diff --git a/examples/Makefile.am b/examples/Makefile.am
index e9a7a59112fa3cea392ef5c7b035454b00aa4884..179db883582780dad2158d39d52f87b354f06724 100644
--- a/examples/Makefile.am
+++ b/examples/Makefile.am
@@ -31,7 +31,7 @@ AM_CFLAGS = -g -O3 -Wall -Werror -I../src -ffast-math -fstrict-aliasing \
AM_LDFLAGS = -lm # -fsanitize=address
# Set-up the library
-bin_PROGRAMS = test test_qr test_bh test_bh_sorted
+bin_PROGRAMS = test test_qr test_bh test_bh_sorted test_fmm_sorted
# Sources for test
test_SOURCES = test.c
@@ -53,3 +53,8 @@ test_bh_sorted_SOURCES = test_bh_sorted.c
test_bh_sorted_CFLAGS = $(AM_CFLAGS)
test_bh_sorted_LDADD = ../src/.libs/libquicksched.a
+# Sources for test_fmm_sorted
+test_fmm_sorted_SOURCES = test_fmm_sorted.c
+test_fmm_sorted_CFLAGS = $(AM_CFLAGS)
+test_fmm_sorted_LDADD = ../src/.libs/libquicksched.a
+
diff --git a/examples/test_fmm_sorted.c b/examples/test_fmm_sorted.c
new file mode 100644
index 0000000000000000000000000000000000000000..53ce537d9d672b0fba11fd4924e3a26921e71edc
--- /dev/null
+++ b/examples/test_fmm_sorted.c
@@ -0,0 +1,2534 @@
+/*******************************************************************************
+ * This file is part of QuickSched.
+ * Coypright (c) 2014 Pedro Gonnet (pedro.gonnet@durham.ac.uk),
+ * Matthieu Schaller (matthieu.schaller@durham.ac.uk)
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU Lesser General Public License as published
+ * by the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public License
+ * along with this program. If not, see <http://www.gnu.org/licenses/>.
+ *
+* *****************************************************************************/
+
+/* Config parameters. */
+#include "../config.h"
+
+/* Standard includes. */
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <unistd.h>
+#include <math.h>
+#include <float.h>
+#include <limits.h>
+#include <omp.h>
+#include <fenv.h>
+
+/* Local includes. */
+#include "quicksched.h"
+
+/* Some local constants. */
+#define cell_pool_grow 1000
+#define cell_maxparts 1
+#define task_limit 1e8
+#define const_G 1 // 6.6738e-8
+#define dist_min 0.5 /* Used for legacy walk only */
+#define dist_cutoff_ratio 1.5
+#define iact_pair_direct iact_pair_direct_sorted_multipole
+#define ICHECK -1
+#define NO_SANITY_CHECKS
+#define NO_COM_AS_TASK
+//#define COUNTERS
+
+
+/** Data structure for the particles. */
+struct part {
+ double x[3];
+ // union {
+ float a[3];
+ float a_legacy[3];
+ float a_exact[3];
+ // };
+ float mass;
+ int id;
+}; // __attribute__((aligned(64)));
+
+/** Data structure for the sorted particle positions. */
+struct index {
+ int ind;
+ float d;
+};
+
+struct monopole {
+ double com[3];
+ float mass;
+};
+
+/** Data structure for the BH tree cell. */
+struct cell {
+ double loc[3];
+ double h;
+
+ int count;
+ unsigned short int split, sorted;
+ struct part *parts;
+
+ struct cell *firstchild; /* Next node if opening */
+ struct cell *sibling; /* Next node */
+
+ /* We keep both CoMs and masses to make sure the comp_com calculation is
+ * correct (use an anonymous union to keep variable names compact). */
+ union {
+
+ /* Information for the legacy walk */
+ struct monopole legacy;
+
+ /* Information for the QuickShed walk */
+ struct monopole new;
+ };
+
+ int res, com_tid;
+ struct index *indices;
+
+} __attribute__((aligned(128)));
+
+/** Task types. */
+enum task_type {
+ task_type_self = 0,
+ task_type_pair,
+ task_type_self_pc,
+ task_type_pair_direct,
+ task_type_com,
+ task_type_count
+};
+
+
+
+
+/** Multipole stuff. */
+struct multipole {
+ float mass;
+ float mu[3]; /* Centre of Mass */
+ float sigma_00, sigma_11, sigma_22, sigma_01, sigma_02, sigma_12;
+};
+
+static inline void multipole_reset(struct multipole *d) {
+ d->mu[0] = 0.0;
+ d->mu[1] = 0.0;
+ d->mu[2] = 0.0;
+
+ d->sigma_00 = 0.0;
+ d->sigma_11 = 0.0;
+ d->sigma_22 = 0.0;
+ d->sigma_01 = 0.0;
+ d->sigma_02 = 0.0;
+ d->sigma_12 = 0.0;
+
+ d->mass = 0.0;
+}
+
+static inline void multipole_add(struct multipole *d, const float *x, float mass) {
+ d->mu[0] += x[0] * mass;
+ d->mu[1] += x[1] * mass;
+ d->mu[2] += x[2] * mass;
+
+ d->sigma_00 += mass * x[0] * x[0];
+ d->sigma_11 += mass * x[1] * x[1];
+ d->sigma_22 += mass * x[2] * x[2];
+ d->sigma_01 += mass * x[0] * x[1];
+ d->sigma_02 += mass * x[0] * x[2];
+ d->sigma_12 += mass * x[1] * x[2];
+
+ d->mass += mass;
+}
+
+
+static inline void multipole_iact(struct multipole *d, const float *x, float* a) {
+
+ int k;
+ float r2,ir,w, dx[3];
+
+ /* early abort */
+ if (d->mass == 0.) return;
+
+ float inv_mass = 1. / d->mass;
+
+ /* Temporary quantity */
+ dx[0] = d->sigma_00 - inv_mass*d->mu[0]*d->mu[0]; /* Abusing a so far unused */
+ dx[1] = d->sigma_11 - inv_mass*d->mu[1]*d->mu[1]; /* variable temporarily... */
+ dx[2] = d->sigma_22 - inv_mass*d->mu[2]*d->mu[2];
+
+ /* Construct quadrupole matrix */
+ float Q_00 = 2.0f*dx[0] - dx[1] - dx[2];
+ float Q_11 = 2.0f*dx[1] - dx[0] - dx[2];
+ float Q_22 = Q_00 + Q_11; /* Q_ij is traceless */
+ Q_22 *= -1.0f;
+
+ float Q_01 = d->sigma_01 - inv_mass*d->mu[0]*d->mu[1];
+ float Q_02 = d->sigma_02 - inv_mass*d->mu[0]*d->mu[2];
+ float Q_12 = d->sigma_12 - inv_mass*d->mu[1]*d->mu[2];
+ Q_01 *= 3.0f;
+ Q_02 *= 3.0f;
+ Q_12 *= 3.0f;
+
+ /* Compute the distance to the CoM. */
+ for (r2 = 0.0f, k = 0; k < 3; k++) {
+ dx[k] = x[k] - d->mu[k] * inv_mass;
+ r2 += dx[k] * dx[k];
+ }
+ ir = 1.0f / sqrtf(r2);
+
+ /* Compute the acceleration from the monopole */
+ w = const_G * ir * ir * ir * d->mass;
+ for (k = 0; k < 3; k++) a[k] -= w * dx[k];
+
+ /* Compute some helpful terms */
+ float w1 = const_G * ir * ir * ir * ir * ir;
+ float w2 = -2.5f * const_G * ir * ir * ir * ir * ir * ir * ir;
+ float xi = 0.;
+
+ xi += dx[0] * dx[0] * Q_00;
+ xi += dx[1] * dx[1] * Q_11;
+ xi += dx[2] * dx[2] * Q_22;
+ xi += 2.f * dx[0] * dx[1] * Q_01;
+ xi += 2.f * dx[0] * dx[2] * Q_02;
+ xi += 2.f * dx[1] * dx[2] * Q_12;
+
+ /* Compute the acceleration from the quadrupole */
+ a[0] += w2 * xi * dx[0] + w1 * (dx[0]*Q_00 + dx[1]*Q_01 + dx[2]*Q_02);
+ a[1] += w2 * xi * dx[1] + w1 * (dx[0]*Q_01 + dx[1]*Q_11 + dx[2]*Q_12);
+ a[2] += w2 * xi * dx[2] + w1 * (dx[0]*Q_02 + dx[1]*Q_12 + dx[2]*Q_22);
+
+}
+
+
+
+
+
+
+#ifdef COUNTERS
+int count_direct_unsorted;
+int count_direct_sorted_pp;
+int count_direct_sorted_pm_i;
+int count_direct_sorted_pm_j;
+#endif
+
+/** Per-type timers. */
+ticks task_timers[task_type_count];
+
+/** Global variable for the pool of allocated cells. */
+struct cell *cell_pool = NULL;
+
+/** Constants for the sorting axes. */
+const float axis_shift[13 * 3] = {
+ 5.773502691896258e-01, 5.773502691896258e-01, 5.773502691896258e-01,
+ 7.071067811865475e-01, 7.071067811865475e-01, 0.0,
+ 5.773502691896258e-01, 5.773502691896258e-01, -5.773502691896258e-01,
+ 7.071067811865475e-01, 0.0, 7.071067811865475e-01,
+ 1.0, 0.0, 0.0,
+ 7.071067811865475e-01, 0.0, -7.071067811865475e-01,
+ 5.773502691896258e-01, -5.773502691896258e-01, 5.773502691896258e-01,
+ 7.071067811865475e-01, -7.071067811865475e-01, 0.0,
+ 5.773502691896258e-01, -5.773502691896258e-01, -5.773502691896258e-01,
+ 0.0, 7.071067811865475e-01, 7.071067811865475e-01,
+ 0.0, 1.0, 0.0,
+ 0.0, 7.071067811865475e-01, -7.071067811865475e-01,
+ 0.0, 0.0, 1.0,
+};
+
+const char axis_flip[27] = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0,
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
+
+/* Map shift vector to sortlist. */
+const int axis_sid[27] = {
+ /* ( -1 , -1 , -1 ) */ 0,
+ /* ( -1 , -1 , 0 ) */ 1,
+ /* ( -1 , -1 , 1 ) */ 2,
+ /* ( -1 , 0 , -1 ) */ 3,
+ /* ( -1 , 0 , 0 ) */ 4,
+ /* ( -1 , 0 , 1 ) */ 5,
+ /* ( -1 , 1 , -1 ) */ 6,
+ /* ( -1 , 1 , 0 ) */ 7,
+ /* ( -1 , 1 , 1 ) */ 8,
+ /* ( 0 , -1 , -1 ) */ 9,
+ /* ( 0 , -1 , 0 ) */ 10,
+ /* ( 0 , -1 , 1 ) */ 11,
+ /* ( 0 , 0 , -1 ) */ 12,
+ /* ( 0 , 0 , 0 ) */ 0,
+ /* ( 0 , 0 , 1 ) */ 12,
+ /* ( 0 , 1 , -1 ) */ 11,
+ /* ( 0 , 1 , 0 ) */ 10,
+ /* ( 0 , 1 , 1 ) */ 9,
+ /* ( 1 , -1 , -1 ) */ 8,
+ /* ( 1 , -1 , 0 ) */ 7,
+ /* ( 1 , -1 , 1 ) */ 6,
+ /* ( 1 , 0 , -1 ) */ 5,
+ /* ( 1 , 0 , 0 ) */ 4,
+ /* ( 1 , 0 , 1 ) */ 3,
+ /* ( 1 , 1 , -1 ) */ 2,
+ /* ( 1 , 1 , 0 ) */ 1,
+ /* ( 1 , 1 , 1 ) */ 0
+};
+
+/* Some forward declarations. */
+void comp_com(struct cell *c);
+
+/**
+ * @brief Sort the entries in ascending order using QuickSort.
+ *
+ * @param sort The indices
+ * @param N The number of entries.
+ */
+void indices_sort(struct index *sort, int N) {
+
+ struct {
+ short int lo, hi;
+ } qstack[10];
+ int qpos, i, j, lo, hi, imin;
+ struct index temp;
+ float pivot;
+
+ /* Sort parts in cell_i in decreasing order with quicksort */
+ qstack[0].lo = 0;
+ qstack[0].hi = N - 1;
+ qpos = 0;
+ while (qpos >= 0) {
+ lo = qstack[qpos].lo;
+ hi = qstack[qpos].hi;
+ qpos -= 1;
+ if (hi - lo < 15) {
+ for (i = lo; i < hi; i++) {
+ imin = i;
+ for (j = i + 1; j <= hi; j++)
+ if (sort[j].d < sort[imin].d) imin = j;
+ if (imin != i) {
+ temp = sort[imin];
+ sort[imin] = sort[i];
+ sort[i] = temp;
+ }
+ }
+ } else {
+ pivot = sort[(lo + hi) / 2].d;
+ i = lo;
+ j = hi;
+ while (i <= j) {
+ while (sort[i].d < pivot) i++;
+ while (sort[j].d > pivot) j--;
+ if (i <= j) {
+ if (i < j) {
+ temp = sort[i];
+ sort[i] = sort[j];
+ sort[j] = temp;
+ }
+ i += 1;
+ j -= 1;
+ }
+ }
+ if (j > (lo + hi) / 2) {
+ if (lo < j) {
+ qpos += 1;
+ qstack[qpos].lo = lo;
+ qstack[qpos].hi = j;
+ }
+ if (i < hi) {
+ qpos += 1;
+ qstack[qpos].lo = i;
+ qstack[qpos].hi = hi;
+ }
+ } else {
+ if (i < hi) {
+ qpos += 1;
+ qstack[qpos].lo = i;
+ qstack[qpos].hi = hi;
+ }
+ if (lo < j) {
+ qpos += 1;
+ qstack[qpos].lo = lo;
+ qstack[qpos].hi = j;
+ }
+ }
+ }
+ }
+}
+
+/**
+ * @brief Sort the particles in the given cell along the given axis.
+ *
+ * @param c The #cell.
+ * @param axis The normalized axis along which to sort.
+ * @param aid The axis ID at which to store the indices.
+ */
+void cell_sort(struct cell *c, const float *axis, int aid) {
+
+ /* Has the indices array even been allocated? */
+ if (c->indices == NULL) {
+ if ((c->indices = (struct index *)malloc((c->count + 1) * 13 *
+ sizeof(struct index))) ==
+ NULL)
+ error("Failed to allocate cell sorting indices.");
+ } else if (c->sorted & (1 << aid)) {
+ return;
+ }
+
+ /* If this cell has been split, merge from the progeny. */
+ if (c->split) {
+
+ /* Heap of pointers to the progeny's indices. */
+ struct {
+ struct index *index;
+ int offset;
+ } temp, pindex[8];
+ int k = 0;
+
+ /* First, make sure all the progeny have been sorted, and get the pointers
+ to their first entries. */
+ for (struct cell *cp = c->firstchild; cp != c->sibling; cp = cp->sibling) {
+ if (!(cp->sorted & (1 << aid))) cell_sort(cp, axis, aid);
+ pindex[k].index = &cp->indices[(cp->count + 1) * aid];
+ pindex[k].offset = cp->parts - c->parts;
+ k++;
+ }
+
+ /* Fill any remaining gaps with the sentinel. */
+ c->indices[(c->count + 1) * aid + c->count].d = FLT_MAX;
+ for (; k < 8; k++)
+ pindex[k].index = &c->indices[(c->count + 1) * aid + c->count];
+
+ /* Heapify the pindices. */
+ for (k = 3; k >= 0; k--) {
+ int j = k;
+ while (j < 4) {
+ int jj = 2 * j + 1;
+ if (jj + 1 < 8 && pindex[jj + 1].index->d < pindex[jj].index->d)
+ jj = jj + 1;
+ if (pindex[jj].index->d < pindex[j].index->d) {
+ temp = pindex[jj];
+ pindex[jj] = pindex[j];
+ pindex[j] = temp;
+ j = jj;
+ } else
+ break;
+ }
+ }
+
+ /* Copy the indices into the local index in increasing order. */
+ struct index *dest = &c->indices[(c->count + 1) * aid];
+ for (int k = 0; k < c->count; k++) {
+
+ /* Copy the top of the heap to the destination. */
+ *dest = *pindex[0].index;
+ dest->ind += pindex[0].offset;
+
+ /* Increase the pointers. */
+ dest++;
+ pindex[0].index++;
+
+ /* Fix the heap. */
+ int j = 0;
+ while (j < 4) {
+ int jj = 2 * j + 1;
+ if (jj + 1 < 8 && pindex[jj + 1].index->d < pindex[jj].index->d)
+ jj = jj + 1;
+ if (pindex[jj].index->d < pindex[j].index->d) {
+ temp = pindex[jj];
+ pindex[jj] = pindex[j];
+ pindex[j] = temp;
+ j = jj;
+ } else
+ break;
+ }
+ }
+
+ /* Add a sentinel at the end. */
+ dest->ind = -1;
+ dest->d = FLT_MAX;
+
+ /* Otherwise, just sort the entries. */
+ } else {
+
+ /* Fill the indices. */
+ struct index *dest = &c->indices[(c->count + 1) * aid];
+ for (int k = 0; k < c->count; k++) {
+ dest[k].ind = k;
+ dest[k].d = c->parts[k].x[0] * axis[0] + c->parts[k].x[1] * axis[1] +
+ c->parts[k].x[2] * axis[2];
+ }
+
+ /* Sort the indices. */
+ indices_sort(&c->indices[(c->count + 1) * aid], c->count);
+
+ /* Set the sentinel on the last entry. */
+ dest[c->count].ind = -1;
+ dest[c->count].d = FLT_MAX;
+ }
+
+ /* Mark this cell as sorted in the given direction. */
+ c->sorted |= (1 << aid);
+
+ /* Verify the sort. */
+ /* int offset = (c->count + 1) * aid;
+ for (int k = 0; k < c->count; k++)
+ if (c->indices[offset + k].d > c->indices[offset + k + 1].d)
+ error( "Sorting failed." ); */
+} /* */
+
+/**
+ * @brief Get all the data needed for computing a sorted pair.
+ *
+ * @param ci Pointer to a pointer to the first cell.
+ * @param cj Pointer to a pointer to the second cell.
+ * @param ind_i Sorted indices of the cell @c ci.
+ * @param ind_j Sorted indices of the cell @c cj.
+ */
+void get_axis(struct cell **ci, struct cell **cj, struct index **ind_i,
+ struct index **ind_j) {
+
+ float axis[3];
+ float dx[3];
+ int aid = 0;
+
+ /* Get the cell pair separation and the axis index. */
+ for (int k = 0; k < 3; k++) {
+ dx[k] = (*cj)->loc[k] - (*ci)->loc[k];
+ aid = 3 * aid + ((dx[k] < 0) ? 0 : (dx[k] > 0) ? 2 : 1);
+ }
+
+ /* Flip the cells? */
+ if (axis_flip[aid]) {
+ struct cell *temp = *ci;
+ *ci = *cj;
+ *cj = temp;
+ }
+ aid = axis_sid[aid];
+
+ /* Copy the shift vector to the output parameter. */
+ axis[0] = axis_shift[aid * 3 + 0];
+ axis[1] = axis_shift[aid * 3 + 1];
+ axis[2] = axis_shift[aid * 3 + 2];
+
+ /* Make sure the cells are sorted. */
+ if (!((*ci)->sorted & (1 << aid))) cell_sort(*ci, axis, aid);
+ if (!((*cj)->sorted & (1 << aid))) cell_sort(*cj, axis, aid);
+
+ /* Set the indices. */
+ *ind_i = &(*ci)->indices[aid * ((*ci)->count + 1)];
+ *ind_j = &(*cj)->indices[aid * ((*cj)->count + 1)];
+
+
+ /* Make sure the sorts are ok. */
+ /* for (int k = 1; k < (*ci)->count; k++)
+ if ((*ind_i)[k].d < (*ind_i)[k-1].d)
+ error("Sorting failed.");
+ for (int k = 1; k < (*cj)->count; k++)
+ if ((*ind_j)[k].d < (*ind_j)[k-1].d)
+ error("Sorting failed."); */
+}
+
+/**
+ * @brief Get a #cell from the pool.
+ */
+struct cell *cell_get() {
+
+ struct cell *res;
+ int k;
+
+ /* Allocate a new batch? */
+ if (cell_pool == NULL) {
+
+ /* Allocate the cell array. */
+ if ((cell_pool =
+ (struct cell *)calloc(cell_pool_grow, sizeof(struct cell))) ==
+ NULL)
+ error("Failed to allocate fresh batch of cells.");
+
+ /* Link them up via their progeny pointers. */
+ for (k = 1; k < cell_pool_grow; k++)
+ cell_pool[k - 1].firstchild = &cell_pool[k];
+ }
+
+ /* Pick a cell off the pool. */
+ res = cell_pool;
+ cell_pool = cell_pool->firstchild;
+
+ /* Clean up a few things. */
+ res->res = qsched_res_none;
+ res->firstchild = 0;
+
+ /* Return the cell. */
+ return res;
+}
+
+/**
+ * @brief Sort the parts into eight bins along the given pivots and
+ * fill the multipoles. Also adds the hierarchical resources
+ * to the sched.
+ *
+ * @param c The #cell to be split.
+ * @param N The total number of parts.
+ * @param s The #sched to store the resources.
+ */
+void cell_split(struct cell *c, struct qsched *s) {
+
+ int i, j, k, kk, count = c->count;
+ struct part temp, *parts = c->parts;
+ struct cell *cp;
+ int left[8], right[8];
+ double pivot[3];
+ static struct cell *root = NULL;
+ struct cell *progenitors[8];
+
+ /* Set the root cell. */
+ if (root == NULL) {
+ root = c;
+ c->sibling = 0;
+ }
+
+ /* Add a resource for this cell if it doesn't have one yet. */
+ if (c->res == qsched_res_none)
+ c->res = qsched_addres(s, qsched_owner_none, qsched_res_none);
+
+/* Attach a center-of-mass task to the cell. */
+#ifdef COM_AS_TASK
+ if (count > 0)
+ c->com_tid = qsched_addtask(s, task_type_com, task_flag_none, &c,
+ sizeof(struct cell *), 1);
+#endif
+
+ /* Does this cell need to be split? */
+ if (count > cell_maxparts) {
+
+ /* Mark this cell as split. */
+ c->split = 1;
+
+ /* Create the progeny. */
+ for (k = 0; k < 8; k++) {
+ progenitors[k] = cp = cell_get();
+ cp->loc[0] = c->loc[0];
+ cp->loc[1] = c->loc[1];
+ cp->loc[2] = c->loc[2];
+ cp->h = c->h * 0.5;
+ cp->res = qsched_addres(s, qsched_owner_none, c->res);
+ if (k & 4) cp->loc[0] += cp->h;
+ if (k & 2) cp->loc[1] += cp->h;
+ if (k & 1) cp->loc[2] += cp->h;
+ }
+
+ /* Init the pivots. */
+ for (k = 0; k < 3; k++) pivot[k] = c->loc[k] + c->h * 0.5;
+
+ /* Split along the x-axis. */
+ i = 0;
+ j = count - 1;
+ while (i <= j) {
+ while (i <= count - 1 && parts[i].x[0] < pivot[0]) i += 1;
+ while (j >= 0 && parts[j].x[0] >= pivot[0]) j -= 1;
+ if (i < j) {
+ temp = parts[i];
+ parts[i] = parts[j];
+ parts[j] = temp;
+ }
+ }
+ left[1] = i;
+ right[1] = count - 1;
+ left[0] = 0;
+ right[0] = j;
+
+ /* Split along the y axis, twice. */
+ for (k = 1; k >= 0; k--) {
+ i = left[k];
+ j = right[k];
+ while (i <= j) {
+ while (i <= right[k] && parts[i].x[1] < pivot[1]) i += 1;
+ while (j >= left[k] && parts[j].x[1] >= pivot[1]) j -= 1;
+ if (i < j) {
+ temp = parts[i];
+ parts[i] = parts[j];
+ parts[j] = temp;
+ }
+ }
+ left[2 * k + 1] = i;
+ right[2 * k + 1] = right[k];
+ left[2 * k] = left[k];
+ right[2 * k] = j;
+ }
+
+ /* Split along the z axis, four times. */
+ for (k = 3; k >= 0; k--) {
+ i = left[k];
+ j = right[k];
+ while (i <= j) {
+ while (i <= right[k] && parts[i].x[2] < pivot[2]) i += 1;
+ while (j >= left[k] && parts[j].x[2] >= pivot[2]) j -= 1;
+ if (i < j) {
+ temp = parts[i];
+ parts[i] = parts[j];
+ parts[j] = temp;
+ }
+ }
+ left[2 * k + 1] = i;
+ right[2 * k + 1] = right[k];
+ left[2 * k] = left[k];
+ right[2 * k] = j;
+ }
+
+ /* Store the counts and offsets. */
+ for (k = 0; k < 8; k++) {
+ progenitors[k]->count = right[k] - left[k] + 1;
+ progenitors[k]->parts = &c->parts[left[k]];
+ }
+
+ /* Find the first non-empty progenitor */
+ for (k = 0; k < 8; k++)
+ if (progenitors[k]->count > 0) {
+ c->firstchild = progenitors[k];
+ break;
+ }
+
+#ifdef SANITY_CHECKS
+ if (c->firstchild == NULL)
+ error("Cell has been split but all progenitors have 0 particles");
+#endif
+
+ /* Prepare the pointers. */
+ for (k = 0; k < 8; k++) {
+
+ /* Find the next non-empty sibling */
+ for (kk = k + 1; kk < 8; ++kk) {
+ if (progenitors[kk]->count > 0) {
+ progenitors[k]->sibling = progenitors[kk];
+ break;
+ }
+ }
+
+ /* No non-empty sibling ? Go back a level */
+ if (kk == 8) progenitors[k]->sibling = c->sibling;
+ }
+
+ /* Recurse. */
+ for (k = 0; k < 8; k++)
+ if (progenitors[k]->count > 0) cell_split(progenitors[k], s);
+
+/* Link the COM tasks. */
+#ifdef COM_AS_TASK
+ for (k = 0; k < 8; k++)
+ if (progenitors[k]->count > 0)
+ qsched_addunlock(s, progenitors[k]->com_tid, c->com_tid);
+#endif
+
+ /* Otherwise, we're at a leaf, so create the cell's particle-cell task. */
+ } else {
+ struct cell *data[2] = {root, c};
+ int tid = qsched_addtask(s, task_type_self_pc, task_flag_none, data,
+ 2 * sizeof(struct cell *), 1);
+ qsched_addlock(s, tid, c->res);
+#ifdef COM_AS_TASK
+ qsched_addunlock(s, root->com_tid, tid);
+#endif
+ } /* does the cell need to be split? */
+
+/* Compute the cell's center of mass. */
+#ifndef COM_AS_TASK
+ comp_com(c);
+#endif
+
+ /* Set this cell's resources ownership. */
+ qsched_res_own(s, c->res,
+ s->nr_queues * (c->parts - root->parts) / root->count);
+}
+
+/* -------------------------------------------------------------------------- */
+/* New tree walk */
+/* -------------------------------------------------------------------------- */
+
+/**
+ * @brief Compute the center of mass of a given cell.
+ *
+ * @param c The #cell.
+ */
+void comp_com(struct cell *c) {
+
+ int k, count = c->count;
+ struct cell *cp;
+ struct part *parts = c->parts;
+ double com[3] = {0.0, 0.0, 0.0}, mass = 0.0;
+
+ if (c->split) {
+
+ /* Loop over the projenitors and collect the multipole information. */
+ for (cp = c->firstchild; cp != c->sibling; cp = cp->sibling) {
+ float cp_mass = cp->new.mass;
+ com[0] += cp->new.com[0] * cp_mass;
+ com[1] += cp->new.com[1] * cp_mass;
+ com[2] += cp->new.com[2] * cp_mass;
+ mass += cp_mass;
+ }
+
+ /* Otherwise, collect the multipole from the particles. */
+ } else {
+
+ for (k = 0; k < count; k++) {
+ float p_mass = parts[k].mass;
+ com[0] += parts[k].x[0] * p_mass;
+ com[1] += parts[k].x[1] * p_mass;
+ com[2] += parts[k].x[2] * p_mass;
+ mass += p_mass;
+ }
+ }
+
+ /* Store the COM data, if any was collected. */
+ if (mass > 0.0) {
+ float imass = 1.0f / mass;
+ c->new.com[0] = com[0] * imass;
+ c->new.com[1] = com[1] * imass;
+ c->new.com[2] = com[2] * imass;
+ c->new.mass = mass;
+ } else {
+ c->new.com[0] = 0.0;
+ c->new.com[1] = 0.0;
+ c->new.com[2] = 0.0;
+ c->new.mass = 0.0;
+ }
+}
+
+/**
+ * @brief Interacts all particles in ci with the monopole in cj
+ */
+static inline void make_interact_pc(struct cell *leaf, struct cell *cj) {
+
+ int j, k;
+ double com[3] = {0.0, 0.0, 0.0};
+ float mcom, dx[3] = {0.0, 0.0, 0.0}, r2, ir, w;
+
+#ifdef SANITY_CHECKS
+
+ /* Sanity checks */
+ if (leaf->count == 0) error("Empty cell!");
+
+ /* Sanity check. */
+ if (cj->new.mass == 0.0) {
+ message("%e %e %e %d %p %d %p", cj->new.com[0], cj->new.com[1],
+ cj->new.com[2], cj->count, cj, cj->split, cj->sibling);
+
+ for (j = 0; j < cj->count; ++j)
+ message("part %d mass=%e id=%d", j, cj->parts[j].mass, cj->parts[j].id);
+
+ error("com does not seem to have been set.");
+ }
+
+#endif
+
+ /* Init the com's data. */
+ for (k = 0; k < 3; k++) com[k] = cj->new.com[k];
+ mcom = cj->new.mass;
+
+ /* Loop over every particle in leaf. */
+ for (j = 0; j < leaf->count; j++) {
+
+ /* Compute the pairwise distance. */
+ for (r2 = 0.0, k = 0; k < 3; k++) {
+ dx[k] = com[k] - leaf->parts[j].x[k];
+ r2 += dx[k] * dx[k];
+ }
+
+ /* Apply the gravitational acceleration. */
+ ir = 1.0f / sqrtf(r2);
+ w = mcom * const_G * ir * ir * ir;
+ for (k = 0; k < 3; k++) leaf->parts[j].a[k] += w * dx[k];
+
+#if ICHECK >= 0
+ if (leaf->parts[j].id == ICHECK)
+ printf("[DEBUG] cell [%f,%f,%f] interacting with cj->loc=[%f,%f,%f] "
+ "m=%f h=%f\n",
+ leaf->loc[0], leaf->loc[1], leaf->loc[2], cj->loc[0], cj->loc[1],
+ cj->loc[2], mcom, cj->h);
+
+ if (leaf->parts[j].id == ICHECK)
+ printf("[NEW] Interaction with monopole a=( %e %e %e ) h= %f Nj= %d m_j= "
+ "%f\n",
+ w * dx[0], w * dx[1], w * dx[2], cj->h, cj->count, mcom);
+#endif
+
+ } /* loop over every particle. */
+}
+
+/**
+ * @brief Checks whether the cell leaf is a subvolume of the cell c
+ */
+static inline int is_inside(struct cell *leaf, struct cell *c) {
+ return (leaf->parts >= c->parts) && (leaf->parts < c->parts + c->count);
+}
+
+/**
+ * @brief Checks whether the cells are direct neighbours ot not
+ */
+static inline int are_neighbours_different_size(struct cell *ci,
+ struct cell *cj) {
+
+ int k;
+ float dx[3];
+ double cih = ci->h, cjh = cj->h;
+
+ /* Maximum allowed distance */
+ float min_dist = 0.5 * (cih + cjh);
+
+ /* (Manhattan) Distance between the cells */
+ for (k = 0; k < 3; k++) {
+ float center_i = ci->loc[k] + 0.5 * cih;
+ float center_j = cj->loc[k] + 0.5 * cjh;
+ dx[k] = fabs(center_i - center_j);
+ }
+
+ return (dx[0] <= min_dist) && (dx[1] <= min_dist) && (dx[2] <= min_dist);
+}
+
+/**
+ * @brief Checks whether the cells are direct neighbours ot not. Both cells have
+ * to be of the same size
+ */
+static inline int are_neighbours(struct cell *ci, struct cell *cj) {
+
+ int k;
+ float dx[3];
+
+#ifdef SANITY_CHECKS
+ if (ci->h != cj->h)
+ error(" Cells of different size in distance calculation.");
+#endif
+
+ /* Maximum allowed distance */
+ float min_dist = ci->h;
+
+ /* (Manhattan) Distance between the cells */
+ for (k = 0; k < 3; k++) {
+ float center_i = ci->loc[k];
+ float center_j = cj->loc[k];
+ dx[k] = fabs(center_i - center_j);
+ }
+
+ return (dx[0] <= min_dist) && (dx[1] <= min_dist) && (dx[2] <= min_dist);
+}
+
+/**
+ * @brief Compute the interactions between all particles in a cell leaf
+ * and the center of mass of all the cells in a part of the tree
+* described by ci and cj
+ *
+ * @param ci The #cell containing the particle
+ * @param cj The #cell containing the center of mass.
+ */
+static inline void iact_pair_pc(struct cell *ci, struct cell *cj,
+ struct cell *leaf) {
+
+ struct cell *cp, *cps;
+
+#ifdef SANITY_CHECKS
+
+ /* Early abort? */
+ if (ci->count == 0 || cj->count == 0) error("Empty cell !");
+
+ /* Sanity check */
+ if (ci == cj)
+ error("The impossible has happened: pair interaction between a cell and "
+ "itself.");
+
+ /* Sanity check */
+ if (!is_inside(leaf, ci))
+ error("The impossible has happened: The leaf is not within ci");
+
+ /* Are the cells direct neighbours? */
+ if (!are_neighbours(ci, cj)) error("Cells are not neighours");
+
+ /* Are both cells split ? */
+ if (!ci->split || !cj->split) error("One of the cells is not split !");
+#endif
+
+ /* Let's find in which subcell of ci the leaf is */
+ for (cp = ci->firstchild; cp != ci->sibling; cp = cp->sibling) {
+
+ if (is_inside(leaf, cp)) break;
+ }
+
+ if (are_neighbours_different_size(cp, cj)) {
+
+ /* Now interact this subcell with all subcells of cj */
+ for (cps = cj->firstchild; cps != cj->sibling; cps = cps->sibling) {
+
+ /* Check whether we have to recurse or can directly jump to the multipole
+ * calculation */
+ if (are_neighbours(cp, cps)) {
+
+ /* We only recurse if the children are split */
+ if (cp->split && cps->split) {
+ iact_pair_pc(cp, cps, leaf);
+ }
+
+ } else {
+ make_interact_pc(leaf, cps);
+ }
+ }
+ } else {
+
+ /* If cp is not a neoghbour of cj, we can directly interact with the
+ * multipoles */
+ for (cps = cj->firstchild; cps != cj->sibling; cps = cps->sibling) {
+
+ make_interact_pc(leaf, cps);
+ }
+ }
+}
+
+/**
+ * @brief Compute the interactions between all particles in a leaf and
+ * and all the monopoles in the cell c
+ *
+ * @param c The #cell containing the monopoles
+ * @param leaf The #cell containing the particles
+ */
+static inline void iact_self_pc(struct cell *c, struct cell *leaf) {
+
+ struct cell *cp, *cps;
+
+#ifdef SANITY_CHECKS
+
+ /* Early abort? */
+ if (c->count == 0) error("Empty cell !");
+
+ if (!c->split) error("Cell is not split !");
+
+#endif
+
+ /* Find in which subcell of c the leaf is */
+ for (cp = c->firstchild; cp != c->sibling; cp = cp->sibling) {
+
+ /* Only recurse if the leaf is in this part of the tree */
+ if (is_inside(leaf, cp)) break;
+ }
+
+ if (cp->split) {
+
+ /* Recurse if the cell can be split */
+ iact_self_pc(cp, leaf);
+
+ /* Now, interact with every other subcell */
+ for (cps = c->firstchild; cps != c->sibling; cps = cps->sibling) {
+
+ /* Since cp and cps will be direct neighbours it is only worth recursing
+ */
+ /* if the cells can both be split */
+ if (cp != cps && cps->split) iact_pair_pc(cp, cps, leaf);
+ }
+ }
+}
+
+/**
+ * @brief Starts the recursive tree walk of a given leaf
+ */
+void init_multipole_walk(struct cell *root, struct cell *leaf) {
+
+ /* Pre-fetch the leaf's particles */
+ __builtin_prefetch(leaf->parts, 1, 3);
+
+ /* Start the recursion */
+ iact_self_pc(root, leaf);
+}
+
+/**
+ * @brief Compute the interactions between all particles in a cell
+ * and all particles in the other cell (N^2 algorithm)
+ *
+ * @param ci The #cell containing the particles.
+ * @param cj The #cell containing the other particles
+ */
+static inline void iact_pair_direct_unsorted(struct cell *ci, struct cell *cj) {
+
+ int i, j, k;
+ int count_i = ci->count, count_j = cj->count;
+ struct part *parts_i = ci->parts, *parts_j = cj->parts;
+ double xi[3];
+ float dx[3], ai[3], mi, mj, r2, w, ir;
+
+#ifdef SANITY_CHECKS
+
+ /* Bad stuff will happen if cell sizes are different */
+ if (ci->h != cj->h)
+ error("Non matching cell sizes !! h_i=%f h_j=%f\n", ci->h, cj->h);
+
+#endif
+
+ /* Loop over all particles in ci... */
+ for (i = 0; i < count_i; i++) {
+
+ /* Init the ith particle's data. */
+ for (k = 0; k < 3; k++) {
+ xi[k] = parts_i[i].x[k];
+ ai[k] = 0.0f;
+ }
+ mi = parts_i[i].mass;
+
+ /* Loop over every particle in the other cell. */
+ for (j = 0; j < count_j; j++) {
+
+ /* Compute the pairwise distance. */
+ for (r2 = 0.0, k = 0; k < 3; k++) {
+ dx[k] = xi[k] - parts_j[j].x[k];
+ r2 += dx[k] * dx[k];
+ }
+
+ /* Apply the gravitational acceleration. */
+ ir = 1.0f / sqrtf(r2);
+ w = const_G * ir * ir * ir;
+ mj = parts_j[j].mass;
+ for (k = 0; k < 3; k++) {
+ float wdx = w * dx[k];
+ parts_j[j].a[k] += wdx * mi;
+ ai[k] -= wdx * mj;
+ }
+
+#ifdef COUNTERS
+ ++count_direct_unsorted;
+#endif
+
+#if ICHECK >= 0 && 0
+ if (parts_i[i].id == ICHECK)
+ printf(
+ "[NEW] Interaction with particle id= %d (pair i) a=( %e %e %e )\n",
+ parts_j[j].id, -mi * w * dx[0], -mi * w * dx[1], -mi * w * dx[2]);
+
+ if (parts_j[j].id == ICHECK)
+ printf(
+ "[NEW] Interaction with particle id= %d (pair j) a=( %e %e %e )\n",
+ parts_i[i].id, mj * w * dx[0], mj * w * dx[1], mj * w * dx[2]);
+#endif
+
+ } /* loop over every other particle. */
+
+ /* Store the accumulated acceleration on the ith part. */
+ for (k = 0; k < 3; k++) parts_i[i].a[k] += ai[k];
+
+ } /* loop over all particles. */
+}
+
+
+
+
+
+
+static inline void iact_pair_direct_sorted_multipole(struct cell *ci,
+ struct cell *cj) {
+
+ struct part_local {
+ float x[3];
+ float a[3];
+ float mass, d;
+ };
+
+ int i, j, k;
+ int count_i, count_j;
+ struct part_local *parts_i, *parts_j;
+ float cjh = cj->h;
+ float xi[3];
+ float dx[3], ai[3], mi, mj, r2, w, ir;
+
+#ifdef SANITY_CHECKS
+
+ /* Bad stuff will happen if cell sizes are different */
+ if (ci->h != cj->h)
+ error("Non matching cell sizes !! h_i=%f h_j=%f\n", ci->h, cj->h);
+
+#endif
+
+ /* Get the sorted indices and stuff. */
+ struct index *ind_i, *ind_j;
+ struct multipole multi;
+ get_axis(&ci, &cj, &ind_i, &ind_j);
+ multipole_reset(&multi);
+ cjh = cj->h;
+
+ /* Allocate and fill-in the local parts. */
+ count_i = ci->count;
+ count_j = cj->count;
+ if ((parts_i =
+ (struct part_local *)alloca(sizeof(struct part_local) *count_i)) ==
+ NULL ||
+ (parts_j =
+ (struct part_local *)alloca(sizeof(struct part_local) * count_j)) ==
+ NULL)
+ error("Failed to allocate local part arrays.");
+ for (i = 0; i < count_i; i++) {
+ int pid = ind_i[i].ind;
+ parts_i[i].d = ind_i[i].d;
+ for (k = 0; k < 3; k++) {
+ parts_i[i].x[k] = ci->parts[pid].x[k] - cj->loc[k];
+ parts_i[i].a[k] = 0.0f;
+ }
+ parts_i[i].mass = ci->parts[pid].mass;
+ }
+ for (j = 0; j < count_j; j++) {
+ int pjd = ind_j[j].ind;
+ parts_j[j].d = ind_j[j].d;
+ for (k = 0; k < 3; k++) {
+ parts_j[j].x[k] = cj->parts[pjd].x[k] - cj->loc[k];
+ parts_j[j].a[k] = 0.0f;
+ }
+ parts_j[j].mass = cj->parts[pjd].mass;
+ }
+
+#if ICHECK >= 0
+ for (k = 0; k < count_i; k++)
+ if (parts_i[k].id == ICHECK)
+ message("[DEBUG] interacting cells loc=[%f,%f,%f], h=%f and "
+ "loc=[%f,%f,%f], h=%f.",
+ ci->loc[0], ci->loc[1], ci->loc[2], ci->h, cj->loc[0], cj->loc[1],
+ cj->loc[2], cj->h);
+ for (k = 0; k < count_j; k++)
+ if (parts_j[k].id == ICHECK)
+ message("[DEBUG] interacting cells loc=[%f,%f,%f], h=%f and "
+ "loc=[%f,%f,%f], h=%f.",
+ cj->loc[0], cj->loc[1], cj->loc[2], cj->h, ci->loc[0], ci->loc[1],
+ ci->loc[2], ci->h);
+#endif
+
+ /* Distance along the axis as of which we will use a multipole. */
+ float d_max = dist_cutoff_ratio * cjh;
+
+ /* Loop over all particles in ci... */
+ for (i = count_i - 1; i >= 0; i--) {
+
+ /* Get a local copy of the distance along the axis. */
+ float di = parts_i[i].d;
+
+ /* Init the ith particle's data. */
+ for (k = 0; k < 3; k++) {
+ xi[k] = parts_i[i].x[k];
+ ai[k] = 0.0;
+ }
+ mi = parts_i[i].mass;
+
+ /* Loop over every following particle within d_max along the axis. */
+ for (j = 0; j < count_j && (parts_j[j].d - di) < d_max; j++) {
+
+ /* Compute the pairwise distance. */
+ for (r2 = 0.0, k = 0; k < 3; k++) {
+ dx[k] = xi[k] - parts_j[j].x[k];
+ r2 += dx[k] * dx[k];
+ }
+
+ /* Apply the gravitational acceleration. */
+ ir = 1.0f / sqrtf(r2);
+ w = const_G * ir * ir * ir;
+ mj = parts_j[j].mass;
+ for (k = 0; k < 3; k++) {
+ float wdx = w * dx[k];
+ parts_j[j].a[k] += wdx * mi;
+ ai[k] -= wdx * mj;
+ }
+
+#if ICHECK >= 0
+ if (parts_i[i].id == ICHECK)
+ message("Interaction with part %d - d= %f", parts_j[j].id, sqrt(r2));
+#endif
+
+#ifdef COUNTERS
+ ++count_direct_sorted_pp;
+#endif
+
+#if ICHECK >= 0 && 0
+ if (parts_i[i].id == ICHECK)
+ printf("[NEW] Interaction with particle id= %d (pair i)\n",
+ parts_j[pjd].id);
+
+ if (parts_j[j].id == ICHECK)
+ printf("[NEW] Interaction with particle id= %d (pair j) h_i= %f h_j= "
+ "%f ci= %p cj= %p count_i= %d count_j= %d d_i= %d d_j= %d\n",
+ parts_i[pid].id, ci->h, cj->h, ci, cj, count_i, count_j, ci->res,
+ cj->res);
+#endif
+
+ } /* loop over every other particle. */
+
+ /* Add any remaining particles to the COM. */
+ for (int jj = j; jj < count_j; jj++) {
+ multipole_add(&multi, parts_j[jj].x, parts_j[jj].mass);
+ }
+
+ /* Shrink count_j to the latest valid particle. */
+ count_j = j;
+
+ /* Interact part_i with the center of mass. */
+ multipole_iact(&multi, xi, ai);
+
+#if ICHECK >= 0
+ if (parts_i[i].id == ICHECK)
+ message("Interaction with multipole"); //, parts_j[j].id );
+#endif
+
+#ifdef COUNTERS
+ ++count_direct_sorted_pm_i;
+#endif
+
+
+ /* Store the accumulated acceleration on the ith part. */
+ for (k = 0; k < 3; k++) parts_i[i].a[k] += ai[k];
+
+ } /* loop over all particles in ci. */
+
+
+
+ /* Re-init some values. */
+ count_j = cj->count;
+ int last_i = 0;
+ multipole_reset(&multi);
+
+ /* Loop over the particles in cj, catch the COM interactions. */
+ for (j = 0; j < count_j; j++) {
+
+ /* Get the sorted index. */
+ float dj = parts_j[j].d;
+
+ /* Fill the COM with any new particles. */
+ for (i = last_i; i < count_i && (dj - parts_i[i].d) > d_max; i++) {
+ multipole_add(&multi, parts_i[i].x, parts_i[i].mass);
+ }
+
+ /* Set the new last_i to the last particle checked. */
+ last_i = i;
+
+ /* Interact part_j with the COM. */
+ multipole_iact(&multi, parts_j[j].x, parts_j[j].a);
+
+#ifdef COUNTERS
+ ++count_direct_sorted_pm_j;
+#endif
+
+ }
+
+ /* Copy the accelerations back to the original particles. */
+ for (i = 0; i < count_i; i++) {
+ int pid = ind_i[i].ind;
+ for (k = 0; k < 3; k++) ci->parts[pid].a[k] += parts_i[i].a[k];
+ }
+ for (j = 0; j < count_j; j++) {
+ int pjd = ind_j[j].ind;
+ for (k = 0; k < 3; k++) cj->parts[pjd].a[k] += parts_j[j].a[k];
+ }
+}
+
+
+
+
+
+/**
+ * @brief Decides whether two cells use the direct summation interaction or the
+* multipole interactions
+ *
+ * @param ci The #cell.
+ * @param cj The other #cell.
+ */
+void iact_pair(struct cell *ci, struct cell *cj) {
+
+ struct cell *cp, *cps;
+
+#ifdef SANITY_CHECKS
+
+ /* Early abort? */
+ if (ci->count == 0 || cj->count == 0) error("Empty cell !");
+
+ /* Bad stuff will happen if cell sizes are different */
+ if (ci->h != cj->h)
+ error("Non matching cell sizes !! h_i=%f h_j=%f\n", ci->h, cj->h);
+
+ /* Sanity check */
+ if (ci == cj)
+ error("The impossible has happened: pair interaction between a cell and "
+ "itself.");
+
+#endif
+
+ /* Are the cells direct neighbours? */
+ if (are_neighbours(ci, cj)) {
+
+ /* Are both cells split ? */
+ if (ci->split && cj->split) {
+
+ /* Let's split both cells and build all possible pairs */
+ for (cp = ci->firstchild; cp != ci->sibling; cp = cp->sibling) {
+ for (cps = cj->firstchild; cps != cj->sibling; cps = cps->sibling) {
+
+ /* If the cells are neighbours, recurse. */
+ if (are_neighbours(cp, cps)) {
+ iact_pair(cp, cps);
+ }
+ }
+ }
+ } else {/* Otherwise, compute the interactions at this level directly. */
+ iact_pair_direct(ci, cj);
+ }
+ }
+}
+
+/**
+ * @brief Compute the interactions between all particles in a cell.
+ *
+ * @param c The #cell.
+ */
+void iact_self_direct(struct cell *c) {
+ int i, j, k, count = c->count;
+ double xi[3] = {0.0, 0.0, 0.0};
+ float ai[3] = {0.0, 0.0, 0.0}, mi, mj, dx[3] = {0.0, 0.0, 0.0}, r2, ir, w;
+ struct part *parts = c->parts;
+ struct cell *cp, *cps;
+
+#ifdef SANITY_CHECKS
+
+ /* Early abort? */
+ if (count == 0) error("Empty cell !");
+
+#endif
+
+ /* If the cell is split, interact each progeny with itself, and with
+ each of its siblings. */
+ if (c->split) {
+ for (cp = c->firstchild; cp != c->sibling; cp = cp->sibling) {
+ iact_self_direct(cp);
+ for (cps = cp->sibling; cps != c->sibling; cps = cps->sibling)
+ iact_pair(cp, cps);
+ }
+
+ /* Otherwise, compute the interactions directly. */
+ } else {
+
+ /* Loop over all particles... */
+ for (i = 0; i < count; i++) {
+
+ /* Init the ith particle's data. */
+ for (k = 0; k < 3; k++) {
+ xi[k] = parts[i].x[k];
+ ai[k] = 0.0;
+ }
+ mi = parts[i].mass;
+
+ /* Loop over every following particle. */
+ for (j = i + 1; j < count; j++) {
+
+ /* Compute the pairwise distance. */
+ for (r2 = 0.0, k = 0; k < 3; k++) {
+ dx[k] = xi[k] - parts[j].x[k];
+ r2 += dx[k] * dx[k];
+ }
+
+ /* Apply the gravitational acceleration. */
+ ir = 1.0f / sqrtf(r2);
+ w = const_G * ir * ir * ir;
+ mj = parts[j].mass;
+ for (k = 0; k < 3; k++) {
+ float wdx = w * dx[k];
+ parts[j].a[k] += wdx * mi;
+ ai[k] -= wdx * mj;
+ }
+
+#if ICHECK >= 0
+ if (parts[i].id == ICHECK)
+ message("[NEW] Interaction with particle id= %d (self i)",
+ parts[j].id);
+
+ if (parts[j].id == ICHECK)
+ message("[NEW] Interaction with particle id= %d (self j)",
+ parts[i].id);
+#endif
+
+ } /* loop over every other particle. */
+
+ /* Store the accumulated acceleration on the ith part. */
+ for (k = 0; k < 3; k++) parts[i].a[k] += ai[k];
+
+ } /* loop over all particles. */
+
+ } /* otherwise, compute interactions directly. */
+}
+
+/**
+ * @brief Create the tasks for the cell pair/self.
+ *
+ * @param s The #sched in which to create the tasks.
+ * @param ci The first #cell.
+ * @param cj The second #cell.
+ */
+void create_tasks(struct qsched *s, struct cell *ci, struct cell *cj) {
+
+ qsched_task_t tid;
+ struct cell *data[2], *cp, *cps;
+
+#ifdef SANITY_CHECKS
+
+ /* If either cell is empty, stop. */
+ if (ci->count == 0 || (cj != NULL && cj->count == 0)) error("Empty cell !");
+
+#endif
+
+ /* Single cell? */
+ if (cj == NULL) {
+
+ /* Is this cell split and above the task limit ? */
+ if (ci->split && ci->count > task_limit / ci->count) {
+
+ /* Loop over each of this cell's progeny. */
+ for (cp = ci->firstchild; cp != ci->sibling; cp = cp->sibling) {
+
+ /* Make self-interaction task. */
+ create_tasks(s, cp, NULL);
+
+ /* Make all pair-interaction tasks. */
+ for (cps = cp->sibling; cps != ci->sibling; cps = cps->sibling)
+ create_tasks(s, cp, cps);
+ }
+
+ /* Otherwise, add a self-interaction task. */
+ } else {
+
+ /* Set the data. */
+ data[0] = ci;
+ data[1] = NULL;
+
+ /* Create the task. */
+ tid =
+ qsched_addtask(s, task_type_self, task_flag_none, data,
+ sizeof(struct cell *) * 2, ci->count * ci->count / 2);
+
+ /* Add the resource (i.e. the cell) to the new task. */
+ qsched_addlock(s, tid, ci->res);
+
+/* If this call might recurse, add a dependency on the cell's COM
+ task. */
+#ifdef COM_AS_TASK
+ if (ci->split) qsched_addunlock(s, ci->com_tid, tid);
+#endif
+ }
+
+ /* Otherwise, it's a pair. */
+ } else {
+
+ /* Are the cells NOT neighbours ? */
+ if (!are_neighbours(ci, cj)) {
+
+ } else {/* Cells are direct neighbours */
+
+ /* Are both cells split ? */
+ if (ci->split && cj->split && ci->count > task_limit / cj->count) {
+
+ /* Let's split both cells and build all possible pairs */
+ for (cp = ci->firstchild; cp != ci->sibling; cp = cp->sibling) {
+ for (cps = cj->firstchild; cps != cj->sibling; cps = cps->sibling) {
+ /* Recurse */
+ create_tasks(s, cp, cps);
+ }
+ }
+ /* Otherwise, at least one of the cells is not split, build a direct
+ * interaction. */
+ } else {
+
+ /* Set the data. */
+ data[0] = ci;
+ data[1] = cj;
+
+ /* Create the task. */
+ tid = qsched_addtask(s, task_type_pair, task_flag_none, data,
+ sizeof(struct cell *) * 2, ci->count * cj->count);
+
+ /* Add the resources. */
+ qsched_addlock(s, tid, ci->res);
+ qsched_addlock(s, tid, cj->res);
+ }
+ } /* Cells are direct neighbours */
+ } /* Otherwise it's a pair */
+}
+
+/* -------------------------------------------------------------------------- */
+/* Legacy tree walk */
+/* -------------------------------------------------------------------------- */
+
+/**
+ * @brief Compute the center of mass of a given cell recursively.
+ *
+ * @param c The #cell.
+ */
+void legacy_comp_com(struct cell *c, int *countCoMs) {
+
+ int k, count = c->count;
+ struct cell *cp;
+ struct part *p, *parts = c->parts;
+ double com[3] = {0.0, 0.0, 0.0}, mass = 0.0;
+
+ ++(*countCoMs);
+
+ /* Is the cell split? */
+ if (c->split) {
+
+ /* Loop over the progeny. */
+ for (cp = c->firstchild; cp != c->sibling; cp = cp->sibling) {
+ /* Recurse */
+ legacy_comp_com(cp, countCoMs);
+
+ /* Collect multipole information */
+ float cp_mass = cp->legacy.mass;
+ com[0] += cp->legacy.com[0] * cp_mass;
+ com[1] += cp->legacy.com[1] * cp_mass;
+ com[2] += cp->legacy.com[2] * cp_mass;
+ mass += cp_mass;
+ }
+
+ /* Otherwise, collect the multipole from local data. */
+ } else {
+
+ for (k = 0; k < count; k++) {
+ p = &parts[k];
+ float p_mass = p->mass;
+ com[0] += p->x[0] * p_mass;
+ com[1] += p->x[1] * p_mass;
+ com[2] += p->x[2] * p_mass;
+ mass += p_mass;
+ }
+ }
+
+ /* Finish multipole calculation */
+ if (mass > 0.0) {
+ float imass = 1.0f / mass;
+ c->legacy.com[0] = com[0] * imass;
+ c->legacy.com[1] = com[1] * imass;
+ c->legacy.com[2] = com[2] * imass;
+ c->legacy.mass = mass;
+ } else {
+ c->legacy.com[0] = 0.0;
+ c->legacy.com[1] = 0.0;
+ c->legacy.com[2] = 0.0;
+ c->legacy.mass = 0.0;
+ }
+}
+
+/**
+ * @brief Interacts a particle with a cell recursively using the original B-H
+ * tree walk procedure
+ *
+ * @param parts The array of particles
+ * @param i The particle of interest
+ * @param root The root of the tree under which we will search.
+ * @param monitor If set to @c parts[i].id, will produce debug output when
+ * ICHECK is set.
+ * @param cell The cell the particle interacts with
+ */
+void legacy_interact(struct part *parts, int i, struct cell *root, int monitor,
+ int *countMultipoles, int *countPairs) {
+
+ int j, k;
+ float r2, dx[3], ir, w;
+ float a[3] = {0.0, 0.0, 0.0};
+ double pix[3] = {parts[i].x[0], parts[i].x[1], parts[i].x[2]};
+ int pid = parts[i].id;
+ struct cell *cell = root;
+
+ /* Traverse the cells of the tree. */
+ while (cell != NULL) {
+
+ /* Are we in a leaf ? */
+ if (!cell->split) {
+
+ /* Interact the particle with the particles in the leaf */
+ for (j = 0; j < cell->count; ++j) {
+ if (cell->parts[j].id == pid) continue;
+
+ /* Compute the pairwise distance. */
+ for (r2 = 0.0, k = 0; k < 3; k++) {
+ dx[k] = cell->parts[j].x[k] - pix[k];
+ r2 += dx[k] * dx[k];
+ }
+
+ /* Apply the gravitational acceleration. */
+ ir = 1.0f / sqrtf(r2);
+ w = cell->parts[j].mass * const_G * ir * ir * ir;
+ for (k = 0; k < 3; k++) a[k] += w * dx[k];
+
+ (*countPairs)++;
+
+#if ICHECK >= 0
+ if (pid == monitor)
+ message("[BH_] Interaction with particle id= %d a=( %e %e %e ) h= %f "
+ "loc=( %e %e %e )\n",
+ cell->parts[j].id, w * dx[0], w * dx[1], w * dx[2], cell->h,
+ cell->loc[0], cell->loc[1], cell->loc[2]);
+#endif
+ }
+
+ cell = cell->sibling;
+ } else {
+
+ /* We are in a node */
+ for (r2 = 0.0, k = 0; k < 3; k++) {
+ dx[k] = cell->legacy.com[k] - pix[k];
+ r2 += dx[k] * dx[k];
+ }
+
+#if ICHECK >= 0
+ if (pid == monitor)
+ message("This is a node with %d particles h= %f. r= %f theta= %f",
+ cell->count, cell->h, sqrt(r2), dist_min);
+#endif
+
+ /* Is the cell far enough ? */
+ if (dist_min * dist_min * r2 < cell->h * cell->h) {
+
+#if ICHECK >= 0
+ if (pid == monitor) printf("Recursing...\n");
+#endif
+ cell = cell->firstchild;
+ continue;
+ }
+
+#if ICHECK >= 0
+ if (pid == monitor)
+ message("[BH_] Can interact with the monopole. x= %f %f %f m= %f h= %f",
+ cell->legacy.com[0], cell->legacy.com[1], cell->legacy.com[2],
+ cell->legacy.mass, cell->h);
+#endif
+
+ /* Apply the gravitational acceleration. */
+ ir = 1.0f / sqrtf(r2);
+ w = cell->legacy.mass * const_G * ir * ir * ir;
+ for (k = 0; k < 3; k++) a[k] += w * dx[k];
+
+ (*countMultipoles)++;
+
+ /* Move to the next node */
+ cell = cell->sibling;
+ }
+ }
+
+ /* Store the locally computed acceleration back to the particle. */
+ for (k = 0; k < 3; k++) parts[i].a_legacy[k] += a[k];
+}
+
+/**
+ * @brief Does a tree walk as in the B-H original work for all particles
+ *
+ * @param N The number of particles
+ * @param parts The array of particles
+ * @param root The root cell of the tree
+ * @param monitor ID of the particle to monitor and output interactions to
+ * stdout
+ */
+void legacy_tree_walk(int N, struct part *parts, struct cell *root, int monitor,
+ int *countMultipoles, int *countPairs, int *countCoMs) {
+
+ int i;
+
+ /* Compute multipoles (recursively) */
+ legacy_comp_com(root, countCoMs);
+
+ //#pragma omp parallel for
+ for (i = 0; i < N; ++i) {
+ if (parts[i].id == monitor)
+ message("tree walk for particle %d x= %f %f %f", parts[i].id,
+ parts[i].x[0], parts[i].x[1], parts[i].x[2]);
+
+ legacy_interact(parts, i, root, monitor, countMultipoles, countPairs);
+
+ if (parts[i].id == monitor)
+ message("[check] legacy acceleration for particle %d a= %.3e %.3e %.3e",
+ parts[i].id, parts[i].a_legacy[0], parts[i].a_legacy[1],
+ parts[i].a_legacy[2]);
+ }
+}
+
+/* -------------------------------------------------------------------------- */
+/* Exact interaction */
+/* -------------------------------------------------------------------------- */
+
+/**
+ * @brief Solve the particle interactions using the stupid N^2 algorithm
+ *
+ * @param N The number of particles
+ * @param parts The array of particles
+ */
+void interact_exact(int N, struct part *parts, int monitor) {
+
+ int i, j, k;
+ float ir, w, r2, dx[3];
+
+ /* Loop over all particles. */
+ for (i = 0; i < N; ++i) {
+
+ /* Some things to store locally. */
+ double pix[3] = {parts[i].x[0], parts[i].x[1], parts[i].x[2]};
+ float mi = parts[i].mass;
+
+ /* Loop over every other particle. */
+ for (j = i + 1; j < N; ++j) {
+
+ /* Compute the pairwise distance. */
+ for (r2 = 0.0, k = 0; k < 3; k++) {
+ dx[k] = parts[j].x[k] - pix[k];
+ r2 += dx[k] * dx[k];
+ }
+
+ /* Apply the gravitational acceleration. */
+ ir = 1.0f / sqrtf(r2);
+ w = const_G * ir * ir * ir;
+
+ for (k = 0; k < 3; k++) {
+ float wdx = w * dx[k];
+ parts[j].a_exact[k] -= wdx * mi;
+ parts[i].a_exact[k] += wdx * parts[j].mass;
+ }
+ }
+ }
+
+#if ICHECK >= 0
+ for (i = 0; i < N; ++i)
+ if (parts[i].id == monitor)
+ message("[check] exact acceleration for particle %d a= %.3e %.3e %.3e\n",
+ parts[i].id, parts[i].a_exact[0], parts[i].a_exact[1],
+ parts[i].a_exact[2]);
+#endif
+}
+
+/**
+ * @brief Set up and run a task-based Barnes-Hutt N-body solver.
+ *
+ * @param N The number of random particles to use.
+ * @param nr_threads Number of threads to use.
+ * @param runs Number of force evaluations to use as a benchmark.
+ * @param fileName Input file name. If @c NULL or an empty string, random
+ * particle positions will be used.
+ */
+void test_bh(int N, int nr_threads, int runs, char *fileName) {
+
+ int i, k;
+ struct cell *root;
+ struct part *parts;
+ FILE *file;
+ struct qsched s;
+ ticks tic, toc_run, tot_setup = 0, tot_run = 0;
+ int countMultipoles = 0, countPairs = 0, countCoMs = 0;
+
+ /* Runner function. */
+ void runner(int type, void * data) {
+
+ ticks tic = getticks();
+
+ /* Decode the data. */
+ struct cell **d = (struct cell **)data;
+
+ /* Decode and execute the task. */
+ switch (type) {
+ case task_type_self:
+ iact_self_direct(d[0]);
+ break;
+ case task_type_pair:
+ iact_pair(d[0], d[1]);
+ break;
+ case task_type_pair_direct:
+ iact_pair_direct(d[0], d[1]);
+ break;
+ case task_type_self_pc:
+ init_multipole_walk(d[0], d[1]);
+ break;
+ case task_type_com:
+ comp_com(d[0]);
+ break;
+ default:
+ error("Unknown task type.");
+ }
+
+ atomic_add(&task_timers[type], getticks() - tic);
+ }
+
+ /* Initialize the per-task type timers. */
+ for (k = 0; k < task_type_count; k++) task_timers[k] = 0;
+
+ /* Initialize the scheduler. */
+ qsched_init(&s, nr_threads, qsched_flag_noreown);
+
+ /* Init and fill the particle array. */
+ if ((parts = (struct part *)malloc(sizeof(struct part) * N)) == NULL)
+ error("Failed to allocate particle buffer.");
+
+ /* If no input file was specified, generate random particle positions. */
+ if (fileName == NULL || fileName[0] == 0) {
+ for (k = 0; k < N; k++) {
+ parts[k].id = k;
+ parts[k].x[0] = ((double)rand()) / RAND_MAX;
+ parts[k].x[1] = ((double)rand()) / RAND_MAX;
+ parts[k].x[2] = ((double)rand()) / RAND_MAX;
+ parts[k].mass = ((double)rand()) / RAND_MAX;
+ parts[k].a_legacy[0] = 0.0;
+ parts[k].a_legacy[1] = 0.0;
+ parts[k].a_legacy[2] = 0.0;
+ }
+
+ /* Otherwise, read them from a file. */
+ } else {
+ file = fopen(fileName, "r");
+ if (file) {
+ for (k = 0; k < N; k++) {
+ if (fscanf(file, "%d", &parts[k].id) != 1)
+ error("Failed to read ID of part %i.", k);
+ if (fscanf(file, "%lf%lf%lf", &parts[k].x[0], &parts[k].x[1],
+ &parts[k].x[2]) !=
+ 3)
+ error("Failed to read position of part %i.", k);
+ if (fscanf(file, "%f", &parts[k].mass) != 1)
+ error("Failed to read mass of part %i.", k);
+ }
+ fclose(file);
+ }
+ }
+
+ /* Init the cells. */
+ root = cell_get();
+ root->loc[0] = 0.0;
+ root->loc[1] = 0.0;
+ root->loc[2] = 0.0;
+ root->h = 1.0;
+ root->count = N;
+ root->parts = parts;
+ cell_split(root, &s);
+
+ /* Iterate over the cells and get the average number of particles
+ per leaf. */
+ struct cell *c = root;
+ int nr_leaves = 0;
+ while (c != NULL) {
+ if (!c->split) {
+ nr_leaves++;
+ c = c->sibling;
+ } else {
+ c = c->firstchild;
+ }
+ }
+ message("Average number of parts per leaf is %f.", ((double)N) / nr_leaves);
+
+#if ICHECK > 0
+ printf("----------------------------------------------------------\n");
+
+ /* Do a N^2 interactions calculation */
+
+ ticks tic_exact = getticks();
+ interact_exact(N, parts, ICHECK);
+ ticks toc_exact = getticks();
+
+ printf("Exact calculation (1 thread) took %lli (= %e) ticks\n",
+ toc_exact - tic_exact, (float)(toc_exact - tic_exact));
+
+ printf("----------------------------------------------------------\n");
+#endif
+
+ /* Create the tasks. */
+ tic = getticks();
+ create_tasks(&s, root, NULL);
+ tot_setup += getticks() - tic;
+
+ /* Dump the number of tasks. */
+ message("total nr of tasks: %i.", s.count);
+ message("total nr of deps: %i.", s.count_deps);
+ message("total nr of res: %i.", s.count_res);
+ message("total nr of locks: %i.", s.count_locks);
+ message("total nr of uses: %i.", s.count_uses);
+ int counts[task_type_count];
+ for (k = 0; k < task_type_count; k++) counts[k] = 0;
+ for (k = 0; k < s.count; k++) counts[s.tasks[k].type] += 1;
+
+ // char buffer[200];
+ // sprintf(buffer, "timings_legacy_%d_%d.dat", cell_maxparts, nr_threads);
+ // FILE *fileTime = fopen(buffer, "w");
+
+ /* Loop over the number of runs. */
+ for (k = 0; k < 0 /* runs */; k++) {
+
+ countMultipoles = 0;
+ countPairs = 0;
+ countCoMs = 0;
+
+ /* Execute the legacy walk. */
+ tic = getticks();
+ legacy_tree_walk(N, parts, root, ICHECK, &countMultipoles, &countPairs,
+ &countCoMs);
+ toc_run = getticks();
+
+ /* Dump some timings. */
+ message("%ith legacy run took %lli (= %e) ticks...", k, toc_run - tic,
+ (float)(toc_run - tic));
+ tot_run += toc_run - tic;
+ // fprintf(fileTime, "%lli %e\n", toc_run - tic, (float)(toc_run - tic));
+ }
+
+// fclose(fileTime);
+
+#if ICHECK >= 0
+ message("[check] accel of part %i is [%.3e,%.3e,%.3e]", ICHECK,
+ root->parts[ICHECK].a[0], root->parts[ICHECK].a[1],
+ root->parts[ICHECK].a[2]);
+#endif
+ printf("task counts: [ %8s %8s %8s %8s %8s ]\n", "self", "pair", "m-poles",
+ "direct", "CoMs");
+ printf("task counts: [ %8i %8i %8i %8i %8i ] (legacy).\n", 0, 0,
+ countMultipoles, countPairs, countCoMs);
+ printf("task counts: [ ");
+ for (k = 0; k < task_type_count; k++) printf("%8i ", counts[k]);
+ printf("] (new).\n");
+
+ /* Loop over the number of runs. */
+ for (k = 0; k < runs; k++) {
+
+ for (i = 0; i < N; ++i) {
+ parts[i].a[0] = 0.0;
+ parts[i].a[1] = 0.0;
+ parts[i].a[2] = 0.0;
+ }
+
+ struct cell *finger = root;
+ while (finger != NULL) {
+ finger->sorted = 0;
+ if (finger->split)
+ finger = finger->firstchild;
+ else
+ finger = finger->sibling;
+ }
+
+ /* Execute the tasks. */
+ tic = getticks();
+ qsched_run(&s, nr_threads, runner);
+ toc_run = getticks();
+ message("%ith run took %lli (= %e) ticks...", k, toc_run - tic,
+ (float)(toc_run - tic));
+ tot_run += toc_run - tic;
+ }
+
+ message("[check] root mass= %f %f", root->legacy.mass, root->new.mass);
+ message("[check] root CoMx= %f %f", root->legacy.com[0], root->new.com[0]);
+ message("[check] root CoMy= %f %f", root->legacy.com[1], root->new.com[1]);
+ message("[check] root CoMz= %f %f", root->legacy.com[2], root->new.com[2]);
+#if ICHECK >= 0
+ for (i = 0; i < N; ++i)
+ if (root->parts[i].id == ICHECK)
+ message("[check] accel of part %i is [%.3e,%.3e,%.3e]", ICHECK,
+ root->parts[i].a[0], root->parts[i].a[1], root->parts[i].a[2]);
+#endif
+
+ /* Dump the tasks. */
+ /* for ( k = 0 ; k < s.count ; k++ )
+ printf( " %i %i %lli %lli\n" , s.tasks[k].type , s.tasks[k].qid ,
+ s.tasks[k].tic , s.tasks[k].toc ); */
+
+ /* Dump the costs. */
+ message("costs: setup=%lli ticks, run=%lli ticks.", tot_setup,
+ tot_run / runs);
+
+ /* Dump the timers. */
+ for (k = 0; k < qsched_timer_count; k++)
+ message("timer %s is %lli ticks.", qsched_timer_names[k],
+ s.timers[k] / runs);
+
+ /* Dump the per-task type timers. */
+ printf("task timers: [ ");
+ for (k = 0; k < task_type_count; k++) printf("%lli ", task_timers[k] / runs);
+ printf("] ticks.\n");
+
+ /* Dump the particles to a file */
+ file = fopen("particle_dump.dat", "w");
+ fprintf(file,
+ "# ID m x y z a_exact.x a_exact.y a_exact.z a_legacy.x "
+ "a_legacy.y a_legacy.z a_new.x a_new.y a_new.z\n");
+ for (k = 0; k < N; ++k)
+ fprintf(file, "%d %e %e %e %e %e %e %e %e %e %e %e %e %e\n", parts[k].id,
+ parts[k].mass, parts[k].x[0], parts[k].x[1], parts[k].x[2],
+ parts[k].a_exact[0], parts[k].a_exact[1], parts[k].a_exact[2],
+ parts[k].a_legacy[0], parts[k].a_legacy[1], parts[k].a_legacy[2],
+ parts[k].a[0], parts[k].a[1], parts[k].a[2]);
+ fclose(file);
+
+ /* Clean up. */
+ qsched_free(&s);
+ free(parts);
+}
+
+/* All 26 configurations for the cell tests */
+const float cell_shift[27 * 3] = {1.0, 1.0, 1.0, /* 0 */
+ 1.0, 1.0, 0.0, /* 1 */
+ 1.0, 1.0, -1.0, /* 2 */
+ 1.0, 0.0, 1.0, /* 3 */
+ 1.0, 0.0, 0.0, /* 4 */
+ 1.0, 0.0, -1.0, /* 5 */
+ 1.0, -1.0, 1.0, /* 6 */
+ 1.0, -1.0, 0.0, /* 7 */
+ 1.0, -1.0, -1.0, /* 8 */
+ 0.0, 1.0, 1.0, /* 9 */
+ 0.0, 1.0, 0.0, /* 10 */
+ 0.0, 1.0, -1.0, /* 11 */
+ 0.0, 0.0, 1.0, /* 12 */
+ -1.0, -1.0, -1.0, /* 13 */
+ -1.0, -1.0, 0.0, /* 14 */
+ -1.0, -1.0, 1.0, /* 15 */
+ -1.0, 0.0, -1.0, /* 16 */
+ -1.0, 0.0, 0.0, /* 17 */
+ -1.0, 0.0, 1.0, /* 18 */
+ -1.0, 1.0, -1.0, /* 19 */
+ -1.0, 1.0, 0.0, /* 20 */
+ -1.0, 1.0, 1.0, /* 21 */
+ 0.0, -1.0, -1.0, /* 22 */
+ 0.0, -1.0, 0.0, /* 23 */
+ 0.0, -1.0, 1.0, /* 24 */
+ 0.0, 0.0, -1.0, /* 25 */
+ 0.0, 0.0,
+ 0.0 /* 26 */ /* <-- The cell itself */
+};
+
+/**
+ * @brief Creates two neighbouring cells wiht N_parts per celland makes them
+ * interact using both the
+ * sorted and unsortde interactions. Outputs then the tow sets of accelerations
+ * for accuracy tests.
+ * @param N_parts Number of particles in each cell
+ * @param orientation Orientation of the cells ( 0 <= orientation < 26 )
+ */
+void test_direct_neighbour(int N_parts, int orientation) {
+
+ int k;
+ struct part *parts;
+ struct cell left, right;
+
+ if (orientation >= 26) error("Wrong orientation !");
+
+ /* Select configuration */
+ float shift[3];
+ for (k = 0; k < 3; ++k) shift[k] = cell_shift[3 * orientation + k];
+
+ /* Init and fill the particle array. */
+ if ((parts = (struct part *)malloc(sizeof(struct part) * N_parts * 2)) ==
+ NULL)
+ error("Failed to allocate particle buffer.");
+
+ /* Create random set of particles in both cells */
+ for (k = 0; k < 2 * N_parts; k++) {
+ parts[k].id = k;
+
+ parts[k].x[0] = ((double)rand()) / RAND_MAX;
+ parts[k].x[1] = ((double)rand()) / RAND_MAX;
+ parts[k].x[2] = ((double)rand()) / RAND_MAX;
+
+ /* Shift the second cell */
+ if (k >= N_parts) {
+ parts[k].x[0] += shift[0];
+ parts[k].x[1] += shift[1];
+ parts[k].x[2] += shift[2];
+ }
+
+ parts[k].mass = ((double)rand()) / RAND_MAX;
+ parts[k].a[0] = 0.0;
+ parts[k].a[1] = 0.0;
+ parts[k].a[2] = 0.0;
+ }
+
+ /* Get the cell geometry right */
+ left.loc[0] = 0.;
+ left.loc[1] = 0.;
+ left.loc[2] = 0.;
+ left.h = 1.;
+
+ right.loc[0] = shift[0];
+ right.loc[1] = shift[1];
+ right.loc[2] = shift[2];
+ right.h = 1.;
+
+ /* Put the particles in the cell */
+ left.parts = parts;
+ left.count = N_parts;
+ right.parts = parts + N_parts;
+ right.count = N_parts;
+
+ /* Get the linked list right (functions should not recurse but hey...) */
+ left.firstchild = NULL;
+ left.sibling = NULL;
+ left.split = 0;
+ right.firstchild = NULL;
+ right.sibling = NULL;
+ right.split = 0;
+
+ /* Get the multipoles right (should also be useless) */
+ comp_com(&left);
+ comp_com(&right);
+
+ /* Nothing has been sorted yet */
+ left.indices = NULL;
+ left.sorted = 0;
+ right.indices = NULL;
+ right.sorted = 0;
+
+#ifdef COUNTERS
+ count_direct_unsorted = 0;
+ count_direct_sorted_pp = 0;
+ count_direct_sorted_pm_i = 0;
+ count_direct_sorted_pm_j = 0;
+#endif
+
+ /* Do the interactions without sorting */
+ iact_pair_direct_unsorted(&left, &right);
+
+ message("Unsorted interactions done ");
+
+ /* Store accelerations */
+ for (k = 0; k < 2 * N_parts; k++) {
+ parts[k].a_exact[0] = parts[k].a[0];
+ parts[k].a_exact[1] = parts[k].a[1];
+ parts[k].a_exact[2] = parts[k].a[2];
+ parts[k].a[0] = 0.0;
+ parts[k].a[1] = 0.0;
+ parts[k].a[2] = 0.0;
+ }
+
+ /* Do the interactions with sorting */
+ iact_pair_direct(&left, &right);
+
+ message("Sorted interactions done ");
+
+ for (k = 0; k < 2 * N_parts; ++k) {
+ if (parts[k].id == ICHECK) {
+
+ message("Accel exact : [ %e %e %e ]", parts[k].a_exact[0],
+ parts[k].a_exact[1], parts[k].a_exact[2]);
+ message("Accel sorted: [ %e %e %e ]", parts[k].a[0], parts[k].a[1],
+ parts[k].a[2]);
+ }
+ }
+
+ /* Position along the axis */
+ double *position, *ortho_dist;
+ if ((position = (double *)malloc(sizeof(double) * N_parts * 2)) == NULL)
+ error("Failed to allocate position buffer.");
+ if ((ortho_dist = (double *)malloc(sizeof(double) * N_parts * 2)) == NULL)
+ error("Failed to allocate orthogonal distance buffer.");
+
+ float w = 1.0f / sqrtf(shift[0]*shift[0] + shift[1]*shift[1] + shift[2]*shift[2]);
+ shift[0] *= w;
+ shift[1] *= w;
+ shift[2] *= w;
+
+ for (k = 0; k < 2 * N_parts; ++k) {
+ float dx = parts[k].x[0] * shift[0];
+ float dy = parts[k].x[1] * shift[1];
+ float dz = parts[k].x[2] * shift[2];
+
+ position[k] = dx + dy + dz;
+
+ dx = (parts[k].x[1] - 0.5f)*shift[2] - (parts[k].x[2] - 0.5f)*shift[1];
+ dy = (parts[k].x[2] - 0.5f)*shift[0] - (parts[k].x[0] - 0.5f)*shift[2];
+ dz = (parts[k].x[0] - 0.5f)*shift[1] - (parts[k].x[1] - 0.5f)*shift[0];
+
+ ortho_dist[k] = sqrtf(dx*dx + dy*dy + dz*dz);
+ }
+
+ /* Now, output everything */
+ char fileName[100];
+ sprintf(fileName, "interaction_dump_%d.dat", orientation);
+ message("Writing file '%s'", fileName);
+ FILE *file = fopen(fileName, "w");
+ fprintf(file,
+ "# ID m r x y z a_u.x a_u.y a_u.z a_s.x a_s.y a_s.z ortho\n");
+ for (k = 0; k < 2 * N_parts; k++) {
+ fprintf(file, "%d %e %e %e %e %e %e %e %e %e %e %e %e\n", parts[k].id,
+ parts[k].mass, position[k], parts[k].x[0], parts[k].x[1],
+ parts[k].x[2], parts[k].a_exact[0], parts[k].a_exact[1],
+ parts[k].a_exact[2], parts[k].a[0], parts[k].a[1], parts[k].a[2],
+ ortho_dist[k]);
+ }
+ fclose(file);
+
+#ifdef COUNTERS
+ message("Unsorted intereactions: %d", count_direct_unsorted);
+ message("Sorted intereactions PP: %d", count_direct_sorted_pp);
+ message("Sorted intereactions PM (part i): %d", count_direct_sorted_pm_i);
+ message("Sorted intereactions PM (part j): %d", count_direct_sorted_pm_j);
+ message("Sorted intereactions total: %d",
+ count_direct_sorted_pm_j + count_direct_sorted_pm_i +
+ count_direct_sorted_pp);
+// message( "%f %d %d %d %d\n", dist_cutoff_ratio, count_direct_unsorted,
+// count_direct_sorted_pp, count_direct_sorted_pm_i, count_direct_sorted_pm_j );
+#endif
+
+ /* Clean up */
+ free(parts);
+}
+
+/**
+ * @brief Creates 27 cells and makes the particles in the central one
+ * interact with the other cells
+ * using both the sorted and unsorted interactions
+ * Outputs then the two sets of accelerations for accuracy tests.
+ * @param N_parts Number of particles in each cell
+ * @param N_test Number of times the test has to be run
+ */
+void test_all_direct_neighbours(int N_parts, int N_test) {
+
+ int i, k, j;
+ struct part *parts;
+ struct cell cells[27];
+
+ /* Init and fill the particle array. */
+ if ((parts = (struct part *)malloc(sizeof(struct part) * N_parts * 27)) ==
+ NULL)
+ error("Failed to allocate particle buffer.");
+
+#ifdef COUNTERS
+ count_direct_unsorted = 0;
+ count_direct_sorted_pp = 0;
+ count_direct_sorted_pm_i = 0;
+ count_direct_sorted_pm_j = 0;
+#endif
+ int countMultipoles = 0;
+ int countPairs = 0;
+ int countCoMs = 0;
+
+ /* Loop over the number of tests */
+ for (i = 0; i < N_test; ++i) {
+
+ /* Loop over the 27 cells */
+ for (j = 0; j < 27; ++j) {
+
+ float shift[3];
+ for (k = 0; k < 3; ++k) shift[k] = cell_shift[3 * j + k];
+
+ /* Create random set of particles in all cells */
+ for (k = 0; k < N_parts; k++) {
+ parts[j * N_parts + k].id = j * N_parts + k;
+
+ parts[j * N_parts + k].x[0] = ((double)rand()) / RAND_MAX + shift[0];
+ parts[j * N_parts + k].x[1] = ((double)rand()) / RAND_MAX + shift[1];
+ parts[j * N_parts + k].x[2] = ((double)rand()) / RAND_MAX + shift[2];
+
+ parts[j * N_parts + k].mass = ((double)rand()) / RAND_MAX;
+ parts[j * N_parts + k].a[0] = 0.0;
+ parts[j * N_parts + k].a[1] = 0.0;
+ parts[j * N_parts + k].a[2] = 0.0;
+ parts[j * N_parts + k].a_exact[0] = 0.0;
+ parts[j * N_parts + k].a_exact[1] = 0.0;
+ parts[j * N_parts + k].a_exact[2] = 0.0;
+ parts[j * N_parts + k].a_legacy[0] = 0.0;
+ parts[j * N_parts + k].a_legacy[1] = 0.0;
+ parts[j * N_parts + k].a_legacy[2] = 0.0;
+ }
+
+ /* Get the cell geometry right */
+ cells[j].loc[0] = shift[0];
+ cells[j].loc[1] = shift[1];
+ cells[j].loc[2] = shift[2];
+ cells[j].h = 1.;
+
+ /* Put the particles in the cell */
+ cells[j].parts = parts + N_parts * j;
+ cells[j].count = N_parts;
+
+ /* Get the linked list right (functions should not recurse but hey...) */
+ cells[j].firstchild = NULL;
+ cells[j].sibling = NULL;
+ cells[j].split = 0;
+
+ /* Get the multipoles right (should also be useless) */
+ comp_com(&cells[j]);
+
+ /* Nothing has been sorted yet */
+ cells[j].indices = NULL;
+ cells[j].sorted = 0;
+ }
+
+ /* Do the interactions without sorting */
+ for (j = 0; j < 26; ++j) iact_pair_direct_unsorted(&cells[26], &cells[j]);
+ iact_self_direct(&cells[26]);
+
+ // message("Unsorted interactions done ");
+
+ /* Store accelerations */
+ for (k = 0; k < 27 * N_parts; k++) {
+ parts[k].a_exact[0] = parts[k].a[0];
+ parts[k].a_exact[1] = parts[k].a[1];
+ parts[k].a_exact[2] = parts[k].a[2];
+ parts[k].a[0] = 0.0;
+ parts[k].a[1] = 0.0;
+ parts[k].a[2] = 0.0;
+ }
+
+ /* Do the interactions with sorting */
+ for (j = 0; j < 26; ++j) iact_pair_direct(&cells[26], &cells[j]);
+ iact_self_direct(&cells[26]);
+
+ // message("Sorted interactions done ");
+
+ /* Now, do a B-H calculation on the same set of particles */
+ struct cell *root = cell_get();
+ root->loc[0] = -1.0;
+ root->loc[1] = -1.0;
+ root->loc[2] = -1.0;
+ root->h = 3.0;
+ root->count = 27 * N_parts;
+ root->parts = parts;
+ struct qsched s;
+ qsched_init(&s, 1, qsched_flag_noreown);
+ cell_split(root, &s);
+ legacy_tree_walk(27 * N_parts, parts, root, ICHECK, &countMultipoles,
+ &countPairs, &countCoMs);
+
+ // free(root);
+ //++countCoMs;
+
+ /* Now, output everything */
+ char fileName[100];
+ sprintf(fileName, "interaction_dump_all.dat");
+ // message("Writing file '%s'", fileName);
+ FILE *file = fopen(fileName, (i == 0 ? "w" : "a"));
+ if (i == 0)
+ fprintf(file,
+ "# ID m x y z a_u.x a_u.y a_u.z a_s.x a_s.y a_s.z"
+ " a_bh.x a_bh.y a_bh.z\n");
+ for (k = 0; k < 27 * N_parts; k++) {
+ if (parts[k].id >= 26 * N_parts)
+ fprintf(file, "%d %e %e %e %e %e %e %e %e %e %e %e %e %e\n",
+ parts[k].id, parts[k].mass, parts[k].x[0], parts[k].x[1],
+ parts[k].x[2], parts[k].a_exact[0], parts[k].a_exact[1],
+ parts[k].a_exact[2], parts[k].a[0], parts[k].a[1],
+ parts[k].a[2], parts[k].a_legacy[0], parts[k].a_legacy[1],
+ parts[k].a_legacy[2]);
+ }
+ fclose(file);
+ }
+
+#ifdef COUNTERS
+ message("Unsorted intereactions: %d", count_direct_unsorted);
+ message("B-H intereactions: PP %d", countPairs);
+ message("B-H intereactions: PM %d", countMultipoles);
+ message("B-H intereactions: total %d", countPairs + countMultipoles);
+ message("Sorted intereactions PP: %d", count_direct_sorted_pp);
+ message("Sorted intereactions PM (part i): %d", count_direct_sorted_pm_i);
+ message("Sorted intereactions PM (part j): %d", count_direct_sorted_pm_j);
+ message("Sorted intereactions total: %d",
+ count_direct_sorted_pm_j + count_direct_sorted_pm_i +
+ count_direct_sorted_pp);
+// message( "%f %d %d %d %d\n", dist_cutoff_ratio, count_direct_unsorted,
+// count_direct_sorted_pp, count_direct_sorted_pm_i, count_direct_sorted_pm_j );
+#endif
+
+ /* Clean up */
+ free(parts);
+}
+
+/**
+ * @brief Main function.
+ */
+
+int main(int argc, char *argv[]) {
+
+ int c, k, nr_threads;
+ int N = 1000, runs = 1;
+ char fileName[100] = {0};
+ int N_parts = 0;
+ int N_iterations = 0;
+
+ /* Die on FP-exceptions. */
+ feenableexcept(FE_DIVBYZERO | FE_INVALID | FE_OVERFLOW);
+
+ srand(0);
+
+/* Get the number of threads. */
+#pragma omp parallel shared(nr_threads)
+ {
+ if (omp_get_thread_num() == 0) nr_threads = omp_get_num_threads();
+ }
+
+ /* Parse the options */
+ while ((c = getopt(argc, argv, "n:r:t:f:c:i:")) != -1) switch (c) {
+ case 'n':
+ if (sscanf(optarg, "%d", &N) != 1)
+ error("Error parsing number of particles.");
+ break;
+ case 'r':
+ if (sscanf(optarg, "%d", &runs) != 1)
+ error("Error parsing number of runs.");
+ break;
+ case 't':
+ if (sscanf(optarg, "%d", &nr_threads) != 1)
+ error("Error parsing number of threads.");
+ omp_set_num_threads(nr_threads);
+ break;
+ case 'f':
+ if (sscanf(optarg, "%s", &fileName[0]) != 1)
+ error("Error parsing file name.");
+ break;
+ case 'c':
+ if (sscanf(optarg, "%d", &N_parts) != 1)
+ error(
+ "Error parsing number of particles in neighbouring cells test.");
+ break;
+ case 'i':
+ if (sscanf(optarg, "%d", &N_iterations) != 1)
+ error(
+ "Error parsing number of particles in neighbouring cells test.");
+ break;
+ case '?':
+ fprintf(stderr, "Usage: %s [-t nr_threads] [-n N] [-r runs] [-f file] "
+ "[-c Nparts] [-i Niterations] \n",
+ argv[0]);
+ fprintf(stderr, "Solves the N-body problem using a Barnes-Hut\n"
+ "tree code with N random particles read from a file in "
+ "[0,1]^3 using"
+ "nr_threads threads.\n"
+ "A test of the neighbouring cells interaction with "
+ "Nparts per cell is also run Niterations times.\n");
+ exit(EXIT_FAILURE);
+ }
+
+ /* Tree node information */
+ printf("Size of cell: %zu bytes.\n", sizeof(struct cell));
+
+ /* Part information */
+ printf("Size of part: %zu bytes.\n", sizeof(struct part));
+
+ /* Run the neighbour direct integration test */
+ if (N_parts > 0) {
+
+ /* Dump arguments */
+ message("Interacting 2 neighbouring cells with %d particles per cell",
+ N_parts);
+
+ /* Run the test */
+ for (k = 0; k < 26; ++k) test_direct_neighbour(N_parts, k);
+
+ /* Dump arguments */
+ message("Interacting one cell with %d particles with its 27 neighbours"
+ " %d times to get the statistics.",
+ N_parts, N_iterations);
+
+ test_all_direct_neighbours(N_parts, N_iterations);
+
+ } else {
+
+ /* Dump arguments. */
+ if (fileName[0] == 0) {
+ message("Computing the N-body problem over %i random particles using %i "
+ "threads (%i runs).",
+ N, nr_threads, runs);
+ } else {
+ message("Computing the N-body problem over %i particles read from '%s' "
+ "using %i threads (%i runs).",
+ N, fileName, nr_threads, runs);
+ }
+
+ /* Run the BH test. */
+ test_bh(N, nr_threads, runs, fileName);
+ }
+
+ return 0;
+}
+