cell.c

/*******************************************************************************
 * This file is part of SWIFT.
 * Copyright (c) 2012 Pedro Gonnet (pedro.gonnet@durham.ac.uk)
 *                    Matthieu Schaller (matthieu.schaller@durham.ac.uk)
 *               2015 Peter W. Draper (p.w.draper@durham.ac.uk)
 *               2016 John A. Regan (john.a.regan@durham.ac.uk)
 *                    Tom Theuns (tom.theuns@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"

/* Some standard headers. */
#include <float.h>
#include <limits.h>
#include <math.h>
#include <pthread.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

/* MPI headers. */
#ifdef WITH_MPI
#include <mpi.h>
#endif

/* Switch off timers. */
#ifdef TIMER
#undef TIMER
#endif

/* This object's header. */
#include "cell.h"

/* Local headers. */
#include "active.h"
#include "atomic.h"
#include "chemistry.h"
#include "drift.h"
#include "engine.h"
#include "error.h"
#include "gravity.h"
#include "hydro.h"
#include "hydro_properties.h"
#include "memswap.h"
#include "minmax.h"
#include "scheduler.h"
#include "space.h"
#include "space_getsid.h"
#include "stars.h"
#include "timers.h"
#include "tools.h"
#include "tracers.h"

/* Global variables. */
int cell_next_tag = 0;

/**
 * @brief Get the size of the cell subtree.
 *
 * @param c The #cell.
 */
int cell_getsize(struct cell *c) {

  /* Number of cells in this subtree. */
  int count = 1;

  /* Sum up the progeny if split. */
  if (c->split)
    for (int k = 0; k < 8; k++)
      if (c->progeny[k] != NULL) count += cell_getsize(c->progeny[k]);

  /* Return the final count. */
  return count;
}

/**
 * @brief Link the cells recursively to the given #part array.
 *
 * @param c The #cell.
 * @param parts The #part array.
 *
 * @return The number of particles linked.
 */
int cell_link_parts(struct cell *c, struct part *parts) {

  c->hydro.parts = parts;

  /* Fill the progeny recursively, depth-first. */
  if (c->split) {
    int offset = 0;
    for (int k = 0; k < 8; k++) {
      if (c->progeny[k] != NULL)
        offset += cell_link_parts(c->progeny[k], &parts[offset]);
    }
  }

  /* Return the total number of linked particles. */
  return c->hydro.count;
}

/**
 * @brief Link the cells recursively to the given #gpart array.
 *
 * @param c The #cell.
 * @param gparts The #gpart array.
 *
 * @return The number of particles linked.
 */
int cell_link_gparts(struct cell *c, struct gpart *gparts) {

  c->grav.parts = gparts;

  /* Fill the progeny recursively, depth-first. */
  if (c->split) {
    int offset = 0;
    for (int k = 0; k < 8; k++) {
      if (c->progeny[k] != NULL)
        offset += cell_link_gparts(c->progeny[k], &gparts[offset]);
    }
  }

  /* Return the total number of linked particles. */
  return c->grav.count;
}

/**
 * @brief Link the cells recursively to the given #spart array.
 *
 * @param c The #cell.
 * @param sparts The #spart array.
 *
 * @return The number of particles linked.
 */
int cell_link_sparts(struct cell *c, struct spart *sparts) {

  c->stars.parts = sparts;

  /* Fill the progeny recursively, depth-first. */
  if (c->split) {
    int offset = 0;
    for (int k = 0; k < 8; k++) {
      if (c->progeny[k] != NULL)
        offset += cell_link_sparts(c->progeny[k], &sparts[offset]);
    }
  }

  /* Return the total number of linked particles. */
  return c->stars.count;
}

/**
 * @brief Pack the data of the given cell and all it's sub-cells.
 *
 * @param c The #cell.
 * @param pc Pointer to an array of packed cells in which the
 *      cells will be packed.
 * @param with_gravity Are we running with gravity and hence need
 *      to exchange multipoles?
 *
 * @return The number of packed cells.
 */
int cell_pack(struct cell *restrict c, struct pcell *restrict pc,
              const int with_gravity) {

#ifdef WITH_MPI

  /* Start by packing the data of the current cell. */
  pc->hydro.h_max = c->hydro.h_max;
  pc->hydro.ti_end_min = c->hydro.ti_end_min;
  pc->hydro.ti_end_max = c->hydro.ti_end_max;
  pc->grav.ti_end_min = c->grav.ti_end_min;
  pc->grav.ti_end_max = c->grav.ti_end_max;
  pc->stars.ti_end_min = c->stars.ti_end_min;
  pc->hydro.ti_old_part = c->hydro.ti_old_part;
  pc->grav.ti_old_part = c->grav.ti_old_part;
  pc->grav.ti_old_multipole = c->grav.ti_old_multipole;
  pc->hydro.count = c->hydro.count;
  pc->grav.count = c->grav.count;
  pc->stars.count = c->stars.count;
  pc->maxdepth = c->maxdepth;

  /* Copy the Multipole related information */
  if (with_gravity) {
    const struct gravity_tensors *mp = c->grav.multipole;

    pc->grav.m_pole = mp->m_pole;
    pc->grav.CoM[0] = mp->CoM[0];
    pc->grav.CoM[1] = mp->CoM[1];
    pc->grav.CoM[2] = mp->CoM[2];
    pc->grav.CoM_rebuild[0] = mp->CoM_rebuild[0];
    pc->grav.CoM_rebuild[1] = mp->CoM_rebuild[1];
    pc->grav.CoM_rebuild[2] = mp->CoM_rebuild[2];
    pc->grav.r_max = mp->r_max;
    pc->grav.r_max_rebuild = mp->r_max_rebuild;
  }

#ifdef SWIFT_DEBUG_CHECKS
  pc->cellID = c->cellID;
#endif

  /* Fill in the progeny, depth-first recursion. */
  int count = 1;
  for (int k = 0; k < 8; k++)
    if (c->progeny[k] != NULL) {
      pc->progeny[k] = count;
      count += cell_pack(c->progeny[k], &pc[count], with_gravity);
    } else {
      pc->progeny[k] = -1;
    }

  /* Return the number of packed cells used. */
  c->mpi.pcell_size = count;
  return count;

#else
  error("SWIFT was not compiled with MPI support.");
  return 0;
#endif
}

/**
 * @brief Pack the tag of the given cell and all it's sub-cells.
 *
 * @param c The #cell.
 * @param tags Pointer to an array of packed tags.
 *
 * @return The number of packed tags.
 */
int cell_pack_tags(const struct cell *c, int *tags) {

#ifdef WITH_MPI

  /* Start by packing the data of the current cell. */
  tags[0] = c->mpi.tag;

  /* Fill in the progeny, depth-first recursion. */
  int count = 1;
  for (int k = 0; k < 8; k++)
    if (c->progeny[k] != NULL)
      count += cell_pack_tags(c->progeny[k], &tags[count]);

#ifdef SWIFT_DEBUG_CHECKS
  if (c->mpi.pcell_size != count) error("Inconsistent tag and pcell count!");
#endif  // SWIFT_DEBUG_CHECKS

  /* Return the number of packed tags used. */
  return count;

#else
  error("SWIFT was not compiled with MPI support.");
  return 0;
#endif
}

/**
 * @brief Unpack the data of a given cell and its sub-cells.
 *
 * @param pc An array of packed #pcell.
 * @param c The #cell in which to unpack the #pcell.
 * @param s The #space in which the cells are created.
 * @param with_gravity Are we running with gravity and hence need
 *      to exchange multipoles?
 *
 * @return The number of cells created.
 */
int cell_unpack(struct pcell *restrict pc, struct cell *restrict c,
                struct space *restrict s, const int with_gravity) {

#ifdef WITH_MPI

  /* Unpack the current pcell. */
  c->hydro.h_max = pc->hydro.h_max;
  c->hydro.ti_end_min = pc->hydro.ti_end_min;
  c->hydro.ti_end_max = pc->hydro.ti_end_max;
  c->grav.ti_end_min = pc->grav.ti_end_min;
  c->grav.ti_end_max = pc->grav.ti_end_max;
  c->stars.ti_end_min = pc->stars.ti_end_min;
  c->hydro.ti_old_part = pc->hydro.ti_old_part;
  c->grav.ti_old_part = pc->grav.ti_old_part;
  c->grav.ti_old_multipole = pc->grav.ti_old_multipole;
  c->hydro.count = pc->hydro.count;
  c->grav.count = pc->grav.count;
  c->stars.count = pc->stars.count;
  c->maxdepth = pc->maxdepth;

#ifdef SWIFT_DEBUG_CHECKS
  c->cellID = pc->cellID;
#endif

  /* Copy the Multipole related information */
  if (with_gravity) {

    struct gravity_tensors *mp = c->grav.multipole;

    mp->m_pole = pc->grav.m_pole;
    mp->CoM[0] = pc->grav.CoM[0];
    mp->CoM[1] = pc->grav.CoM[1];
    mp->CoM[2] = pc->grav.CoM[2];
    mp->CoM_rebuild[0] = pc->grav.CoM_rebuild[0];
    mp->CoM_rebuild[1] = pc->grav.CoM_rebuild[1];
    mp->CoM_rebuild[2] = pc->grav.CoM_rebuild[2];
    mp->r_max = pc->grav.r_max;
    mp->r_max_rebuild = pc->grav.r_max_rebuild;
  }

  /* Number of new cells created. */
  int count = 1;

  /* Fill the progeny recursively, depth-first. */
  c->split = 0;
  for (int k = 0; k < 8; k++)
    if (pc->progeny[k] >= 0) {
      struct cell *temp;
      space_getcells(s, 1, &temp);
      temp->hydro.count = 0;
      temp->grav.count = 0;
      temp->stars.count = 0;
      temp->loc[0] = c->loc[0];
      temp->loc[1] = c->loc[1];
      temp->loc[2] = c->loc[2];
      temp->width[0] = c->width[0] / 2;
      temp->width[1] = c->width[1] / 2;
      temp->width[2] = c->width[2] / 2;
      temp->dmin = c->dmin / 2;
      if (k & 4) temp->loc[0] += temp->width[0];
      if (k & 2) temp->loc[1] += temp->width[1];
      if (k & 1) temp->loc[2] += temp->width[2];
      temp->depth = c->depth + 1;
      temp->split = 0;
      temp->hydro.dx_max_part = 0.f;
      temp->hydro.dx_max_sort = 0.f;
      temp->stars.dx_max_part = 0.f;
      temp->stars.dx_max_sort = 0.f;
      temp->nodeID = c->nodeID;
      temp->parent = c;
      c->progeny[k] = temp;
      c->split = 1;
      count += cell_unpack(&pc[pc->progeny[k]], temp, s, with_gravity);
    }

  /* Return the total number of unpacked cells. */
  c->mpi.pcell_size = count;
  return count;

#else
  error("SWIFT was not compiled with MPI support.");
  return 0;
#endif
}

/**
 * @brief Unpack the tags of a given cell and its sub-cells.
 *
 * @param tags An array of tags.
 * @param c The #cell in which to unpack the tags.
 *
 * @return The number of tags created.
 */
int cell_unpack_tags(const int *tags, struct cell *restrict c) {

#ifdef WITH_MPI

  /* Unpack the current pcell. */
  c->mpi.tag = tags[0];

  /* Number of new cells created. */
  int count = 1;

  /* Fill the progeny recursively, depth-first. */
  for (int k = 0; k < 8; k++)
    if (c->progeny[k] != NULL) {
      count += cell_unpack_tags(&tags[count], c->progeny[k]);
    }

#ifdef SWIFT_DEBUG_CHECKS
  if (c->mpi.pcell_size != count) error("Inconsistent tag and pcell count!");
#endif  // SWIFT_DEBUG_CHECKS

  /* Return the total number of unpacked tags. */
  return count;

#else
  error("SWIFT was not compiled with MPI support.");
  return 0;
#endif
}

/**
 * @brief Pack the time information of the given cell and all it's sub-cells.
 *
 * @param c The #cell.
 * @param pcells (output) The end-of-timestep information we pack into
 *
 * @return The number of packed cells.
 */
int cell_pack_end_step(struct cell *restrict c,
                       struct pcell_step *restrict pcells) {

#ifdef WITH_MPI

  /* Pack this cell's data. */
  pcells[0].hydro.ti_end_min = c->hydro.ti_end_min;
  pcells[0].hydro.ti_end_max = c->hydro.ti_end_max;
  pcells[0].grav.ti_end_min = c->grav.ti_end_min;
  pcells[0].grav.ti_end_max = c->grav.ti_end_max;
  pcells[0].stars.ti_end_min = c->stars.ti_end_min;
  pcells[0].hydro.dx_max_part = c->hydro.dx_max_part;
  pcells[0].stars.dx_max_part = c->stars.dx_max_part;

  /* Fill in the progeny, depth-first recursion. */
  int count = 1;
  for (int k = 0; k < 8; k++)
    if (c->progeny[k] != NULL) {
      count += cell_pack_end_step(c->progeny[k], &pcells[count]);
    }

  /* Return the number of packed values. */
  return count;

#else
  error("SWIFT was not compiled with MPI support.");
  return 0;
#endif
}

/**
 * @brief Unpack the time information of a given cell and its sub-cells.
 *
 * @param c The #cell
 * @param pcells The end-of-timestep information to unpack
 *
 * @return The number of cells created.
 */
int cell_unpack_end_step(struct cell *restrict c,
                         struct pcell_step *restrict pcells) {

#ifdef WITH_MPI

  /* Unpack this cell's data. */
  c->hydro.ti_end_min = pcells[0].hydro.ti_end_min;
  c->hydro.ti_end_max = pcells[0].hydro.ti_end_max;
  c->grav.ti_end_min = pcells[0].grav.ti_end_min;
  c->grav.ti_end_max = pcells[0].grav.ti_end_max;
  c->stars.ti_end_min = pcells[0].stars.ti_end_min;
  c->hydro.dx_max_part = pcells[0].hydro.dx_max_part;
  c->stars.dx_max_part = pcells[0].stars.dx_max_part;

  /* Fill in the progeny, depth-first recursion. */
  int count = 1;
  for (int k = 0; k < 8; k++)
    if (c->progeny[k] != NULL) {
      count += cell_unpack_end_step(c->progeny[k], &pcells[count]);
    }

  /* Return the number of packed values. */
  return count;

#else
  error("SWIFT was not compiled with MPI support.");
  return 0;
#endif
}

/**
 * @brief Pack the multipole information of the given cell and all it's
 * sub-cells.
 *
 * @param c The #cell.
 * @param pcells (output) The multipole information we pack into
 *
 * @return The number of packed cells.
 */
int cell_pack_multipoles(struct cell *restrict c,
                         struct gravity_tensors *restrict pcells) {

#ifdef WITH_MPI

  /* Pack this cell's data. */
  pcells[0] = *c->grav.multipole;

  /* Fill in the progeny, depth-first recursion. */
  int count = 1;
  for (int k = 0; k < 8; k++)
    if (c->progeny[k] != NULL) {
      count += cell_pack_multipoles(c->progeny[k], &pcells[count]);
    }

  /* Return the number of packed values. */
  return count;

#else
  error("SWIFT was not compiled with MPI support.");
  return 0;
#endif
}

/**
 * @brief Unpack the multipole information of a given cell and its sub-cells.
 *
 * @param c The #cell
 * @param pcells The multipole information to unpack
 *
 * @return The number of cells created.
 */
int cell_unpack_multipoles(struct cell *restrict c,
                           struct gravity_tensors *restrict pcells) {

#ifdef WITH_MPI

  /* Unpack this cell's data. */
  *c->grav.multipole = pcells[0];

  /* Fill in the progeny, depth-first recursion. */
  int count = 1;
  for (int k = 0; k < 8; k++)
    if (c->progeny[k] != NULL) {
      count += cell_unpack_multipoles(c->progeny[k], &pcells[count]);
    }

  /* Return the number of packed values. */
  return count;

#else
  error("SWIFT was not compiled with MPI support.");
  return 0;
#endif
}

/**
 * @brief Lock a cell for access to its array of #part and hold its parents.
 *
 * @param c The #cell.
 * @return 0 on success, 1 on failure
 */
int cell_locktree(struct cell *c) {

  TIMER_TIC

  /* First of all, try to lock this cell. */
  if (c->hydro.hold || lock_trylock(&c->hydro.lock) != 0) {
    TIMER_TOC(timer_locktree);
    return 1;
  }

  /* Did somebody hold this cell in the meantime? */
  if (c->hydro.hold) {

    /* Unlock this cell. */
    if (lock_unlock(&c->hydro.lock) != 0) error("Failed to unlock cell.");

    /* Admit defeat. */
    TIMER_TOC(timer_locktree);
    return 1;
  }

  /* Climb up the tree and lock/hold/unlock. */
  struct cell *finger;
  for (finger = c->parent; finger != NULL; finger = finger->parent) {

    /* Lock this cell. */
    if (lock_trylock(&finger->hydro.lock) != 0) break;

    /* Increment the hold. */
    atomic_inc(&finger->hydro.hold);

    /* Unlock the cell. */
    if (lock_unlock(&finger->hydro.lock) != 0) error("Failed to unlock cell.");
  }

  /* If we reached the top of the tree, we're done. */
  if (finger == NULL) {
    TIMER_TOC(timer_locktree);
    return 0;
  }

  /* Otherwise, we hit a snag. */
  else {

    /* Undo the holds up to finger. */
    for (struct cell *finger2 = c->parent; finger2 != finger;
         finger2 = finger2->parent)
      atomic_dec(&finger2->hydro.hold);

    /* Unlock this cell. */
    if (lock_unlock(&c->hydro.lock) != 0) error("Failed to unlock cell.");

    /* Admit defeat. */
    TIMER_TOC(timer_locktree);
    return 1;
  }
}

/**
 * @brief Lock a cell for access to its array of #gpart and hold its parents.
 *
 * @param c The #cell.
 * @return 0 on success, 1 on failure
 */
int cell_glocktree(struct cell *c) {

  TIMER_TIC

  /* First of all, try to lock this cell. */
  if (c->grav.phold || lock_trylock(&c->grav.plock) != 0) {
    TIMER_TOC(timer_locktree);
    return 1;
  }

  /* Did somebody hold this cell in the meantime? */
  if (c->grav.phold) {

    /* Unlock this cell. */
    if (lock_unlock(&c->grav.plock) != 0) error("Failed to unlock cell.");

    /* Admit defeat. */
    TIMER_TOC(timer_locktree);
    return 1;
  }

  /* Climb up the tree and lock/hold/unlock. */
  struct cell *finger;
  for (finger = c->parent; finger != NULL; finger = finger->parent) {

    /* Lock this cell. */
    if (lock_trylock(&finger->grav.plock) != 0) break;

    /* Increment the hold. */
    atomic_inc(&finger->grav.phold);

    /* Unlock the cell. */
    if (lock_unlock(&finger->grav.plock) != 0) error("Failed to unlock cell.");
  }

  /* If we reached the top of the tree, we're done. */
  if (finger == NULL) {
    TIMER_TOC(timer_locktree);
    return 0;
  }

  /* Otherwise, we hit a snag. */
  else {

    /* Undo the holds up to finger. */
    for (struct cell *finger2 = c->parent; finger2 != finger;
         finger2 = finger2->parent)
      atomic_dec(&finger2->grav.phold);

    /* Unlock this cell. */
    if (lock_unlock(&c->grav.plock) != 0) error("Failed to unlock cell.");

    /* Admit defeat. */
    TIMER_TOC(timer_locktree);
    return 1;
  }
}

/**
 * @brief Lock a cell for access to its #multipole and hold its parents.
 *
 * @param c The #cell.
 * @return 0 on success, 1 on failure
 */
int cell_mlocktree(struct cell *c) {

  TIMER_TIC

  /* First of all, try to lock this cell. */
  if (c->grav.mhold || lock_trylock(&c->grav.mlock) != 0) {
    TIMER_TOC(timer_locktree);
    return 1;
  }

  /* Did somebody hold this cell in the meantime? */
  if (c->grav.mhold) {

    /* Unlock this cell. */
    if (lock_unlock(&c->grav.mlock) != 0) error("Failed to unlock cell.");

    /* Admit defeat. */
    TIMER_TOC(timer_locktree);
    return 1;
  }

  /* Climb up the tree and lock/hold/unlock. */
  struct cell *finger;
  for (finger = c->parent; finger != NULL; finger = finger->parent) {

    /* Lock this cell. */
    if (lock_trylock(&finger->grav.mlock) != 0) break;

    /* Increment the hold. */
    atomic_inc(&finger->grav.mhold);

    /* Unlock the cell. */
    if (lock_unlock(&finger->grav.mlock) != 0) error("Failed to unlock cell.");
  }

  /* If we reached the top of the tree, we're done. */
  if (finger == NULL) {
    TIMER_TOC(timer_locktree);
    return 0;
  }

  /* Otherwise, we hit a snag. */
  else {

    /* Undo the holds up to finger. */
    for (struct cell *finger2 = c->parent; finger2 != finger;
         finger2 = finger2->parent)
      atomic_dec(&finger2->grav.mhold);

    /* Unlock this cell. */
    if (lock_unlock(&c->grav.mlock) != 0) error("Failed to unlock cell.");

    /* Admit defeat. */
    TIMER_TOC(timer_locktree);
    return 1;
  }
}

/**
 * @brief Lock a cell for access to its array of #spart and hold its parents.
 *
 * @param c The #cell.
 * @return 0 on success, 1 on failure
 */
int cell_slocktree(struct cell *c) {

  TIMER_TIC

  /* First of all, try to lock this cell. */
  if (c->stars.hold || lock_trylock(&c->stars.lock) != 0) {
    TIMER_TOC(timer_locktree);
    return 1;
  }

  /* Did somebody hold this cell in the meantime? */
  if (c->stars.hold) {

    /* Unlock this cell. */
    if (lock_unlock(&c->stars.lock) != 0) error("Failed to unlock cell.");

    /* Admit defeat. */
    TIMER_TOC(timer_locktree);
    return 1;
  }

  /* Climb up the tree and lock/hold/unlock. */
  struct cell *finger;
  for (finger = c->parent; finger != NULL; finger = finger->parent) {

    /* Lock this cell. */
    if (lock_trylock(&finger->stars.lock) != 0) break;

    /* Increment the hold. */
    atomic_inc(&finger->stars.hold);

    /* Unlock the cell. */
    if (lock_unlock(&finger->stars.lock) != 0) error("Failed to unlock cell.");
  }

  /* If we reached the top of the tree, we're done. */
  if (finger == NULL) {
    TIMER_TOC(timer_locktree);
    return 0;
  }

  /* Otherwise, we hit a snag. */
  else {

    /* Undo the holds up to finger. */
    for (struct cell *finger2 = c->parent; finger2 != finger;
         finger2 = finger2->parent)
      atomic_dec(&finger2->stars.hold);

    /* Unlock this cell. */
    if (lock_unlock(&c->stars.lock) != 0) error("Failed to unlock cell.");

    /* Admit defeat. */
    TIMER_TOC(timer_locktree);
    return 1;
  }
}

/**
 * @brief Unlock a cell's parents for access to #part array.
 *
 * @param c The #cell.
 */
void cell_unlocktree(struct cell *c) {

  TIMER_TIC

  /* First of all, try to unlock this cell. */
  if (lock_unlock(&c->hydro.lock) != 0) error("Failed to unlock cell.");

  /* Climb up the tree and unhold the parents. */
  for (struct cell *finger = c->parent; finger != NULL; finger = finger->parent)
    atomic_dec(&finger->hydro.hold);

  TIMER_TOC(timer_locktree);
}

/**
 * @brief Unlock a cell's parents for access to #gpart array.
 *
 * @param c The #cell.
 */
void cell_gunlocktree(struct cell *c) {

  TIMER_TIC

  /* First of all, try to unlock this cell. */
  if (lock_unlock(&c->grav.plock) != 0) error("Failed to unlock cell.");

  /* Climb up the tree and unhold the parents. */
  for (struct cell *finger = c->parent; finger != NULL; finger = finger->parent)
    atomic_dec(&finger->grav.phold);

  TIMER_TOC(timer_locktree);
}

/**
 * @brief Unlock a cell's parents for access to its #multipole.
 *
 * @param c The #cell.
 */
void cell_munlocktree(struct cell *c) {

  TIMER_TIC

  /* First of all, try to unlock this cell. */
  if (lock_unlock(&c->grav.mlock) != 0) error("Failed to unlock cell.");

  /* Climb up the tree and unhold the parents. */
  for (struct cell *finger = c->parent; finger != NULL; finger = finger->parent)
    atomic_dec(&finger->grav.mhold);

  TIMER_TOC(timer_locktree);
}

/**
 * @brief Unlock a cell's parents for access to #spart array.
 *
 * @param c The #cell.
 */
void cell_sunlocktree(struct cell *c) {

  TIMER_TIC

  /* First of all, try to unlock this cell. */
  if (lock_unlock(&c->stars.lock) != 0) error("Failed to unlock cell.");

  /* Climb up the tree and unhold the parents. */
  for (struct cell *finger = c->parent; finger != NULL; finger = finger->parent)
    atomic_dec(&finger->stars.hold);

  TIMER_TOC(timer_locktree);
}

/**
 * @brief Sort the parts into eight bins along the given pivots.
 *
 * @param c The #cell array to be sorted.
 * @param parts_offset Offset of the cell parts array relative to the
 *        space's parts array, i.e. c->hydro.parts - s->parts.
 * @param sparts_offset Offset of the cell sparts array relative to the
 *        space's sparts array, i.e. c->stars.parts - s->stars.parts.
 * @param buff A buffer with at least max(c->hydro.count, c->grav.count)
 * entries, used for sorting indices.
 * @param sbuff A buffer with at least max(c->stars.count, c->grav.count)
 * entries, used for sorting indices for the sparts.
 * @param gbuff A buffer with at least max(c->hydro.count, c->grav.count)
 * entries, used for sorting indices for the gparts.
 */
void cell_split(struct cell *c, ptrdiff_t parts_offset, ptrdiff_t sparts_offset,
                struct cell_buff *buff, struct cell_buff *sbuff,
                struct cell_buff *gbuff) {

  const int count = c->hydro.count, gcount = c->grav.count,
            scount = c->stars.count;
  struct part *parts = c->hydro.parts;
  struct xpart *xparts = c->hydro.xparts;
  struct gpart *gparts = c->grav.parts;
  struct spart *sparts = c->stars.parts;
  const double pivot[3] = {c->loc[0] + c->width[0] / 2,
                           c->loc[1] + c->width[1] / 2,
                           c->loc[2] + c->width[2] / 2};
  int bucket_count[8] = {0, 0, 0, 0, 0, 0, 0, 0};
  int bucket_offset[9];

#ifdef SWIFT_DEBUG_CHECKS
  /* Check that the buffs are OK. */
  for (int k = 0; k < count; k++) {
    if (buff[k].x[0] != parts[k].x[0] || buff[k].x[1] != parts[k].x[1] ||
        buff[k].x[2] != parts[k].x[2])
      error("Inconsistent buff contents.");
  }
  for (int k = 0; k < gcount; k++) {
    if (gbuff[k].x[0] != gparts[k].x[0] || gbuff[k].x[1] != gparts[k].x[1] ||
        gbuff[k].x[2] != gparts[k].x[2])
      error("Inconsistent gbuff contents.");
  }
  for (int k = 0; k < scount; k++) {
    if (sbuff[k].x[0] != sparts[k].x[0] || sbuff[k].x[1] != sparts[k].x[1] ||
        sbuff[k].x[2] != sparts[k].x[2])
      error("Inconsistent sbuff contents.");
  }
#endif /* SWIFT_DEBUG_CHECKS */

  /* Fill the buffer with the indices. */
  for (int k = 0; k < count; k++) {
    const int bid = (buff[k].x[0] >= pivot[0]) * 4 +
                    (buff[k].x[1] >= pivot[1]) * 2 + (buff[k].x[2] >= pivot[2]);
    bucket_count[bid]++;
    buff[k].ind = bid;
  }

  /* Set the buffer offsets. */
  bucket_offset[0] = 0;
  for (int k = 1; k <= 8; k++) {
    bucket_offset[k] = bucket_offset[k - 1] + bucket_count[k - 1];
    bucket_count[k - 1] = 0;
  }

  /* Run through the buckets, and swap particles to their correct spot. */
  for (int bucket = 0; bucket < 8; bucket++) {
    for (int k = bucket_offset[bucket] + bucket_count[bucket];
         k < bucket_offset[bucket + 1]; k++) {
      int bid = buff[k].ind;
      if (bid != bucket) {
        struct part part = parts[k];
        struct xpart xpart = xparts[k];
        struct cell_buff temp_buff = buff[k];
        while (bid != bucket) {
          int j = bucket_offset[bid] + bucket_count[bid]++;
          while (buff[j].ind == bid) {
            j++;
            bucket_count[bid]++;
          }
          memswap(&parts[j], &part, sizeof(struct part));
          memswap(&xparts[j], &xpart, sizeof(struct xpart));
          memswap(&buff[j], &temp_buff, sizeof(struct cell_buff));
          if (parts[j].gpart)
            parts[j].gpart->id_or_neg_offset = -(j + parts_offset);
          bid = temp_buff.ind;
        }
        parts[k] = part;
        xparts[k] = xpart;
        buff[k] = temp_buff;
        if (parts[k].gpart)
          parts[k].gpart->id_or_neg_offset = -(k + parts_offset);
      }
      bucket_count[bid]++;
    }
  }

  /* Store the counts and offsets. */
  for (int k = 0; k < 8; k++) {
    c->progeny[k]->hydro.count = bucket_count[k];
    c->progeny[k]->hydro.count_total = c->progeny[k]->hydro.count;
    c->progeny[k]->hydro.parts = &c->hydro.parts[bucket_offset[k]];
    c->progeny[k]->hydro.xparts = &c->hydro.xparts[bucket_offset[k]];
  }

#ifdef SWIFT_DEBUG_CHECKS
  /* Check that the buffs are OK. */
  for (int k = 1; k < count; k++) {
    if (buff[k].ind < buff[k - 1].ind) error("Buff not sorted.");
    if (buff[k].x[0] != parts[k].x[0] || buff[k].x[1] != parts[k].x[1] ||
        buff[k].x[2] != parts[k].x[2])
      error("Inconsistent buff contents (k=%i).", k);
  }

  /* Verify that _all_ the parts have been assigned to a cell. */
  for (int k = 1; k < 8; k++)
    if (&c->progeny[k - 1]->hydro.parts[c->progeny[k - 1]->hydro.count] !=
        c->progeny[k]->hydro.parts)
      error("Particle sorting failed (internal consistency).");
  if (c->progeny[0]->hydro.parts != c->hydro.parts)
    error("Particle sorting failed (left edge).");
  if (&c->progeny[7]->hydro.parts[c->progeny[7]->hydro.count] !=
      &c->hydro.parts[count])
    error("Particle sorting failed (right edge).");

  /* Verify a few sub-cells. */
  for (int k = 0; k < c->progeny[0]->hydro.count; k++)
    if (c->progeny[0]->hydro.parts[k].x[0] >= pivot[0] ||
        c->progeny[0]->hydro.parts[k].x[1] >= pivot[1] ||
        c->progeny[0]->hydro.parts[k].x[2] >= pivot[2])
      error("Sorting failed (progeny=0).");
  for (int k = 0; k < c->progeny[1]->hydro.count; k++)
    if (c->progeny[1]->hydro.parts[k].x[0] >= pivot[0] ||
        c->progeny[1]->hydro.parts[k].x[1] >= pivot[1] ||
        c->progeny[1]->hydro.parts[k].x[2] < pivot[2])
      error("Sorting failed (progeny=1).");
  for (int k = 0; k < c->progeny[2]->hydro.count; k++)
    if (c->progeny[2]->hydro.parts[k].x[0] >= pivot[0] ||
        c->progeny[2]->hydro.parts[k].x[1] < pivot[1] ||
        c->progeny[2]->hydro.parts[k].x[2] >= pivot[2])
      error("Sorting failed (progeny=2).");
  for (int k = 0; k < c->progeny[3]->hydro.count; k++)
    if (c->progeny[3]->hydro.parts[k].x[0] >= pivot[0] ||
        c->progeny[3]->hydro.parts[k].x[1] < pivot[1] ||
        c->progeny[3]->hydro.parts[k].x[2] < pivot[2])
      error("Sorting failed (progeny=3).");
  for (int k = 0; k < c->progeny[4]->hydro.count; k++)
    if (c->progeny[4]->hydro.parts[k].x[0] < pivot[0] ||
        c->progeny[4]->hydro.parts[k].x[1] >= pivot[1] ||
        c->progeny[4]->hydro.parts[k].x[2] >= pivot[2])
      error("Sorting failed (progeny=4).");
  for (int k = 0; k < c->progeny[5]->hydro.count; k++)
    if (c->progeny[5]->hydro.parts[k].x[0] < pivot[0] ||
        c->progeny[5]->hydro.parts[k].x[1] >= pivot[1] ||
        c->progeny[5]->hydro.parts[k].x[2] < pivot[2])
      error("Sorting failed (progeny=5).");
  for (int k = 0; k < c->progeny[6]->hydro.count; k++)
    if (c->progeny[6]->hydro.parts[k].x[0] < pivot[0] ||
        c->progeny[6]->hydro.parts[k].x[1] < pivot[1] ||
        c->progeny[6]->hydro.parts[k].x[2] >= pivot[2])
      error("Sorting failed (progeny=6).");
  for (int k = 0; k < c->progeny[7]->hydro.count; k++)
    if (c->progeny[7]->hydro.parts[k].x[0] < pivot[0] ||
        c->progeny[7]->hydro.parts[k].x[1] < pivot[1] ||
        c->progeny[7]->hydro.parts[k].x[2] < pivot[2])
      error("Sorting failed (progeny=7).");
#endif

  /* Now do the same song and dance for the sparts. */
  for (int k = 0; k < 8; k++) bucket_count[k] = 0;

  /* Fill the buffer with the indices. */
  for (int k = 0; k < scount; k++) {
    const int bid = (sbuff[k].x[0] > pivot[0]) * 4 +
                    (sbuff[k].x[1] > pivot[1]) * 2 + (sbuff[k].x[2] > pivot[2]);
    bucket_count[bid]++;
    sbuff[k].ind = bid;
  }

  /* Set the buffer offsets. */
  bucket_offset[0] = 0;
  for (int k = 1; k <= 8; k++) {
    bucket_offset[k] = bucket_offset[k - 1] + bucket_count[k - 1];
    bucket_count[k - 1] = 0;
  }

  /* Run through the buckets, and swap particles to their correct spot. */
  for (int bucket = 0; bucket < 8; bucket++) {
    for (int k = bucket_offset[bucket] + bucket_count[bucket];
         k < bucket_offset[bucket + 1]; k++) {
      int bid = sbuff[k].ind;
      if (bid != bucket) {
        struct spart spart = sparts[k];
        struct cell_buff temp_buff = sbuff[k];
        while (bid != bucket) {
          int j = bucket_offset[bid] + bucket_count[bid]++;
          while (sbuff[j].ind == bid) {
            j++;
            bucket_count[bid]++;
          }
          memswap(&sparts[j], &spart, sizeof(struct spart));
          memswap(&sbuff[j], &temp_buff, sizeof(struct cell_buff));
          if (sparts[j].gpart)
            sparts[j].gpart->id_or_neg_offset = -(j + sparts_offset);
          bid = temp_buff.ind;
        }
        sparts[k] = spart;
        sbuff[k] = temp_buff;
        if (sparts[k].gpart)
          sparts[k].gpart->id_or_neg_offset = -(k + sparts_offset);
      }
      bucket_count[bid]++;
    }
  }

  /* Store the counts and offsets. */
  for (int k = 0; k < 8; k++) {