrdiff_t incCol)
{
    for (size_t i=0; i<m; ++i) {
        for (size_t j=0; j<n; ++j) {
            A[i*incRow+j*incCol] = i*n+j+1;
        }
    }
}

void
printMatrix(size_t m, size_t n,
            const double *A,
            ptrdiff_t incRow, ptrdiff_t incCol)
{
    for (size_t i=0; i<m; ++i) {
        for (size_t j=0; j<n; ++j) {
            printf("%10.3lf", A[i*incRow+j*incCol]);
        }
        printf("\n");
    }
    printf("\n");
}

//-- BLAS Level 1 --------------------------------------------------------------

size_t
idamax(size_t n, const double *x, ptrdiff_t incX)
{
    size_t iMax = 0;
    for (size_t i=1; i<n; ++i) {
        if (fabs(x[i*incX]) > fabs(x[iMax*incX])) {
            iMax = i;
        }
    }
    return iMax;
}


void
dcopy(size_t n,
      const double *x, ptrdiff_t incX,
      double *y, ptrdiff_t incY)
{
    for (size_t i=0; i<n; ++i) {
        y[i*incY] = x[i*incX];
    }
}

void
dswap(size_t n,
      double *x, ptrdiff_t incX,
      double *y, ptrdiff_t incY)
{
    for (size_t i=0; i<n; ++i) {
        double tmp = x[i*incX];
        x[i*incX] = y[i*incY];
        y[i*incY] = tmp;
    }
}

void
daxpy(size_t n, double alpha,
      const double *x, ptrdiff_t incX,
      double *y, ptrdiff_t incY)
{
    if (alpha==0) {
        return;
    }
    for (size_t i=0; i<n; ++i) {
        y[i*incY] += alpha*x[i*incX];
    }
}

void
dscal(size_t n, double alpha,
      double *x, ptrdiff_t incX)
{
    if (alpha==1) {
        return;
    }
    if (alpha==0) {
        for (size_t i=0; i<n; ++i) {
            x[i*incX] = 0;
        }
    } else {
        for (size_t i=0; i<n; ++i) {
            x[i*incX] *= alpha;
        }
    }
}

double
ddot(size_t n,
     const double *x, ptrdiff_t incX,
     const double *y, ptrdiff_t incY)
{
    double alpha = 0;
    for (size_t i=0; i<n; ++i) {
        alpha += x[i*incX]*y[i*incY];
    }
    return alpha;
}

//-- BLAS Level 2 --------------------------------------------------------------

void
dger(size_t m, size_t n, double alpha,
     const double *x, ptrdiff_t incX,
     const double *y, ptrdiff_t incY,
     double *A, ptrdiff_t incRowA, ptrdiff_t incColA)
{
    if (alpha==0 || m==0 || n==0) {
        return;
    }
    if (incRowA<incColA) {
        // col major case
        for (size_t j=0; j<n; ++j) {
            daxpy(m, alpha*y[j*incY], x, incX, &A[j*incColA], incRowA);
        }
    } else {
        // row major case
        for (size_t i=0; i<m; ++i) {
            daxpy(n, alpha*x[i*incX], y, incY, &A[i*incRowA], incColA);
        }
    }
}

//-- LAPACK function -----------------------------------------------------------

ptrdiff_t
lu_unblk(size_t m, size_t n,
         double *A, ptrdiff_t incRowA, ptrdiff_t incColA,
         size_t *p, ptrdiff_t incP)
{
    size_t    min_mn = (m<n) ? m : n;
    ptrdiff_t info   = -1;

    for (size_t j=0; j<min_mn; ++j) {
        size_t jp = j + idamax(m-j, &A[j*(incRowA+incColA)], incRowA);

        p[j*incP] = jp;
        if (A[jp*incRowA + j*incColA] != 0) {
            if (j!=jp) {
                dswap(n, &A[j*incRowA], incColA, &A[jp*incRowA], incColA);
            }
            dscal(m-j-1,
                  1.0/A[j*(incRowA+incColA)],
                  &A[(j+1)*incRowA+j*incColA], incRowA);
            dger(m-j-1, n-j-1,
                 -1.0,
                 &A[(j+1)*incRowA+j*incColA], incRowA,
                 &A[j*incRowA+(j+1)*incColA], incColA,
                 &A[(j+1)*(incRowA+incColA)], incRowA, incColA);
        } else if (info==-1) {
            info = j;
        }
    }
    return info;
}

//-- Function for benchmarking and testing -------------------------------------

double
walltime()
{
   struct tms    ts;
   static double ClockTick=0.0;

   if (ClockTick==0.0) {
        ClockTick = 1.0 / ((double) sysconf(_SC_CLK_TCK));
   }
   return ((double) times(&ts)) * ClockTick;
}

void
randGeMatrix(int m, int n, double *A, int incRowA, int incColA)
{
    int i, j;
    for (j=0; j<n; ++j) {
        for (i=0; i<m; ++i) {
            A[i*incRowA+j*incColA] = ((double)rand()-RAND_MAX/2)*200/RAND_MAX;
        }
    }
}

void
dgecopy(size_t m, size_t n,
        const double *X, ptrdiff_t incRowX, ptrdiff_t incColX,
        double *Y, ptrdiff_t incRowY, ptrdiff_t incColY)
{
    size_t i, j;

    for (i=0; i<m; ++i) {
        for (j=0; j<n; ++j) {
            Y[i*incRowY+j*incColY] = X[i*incRowX+j*incColX];
        }
    }
}

void
dgemm(size_t m, size_t n, size_t k,
      double alpha,
      const double *A, ptrdiff_t incRowA, ptrdiff_t incColA,
      const double *B, ptrdiff_t incRowB, ptrdiff_t incColB,
      double beta,
      double *C, ptrdiff_t incRowC, ptrdiff_t incColC)
{
    size_t i, j, l;

    if (beta!=1) {
        for (i=0; i<m; ++i) {
            for (j=0; j<n; ++j) {
                C[i*incRowC+j*incColC] *= beta;
            }
        }
    }
    if (alpha!=0) {
        for (i=0; i<m; ++i) {
            for (j=0; j<n; ++j) {
                for (l=0; l<k; ++l) {
                    C[i*incRowC+j*incColC] += alpha*A[i*incRowA+l*incColA]
                                                   *B[l*incRowB+j*incColB];
                }
            }
        }
    }
}

double
err_lu(size_t m, size_t n,
       const double *A, ptrdiff_t incRowA, ptrdiff_t incColA,
       double *LU, ptrdiff_t incRowLU, ptrdiff_t incColLU,
       size_t *P, ptrdiff_t incP)
{
    double aNrm1 = 0;
    double err   = 0;

    size_t  i,j;
    size_t  k     = (m<n) ? m : n;
    double *L    = (double *)malloc(m*k*sizeof(double));
    double *U    = (double *)malloc(k*n*sizeof(double));

    for (j=0; j<k; ++j) {
        for (i=0; i<m; ++i) {
            L[i+j*m] = (i>j) ? LU[i*incRowLU+j*incColLU]
                             : (i==j) ? 1
                                      : 0;
        }
    }
    for (j=0; j<n; ++j) {
        for (i=0; i<k; ++i) {
            U[i+j*k] = (i<=j) ? LU[i*incRowLU+j*incColLU]
                              : 0;
        }
    }
    for (j=0; j<n; ++j) {
        for (i=0; i<m; ++i) {
            aNrm1 += fabs(A[i*incRowA+j*incColA]);
        }
    }

    dgemm(m, n, k, 1.0,
          L, 1, m,
          U, 1, k,
          0.0,
          LU, incRowLU, incColLU);

    for (size_t i=m; i>0; --i) {
        if (i-1 != P[(i-1)*incP]) {
            dswap(n,
                  &LU[(i-1)*incRowLU], incColLU, 
                  &LU[P[(i-1)*incP]*incRowLU], incColLU);
        }
    }

    for (j=0; j<n; ++j) {
        for (i=0; i<m; ++i) {
            err += fabs(A[i*incRowA+j*incColA]-LU[i*incRowLU+j*incColLU]);
        }
    }
    err /= (aNrm1*k);

    free(L);
    free(U);
    return err;
}

//------------------------------------------------------------------------------

#ifndef MIN_N
#define MIN_N 100
#endif

#ifndef MAX_N
#define MAX_N 8000
#endif

#ifndef INC_N
#define INC_N 100
#endif

#ifndef MIN_M
#define MIN_M 100
#endif

#ifndef MAX_M
#define MAX_M 8000
#endif

#ifndef INC_M
#define INC_M 100
#endif

#ifndef ROWMAJOR
#define ROWMAJOR 0
#endif

double A_[MAX_M*MAX_N];
double A_0[MAX_M*MAX_N];
size_t P_0[(MAX_M<MAX_N) ? MAX_M : MAX_N];

int
main()
{
    randGeMatrix(MAX_N, MAX_N, A_, 1, MAX_M);

    printf("#%9s %9s %9s %9s", "m", "n", "INCROW_A", "INCCOL_A");
    printf(" %12s %12s %17s", "t", "MFLOPS", "Residual Error");
    printf("\n");

    for (size_t m=MIN_M, n=MIN_N; n<=MAX_N && m<=MAX_M; m+=INC_M, n+=INC_N) {
        double t, dt, err;
        size_t runs  = 1;
        size_t minMN = (m<n) ? m : n;
        size_t maxMN = (m>n) ? m : n;
        double ops   = minMN*minMN*maxMN
                     -(minMN*minMN*minMN/3.)
                     -(minMN*minMN/2.);

        ptrdiff_t incRowA = (ROWMAJOR==1) ? n : 1;
        ptrdiff_t incColA = (ROWMAJOR==1) ? 1 : m;

        printf(" %9zu %9zu %9td %9td", m, n, incRowA, incColA);

        t    = 0;
        runs = 0;
        do {
            dgecopy(m, n, A_, 1, MAX_M, A_0, incRowA, incColA);
            dt = walltime();
            lu_unblk(m, n, A_0, incRowA, incColA, P_0, 1);
            dt = walltime() - dt;
            t += dt;
            ++runs;
        } while (t<0.3);
        t /= runs;

        err = err_lu(m, n,
                     A_, 1, MAX_M,
                     A_0, incRowA, incColA,
                     P_0, 1);

        printf(" %12.2e %12.2lf %12.2e %4s", t, ops/(1000*1000*t), err, (err<DBL_EPSILON) ? "PASS" : "FAIL");

        printf("\n");
    }

    return 0;
}