lambda2_kernel.h

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#ifndef __MATH_LAMBDA2_KERNEL_H__
#define __MATH_LAMBDA2_KERNEL_H__
/*
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template< typename T>
__inline__ __device__ T eigen_val_calc(T grad11, T grad12, T grad13,
                                       T grad21, T grad22, T grad23,
                                       T grad31, T grad32, T grad33 ) {
    T s11 = grad11;
    T s22 = grad22;
    T s33 = grad33;
    T s12 = 0.5*(grad12+grad21);
    T s13 = 0.5*(grad13+grad31);
    T s23 = 0.5*(grad23+grad32);
 
    T o12 = 0.5*(grad12-grad21);
    T o13 = 0.5*(grad13-grad31);
    T o23 = 0.5*(grad23-grad32);
 
    T a11 = s11*s11 + s12*s12 + s13*s13 - o12*o12 - o13*o13;
    T a12 = s11 * s12  +  s12 * s22  +  s13 * s23 - o13 * o23;
    T a13 = s11 * s13  +  s12 * s23  +  s13 * s33 + o12 * o23;
        
    T a22 = s12*s12 + s22*s22 + s23*s23 - o12*o12 - o23*o23;
    T a23 = s12 * s13 + s22 * s23 + s23 * s33 - o12 * o13;
    T a33 = s13*s13 + s23*s23 + s33*s33 - o13*o13 - o23*o23;
               
               
    T B = -(a11 + a22 + a33);
    T C = -(a12*a12 + a13*a13 + a23*a23 - a11 * a22 - a11 * a33 - a22 * a33);
    T D = -(2.0 * a12 * a13 * a23 - a11 * a23*a23 - a22 * a13*a13
            - a33 * a12*a12  +  a11 * a22 * a33);
                     
                     
    T q = (3.0 * C - B*B) / 9.0;
    T r = (9.0 * C * B - 27.0 * D - 2.0 * B*B*B) / 54.0;
 
    T theta = acos( r / sqrt(-q*q*q) ); 
    T pi = 4.0*atan(1.0);
    T eigen1 = 2.0 * sqrt(-q) * cos(theta / 3.0) - B / 3.0;
    T eigen2 = 2.0 * sqrt(-q) * cos((theta + 2.0 * pi) / 3.0) - B / 3.0;
    T eigen3 = 2.0 * sqrt(-q) * cos((theta + 4.0 * pi) / 3.0) - B / 3.0;
                                 
    if (eigen1 <= eigen2 && eigen2 <= eigen3)
        return eigen2;
    else if (eigen3 <= eigen2 && eigen2 <= eigen1)
        return eigen2;
    else if (eigen1 <= eigen3 && eigen3 <= eigen2)
        return eigen3;
    else if (eigen2 <= eigen3 && eigen3 <= eigen1)
        return eigen3;
    else if (eigen2 <= eigen1 && eigen1 <= eigen3)
        return eigen1;
    else if (eigen3 <= eigen1 && eigen1 <= eigen2)
        return eigen1;
    return 0.0;
}
 
 
template< typename T, const int LX, const int CHUNKS >
__global__ void lambda2_kernel_1d(T * __restrict__ lambda2,
                                 const T * __restrict__ u,
                                 const T * __restrict__ v,
                                 const T * __restrict__ w,
                                 const T * __restrict__ dx,
                                 const T * __restrict__ dy,
                                 const T * __restrict__ dz,
                                 const T * __restrict__ drdx,
                                 const T * __restrict__ dsdx,
                                 const T * __restrict__ dtdx,
                                 const T * __restrict__ drdy,
                                 const T * __restrict__ dsdy,
                                 const T * __restrict__ dtdy,
                                 const T * __restrict__ drdz,
                                 const T * __restrict__ dsdz,
                                 const T * __restrict__ dtdz,
                                 const T * __restrict__ jacinv) {
 
  __shared__ T shu[LX * LX * LX];
  __shared__ T shv[LX * LX * LX];
  __shared__ T shw[LX * LX * LX];
 
  __shared__ T shdx[LX * LX];
  __shared__ T shdy[LX * LX];
  __shared__ T shdz[LX * LX];
 
 
  
  
  int i,j,k;
  
  const int e = blockIdx.x;
  const int ele = blockIdx.x*LX*LX*LX;
  const int iii = threadIdx.x;
  const int nchunks = (LX * LX * LX - 1) / CHUNKS + 1;
 
 
  if (iii < (LX * LX)) {
    shdx[iii] = dx[iii];
    shdy[iii] = dy[iii];
    shdz[iii] = dz[iii];
  }
 
  j = iii;
  while(j < (LX * LX * LX)) {
    shu[j] = u[j + ele];
    shv[j] = v[j + ele];
    shw[j] = w[j + ele];
    j = j + CHUNKS;
  }
  
  __syncthreads();
  
  for (int n = 0; n < nchunks; n++) {
    const int ijk = iii + n * CHUNKS;
    const int jk = ijk / LX;
    i = ijk - jk * LX;
    k = jk / LX;
    j = jk - k * LX;
    if ( i < LX && j < LX && k < LX ) {
      T rtmpu = 0.0;
      T stmpu = 0.0;
      T ttmpu = 0.0;
      
      T rtmpv = 0.0;
      T stmpv = 0.0;
      T ttmpv = 0.0;
 
      T rtmpw = 0.0;
      T stmpw = 0.0;
      T ttmpw = 0.0;
      for (int l = 0; l < LX; l++) {        
          rtmpu += shdx[i + l * LX] * shu[l + j * LX + k * LX * LX];    
          stmpu += shdy[j + l * LX] * shu[i + l * LX + k * LX * LX];
          ttmpu += shdz[k + l * LX] * shu[i + j * LX + l * LX * LX];
          
          rtmpv += shdx[i + l * LX] * shv[l + j * LX + k * LX * LX];    
          stmpv += shdy[j + l * LX] * shv[i + l * LX + k * LX * LX];
          ttmpv += shdz[k + l * LX] * shv[i + j * LX + l * LX * LX];
          
          rtmpw += shdx[i + l * LX] * shw[l + j * LX + k * LX * LX];    
          stmpw += shdy[j + l * LX] * shw[i + l * LX + k * LX * LX];
          ttmpw += shdz[k + l * LX] * shw[i + j * LX + l * LX * LX];
      }
 
      T jinv = jacinv[ijk + ele];
 
      T grad11 = jinv 
      * (drdx[ijk + ele] * rtmpu
       + dsdx[ijk + ele] * stmpu
       + dtdx[ijk + ele] * ttmpu);
 
      T grad12 = jinv 
      * (drdy[ijk + ele] * rtmpu
       + dsdy[ijk + ele] * stmpu
       + dtdy[ijk + ele] * ttmpu);
      
      T grad13 = jinv 
      * (drdz[ijk + ele] * rtmpu
       + dsdz[ijk + ele] * stmpu
       + dtdz[ijk + ele] * ttmpu);
 
      T grad21 = jinv 
      * (drdx[ijk + ele] * rtmpv
       + dsdx[ijk + ele] * stmpv
       + dtdx[ijk + ele] * ttmpv);
 
      T grad22 = jinv 
      * (drdy[ijk + ele] * rtmpv
       + dsdy[ijk + ele] * stmpv
       + dtdy[ijk + ele] * ttmpv);
      
      T grad23 = jinv 
      * (drdz[ijk + ele] * rtmpv
       + dsdz[ijk + ele] * stmpv
       + dtdz[ijk + ele] * ttmpv);
 
 
      T grad31 = jinv
      * (drdx[ijk + ele] * rtmpw
       + dsdx[ijk + ele] * stmpw
       + dtdx[ijk + ele] * ttmpw);
 
      T grad32 = jinv
      * (drdy[ijk + ele] * rtmpw
       + dsdy[ijk + ele] * stmpw
       + dtdy[ijk + ele] * ttmpw);
      
      T grad33 = jinv
      * (drdz[ijk + ele] * rtmpw
       + dsdz[ijk + ele] * stmpw
       + dtdz[ijk + ele] * ttmpw);
      lambda2[ijk + e*LX*LX*LX] = eigen_val_calc<T>( grad11, grad12, grad13,
                                                     grad21, grad22, grad23,
                                                     grad31, grad32, grad33);
    }
  } 
  
}
 
template< typename T, const int LX >
__global__ void __launch_bounds__(LX*LX,3)
lambda2_kernel_kstep(T * __restrict__ lambda2,
                    const T * __restrict__ u,
                    const T * __restrict__ v,
                    const T * __restrict__ w,
                    const T * __restrict__ dx,
                    const T * __restrict__ dy,
                    const T * __restrict__ dz,
                    const T * __restrict__ drdx,
                    const T * __restrict__ dsdx,
                    const T * __restrict__ dtdx,
                    const T * __restrict__ drdy,
                    const T * __restrict__ dsdy,
                    const T * __restrict__ dtdy,
                    const T * __restrict__ drdz,
                    const T * __restrict__ dsdz,
                    const T * __restrict__ dtdz,
                    const T * __restrict__ jacinv) {
 
  __shared__ T shu[LX * LX];
  __shared__ T shv[LX * LX];
  __shared__ T shw[LX * LX];
 
  __shared__ T shdx[LX * LX];
  __shared__ T shdy[LX * LX];
  __shared__ T shdz[LX * LX];
    
  const int e = blockIdx.x;
  const int j = threadIdx.y;
  const int i = threadIdx.x;
  const int ij = i + j * LX;
  const int ele = e*LX*LX*LX;
  
  shdx[ij] = dx[ij];
  shdy[ij] = dy[ij];
  shdz[ij] = dz[ij];
 
  T ru[LX];
  T rv[LX];
  T rw[LX];
  
#pragma unroll LX
  for (int k = 0; k < LX; ++k) {
    ru[k] = u[ij + k*LX*LX + ele];
    rv[k] = v[ij + k*LX*LX + ele];
    rw[k] = w[ij + k*LX*LX + ele];
  }
    
  __syncthreads();
 
  #pragma unroll
  for (int k = 0; k < LX; ++k) {
    const int ijk = ij + k*LX*LX;
    const T jinv = jacinv[ijk+ele];
    T ttmpu = 0.0;
    T ttmpv = 0.0;
    T ttmpw = 0.0;
    shu[ij] = ru[k];
    shv[ij] = rv[k];
    shw[ij] = rw[k];
    for (int l = 0; l < LX; l++) {
      ttmpu += shdz[k+l*LX] * ru[l];
      ttmpv += shdz[k+l*LX] * rv[l];
      ttmpw += shdz[k+l*LX] * rw[l];
    }
    __syncthreads();
 
    T rtmpu = 0.0;
    T stmpu = 0.0;
    T rtmpv = 0.0;
    T stmpv = 0.0;
    T rtmpw = 0.0;
    T stmpw = 0.0;
#pragma unroll
    for (int l = 0; l < LX; l++) {
      rtmpu += shdx[i+l*LX] * shu[l+j*LX];
      stmpu += shdy[j+l*LX] * shu[i+l*LX];
      rtmpv += shdx[i+l*LX] * shv[l+j*LX];
      stmpv += shdy[j+l*LX] * shv[i+l*LX];
      rtmpw += shdx[i+l*LX] * shw[l+j*LX];
      stmpw += shdy[j+l*LX] * shw[i+l*LX];
    }
 
    T grad11 = jinv * (drdx[ijk + ele] * rtmpu
                          + dsdx[ijk + ele] * stmpu
                          + dtdx[ijk + ele] * ttmpu);
 
    T grad12 = jinv * (drdy[ijk + ele] * rtmpu
                          + dsdy[ijk + ele] * stmpu
                          + dtdy[ijk + ele] * ttmpu);
 
    T grad13 = jinv * (drdz[ijk + ele] * rtmpu
                          + dsdz[ijk + ele] * stmpu
                          + dtdz[ijk + ele] * ttmpu);
    T grad21 = jinv * (drdx[ijk + ele] * rtmpv
                          + dsdx[ijk + ele] * stmpv
                          + dtdx[ijk + ele] * ttmpv);
 
    T grad22 = jinv * (drdy[ijk + ele] * rtmpv
                          + dsdy[ijk + ele] * stmpv
                          + dtdy[ijk + ele] * ttmpv);
 
    T grad23 = jinv * (drdz[ijk + ele] * rtmpv
                          + dsdz[ijk + ele] * stmpv
                          + dtdz[ijk + ele] * ttmpv);
    T grad31 = jinv * (drdx[ijk + ele] * rtmpw
                          + dsdx[ijk + ele] * stmpw
                          + dtdx[ijk + ele] * ttmpw);
 
    T grad32 = jinv * (drdy[ijk + ele] * rtmpw
                          + dsdy[ijk + ele] * stmpw
                          + dtdy[ijk + ele] * ttmpw);
 
    T grad33 = jinv * (drdz[ijk + ele] * rtmpw
                          + dsdz[ijk + ele] * stmpw
                          + dtdz[ijk + ele] * ttmpw);
    lambda2[ijk + ele] = eigen_val_calc<T>( grad11, grad12, grad13,
                                            grad21, grad22, grad23,
                                            grad31, grad32, grad33);
    __syncthreads();
  }
}
 
 
#endif // __MATH_LAMBDA2_KERNEL_H__