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Diffstat (limited to 'src/fsmmin.cc')
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diff --git a/src/fsmmin.cc b/src/fsmmin.cc new file mode 100644 index 0000000..cbb2b99 --- /dev/null +++ b/src/fsmmin.cc @@ -0,0 +1,732 @@ +/* + * Copyright 2006-2012 Adrian Thurston <thurston@complang.org> + */ + +/* This file is part of Colm. + * + * Colm is free software; you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation; either version 2 of the License, or + * (at your option) any later version. + * + * Colm 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 General Public License + * along with Colm; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + */ + +#include "fsmgraph.h" +#include "mergesort.h" + +int FsmGraph::partitionRound( FsmState **statePtrs, MinPartition *parts, int numParts ) +{ + /* Need a mergesort object and a single partition compare. */ + MergeSort<FsmState*, PartitionCompare> mergeSort; + PartitionCompare partCompare; + + /* For each partition. */ + for ( int p = 0; p < numParts; p++ ) { + /* Fill the pointer array with the states in the partition. */ + StateList::Iter state = parts[p].list; + for ( int s = 0; state.lte(); state++, s++ ) + statePtrs[s] = state; + + /* Sort the states using the partitioning compare. */ + int numStates = parts[p].list.length(); + mergeSort.sort( statePtrs, numStates ); + + /* Assign the states into partitions based on the results of the sort. */ + int destPart = p, firstNewPart = numParts; + for ( int s = 1; s < numStates; s++ ) { + /* If this state differs from the last then move to the next partition. */ + if ( partCompare.compare( statePtrs[s-1], statePtrs[s] ) < 0 ) { + /* The new partition is the next avail spot. */ + destPart = numParts; + numParts += 1; + } + + /* If the state is not staying in the first partition, then + * transfer it to its destination partition. */ + if ( destPart != p ) { + FsmState *state = parts[p].list.detach( statePtrs[s] ); + parts[destPart].list.append( state ); + } + } + + /* Fix the partition pointer for all the states that got moved to a new + * partition. This must be done after the states are transfered so the + * result of the sort is not altered. */ + for ( int newPart = firstNewPart; newPart < numParts; newPart++ ) { + StateList::Iter state = parts[newPart].list; + for ( ; state.lte(); state++ ) + state->alg.partition = &parts[newPart]; + } + } + + return numParts; +} + +/** + * \brief Minimize by partitioning version 1. + * + * Repeatedly tries to split partitions until all partitions are unsplittable. + * Produces the most minimal FSM possible. + */ +void FsmGraph::minimizePartition1() +{ + /* Need one mergesort object and partition compares. */ + MergeSort<FsmState*, InitPartitionCompare> mergeSort; + InitPartitionCompare initPartCompare; + + /* Nothing to do if there are no states. */ + if ( stateList.length() == 0 ) + return; + + /* + * First thing is to partition the states by final state status and + * transition functions. This gives us an initial partitioning to work + * with. + */ + + /* Make a array of pointers to states. */ + int numStates = stateList.length(); + FsmState** statePtrs = new FsmState*[numStates]; + + /* Fill up an array of pointers to the states for easy sorting. */ + StateList::Iter state = stateList; + for ( int s = 0; state.lte(); state++, s++ ) + statePtrs[s] = state; + + /* Sort the states using the array of states. */ + mergeSort.sort( statePtrs, numStates ); + + /* An array of lists of states is used to partition the states. */ + MinPartition *parts = new MinPartition[numStates]; + + /* Assign the states into partitions. */ + int destPart = 0; + for ( int s = 0; s < numStates; s++ ) { + /* If this state differs from the last then move to the next partition. */ + if ( s > 0 && initPartCompare.compare( statePtrs[s-1], statePtrs[s] ) < 0 ) { + /* Move to the next partition. */ + destPart += 1; + } + + /* Put the state into its partition. */ + statePtrs[s]->alg.partition = &parts[destPart]; + parts[destPart].list.append( statePtrs[s] ); + } + + /* We just moved all the states from the main list into partitions without + * taking them off the main list. So clean up the main list now. */ + stateList.abandon(); + + /* Split partitions. */ + int numParts = destPart + 1; + while ( true ) { + /* Test all partitions for splitting. */ + int newNum = partitionRound( statePtrs, parts, numParts ); + + /* When no partitions can be split, stop. */ + if ( newNum == numParts ) + break; + + numParts = newNum; + } + + /* Fuse states in the same partition. The states will end up back on the + * main list. */ + fusePartitions( parts, numParts ); + + /* Cleanup. */ + delete[] statePtrs; + delete[] parts; +} + +/* Split partitions that need splittting, decide which partitions might need + * to be split as a result, continue until there are no more that might need + * to be split. */ +int FsmGraph::splitCandidates( FsmState **statePtrs, MinPartition *parts, int numParts ) +{ + /* Need a mergesort and a partition compare. */ + MergeSort<FsmState*, PartitionCompare> mergeSort; + PartitionCompare partCompare; + + /* The lists of unsplitable (partList) and splitable partitions. + * Only partitions in the splitable list are check for needing splitting. */ + PartitionList partList, splittable; + + /* Initially, all partitions are born from a split (the initial + * partitioning) and can cause other partitions to be split. So any + * partition with a state with a transition out to another partition is a + * candidate for splitting. This will make every partition except possibly + * partitions of final states split candidates. */ + for ( int p = 0; p < numParts; p++ ) { + /* Assume not active. */ + parts[p].active = false; + + /* Look for a trans out of any state in the partition. */ + for ( StateList::Iter state = parts[p].list; state.lte(); state++ ) { + /* If there is at least one transition out to another state then + * the partition becomes splittable. */ + if ( state->outList.length() > 0 ) { + parts[p].active = true; + break; + } + } + + /* If it was found active then it goes on the splittable list. */ + if ( parts[p].active ) + splittable.append( &parts[p] ); + else + partList.append( &parts[p] ); + } + + /* While there are partitions that are splittable, pull one off and try + * to split it. If it splits, determine which partitions may now be split + * as a result of the newly split partition. */ + while ( splittable.length() > 0 ) { + MinPartition *partition = splittable.detachFirst(); + + /* Fill the pointer array with the states in the partition. */ + StateList::Iter state = partition->list; + for ( int s = 0; state.lte(); state++, s++ ) + statePtrs[s] = state; + + /* Sort the states using the partitioning compare. */ + int numStates = partition->list.length(); + mergeSort.sort( statePtrs, numStates ); + + /* Assign the states into partitions based on the results of the sort. */ + MinPartition *destPart = partition; + int firstNewPart = numParts; + for ( int s = 1; s < numStates; s++ ) { + /* If this state differs from the last then move to the next partition. */ + if ( partCompare.compare( statePtrs[s-1], statePtrs[s] ) < 0 ) { + /* The new partition is the next avail spot. */ + destPart = &parts[numParts]; + numParts += 1; + } + + /* If the state is not staying in the first partition, then + * transfer it to its destination partition. */ + if ( destPart != partition ) { + FsmState *state = partition->list.detach( statePtrs[s] ); + destPart->list.append( state ); + } + } + + /* Fix the partition pointer for all the states that got moved to a new + * partition. This must be done after the states are transfered so the + * result of the sort is not altered. */ + int newPart; + for ( newPart = firstNewPart; newPart < numParts; newPart++ ) { + StateList::Iter state = parts[newPart].list; + for ( ; state.lte(); state++ ) + state->alg.partition = &parts[newPart]; + } + + /* Put the partition we just split and any new partitions that came out + * of the split onto the inactive list. */ + partition->active = false; + partList.append( partition ); + for ( newPart = firstNewPart; newPart < numParts; newPart++ ) { + parts[newPart].active = false; + partList.append( &parts[newPart] ); + } + + if ( destPart == partition ) + continue; + + /* Now determine which partitions are splittable as a result of + * splitting partition by walking the in lists of the states in + * partitions that got split. Partition is the faked first item in the + * loop. */ + MinPartition *causalPart = partition; + newPart = firstNewPart - 1; + while ( newPart < numParts ) { + /* Loop all states in the causal partition. */ + StateList::Iter state = causalPart->list; + for ( ; state.lte(); state++ ) { + /* Walk all transition into the state and put the partition + * that the from state is in onto the splittable list. */ + for ( TransInList::Iter trans = state->inList; trans.lte(); trans++ ) { + MinPartition *fromPart = trans->fromState->alg.partition; + if ( ! fromPart->active ) { + fromPart->active = true; + partList.detach( fromPart ); + splittable.append( fromPart ); + } + } + } + + newPart += 1; + causalPart = &parts[newPart]; + } + } + return numParts; +} + + +/** + * \brief Minimize by partitioning version 2 (best alg). + * + * Repeatedly tries to split partitions that may splittable until there are no + * more partitions that might possibly need splitting. Runs faster than + * version 1. Produces the most minimal fsm possible. + */ +void FsmGraph::minimizePartition2() +{ + /* Need a mergesort and an initial partition compare. */ + MergeSort<FsmState*, InitPartitionCompare> mergeSort; + InitPartitionCompare initPartCompare; + + /* Nothing to do if there are no states. */ + if ( stateList.length() == 0 ) + return; + + /* + * First thing is to partition the states by final state status and + * transition functions. This gives us an initial partitioning to work + * with. + */ + + /* Make a array of pointers to states. */ + int numStates = stateList.length(); + FsmState** statePtrs = new FsmState*[numStates]; + + /* Fill up an array of pointers to the states for easy sorting. */ + StateList::Iter state = stateList; + for ( int s = 0; state.lte(); state++, s++ ) + statePtrs[s] = state; + + /* Sort the states using the array of states. */ + mergeSort.sort( statePtrs, numStates ); + + /* An array of lists of states is used to partition the states. */ + MinPartition *parts = new MinPartition[numStates]; + + /* Assign the states into partitions. */ + int destPart = 0; + for ( int s = 0; s < numStates; s++ ) { + /* If this state differs from the last then move to the next partition. */ + if ( s > 0 && initPartCompare.compare( statePtrs[s-1], statePtrs[s] ) < 0 ) { + /* Move to the next partition. */ + destPart += 1; + } + + /* Put the state into its partition. */ + statePtrs[s]->alg.partition = &parts[destPart]; + parts[destPart].list.append( statePtrs[s] ); + } + + /* We just moved all the states from the main list into partitions without + * taking them off the main list. So clean up the main list now. */ + stateList.abandon(); + + /* Split partitions. */ + int numParts = splitCandidates( statePtrs, parts, destPart+1 ); + + /* Fuse states in the same partition. The states will end up back on the + * main list. */ + fusePartitions( parts, numParts ); + + /* Cleanup. */ + delete[] statePtrs; + delete[] parts; +} + +void FsmGraph::initialMarkRound( MarkIndex &markIndex ) +{ + /* P and q for walking pairs. */ + FsmState *p = stateList.head, *q; + + /* Need an initial partition compare. */ + InitPartitionCompare initPartCompare; + + /* Walk all unordered pairs of (p, q) where p != q. + * The second depth of the walk stops before reaching p. This + * gives us all unordered pairs of states (p, q) where p != q. */ + while ( p != 0 ) { + q = stateList.head; + while ( q != p ) { + /* If the states differ on final state status, out transitions or + * any transition data then they should be separated on the initial + * round. */ + if ( initPartCompare.compare( p, q ) != 0 ) + markIndex.markPair( p->alg.stateNum, q->alg.stateNum ); + + q = q->next; + } + p = p->next; + } +} + +bool FsmGraph::markRound( MarkIndex &markIndex ) +{ + /* P an q for walking pairs. Take note if any pair gets marked. */ + FsmState *p = stateList.head, *q; + bool pairWasMarked = false; + + /* Need a mark comparison. */ + MarkCompare markCompare; + + /* Walk all unordered pairs of (p, q) where p != q. + * The second depth of the walk stops before reaching p. This + * gives us all unordered pairs of states (p, q) where p != q. */ + while ( p != 0 ) { + q = stateList.head; + while ( q != p ) { + /* Should we mark the pair? */ + if ( !markIndex.isPairMarked( p->alg.stateNum, q->alg.stateNum ) ) { + if ( markCompare.shouldMark( markIndex, p, q ) ) { + markIndex.markPair( p->alg.stateNum, q->alg.stateNum ); + pairWasMarked = true; + } + } + q = q->next; + } + p = p->next; + } + + return pairWasMarked; +} + + +/** + * \brief Minimize by pair marking. + * + * Decides if each pair of states is distinct or not. Uses O(n^2) memory and + * should only be used on small graphs. Produces the most minmimal FSM + * possible. + */ +void FsmGraph::minimizeStable() +{ + /* Set the state numbers. */ + setStateNumbers( 0 ); + + /* This keeps track of which pairs have been marked. */ + MarkIndex markIndex( stateList.length() ); + + /* Mark pairs where final stateness, out trans, or trans data differ. */ + initialMarkRound( markIndex ); + + /* While the last round of marking succeeded in marking a state + * continue to do another round. */ + int modified = markRound( markIndex ); + while (modified) + modified = markRound( markIndex ); + + /* Merge pairs that are unmarked. */ + fuseUnmarkedPairs( markIndex ); +} + +bool FsmGraph::minimizeRound() +{ + /* Nothing to do if there are no states. */ + if ( stateList.length() == 0 ) + return false; + + /* Need a mergesort on approx compare and an approx compare. */ + MergeSort<FsmState*, ApproxCompare> mergeSort; + ApproxCompare approxCompare; + + /* Fill up an array of pointers to the states. */ + FsmState **statePtrs = new FsmState*[stateList.length()]; + StateList::Iter state = stateList; + for ( int s = 0; state.lte(); state++, s++ ) + statePtrs[s] = state; + + bool modified = false; + + /* Sort The list. */ + mergeSort.sort( statePtrs, stateList.length() ); + + /* Walk the list looking for duplicates next to each other, + * merge in any duplicates. */ + FsmState **pLast = statePtrs; + FsmState **pState = statePtrs + 1; + for ( int i = 1; i < stateList.length(); i++, pState++ ) { + if ( approxCompare.compare( *pLast, *pState ) == 0 ) { + /* Last and pState are the same, so fuse together. Move forward + * with pState but not with pLast. If any more are identical, we + * must */ + fuseEquivStates( *pLast, *pState ); + modified = true; + } + else { + /* Last and this are different, do not set to merge them. Move + * pLast to the current (it may be way behind from merging many + * states) and pState forward one to consider the next pair. */ + pLast = pState; + } + } + delete[] statePtrs; + return modified; +} + +/** + * \brief Minmimize by an approximation. + * + * Repeatedly tries to find states with transitions out to the same set of + * states on the same set of keys until no more identical states can be found. + * Does not produce the most minimial FSM possible. + */ +void FsmGraph::minimizeApproximate() +{ + /* While the last minimization round succeeded in compacting states, + * continue to try to compact states. */ + while ( true ) { + bool modified = minimizeRound(); + if ( ! modified ) + break; + } +} + + +/* Remove states that have no path to them from the start state. Recursively + * traverses the graph marking states that have paths into them. Then removes + * all states that did not get marked. */ +void FsmGraph::removeUnreachableStates() +{ + /* Misfit accounting should be off and there should be no states on the + * misfit list. */ + assert( !misfitAccounting && misfitList.length() == 0 ); + + /* Mark all the states that can be reached + * through the existing set of entry points. */ + markReachableFromHere( startState ); + for ( EntryMap::Iter en = entryPoints; en.lte(); en++ ) + markReachableFromHere( en->value ); + + /* Delete all states that are not marked + * and unmark the ones that are marked. */ + FsmState *state = stateList.head; + while ( state ) { + FsmState *next = state->next; + + if ( state->stateBits & SB_ISMARKED ) + state->stateBits &= ~ SB_ISMARKED; + else { + detachState( state ); + stateList.detach( state ); + delete state; + } + + state = next; + } +} + +bool FsmGraph::outListCovers( FsmState *state ) +{ + /* Must be at least one range to cover. */ + if ( state->outList.length() == 0 ) + return false; + + /* The first must start at the lower bound. */ + TransList::Iter trans = state->outList.first(); + if ( keyOps->minKey < trans->lowKey ) + return false; + + /* Loop starts at second el. */ + trans.increment(); + + /* Loop checks lower against prev upper. */ + for ( ; trans.lte(); trans++ ) { + /* Lower end of the trans must be one greater than the + * previous' high end. */ + Key lowKey = trans->lowKey; + lowKey.decrement(); + if ( trans->prev->highKey < lowKey ) + return false; + } + + /* Require that the last range extends to the upper bound. */ + trans = state->outList.last(); + if ( trans->highKey < keyOps->maxKey ) + return false; + + return true; +} + +/* Remove states that that do not lead to a final states. Works recursivly traversing + * the graph in reverse (starting from all final states) and marking seen states. Then + * removes states that did not get marked. */ +void FsmGraph::removeDeadEndStates() +{ + /* Misfit accounting should be off and there should be no states on the + * misfit list. */ + assert( !misfitAccounting && misfitList.length() == 0 ); + + /* Mark all states that have paths to the final states. */ + FsmState **st = finStateSet.data; + int nst = finStateSet.length(); + for ( int i = 0; i < nst; i++, st++ ) + markReachableFromHereReverse( *st ); + + /* Start state gets honorary marking. If the machine accepts nothing we + * still want the start state to hang around. This must be done after the + * recursive call on all the final states so that it does not cause the + * start state in transitions to be skipped when the start state is + * visited by the traversal. */ + startState->stateBits |= SB_ISMARKED; + + /* Delete all states that are not marked + * and unmark the ones that are marked. */ + FsmState *state = stateList.head; + while ( state != 0 ) { + FsmState *next = state->next; + + if ( state->stateBits & SB_ISMARKED ) + state->stateBits &= ~ SB_ISMARKED; + else { + detachState( state ); + stateList.detach( state ); + delete state; + } + + state = next; + } +} + +/* Remove states on the misfit list. To work properly misfit accounting should + * be on when this is called. The detaching of a state will likely cause + * another misfit to be collected and it can then be removed. */ +void FsmGraph::removeMisfits() +{ + while ( misfitList.length() > 0 ) { + /* Get the first state. */ + FsmState *state = misfitList.head; + + /* Detach and delete. */ + detachState( state ); + + /* The state was previously on the misfit list and detaching can only + * remove in transitions so the state must still be on the misfit + * list. */ + misfitList.detach( state ); + delete state; + } +} + +/* Fuse src into dest because they have been deemed equivalent states. + * Involves moving transitions into src to go into dest and invoking + * callbacks. Src is deleted detached from the graph and deleted. */ +void FsmGraph::fuseEquivStates( FsmState *dest, FsmState *src ) +{ + /* This would get ugly. */ + assert( dest != src ); + + /* Cur is a duplicate. We can merge it with trail. */ + inTransMove( dest, src ); + + detachState( src ); + stateList.detach( src ); + delete src; +} + +void FsmGraph::fuseUnmarkedPairs( MarkIndex &markIndex ) +{ + FsmState *p = stateList.head, *nextP, *q; + + /* Definition: The primary state of an equivalence class is the first state + * encounterd that belongs to the equivalence class. All equivalence + * classes have primary state including equivalence classes with one state + * in it. */ + + /* For each unmarked pair merge p into q and delete p. q is always the + * primary state of it's equivalence class. We wouldn't have landed on it + * here if it were not, because it would have been deleted. + * + * Proof that q is the primaray state of it's equivalence class: Assume q + * is not the primary state of it's equivalence class, then it would be + * merged into some state that came before it and thus p would be + * equivalent to that state. But q is the first state that p is equivalent + * to so we have a contradiction. */ + + /* Walk all unordered pairs of (p, q) where p != q. + * The second depth of the walk stops before reaching p. This + * gives us all unordered pairs of states (p, q) where p != q. */ + while ( p != 0 ) { + nextP = p->next; + + q = stateList.head; + while ( q != p ) { + /* If one of p or q is a final state then mark. */ + if ( ! markIndex.isPairMarked( p->alg.stateNum, q->alg.stateNum ) ) { + fuseEquivStates( q, p ); + break; + } + q = q->next; + } + p = nextP; + } +} + +void FsmGraph::fusePartitions( MinPartition *parts, int numParts ) +{ + /* For each partition, fuse state 2, 3, ... into state 1. */ + for ( int p = 0; p < numParts; p++ ) { + /* Assume that there will always be at least one state. */ + FsmState *first = parts[p].list.head, *toFuse = first->next; + + /* Put the first state back onto the main state list. Don't bother + * removing it from the partition list first. */ + stateList.append( first ); + + /* Fuse the rest of the state into the first. */ + while ( toFuse != 0 ) { + /* Save the next. We will trash it before it is needed. */ + FsmState *next = toFuse->next; + + /* Put the state to be fused in to the first back onto the main + * list before it is fuse. the graph. The state needs to be on + * the main list for the detach from the graph to work. Don't + * bother removing the state from the partition list first. We + * need not maintain it. */ + stateList.append( toFuse ); + + /* Now fuse to the first. */ + fuseEquivStates( first, toFuse ); + + /* Go to the next that we saved before trashing the next pointer. */ + toFuse = next; + } + + /* We transfered the states from the partition list into the main list without + * removing the states from the partition list first. Clean it up. */ + parts[p].list.abandon(); + } +} + + +/* Merge neighboring transitions go to the same state and have the same + * transitions data. */ +void FsmGraph::compressTransitions() +{ + for ( StateList::Iter st = stateList; st.lte(); st++ ) { + if ( st->outList.length() > 1 ) { + for ( TransList::Iter trans = st->outList, next = trans.next(); next.lte(); ) { + Key nextLow = next->lowKey; + nextLow.decrement(); + if ( trans->highKey == nextLow && trans->toState == next->toState && + CmpActionTable::compare( trans->actionTable, next->actionTable ) == 0 ) + { + trans->highKey = next->highKey; + st->outList.detach( next ); + detachTrans( next->fromState, next->toState, next ); + delete next; + next = trans.next(); + } + else { + trans.increment(); + next.increment(); + } + } + } + } +} |