add libsat

1 files changed, 887 insertions, 0 deletions

diff --git a/sys/src/libsat/satsolve.c b/sys/src/libsat/satsolve.c
new file mode 100644
index 000000000..94dec8598
--- /dev/null
+++ b/sys/src/libsat/satsolve.c
@@ -0,0 +1,887 @@
+#include <u.h>
+#include <libc.h>
+#include <sat.h>
+#include "impl.h"
+
+/* the solver follows Algorithm C from Knuth's The Art of Computer Programming, Vol. 4, Fascicle 6 */
+
+#define verbosestate 0
+#define verboseforcing 0
+#define verboseconflict 0
+#define paranoia 0
+#define sanity(s) if(paranoia) satsanity(s)
+
+void
+sataddtrail(SATSolve *s, int l)
+{
+	s->trail[s->ntrail++] = l;
+	s->lit[l].val = 1;
+	s->lit[NOT(l)].val = 0;
+	s->var[VAR(l)].lvl = s->lvl;
+	s->agility -= s->agility >> 13;
+	if(((s->var[VAR(l)].flags ^ l) & 1) != 0)
+		s->agility += 1<<19;
+	if(verbosestate) satprintstate(s);
+}
+
+/* compute watchlists from scratch */
+static void
+rewatch(SATSolve *s)
+{
+	SATLit *l;
+	SATClause *c;
+	int i, j, x;
+	
+	for(l = s->lit; l < s->lit + 2*s->nvar; l++)
+		l->watch = nil;
+	for(c = s->cl; c != nil; c = c->next)
+		for(i = 0; i < 2; i++){
+			if(s->lit[c->l[i]].val == 0)
+				for(j = 2; j < c->n; j++)
+					if(s->lit[c->l[j]].val != 0){
+						x = c->l[i], c->l[i] = c->l[j], c->l[j] = x;
+						break;
+					}
+			c->watch[i] = s->lit[c->l[i]].watch;
+			s->lit[c->l[i]].watch = c;
+		}
+}
+
+/* jump back to decision level d */
+void
+satbackjump(SATSolve *s, int d)
+{
+	int l;
+	SATVar *v;
+
+	if(s->lvl == d) return;
+	while(s->ntrail > s->decbd[d + 1]){
+		l = s->trail[--s->ntrail];
+		v = &s->var[VAR(l)];
+		if((v->flags & VARUSER) != 0){ /* don't delete user assignments */
+			s->ntrail++;
+			break;
+		}
+		s->lit[l].val = -1;
+		s->lit[NOT(l)].val = -1;
+		v->flags = v->flags & ~1 | l & 1;
+		v->lvl = -1;
+		v->reason = nil;
+		v->isbinreason = 0;
+		if(v->heaploc < 0)
+			satheapput(s, v);
+	}
+	s->lvl = d;
+	if(s->forptr > s->ntrail) s->forptr = s->ntrail;
+	if(s->binptr > s->ntrail) s->binptr = s->ntrail;
+	if(verbosestate) satprintstate(s);
+}
+
+static void
+solvinit(SATSolve *s)
+{
+	satdebuginit(s);
+	satheapreset(s);
+	s->decbd = satrealloc(s, s->decbd, s->nvar * sizeof(int));
+	s->decbd[0] = 0;
+	s->trail = satrealloc(s, s->trail, sizeof(int) * s->nvar);
+	s->fullrlits = satrealloc(s, s->fullrlits, sizeof(int) * s->nvar);
+	s->lvlstamp = satrealloc(s, s->lvlstamp, sizeof(int) * s->nvar);
+	memset(s->lvlstamp, 0, sizeof(int) * s->nvar);
+	if(s->cflclalloc == 0){
+		s->cflcl = satrealloc(s, s->cflcl, CFLCLALLOC * sizeof(int));
+		s->cflclalloc = CFLCLALLOC;
+	}
+	rewatch(s);
+	
+	s->conflicts = 0;
+	s->nextpurge = s->purgeΔ;
+	s->purgeival = s->purgeΔ;
+	s->nextflush = 1;
+	s->flushu = 1;
+	s->flushv = 1;
+	s->flushθ = s->flushψ;
+	s->agility = 0;
+	
+	satbackjump(s, 0);
+	s->forptr = 0;
+	s->binptr = 0;
+}
+
+void
+satcleanup(SATSolve *s, int all)
+{
+	SATBlock *b, *bn;
+	
+	if(all){
+		*s->lastp[0] = nil;
+		s->learncl = nil;
+		s->lastp[1] = &s->learncl;
+		s->ncl = s->ncl0;
+	}
+	for(b = s->bl[1].next; b != &s->bl[1]; b = bn){
+		bn = b->next;
+		if(b->last != nil && !all) continue;
+		b->next->prev = b->prev;
+		b->prev->next = b->next;
+		free(b);
+	}
+	s->lastbl = s->bl[1].prev;
+	free(s->fullrlits);
+	s->fullrlits = nil;
+	free(s->lvlstamp);
+	s->lvlstamp = nil;
+	free(s->cflcl);
+	s->cflcl = nil;
+	s->cflclalloc = 0;
+}
+
+static void
+stampoverflow(SATSolve *s)
+{
+	int i;
+	
+	for(i = 0; i < s->nvar; i++){
+		s->var[i].stamp = 0;
+		s->lvlstamp[i] = 0;
+	}
+	s->stamp = -2;
+}
+
+/* "bump" the variable, i.e. increase its activity score. reduce all score when one exceeds MAXACTIVITY (1e100) */
+static void
+varbump(SATSolve *s, SATVar *v)
+{
+	v->activity += s->Δactivity;
+	satreheap(s, v);
+	if(v->activity < MAXACTIVITY) return;
+	for(v = s->var; v < s->var + s->nvar; v++)
+		if(v->activity != 0){
+			v->activity /= MAXACTIVITY;
+			if(v->activity < ε)
+				v->activity = ε;
+		}
+	s->Δactivity /= MAXACTIVITY;
+}
+
+/* ditto for clauses */
+static void
+clausebump(SATSolve *s, SATClause *c)
+{
+	c->activity += s->Δclactivity;
+	if(c->activity < MAXACTIVITY) return;
+	for(c = s->cl; c != nil; c = c->next)
+		if(c->activity != 0){
+			c->activity /= MAXACTIVITY;
+			if(c->activity < ε)
+				c->activity = ε;
+		}
+	s->Δclactivity /= MAXACTIVITY;
+}
+
+/* pick a literal. normally we pick the variable with highest activity from the heap. sometimes we goof and pick a random one. */
+static void
+decision(SATSolve *s)
+{
+	SATVar *v;
+
+	s->decbd[++s->lvl] = s->ntrail;
+	if((uint)s->randfn(s->randaux) < s->goofprob){
+		v = s->heap[satnrand(s, s->nheap)];
+		if(v->lvl < 0)
+			goto gotv;
+	}
+	do
+		v = satheaptake(s);
+	while(v->lvl >= 0);
+gotv:
+	sataddtrail(s, 2 * (v - s->var) + (v->flags & VARPHASE));
+}
+
+/* go through the watchlist of a literal that just turned out false. */
+/* full == 1 records the first conflict and goes on rather than aborting immediately */
+static SATClause *
+forcing(SATSolve *s, int l, int full)
+{
+	SATClause **cp, *rc, *c, *xp;
+	int v0;
+	int x, j;
+	
+	cp = &s->lit[l].watch;
+	rc = nil;
+	if(verboseforcing) print("forcing literal %d\n", signf(l));
+	while(c = *cp, c != nil){
+		if(l == c->l[0]){
+			/* this swap implies that the reason r for a literal l always has r->l[0]==l */
+			x = c->l[1], c->l[1] = c->l[0], c->l[0] = x;
+			xp = c->watch[1], c->watch[1] = c->watch[0], c->watch[0] = xp;
+		}
+		assert(c->l[1] == l);
+		v0 = s->lit[c->l[0]].val;
+		if(v0 > 0) /* the clause is true anyway */
+			goto next;
+		for(j = 2; j < c->n; j++)
+			if(s->lit[c->l[j]].val != 0){
+				/* found another literal to watch for this clause */
+				if(verboseforcing) print("moving clause %+Γ onto watchlist %d\n", c, signf(c->l[j]));
+				*cp = c->watch[1];
+				x = c->l[j], c->l[j] = c->l[1], c->l[1] = x;
+				c->watch[1] = s->lit[x].watch;
+				s->lit[x].watch = c;
+				goto cont;
+			}
+		if(v0 == 0){
+			/* conflict */
+			if(!full) return c;
+			if(rc == nil) rc = c;
+			goto next;
+		}
+		if(verboseforcing) print("inferring %d using clause %+Γ\n", signf(c->l[0]), c);
+		sataddtrail(s, c->l[0]);
+		s->var[VAR(c->l[0])].reason = c;
+	next:
+		cp = &c->watch[1];
+	cont: ;
+	}
+	return rc;
+}
+
+/* forcing() for binary implications */
+static uvlong
+binforcing(SATSolve *s, int l, int full)
+{
+	SATLit *lp;
+	int i, m;
+	uvlong rc;
+	
+	lp = &s->lit[l];
+	rc = 0;
+	if(verboseforcing && lp->nbimp > 0) print("forcing literal %d (binary)\n", signf(l));
+	for(i = 0; i < lp->nbimp; i++){
+		m = lp->bimp[i];
+		switch(s->lit[m].val){
+		case -1:
+			if(verboseforcing) print("inferring %d using binary clause (%d) ∨ %d\n", signf(m), -signf(l), signf(m));
+			sataddtrail(s, m);
+			s->var[VAR(m)].binreason = NOT(l);
+			s->var[VAR(m)].isbinreason = 1;
+			break;
+		case 0:
+			if(verboseforcing) print("conflict (%d) ∨ (%d)\n", -signf(l), signf(m));
+			if(rc == 0) rc = (uvlong)NOT(l) << 32 | (uint)m;
+			if(!full) return rc;
+			break;
+		}
+	}
+	return rc;
+}
+
+/* check if we can discard the previously learned clause because the current one subsumes it */
+static int
+checkdiscard(SATSolve *s)
+{
+	SATClause *c;
+	SATVar *v;
+	int q, j;
+	
+	if(s->lastp[1] == &s->learncl) return 0;
+	c = (SATClause*) ((uchar*) s->lastp[1] - (uchar*) &((SATClause*)0)->next);
+	if(s->lit[c->l[0]].val >= 0) return 0; /* clause is a reason, hands off */
+	q = s->ncflcl;
+	for(j = c->n - 1; q > 0 && j >= q; j--){
+		v = &s->var[VAR(c->l[j])];
+		/* check if literal is in the current clause */
+		if(c->l[j] == s->cflcl[0] || (uint)v->lvl <= s->cfllvl && v->stamp == s->stamp)
+			q--;
+	}
+	return q == 0;
+}
+
+/* add the clause we just learned to our collection */
+static SATClause *
+learn(SATSolve *s, int notriv)
+{
+	SATClause *r;
+	int i, l, triv;
+	
+	/* clauses that are too complicated are not worth it. learn the trivial clause (all decisions negated) instead */
+	if(triv = !notriv && s->ncflcl > s->lvl + s->trivlim){
+		assert(s->lvl + 1 <= s->cflclalloc);
+		for(i = 1; i <= s->lvl; i++)
+			s->cflcl[i] = NOT(s->trail[s->decbd[s->lvl + 1 - i]]);
+		s->ncflcl = s->lvl + 1;
+	}
+	if(s->ncflcl == 1) /* unit clauses are handled by putting them on the trail in conflict() */
+		return nil;
+	if(!triv && checkdiscard(s))
+		r = satreplclause(s, s->ncflcl);
+	else
+		r = satnewclause(s, s->ncflcl, 1);
+	r->n = s->ncflcl;
+	memcpy(r->l, s->cflcl, s->ncflcl * sizeof(int));
+	for(i = 0; i < 2; i++){
+		l = r->l[i];
+		r->watch[i] = s->lit[l].watch;
+		s->lit[l].watch = r;
+	}
+	return r;
+}
+
+/* recursive procedure to determine if a literal is redundant.
+ * to avoid repeated work, each known redundant literal is stamped with stamp+1
+ * and each known nonredundant literal is stamped with stamp+2.
+ */
+static int
+redundant(SATSolve *s, int l)
+{
+	SATVar *v, *w;
+	SATClause *c;
+	int i, r;
+	
+	v = &s->var[VAR(l)];
+	if(v->isbinreason){
+		/* stupid special case code */
+		r = v->binreason;
+		w = &s->var[VAR(r)];
+		if(w->lvl != 0){
+			if(w->stamp == s->stamp + 2)
+				return 0;
+			if(w->stamp < s->stamp && (s->lvlstamp[w->lvl] < s->stamp || !redundant(s, r))){
+				w->stamp = s->stamp + 2;
+				return 0;
+			}
+		}
+		v->stamp = s->stamp + 1;
+		return 1;
+	}
+	if(v->reason == nil) return 0; /* decision literals are never redundant */
+	c = v->reason;
+	for(i = 0; i < c->n; i++){
+		if(c->l[i] == NOT(l)) continue;
+		w = &s->var[VAR(c->l[i])];
+		if(w->lvl == 0)
+			continue; /* literals at level 0 are redundant */
+		if(w->stamp == s->stamp + 2)
+			return 0;
+		/* if the literal is not in the clause or known redundant, check if it is redundant */
+		/* we can skip the check if the level is not stamped: */
+		/* if there are no literals at the same level in the clause, it must be nonredundant */
+		if(w->stamp < s->stamp && (s->lvlstamp[w->lvl] < s->stamp || !redundant(s, c->l[i]))){
+			w->stamp = s->stamp + 2;
+			return 0;
+		}
+	}
+	v->stamp = s->stamp + 1;
+	return 1;
+}
+
+/* "blitting" a literal means to either add it to the conflict clause
+ * (if v->lvl < s->lvl) or to increment the counter of literals to be
+ * resolved, plus some bookkeeping.  */
+static void
+blit(SATSolve *s, int l)
+{
+	SATVar *v;
+	int p;
+	
+	v = &s->var[VAR(l)];
+	if(v->stamp == s->stamp) return;
+	v->stamp = s->stamp;
+	p = v->lvl;
+	if(p == 0) return;
+	if(verboseconflict) print("stamp %d %s (ctr=%d)\n", signf(l), p == s->lvl ? "and increment" : "and collect", s->cflctr);
+	varbump(s, v);
+	if(p == s->lvl){
+		s->cflctr++;
+		return;
+	}
+	if(s->ncflcl >= s->cflclalloc){
+		s->cflcl = satrealloc(s, s->cflcl, (s->cflclalloc + CFLCLALLOC) * sizeof(int));
+		s->cflclalloc += CFLCLALLOC;
+	}
+	s->cflcl[s->ncflcl++] = l;
+	if(p > s->cfllvl) s->cfllvl = p;
+	/* lvlstamp[p] == stamp if there is exactly one literal and ==stamp+1 if there is more than one literal on level p */
+	if(s->lvlstamp[p] <= s->stamp)
+		s->lvlstamp[p] = s->stamp + (s->lvlstamp[p] == s->stamp);
+}
+
+/* to resolve a conflict, we start with the conflict clause and use
+ * resolution (a ∨ b and ¬a ∨ c imply b ∨ c) with the reasons for the
+ * literals to remove all but one literal at the current level.  this
+ * gives a new "learned" clause with all literals false and we jump back
+ * to the second-highest level in it.  at this point, the clause implies
+ * the one remaining literal and we can continue.
+ * to do this quickly, rather than explicitly apply resolution, we keep a
+ * counter of literals at the highest level (unresolved literals) and an
+ * array with all other literals (which will become the learned clause). */
+static void
+conflict(SATSolve *s, SATClause *c, uvlong bin, int full)
+{
+	int i, j, l, p, *nl, found;
+	SATVar *v;
+	SATClause *r;
+
+	if(verboseconflict) satprintstate(s);
+	/* choose a new unique stamp value */
+	if(s->stamp >= (uint)-3)
+		stampoverflow(s);
+	s->stamp += 3;
+	s->ncflcl = 1;
+	s->cflctr = 0;
+	s->cfllvl = 0;
+	/* we start by blitting each literal in the conflict clause */
+	if(c != nil){
+		clausebump(s, c);
+		for(i = 0; i < c->n; i++)
+			blit(s, c->l[i]);
+		/* if there is only one literal l at the current level, we should have inferred ¬l at a lower level (bug). */
+		if(s->cflctr <= 1){
+			satprintstate(s);
+			print("conflict clause %+Γ\n", c);
+			assert(s->cflctr > 1);
+		}
+	}else{
+		blit(s, bin);
+		blit(s, bin>>32);
+		if(s->cflctr <= 1){
+			satprintstate(s);
+			print("binary conflict clause %d ∨ %d\n", (int)(bin>>32), (int)bin);
+			assert(s->cflctr > 1);
+		}
+	}
+	/* now we go backwards through the trail, decrementing the unresolved literal counter at each stamped literal */
+	/* and blitting the literals in their reason */
+	for(i = s->ntrail; --i >= 0; ){
+		v = &s->var[VAR(s->trail[i])];
+		if(v->stamp != s->stamp) continue;
+		if(verboseconflict) print("trail literal %d\n", signf(s->trail[i]));
+		if(--s->cflctr == 0) break;
+		if(v->isbinreason)
+			blit(s, v->binreason);
+		else if((r = v->reason) != nil){
+			clausebump(s, r);
+			for(j = 0; j < r->n; j++)
+				blit(s, r->l[j]);
+		}
+	}
+	/* i should point to the one remaining literal at the current level */
+	assert(i >= 0);
+	nl = s->cflcl;
+	nl[0] = NOT(s->trail[i]);
+	found = 0;
+	/* delete redundant literals. note we must watch a literal at cfllvl, so put it in l[1]. */
+	for(i = 1, j = 1; i < s->ncflcl; i++){
+		l = nl[i];
+		p = s->var[VAR(nl[i])].lvl;
+		/* lvlstamp[p] != s->stamp + 1 => only one literal at level p => must be nonredundant */
+		if(s->lvlstamp[p] != s->stamp + 1 || !redundant(s, l))
+			if(found || p < s->cfllvl)
+				nl[j++] = nl[i];
+			else{
+				/* watch this literal */
+				l = nl[i], nl[j++] = nl[1], nl[1] = l;
+				found = 1;
+			}
+	}
+	s->ncflcl = j;
+	if(!full){
+		/* normal mode: jump back and add to trail right away */
+		satbackjump(s, s->cfllvl);
+		sataddtrail(s, nl[0]);
+	}else{
+		/* purging: record minimum cfllvl and literals at that level */
+		if(s->cfllvl < s->fullrlvl){
+			s->fullrlvl = s->cfllvl;
+			s->nfullrlits = 0;
+		}
+		s->fullrlits[s->nfullrlits++] = nl[0];
+	}
+	r = learn(s, full);
+	if(!full && r != nil)
+		s->var[VAR(nl[0])].reason = r;
+	if(verboseconflict)
+		if(r != nil)
+			print("learned %+Γ\n", r);
+		else
+			print("learned %d\n", signf(nl[0]));
+	s->Δactivity *= s->varρ;
+	s->Δclactivity *= s->clauseρ;
+	s->conflicts++;
+}
+
+/* to purge, we need a fullrun that assigns values to all variables.
+ * during this we record the first conflict at each level, to be resolved
+ * later.  otherwise this is just a copy of the main loop which never
+ * purges or flushes. */
+static int
+fullrun(SATSolve *s)
+{
+	int l;
+	uvlong b;
+	SATClause *c;
+
+	while(s->ntrail < s->nvar){
+		decision(s);
+	re:
+		while(s->binptr < s->ntrail){
+			l = s->trail[s->binptr++];
+			b = binforcing(s, l, 1);
+			if(b != 0){
+				if(s->lvl == 0){
+					s->unsat = 1;
+					return -1;
+				}
+				if(s->nfullrcfl == 0 || s->lvl > CFLLVL(s->fullrcfl[s->nfullrcfl-1])){
+					s->fullrcfl = satrealloc(s, s->fullrcfl, sizeof(SATConflict) * (s->nfullrcfl + 1));
+					s->fullrcfl[s->nfullrcfl].lvl = 1<<31 | s->lvl;
+					s->fullrcfl[s->nfullrcfl++].b = b;
+				}
+			}
+			sanity(s);
+		}
+		while(s->forptr < s->ntrail){
+			l = s->trail[s->forptr++];
+			c = forcing(s, NOT(l), 1);
+			if(c != nil){
+				if(s->lvl == 0){
+					s->unsat = 1;
+					return -1;
+				}
+				if(s->nfullrcfl == 0 || s->lvl > CFLLVL(s->fullrcfl[s->nfullrcfl-1])){
+					s->fullrcfl = satrealloc(s, s->fullrcfl, sizeof(SATConflict) * (s->nfullrcfl + 1));
+					s->fullrcfl[s->nfullrcfl].lvl = s->lvl;
+					s->fullrcfl[s->nfullrcfl++].c = c;
+				}
+			}
+		}
+		if(s->binptr < s->ntrail) goto re;
+	}
+	return 0;
+}
+
+/* assign range scores to all clauses.
+ * p == number of levels that have positive literals in the clause.
+ * r == number of levels that have literals in the clause.
+ * range == min(floor(16 * (p + α (r - p))), 255) with magic constant α. */
+static void
+ranges(SATSolve *s)
+{
+	SATClause *c;
+	int p, r, k, l, v;
+	uint ci;
+
+	ci = 2;
+	memset(s->lvlstamp, 0, sizeof(int) * s->nvar);
+	memset(s->rangecnt, 0, sizeof(s->rangecnt));
+	for(c = s->learncl; c != nil; c = c->next, ci += 2){
+		if(!s->var[VAR(c->l[0])].binreason && s->var[VAR(c->l[0])].reason == c){
+			c->range = 0;
+			s->rangecnt[0]++;
+			continue;
+		}
+		p = 0;
+		r = 0;
+		for(k = 0; k < c->n; k++){
+			l = c->l[k];
+			v = s->var[VAR(l)].lvl;
+			if(v == 0){
+				if(s->lit[l].val == 1){
+					c->range = 256;
+					goto next;
+				}
+			}else{
+				if(s->lvlstamp[v] < ci){
+					s->lvlstamp[v] = ci;
+					r++;
+				}
+				if(s->lvlstamp[v] == ci && s->lit[l].val == 1){
+					s->lvlstamp[v] = ci + 1;
+					p++;
+				}
+			}
+		}
+		r = 16 * (p + s->purgeα * (r - p));
+		if(r > 255) r = 255;
+		c->range = r;
+		s->rangecnt[r]++;
+	next: ;
+	}
+}
+
+/* resolve conflicts found during fullrun() */
+static void
+fullrconflicts(SATSolve *s)
+{
+	SATConflict *cfl;
+	int i;
+	
+	s->fullrlvl = s->lvl;
+	s->nfullrlits = 0;
+	for(cfl = &s->fullrcfl[s->nfullrcfl - 1]; cfl >= s->fullrcfl; cfl--){
+		satbackjump(s, CFLLVL(*cfl));
+		if(cfl->lvl < 0)
+			conflict(s, nil, cfl->b, 1);
+		else
+			conflict(s, cfl->c, 0, 1);
+	}
+	satbackjump(s, 0);
+	if(s->fullrlvl == 0)
+		for(i = 0; i < s->nfullrlits; i++)
+			sataddtrail(s, s->fullrlits[i]);
+	free(s->fullrcfl);
+	s->fullrcfl = nil;
+}
+
+/* note that nil > *, this simplifies the algorithm by having nil "bubble" to the top */
+static int
+actgt(SATClause *a, SATClause *b)
+{
+	if(b == nil) return 0;
+	if(a == nil) return 1;
+	return a->activity > b->activity || a->activity == b->activity && a > b;
+}
+
+/* select n clauses to keep
+ * first we find the upper limit j on the range score
+ * to get the exact number, we move htot clauses from j to j+1
+ * to this end, we put them in a max-heap of size htot, sorted by activity,
+ * continually replacing the largest element if we find a less active clause.
+ * the heap starts out filled with nil and the nil are replaced during the first
+ * htot iterations. */
+#define LEFT(i) (2*(i)+1)
+#define RIGHT(i) (2*(i)+2)
+static int
+judgement(SATSolve *s, int n)
+{
+	int cnt, i, j, htot, m;
+	SATClause *c, **h, *z;
+	
+	cnt = 0;
+	for(j = 0; j < 256; j++){
+		cnt += s->rangecnt[j];
+		if(cnt >= n) break;
+	}
+	if(j == 256) return j;
+	if(cnt > n){
+		htot = cnt - n;
+		h = satrealloc(s, nil, sizeof(SATClause *) * htot);
+		memset(h, 0, sizeof(SATClause *) * htot);
+		for(c = s->learncl; c != nil; c = c->next){
+			if(c->range != j || actgt(c, h[0])) continue;
+			h[0] = c;
+			m = 0;
+			for(;;){
+				i = m;
+				if(LEFT(i) < htot && actgt(h[LEFT(i)], h[m])) m = LEFT(i);
+				if(RIGHT(i) < htot && actgt(h[RIGHT(i)], h[m])) m = RIGHT(i);
+				if(i == m) break;
+				z = h[i], h[i] = h[m], h[m] = z;
+			}
+		}
+		for(i = 0; i < htot; i++)
+			if(h[i] != nil)
+				h[i]->range = j + 1;
+		free(h);
+	}
+	return j;
+}
+
+/* during purging we remove permanently false literals from learned clauses.
+ * returns 1 if the clause can be deleted entirely. */
+static int
+cleanupclause(SATSolve *s, SATClause *c)
+{
+	int i, k;
+	
+	for(i = 0; i < c->n; i++)
+		if(s->lit[c->l[i]].val == 0)
+			break;
+	if(i == c->n) return 0;
+	for(k = i; i < c->n; i++)
+		if(s->lit[c->l[i]].val != 0)
+			c->l[k++] = c->l[i];
+	c->n = k;
+	if(k > 1) return 0;
+	if(k == 0)
+		s->unsat = 1;
+	else if(s->lit[c->l[0]].val < 0)
+		sataddtrail(s, c->l[0]);
+	return 1;
+}
+
+/* delete clauses by overwriting them. don't delete empty blocks; we're going to fill them up soon enough again. */
+static void
+execution(SATSolve *s, int j)
+{
+	SATClause *c, *n, **cp, *p;
+	SATBlock *b;
+	SATVar *v0;
+	int f, sz;
+
+	b = s->bl[1].next;
+	p = (SATClause*) b->data;
+	s->ncl = s->ncl0;
+	cp = &s->learncl;
+	for(c = p; c != nil; c = n){
+		n = c->next;
+		if(c->range > j || cleanupclause(s, c))
+			continue;
+		sz = sizeof(SATClause) + (c->n - 1) * sizeof(int);
+		f = (uchar*)b + SATBLOCKSZ - (uchar*)p;
+		if(f < sz){
+			memset(p, 0, f);
+			b = b->next;
+			assert(b != &s->bl[1]);
+			p = (SATClause *) b->data;
+		}
+		b->last = p;
+		/* update reason field of the first variable (if applicable) */
+		v0 = &s->var[VAR(c->l[0])];
+		if(!v0->isbinreason && v0->reason == c)
+			v0->reason = p;
+		memmove(p, c, sz);
+		*cp = p;
+		cp = &p->next;
+		p = (void*)((uintptr)p + sz + CLAUSEALIGN - 1 & -CLAUSEALIGN);
+		b->end = p;
+		s->ncl++;
+	}
+	*cp = nil;
+	*s->lastp[0] = s->learncl;
+	s->lastp[1] = cp;
+	s->lastbl = b;
+	f = (uchar*)b + SATBLOCKSZ - (uchar*)p;
+	memset(p, 0, f);
+	for(b = b->next; b != &s->bl[1]; b = b->next){
+		b->last = nil;
+		b->end = b->data;
+	}
+}
+
+static void
+thepurge(SATSolve *s)
+{
+	int nkeep, i, j;
+	SATVar *v;
+	
+	s->purgeival += s->purgeδ;
+	s->nextpurge = s->conflicts + s->purgeival;
+	nkeep = (s->ncl - s->ncl0) / 2;
+	for(i = 0; i < s->ntrail; i++){
+		v = &s->var[VAR(s->trail[i])];
+		if(!v->isbinreason && v->reason != nil)
+			nkeep++;
+	}
+	if(nkeep <= 0) return; /* shouldn't happen */
+	s->nfullrcfl = 0;
+	if(fullrun(s) < 0){ /* accidentally determined UNSAT during fullrun() */
+		free(s->fullrcfl);
+		s->fullrcfl = nil;
+		return;
+	}
+	ranges(s);
+	fullrconflicts(s);
+	j = judgement(s, nkeep);
+	execution(s, j);
+	rewatch(s);
+}
+
+/* to avoid getting stuck, flushing backs up the trail to remove low activity variables.
+ * don't worry about throwing out high activity ones, they'll get readded quickly. */
+static void
+theflush(SATSolve *s)
+{
+	double actk;
+	int dd, l;
+
+	/* "reluctant doubling" wizardry to determine when to flush */
+	if((s->flushu & -s->flushu) == s->flushv){
+		s->flushu++;
+		s->flushv = 1;
+		s->flushθ = s->flushψ;
+	}else{
+		s->flushv *= 2;
+		s->flushθ += s->flushθ >> 4;
+	}
+	s->nextflush = s->conflicts + s->flushv;
+	if(s->agility > s->flushθ) return; /* don't flush when we're too busy */
+	/* clean up the heap so that a free variable is at the top */
+	while(s->nheap > 0 && s->heap[0]->lvl >= 0)
+		satheaptake(s);
+	if(s->nheap == 0) return; /* shouldn't happen */
+	actk = s->heap[0]->activity;
+	for(dd = 0; dd < s->lvl; dd++){
+		l = s->trail[s->decbd[dd+1]];
+		if(s->var[VAR(l)].activity < actk)
+			break;
+	}
+	satbackjump(s, dd);
+}
+
+int
+satsolve(SATSolve *s)
+{
+	int l;
+	SATClause *c;
+	uvlong b;
+
+	if(s == nil) return 1;
+	if(s->scratched) return -1;
+	if(s->nvar == 0) return 1;
+	solvinit(s);
+	
+	while(!s->unsat){
+	re:
+		while(s->binptr < s->ntrail){
+			l = s->trail[s->binptr++];
+			b = binforcing(s, l, 0);
+			sanity(s);
+			if(b != 0){
+				if(s->lvl == 0) goto unsat;
+				conflict(s, nil, b, 0);
+				sanity(s);
+			}
+		}
+		while(s->forptr < s->ntrail){
+			l = s->trail[s->forptr++];
+			c = forcing(s, NOT(l), 0);
+			sanity(s);
+			if(c != nil){
+				if(s->lvl == 0) goto unsat;
+				conflict(s, c, 0, 0);
+				sanity(s);
+			}
+		}
+		if(s->binptr < s->ntrail) goto re;
+		if(s->ntrail == s->nvar) goto out;
+		if(s->conflicts >= s->nextpurge)
+			thepurge(s);
+		else if(s->conflicts >= s->nextflush)
+			theflush(s);
+		else
+			decision(s);
+	}
+unsat:
+	s->unsat = 1;
+out:
+	satcleanup(s, 0);
+	return !s->unsat;
+}
+
+void
+satreset(SATSolve *s)
+{
+	int i;
+
+	if(s == nil || s->decbd == nil) return;
+	satbackjump(s, -1);
+	s->lvl = 0;
+	for(i = 0; i < s->nvar; i++){
+		s->var[i].activity = 0;
+		s->var[i].flags |= VARPHASE;
+	}
+	satcleanup(s, 1);
+	s->Δactivity = 1;
+	s->Δclactivity = 1;
+}