Optimize BSSN surface interpolation fast path

AMSS_NCKU_source/MPatch.C

@@ -178,6 +178,433 @@ int find_block_index_for_point(const BlockBinIndex &index, const double *pox, co
 
   return -1;
 }
+
+inline int fortran_idint_local(double x)
+{
+  return int(x);
+}
+
+bool interp_fast_enabled()
+{
+  static int enabled = -1;
+  if (enabled < 0)
+  {
+    const char *env = getenv("AMSS_INTERP_FAST");
+    enabled = (!env || atoi(env) != 0) ? 1 : 0;
+  }
+  return enabled != 0;
+}
+
+bool interp_fast_compare_enabled()
+{
+  static int enabled = -1;
+  if (enabled < 0)
+  {
+    const char *env = getenv("AMSS_INTERP_FAST_COMPARE");
+    enabled = (env && atoi(env) != 0) ? 1 : 0;
+  }
+  return enabled != 0;
+}
+
+double interp_fast_compare_tol()
+{
+  static double tol = -1.0;
+  if (tol < 0.0)
+  {
+    const char *env = getenv("AMSS_INTERP_FAST_COMPARE_TOL");
+    tol = (env && atof(env) > 0.0) ? atof(env) : 1.0e-11;
+  }
+  return tol;
+}
+
+long long interp_fast_compare_limit()
+{
+  static long long limit = -1;
+  if (limit < 0)
+  {
+    const char *env = getenv("AMSS_INTERP_FAST_COMPARE_LIMIT");
+    limit = (env && atoll(env) > 0) ? atoll(env) : 4096;
+  }
+  return limit;
+}
+
+struct FastInterpStencil
+{
+  int cxB[dim];
+  double cx[dim];
+  double wx[8];
+  double wy[8];
+  double wz[8];
+  int nsamples;
+  int loc[512];
+  unsigned char sign_mask[512];
+  double weight[512];
+};
+
+inline void lagrange_unit_weights(double x, int ordn, double *w)
+{
+  for (int i = 0; i < ordn; i++)
+  {
+    double num = 1.0;
+    double den = 1.0;
+    for (int j = 0; j < ordn; j++)
+    {
+      if (j == i)
+        continue;
+      num *= (x - double(j));
+      den *= double(i - j);
+    }
+    w[i] = num / den;
+  }
+}
+
+inline void z_unit_weights(double x, int ordn, double *w)
+{
+  if (ordn == 6)
+  {
+    static const double c_uniform[6] = {-1.0, 5.0, -10.0, 10.0, -5.0, 1.0};
+    for (int i = 0; i < 6; i++)
+    {
+      if (x == double(i))
+      {
+        for (int j = 0; j < 6; j++)
+          w[j] = (j == i) ? 1.0 : 0.0;
+        return;
+      }
+    }
+    double den = 0.0;
+    for (int i = 0; i < 6; i++)
+    {
+      w[i] = c_uniform[i] / (x - double(i));
+      den += w[i];
+    }
+    for (int i = 0; i < 6; i++)
+      w[i] /= den;
+    return;
+  }
+  lagrange_unit_weights(x, ordn, w);
+}
+
+inline bool fast_interp_map_index(int idx, int extent, int d,
+                                  int &mapped, unsigned char &mask)
+{
+  if (idx > 0)
+    mapped = idx;
+  else
+  {
+    mask |= (unsigned char)(1u << d);
+#ifdef Vertex
+#ifdef Cell
+#error Both Cell and Vertex are defined
+#endif
+    mapped = 2 - idx;
+#else
+#ifdef Cell
+    mapped = 1 - idx;
+#else
+#error Not define Vertex nor Cell
+#endif
+#endif
+  }
+  return mapped >= 1 && mapped <= extent;
+}
+
+bool prepare_fast_interp_stencil(Block *BP, const double *pox, int ordn,
+                                 int Symmetry, FastInterpStencil &st)
+{
+  if (!BP || ordn <= 0 || ordn > 8)
+    return false;
+
+  st.nsamples = 0;
+
+  const int NO_SYMM = 0;
+  const int OCTANT = 2;
+  int cmin[dim], cmax[dim], cxT[dim];
+  for (int d = 0; d < dim; d++)
+  {
+    const double *X = BP->X[d];
+    const double dX = X[1] - X[0];
+    const int cxI = fortran_idint_local((pox[d] - X[0]) / dX + 0.4) + 1;
+    st.cxB[d] = cxI - ordn / 2 + 1;
+    cxT[d] = st.cxB[d] + ordn - 1;
+    cmin[d] = 1;
+    cmax[d] = BP->shape[d];
+
+#ifdef Vertex
+#ifdef Cell
+#error Both Cell and Vertex are defined
+#endif
+    if (Symmetry == OCTANT && d < 2 && fabs(X[0]) < dX)
+      cmin[d] = -ordn / 2 + 2;
+    if (Symmetry != NO_SYMM && d == 2 && fabs(X[0]) < dX)
+      cmin[d] = -ordn / 2 + 2;
+#else
+#ifdef Cell
+    if (Symmetry == OCTANT && d < 2 && fabs(X[0]) < dX)
+      cmin[d] = -ordn / 2 + 1;
+    if (Symmetry != NO_SYMM && d == 2 && fabs(X[0]) < dX)
+      cmin[d] = -ordn / 2 + 1;
+#else
+#error Not define Vertex nor Cell
+#endif
+#endif
+
+    if (st.cxB[d] < cmin[d])
+    {
+      st.cxB[d] = cmin[d];
+      cxT[d] = st.cxB[d] + ordn - 1;
+    }
+    if (cxT[d] > cmax[d])
+    {
+      cxT[d] = cmax[d];
+      st.cxB[d] = cxT[d] + 1 - ordn;
+    }
+
+    if (st.cxB[d] > 0)
+      st.cx[d] = (pox[d] - X[st.cxB[d] - 1]) / dX;
+    else
+    {
+#ifdef Vertex
+#ifdef Cell
+#error Both Cell and Vertex are defined
+#endif
+      st.cx[d] = (pox[d] + X[1 - st.cxB[d]]) / dX;
+#else
+#ifdef Cell
+      st.cx[d] = (pox[d] + X[-st.cxB[d]]) / dX;
+#else
+#error Not define Vertex nor Cell
+#endif
+#endif
+    }
+  }
+
+  lagrange_unit_weights(st.cx[0], ordn, st.wx);
+  lagrange_unit_weights(st.cx[1], ordn, st.wy);
+  z_unit_weights(st.cx[2], ordn, st.wz);
+
+  for (int kk = 0; kk < ordn; kk++)
+  {
+    for (int jj = 0; jj < ordn; jj++)
+    {
+      for (int ii = 0; ii < ordn; ii++)
+      {
+        unsigned char mask = 0;
+        int ix, iy, iz;
+        if (!fast_interp_map_index(st.cxB[0] + ii, BP->shape[0], 0, ix, mask) ||
+            !fast_interp_map_index(st.cxB[1] + jj, BP->shape[1], 1, iy, mask) ||
+            !fast_interp_map_index(st.cxB[2] + kk, BP->shape[2], 2, iz, mask))
+          return false;
+        const int s = st.nsamples++;
+        st.loc[s] = (ix - 1) + (iy - 1) * BP->shape[0] +
+                    (iz - 1) * BP->shape[0] * BP->shape[1];
+        st.sign_mask[s] = mask;
+        st.weight[s] = st.wx[ii] * st.wy[jj] * st.wz[kk];
+      }
+    }
+  }
+  return true;
+}
+
+bool interpolate_var_list_with_stencil(Block *BP, MyList<var> *VarList,
+                                       int num_var, const double *pox,
+                                       int ordn, int Symmetry,
+                                       const FastInterpStencil &st,
+                                       double *out)
+{
+  if (num_var <= 0 || num_var > 128)
+    return false;
+
+  double *data_ptrs[128];
+  double *soa_ptrs[128];
+  var *vars[128];
+  MyList<var> *varl = VarList;
+  int k = 0;
+  while (varl)
+  {
+    if (k >= num_var)
+      return false;
+    vars[k] = varl->data;
+    data_ptrs[k] = BP->fgfs[vars[k]->sgfn];
+    soa_ptrs[k] = vars[k]->SoA;
+    out[k] = 0.0;
+    varl = varl->next;
+    k++;
+  }
+
+  if (k != num_var)
+    return false;
+
+  for (int s = 0; s < st.nsamples; s++)
+  {
+    const int loc = st.loc[s];
+    const double w = st.weight[s];
+    const unsigned char mask = st.sign_mask[s];
+    if (mask == 0)
+    {
+      for (int v = 0; v < num_var; v++)
+        out[v] += w * data_ptrs[v][loc];
+    }
+    else
+    {
+      for (int v = 0; v < num_var; v++)
+      {
+        const double *SoA = soa_ptrs[v];
+        double sgn = 1.0;
+        if (mask & 1u)
+          sgn *= SoA[0];
+        if (mask & 2u)
+          sgn *= SoA[1];
+        if (mask & 4u)
+          sgn *= SoA[2];
+        out[v] += w * sgn * data_ptrs[v][loc];
+      }
+    }
+  }
+
+  if (interp_fast_compare_enabled())
+  {
+    static int report_count = 0;
+    static long long compare_calls = 0;
+    if (compare_calls++ >= interp_fast_compare_limit())
+      return true;
+    const double tol = interp_fast_compare_tol();
+    varl = VarList;
+    k = 0;
+    while (varl)
+    {
+      var *vp = vars[k];
+      double ref = 0.0;
+      double x = pox[0], y = pox[1], z = pox[2];
+      f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2],
+                      BP->fgfs[vp->sgfn], ref,
+                      x, y, z, ordn, vp->SoA, Symmetry);
+      const double diff = fabs(ref - out[k]);
+      const double scale = 1.0 + fabs(ref);
+      if (diff > tol * scale && report_count < 32)
+      {
+        int rank = 0;
+        MPI_Comm_rank(MPI_COMM_WORLD, &rank);
+        fprintf(stderr,
+                "[AMSS-INTERP-CMP][rank %d] var=%s diff=%.17e ref=%.17e fast=%.17e p=(%.17e,%.17e,%.17e)\n",
+                rank, vp->name, diff, ref, out[k], pox[0], pox[1], pox[2]);
+        report_count++;
+      }
+      varl = varl->next;
+      k++;
+    }
+  }
+
+  return true;
+}
+
+bool interpolate_var_list_fast(Block *BP, MyList<var> *VarList, int num_var,
+                               const double *pox, int ordn, int Symmetry,
+                               double *out)
+{
+  if (!interp_fast_enabled())
+    return false;
+
+  FastInterpStencil st;
+  if (!prepare_fast_interp_stencil(BP, pox, ordn, Symmetry, st))
+    return false;
+
+  return interpolate_var_list_with_stencil(BP, VarList, num_var, pox,
+                                           ordn, Symmetry, st, out);
+}
+
+struct CachedInterpPoint
+{
+  Block *bp;
+  int owner_rank;
+  FastInterpStencil stencil;
+};
+
+struct SurfaceInterpCache
+{
+  Patch *patch;
+  int NN;
+  int symmetry;
+  double key[9];
+  vector<CachedInterpPoint> points;
+
+  SurfaceInterpCache() : patch(0), NN(0), symmetry(-1) {}
+};
+
+bool surface_cache_key_matches(const SurfaceInterpCache &cache, Patch *patch,
+                               int NN, double **XX, int Symmetry)
+{
+  if (cache.patch != patch || cache.NN != NN || cache.symmetry != Symmetry ||
+      int(cache.points.size()) != NN || NN <= 0)
+    return false;
+  const int mid = NN / 2;
+  const int last = NN - 1;
+  const int ids[3] = {0, mid, last};
+  int p = 0;
+  for (int q = 0; q < 3; q++)
+    for (int d = 0; d < dim; d++)
+      if (cache.key[p++] != XX[d][ids[q]])
+        return false;
+  return true;
+}
+
+SurfaceInterpCache *find_surface_cache(Patch *patch, int NN, double **XX,
+                                       int Symmetry)
+{
+  static vector<SurfaceInterpCache> caches;
+  for (size_t i = 0; i < caches.size(); i++)
+    if (surface_cache_key_matches(caches[i], patch, NN, XX, Symmetry))
+      return &caches[i];
+  if (caches.size() >= 24)
+    caches.erase(caches.begin());
+  caches.push_back(SurfaceInterpCache());
+  return &caches.back();
+}
+
+bool build_surface_cache(SurfaceInterpCache &cache, Patch *patch, int NN,
+                         double **XX, int Symmetry, const double *DH,
+                         const BlockBinIndex &block_index, int ordn)
+{
+  int myrank = 0;
+  MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
+  cache.patch = patch;
+  cache.NN = NN;
+  cache.symmetry = Symmetry;
+  cache.points.clear();
+  cache.points.resize(NN);
+  const int mid = NN / 2;
+  const int last = NN - 1;
+  const int ids[3] = {0, mid, last};
+  int p = 0;
+  for (int q = 0; q < 3; q++)
+    for (int d = 0; d < dim; d++)
+      cache.key[p++] = XX[d][ids[q]];
+
+  for (int j = 0; j < NN; j++)
+  {
+    double pox[dim];
+    for (int d = 0; d < dim; d++)
+      pox[d] = XX[d][j];
+    const int block_i = find_block_index_for_point(block_index, pox, DH);
+    if (block_i < 0)
+    {
+      cache.points[j].bp = 0;
+      cache.points[j].owner_rank = -1;
+      continue;
+    }
+    Block *BP = block_index.views[block_i].bp;
+    cache.points[j].bp = BP;
+    cache.points[j].owner_rank = BP->rank;
+    cache.points[j].stencil.nsamples = 0;
+    if (BP->rank == myrank)
+    {
+      if (!prepare_fast_interp_stencil(BP, pox, ordn, Symmetry,
+                                       cache.points[j].stencil))
+        return false;
+    }
+  }
+  return true;
+}
 } // namespace
 
 Patch::Patch(int DIM, int *shapei, double *bboxi, int levi, bool buflog, int Symmetry) : lev(levi)
@@ -565,6 +992,9 @@ void Patch::Interp_Points(MyList<var> *VarList,
       if (myrank == BP->rank)
       {
         //---> interpolation
+        if (!interpolate_var_list_fast(BP, VarList, num_var, pox, ordn,
+                                       Symmetry, Shellf + j * num_var))
+        {
           varl = VarList;
           int k = 0;
           while (varl) // run along variables
@@ -577,6 +1007,7 @@ void Patch::Interp_Points(MyList<var> *VarList,
         }
       }
     }
+  }
 
   // Replace MPI_Allreduce with per-owner MPI_Bcast:
   // Group consecutive points by owner rank and broadcast each group.
@@ -659,8 +1090,6 @@ void Patch::Interp_Points(MyList<var> *VarList,
     varl = varl->next;
   }
 
-  memset(Shellf, 0, sizeof(double) * NN * num_var);
-
   // owner_rank[j] records which MPI rank owns point j
   int *owner_rank;
   owner_rank = new int[NN];
@@ -672,6 +1101,16 @@ void Patch::Interp_Points(MyList<var> *VarList,
     DH[i] = getdX(i);
   BlockBinIndex block_index;
   build_block_bin_index(this, DH, block_index);
+  SurfaceInterpCache *surface_cache = 0;
+  bool use_surface_cache = false;
+  if (interp_fast_enabled())
+  {
+    surface_cache = find_surface_cache(this, NN, XX, Symmetry);
+    use_surface_cache = surface_cache_key_matches(*surface_cache, this, NN, XX, Symmetry);
+    if (!use_surface_cache)
+      use_surface_cache = build_surface_cache(*surface_cache, this, NN, XX,
+                                              Symmetry, DH, block_index, ordn);
+  }
 
   // --- Interpolation phase (identical to original) ---
   for (int j = 0; j < NN; j++)
@@ -695,6 +1134,31 @@ void Patch::Interp_Points(MyList<var> *VarList,
       }
     }
 
+    if (use_surface_cache)
+    {
+      CachedInterpPoint &cp = surface_cache->points[j];
+      Block *BP = cp.bp;
+      owner_rank[j] = cp.owner_rank;
+      if (BP && myrank == BP->rank)
+      {
+        if (!interpolate_var_list_with_stencil(BP, VarList, num_var, pox,
+                                               ordn, Symmetry, cp.stencil,
+                                               Shellf + j * num_var))
+        {
+          MyList<var> *varl_fallback = VarList;
+          int k = 0;
+          while (varl_fallback)
+          {
+            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl_fallback->data->sgfn], Shellf[j * num_var + k],
+                            pox[0], pox[1], pox[2], ordn, varl_fallback->data->SoA, Symmetry);
+            varl_fallback = varl_fallback->next;
+            k++;
+          }
+        }
+      }
+    }
+    else
+    {
       const int block_i = find_block_index_for_point(block_index, pox, DH);
       if (block_i >= 0)
       {
@@ -702,18 +1166,23 @@ void Patch::Interp_Points(MyList<var> *VarList,
         owner_rank[j] = BP->rank;
       if (myrank == BP->rank)
       {
-        varl = VarList;
-        int k = 0;
-        while (varl)
+        if (!interpolate_var_list_fast(BP, VarList, num_var, pox, ordn,
+                                       Symmetry, Shellf + j * num_var))
         {
-          f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl->data->sgfn], Shellf[j * num_var + k],
-                          pox[0], pox[1], pox[2], ordn, varl->data->SoA, Symmetry);
-          varl = varl->next;
+          MyList<var> *varl_fallback = VarList;
+          int k = 0;
+          while (varl_fallback)
+          {
+            f_global_interp(BP->shape, BP->X[0], BP->X[1], BP->X[2], BP->fgfs[varl_fallback->data->sgfn], Shellf[j * num_var + k],
+                            pox[0], pox[1], pox[2], ordn, varl_fallback->data->SoA, Symmetry);
+            varl_fallback = varl_fallback->next;
             k++;
           }
         }
       }
       }
+    }
+  }
 
 #ifdef INTERP_LB_PROFILE
   double t_interp_end = MPI_Wtime();
@@ -969,6 +1438,9 @@ void Patch::Interp_Points(MyList<var> *VarList,
       if (myrank == BP->rank)
       {
         //---> interpolation
+        if (!interpolate_var_list_fast(BP, VarList, num_var, pox, ordn,
+                                       Symmetry, Shellf + j * num_var))
+        {
           varl = VarList;
           int k = 0;
           while (varl) // run along variables
@@ -981,6 +1453,7 @@ void Patch::Interp_Points(MyList<var> *VarList,
         }
       }
     }
+  }
 
   // Collect unique global owner ranks and translate to local ranks in Comm_here
   // Then broadcast each owner's points via MPI_Bcast on Comm_here

AMSS_NCKU_source/bssn_class.C

@@ -45,6 +45,20 @@ using namespace std;
 #include "derivatives.h"
 #include "ricci_gamma.h"
 
+namespace
+{
+bool amss_analysis_timing_enabled()
+{
+  static int enabled = -1;
+  if (enabled < 0)
+  {
+    const char *env = getenv("AMSS_ANALYSIS_TIMING");
+    enabled = (env && atoi(env) != 0) ? 1 : 0;
+  }
+  return enabled != 0;
+}
+}
+
 // Compile-time switch for per-timestep memory usage collection/printing.
 // Default is OFF to reduce overhead in production runs.
 #ifndef BSSN_ENABLE_MEM_USAGE_LOG
@@ -7942,6 +7956,10 @@ void bssn_class::AnalysisStuff(int lev, double dT_lev)
 
   if (LastAnas >= AnasTime)
   {
+    const bool analysis_timing = amss_analysis_timing_enabled();
+    const double t_analysis_start = analysis_timing ? MPI_Wtime() : 0.0;
+    double t_psi4_sec = 0.0;
+    double t_surface_sec = 0.0;
 #ifdef Point_Psi4
 #error "not support parallel levels yet"
     // Gam_ijk and R_ij have been calculated in Interp_Constraint()
@@ -8134,7 +8152,12 @@ void bssn_class::AnalysisStuff(int lev, double dT_lev)
 #endif
     }
 #else
+    {
+      const double t0 = analysis_timing ? MPI_Wtime() : 0.0;
     Compute_Psi4(lev);
+      if (analysis_timing)
+        t_psi4_sec += MPI_Wtime() - t0;
+    }
 #endif
     double *RP, *IP, *RoutMAP;
     int NN = 0;
@@ -8151,6 +8174,7 @@ void bssn_class::AnalysisStuff(int lev, double dT_lev)
 #endif
     for (int i = 0; i < decn; i++)
       {
+        const double t_surface0 = analysis_timing ? MPI_Wtime() : 0.0;
 #ifdef Point_Psi4
       Waveshell->surf_Wave(Rex, GH, SH,
                            phi, trK,
@@ -8243,6 +8267,8 @@ void bssn_class::AnalysisStuff(int lev, double dT_lev)
 #endif
 #endif
 //        misc::tillherecheck(GH->Commlev[lev],GH->start_rank[lev],"end surface integral");
+        if (analysis_timing)
+          t_surface_sec += MPI_Wtime() - t_surface0;
 #endif
       if (i == 0)
       {
@@ -8275,6 +8301,13 @@ void bssn_class::AnalysisStuff(int lev, double dT_lev)
     delete[] RP;
     delete[] IP;
     delete[] RoutMAP;
+    if (analysis_timing)
+    {
+      fprintf(stderr,
+              "[AMSS-ANALYSIS][rank %d] lev=%d psi4=%.6f surface=%.6f total_before_bh=%.6f detectors=%d modes=%d\n",
+              myrank, lev, t_psi4_sec, t_surface_sec,
+              MPI_Wtime() - t_analysis_start, decn, NN);
+    }
 
     // black hole's position
     {

AMSS_NCKU_source/surface_integral.C

@@ -11,6 +11,7 @@
 #include <strstream>
 #include <cmath>
 #include <map>
+#include <cstdlib>
 using namespace std;
 #else
 #include <iostream.h>
@@ -32,6 +33,20 @@ using namespace std;
 #include "parameters.h"
 
 #define PI M_PI
+
+namespace
+{
+bool amss_surface_timing_enabled()
+{
+  static int enabled = -1;
+  if (enabled < 0)
+  {
+    const char *env = getenv("AMSS_SURFACE_TIMING");
+    enabled = (env && atoi(env) != 0) ? 1 : 0;
+  }
+  return enabled != 0;
+}
+}
 //|============================================================================
 //| Constructor
 //|============================================================================
@@ -3281,6 +3296,8 @@ void surface_integral::surf_WaveMassPAng(double rex, int lev, cgh *GH,
                                          var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
                                          double *Rout, monitor *Monitor, bool refresh_mass_fields)
 {
+  const bool timing = amss_surface_timing_enabled();
+  const double t_start = timing ? MPI_Wtime() : 0.0;
   if (Symmetry != 0 && Symmetry != 1)
   {
     surf_Wave(rex, lev, GH, Rpsi4, Ipsi4, spinw, maxl, NN, RP, IP, Monitor);
@@ -3325,6 +3342,7 @@ void surface_integral::surf_WaveMassPAng(double rex, int lev, cgh *GH,
       Pp = Pp->next;
     }
   }
+  const double t_refresh_done = timing ? MPI_Wtime() : 0.0;
 
   const int InList = 19;
   const int idx_rpsi4 = 0, idx_ipsi4 = 1;
@@ -3380,6 +3398,7 @@ void surface_integral::surf_WaveMassPAng(double rex, int lev, cgh *GH,
 
   double *shellf = new double[n_tot * InList];
   GH->PatL[lev]->data->Interp_Points(DG_List, n_tot, pox, shellf, Symmetry, Nmin, Nmax);
+  const double t_interp_done = timing ? MPI_Wtime() : 0.0;
 
   double *RP_out = new double[NN];
   double *IP_out = new double[NN];
@@ -3496,6 +3515,7 @@ void surface_integral::surf_WaveMassPAng(double rex, int lev, cgh *GH,
     if (Symmetry == 0)
       p_outz += f1o8 * Psi * (nx_g[n] * axz + ny_g[n] * ayz + nz_g[n] * azz) * theta_weight;
   }
+  const double t_integral_done = timing ? MPI_Wtime() : 0.0;
 
   for (int ii = 0; ii < NN; ii++)
   {
@@ -3534,6 +3554,7 @@ void surface_integral::surf_WaveMassPAng(double rex, int lev, cgh *GH,
     delete[] reduce_out;
     delete[] reduce_in;
   }
+  const double t_reduce_done = timing ? MPI_Wtime() : 0.0;
 
 #ifdef GaussInt
   mass = mass * rex * rex * dphi * factor;
@@ -3565,6 +3586,19 @@ void surface_integral::surf_WaveMassPAng(double rex, int lev, cgh *GH,
   Rout[5] = sy;
   Rout[6] = sz;
 
+  if (timing)
+  {
+    fprintf(stderr,
+            "[AMSS-SURFACE][rank %d] rex=%.6g lev=%d refresh=%.6f interp=%.6f integral=%.6f reduce=%.6f total=%.6f nlocal=%d ntotal=%d modes=%d\n",
+            myrank, rex, lev,
+            t_refresh_done - t_start,
+            t_interp_done - t_refresh_done,
+            t_integral_done - t_interp_done,
+            t_reduce_done - t_integral_done,
+            t_reduce_done - t_start,
+            Nmax - Nmin + 1, n_tot, NN);
+  }
+
   delete[] pox[0];
   delete[] pox[1];
   delete[] pox[2];