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hilbert.cpp
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//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// Filename: hilbert.c
//
// Purpose: Hilbert and Linked-list utility procedures for BayeSys3.
//
// History: TreeSys.c 17 Apr 1996 - 31 Dec 2002
// Peano.c 10 Apr 2001 - 11 Jan 2003
// merged 1 Feb 2003
// Arith debug 28 Aug 2003
// Hilbert.c 14 Oct 2003
// 2 Dec 2003
//-----------------------------------------------------------------------------
/*
Copyright (c) 1996-2003 Maximum Entropy Data Consultants Ltd,
114c Milton Road, Cambridge CB4 1XE, England
This library 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 2.1 of the License, or (at your option) any later version.
This library 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
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
#include "license.txt"
*/
#include <stdlib.h>
#include "hilbert.h"
typedef Atom* pAtom; // Atom address
typedef Node* pNode; // Node address
// Internal prototypes
static void LinetoTranspose(coord_t*, coord_t*, int, int);
static void TransposetoLine(coord_t*, coord_t*, int, int);
static void TransposetoAxes(coord_t*, int, int);
static void AxestoTranspose(coord_t*, int, int);
static int ResetLink (pNode);
static void Balance (pNode);
// Internal macros
#undef CALLOC // allocates vector p[0:n-1] of type t
#define CALLOC(p,n,t) {p=NULL;\
if((n)>0&&!(p=(t*)calloc((size_t)(n),sizeof(t))))\
{CALLvalue=E_MALLOC;goto Exit;}/*printf("%p %d\n",p,(size_t)(n)*sizeof(t));*/}
#undef FREE // frees CALLOC or REALLOC or NULL vector p[0:*], sets p=NULL
#define FREE(p) {if(p){/*printf("%p -1\n",p);*/(void)free((void*)p);} p=NULL;}
#undef CALL // catches negative error codes
#define CALL(x) {if( (CALLvalue = (x)) < 0 ) goto Exit;}
//=============================================================================
// Composite-integer arithmetic library
//=============================================================================
//
// A composite-integer is a multi-word unsigned integer "Label" stored
// "big endian" in N conventional unsigned integers with [0] high.
// ___________________________________________________
// | | | | |
// | Label[0] | Label[1] | .... | Label[N-1] |
// |____________|____________|____________|____________|
// high low
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// Function: CmpLabel
//
// Purpose: Compare labels by generating
// +1 if u > v,
// sign(u - v) = 0 if u = v,
// -1 if u < v.
//
// History: John Skilling 12 Apr 2001
//-----------------------------------------------------------------------------
//
int CmpLabel( // O comparison
coord_t* u, // I composite integer ([0] high)
coord_t* v, // I composite integer ([0] high)
int Ndim) // I dimension
{
int j;
for ( j = 0; j < Ndim; j++ )
if ( u[j] < v[j] )
return -1;
else if ( u[j] > v[j] )
return 1;
return 0;
}
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// Function: AddLabel
//
// Purpose: Set w = u + v
//
// History: JS 28 Jan 2002, 31 Dec 2002
// Julian Center 28 Aug 2003 debug
//-----------------------------------------------------------------------------
//
void AddLabel(
coord_t* w, // O w = u + v [Ndim]
coord_t* u, // I can be overwritten [Ndim]
coord_t* v, // I must not be overwritten [Ndim]
int Ndim) // I dimension
{
int carry = 0;
int i;
for ( i = Ndim - 1; i >= 0; i-- )
{
w[i] = u[i] + v[i];
carry = carry ? (++w[i] <= v[i]) : (w[i] < v[i]);
}
}
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// Function: SubLabel
//
// Purpose: Set w = u - v
//
// History: JS 28 Jan 2002, 31 Dec 2002
// Julian Center 28 Aug 2003 debug
//-----------------------------------------------------------------------------
//
void SubLabel(
coord_t* w, // O w = u - v [Ndim]
coord_t* u, // I can be overwritten [Ndim]
coord_t* v, // I must not be overwritten [Ndim]
int Ndim) // I dimension
{
int carry = 0;
int i;
for ( i = Ndim - 1; i >= 0; i-- )
{
w[i] = u[i] - v[i];
carry = carry ? (--w[i] >= u[i]) : (w[i] > u[i]);
}
}
//=============================================================================
// Hilbert-curve (a space-filling Peano curve) library
//=============================================================================
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// Functions: LinetoAxes
// AxestoLine
//
// Purpose: Serial Hilbert length <----> multidimensional Axes position.
//
// Space = n-dimensional hypercube of side R = 2^b
// Number of cells = N = R^n = 2^(n*b)
//
// Line = serial number of cell along Hilbert curve through hypercube
// = extended integer of n*b bits ranging from 0 to N-1,
// stored as vector of n unsigned b-bit integers with [0] high.
//
// Axes = Geometrical position of cell
// = n b-bit integers representing coordinates.
//
// Example: side R = 16, dimension n = 2, number of cells = N = 256.
// Line = 9, stored in base-16 words as
// Line[0] = 0 (high), Line[1] = 9 (low),
// corresponds to position (2,3) as in diagram, stored as
// Axes[0] = 2, Axes[1] = 3.
//
// |
// 15 | @---@ @---@ @---@ @---@ @---@ @---@ @---@ @---@
// | | | | | | | | | | | | | | | | |
// | @ @---@ @ @ @---@ @ @ @---@ @ @ @---@ @
// | | | | | | | | |
// | @---@ @---@ @---@ @---@ @---@ @---@ @---@ @---@
// | | | | | | | | |
// | @---@ @---@---@---@ @---@ @---@ @---@---@---@ @---@
// | | | | |
// | @ @---@---@ @---@---@ @ @ @---@---@ @---@---@ @
// | | | | | | | | | | | | |
// Axes[1]| @---@ @---@ @---@ @---@ @---@ @---@ @---@ @---@
// | | | | |
// | @---@ @---@ @---@ @---@ @---@ @---@ @---@ @---@
// | | | | | | | | | | | | |
// | @ @---@---@ @---@---@ @---@ @---@---@ @---@---@ @
// | | |
// | @---@ @---@---@ @---@---@ @---@---@ @---@---@ @---@
// | | | | | | | | | | |
// | @---@ @---@ @---@ @---@ @---@ @---@ @---@ @---@
// | | | | | | |
// | @ @---@ @ @---@ @---@ @---@ @---@ @ @---@ @
// | | | | | | | | | | | | | | |
// | @---@ @---@ @ @---@---@ @---@---@ @ @---@ @---@
// | | |
// 3 | 5---6 9---@ @ @---@---@ @---@---@ @ @---@ @---@
// | | | | | | | | | | | | | | |
// 2 | 4 7---8 @ @---@ @---@ @---@ @---@ @ @---@ @
// | | | | | | |
// 1 | 3---2 @---@ @---@ @---@ @---@ @---@ @---@ @---@
// | | | | | | | | | | |
// 0 | 0---1 @---@---@ @---@---@ @---@---@ @---@---@ @--255
// |
// -------------------------------------------------------------------
// 0 1 2 3 ---> Axes[0] 15
//
// Notes: (1) Unit change in Line yields single unit change in Axes position:
// the Hilbert curve is maximally local.
// (2) CPU proportional to total number of bits, = b * n.
//
// History: John Skilling 20 Apr 2001, 11 Jan 2003, 3 Sep 2003
//-----------------------------------------------------------------------------
//
void LinetoAxes(
coord_t* Axes, // O multidimensional geometrical axes [n]
coord_t* Line, // I linear serial number, stored as [n]
int b, // I # bits used in each word
int n) // I dimension
{
if ( n <= 1 ) // trivial case
*Axes = *Line;
else
{
LinetoTranspose(Axes, Line, b, n);
TransposetoAxes(Axes, b, n);
}
}
void AxestoLine(
coord_t* Line, // O linear serial number, stored as [n]
coord_t* Axes, // I multidimensional geometrical axes [n]
int b, // I # bits used in each word
int n) // I dimension
{
coord_t store[1024]; // avoid overwriting Axes
int i; // counter
if ( n <= 1 ) // trivial case
*Line = *Axes;
else if ( n <= 1024 ) // surely the usual case
{
for ( i = 0; i < n; ++i )
store[i] = Axes[i];
AxestoTranspose( store, b, n);
TransposetoLine(Line, store, b, n);
}
else // must do in place at greater cost
{
AxestoTranspose( Axes, b, n);
TransposetoLine(Line, Axes, b, n);
TransposetoAxes( Axes, b, n);
}
}
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// Functions: LinetoTranspose
// TransposetoLine
//
// Purpose: Recover Hilbert integer by bit-transposition
//
// Example: b=5 bits for each of n=3 coordinates
// 15-bit Hilbert integer = A B C D E a b c d e 1 2 3 4 5
// X[0]..... X[1]..... X[2].....
// transposed to
// X[0](high) = A D b e 3
// X[1] = B E c 1 4
// X[2](low) = C a d 2 5
// high low
//
// History: John Skilling 20 Apr 2001, 3 Sep 2003, 14 Oct 2003
//-----------------------------------------------------------------------------
//
static void LinetoTranspose(
coord_t* X, // O Transpose [n]
coord_t* Line, // I Hilbert integer [n]
int b, // I # bits
int n) // I dimension
{
coord_t j, p, M;
int i, q;
M = 1 << (b - 1);
for ( i = 0; i < n; i++ )
X[i] = 0;
q = 0;
p = M;
for ( i = 0; i < n; i++ )
{
for ( j = M; j; j >>= 1 )
{
if ( Line[i] & j )
X[q] |= p;
if ( ++q == n )
{
q = 0;
p >>= 1;
}
}
}
}
static void TransposetoLine(
coord_t* Line, // O Hilbert integer [n]
coord_t* X, // I Transpose [n]
int b, // I # bits
int n) // I dimension
{
coord_t j, p, M;
int i, q;
M = 1 << (b - 1);
q = 0;
p = M;
for ( i = 0; i < n; i++ )
{
Line[i] = 0;
for ( j = M; j; j >>= 1 )
{
if ( X[q] & p )
Line[i] |= j;
if ( ++q == n )
{
q = 0;
p >>= 1;
}
}
}
}
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// Functions: TransposetoAxes
// AxestoTranspose
//
// Purpose: Transform between Hilbert transpose and geometrical axes
//
// Example: b=5 bits for each of n=3 coordinates
// Hilbert transpose
// X[0] = A D b e 3 X[1]|
// X[1] = B E c 1 4 <-------> | /X[2]
// X[2] = C a d 2 5 axes | /
// high low |/______
// X[0]
// Axes are stored conventially as b-bit integers.
//
// History: John Skilling 20 Apr 2001, 3 Sep 2003, 14 Oct 2003
//-----------------------------------------------------------------------------
//
static void TransposetoAxes(
coord_t* X, // I O position [n]
int b, // I # bits
int n) // I dimension
{
coord_t M, P, Q, t;
int i;
// Gray decode by H ^ (H/2)
t = X[n-1] >> 1;
for ( i = n - 1; i; i-- )
X[i] ^= X[i-1];
X[0] ^= t;
// Undo excess work
M = 2 << (b - 1);
for ( Q = 2; Q != M; Q <<= 1 )
{
P = Q - 1;
for ( i = n - 1; i; i-- )
if ( X[i] & Q ) X[0] ^= P; // invert
else
{
t = (X[0] ^ X[i]) & P; // exchange
X[0] ^= t;
X[i] ^= t;
}
if ( X[0] & Q ) X[0] ^= P; // invert
}
}
static void AxestoTranspose(
coord_t* X, // I O position [n]
int b, // I # bits
int n) // I dimension
{
coord_t P, Q, t;
int i;
// Inverse undo
for ( Q = 1 << (b - 1); Q > 1; Q >>= 1 )
{
P = Q - 1;
if ( X[0] & Q ) X[0] ^= P; // invert
for ( i = 1; i < n; i++ )
if ( X[i] & Q ) X[0] ^= P; // invert
else
{
t = (X[0] ^ X[i]) & P; // exchange
X[0] ^= t;
X[i] ^= t;
}
}
// Gray encode (inverse of decode)
for ( i = 1; i < n; i++ )
X[i] ^= X[i-1];
t = X[n-1];
for ( i = 1; i < b; i <<= 1 )
X[n-1] ^= X[n-1] >> i;
t ^= X[n-1];
for ( i = n - 2; i >= 0; i-- )
X[i] ^= t;
}
//=============================================================================
// Linked-list library
//=============================================================================
// atom___________________________________
// Base| | | Ptr | Ptr | Ptr | Ptr |
// Free| Ptr | ... | Ptr | Ptr | Ptr | Ptr |
// |_____|_____|_____|_____|_____|_____|
// / / / / / / / / /
// 0 / / / / / / / / /
// : / / / / / / / / /
// : / vacant nodes
// ______/
// | Node |
// |depth3|
// |______|
// /: \.
// /: \.
// /: \.
// /: \.
// /: \.
// /: \.
// /: \.
// /: ______
// /: | Node |
// /: |depth2|
// /: |______|
// /: /: \.
// /: /: \.
// ______ /: ______
// | Node | /: | Node |
// |depth1| /: |depth1|
// |______| /: |______|
// /: \ /: /: \.
// /: \ /: /: \.
// /: \ /: /: \.
// Base______ ______ ______ ______ ______
// | Node | | Node | | Node | | Node | | Node |
// 0----|depth0|----|depth0|----|depth0|----|depth0|----|depth0|----0
// |______| |______| |______| |______| |______|
// : : : : :
// : : : : :
// : : : : :
// atom_____ _____ _____ _____ _____
// |extra| |Atom2| |Atom0| |Atom3| |Atom1|
// | 0 | |Label| |Label| |Label| |Label|
// |atom | | etc.| | etc.| | etc.| | etc.|
// |_____| |_____| |_____| |_____| |_____|
// <---------- random-order storage --------->
//
// 0 <= < < < < < < Label < < < < <
//
// Inserted atoms have serial numbers 0, 1, 2, ..., N-1 with labels x >= 0,
// and occupy consecutive storage. To maintain this efficiently under random
// insertion and deletion demands that they be stored in dynamically changing
// order. Hence coupling to their neighbours in x must be by a linked list,
// and to avoid ambiguity all labels must be different.
//
// The binary tree allows insertion of a new atom with known label x,
// and deletion of a random atom, at a cost that is asymptotically
// logarithmic O(log N) because of the search.
// After each insertion, the newly inserted atom is at the end of storage.
// and after each deletion, the newly deleted atom is just beyond the end.
// After each insertion or deletion, the tree is re-balanced to keep its
// maximum depth close to log2(N).
//
// There are 2N+1 nodes of the tree, which only occupy consecutive storage
// when N is at a historic maximum: when N falls away through deletions,
// holes appear in memory. These are tracked and re-used by a consecutive
// vector of controlling pointers (which is conveniently stored in the
// unused atoms to save memory).
//
// Memory = sizeof(Atom) + 2 * sizeof(Node), per atom.
//
// CPU = asymptotically O(log N) per insertion or deletion.
// Tests with a range of practical N give roughly
// =======================================
// CPU = 10 N (log10(N) + 5) multiply-adds per (insertion and deletion) cycle.
// =======================================
// (Compare 10 N log10(N) multiply-adds for a single FFT.)
//
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// Function: SetLink
//
// Purpose: Allocate and initialise memory,
// using guess for maximum number of atoms needed.
//
// See also ResetLink and FreeLink
//
// History: John Skilling 9 Mar 1996, 6 Feb 1998, 12 Apr 2001, 10 Sep 2001,
// 22 Jan 2003
//=============================================================================
// STRUCTURE OF ATOMS
// Node = apex of linked list
// \.
// \.
// \.
// List \______
// 0 | Label| (unused)
// | flux | (unused)
// | base | Link up to origin base of tree
// | free | Point to apex of tree
// |______|
// 1 | Label| x ./|\.
// | flux | extra properties of atom |
// | base | Link up to base of tree |
// | free | (unused) |
// |______| | Surviving atoms
// | | |
// ........ | in scrambled
// |______| |
// Natoms | | | storage order
// | .... | |
// | | |
// | .... | |
// |______| \|/
// Natoms+1 | Label| (unused)
// | flux | (unused)
// | base | Point to vacant node address
// | free | Point to vacant node address
// |______|
// | |
// ........
// |______|
// NMAX | |
// | .... |
// | |
// | .... |
// |______| Reallocate memory if Natoms attempts to exceed NMAX
//
//=============================================================================
// STRUCTURE OF NODES
//
// Link node ______
// | depth| >= 1
// |number| >= 2
// |parent| Link up to parent (NULL if apex)
// | lo | Link down to "next" child
// | hi | Link down to "previous" child
// | atom | Point down "previous" branches to atom
// |______|
//
// Base node ______
// | depth| 0
// |number| 1
// |parent| Link up to parent (NULL if apex of empty tree)
// | lo | Link across to "next" neighbour (NULL if last)
// | hi | Link across to "previous" neighbour (NULL if first)
// | atom | Link down to atom
// |______|
//
//-----------------------------------------------------------------------------
//
int SetLink( // O 0, or -ve error code
int Ndim, // I # words per label
Node* psLink) // I O Linked list
{
int NMAX = 100; // Initial number of allowed insertions of an atom
pNode Nodes = NULL; // Begin tree storage
pAtom List = NULL; // List of atoms
int i; // Local counter
int CALLvalue = 0;
psLink->atom = NULL;
psLink->parent = NULL;
// Allocate storage for tree
CALLOC( Nodes, NMAX + NMAX + 1, Node )
CALLOC( List, NMAX + 1, Atom )
CALLOC( List->Label, Ndim * (NMAX + 1), coord_t )
// Initialise artificial header atom
List->Base = Nodes;
List->Free = Nodes;
// Initialise pointers to available nodes
for ( i = 1; i <= NMAX; ++i )
{
List[i].Base = &Nodes[i+i-1];
List[i].Free = &Nodes[i+i];
List[i].Label = List[i-1].Label + Ndim;
}
// Initialise top of tree
Nodes->depth = 0;
Nodes->number = 1;
Nodes->parent = NULL;
Nodes->hi = NULL;
Nodes->lo = NULL;
Nodes->atom = List;
psLink->depth = NMAX;
psLink->number = Ndim;
psLink->atom = List;
psLink->parent = Nodes;
return 0;
Exit:
FREE( List->Label )
FREE( List )
FREE( Nodes )
return CALLvalue;
}
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// Function: FreeLink
//
// Purpose: Free memory allocated by SetLink.
//
// History: John Skilling 9 Mar 1996, 20 Apr 2001
//-----------------------------------------------------------------------------
//
int FreeLink( // O 0 (or -ve debug code)
Node* psLink) // I O Linked list
{
if ( psLink )
{
if ( psLink->atom ) FREE( psLink->atom->Label )
FREE( psLink->atom )
FREE( psLink->parent )
psLink->parent = NULL;
psLink->atom = NULL;
psLink->depth = 0;
}
return 0;
}
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// Function: ResetLink
//
// Purpose: Rellocate memory, if initial guess in SetLink was inadequate
//
// History: John Skilling 9 Mar 1996, 6 Feb 1998, 12 Apr 2001
//-----------------------------------------------------------------------------
//
static int ResetLink( // O 0, or -ve error code
pNode psLink) // I O Linked list
{
int NMAX = psLink->depth; // Initial # allowed atoms
pAtom List = psLink->atom; // Old list of atoms
pNode Nodes = psLink->parent; // Old nodes of tree
int Ndim = psLink->number; // # words per label
int MORE = NMAX + NMAX / 2; // Extended # allowed atoms
pAtom ListX = NULL; // Replacement list of atoms
pNode NodesX = NULL; // Replacement nodes of tree
int i; // Local counter
int j; // Counter
int CALLvalue = 0;
// Allocate new tree
CALLOC( NodesX, MORE + MORE + 1, Node )
CALLOC( ListX, MORE + 1, Atom )
CALLOC( ListX->Label, Ndim * (MORE + 1), coord_t )
for ( i = 1; i <= MORE; ++i )
ListX[i].Label = ListX[i-1].Label + Ndim;
// Copy across
for ( i = 0; i <= NMAX + NMAX; ++i )
NodesX[i] = Nodes[i];
for ( j = 0; j < Ndim; j++ )
ListX[0].Label[j] = List[0].Label[j];
for ( i = 1; i <= NMAX; ++i )
for ( j = 0; j < Ndim; j++ )
ListX[i].Label[j] = List[i].Label[j];
// Correct all internal pointers
for ( i = 0; i <= NMAX; ++i )
{
ListX[i].Base = NodesX + (List[i].Base - Nodes);
ListX[i].Free = NodesX + (List[i].Free - Nodes);
}
for ( i = NMAX + 1; i <= MORE; ++i )
{
ListX[i].Base = &NodesX[i+i-1];
ListX[i].Free = &NodesX[i+i];
}
for ( i = 0; i <= NMAX + NMAX; ++i )
{
if ( NodesX[i].parent )
NodesX[i].parent = NodesX + (Nodes[i].parent - Nodes);
if ( NodesX[i].lo )
NodesX[i].lo = NodesX + (Nodes[i].lo - Nodes);
if ( NodesX[i].hi )
NodesX[i].hi = NodesX + (Nodes[i].hi - Nodes);
NodesX[i].atom = ListX + (Nodes[i].atom - List);
}
psLink->atom = ListX;
psLink->parent = NodesX;
psLink->depth = MORE;
// Free old tree
FREE( List->Label )
FREE( List )
FREE( Nodes )
return 0;
Exit:
FREE( ListX->Label )
FREE( ListX )
FREE( NodesX )
return CALLvalue;
}
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// Function: InsAtom
//
// Purpose: Update list to insert new atom, if new label is distinct.
// Split node to left, forking to new and previous nodes,
// then re-balance the tree.
//
// Notes: After InsAtom, the serial number of the inserted atom is Natoms-1
//
// History: John Skilling 6 Mar 1996, 7 Oct 1996, 15 Dec 1997, 21 Jan 1998
// 6 Feb 1998, 12 Apr 2001, 10 Sep 2001, 22 Jan 2003
//=============================================================================
// Original configuration Final configuration before balancing
//
// \ /: /: \ /: /:
// ____ ____ ____ ____ ____ ____
// ___|Node|___|Node|___|Node|___ ___|Node| |Node| |Node|___
// |____| |____| |____| |____| |____| |____|
// : : \ /: \ / :
// : : \ /: \ / :
// ____ ____ ____ ____ :
// |Atom| |Atom| |New2|___|New1| :
// | x- | | x+ | |____| |____| :
// |____| |____| : : :
// : : :
// ____ ____ ____ ____
// | | |Atom| | | |Atom|
// InsAtom | x | > x- | x- | | x | | x+ |
// |____| |____| |____| |____|
//
//-----------------------------------------------------------------------------
//
int InsAtom( // O 1 = accept,
// 0 = reject because same label,
// -ve = error
pAtom insertion, // I New atom to be inserted into list
pNode psLink) // I O Linked list
{
int Natoms; // # inserted atoms
pAtom patom; // Copy insertion atom into list
pAtom List; // List of atoms
pNode node; // Node of tree
pNode New1; // Available node for inclusion in tree
pNode New2; // Available node for inclusion in tree
int Ndim; // # words per label
int j; // Counter
int CALLvalue = 0;
if ( psLink->number <= 0 )
return CALLvalue;
// Ensure memory is available
if ( psLink->depth < 2 )
return E_TREEDATA;
if ( NumAtoms(psLink) >= psLink->depth )
CALL( ResetLink(psLink) )
// Goto base node at or just left of insertion
List = psLink->atom;
node = List->Free;
Ndim = psLink->number;
// log(N) loop
while ( node->depth )
node = (CmpLabel(insertion->Label, node->hi->atom->Label, Ndim) < 0)
? node->lo : node->hi;
if ( CmpLabel(insertion->Label, node->atom->Label, Ndim) == 0 )
{
if ( CmpLabel(insertion->Label, psLink->atom->Label, Ndim) > 0 )
return 0; // Avoid overlapping existing user atom
if ( node->lo ) // but allow one user atom at Label=0
return 0;
}
Natoms = NumAtoms(psLink) + 1;
// Copy atom to vacancy at top of list
patom = List + Natoms;
New1 = patom->Free;
New2 = patom->Base;
for ( j = 0; j < psLink->number; j++ )
patom->Label[j] = insertion->Label[j];
// Reconnect base with additional node and twig
patom->Free = NULL;
patom->Base = New1;
New1->atom = patom;
New1->parent = node;
New1->hi = node->hi;
if ( New1->hi )
New1->hi->lo = New1;
New1->lo = New2;
New1->depth = 0;
New1->number = 1;
node->hi = New1;
node->atom->Base = New2;
New2->atom = node->atom;
New2->parent = node;
New2->hi = New1;
New2->lo = node->lo;
if ( New2->lo )
New2->lo->hi = New2;
New2->depth = 0;
New2->number = 1;
node->lo = New2;
// Update depth information back up tree, and equilibrate accordingly
Balance(New1);
return 1; // accepted
Exit:
return CALLvalue;
}
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// Function: DelAtom
//
// Purpose: Update list to delete an atom.
// Cut out specified node and its parent, then re-balance the tree.
//
// History: John Skilling 6 Mar 1996, 6 Feb 1998, 22 Jan 2003, 2 Dec 2003
//=============================================================================
// Original configuration Final configuration before balancing
// (sibling can be to left or right) (sibling can be same as lo or hi)
//
// / \.
// ____ \.
// | del| \.
// |____| \.
// / \. \.
// / \. \.
// ____ \. ____
// |sibl| \. |sibl|
// |____| \. |____|
// / \ \. / \.
// \.
// \ \. \ /
// ____ ____ ____ ____ ____
// ___| lo |___|kill|___| hi |___ ___| lo |___| hi |___
// |____| |____| |____| |____| |____|
// : : : : :
// : : : : :
// ____ ____ ____ ____ ____
// |Atom| | | |Atom| |Atom| |Atom|
// | x- | | x | | x+ | | x- | | x+ |
// |____| |____| |____| |____| |____|
// deletion
//-----------------------------------------------------------------------------
//
int DelAtom( // O 0 (or -ve error code)
pAtom deletion, // I New atom to be deleted from list
pNode psLink) // I O Linked list
{
pAtom xatom; // Interacting atom
pAtom List; // List of atoms
pAtom Top; // Top of list of atoms
pNode node; // Current node
pNode kill; // Node on tree base, to be killed
pNode del; // kill->parent, also to be killed
pNode sibling; // del->otherchild
int Natoms; // Decremented # atoms
int j; // Counter
if ( psLink->number <= 0 )
return 0;
Natoms = NumAtoms(psLink);
// Ensure deletion is from list
List = psLink->atom;
Top = List + Natoms;
if ( deletion <= List || deletion > Top )
return E_TREEDATA;
// Cut node out of base of tree
kill = deletion->Base;
if ( kill->hi )
kill->hi->lo = kill->lo;
kill->lo->hi = kill->hi;
// Cut kill and del out of the tree
del = kill->parent;
sibling = ( del->hi == kill ) ? del->lo : del->hi;
xatom = sibling->atom;
sibling->parent = del->parent;
if ( del->parent )
{
if ( del->parent->hi == del )
del->parent->hi = sibling;
else
del->parent->lo = sibling;
// Replace all references to killed atom with refs to its sibling
for ( node = del; node->atom == deletion; node = node->parent )
node->atom = xatom;
}
else
{
List->Free = sibling;
}
// Copy atom at top of list into freed slot to keep list storage consecutive
if ( deletion < Top )
{
xatom = List + Natoms;
for ( node = xatom->Base; node->atom == xatom; node = node->parent )
node->atom = deletion;
deletion->Base = xatom->Base;
deletion->Free = xatom->Free;
for ( j = 0; j < psLink->number; ++j )
deletion->Label[j] = xatom->Label[j];
}
// Collect addresses of two freed leaves
List[Natoms].Base = del;
List[Natoms].Free = kill;
// Update depth information back up tree, and equilibrate accordingly
Balance(sibling);
return 0;
}
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// Function: FindOrder
//
// Purpose: Find n'th atom in ordered list, or NULL if out of range.
// Inverse of OrderNum.
//
// History: John Skilling 10 Sep 2001
//-----------------------------------------------------------------------------
//
pAtom FindOrder( // O & required atom
int n, // I order number (0,1,...,NumAtoms-1)
const Node* psLink) // I Linked list
{
pNode node;
if ( n < 0 || n >= NumAtoms(psLink) )
return NULL;
n++;
node = psLink->atom->Free;
while ( node->depth )
{
if ( n >= node->lo->number )
{
n -= node->lo->number;
node = node->hi;
}
else
node = node->lo;
}
return node->atom;
}
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// Function: FindLeft
//
// Purpose: Find atom at or left of label.
// If absent, return NULL.
// If present, return right-hand such atom.
//
// History: John Skilling 6 Mar 1996, 30 Dec 1997, 21 Jan 1998, 12 Apr 2001
//-----------------------------------------------------------------------------
//
pAtom FindLeft( // O & required atom
coord_t* Label, // I Label limit
const Node* psLink) // I Linked list
{
int Ndim = psLink->number;
pNode node = psLink->atom->Free;
if ( Ndim <= 0 )
return NULL;
while ( node->depth )
node = ( CmpLabel(Label, node->hi->atom->Label, Ndim) < 0 )
? node->lo : node->hi;
return node->lo ? node->atom : NULL;
}
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// Function: FindRight
//
// Purpose: Find atom at or right of label.
// If absent, return NULL.
// If present, return left-hand such atom.
//
// History: John Skilling 12 Apr 2001
//-----------------------------------------------------------------------------
//
pAtom FindRight( // O & required atom
coord_t* Label, // I Label limit
const Node* psLink) // I Linked list
{
int Ndim = psLink->number;
pNode node = psLink->atom->Free;
if ( Ndim <= 0 )
return NULL;
while ( node->depth )
node = ( CmpLabel(Label, node->hi->atom->Label, Ndim) <= 0 )
? node->lo : node->hi;
return node->hi ? node->hi->atom : NULL;
}
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// Function: FindHere
//
// Purpose: Find atom exactly at label.
// If absent, return NULL.
// If present, return address.
//
// History: John Skilling 2 Dec 2001
//-----------------------------------------------------------------------------
//
pAtom FindHere( // O & required atom
coord_t* Label, // I Label limit
const Node* psLink) // I Linked list
{
int Ndim = psLink->number;
pNode node = psLink->atom->Free;
if ( Ndim <= 0 )
return NULL;
while ( node->depth )
node = ( CmpLabel(Label, node->hi->atom->Label, Ndim) < 0 )
? node->lo : node->hi;
if ( node->lo && CmpLabel(Label, node->atom->Label, Ndim) == 0 )
return node->atom;
else
return NULL;
}
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// Function: EndLink
//
// Purpose: Find right-most atom.
//
// History: John Skilling 12 Apr 2001
//-----------------------------------------------------------------------------
//
pAtom EndLink( // O & atom in required label range
const Node* psLink) // I Linked list
{
pNode node;
if ( NumAtoms(psLink) )
{
node = psLink->atom->Free;
while ( node->depth )
node = node->hi;
return node->atom;
}
else
return NULL;
}
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// Function: Storage
//
// Purpose: Locate atom in current storage list. Inverse of FindAtom.
//
// History: John Skilling 22 Jan 2003
//-----------------------------------------------------------------------------
//
int Storage( // O location in current storage list 0,,..,NumAtoms-1
pAtom atom) // I & atom in list
{
pNode node;
for ( node = atom->Base; node->parent; node = node->parent );
return atom - node->atom - 1;
}
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// Function: OrderNum
//
// Purpose: Order number of atom in linked list. Inverse of FindOrder.
//
// History: John Skilling 22 Jan 2003
//-----------------------------------------------------------------------------
//
int OrderNum( // O location in ordered list 0,1,..,NumAtoms-1
pAtom atom) // I & atom in list
{
pNode node;
int number = -1;
for ( node = atom->Base; node->parent; node = node->parent )
if ( node == node->parent->hi )
number += node->parent->lo->number;
return number;
}
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// Function: Balance
//
// Purpose: Re-balance the tree depths, after insertion or deletion.
//
// History: John Skilling 25 Jan 1996, 10 Sep 2001
//=============================================================================
// Original configurations Final configurations
//
// Case A / /
// Node Node
// / \ / \.
// / Node Node \.
// / / \ / \ \.
//
//
// Case B / /
// Node Node
// / \ / \.
// / Node Node Node
// / / \ / \ / \.
// / Node \.
// / / \ \.
//
//
// Case C / /
// Node Node
// / \ / \.
// Node \ / Node
// / \ \ / / \.
//
//
// Case D / /
// Node Node
// / \ / \.
// Node \ Node Node
// / \ \ / \ / \.
// / Node \.
// / / \ \.
//
//-----------------------------------------------------------------------------
//
static void Balance(
pNode node) // I Base node of revised tree
{
#define DEPTH(x,y) (((x) > (y) ? (x) : (y)) + 1)
pNode t; // Temporary pointer for swapping
int asymmetry; // Depth difference between branches
int deep; // Recalculated depth of node
for ( node = node->parent; node; node = node->parent )
{
asymmetry = node->hi->depth - node->lo->depth;
if ( asymmetry > 1 )
{
if ( node->hi->hi->depth >= node->hi->lo->depth )
{
// Case A
t = node->hi;
node->hi = t->hi;
node->hi->parent = node;
t->hi = t->lo;
t->lo = node->lo;
t->lo->parent = t;
node->lo = t;
t->atom = node->atom;
t->depth = DEPTH(t->hi->depth, t->lo->depth);
t->number = t->hi->number + t->lo->number;
}
else
{
// Case B
t = node->hi->lo;
node->hi->atom = t->hi->atom;
t->atom = node->atom;
node->hi->lo = t->hi;
t->hi->parent = node->hi;
t->hi = t->lo;
t->lo = node->lo;
t->lo->parent = t;
node->lo = t;
t->parent = node;
t->depth = DEPTH(t->hi->depth, t->lo->depth);
t->number = t->hi->number + t->lo->number;
t = node->hi;
t->depth = DEPTH(t->hi->depth, t->lo->depth);
t->number = t->hi->number + t->lo->number;
}
}
if ( asymmetry < -1 )
{
if ( node->lo->lo->depth >= node->lo->hi->depth )
{
// Case C
t = node->lo;
node->lo = t->lo;
node->lo->parent = node;
t->lo = t->hi;
t->hi = node->hi;
t->hi->parent = t;
node->hi = t;
t->atom = t->lo->atom;
t->depth = DEPTH(t->hi->depth, t->lo->depth);
t->number = t->hi->number + t->lo->number;
}
else
{
// Case D
t = node->lo->hi;
t->atom = t->hi->atom;
node->lo->hi = t->lo;
t->lo->parent = node->lo;
t->lo = t->hi;
t->hi = node->hi;
t->hi->parent = t;
node->hi = t;
t->parent = node;
t->depth = DEPTH(t->hi->depth, t->lo->depth);
t->number = t->hi->number + t->lo->number;
t = node->lo;
t->depth = DEPTH(t->hi->depth, t->lo->depth);
t->number = t->hi->number + t->lo->number;
}
}
deep = node->depth;
node->depth = DEPTH(node->hi->depth, node->lo->depth);
node->number = node->hi->number + node->lo->number;
if ( node->depth == deep )
break;
}
for ( ; node; node = node->parent )
node->number = node->hi->number + node->lo->number;
}

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