peano.c

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <mpi.h>

#include "allvars.h"
#include "proto.h"

/*! \file peano.c 
 *  \brief Routines to compute a Peano-Hilbert order
 *
 *  This file contains routines to compute Peano-Hilbert keys, and to put the
 *  particle data into the order of these keys, i.e. into the order of a
 *  space-filling fractal curve.
 */


static struct peano_hilbert_data
{
  peanokey key;
  int index;
}
 *mp;

static int *Id;


/*! This function puts the particles into Peano-Hilbert order by sorting them
 *  according to their keys. The latter half already been computed in the
 *  domain decomposition. Since gas particles need to stay at the beginning of
 *  the particle list, they are sorted as a separate block.
 */
void peano_hilbert_order(void)
{
  int i;

  if(ThisTask == 0)
    printf("begin Peano-Hilbert order...\n");

  if(N_gas)
    {
      mp = malloc(sizeof(struct peano_hilbert_data) * N_gas);
      Id = malloc(sizeof(int) * N_gas);

      for(i = 0; i < N_gas; i++)
	{
	  mp[i].index = i;
	  mp[i].key = Key[i];
	}

      qsort(mp, N_gas, sizeof(struct peano_hilbert_data), compare_key);

      for(i = 0; i < N_gas; i++)
	Id[mp[i].index] = i;

      reorder_gas();

      free(Id);
      free(mp);
    }


  if(NumPart - N_gas > 0)
    {
      mp = malloc(sizeof(struct peano_hilbert_data) * (NumPart - N_gas));
      mp -= (N_gas);

      Id = malloc(sizeof(int) * (NumPart - N_gas));
      Id -= (N_gas);

      for(i = N_gas; i < NumPart; i++)
	{
	  mp[i].index = i;
	  mp[i].key = Key[i];
	}

      qsort(mp + N_gas, NumPart - N_gas, sizeof(struct peano_hilbert_data), compare_key);

      for(i = N_gas; i < NumPart; i++)
	Id[mp[i].index] = i;

      reorder_particles();

      Id += N_gas;
      free(Id);
      mp += N_gas;
      free(mp);
    }

  if(ThisTask == 0)
    printf("Peano-Hilbert done.\n");
}


/*! This function is a comparison kernel for sorting the Peano-Hilbert keys.
 */
int compare_key(const void *a, const void *b)
{
  if(((struct peano_hilbert_data *) a)->key < (((struct peano_hilbert_data *) b)->key))
    return -1;

  if(((struct peano_hilbert_data *) a)->key > (((struct peano_hilbert_data *) b)->key))
    return +1;

  return 0;
}


/*! This function brings the gas particles into the same order as the sorted
 *  keys. (The sort is first done only on the keys themselves and done
 *  directly on the gas particles in order to reduce the amount of data that
 *  needs to be moved in memory. Only once the order is established, the gas
 *  particles are rearranged, such that each particle has to be moved at most
 *  once.)
 */
void reorder_gas(void)
{
  int i;
  struct particle_data Psave, Psource;
  struct sph_particle_data SphPsave, SphPsource;
  int idsource, idsave, dest;

  for(i = 0; i < N_gas; i++)
    {
      if(Id[i] != i)
	{
	  Psource = P[i];
	  SphPsource = SphP[i];

	  idsource = Id[i];
	  dest = Id[i];

	  do
	    {
	      Psave = P[dest];
	      SphPsave = SphP[dest];
	      idsave = Id[dest];

	      P[dest] = Psource;
	      SphP[dest] = SphPsource;
	      Id[dest] = idsource;

	      if(dest == i)
		break;

	      Psource = Psave;
	      SphPsource = SphPsave;
	      idsource = idsave;

	      dest = idsource;
	    }
	  while(1);
	}
    }
}


/*! This function brings the collisionless particles into the same order as
 *  the sorted keys. (The sort is first done only on the keys themselves and
 *  done directly on the particles in order to reduce the amount of data that
 *  needs to be moved in memory. Only once the order is established, the
 *  particles are rearranged, such that each particle has to be moved at most
 *  once.)
 */
void reorder_particles(void)
{
  int i;
  struct particle_data Psave, Psource;
  int idsource, idsave, dest;

  for(i = N_gas; i < NumPart; i++)
    {
      if(Id[i] != i)
	{
	  Psource = P[i];
	  idsource = Id[i];

	  dest = Id[i];

	  do
	    {
	      Psave = P[dest];
	      idsave = Id[dest];

	      P[dest] = Psource;
	      Id[dest] = idsource;

	      if(dest == i)
		break;

	      Psource = Psave;
	      idsource = idsave;

	      dest = idsource;
	    }
	  while(1);
	}
    }
}






static int quadrants[24][2][2][2] = {
  /* rotx=0, roty=0-3 */
  {{{0, 7}, {1, 6}}, {{3, 4}, {2, 5}}},
  {{{7, 4}, {6, 5}}, {{0, 3}, {1, 2}}},
  {{{4, 3}, {5, 2}}, {{7, 0}, {6, 1}}},
  {{{3, 0}, {2, 1}}, {{4, 7}, {5, 6}}},
  /* rotx=1, roty=0-3 */
  {{{1, 0}, {6, 7}}, {{2, 3}, {5, 4}}},
  {{{0, 3}, {7, 4}}, {{1, 2}, {6, 5}}},
  {{{3, 2}, {4, 5}}, {{0, 1}, {7, 6}}},
  {{{2, 1}, {5, 6}}, {{3, 0}, {4, 7}}},
  /* rotx=2, roty=0-3 */
  {{{6, 1}, {7, 0}}, {{5, 2}, {4, 3}}},
  {{{1, 2}, {0, 3}}, {{6, 5}, {7, 4}}},
  {{{2, 5}, {3, 4}}, {{1, 6}, {0, 7}}},
  {{{5, 6}, {4, 7}}, {{2, 1}, {3, 0}}},
  /* rotx=3, roty=0-3 */
  {{{7, 6}, {0, 1}}, {{4, 5}, {3, 2}}},
  {{{6, 5}, {1, 2}}, {{7, 4}, {0, 3}}},
  {{{5, 4}, {2, 3}}, {{6, 7}, {1, 0}}},
  {{{4, 7}, {3, 0}}, {{5, 6}, {2, 1}}},
  /* rotx=4, roty=0-3 */
  {{{6, 7}, {5, 4}}, {{1, 0}, {2, 3}}},
  {{{7, 0}, {4, 3}}, {{6, 1}, {5, 2}}},
  {{{0, 1}, {3, 2}}, {{7, 6}, {4, 5}}},
  {{{1, 6}, {2, 5}}, {{0, 7}, {3, 4}}},
  /* rotx=5, roty=0-3 */
  {{{2, 3}, {1, 0}}, {{5, 4}, {6, 7}}},
  {{{3, 4}, {0, 7}}, {{2, 5}, {1, 6}}},
  {{{4, 5}, {7, 6}}, {{3, 2}, {0, 1}}},
  {{{5, 2}, {6, 1}}, {{4, 3}, {7, 0}}}
};


static int rotxmap_table[24] = { 4, 5, 6, 7, 8, 9, 10, 11,
  12, 13, 14, 15, 0, 1, 2, 3, 17, 18, 19, 16, 23, 20, 21, 22
};

static int rotymap_table[24] = { 1, 2, 3, 0, 16, 17, 18, 19,
  11, 8, 9, 10, 22, 23, 20, 21, 14, 15, 12, 13, 4, 5, 6, 7
};

static int rotx_table[8] = { 3, 0, 0, 2, 2, 0, 0, 1 };
static int roty_table[8] = { 0, 1, 1, 2, 2, 3, 3, 0 };

static int sense_table[8] = { -1, -1, -1, +1, +1, -1, -1, -1 };

static int flag_quadrants_inverse = 1;
static char quadrants_inverse_x[24][8];
static char quadrants_inverse_y[24][8];
static char quadrants_inverse_z[24][8];


/*! This function computes a Peano-Hilbert key for an integer triplet (x,y,z),
 *  with x,y,z in the range between 0 and 2^bits-1.
 */
peanokey peano_hilbert_key(int x, int y, int z, int bits)
{
  int i, quad, bitx, bity, bitz;
  int mask, rotation, rotx, roty, sense;
  peanokey key;


  mask = 1 << (bits - 1);
  key = 0;
  rotation = 0;
  sense = 1;


  for(i = 0; i < bits; i++, mask >>= 1)
    {
      bitx = (x & mask) ? 1 : 0;
      bity = (y & mask) ? 1 : 0;
      bitz = (z & mask) ? 1 : 0;

      quad = quadrants[rotation][bitx][bity][bitz];

      key <<= 3;
      key += (sense == 1) ? (quad) : (7 - quad);

      rotx = rotx_table[quad];
      roty = roty_table[quad];
      sense *= sense_table[quad];

      while(rotx > 0)
	{
	  rotation = rotxmap_table[rotation];
	  rotx--;
	}

      while(roty > 0)
	{
	  rotation = rotymap_table[rotation];
	  roty--;
	}
    }

  return key;
}


/*! This function computes for a given Peano-Hilbert key, the inverse,
 *  i.e. the integer triplet (x,y,z) with a Peano-Hilbert key equal to the
 *  input key. (This functionality is actually not needed in the present
 *  code.)
 */
void peano_hilbert_key_inverse(peanokey key, int bits, int *x, int *y, int *z)
{
  int i, keypart, bitx, bity, bitz, mask, quad, rotation, shift;
  char sense, rotx, roty;

  if(flag_quadrants_inverse)
    {
      flag_quadrants_inverse = 0;
      for(rotation = 0; rotation < 24; rotation++)
        for(bitx = 0; bitx < 2; bitx++)
          for(bity = 0; bity < 2; bity++)
            for(bitz = 0; bitz < 2; bitz++)
              {
                quad = quadrants[rotation][bitx][bity][bitz];
                quadrants_inverse_x[rotation][quad] = bitx;
                quadrants_inverse_y[rotation][quad] = bity;
                quadrants_inverse_z[rotation][quad] = bitz;
              }
    }

  shift = 3 * (bits - 1);
  mask = 7 << shift;

  rotation = 0;
  sense = 1;

  *x = *y = *z = 0;

  for(i = 0; i < bits; i++, mask >>= 3, shift -= 3)
    {
      keypart = (key & mask) >> shift;

      quad = (sense == 1) ? (keypart) : (7 - keypart);

      *x = (*x << 1) + quadrants_inverse_x[rotation][quad];
      *y = (*y << 1) + quadrants_inverse_y[rotation][quad];
      *z = (*z << 1) + quadrants_inverse_z[rotation][quad];

      rotx = rotx_table[quad];
      roty = roty_table[quad];
      sense *= sense_table[quad];

      while(rotx > 0)
        {
          rotation = rotxmap_table[rotation];
          rotx--;
        }

      while(roty > 0)
        {
          rotation = rotymap_table[rotation];
          roty--;
        }
    }
}