space.c 70.4 KB
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/*******************************************************************************
 * This file is part of GadgetSMP.
 * Coypright (c) 2012 Pedro Gonnet (pedro.gonnet@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 <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <pthread.h>
#include <float.h>
#include <limits.h>
#include <math.h>

/* Local headers. */
#include "cycle.h"
#include "lock.h"
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#include "task.h"
#include "part.h"
#include "cell.h"
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#include "space.h"
#include "runner.h"

/* Error macro. */
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#define error(s) { fprintf( stderr , "%s:%s:%i: %s\n" , __FILE__ , __FUNCTION__ , __LINE__ , s ); abort(); }
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/* Split size. */
int space_splitsize = space_splitsize_default;

/* Map shift vector to sortlist. */
const int sortlistID[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 
    };
    
    
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/**
 * @breif Recursively dismantle a cell tree.
 *
 */
 
void space_rebuild_recycle ( struct space *s , struct cell *c ) {
    
    int k;
    
    if ( c->split )
        for ( k = 0 ; k < 8 ; k++ )
            if ( c->progeny[k] != NULL ) {
                space_rebuild_recycle( s , c->progeny[k] );
                space_recycle( s , c->progeny[k] );
                c->progeny[k] = NULL;
                }
    
    }

/**
 * @breif Recursively rebuild a cell tree.
 *
 */
 
int space_rebuild_recurse ( struct space *s , struct cell *c ) {
    
    int k, count, changes = 0, wasmt[8];
    float h, h_limit, h_max = 0.0f;
    struct cell *temp;
    
    /* If the cell is already split, check that the split is still ok. */
    if ( c->split ) {
    
        /* Check the depth. */
        if ( c->depth > s->maxdepth )
            s->maxdepth = c->depth;

        /* Set the minimum cutoff. */
        h_limit = fmin( c->h[0] , fmin( c->h[1] , c->h[2] ) ) / 2;

        /* Count the particles below that. */
        for ( count = 0 , k = 0 ; k < c->count ; k++ ) {
            h = c->parts[k].h;
            if ( h <= h_limit )
                count += 1;
            if ( h > h_max )
                h_max = h;
            }
        c->h_max = h_max;
            
        /* Un-split? */
        if ( count < c->count*space_splitratio || c->count < space_splitsize ) {
        
            /* Get rid of the progeny. */
            space_rebuild_recycle( s , c );
            
            /* Re-set the split flag. */
            c->split = 0;
        
            }
        
        /* Otherwise, recurse on the kids. */
        else {
        
            /* Populate all progeny. */
            for ( k = 0 ; k < 8 ; k++ )
                if ( ( wasmt[k] = ( c->progeny[k] == NULL ) ) ) {
                    temp = space_getcell( s );
                    temp->count = 0;
                    temp->loc[0] = c->loc[0];
                    temp->loc[1] = c->loc[1];
                    temp->loc[2] = c->loc[2];
                    temp->h[0] = c->h[0]/2;
                    temp->h[1] = c->h[1]/2;
                    temp->h[2] = c->h[2]/2;
                    if ( k & 4 )
                        temp->loc[0] += temp->h[0];
                    if ( k & 2 )
                        temp->loc[1] += temp->h[1];
                    if ( k & 1 )
                        temp->loc[2] += temp->h[2];
                    temp->depth = c->depth + 1;
                    temp->split = 0;
                    temp->h_max = 0.0;
                    temp->parent = c;
                    c->progeny[k] = temp;
                    }
        
            /* Make sure each part is in its place. */
            cell_split( c );
            
            /* Remove empty progeny. */
            for ( k = 0 ; k < 8 ; k++ )
                if ( c->progeny[k]->count == 0 ) {
                    changes += !wasmt[k];
                    space_recycle( s , c->progeny[k] );
                    c->progeny[k] = NULL;
                    }
                else
                    changes += wasmt[k];
        
            /* Recurse. */
            for ( k = 0 ; k < 8 ; k++ )
                if ( c->progeny[k] != NULL )
                    changes += space_rebuild_recurse( s , c->progeny[k] );
                    
            }
    
        }
        
    /* Otherwise, try to split it anyway. */
    else {
        space_split( s , c );
        changes += c->split;
        }
        
    /* Return the grand total. */
    return changes;
    
    }

/**
 * @breif Re-build the cells as well as the tasks.
 *
 * @param s The #space in which to update the cells.
 * @param force Flag to force re-building the cells and tasks.
 *
 * @return 1 if changes to the cells and/or tasks were made.
 */
 
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int space_rebuild ( struct space *s , int force , double cell_max ) {
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    float h_max = s->parts[0].h, h_min = s->parts[0].h;
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    int i, j, k, cdim[3];
    struct cell *c;
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    struct part *finger;
    int *ind, changes = 0;
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    /* Run through the parts and get the current h_max. */
    for ( k = 0 ; k < s->nr_parts ; k++ )
        if ( s->parts[k].h > h_max )
            h_max = s->parts[k].h;
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        else if ( s->parts[k].h < h_min )
            h_min = s->parts[k].h;
    s->h_min = h_min;
    s->h_max = h_max;
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    /* Get the new putative cell dimensions. */
    for ( k = 0 ; k < 3 ; k++ )
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        cdim[k] = floor( s->dim[k] / fmax( h_max*space_stretch , cell_max ) );
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    /* Do we need to re-build the upper-level cells? */
    if ( force || cdim[0] < s->cdim[0] || cdim[1] < s->cdim[1] || cdim[2] < s->cdim[2] ) {
    
        /* Free the old cells, if they were allocated. */
        if ( s->cells != NULL ) {
            for ( k = 0 ; k < s->nr_cells ; k++ )
                space_rebuild_recycle( s , &s->cells[k] );
            free( s->cells );
            s->maxdepth = 0;
            }
            
        /* Set the new cell dimensions. */
        for ( k = 0 ; k < 3 ; k++ ) {
            s->cdim[k] = cdim[k];
            s->h[k] = s->dim[k] / cdim[k];
            s->ih[k] = 1.0 / s->h[k];
            }
    
        /* Allocate the highest level of cells. */
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        s->tot_cells = s->nr_cells = cdim[0] * cdim[1] * cdim[2];
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        if ( posix_memalign( (void *)&s->cells , 64 , s->nr_cells * sizeof(struct cell) ) != 0 )
            error( "Failed to allocate cells." );
        bzero( s->cells , s->nr_cells * sizeof(struct cell) );
        for ( k = 0 ; k < s->nr_cells ; k++ )
            if ( lock_init( &s->cells[k].lock ) != 0 )
                error( "Failed to init spinlock." );

        /* Set the cell location and sizes. */
        for ( i = 0 ; i < cdim[0] ; i++ )
            for ( j = 0 ; j < cdim[1] ; j++ )
                for ( k = 0 ; k < cdim[2] ; k++ ) {
                    c = &s->cells[ cell_getid( cdim , i , j , k ) ];
                    c->loc[0] = i*s->h[0]; c->loc[1] = j*s->h[1]; c->loc[2] = k*s->h[2];
                    c->h[0] = s->h[0]; c->h[1] = s->h[1]; c->h[2] = s->h[2];
                    c->depth = 0;
                    }
                    
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        /* Run through the particles and get their cell index. */
        ind = (int *)alloca( sizeof(int) * s->nr_parts );
        for ( k = 0 ; k < s->nr_parts ; k++ )  {
            ind[k] = cell_getid( cdim , s->parts[k].x[0]*s->ih[0] , s->parts[k].x[1]*s->ih[1] , s->parts[k].x[2]*s->ih[2] );
            s->cells[ ind[k] ].count += 1;
            }

        /* Sort the parts according to their cells. */
        parts_sort( s->parts , ind , s->nr_parts , 0 , s->nr_cells );        
                    
        /* Hook the cells up to the parts. */
        for ( finger = s->parts , k = 0 ; k < s->nr_cells ; k++ ) {
            c = &s->cells[ k ];
            c->parts = finger;
            finger = &finger[ c->count ];
            }
        
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        /* There were massive changes. */
        changes = 1;
        
        } /* re-build upper-level cells? */
        
    /* At this point, we have the upper-level cells, old or new. Now make
       sure that the parts in each cell are ok. */
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    #pragma omp parallel for shared(s) reduction(+:changes)
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    for ( k = 0 ; k < s->nr_cells ; k++ )
        changes += space_rebuild_recurse( s , &s->cells[k] );
        
    /* Now that we have the cell structre, re-build the tasks. */
    if ( changes )
        space_maketasks( s , 1 );
    
    /* Return the number of changes. */
    return changes;

    }


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/**
 * @brief Sort the particles according to the given indices.
 *
 * @param parts The list of #part
 * @param ind The indices with respect to which the parts are sorted.
 * @param N The number of parts
 * @param min Lowest index.
 * @param max highest index.
 *
 * This function calls itself recursively.
 */
 
void parts_sort ( struct part *parts , int *ind , int N , int min , int max ) {

    int pivot = (min + max) / 2;
    int i = 0, j = N-1;
    int temp_i;
    struct part temp_p;
    
    /* One pass of quicksort. */
    while ( i < j ) {
        while ( i < N && ind[i] <= pivot )
            i++;
        while ( j >= 0 && ind[j] > pivot )
            j--;
        if ( i < j ) {
            temp_i = ind[i]; ind[i] = ind[j]; ind[j] = temp_i;
            temp_p = parts[i]; parts[i] = parts[j]; parts[j] = temp_p;
            }
        }
        
    /* Verify sort. */
    for ( int k = 0 ; k <= j ; k++ )
        if ( ind[k] > pivot ) {
            printf( "parts_sort: sorting failed at k=%i, ind[k]=%i, pivot=%i, i=%i, j=%i, N=%i.\n" , k , ind[k] , pivot , i , j , N );
            error( "Sorting failed (<=pivot)." );
            }
    for ( int k = j+1 ; k < N ; k++ )
        if ( ind[k] <= pivot ) {
            printf( "parts_sort: sorting failed at k=%i, ind[k]=%i, pivot=%i, i=%i, j=%i, N=%i.\n" , k , ind[k] , pivot , i , j , N );
            error( "Sorting failed (>pivot)." );
            }
        
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    /* Try to recurse in parallel. */
    if ( N < 100 ) {
    
        /* Recurse on the left? */
        if ( j > 0 && pivot > min )
            parts_sort( parts , ind , j+1 , min , pivot );

        /* Recurse on the right? */
        if ( i < N && pivot+1 < max )
            parts_sort( &parts[i], &ind[i], N-i , pivot+1 , max );

        }
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    else
    #pragma omp parallel sections
    {
    
        /* Recurse on the left? */
        #pragma omp section
        if ( j > 0 && pivot > min )
            parts_sort( parts , ind , j+1 , min , pivot );

        /* Recurse on the right? */
        #pragma omp section
        if ( i < N && pivot+1 < max )
            parts_sort( &parts[i], &ind[i], N-i , pivot+1 , max );
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        }
    
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    }


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/**
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 * @brief Mapping function to free the sorted indices buffers.
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 */

void space_map_clearsort ( struct cell *c , void *data ) {

    if ( c->sort != NULL ) {
        free( c->sort );
        c->sort = NULL;
        }

    }


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/**
 * @brief Mapping function to append a ghost task to each cell.
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 *
 * Looks for the super cell, e.g. the highest-level cell above each
 * cell for which a pair is defined. All ghosts below this cell will
 * depend on the ghost of their parents (sounds spooky, but it isn't).
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 */

void space_map_mkghosts ( struct cell *c , void *data ) {

    struct space *s = (struct space *)data;
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    struct cell *finger;
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    /* Find the super cell, i.e. the highest cell hierarchically above
       this one to still have at least one task associated with it. */
    c->super = c;
    for ( finger = c->parent ; finger != NULL ; finger = finger->parent )
        if ( finger->nr_tasks > 0 )
            c->super = finger;
            
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    /* Make the ghost task */
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    if ( c->super != c || c->nr_tasks > 0 )
        c->ghost = space_addtask( s , task_type_ghost , task_subtype_none , 0 , 0 , c , NULL , NULL , 0 , NULL , 0 );

    /* If we are not the super cell ourselves, make our ghost depend
       on our parent cell. */
    if ( c->super != c )
        task_addunlock( c->parent->ghost , c->ghost );
    
    }


/**
 * @brief Mapping function to clear the number of tasks in each cell.
 */

void space_map_clearnrtasks ( struct cell *c , void *data ) {

    c->nr_tasks = 0;
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    c->nr_density = 0;
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    }


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/**
 * @brief Map a function to all particles in a aspace.
 *
 * @param s The #space we are working in.
 */
 
void space_map_parts ( struct space *s , void (*fun)( struct part *p , struct cell *c , void *data ) , void *data ) {

    int i;

    void rec_map ( struct cell *c ) {
    
        int k;
        
        /* No progeny? */
        if ( !c->split )
            for ( k = 0 ; k < c->count ; k++ )
                fun( &c->parts[k] , c , data );
                
        /* Otherwise, recurse. */
        else
            for ( k = 0 ; k < 8 ; k++ )
                if ( c->progeny[k] != NULL )
                    rec_map( c->progeny[k] );
                
        }
        
    /* Call the recursive function on all higher-level cells. */
    for ( i = 0 ; i < s->nr_cells ; i++ )
        rec_map( &s->cells[i] );

    }


/**
 * @brief Map a function to all particles in a aspace.
 *
 * @param s The #space we are working in.
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 * @param full Map to all cells, including cells with sub-cells.
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 */
 
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void space_map_cells ( struct space *s , int full , void (*fun)( struct cell *c , void *data ) , void *data ) {
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    int i;

    void rec_map ( struct cell *c ) {
    
        int k;
        
        /* No progeny? */
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        if ( full || !c->split )
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            fun( c , data );
                
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        /* Recurse. */
        if ( c->split )
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            for ( k = 0 ; k < 8 ; k++ )
                if ( c->progeny[k] != NULL )
                    rec_map( c->progeny[k] );
                
        }
        
    /* Call the recursive function on all higher-level cells. */
    for ( i = 0 ; i < s->nr_cells ; i++ )
        rec_map( &s->cells[i] );

    }


/**
 * @brief Add a #task to the #space.
 *
 * @param s The #space we are working in.
 */
 
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struct task *space_addtask ( struct space *s , int type , int subtype , int flags , int wait , struct cell *ci , struct cell *cj , struct task *unlock_tasks[] , int nr_unlock_tasks , struct cell *unlock_cells[] , int nr_unlock_cells ) {
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    struct task *t;
    
    /* Lock the space. */
    lock_lock( &s->lock );
    
    /* Get the next free task. */
    t = &s->tasks[ s->nr_tasks ];
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    /* Copy the data. */
    t->type = type;
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    t->subtype = subtype;
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    t->flags = flags;
    t->wait = wait;
    t->ci = ci;
    t->cj = cj;
    if ( unlock_tasks != NULL )
        memcpy( t->unlock_tasks , unlock_tasks , sizeof(struct task *) * nr_unlock_tasks );
    t->nr_unlock_tasks = nr_unlock_tasks;
    if ( unlock_cells != NULL )
        memcpy( t->unlock_cells , unlock_cells , sizeof(struct task *) * nr_unlock_cells );
    t->nr_unlock_cells = nr_unlock_cells;
    
    /* Increase the task counter. */
    s->nr_tasks += 1;
    
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    /* Unock the space. */
    lock_unlock_blind( &s->lock );
    
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    /* Return a pointer to the new task. */
    return t;

    }



/**
 * @brief Split tasks that may be too large.
 *
 * @param s The #space we are working in.
 */
 
void space_splittasks ( struct space *s ) {

    int k, sid, tid;
    struct cell *ci, *cj;
    double hi, hj, shift[3];
    struct task *t;

    /* Loop through the tasks... */
    for ( tid = 0 ; tid < s->nr_tasks ; tid++ ) {
    
        /* Get a pointer on the task. */
        t = &s->tasks[tid];
    
        /* If this task isn't a pair, i'm not interested. */
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        if ( t->type != task_type_pair )
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            continue;
            
        /* Get a handle on the cells involved. */
        ci = t->ci;
        cj = t->cj;
        hi = fmax( ci->h[0] , fmax( ci->h[1] , ci->h[2] ) );
        hj = fmax( cj->h[0] , fmax( cj->h[1] , cj->h[2] ) );
            
        /* Should this task be split-up? */
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        if ( ci->split && cj->split && ci->h_max*space_stretch < hi/2 && cj->h_max*space_stretch < hj/2 ) {
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            /* Get the relative distance between the pairs, wrapping. */
            for ( k = 0 ; k < 3 ; k++ ) {
                if ( cj->loc[k] - ci->loc[k] < -s->dim[k]/2 )
                    shift[k] = s->dim[k];
                else if ( cj->loc[k] - ci->loc[k] > s->dim[k]/2 )
                    shift[k] = -s->dim[k];
                else
                    shift[k] = 0.0;
                }

            /* Get the sorting index. */
            for ( sid = 0 , k = 0 ; k < 3 ; k++ )
                sid = 3*sid + ( (cj->loc[k] - ci->loc[k] + shift[k] < 0) ? 0 : (cj->loc[k] - ci->loc[k] + shift[k] > 0) ? 2 : 1 );

            /* Flip? */
            if ( sid < 13 ) {
                cj = t->ci;
                ci = t->cj;
                t->ci = ci; t->cj = cj;
                }
            else
                sid = 26 - sid;
                
            /* Remove the dependency of this task on the sorts of ci and cj. */
            task_rmunlock( ci->sorts[sid] , t );
            task_rmunlock( cj->sorts[sid] , t );
            ci->nr_pairs -= 1;
            cj->nr_pairs -= 1;
            t->nr_unlock_cells = 0;
                
            /* For each different sorting type... */
            switch ( sid ) {
            
                case 0: /* (  1 ,  1 ,  1 ) */
                    t->ci = ci->progeny[7]; t->cj = cj->progeny[0];
                    task_addunlock( ci->progeny[7]->sorts[0] , t ); task_addunlock( cj->progeny[0]->sorts[0] , t );
                    ci->progeny[7]->nr_pairs += 1;
                    cj->progeny[0]->nr_pairs += 1;
                    break;
                    
                case 1: /* (  1 ,  1 ,  0 ) */
                    if ( space_dosub &&
                         !ci->progeny[6]->split && !ci->progeny[7]->split &&
                         !cj->progeny[0]->split && !cj->progeny[1]->split ) {
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                        t->type = task_type_sub; t->flags = 1;
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                        task_addunlock( ci->progeny[6]->sorts[1] , t ); task_addunlock( cj->progeny[0]->sorts[1] , t );
                        task_addunlock( ci->progeny[7]->sorts[1] , t ); task_addunlock( cj->progeny[1]->sorts[1] , t );
                        task_addunlock( ci->progeny[6]->sorts[0] , t ); task_addunlock( cj->progeny[1]->sorts[0] , t );
                        task_addunlock( ci->progeny[7]->sorts[2] , t ); task_addunlock( cj->progeny[0]->sorts[2] , t );
                        }
                    else {
                        t->ci = ci->progeny[6]; t->cj = cj->progeny[0];
                        task_addunlock( ci->progeny[6]->sorts[1] , t ); task_addunlock( cj->progeny[0]->sorts[1] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[7] , cj->progeny[1] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[7]->sorts[1] , t ); task_addunlock( cj->progeny[1]->sorts[1] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[6] , cj->progeny[1] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[6]->sorts[0] , t ); task_addunlock( cj->progeny[1]->sorts[0] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[7] , cj->progeny[0] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[7]->sorts[2] , t ); task_addunlock( cj->progeny[0]->sorts[2] , t );
                        }
                    ci->progeny[6]->nr_pairs += 2;
                    ci->progeny[7]->nr_pairs += 2;
                    cj->progeny[0]->nr_pairs += 2;
                    cj->progeny[1]->nr_pairs += 2;
                    break;
                    
                case 2: /* (  1 ,  1 , -1 ) */
                    t->ci = ci->progeny[6]; t->cj = cj->progeny[1];
                    task_addunlock( ci->progeny[6]->sorts[2] , t ); task_addunlock( cj->progeny[1]->sorts[2] , t );
                    ci->progeny[6]->nr_pairs += 1;
                    cj->progeny[1]->nr_pairs += 1;
                    break;
                    
                case 3: /* (  1 ,  0 ,  1 ) */
                    if ( space_dosub &&
                         !ci->progeny[5]->split && !ci->progeny[7]->split &&
                         !cj->progeny[0]->split && !cj->progeny[2]->split ) {
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                        t->type = task_type_sub; t->flags = 3;
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                        task_addunlock( ci->progeny[5]->sorts[3] , t ); task_addunlock( cj->progeny[0]->sorts[3] , t );
                        task_addunlock( ci->progeny[7]->sorts[3] , t ); task_addunlock( cj->progeny[2]->sorts[3] , t );
                        task_addunlock( ci->progeny[5]->sorts[0] , t ); task_addunlock( cj->progeny[2]->sorts[0] , t );
                        task_addunlock( ci->progeny[7]->sorts[6] , t ); task_addunlock( cj->progeny[0]->sorts[6] , t );
                        }
                    else {
                        t->ci = ci->progeny[5]; t->cj = cj->progeny[0];
                        task_addunlock( ci->progeny[5]->sorts[3] , t ); task_addunlock( cj->progeny[0]->sorts[3] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[7] , cj->progeny[2] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[7]->sorts[3] , t ); task_addunlock( cj->progeny[2]->sorts[3] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[5] , cj->progeny[2] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[5]->sorts[0] , t ); task_addunlock( cj->progeny[2]->sorts[0] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[7] , cj->progeny[0] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[7]->sorts[6] , t ); task_addunlock( cj->progeny[0]->sorts[6] , t );
                        }
                    ci->progeny[5]->nr_pairs += 2;
                    ci->progeny[7]->nr_pairs += 2;
                    cj->progeny[0]->nr_pairs += 2;
                    cj->progeny[2]->nr_pairs += 2;
                    break;
                    
                case 4: /* (  1 ,  0 ,  0 ) */
                    if ( space_dosub &&
                         !ci->progeny[4]->split && !ci->progeny[5]->split && !ci->progeny[6]->split && !ci->progeny[7]->split &&
                         !cj->progeny[0]->split && !cj->progeny[1]->split && !cj->progeny[2]->split && !cj->progeny[3]->split ) {
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                        t->type = task_type_sub; t->flags = 4;
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                        task_addunlock( ci->progeny[4]->sorts[4] , t ); task_addunlock( cj->progeny[0]->sorts[4] , t );
                        task_addunlock( ci->progeny[5]->sorts[5] , t ); task_addunlock( cj->progeny[0]->sorts[5] , t );
                        task_addunlock( ci->progeny[6]->sorts[7] , t ); task_addunlock( cj->progeny[0]->sorts[7] , t );
                        task_addunlock( ci->progeny[7]->sorts[8] , t ); task_addunlock( cj->progeny[0]->sorts[8] , t );
                        task_addunlock( ci->progeny[4]->sorts[3] , t ); task_addunlock( cj->progeny[1]->sorts[3] , t );
                        task_addunlock( ci->progeny[5]->sorts[4] , t ); task_addunlock( cj->progeny[1]->sorts[4] , t );
                        task_addunlock( ci->progeny[6]->sorts[6] , t ); task_addunlock( cj->progeny[1]->sorts[6] , t );
                        task_addunlock( ci->progeny[7]->sorts[7] , t ); task_addunlock( cj->progeny[1]->sorts[7] , t );
                        task_addunlock( ci->progeny[4]->sorts[1] , t ); task_addunlock( cj->progeny[2]->sorts[1] , t );
                        task_addunlock( ci->progeny[5]->sorts[2] , t ); task_addunlock( cj->progeny[2]->sorts[2] , t );
                        task_addunlock( ci->progeny[6]->sorts[4] , t ); task_addunlock( cj->progeny[2]->sorts[4] , t );
                        task_addunlock( ci->progeny[7]->sorts[5] , t ); task_addunlock( cj->progeny[2]->sorts[5] , t );
                        task_addunlock( ci->progeny[4]->sorts[0] , t ); task_addunlock( cj->progeny[3]->sorts[0] , t );
                        task_addunlock( ci->progeny[5]->sorts[1] , t ); task_addunlock( cj->progeny[3]->sorts[1] , t );
                        task_addunlock( ci->progeny[6]->sorts[3] , t ); task_addunlock( cj->progeny[3]->sorts[3] , t );
                        task_addunlock( ci->progeny[7]->sorts[4] , t ); task_addunlock( cj->progeny[3]->sorts[4] , t );
                        }
                    else {
                        t->ci = ci->progeny[4]; t->cj = cj->progeny[0];
                        task_addunlock( ci->progeny[4]->sorts[4] , t ); task_addunlock( cj->progeny[0]->sorts[4] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[5] , cj->progeny[0] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[5]->sorts[5] , t ); task_addunlock( cj->progeny[0]->sorts[5] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[6] , cj->progeny[0] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[6]->sorts[7] , t ); task_addunlock( cj->progeny[0]->sorts[7] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[7] , cj->progeny[0] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[7]->sorts[8] , t ); task_addunlock( cj->progeny[0]->sorts[8] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[4] , cj->progeny[1] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[4]->sorts[3] , t ); task_addunlock( cj->progeny[1]->sorts[3] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[5] , cj->progeny[1] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[5]->sorts[4] , t ); task_addunlock( cj->progeny[1]->sorts[4] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[6] , cj->progeny[1] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[6]->sorts[6] , t ); task_addunlock( cj->progeny[1]->sorts[6] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[7] , cj->progeny[1] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[7]->sorts[7] , t ); task_addunlock( cj->progeny[1]->sorts[7] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[4] , cj->progeny[2] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[4]->sorts[1] , t ); task_addunlock( cj->progeny[2]->sorts[1] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[5] , cj->progeny[2] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[5]->sorts[2] , t ); task_addunlock( cj->progeny[2]->sorts[2] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[6] , cj->progeny[2] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[6]->sorts[4] , t ); task_addunlock( cj->progeny[2]->sorts[4] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[7] , cj->progeny[2] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[7]->sorts[5] , t ); task_addunlock( cj->progeny[2]->sorts[5] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[4] , cj->progeny[3] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[4]->sorts[0] , t ); task_addunlock( cj->progeny[3]->sorts[0] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[5] , cj->progeny[3] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[5]->sorts[1] , t ); task_addunlock( cj->progeny[3]->sorts[1] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[6] , cj->progeny[3] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[6]->sorts[3] , t ); task_addunlock( cj->progeny[3]->sorts[3] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[7] , cj->progeny[3] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[7]->sorts[4] , t ); task_addunlock( cj->progeny[3]->sorts[4] , t );
                        }
                    ci->progeny[4]->nr_pairs += 4;
                    ci->progeny[5]->nr_pairs += 4;
                    ci->progeny[6]->nr_pairs += 4;
                    ci->progeny[7]->nr_pairs += 4;
                    cj->progeny[0]->nr_pairs += 4;
                    cj->progeny[1]->nr_pairs += 4;
                    cj->progeny[2]->nr_pairs += 4;
                    cj->progeny[3]->nr_pairs += 4;
                    break;
                    
                case 5: /* (  1 ,  0 , -1 ) */
                    if ( space_dosub &&
                         !ci->progeny[4]->split && !ci->progeny[6]->split &&
                         !cj->progeny[1]->split && !cj->progeny[3]->split ) {
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                        t->type = task_type_sub; t->flags = 5;
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                        task_addunlock( ci->progeny[4]->sorts[5] , t ); task_addunlock( cj->progeny[1]->sorts[5] , t );
                        task_addunlock( ci->progeny[6]->sorts[5] , t ); task_addunlock( cj->progeny[3]->sorts[5] , t );
                        task_addunlock( ci->progeny[4]->sorts[2] , t ); task_addunlock( cj->progeny[3]->sorts[2] , t );
                        task_addunlock( ci->progeny[6]->sorts[8] , t ); task_addunlock( cj->progeny[1]->sorts[8] , t );
                        }
                    else {
                        t->ci = ci->progeny[4]; t->cj = cj->progeny[1];
                        task_addunlock( ci->progeny[4]->sorts[5] , t ); task_addunlock( cj->progeny[1]->sorts[5] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[6] , cj->progeny[3] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[6]->sorts[5] , t ); task_addunlock( cj->progeny[3]->sorts[5] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[4] , cj->progeny[3] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[4]->sorts[2] , t ); task_addunlock( cj->progeny[3]->sorts[2] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[6] , cj->progeny[1] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[6]->sorts[8] , t ); task_addunlock( cj->progeny[1]->sorts[8] , t );
                        }
                    ci->progeny[4]->nr_pairs += 2;
                    ci->progeny[6]->nr_pairs += 2;
                    cj->progeny[1]->nr_pairs += 2;
                    cj->progeny[3]->nr_pairs += 2;
                    break;
                    
                case 6: /* (  1 , -1 ,  1 ) */
                    t->ci = ci->progeny[5]; t->cj = cj->progeny[2];
                    task_addunlock( ci->progeny[5]->sorts[6] , t ); task_addunlock( cj->progeny[2]->sorts[6] , t );
                    ci->progeny[5]->nr_pairs += 1;
                    cj->progeny[2]->nr_pairs += 1;
                    break;
                    
                case 7: /* (  1 , -1 ,  0 ) */
                    if ( space_dosub &&
                         !ci->progeny[4]->split && !ci->progeny[5]->split &&
                         !cj->progeny[2]->split && !cj->progeny[3]->split ) {
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                        t->type = task_type_sub; t->flags = 7;
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                        task_addunlock( ci->progeny[4]->sorts[6] , t ); task_addunlock( cj->progeny[3]->sorts[6] , t );
                        task_addunlock( ci->progeny[5]->sorts[8] , t ); task_addunlock( cj->progeny[2]->sorts[8] , t );
                        task_addunlock( ci->progeny[4]->sorts[7] , t ); task_addunlock( cj->progeny[2]->sorts[7] , t );
                        task_addunlock( ci->progeny[5]->sorts[7] , t ); task_addunlock( cj->progeny[3]->sorts[7] , t );
                        }
                    else {
                        t->ci = ci->progeny[4]; t->cj = cj->progeny[3];
                        task_addunlock( ci->progeny[4]->sorts[6] , t ); task_addunlock( cj->progeny[3]->sorts[6] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[5] , cj->progeny[2] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[5]->sorts[8] , t ); task_addunlock( cj->progeny[2]->sorts[8] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[4] , cj->progeny[2] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[4]->sorts[7] , t ); task_addunlock( cj->progeny[2]->sorts[7] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[5] , cj->progeny[3] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[5]->sorts[7] , t ); task_addunlock( cj->progeny[3]->sorts[7] , t );
                        }
                    ci->progeny[4]->nr_pairs += 2;
                    ci->progeny[5]->nr_pairs += 2;
                    cj->progeny[2]->nr_pairs += 2;
                    cj->progeny[3]->nr_pairs += 2;
                    break;
                    
                case 8: /* (  1 , -1 , -1 ) */
                    t->ci = ci->progeny[4]; t->cj = cj->progeny[3];
                    task_addunlock( ci->progeny[4]->sorts[8] , t ); task_addunlock( cj->progeny[3]->sorts[8] , t );
                    ci->progeny[4]->nr_pairs += 1;
                    cj->progeny[3]->nr_pairs += 1;
                    break;
                    
                case 9: /* (  0 ,  1 ,  1 ) */
                    if ( space_dosub &&
                         !ci->progeny[3]->split && !ci->progeny[7]->split &&
                         !cj->progeny[0]->split && !cj->progeny[4]->split ) {
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                        t->type = task_type_sub; t->flags = 9;
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                        task_addunlock( ci->progeny[3]->sorts[9] , t ); task_addunlock( cj->progeny[0]->sorts[9] , t );
                        task_addunlock( ci->progeny[7]->sorts[9] , t ); task_addunlock( cj->progeny[4]->sorts[9] , t );
                        task_addunlock( ci->progeny[3]->sorts[0] , t ); task_addunlock( cj->progeny[4]->sorts[0] , t );
                        task_addunlock( ci->progeny[7]->sorts[8] , t ); task_addunlock( cj->progeny[0]->sorts[8] , t );
                        }
                    else {
                        t->ci = ci->progeny[3]; t->cj = cj->progeny[0];
                        task_addunlock( ci->progeny[3]->sorts[9] , t ); task_addunlock( cj->progeny[0]->sorts[9] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[7] , cj->progeny[4] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[7]->sorts[9] , t ); task_addunlock( cj->progeny[4]->sorts[9] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[3] , cj->progeny[4] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[3]->sorts[0] , t ); task_addunlock( cj->progeny[4]->sorts[0] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[7] , cj->progeny[0] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[7]->sorts[8] , t ); task_addunlock( cj->progeny[0]->sorts[8] , t );
                        }
                    ci->progeny[3]->nr_pairs += 2;
                    ci->progeny[7]->nr_pairs += 2;
                    cj->progeny[0]->nr_pairs += 2;
                    cj->progeny[4]->nr_pairs += 2;
                    break;
                    
                case 10: /* (  0 ,  1 ,  0 ) */
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                    if ( space_dosub &&
                         !ci->progeny[2]->split && !ci->progeny[3]->split && !ci->progeny[6]->split && !ci->progeny[7]->split &&
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                         !cj->progeny[0]->split && !cj->progeny[1]->split && !cj->progeny[4]->split && !cj->progeny[5]->split ) {
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                        t->type = task_type_sub; t->flags = 10;
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                        task_addunlock( ci->progeny[2]->sorts[10] , t ); task_addunlock( cj->progeny[0]->sorts[10] , t );
                        task_addunlock( ci->progeny[3]->sorts[11] , t ); task_addunlock( cj->progeny[0]->sorts[11] , t );
                        task_addunlock( ci->progeny[6]->sorts[7] , t ); task_addunlock( cj->progeny[0]->sorts[7] , t );
                        task_addunlock( ci->progeny[7]->sorts[6] , t ); task_addunlock( cj->progeny[0]->sorts[6] , t );
                        task_addunlock( ci->progeny[2]->sorts[9] , t ); task_addunlock( cj->progeny[1]->sorts[9] , t );
                        task_addunlock( ci->progeny[3]->sorts[10] , t ); task_addunlock( cj->progeny[1]->sorts[10] , t );
                        task_addunlock( ci->progeny[6]->sorts[8] , t ); task_addunlock( cj->progeny[1]->sorts[8] , t );
                        task_addunlock( ci->progeny[7]->sorts[7] , t ); task_addunlock( cj->progeny[1]->sorts[7] , t );
                        task_addunlock( ci->progeny[2]->sorts[1] , t ); task_addunlock( cj->progeny[4]->sorts[1] , t );
                        task_addunlock( ci->progeny[3]->sorts[2] , t ); task_addunlock( cj->progeny[4]->sorts[2] , t );
                        task_addunlock( ci->progeny[6]->sorts[10] , t ); task_addunlock( cj->progeny[4]->sorts[10] , t );
                        task_addunlock( ci->progeny[7]->sorts[11] , t ); task_addunlock( cj->progeny[4]->sorts[11] , t );
                        task_addunlock( ci->progeny[2]->sorts[0] , t ); task_addunlock( cj->progeny[5]->sorts[0] , t );
                        task_addunlock( ci->progeny[3]->sorts[1] , t ); task_addunlock( cj->progeny[5]->sorts[1] , t );
                        task_addunlock( ci->progeny[6]->sorts[9] , t ); task_addunlock( cj->progeny[5]->sorts[9] , t );
                        task_addunlock( ci->progeny[7]->sorts[10] , t ); task_addunlock( cj->progeny[5]->sorts[10] , t );
                        }
                    else {
                        t->ci = ci->progeny[2]; t->cj = cj->progeny[0];
                        task_addunlock( ci->progeny[2]->sorts[10] , t ); task_addunlock( cj->progeny[0]->sorts[10] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[3] , cj->progeny[0] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[3]->sorts[11] , t ); task_addunlock( cj->progeny[0]->sorts[11] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[6] , cj->progeny[0] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[6]->sorts[7] , t ); task_addunlock( cj->progeny[0]->sorts[7] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[7] , cj->progeny[0] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[7]->sorts[6] , t ); task_addunlock( cj->progeny[0]->sorts[6] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[2] , cj->progeny[1] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[2]->sorts[9] , t ); task_addunlock( cj->progeny[1]->sorts[9] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[3] , cj->progeny[1] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[3]->sorts[10] , t ); task_addunlock( cj->progeny[1]->sorts[10] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[6] , cj->progeny[1] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[6]->sorts[8] , t ); task_addunlock( cj->progeny[1]->sorts[8] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[7] , cj->progeny[1] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[7]->sorts[7] , t ); task_addunlock( cj->progeny[1]->sorts[7] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[2] , cj->progeny[4] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[2]->sorts[1] , t ); task_addunlock( cj->progeny[4]->sorts[1] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[3] , cj->progeny[4] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[3]->sorts[2] , t ); task_addunlock( cj->progeny[4]->sorts[2] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[6] , cj->progeny[4] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[6]->sorts[10] , t ); task_addunlock( cj->progeny[4]->sorts[10] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[7] , cj->progeny[4] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[7]->sorts[11] , t ); task_addunlock( cj->progeny[4]->sorts[11] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[2] , cj->progeny[5] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[2]->sorts[0] , t ); task_addunlock( cj->progeny[5]->sorts[0] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[3] , cj->progeny[5] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[3]->sorts[1] , t ); task_addunlock( cj->progeny[5]->sorts[1] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[6] , cj->progeny[5] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[6]->sorts[9] , t ); task_addunlock( cj->progeny[5]->sorts[9] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[7] , cj->progeny[5] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[7]->sorts[10] , t ); task_addunlock( cj->progeny[5]->sorts[10] , t );
                        }
                    ci->progeny[2]->nr_pairs += 4;
                    ci->progeny[3]->nr_pairs += 4;
                    ci->progeny[6]->nr_pairs += 4;
                    ci->progeny[7]->nr_pairs += 4;
                    cj->progeny[0]->nr_pairs += 4;
                    cj->progeny[1]->nr_pairs += 4;
                    cj->progeny[4]->nr_pairs += 4;
                    cj->progeny[5]->nr_pairs += 4;
                    break;
                    
                case 11: /* (  0 ,  1 , -1 ) */
                    if ( space_dosub &&
                         !ci->progeny[2]->split && !ci->progeny[6]->split &&
                         !cj->progeny[1]->split && !cj->progeny[5]->split ) {
908
                        t->type = task_type_sub; t->flags = 11;
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                        task_addunlock( ci->progeny[2]->sorts[11] , t ); task_addunlock( cj->progeny[1]->sorts[11] , t );
                        task_addunlock( ci->progeny[6]->sorts[11] , t ); task_addunlock( cj->progeny[5]->sorts[11] , t );
                        task_addunlock( ci->progeny[2]->sorts[2] , t ); task_addunlock( cj->progeny[5]->sorts[2] , t );
                        task_addunlock( ci->progeny[6]->sorts[6] , t ); task_addunlock( cj->progeny[1]->sorts[6] , t );
                        }
                    else {
                        t->ci = ci->progeny[2]; t->cj = cj->progeny[1];
                        task_addunlock( ci->progeny[2]->sorts[11] , t ); task_addunlock( cj->progeny[1]->sorts[11] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[6] , cj->progeny[5] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[6]->sorts[11] , t ); task_addunlock( cj->progeny[5]->sorts[11] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[2] , cj->progeny[5] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[2]->sorts[2] , t ); task_addunlock( cj->progeny[5]->sorts[2] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[6] , cj->progeny[1] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[6]->sorts[6] , t ); task_addunlock( cj->progeny[1]->sorts[6] , t );
                        }
                    ci->progeny[2]->nr_pairs += 2;
                    ci->progeny[6]->nr_pairs += 2;
                    cj->progeny[1]->nr_pairs += 2;
                    cj->progeny[5]->nr_pairs += 2;
                    break;
                    
                case 12: /* (  0 ,  0 ,  1 ) */
                    if ( space_dosub &&
                         !ci->progeny[1]->split && !ci->progeny[3]->split && !ci->progeny[5]->split && !ci->progeny[7]->split &&
                         !cj->progeny[0]->split && !cj->progeny[2]->split && !cj->progeny[4]->split && !cj->progeny[6]->split ) {
934
                        t->type = task_type_sub; t->flags = 12;
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                        task_addunlock( ci->progeny[1]->sorts[12] , t ); task_addunlock( cj->progeny[0]->sorts[12] , t );
                        task_addunlock( ci->progeny[3]->sorts[11] , t ); task_addunlock( cj->progeny[0]->sorts[11] , t );
                        task_addunlock( ci->progeny[5]->sorts[5] , t ); task_addunlock( cj->progeny[0]->sorts[5] , t );
                        task_addunlock( ci->progeny[7]->sorts[2] , t ); task_addunlock( cj->progeny[0]->sorts[2] , t );
                        task_addunlock( ci->progeny[1]->sorts[9] , t ); task_addunlock( cj->progeny[2]->sorts[9] , t );
                        task_addunlock( ci->progeny[3]->sorts[12] , t ); task_addunlock( cj->progeny[2]->sorts[12] , t );
                        task_addunlock( ci->progeny[5]->sorts[8] , t ); task_addunlock( cj->progeny[2]->sorts[8] , t );
                        task_addunlock( ci->progeny[7]->sorts[5] , t ); task_addunlock( cj->progeny[2]->sorts[5] , t );
                        task_addunlock( ci->progeny[1]->sorts[3] , t ); task_addunlock( cj->progeny[4]->sorts[3] , t );
                        task_addunlock( ci->progeny[3]->sorts[6] , t ); task_addunlock( cj->progeny[4]->sorts[6] , t );
                        task_addunlock( ci->progeny[5]->sorts[12] , t ); task_addunlock( cj->progeny[4]->sorts[12] , t );
                        task_addunlock( ci->progeny[7]->sorts[11] , t ); task_addunlock( cj->progeny[4]->sorts[11] , t );
                        task_addunlock( ci->progeny[1]->sorts[0] , t ); task_addunlock( cj->progeny[6]->sorts[0] , t );
                        task_addunlock( ci->progeny[3]->sorts[3] , t ); task_addunlock( cj->progeny[6]->sorts[3] , t );
                        task_addunlock( ci->progeny[5]->sorts[9] , t ); task_addunlock( cj->progeny[6]->sorts[9] , t );
                        task_addunlock( ci->progeny[7]->sorts[12] , t ); task_addunlock( cj->progeny[6]->sorts[12] , t );
                        }
                    else {
                        t->ci = ci->progeny[1]; t->cj = cj->progeny[0];
                        task_addunlock( ci->progeny[1]->sorts[12] , t ); task_addunlock( cj->progeny[0]->sorts[12] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[3] , cj->progeny[0] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[3]->sorts[11] , t ); task_addunlock( cj->progeny[0]->sorts[11] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[5] , cj->progeny[0] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[5]->sorts[5] , t ); task_addunlock( cj->progeny[0]->sorts[5] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[7] , cj->progeny[0] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[7]->sorts[2] , t ); task_addunlock( cj->progeny[0]->sorts[2] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[1] , cj->progeny[2] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[1]->sorts[9] , t ); task_addunlock( cj->progeny[2]->sorts[9] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[3] , cj->progeny[2] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[3]->sorts[12] , t ); task_addunlock( cj->progeny[2]->sorts[12] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[5] , cj->progeny[2] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[5]->sorts[8] , t ); task_addunlock( cj->progeny[2]->sorts[8] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[7] , cj->progeny[2] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[7]->sorts[5] , t ); task_addunlock( cj->progeny[2]->sorts[5] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[1] , cj->progeny[4] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[1]->sorts[3] , t ); task_addunlock( cj->progeny[4]->sorts[3] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[3] , cj->progeny[4] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[3]->sorts[6] , t ); task_addunlock( cj->progeny[4]->sorts[6] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[5] , cj->progeny[4] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[5]->sorts[12] , t ); task_addunlock( cj->progeny[4]->sorts[12] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[7] , cj->progeny[4] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[7]->sorts[11] , t ); task_addunlock( cj->progeny[4]->sorts[11] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[1] , cj->progeny[6] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[1]->sorts[0] , t ); task_addunlock( cj->progeny[6]->sorts[0] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[3] , cj->progeny[6] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[3]->sorts[3] , t ); task_addunlock( cj->progeny[6]->sorts[3] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[5] , cj->progeny[6] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[5]->sorts[9] , t ); task_addunlock( cj->progeny[6]->sorts[9] , t );
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                        t = space_addtask( s , task_type_pair , t->subtype , 0 , 0 , ci->progeny[7] , cj->progeny[6] , NULL , 0 , NULL , 0 );
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                        task_addunlock( ci->progeny[7]->sorts[12] , t ); task_addunlock( cj->progeny[6]->sorts[12] , t );
                        }
                    ci->progeny[1]->nr_pairs += 4;
                    ci->progeny[3]->nr_pairs += 4;
                    ci->progeny[5]->nr_pairs += 4;
                    ci->progeny[7]->nr_pairs += 4;
                    cj->progeny[0]->nr_pairs += 4;
                    cj->progeny[2]->nr_pairs += 4;
                    cj->progeny[4]->nr_pairs += 4;
                    cj->progeny[6]->nr_pairs += 4;
                    break;
            
                }
                
            /* Take a step back... */
            tid -= 1;
            
            } /* split this task? */
    
        } /* loop over all tasks. */
        
    }
    
    
/**
 * @brief Fill the #space's task list.
 *
 * @param s The #space we are working in.
 * @param do_sort Flag to add sorting tasks to the list.
 */
 
void space_maketasks ( struct space *s , int do_sort ) {

    int i, j, k, ii, jj, kk, iii, jjj, kkk, cid, cjd;
    int *cdim = s->cdim;
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    struct task *t , *t2;
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    int pts[7][8] = { { -1 , 12 , 10 , 9 , 4 , 3 , 1 , 0 } ,
                      { -1 , -1 , 11 , 10 , 5 , 4 , 2 , 1 } ,
                      { -1 , -1 , -1 , 12 , 7 , 6 , 4 , 3 } , 
                      { -1 , -1 , -1 , -1 , 8 , 7 , 5 , 4 } ,
                      { -1 , -1 , -1 , -1 , -1 , 12 , 10 , 9 } ,
                      { -1 , -1 , -1 , -1 , -1 , -1 , 11 , 10 } ,
                      { -1 , -1 , -1 , -1 , -1 , -1 , -1 , 12 } };
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    int counts[task_type_count];
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    /* Recursive function to generate tasks in the cell tree. */
    void maketasks_rec ( struct cell *c , struct task *sort_up[] , int nr_sort_up , struct cell *parent ) {

        int j, k, nr_sort = 0;
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        struct task *sort[7], *t;
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        /* Clear the waits on this cell. */
        c->wait = 0;
        sort[0] = NULL;
        
        /* Start by generating the sort task. */
        if ( c->count > 0 ) {
        
            if ( do_sort ) {
                if ( c->count < 1000 ) {
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                    sort[0] = space_addtask( s , task_type_sort , task_subtype_none , 0x1fff , 0 , c , NULL , sort_up , nr_sort_up , NULL , 0 );
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                    for ( k = 0 ; k < 13 ; k++ )
                        c->sorts[k] = sort[0];
                    nr_sort = 1;
                    }
                else if ( c->count < 5000 ) {
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                    sort[0] = space_addtask( s , task_type_sort , task_subtype_none , 0x7f , 0 , c , NULL , sort_up , nr_sort_up , NULL , 0 );
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                    sort[1] = space_addtask( s , task_type_sort , task_subtype_none , 0x1f80 , 0 , c , NULL , sort_up , nr_sort_up , NULL , 0 );
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                    for ( k = 0 ; k < 7 ; k++ )
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                        c->sorts[k] = sort[0];
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                    for ( k = 7 ; k < 14 ; k++ )
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                        c->sorts[k] = sort[1];
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                    nr_sort = 2;
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                    }
                else {
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                    c->sorts[0] = c->sorts[1] = sort[0] = space_addtask( s , task_type_sort , task_subtype_none , 0x1 + 0x2 , 0 , c , NULL , sort_up , nr_sort_up , NULL , 0 );
                    c->sorts[2] = c->sorts[3] = sort[1] = space_addtask( s , task_type_sort , task_subtype_none , 0x4 + 0x8 , 0 , c , NULL , sort_up , nr_sort_up , NULL , 0 );
                    c->sorts[4] = c->sorts[5] = sort[2] = space_addtask( s , task_type_sort , task_subtype_none , 0x10 + 0x20 , 0 , c , NULL , sort_up , nr_sort_up , NULL , 0 );
                    c->sorts[6] = c->sorts[7] = sort[3] = space_addtask( s , task_type_sort , task_subtype_none , 0x40 + 0x80 , 0 , c , NULL , sort_up , nr_sort_up , NULL , 0 );
                    c->sorts[8] = c->sorts[9] = sort[4] = space_addtask( s , task_type_sort , task_subtype_none , 0x100 + 0x200 , 0 , c , NULL , sort_up , nr_sort_up , NULL , 0 );
                    c->sorts[10] = c->sorts[11] = sort[5] = space_addtask( s , task_type_sort , task_subtype_none , 0x400 + 0x800 , 0 , c , NULL , sort_up , nr_sort_up , NULL , 0 );
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                    c->sorts[12] = c->sorts[13] = sort[6] = space_addtask( s , task_type_sort , task_subtype_none , 0x1000 , 0 , c , NULL , sort_up , nr_sort_up , NULL , 0 );
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                    nr_sort = 7;
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                    }
                }

            /* Generate a self-interaction if not split. */
            if ( !c->split && c->count > 1 )
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                space_addtask( s , task_type_self , task_subtype_density , 0 , 0 , c , NULL , NULL , 0 , NULL , 0 );
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            }
            
        /* Otherwise, add the interactions between progeny. */
        if ( c->split ) {
        
            /* Recurse. */
            for ( k = 0 ; k < 8 ; k++ )
                if ( c->progeny[k] != NULL )
                    maketasks_rec( c->progeny[k] , sort , nr_sort , c );
                        
            /* Worth splitting into several tasks? */
            if ( !space_dosub || c->count > 2*space_splitsize ) {
            
                /* Make a task for each pair of progeny. */
                for ( j = 0 ; j < 8 ; j++ )
                    if ( c->progeny[j] != NULL && c->progeny[j]->count > 0 )
                        for ( k = j + 1 ; k < 8 ; k++ )
                            if ( c->progeny[k] != NULL && c->progeny[k]->count > 0 ) {
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                                t = space_addtask( s , task_type_pair , task_subtype_density , 0 , 0 , c->progeny[j] , c->progeny[k] , NULL , 0 , NULL , 0 );
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                                task_addunlock( c->progeny[j]->sorts[ pts[j][k] ] , t );
                                task_addunlock( c->progeny[k]->sorts[ pts[j][k] ] , t );
                                c->progeny[k]->nr_pairs += 1;
                                c->progeny[j]->nr_pairs += 1;
                                }
                                
                }
                
            /* Otherwise, dispatch as one large task. */
            else {
            
                /* Add the task. */
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                t = space_addtask( s , task_type_sub , task_subtype_density , 0 , 0 , c , NULL , NULL , 0 , NULL , 0 );
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                /* Make it depend on all the sorts of its progeny. */
                for ( k = 0 ; k < 8 ; k++ )
                    for ( j = 0 ; j < 13 ; j++ )
                        if ( c->progeny[k] != NULL )
                            task_addunlock( c->progeny[k]->sorts[j] , t );
            
                }

            }

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        } /* void maketasks_rec. */
        
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    /* Allocate the task-list, if needed. */
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    if ( s->tasks == NULL || s->tasks_size < s->tot_cells * 43 ) {
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        if ( s->tasks != NULL )
            free( s->tasks );
        if ( s->tasks_ind != NULL )
            free( s->tasks_ind );
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        s->tasks_size = s->tot_cells * 43;
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        if ( posix_memalign( (void *)&s->tasks , 64 , sizeof(struct task) * s->tasks_size ) != 0 )
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            error( "Failed to allocate task list." );
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        if ( ( s->tasks_ind = (int *)malloc( sizeof(int) * s->tasks_size ) ) == NULL )
            error( "Failed to allocate task indices." );
        }
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    s->nr_tasks = 0;
    
    /* Loop over the cells and get their sub-tasks. */
    for ( k = 0 ; k < s->nr_cells ; k++ )
        maketasks_rec( &s->cells[k] , NULL , 0 , NULL );

    /* Run through the highest level of cells and add pairs. */
    for ( i = 0 ; i < cdim[0] ; i++ )
        for ( j = 0 ; j < cdim[1] ; j++ )
            for ( k = 0 ; k < cdim[2] ; k++ ) {
                cid = cell_getid( cdim , i , j , k );
                if ( s->cells[cid].count == 0 )
                    continue;
                for ( ii = -1 ; ii < 2 ; ii++ ) {
                    iii = i + ii;
                    if ( !s->periodic && ( iii < 0 || iii >= cdim[0] ) )
                        continue;
                    iii = ( iii + cdim[0] ) % cdim[0];
                    for ( jj = -1 ; jj < 2 ; jj++ ) {
                        jjj = j + jj;
                        if ( !s->periodic && ( jjj < 0 || jjj >= cdim[1] ) )
                            continue;
                        jjj = ( jjj + cdim[1] ) % cdim[1];
                        for ( kk = -1 ; kk < 2 ; kk++ ) {
                            kkk = k + kk;
                            if ( !s->periodic && ( kkk < 0 || kkk >= cdim[2] ) )
                                continue;
                            kkk = ( kkk + cdim[2] ) % cdim[2];
                            cjd = cell_getid( cdim , iii , jjj , kkk );
                            if ( s->cells[cjd].count == 0 )
                                continue;
                            if ( cid >= cjd )
                                continue;
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                            t = space_addtask( s , task_type_pair , task_subtype_density , 0 , 0 , &s->cells[cid] , &s->cells[cjd] , NULL , 0 , NULL , 0 );
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                            task_addunlock( s->cells[cid].sorts[ sortlistID[ (kk+1) + 3*( (jj+1) + 3*(ii+1) ) ] ] , t );
                            task_addunlock( s->cells[cjd].sorts[ sortlistID[ (kk+1) + 3*( (jj+1) + 3*(ii+1) ) ] ] , t );
                            s->cells[cid].nr_pairs += 1;
                            s->cells[cjd].nr_pairs += 1;
                            }
                        }
                    }
                }

    /* Split the tasks. */
    space_splittasks( s );
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    /* Remove sort tasks with no dependencies. */
    for ( k = 0 ; k < s->nr_tasks ; k++ ) {
        t = &s->tasks[k];
        if ( t->type == task_type_sort && t->nr_unlock_tasks == 0 ) {
            if ( t->ci->split )
                for ( i = 0 ; i < 13 ; i++ )
                    if ( t->flags & ( 1 << i ) ) {
                        for ( j = 0 ; j < 8 ; j++ )
                            if ( t->ci->progeny[j] != NULL )
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                                task_rmunlock_blind( t->ci->progeny[j]->sorts[i] , t );
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                        t->ci->sorts[i] = NULL;
                        }
            t->type = task_type_none;
            }
        }
        
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    /* Count the number of tasks associated with each cell and
       store the density tasks in each cell. */
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    space_map_cells( s , 1 , &space_map_clearnrtasks , NULL );
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    for ( k = 0 ; k < s->nr_tasks ; k++ ) {
        t = &s->tasks[k];
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        if ( t->type == task_type_self ) {