/* splay.c: SPLAY TREE IMPLEMENTATION
 *
 * $Id$
 * Copyright (c) 2001 Ravenbrook Limited.  See end of file for license.
 *
 * .purpose: Splay trees are used to manage potentially unbounded
 * collections of ordered things.
 *
 * .source: <design/splay/>
 *
 * .note.stack: It's important that the MPS have a bounded stack
 * size, and this is a problem for tree algorithms.  Basically,
 * we have to avoid recursion.  FIXME: Reference requirement.
 */


#include "splay.h"
#include "mpm.h"

SRCID(splay, "$Id$");


/* SPLAY_DEBUG -- switch for extra debugging
 *
 * Define SPLAY_DEBUG to enable extra consistency checking when modifying
 * splay tree algorithms, which can be tricky to get right.  This will
 * check the tree size and ordering frequently.
 */

/* #define SPLAY_DEBUG */

#define SplayTreeSetRoot(splay, tree) BEGIN ((splay)->root = (tree)); END
#define SplayCompare(tree, key, node) (((tree)->compare)(node, key))
#define SplayHasUpdate(splay) ((splay)->updateNode != SplayTrivUpdate)


Bool SplayTreeCheck(SplayTree splay)
{
  UNUSED(splay);
  CHECKS(SplayTree, splay);
  CHECKL(FUNCHECK(splay->compare));
  CHECKL(FUNCHECK(splay->nodeKey));
  CHECKL(FUNCHECK(splay->updateNode));
  CHECKL(TreeCheck(splay->root));
  return TRUE;
}


void SplayTreeInit(SplayTree splay,
                   TreeCompare compare,
                   TreeKeyMethod nodeKey,
                   SplayUpdateNodeMethod updateNode)
{
  AVER(splay != NULL);
  AVER(FUNCHECK(compare));
  AVER(FUNCHECK(nodeKey));
  AVER(FUNCHECK(updateNode));

  splay->compare = compare;
  splay->nodeKey = nodeKey;
  splay->updateNode = updateNode;
  SplayTreeSetRoot(splay, TreeEMPTY);
  splay->sig = SplayTreeSig;

  AVERT(SplayTree, splay);
}


void SplayTreeFinish(SplayTree splay)
{
  AVERT(SplayTree, splay);
  splay->sig = SigInvalid;
  SplayTreeSetRoot(splay, TreeEMPTY);
  splay->compare = NULL;
  splay->nodeKey = NULL;
  splay->updateNode = NULL;
}


/* SplayTrivUpdate -- trivial update method
 *
 * This is passed to SplayTreeInit to indicate that no client property
 * maintenance is required.  It can also be called to do nothing.
 */

void SplayTrivUpdate(SplayTree splay, Tree tree)
{
  AVERT(SplayTree, splay);
  AVERT(Tree, tree);
}


/* compareLess, compareGreater -- trivial comparisons
 *
 * These comparisons can be passed to SplaySplay to find the leftmost
 * or rightmost nodes in a tree quickly.
 *
 * NOTE: It's also possible to make specialised versions of SplaySplit
 * that traverse left and right unconditionally.  These weren't found
 * to have a significant performance advantage when benchmarking.
 * RB 2014-02-23
 */

static Compare compareLess(Tree tree, TreeKey key)
{
  UNUSED(tree);
  UNUSED(key);
  return CompareLESS;
}

static Compare compareGreater(Tree tree, TreeKey key)
{
  UNUSED(tree);
  UNUSED(key);
  return CompareGREATER;
}


/* SplayDebugUpdate -- force update of client property
 *
 * A debugging utility to recursively update the client property of
 * a subtree.  May not be used in production MPS because it has
 * indefinite stack usage.  FIXME: Ref to requirement.
 */

void SplayDebugUpdate(SplayTree splay, Tree tree)
{
  AVERT(SplayTree, splay);
  AVERT(Tree, tree);
  if (tree == TreeEMPTY)
    return;
  SplayDebugUpdate(splay, TreeLeft(tree));
  SplayDebugUpdate(splay, TreeRight(tree));
  splay->updateNode(splay, tree);
}


/* SplayZig -- move to left child, prepending to right tree
 *
 * Link the top node of the middle tree into the left child of the
 * right tree, then step to the left child.
 *
 * See <design/splay/#impl.link.right>.
 *
 *    middle    rightNext            middle
 *      B          E                   A              E
 *     / \        / \          =>                    / \
 *    A   C      D   F                    rightNext D   F
 *          rightFirst                             /
 *                                     rightFirst B
 *                                                 \
 *                                                  C
 */

static Tree SplayZig(Tree middle, Tree *rightFirstIO, Tree *rightNextReturn)
{
  AVERT_CRITICAL(Tree, middle);
  AVER_CRITICAL(rightFirstIO != NULL);
  AVERT_CRITICAL(Tree, *rightFirstIO);
  TreeSetLeft(*rightFirstIO, middle);
  *rightNextReturn = *rightFirstIO;
  *rightFirstIO = middle;
  return TreeLeft(middle);
}

/* SplayZigZig -- move to left child, rotating on on to right tree
 *
 * Rotate the top node of the middle tree over the left child of the
 * right tree, then step to the left child.
 *
 *    middle     rightNext           middle       rightNext
 *      B          E                   A              E
 *     / \        / \          =>                    / \
 *    A   C      D   F                        right B   F
 *             right                                 \
 *                                                    D
 *                                                   /
 *                                                  C
 */

static Tree SplayZigZig(Tree middle, Tree *rightFirstIO, Tree rightNext)
{
  AVERT_CRITICAL(Tree, middle);
  AVER_CRITICAL(rightFirstIO != NULL);
  AVERT_CRITICAL(Tree, *rightFirstIO);
  TreeSetLeft(*rightFirstIO, TreeRight(middle));
  TreeSetRight(middle, *rightFirstIO);
  TreeSetLeft(rightNext, middle);
  *rightFirstIO = middle;
  return TreeLeft(middle);
}
  
/* SplayZag -- mirror image of SplayZig */

static Tree SplayZag(Tree middle, Tree *leftLastIO, Tree *leftPrevReturn)
{
  AVERT_CRITICAL(Tree, middle);
  AVER_CRITICAL(leftLastIO != NULL);
  AVERT_CRITICAL(Tree, *leftLastIO);
  TreeSetRight(*leftLastIO, middle);
  *leftPrevReturn = *leftLastIO;
  *leftLastIO = middle;
  return TreeRight(middle);
}

/* SplayZagZag -- mirror image of SplayZigZig */

static Tree SplayZagZag(Tree middle, Tree *leftLastIO, Tree leftPrev)
{
  AVERT_CRITICAL(Tree, middle);
  AVER_CRITICAL(leftLastIO != NULL);
  AVERT_CRITICAL(Tree, *leftLastIO);
  TreeSetRight(*leftLastIO, TreeLeft(middle));
  TreeSetLeft(middle, *leftLastIO);
  TreeSetRight(leftPrev, middle);
  *leftLastIO = middle;
  return TreeRight(middle);
}


/* SplaySplitDown -- divide the tree around a key
 *
 * Split a tree into three according to a key and a comparison,
 * splaying nested left and right nodes.  Preserves tree ordering.
 *
 * Returns cmp, the relationship of the root of the middle tree to the key,
 * and a SplayState:
 *   middle -- the middle tree, with the nearest match for the key at the top
 *   leftTop -- a tree of nodes that were less than node
 *   leftLast -- the greatest node in leftTop (rightmost child)
 *   rightTop -- a tree of nodes that were greater than node
 *   rightFirst -- the least node in rightTop (leftmost child)
 *
 * Does *not* maintain client properties.  See SplaySplitRev.
 */

typedef struct SplayStateStruct {
  Tree middle;
  Tree left;
  Tree leftLast;
  Tree right;
  Tree rightFirst;
} SplayStateStruct, *SplayState;

static Compare SplaySplitDown(SplayStateStruct *stateReturn,
                              SplayTree splay, TreeKey key, TreeCompare compare)
{
  TreeStruct sentinel;
  Tree middle, leftLast, rightFirst, leftPrev, rightNext;
  Compare cmp;

  AVERT(SplayTree, splay);
  AVER(FUNCHECK(compare));
  AVER(!SplayTreeIsEmpty(splay));
  
  TreeInit(&sentinel);
  leftLast = &sentinel;
  rightFirst = &sentinel;
  middle = SplayTreeRoot(splay);
  for (;;) {
    cmp = compare(middle, key);
    switch(cmp) {
    default:
      NOTREACHED;
      /* defensive fall-through */
    case CompareEQUAL:
      goto stop;

    case CompareLESS:
      if (!TreeHasLeft(middle))
        goto stop;
      middle = SplayZig(middle, &rightFirst, &rightNext);
      cmp = compare(middle, key);
      switch(cmp) {
      default:
        NOTREACHED;
        /* defensive fall-through */
      case CompareEQUAL:
        goto stop;
      case CompareLESS:
        if (!TreeHasLeft(middle))
          goto stop;
        middle = SplayZigZig(middle, &rightFirst, rightNext);
        break;
      case CompareGREATER:
        if (!TreeHasRight(middle))
          goto stop;
        middle = SplayZag(middle, &leftLast, &leftPrev);
        break;
      }
      break;

    case CompareGREATER:
      if (!TreeHasRight(middle))
        goto stop;
      middle = SplayZag(middle, &leftLast, &leftPrev);
      cmp = compare(middle, key);
      switch(cmp) {
      default:
        NOTREACHED;
        /* defensive fall-through */
      case CompareEQUAL:
        goto stop;
      case CompareGREATER:
        if (!TreeHasRight(middle))
          goto stop;
        middle = SplayZagZag(middle, &leftLast, leftPrev);
        break;
      case CompareLESS:
        if (!TreeHasLeft(middle))
          goto stop;
        middle = SplayZig(middle, &rightFirst, &rightNext);
        break;
      }
      break;
    }
  }

stop:
  stateReturn->middle = middle;
  stateReturn->left = TreeRight(&sentinel);
  stateReturn->leftLast = leftLast == &sentinel ? TreeEMPTY : leftLast;
  stateReturn->right = TreeLeft(&sentinel);
  stateReturn->rightFirst = rightFirst == &sentinel ? TreeEMPTY : rightFirst;
  return cmp;
}


/* SplayAssembleDown -- assemble left right and middle trees into one
 *
 * Takes the result of a SplaySplit and forms a single tree with the
 * root of the middle tree as the root.
 *
 *   left      middle      right                 middle
 *    B          P          V                      P
 *   / \        / \        / \         =>       /     \
 *  A   C      N   Q      U   X               B         V
 *    leftLast       rightFirst              / \       / \
 *                                          A   C     U   X
 *                                               \   /
 *                                                N Q
 *
 * The children of the middle tree are grafted onto the last and first
 * nodes of the side trees, which become the children of the root.
 *
 * Does *not* maintain client properties.  See SplayAssembleRev.
 *
 * See <design/splay/#impl.assemble>.
 */

static void SplayAssembleDown(SplayTree splay, SplayState state)
{
  AVERT(SplayTree, splay);
  AVER(state->middle != TreeEMPTY);

  if (state->left != TreeEMPTY) {
    AVER_CRITICAL(state->leftLast != TreeEMPTY);
    TreeSetRight(state->leftLast, TreeLeft(state->middle));
    TreeSetLeft(state->middle, state->left);
  }

  if (state->right != TreeEMPTY) {
    AVER_CRITICAL(state->rightFirst != TreeEMPTY);
    TreeSetLeft(state->rightFirst, TreeRight(state->middle));
    TreeSetRight(state->middle, state->right);
  }
}


/* SplayZigRev -- move to left child, prepending to reversed right tree
 *
 * Same as SplayZig, except that the left spine of the right tree is
 * pointer-reversed, so that its left children point at their parents
 * instead of their children.  This is fixed up in SplayAssembleRev.
 */

static Tree SplayZigRev(Tree middle, Tree *rightFirstIO)
{
  Tree child;
  AVERT_CRITICAL(Tree, middle);
  AVER_CRITICAL(rightFirstIO != NULL);
  AVERT_CRITICAL(Tree, *rightFirstIO);
  child = TreeLeft(middle);
  TreeSetLeft(middle, *rightFirstIO);
  *rightFirstIO = middle;
  return child;
}

/* SplayZigZigRev -- move to left child, rotating onto reversed right tree
 *
 * Same as SplayZigZig, except that the right tree is pointer reversed
 * (see SplayZigRev)
 */

static Tree SplayZigZigRev(Tree middle, Tree *rightFirstIO)
{
  Tree child;
  AVERT_CRITICAL(Tree, middle);
  AVER_CRITICAL(rightFirstIO != NULL);
  AVERT_CRITICAL(Tree, *rightFirstIO);
  child = TreeLeft(middle);
  TreeSetLeft(middle, TreeLeft(*rightFirstIO));
  TreeSetLeft(*rightFirstIO, TreeRight(middle));
  TreeSetRight(middle, *rightFirstIO);
  *rightFirstIO = middle;
  return child;
}

/* SplayZagRev -- mirror image of SplayZigRev */

static Tree SplayZagRev(Tree middle, Tree *leftLastIO)
{
  Tree child;
  AVERT_CRITICAL(Tree, middle);
  AVER_CRITICAL(leftLastIO != NULL);
  AVERT_CRITICAL(Tree, *leftLastIO);
  child = TreeRight(middle);
  TreeSetRight(middle, *leftLastIO);
  *leftLastIO = middle;
  return child;
}

/* SplayZagZagRev -- mirror image of SplayZigZigRev */

static Tree SplayZagZagRev(Tree middle, Tree *leftLastIO)
{
  Tree child;
  AVERT_CRITICAL(Tree, middle);
  AVER_CRITICAL(leftLastIO != NULL);
  AVERT_CRITICAL(Tree, *leftLastIO);
  child = TreeRight(middle);
  TreeSetRight(middle, TreeRight(*leftLastIO));
  TreeSetRight(*leftLastIO, TreeLeft(middle));
  TreeSetLeft(middle, *leftLastIO);
  *leftLastIO = middle;
  return child;
}


/* SplaySplitRev -- divide the tree around a key
 *
 * This is the same as SplaySplit, except that:
 *   - the left and right trees are pointer reversed on their spines
 *   - client properties for rotated nodes (not on the spines) are
 *     updated
 */

static Compare SplaySplitRev(SplayStateStruct *stateReturn,
                             SplayTree splay, TreeKey key, TreeCompare compare)
{
  Tree middle, leftLast, rightFirst;
  Compare cmp;

  AVERT(SplayTree, splay);
  AVER(FUNCHECK(compare));
  AVER(!SplayTreeIsEmpty(splay));
  
  leftLast = TreeEMPTY;
  rightFirst = TreeEMPTY;
  middle = SplayTreeRoot(splay);
  for (;;) {
    cmp = compare(middle, key);
    switch(cmp) {
    default:
      NOTREACHED;
      /* defensive fall-through */
    case CompareEQUAL:
      goto stop;

    case CompareLESS:
      if (!TreeHasLeft(middle))
        goto stop;
      middle = SplayZigRev(middle, &rightFirst);
      cmp = compare(middle, key);
      switch(cmp) {
      default:
        NOTREACHED;
        /* defensive fall-through */
      case CompareEQUAL:
        goto stop;
      case CompareLESS:
        if (!TreeHasLeft(middle))
          goto stop;
        middle = SplayZigZigRev(middle, &rightFirst);
        splay->updateNode(splay, TreeRight(rightFirst));
        break;
      case CompareGREATER:
        if (!TreeHasRight(middle))
          goto stop;
        middle = SplayZagRev(middle, &leftLast);
        break;
      }
      break;

    case CompareGREATER:
      if (!TreeHasRight(middle))
        goto stop;
      middle = SplayZagRev(middle, &leftLast);
      cmp = compare(middle, key);
      switch(cmp) {
      default:
        NOTREACHED;
        /* defensive fall-through */
      case CompareEQUAL:
        goto stop;
      case CompareGREATER:
        if (!TreeHasRight(middle))
          goto stop;
        middle = SplayZagZagRev(middle, &leftLast);
        splay->updateNode(splay, TreeLeft(leftLast));
        break;
      case CompareLESS:
        if (!TreeHasLeft(middle))
          goto stop;
        middle = SplayZigRev(middle, &rightFirst);
        break;
      }
      break;
    }
  }

stop:
  stateReturn->middle = middle;
  stateReturn->leftLast = leftLast;
  stateReturn->rightFirst = rightFirst;
  return cmp;
}


/* SplayUpdateLeftSpine -- undo pointer reversal, updating client property */

static Tree SplayUpdateLeftSpine(SplayTree splay, Tree node, Tree child)
{
  AVERT_CRITICAL(SplayTree, splay);
  AVERT_CRITICAL(Tree, node);
  AVERT_CRITICAL(Tree, child);
  while(node != TreeEMPTY) {
    Tree parent = TreeLeft(node);
    TreeSetLeft(node, child); /* un-reverse pointer */
    splay->updateNode(splay, node);
    child = node;
    node = parent;
  }
  return child;
}

/* SplayUpdateRightSpine -- mirror of SplayUpdateLeftSpine */

static Tree SplayUpdateRightSpine(SplayTree splay, Tree node, Tree child)
{
  AVERT_CRITICAL(SplayTree, splay);
  AVERT_CRITICAL(Tree, node);
  AVERT_CRITICAL(Tree, child);
  while (node != TreeEMPTY) {
    Tree parent = TreeRight(node);
    TreeSetRight(node, child); /* un-reverse pointer */
    splay->updateNode(splay, node);
    child = node;
    node = parent;
  }
  return child;
}


/* SplayAssembleRev -- pointer reversed SplayAssemble
 *
 * Does the same job as SplayAssemble, but operates on pointer-reversed
 * left and right trees, updating client properties.  When we reach
 * this function, the nodes on the spines of the left and right trees
 * will have out of date client properties because their children have
 * been changed by SplaySplitRev.
 */

static void SplayAssembleRev(SplayTree splay, SplayState state)
{
  Tree left, right;

  AVERT(SplayTree, splay);
  AVER(state->middle != TreeEMPTY);
  
  left = TreeLeft(state->middle);
  left = SplayUpdateRightSpine(splay, state->leftLast, left);
  TreeSetLeft(state->middle, left);

  right = TreeRight(state->middle);
  right = SplayUpdateLeftSpine(splay, state->rightFirst, right);
  TreeSetRight(state->middle, right);

  splay->updateNode(splay, state->middle);
}


static Compare SplaySplit(SplayStateStruct *stateReturn,
                          SplayTree splay, TreeKey key, TreeCompare compare)
{
  if (SplayHasUpdate(splay))
    return SplaySplitRev(stateReturn, splay, key, compare);
  else
    return SplaySplitDown(stateReturn, splay, key, compare);
}

static void SplayAssemble(SplayTree splay, SplayState state)
{
  if (SplayHasUpdate(splay))
    SplayAssembleRev(splay, state);
  else
    SplayAssembleDown(splay, state);
}


/* SplaySplay -- splay the tree around a given key
 *
 * If the key is not found, splays around an arbitrary neighbour.
 * Returns the relationship of the new tree root to the key.
 *
 * See <design/splay/#impl.splay>.
 */

static Compare SplaySplay(SplayTree splay, TreeKey key, TreeCompare compare)
{
  Compare cmp;
  SplayStateStruct stateStruct;

#ifdef SPLAY_DEBUG
  Count count = TreeDebugCount(SplayTreeRoot(tree), tree->compare, tree->nodeKey);
#endif

  /* Short-circuit common cases.  Splay trees often bring recently
     acccessed nodes to the root. */
  if (SplayTreeIsEmpty(splay) ||
      compare(SplayTreeRoot(splay), key) == CompareEQUAL)
    return CompareEQUAL;

  if (SplayHasUpdate(splay)) {
    cmp = SplaySplitRev(&stateStruct, splay, key, compare);
    SplayAssembleRev(splay, &stateStruct);
  } else {
    cmp = SplaySplitDown(&stateStruct, splay, key, compare);
    SplayAssembleDown(splay, &stateStruct);
  }

  SplayTreeSetRoot(splay, stateStruct.middle);

#ifdef SPLAY_DEBUG
  AVER(count == TreeDebugCount(SplayTreeRoot(tree), tree->compare, tree->nodeKey));
#endif

  return cmp;
}


/* SplayTreeInsert -- Insert a node into a splay tree
 *
 * See <design/splay/#function.splay.tree.insert> and
 * <design/splay/#impl.insert>.
 *
 * NOTE: It would be possible to use split here, then assemble around
 * the new node, leaving the neighbour where it was, but it's probably
 * a good thing for key neighbours to be tree neighbours.
 */

Bool SplayTreeInsert(SplayTree splay, Tree node) {
  Tree neighbour;

  AVERT(SplayTree, splay);
  AVERT(Tree, node);
  AVER(TreeLeft(node) == TreeEMPTY);
  AVER(TreeRight(node) == TreeEMPTY);

  if (SplayTreeIsEmpty(splay)) {
    SplayTreeSetRoot(splay, node);
    return TRUE;
  }
  
  switch (SplaySplay(splay, splay->nodeKey(node), splay->compare)) {
  default:
    NOTREACHED;
    /* defensive fall-through */
  case CompareEQUAL: /* duplicate node */
    return FALSE;
    
  case CompareGREATER: /* left neighbour is at root */
    neighbour = SplayTreeRoot(splay);
    SplayTreeSetRoot(splay, node);
    TreeSetRight(node, TreeRight(neighbour));
    TreeSetLeft(node, neighbour);
    TreeSetRight(neighbour, TreeEMPTY);
    break;

  case CompareLESS: /* right neighbour is at root */
    neighbour = SplayTreeRoot(splay);
    SplayTreeSetRoot(splay, node);
    TreeSetLeft(node, TreeLeft(neighbour));
    TreeSetRight(node, neighbour);
    TreeSetLeft(neighbour, TreeEMPTY);
    break;
  }

  splay->updateNode(splay, neighbour);
  splay->updateNode(splay, node);
  return TRUE;
}


/* SplayTreeDelete -- Delete a node from a splay tree
 *
 * See <design/splay/#function.splay.tree.delete> and
 * <design/splay/#impl.delete>.
 *
 * TODO: Consider using SplaySplit.  If the found node has zero
 * or one children, then the replacement will be leftLast or rightFirst.
 */

Bool SplayTreeDelete(SplayTree splay, Tree node) {
  Tree leftLast;
  Compare cmp;

  AVERT(SplayTree, splay);
  AVERT(Tree, node);

  if (SplayTreeIsEmpty(splay))
    return FALSE;

  cmp = SplaySplay(splay, splay->nodeKey(node), splay->compare);
  AVER(cmp != CompareEQUAL || SplayTreeRoot(splay) == node);

  if (cmp != CompareEQUAL) {
    return FALSE;
  } else if (TreeLeft(node) == TreeEMPTY) {
    SplayTreeSetRoot(splay, TreeRight(node));
    TreeClearRight(node);
  } else if (TreeRight(node) == TreeEMPTY) {
    SplayTreeSetRoot(splay, TreeLeft(node));
    TreeClearLeft(node);
  } else {
    Tree rightHalf = TreeRight(node);
    TreeClearRight(node);
    SplayTreeSetRoot(splay, TreeLeft(node));
    TreeClearLeft(node);
    SplaySplay(splay, NULL, compareGreater);
    leftLast = SplayTreeRoot(splay);
    AVER(leftLast != TreeEMPTY);
    AVER(TreeRight(leftLast) == TreeEMPTY);
    TreeSetRight(leftLast, rightHalf);
    splay->updateNode(splay, leftLast);
  }

  TreeFinish(node);

  return TRUE;
}


/* SplayTreeFind -- search for a node in a splay tree matching a key
 *
 * See <design/splay/#function.splay.tree.search> and
 * <design/splay/#impl.search>.
 */

Bool SplayTreeFind(Tree *nodeReturn, SplayTree splay, TreeKey key) {
  AVERT(SplayTree, splay);
  AVER(nodeReturn != NULL);

  if (SplayTreeIsEmpty(splay))
    return FALSE;

  if (SplaySplay(splay, key, splay->compare) != CompareEQUAL)
    return FALSE;

  *nodeReturn = SplayTreeRoot(splay);
  return TRUE;
}


/* SplayTreeSuccessor -- Splays a tree at the root's successor
 *
 * Must not be called on en empty tree.  Successor need not exist,
 * in which case TreeEMPTY is returned, and the tree is unchanged.
 */

static Tree SplayTreeSuccessor(SplayTree splay) {
  Tree oldRoot, newRoot;

  AVERT(SplayTree, splay);
  AVER(!SplayTreeIsEmpty(splay));

  oldRoot = SplayTreeRoot(splay);

  if (!TreeHasRight(oldRoot))
    return TreeEMPTY; /* No successor */

  /* temporarily chop off the left half-tree, inclusive of root */
  SplayTreeSetRoot(splay, TreeRight(oldRoot));
  TreeSetRight(oldRoot, TreeEMPTY);
  SplaySplay(splay, NULL, compareLess);
  newRoot = SplayTreeRoot(splay);
  AVER(newRoot != TreeEMPTY);
  AVER(TreeLeft(newRoot) == TreeEMPTY);
  TreeSetLeft(newRoot, oldRoot);
  splay->updateNode(splay, oldRoot);
  splay->updateNode(splay, newRoot);

  return newRoot;
}


/* SplayTreeNeighbours
 *
 * Search for the two nodes in a splay tree neighbouring a key.
 *
 * TODO: Change to SplayTreeCoalesce that takes a function that can
 * direct the deletion of one of the neighbours, since this is a
 * good moment to do it, avoiding another search and splay.
 *
 * See <design/splay/#function.splay.tree.neighbours> and
 * <design/splay/#impl.neighbours>.
 */

Bool SplayTreeNeighbours(Tree *leftReturn, Tree *rightReturn,
                         SplayTree splay, TreeKey key)
{
  SplayStateStruct stateStruct;
  Bool found;
  Compare cmp;
#ifdef SPLAY_DEBUG
  Count count = TreeDebugCount(SplayTreeRoot(tree), tree->compare, tree->nodeKey);
#endif


  AVERT(SplayTree, splay);
  AVER(leftReturn != NULL);
  AVER(rightReturn != NULL);

  if (SplayTreeIsEmpty(splay)) {
    *leftReturn = *rightReturn = TreeEMPTY;
    return TRUE;
  }

  cmp = SplaySplit(&stateStruct, splay, key, splay->compare);

  switch (cmp) {
  default:
    NOTREACHED;
    /* defensive fall-through */
  case CompareEQUAL:
    found = FALSE;
    break;

  case CompareLESS:
    AVER(!TreeHasLeft(stateStruct.middle));
    *rightReturn = stateStruct.middle;
    *leftReturn = stateStruct.leftLast;
    found = TRUE;
    break;

  case CompareGREATER:
    AVER(!TreeHasRight(stateStruct.middle));
    *leftReturn = stateStruct.middle;
    *rightReturn = stateStruct.rightFirst;
    found = TRUE;
    break;
  }

  SplayAssemble(splay, &stateStruct);
  SplayTreeSetRoot(splay, stateStruct.middle);

#ifdef SPLAY_DEBUG
  AVER(count == TreeDebugCount(SplayTreeRoot(tree), tree->compare, tree->nodeKey));
#endif

  return found;
}


/* SplayTreeFirst, SplayTreeNext -- Iterators
 *
 * SplayTreeFirst receives a key that must precede all
 * nodes in the tree.  It returns TreeEMPTY if the tree is empty.
 * Otherwise, it splays the tree to the first node, and returns the
 * new root.  See <design/splay/#function.splay.tree.first>.
 *
 * SplayTreeNext takes a tree and splays it to the successor of the
 * old root, and returns the new root.  Returns TreeEMPTY is there are
 * no successors.  It takes a key for the old root.  See
 * <design/splay/#function.splay.tree.next>.
 *
 * Iterating over the tree using these functions will leave the tree
 * totally unbalanced.  Consider using TreeTraverse.
 */

Tree SplayTreeFirst(SplayTree splay) {
  Tree node;

  AVERT(SplayTree, splay);

  if (SplayTreeIsEmpty(splay))
    return TreeEMPTY;

  SplaySplay(splay, NULL, compareLess);
  node = SplayTreeRoot(splay);
  AVER(node != TreeEMPTY);
  AVER(TreeLeft(node) == TreeEMPTY);

  return node;
}

Tree SplayTreeNext(SplayTree splay, TreeKey oldKey) {
  AVERT(SplayTree, splay);

  if (SplayTreeIsEmpty(splay))
    return TreeEMPTY;
  
  /* Make old node the root.  Probably already is.  We don't mind if the
     node has been deleted, or replaced by a node with the same key. */
  switch (SplaySplay(splay, oldKey, splay->compare)) {
  default:
    NOTREACHED;
    /* defensive fall-through */
  case CompareGREATER:
    return SplayTreeRoot(splay);

  case CompareLESS:
  case CompareEQUAL:
    return SplayTreeSuccessor(splay);
  }
}


/* SplayNodeDescribe -- Describe a node in the splay tree
 *
 * Note that this breaks the restriction of .note.stack.
 * This is alright as the function is debug only.
 */

static Res SplayNodeDescribe(Tree node, mps_lib_FILE *stream,
                             SplayNodeDescribeMethod nodeDescribe) {
  Res res;

#if defined(AVER_AND_CHECK)
  if (!TreeCheck(node)) return ResFAIL;
  /* stream and nodeDescribe checked by SplayTreeDescribe */
#endif

  res = WriteF(stream, "( ", NULL);
  if (res != ResOK) return res;

  if (TreeLeft(node) != TreeEMPTY) {
    res = SplayNodeDescribe(TreeLeft(node), stream, nodeDescribe);
    if (res != ResOK) return res;

    res = WriteF(stream, " / ", NULL);
    if (res != ResOK) return res;
  }

  res = (*nodeDescribe)(node, stream);
  if (res != ResOK) return res;

  if (TreeRight(node) != TreeEMPTY) {
    res = WriteF(stream, " \\ ", NULL);
    if (res != ResOK) return res;

    res = SplayNodeDescribe(TreeRight(node), stream, nodeDescribe);
    if (res != ResOK) return res;
  }

  res = WriteF(stream, " )", NULL);
  if (res != ResOK) return res;

  return ResOK;
}


typedef struct SplayFindClosureStruct {
  SplayTestNodeMethod testNode;
  SplayTestTreeMethod testTree;
  void *p;
  Size s;
  SplayTree splay;
} SplayFindClosureStruct, *SplayFindClosure;

static Compare SplayFindFirstCompare(Tree node, TreeKey key)
{
  SplayFindClosure closure;
  void *closureP;
  Size closureS;
  SplayTestNodeMethod testNode;
  SplayTestTreeMethod testTree;
  SplayTree splay;

  AVERT(Tree, node);
  AVER(key != NULL);

  closure = (SplayFindClosure)key;
  closureP = closure->p;
  closureS = closure->s;
  testNode = closure->testNode;
  testTree = closure->testTree;
  splay = closure->splay;

  if (TreeHasLeft(node) &&
     (*testTree)(splay, TreeLeft(node), closureP, closureS)) {
    return CompareLESS;
  } else if ((*testNode)(splay, node, closureP, closureS)) {
    return CompareEQUAL;
  } else {
    AVER(TreeHasRight(node));
    AVER((*testTree)(splay, TreeRight(node), closureP, closureS));
    return CompareGREATER;
  }
}

static Compare SplayFindLastCompare(Tree node, TreeKey key)
{
  SplayFindClosure closure;
  void *closureP;
  Size closureS;
  SplayTestNodeMethod testNode;
  SplayTestTreeMethod testTree;
  SplayTree splay;

  AVERT(Tree, node);
  AVER(key != NULL);

  closure = (SplayFindClosure)key;
  closureP = closure->p;
  closureS = closure->s;
  testNode = closure->testNode;
  testTree = closure->testTree;
  splay = closure->splay;

  if (TreeHasRight(node) &&
     (*testTree)(splay, TreeRight(node), closureP, closureS)) {
     return CompareGREATER;
  } else if ((*testNode)(splay, node, closureP, closureS)) {
    return CompareEQUAL;
  } else {
    AVER(TreeHasLeft(node));
    AVER((*testTree)(splay, TreeLeft(node), closureP, closureS));
    return CompareLESS;
  }
}


/* SplayFindFirst -- Find first node that satisfies client property
 *
 * This function finds the first node (in address order) in the given
 * tree that satisfies some property defined by the client.  The
 * property is such that the client can detect, given a sub-tree,
 * whether that sub-tree contains any nodes satisfying the property.
 *
 * The given callbacks testNode and testTree detect this property in
 * a single node or a sub-tree rooted at a node, and both receive the
 * arbitrary closures closureP and closureS.
 */

Bool SplayFindFirst(Tree *nodeReturn, SplayTree splay,
                    SplayTestNodeMethod testNode,
                    SplayTestTreeMethod testTree,
                    void *closureP, Size closureS)
{
  SplayFindClosureStruct closureStruct;

  AVER(nodeReturn != NULL);
  AVERT(SplayTree, splay);
  AVER(FUNCHECK(testNode));
  AVER(FUNCHECK(testTree));

  if (SplayTreeIsEmpty(splay) ||
      !testTree(splay, SplayTreeRoot(splay), closureP, closureS))
    return FALSE; /* no suitable nodes in tree */

  closureStruct.p = closureP;
  closureStruct.s = closureS;
  closureStruct.testNode = testNode;
  closureStruct.testTree = testTree;
  closureStruct.splay = splay;

  if (SplaySplay(splay, &closureStruct, SplayFindFirstCompare) != CompareEQUAL)
    return FALSE;

  *nodeReturn = SplayTreeRoot(splay);
  return TRUE;
}


/* SplayFindLast -- As SplayFindFirst but in reverse address order */

Bool SplayFindLast(Tree *nodeReturn, SplayTree splay,
                   SplayTestNodeMethod testNode,
                   SplayTestTreeMethod testTree,
                   void *closureP, Size closureS)
{
  SplayFindClosureStruct closureStruct;

  AVER(nodeReturn != NULL);
  AVERT(SplayTree, splay);
  AVER(FUNCHECK(testNode));
  AVER(FUNCHECK(testTree));

  if (SplayTreeIsEmpty(splay) ||
      !testTree(splay, SplayTreeRoot(splay), closureP, closureS))
    return FALSE; /* no suitable nodes in tree */

  closureStruct.p = closureP;
  closureStruct.s = closureS;
  closureStruct.testNode = testNode;
  closureStruct.testTree = testTree;
  closureStruct.splay = splay;

  if (SplaySplay(splay, &closureStruct, SplayFindLastCompare) != CompareEQUAL)
    return FALSE;

  *nodeReturn = SplayTreeRoot(splay);
  return TRUE;
}


/* SplayNodeRefresh -- Updates the client property that has changed at a node
 *
 * This function undertakes to call the client updateNode callback for each
 * node affected by the change in properties at the given node (which has
 * the given key) in an appropriate order.
 *
 * The function fullfils its job by first splaying at the given node, and
 * updating the single node.  This may change.
 */

void SplayNodeRefresh(SplayTree splay, Tree node)
{
  Compare cmp;

  AVERT(SplayTree, splay);
  AVERT(Tree, node);
  AVER(!SplayTreeIsEmpty(splay)); /* must contain node, at least */
  AVER(SplayHasUpdate(splay)); /* otherwise, why call? */

  cmp = SplaySplay(splay, splay->nodeKey(node), splay->compare);
  AVER(cmp == CompareEQUAL);
  AVER(SplayTreeRoot(splay) == node);

  splay->updateNode(splay, node);
}


/* SplayTreeDescribe -- Describe a splay tree
 *
 * See <design/splay/#function.splay.tree.describe>.
 */

Res SplayTreeDescribe(SplayTree splay, mps_lib_FILE *stream,
                      SplayNodeDescribeMethod nodeDescribe) {
  Res res;

#if defined(AVER_AND_CHECK)
  if (!SplayTreeCheck(splay)) return ResFAIL;
  if (stream == NULL) return ResFAIL;
  if (!FUNCHECK(nodeDescribe)) return ResFAIL;
#endif

  res = WriteF(stream,
               "Splay $P {\n", (WriteFP)splay,
               "  compare $F\n", (WriteFF)splay->compare,
               NULL);
  if (res != ResOK) return res;

  if (SplayTreeRoot(splay) != TreeEMPTY) {
    res = SplayNodeDescribe(SplayTreeRoot(splay), stream, nodeDescribe);
    if (res != ResOK) return res;
  }

  res = WriteF(stream, "\n}\n", NULL);
  return res;
}


/* C. COPYRIGHT AND LICENSE
 *
 * Copyright (C) 2001-2002 Ravenbrook Limited <http://www.ravenbrook.com/>.
 * All rights reserved.  This is an open source license.  Contact
 * Ravenbrook for commercial licensing options.
 * 
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are
 * met:
 * 
 * 1. Redistributions of source code must retain the above copyright
 * notice, this list of conditions and the following disclaimer.
 * 
 * 2. Redistributions in binary form must reproduce the above copyright
 * notice, this list of conditions and the following disclaimer in the
 * documentation and/or other materials provided with the distribution.
 * 
 * 3. Redistributions in any form must be accompanied by information on how
 * to obtain complete source code for this software and any accompanying
 * software that uses this software.  The source code must either be
 * included in the distribution or be available for no more than the cost
 * of distribution plus a nominal fee, and must be freely redistributable
 * under reasonable conditions.  For an executable file, complete source
 * code means the source code for all modules it contains. It does not
 * include source code for modules or files that typically accompany the
 * major components of the operating system on which the executable file
 * runs.
 * 
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
 * IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
 * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR
 * PURPOSE, OR NON-INFRINGEMENT, ARE DISCLAIMED. IN NO EVENT SHALL THE
 * COPYRIGHT HOLDERS AND CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
 * USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
 * ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */