local_interpolation.cu

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/*
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#include <stdio.h>
#include <device/device_config.h>
#include <device/cuda/check.h>
 
template< typename T, typename xT, const int LX, const int CHUNKS>
__global__ void find_rst_legendre_kernel(T * __restrict__ rst,
                                         const T * pt_x,
                                         const T * pt_y,
                                         const T * pt_z,
                                         const T * x_hat,
                                         const T * y_hat,
                                         const T * z_hat,
                                         T * __restrict__ resx,
                                         T * __restrict__ resy,
                                         T * __restrict__ resz,
                                         const int * el_ids,
                                         const int n_pt,
                                         T tol,
                                         T * __restrict__ conv_pts){
 
  const int pt = blockIdx.x;
  if (conv_pts[pt] < 0.5) return;
  const int e = el_ids[pt];
  const int elx3 = e*LX*LX*LX;
  const int str = blockDim.y;
  const int idx = threadIdx.y;
 
  const xT one = 1.0;
  const xT two = 2.0;
  __shared__ xT dxdr, dydr, dzdr;
  __shared__ xT dxds, dyds, dzds;
  __shared__ xT newx, newy, newz;
  __shared__ xT r_leg[LX];
  __shared__ xT s_leg[LX];
  __shared__ xT t_leg[LX];
  __shared__ xT dr_leg[LX];
  __shared__ xT ds_leg[LX];
  __shared__ xT dt_leg[LX];
 
 
  __shared__ xT xwork[LX*LX];
  __shared__ xT ywork[LX*LX];
  __shared__ xT zwork[LX*LX];
  __shared__ xT xwork2[LX];
  __shared__ xT ywork2[LX];
  __shared__ xT zwork2[LX];
 
  r_leg[0] = 1.0;
  s_leg[0] = 1.0;
  t_leg[0] = 1.0;
  r_leg[1] = rst[3*pt];
  s_leg[1] = rst[1+3*pt];
  t_leg[1] = rst[2+3*pt];
  dr_leg[0] = 0.0;
  ds_leg[0] = 0.0;
  dt_leg[0] = 0.0;
  ds_leg[1] = 1.0;
  dr_leg[1] = 1.0;
  dt_leg[1] = 1.0;
 
  for (int ii = 1; ii<LX-1; ii += 1) {
    xT ir = ii;
    r_leg[ii+1] = ((two*ir+one) * rst[3*pt] * r_leg[ii] - ir * r_leg[ii-1] ) / (ir+one);
    s_leg[ii+1] = ((two*ir+one) * rst[3*pt+1] * s_leg[ii] - ir * s_leg[ii-1] ) / (ir+one);
    t_leg[ii+1] = ((two*ir+one) * rst[3*pt+2] * t_leg[ii] - ir * t_leg[ii-1] ) / (ir+one);
    dr_leg[ii+1] = (ir+one) * r_leg[ii] + rst[3*pt]*dr_leg[ii];
    ds_leg[ii+1] = (ir+one) * s_leg[ii] + rst[3*pt+1]*ds_leg[ii];
    dt_leg[ii+1] = (ir+one) * t_leg[ii] + rst[3*pt+2]*dt_leg[ii];
  }
  __syncthreads();
  for (int ii = idx; ii< LX*LX; ii += str) {
    xT xtmp = 0.0;
    xT ytmp = 0.0;
    xT ztmp = 0.0;
    int j = ii;
    int i = ii - j;
    for( int l = 0; l < LX; l++){
      xtmp += r_leg[i+l]*x_hat[l+LX*j+elx3];
      ytmp += r_leg[i+l]*y_hat[l+LX*j+elx3];
      ztmp += r_leg[i+l]*z_hat[l+LX*j+elx3];
    }
    xwork[ii] = xtmp;
    ywork[ii] = ytmp;
    zwork[ii] = ztmp;
  }
 
  __syncthreads();
 
  for (int ijk = idx; ijk< LX; ijk += str) {
    const int jk = ijk;
    const int i = ijk - jk;
    const int k = jk;
    const int j = jk - k;
    xT xtmp = 0.0;
    xT ytmp = 0.0;
    xT ztmp = 0.0;
    const int ik2 = i + k*LX;
    for( int l = 0; l < LX; l++){
      xtmp += s_leg[l+j*LX]*xwork[l+ik2];
      ytmp += s_leg[l+j*LX]*ywork[l+ik2];
      ztmp += s_leg[l+j*LX]*zwork[l+ik2];
    }
    xwork2[ijk] = xtmp;
    ywork2[ijk] = ytmp;
    zwork2[ijk] = ztmp;
  }
 
  if(idx==0){
    const int ijk = idx;
    const int jk = ijk;
    const int i = ijk - jk;
    const int k = jk ;
    const int j = jk - k;
    const int ij2 = i + j;
    xT xtmp = 0.0;
    xT ytmp = 0.0;
    xT ztmp = 0.0;
    for( int l = 0; l < LX; l++){
      xtmp += t_leg[l+k*LX]*xwork2[ij2 + l];
      ytmp += t_leg[l+k*LX]*ywork2[ij2 + l];
      ztmp += t_leg[l+k*LX]*zwork2[ij2 + l];
    }
    newx = xtmp;
    newy = ytmp;
    newz = ztmp;
  //printf("gpu leg and xhat pt rst1 %lf, %lf, %lf, %d, %lf\n",r_leg[5], dr_leg[5],x_hat[elx3],pt, rst[3*pt]);
  }
  __syncthreads();
  for (int ii = idx; ii< LX*LX; ii += str) {
    xT xtmp = 0.0;
    xT ytmp = 0.0;
    xT ztmp = 0.0;
    int j = ii;
    int i = ii - j;
    for( int l = 0; l < LX; l++){
      xtmp += dr_leg[i+l]*x_hat[l+LX*j+elx3];
      ytmp += dr_leg[i+l]*y_hat[l+LX*j+elx3];
      ztmp += dr_leg[i+l]*z_hat[l+LX*j+elx3];
    }
    xwork[ii] = xtmp;
    ywork[ii] = ytmp;
    zwork[ii] = ztmp;
  }
 
  __syncthreads();
 
  for (int ijk = idx; ijk< LX; ijk += str) {
    const int jk = ijk;
    const int i = ijk - jk;
    const int k = jk;
    const int j = jk - k;
    xT xtmp = 0.0;
    xT ytmp = 0.0;
    xT ztmp = 0.0;
    const int ik2 = i + k*LX;
    for( int l = 0; l < LX; l++){
      xtmp += s_leg[l+j*LX]*xwork[l+ik2];
      ytmp += s_leg[l+j*LX]*ywork[l+ik2];
      ztmp += s_leg[l+j*LX]*zwork[l+ik2];
    }
    xwork2[ijk] = xtmp;
    ywork2[ijk] = ytmp;
    zwork2[ijk] = ztmp;
  }
 
 
  if (idx == 0) {
    const int ijk = idx;
    const int jk = ijk;
    const int i = ijk - jk;
    const int k = jk ;
    const int j = jk - k;
    xT xtmp = 0.0;
    xT ytmp = 0.0;
    xT ztmp = 0.0;
    const int ij2 = i + j;
    for( int l = 0; l < LX; l++){
      xtmp += t_leg[l+k*LX]*xwork2[ij2 + l];
      ytmp += t_leg[l+k*LX]*ywork2[ij2 + l];
      ztmp += t_leg[l+k*LX]*zwork2[ij2 + l];
    }
    dxdr = xtmp;
    dydr = ytmp;
    dzdr = ztmp;
  }
 
  __syncthreads();
  for (int ii = idx; ii< LX*LX; ii += str) {
    xT xtmp = 0.0;
    xT ytmp = 0.0;
    xT ztmp = 0.0;
    int j = ii;
    int i = ii - j;
    for( int l = 0; l < LX; l++){
      xtmp += r_leg[i+l]*x_hat[l+LX*j+elx3];
      ytmp += r_leg[i+l]*y_hat[l+LX*j+elx3];
      ztmp += r_leg[i+l]*z_hat[l+LX*j+elx3];
    }
    xwork[ii] = xtmp;
    ywork[ii] = ytmp;
    zwork[ii] = ztmp;
  }
 
  __syncthreads();
 
  for (int ijk = idx; ijk< LX; ijk += str) {
    const int jk = ijk;
    const int i = ijk - jk;
    const int k = jk;
    const int j = jk - k;
    xT xtmp = 0.0;
    xT ytmp = 0.0;
    xT ztmp = 0.0;
    const int ik2 = i + k*LX;
    for( int l = 0; l < LX; l++){
      xtmp += ds_leg[l+j*LX]*xwork[l+ik2];
      ytmp += ds_leg[l+j*LX]*ywork[l+ik2];
      ztmp += ds_leg[l+j*LX]*zwork[l+ik2];
    }
    xwork2[ijk] = xtmp;
    ywork2[ijk] = ytmp;
    zwork2[ijk] = ztmp;
  }
 
 
  if (idx == 0) {
    const int ijk = idx;
    const int jk = ijk;
    const int i = ijk - jk;
    const int k = jk ;
    const int j = jk - k;
    xT xtmp = 0.0;
    xT ytmp = 0.0;
    xT ztmp = 0.0;
    const int ij2 = i + j;
    for( int l = 0; l < LX; l++){
      xtmp += t_leg[l+k*LX]*xwork2[ij2 + l];
      ytmp += t_leg[l+k*LX]*ywork2[ij2 + l];
      ztmp += t_leg[l+k*LX]*zwork2[ij2 + l];
    }
    dxds = xtmp;
    dyds = ytmp;
    dzds = ztmp;
  }
 
  __syncthreads();
  for (int ii = idx; ii< LX*LX; ii += str) {
    xT xtmp = 0.0;
    xT ytmp = 0.0;
    xT ztmp = 0.0;
    int j = ii;
    int i = ii - j;
    for( int l = 0; l < LX; l++){
      xtmp += r_leg[i+l]*x_hat[l+LX*j+elx3];
      ytmp += r_leg[i+l]*y_hat[l+LX*j+elx3];
      ztmp += r_leg[i+l]*z_hat[l+LX*j+elx3];
    }
    xwork[ii] = xtmp;
    ywork[ii] = ytmp;
    zwork[ii] = ztmp;
  }
 
  __syncthreads();
 
  for (int ijk = idx; ijk< LX; ijk += str) {
    const int jk = ijk;
    const int i = ijk - jk;
    const int k = jk;
    const int j = jk - k;
    xT xtmp = 0.0;
    xT ytmp = 0.0;
    xT ztmp = 0.0;
    const int ik2 = i + k*LX;
    for( int l = 0; l < LX; l++){
      xtmp += s_leg[l+j*LX]*xwork[l+ik2];
      ytmp += s_leg[l+j*LX]*ywork[l+ik2];
      ztmp += s_leg[l+j*LX]*zwork[l+ik2];
    }
    xwork2[ijk] = xtmp;
    ywork2[ijk] = ytmp;
    zwork2[ijk] = ztmp;
  }
 
  __syncthreads();
 
  if( idx == 0){
    xT xtmp = 0.0;
    xT ytmp = 0.0;
    xT ztmp = 0.0;
    for( int l = 0; l < LX; l++){
      xtmp += dt_leg[l]*xwork2[l];
      ytmp += dt_leg[l]*ywork2[l];
      ztmp += dt_leg[l]*zwork2[l];
    }
    xT jacdet;
    xT jacdetinv;
    xT drdx, drdy, drdz;
    xT dsdx, dsdy, dsdz;
    xT dtdx, dtdy, dtdz;
    xT dxdt, dydt, dzdt;
    xT rstd[3];
    xT rstdiff;
    xT tol2;
    xT leg_outside;
 
    dxdt = xtmp;
    dydt = ytmp;
    dzdt = ztmp;
   //printf("rlegdrleg %lf %lf %f \n",r_leg[5], dr_leg[5],x_hat[elx3]);
 
    jacdet = (dxdr * dyds * dzdt)
           + (dxdt * dydr * dzds)
           + (dxds * dydt * dzdr)
           - (dxdr * dydt * dzds)
           - (dxds * dydr * dzdt)
           - (dxdt * dyds * dzdr);
 
    jacdetinv = one / jacdet;
   //check legendre polynoimial, rst, and xhat
 
    drdx =(dyds*dzdt - dydt*dzds);
    drdy =(dxdt*dzds - dxds*dzdt);
    drdz =(dxds*dydt - dxdt*dyds);
    dsdx =(dydt*dzdr - dydr*dzdt);
    dsdy =(dxdr*dzdt - dxdt*dzdr);
    dsdz =(dxdt*dydr - dxdr*dydt);
    dtdx =(dydr*dzds - dyds*dzdr);
    dtdy =(dxds*dzdr - dxdr*dzds);
    dtdz =(dxdr*dyds - dxds*dydr);
    //printf("newx gpu %lf \n",newx);
    resx[pt] = pt_x[pt]-newx;
    resy[pt] = pt_y[pt]-newy;
    resz[pt] = pt_z[pt]-newz;
 
    rstd[0] = jacdetinv*(drdx*resx[pt]+drdy*resy[pt]+drdz*resz[pt]);
    rstd[1] = jacdetinv*(dsdx*resx[pt]+dsdy*resy[pt]+dsdz*resz[pt]);
    rstd[2] = jacdetinv*(dtdx*resx[pt]+dtdy*resy[pt]+dtdz*resz[pt]);
 
    rst[3*pt]     += rstd[0];
    rst[3*pt + 1] += rstd[1];
    rst[3*pt + 2] += rstd[2];
    rstdiff = rstd[0]*rstd[0]+rstd[1]*rstd[1]+rstd[2]*rstd[2];
    conv_pts[pt] = 1.0;
    tol2 = tol*tol;
    if (rstdiff <= tol2) conv_pts[pt] = 0.0;
    if (rstdiff > 12.0) conv_pts[pt] = 0.0;
    //leg_outside = LX*LX*(LX-one)*(LX-one)/4.0;
    //if(r_leg[LX-1]*r_leg[LX-1] > leg_outside) conv_pts[pt] = true;
    //if(s_leg[LX-1]*s_leg[LX-1] > leg_outside) conv_pts[pt] = true;
    //if(t_leg[LX-1]*t_leg[LX-1] > leg_outside) conv_pts[pt] = true;
 
  }
}
 
 
extern "C" {
 
  void cuda_find_rst_legendre(void *rst,
                              void *pt_x, void* pt_y, void* pt_z,
                              void *x_hat, void *y_hat, void *z_hat,
                              void *resx, void *resy, void *resz,
                              int *lx, void *el_ids, int *n_pt, real *tol,
                              void *conv_pts) {
 
    const dim3 nthrds(1, 128, 1);
    const dim3 nblcks((*n_pt), 1, 1);
    const cudaStream_t stream = (cudaStream_t) glb_cmd_queue;
 
#define RST_CASE(LX)                                                            \
    case LX:                                                                    \
      find_rst_legendre_kernel<real,real_xp, LX, 128>                           \
        <<<nblcks, nthrds, 0, stream>>>                                         \
        ((real *) rst,(real *) pt_x, (real *) pt_y, (real *) pt_z,              \
         (real *) x_hat, (real *) y_hat, (real *) z_hat,                        \
         (real *) resx, (real *) resy, (real *) resz, (int *) el_ids,           \
         *n_pt, *tol, (real *) conv_pts);                                       \
      CUDA_CHECK(cudaGetLastError());                                           \
      break
 
    switch(*lx) {
      RST_CASE(2);
      RST_CASE(3);
      RST_CASE(4);
      RST_CASE(5);
      RST_CASE(6);
      RST_CASE(7);
      RST_CASE(8);
      RST_CASE(9);
      RST_CASE(10);
      RST_CASE(11);
      RST_CASE(12);
      RST_CASE(13);
      RST_CASE(14);
      RST_CASE(15);
      RST_CASE(16);
    default:
      {
        fprintf(stderr, __FILE__ ": size not supported: %d\n", *lx);
        exit(1);
      }
    }
  }
}