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+/*
+ * Revision Control Information
+ *
+ * $Source$
+ * $Author$
+ * $Revision$
+ * $Date$
+ *
+ */
+/*
+ * module: compl.c
+ * purpose: compute the complement of a multiple-valued function
+ *
+ * The "unate recursive paradigm" is used. After a set of special
+ * cases are examined, the function is split on the "most active
+ * variable". These two halves are complemented recursively, and then
+ * the results are merged.
+ *
+ * Changes (from Version 2.1 to Version 2.2)
+ * 1. Minor bug in compl_lifting -- cubes in the left half were
+ * not marked as active, so that when merging a leaf from the left
+ * hand side, the active flags were essentially random. This led
+ * to minor impredictability problem, but never affected the
+ * accuracy of the results.
+ */
+
+#include "espresso.h"
+
+#define USE_COMPL_LIFT 0
+#define USE_COMPL_LIFT_ONSET 1
+#define USE_COMPL_LIFT_ONSET_COMPLEX 2
+#define NO_LIFTING 3
+
+static bool compl_special_cases();
+static pcover compl_merge();
+static void compl_d1merge();
+static pcover compl_cube();
+static void compl_lift();
+static void compl_lift_onset();
+static void compl_lift_onset_complex();
+static bool simp_comp_special_cases();
+static bool simplify_special_cases();
+
+
+/* complement -- compute the complement of T */
+pcover complement(T)
+pcube *T; /* T will be disposed of */
+{
+ register pcube cl, cr;
+ register int best;
+ pcover Tbar, Tl, Tr;
+ int lifting;
+ static int compl_level = 0;
+
+ if (debug & COMPL)
+ debug_print(T, "COMPLEMENT", compl_level++);
+
+ if (compl_special_cases(T, &Tbar) == MAYBE) {
+
+ /* Allocate space for the partition cubes */
+ cl = new_cube();
+ cr = new_cube();
+ best = binate_split_select(T, cl, cr, COMPL);
+
+ /* Complement the left and right halves */
+ Tl = complement(scofactor(T, cl, best));
+ Tr = complement(scofactor(T, cr, best));
+
+ if (Tr->count*Tl->count > (Tr->count+Tl->count)*CUBELISTSIZE(T)) {
+ lifting = USE_COMPL_LIFT_ONSET;
+ } else {
+ lifting = USE_COMPL_LIFT;
+ }
+ Tbar = compl_merge(T, Tl, Tr, cl, cr, best, lifting);
+
+ free_cube(cl);
+ free_cube(cr);
+ free_cubelist(T);
+ }
+
+ if (debug & COMPL)
+ debug1_print(Tbar, "exit COMPLEMENT", --compl_level);
+ return Tbar;
+}
+
+static bool compl_special_cases(T, Tbar)
+pcube *T; /* will be disposed if answer is determined */
+pcover *Tbar; /* returned only if answer determined */
+{
+ register pcube *T1, p, ceil, cof=T[0];
+ pcover A, ceil_compl;
+
+ /* Check for no cubes in the cover */
+ if (T[2] == NULL) {
+ *Tbar = sf_addset(new_cover(1), cube.fullset);
+ free_cubelist(T);
+ return TRUE;
+ }
+
+ /* Check for only a single cube in the cover */
+ if (T[3] == NULL) {
+ *Tbar = compl_cube(set_or(cof, cof, T[2]));
+ free_cubelist(T);
+ return TRUE;
+ }
+
+ /* Check for a row of all 1's (implies complement is null) */
+ for(T1 = T+2; (p = *T1++) != NULL; ) {
+ if (full_row(p, cof)) {
+ *Tbar = new_cover(0);
+ free_cubelist(T);
+ return TRUE;
+ }
+ }
+
+ /* Check for a column of all 0's which can be factored out */
+ ceil = set_save(cof);
+ for(T1 = T+2; (p = *T1++) != NULL; ) {
+ INLINEset_or(ceil, ceil, p);
+ }
+ if (! setp_equal(ceil, cube.fullset)) {
+ ceil_compl = compl_cube(ceil);
+ (void) set_or(cof, cof, set_diff(ceil, cube.fullset, ceil));
+ set_free(ceil);
+ *Tbar = sf_append(complement(T), ceil_compl);
+ return TRUE;
+ }
+ set_free(ceil);
+
+ /* Collect column counts, determine unate variables, etc. */
+ massive_count(T);
+
+ /* If single active variable not factored out above, then tautology ! */
+ if (cdata.vars_active == 1) {
+ *Tbar = new_cover(0);
+ free_cubelist(T);
+ return TRUE;
+
+ /* Check for unate cover */
+ } else if (cdata.vars_unate == cdata.vars_active) {
+ A = map_cover_to_unate(T);
+ free_cubelist(T);
+ A = unate_compl(A);
+ *Tbar = map_unate_to_cover(A);
+ sf_free(A);
+ return TRUE;
+
+ /* Not much we can do about it */
+ } else {
+ return MAYBE;
+ }
+}
+
+/*
+ * compl_merge -- merge the two cofactors around the splitting
+ * variable
+ *
+ * The merge operation involves intersecting each cube of the left
+ * cofactor with cl, and intersecting each cube of the right cofactor
+ * with cr. The union of these two covers is the merged result.
+ *
+ * In order to reduce the number of cubes, a distance-1 merge is
+ * performed (note that two cubes can only combine distance-1 in the
+ * splitting variable). Also, a simple expand is performed in the
+ * splitting variable (simple implies the covering check for the
+ * expansion is not full containment, but single-cube containment).
+ */
+
+static pcover compl_merge(T1, L, R, cl, cr, var, lifting)
+pcube *T1; /* Original ON-set */
+pcover L, R; /* Complement from each recursion branch */
+register pcube cl, cr; /* cubes used for cofactoring */
+int var; /* splitting variable */
+int lifting; /* whether to perform lifting or not */
+{
+ register pcube p, last, pt;
+ pcover T, Tbar;
+ pcube *L1, *R1;
+
+ if (debug & COMPL) {
+ (void) printf("compl_merge: left %d, right %d\n", L->count, R->count);
+ (void) printf("%s (cl)\n%s (cr)\nLeft is\n", pc1(cl), pc2(cr));
+ cprint(L);
+ (void) printf("Right is\n");
+ cprint(R);
+ }
+
+ /* Intersect each cube with the cofactored cube */
+ foreach_set(L, last, p) {
+ INLINEset_and(p, p, cl);
+ SET(p, ACTIVE);
+ }
+ foreach_set(R, last, p) {
+ INLINEset_and(p, p, cr);
+ SET(p, ACTIVE);
+ }
+
+ /* Sort the arrays for a distance-1 merge */
+ (void) set_copy(cube.temp[0], cube.var_mask[var]);
+ qsort((char *) (L1 = sf_list(L)), L->count, sizeof(pset), (int (*)()) d1_order);
+ qsort((char *) (R1 = sf_list(R)), R->count, sizeof(pset), (int (*)()) d1_order);
+
+ /* Perform distance-1 merge */
+ compl_d1merge(L1, R1);
+
+ /* Perform lifting */
+ switch(lifting) {
+ case USE_COMPL_LIFT_ONSET:
+ T = cubeunlist(T1);
+ compl_lift_onset(L1, T, cr, var);
+ compl_lift_onset(R1, T, cl, var);
+ free_cover(T);
+ break;
+ case USE_COMPL_LIFT_ONSET_COMPLEX:
+ T = cubeunlist(T1);
+ compl_lift_onset_complex(L1, T, var);
+ compl_lift_onset_complex(R1, T, var);
+ free_cover(T);
+ break;
+ case USE_COMPL_LIFT:
+ compl_lift(L1, R1, cr, var);
+ compl_lift(R1, L1, cl, var);
+ break;
+ case NO_LIFTING:
+ break;
+ default:
+ ;
+ }
+ FREE(L1);
+ FREE(R1);
+
+ /* Re-create the merged cover */
+ Tbar = new_cover(L->count + R->count);
+ pt = Tbar->data;
+ foreach_set(L, last, p) {
+ INLINEset_copy(pt, p);
+ Tbar->count++;
+ pt += Tbar->wsize;
+ }
+ foreach_active_set(R, last, p) {
+ INLINEset_copy(pt, p);
+ Tbar->count++;
+ pt += Tbar->wsize;
+ }
+
+ if (debug & COMPL) {
+ (void) printf("Result %d\n", Tbar->count);
+ if (verbose_debug)
+ cprint(Tbar);
+ }
+
+ free_cover(L);
+ free_cover(R);
+ return Tbar;
+}
+
+/*
+ * compl_lift_simple -- expand in the splitting variable using single
+ * cube containment against the other recursion branch to check
+ * validity of the expansion, and expanding all (or none) of the
+ * splitting variable.
+ */
+static void compl_lift(A1, B1, bcube, var)
+pcube *A1, *B1, bcube;
+int var;
+{
+ register pcube a, b, *B2, lift=cube.temp[4], liftor=cube.temp[5];
+ pcube mask = cube.var_mask[var];
+
+ (void) set_and(liftor, bcube, mask);
+
+ /* for each cube in the first array ... */
+ for(; (a = *A1++) != NULL; ) {
+ if (TESTP(a, ACTIVE)) {
+
+ /* create a lift of this cube in the merging coord */
+ (void) set_merge(lift, bcube, a, mask);
+
+ /* for each cube in the second array */
+ for(B2 = B1; (b = *B2++) != NULL; ) {
+ INLINEsetp_implies(lift, b, /* when_false => */ continue);
+ /* when_true => fall through to next statement */
+
+ /* cube of A1 was contained by some cube of B1, so raise */
+ INLINEset_or(a, a, liftor);
+ break;
+ }
+ }
+ }
+}
+
+
+
+/*
+ * compl_lift_onset -- expand in the splitting variable using a
+ * distance-1 check against the original on-set; expand all (or
+ * none) of the splitting variable. Each cube of A1 is expanded
+ * against the original on-set T.
+ */
+static void compl_lift_onset(A1, T, bcube, var)
+pcube *A1;
+pcover T;
+pcube bcube;
+int var;
+{
+ register pcube a, last, p, lift=cube.temp[4], mask=cube.var_mask[var];
+
+ /* for each active cube from one branch of the complement */
+ for(; (a = *A1++) != NULL; ) {
+ if (TESTP(a, ACTIVE)) {
+
+ /* create a lift of this cube in the merging coord */
+ INLINEset_and(lift, bcube, mask); /* isolate parts to raise */
+ INLINEset_or(lift, a, lift); /* raise these parts in a */
+
+ /* for each cube in the ON-set, check for intersection */
+ foreach_set(T, last, p) {
+ if (cdist0(p, lift)) {
+ goto nolift;
+ }
+ }
+ INLINEset_copy(a, lift); /* save the raising */
+ SET(a, ACTIVE);
+nolift : ;
+ }
+ }
+}
+
+/*
+ * compl_lift_complex -- expand in the splitting variable, but expand all
+ * parts which can possibly expand.
+ * T is the original ON-set
+ * A1 is either the left or right cofactor
+ */
+static void compl_lift_onset_complex(A1, T, var)
+pcube *A1; /* array of pointers to new result */
+pcover T; /* original ON-set */
+int var; /* which variable we split on */
+{
+ register int dist;
+ register pcube last, p, a, xlower;
+
+ /* for each cube in the complement */
+ xlower = new_cube();
+ for(; (a = *A1++) != NULL; ) {
+
+ if (TESTP(a, ACTIVE)) {
+
+ /* Find which parts of the splitting variable are forced low */
+ INLINEset_clear(xlower, cube.size);
+ foreach_set(T, last, p) {
+ if ((dist = cdist01(p, a)) < 2) {
+ if (dist == 0) {
+ fatal("compl: ON-set and OFF-set are not orthogonal");
+ } else {
+ (void) force_lower(xlower, p, a);
+ }
+ }
+ }
+
+ (void) set_diff(xlower, cube.var_mask[var], xlower);
+ (void) set_or(a, a, xlower);
+ free_cube(xlower);
+ }
+ }
+}
+
+
+
+/*
+ * compl_d1merge -- distance-1 merge in the splitting variable
+ */
+static void compl_d1merge(L1, R1)
+register pcube *L1, *R1;
+{
+ register pcube pl, pr;
+
+ /* Find equal cubes between the two cofactors */
+ for(pl = *L1, pr = *R1; (pl != NULL) && (pr != NULL); )
+ switch (d1_order(L1, R1)) {
+ case 1:
+ pr = *(++R1); break; /* advance right pointer */
+ case -1:
+ pl = *(++L1); break; /* advance left pointer */
+ case 0:
+ RESET(pr, ACTIVE);
+ INLINEset_or(pl, pl, pr);
+ pr = *(++R1);
+ default:
+ ;
+ }
+}
+
+
+
+/* compl_cube -- return the complement of a single cube (De Morgan's law) */
+static pcover compl_cube(p)
+register pcube p;
+{
+ register pcube diff=cube.temp[7], pdest, mask, full=cube.fullset;
+ int var;
+ pcover R;
+
+ /* Allocate worst-case size cover (to avoid checking overflow) */
+ R = new_cover(cube.num_vars);
+
+ /* Compute bit-wise complement of the cube */
+ INLINEset_diff(diff, full, p);
+
+ for(var = 0; var < cube.num_vars; var++) {
+ mask = cube.var_mask[var];
+ /* If the bit-wise complement is not empty in var ... */
+ if (! setp_disjoint(diff, mask)) {
+ pdest = GETSET(R, R->count++);
+ INLINEset_merge(pdest, diff, full, mask);
+ }
+ }
+ return R;
+}
+
+/* simp_comp -- quick simplification of T */
+void simp_comp(T, Tnew, Tbar)
+pcube *T; /* T will be disposed of */
+pcover *Tnew;
+pcover *Tbar;
+{
+ register pcube cl, cr;
+ register int best;
+ pcover Tl, Tr, Tlbar, Trbar;
+ int lifting;
+ static int simplify_level = 0;
+
+ if (debug & COMPL)
+ debug_print(T, "SIMPCOMP", simplify_level++);
+
+ if (simp_comp_special_cases(T, Tnew, Tbar) == MAYBE) {
+
+ /* Allocate space for the partition cubes */
+ cl = new_cube();
+ cr = new_cube();
+ best = binate_split_select(T, cl, cr, COMPL);
+
+ /* Complement the left and right halves */
+ simp_comp(scofactor(T, cl, best), &Tl, &Tlbar);
+ simp_comp(scofactor(T, cr, best), &Tr, &Trbar);
+
+ lifting = USE_COMPL_LIFT;
+ *Tnew = compl_merge(T, Tl, Tr, cl, cr, best, lifting);
+
+ lifting = USE_COMPL_LIFT;
+ *Tbar = compl_merge(T, Tlbar, Trbar, cl, cr, best, lifting);
+
+ /* All of this work for nothing ? Let's hope not ... */
+ if ((*Tnew)->count > CUBELISTSIZE(T)) {
+ sf_free(*Tnew);
+ *Tnew = cubeunlist(T);
+ }
+
+ free_cube(cl);
+ free_cube(cr);
+ free_cubelist(T);
+ }
+
+ if (debug & COMPL) {
+ debug1_print(*Tnew, "exit SIMPCOMP (new)", simplify_level);
+ debug1_print(*Tbar, "exit SIMPCOMP (compl)", simplify_level);
+ simplify_level--;
+ }
+}
+
+static bool simp_comp_special_cases(T, Tnew, Tbar)
+pcube *T; /* will be disposed if answer is determined */
+pcover *Tnew; /* returned only if answer determined */
+pcover *Tbar; /* returned only if answer determined */
+{
+ register pcube *T1, p, ceil, cof=T[0];
+ pcube last;
+ pcover A;
+
+ /* Check for no cubes in the cover (function is empty) */
+ if (T[2] == NULL) {
+ *Tnew = new_cover(1);
+ *Tbar = sf_addset(new_cover(1), cube.fullset);
+ free_cubelist(T);
+ return TRUE;
+ }
+
+ /* Check for only a single cube in the cover */
+ if (T[3] == NULL) {
+ (void) set_or(cof, cof, T[2]);
+ *Tnew = sf_addset(new_cover(1), cof);
+ *Tbar = compl_cube(cof);
+ free_cubelist(T);
+ return TRUE;
+ }
+
+ /* Check for a row of all 1's (function is a tautology) */
+ for(T1 = T+2; (p = *T1++) != NULL; ) {
+ if (full_row(p, cof)) {
+ *Tnew = sf_addset(new_cover(1), cube.fullset);
+ *Tbar = new_cover(1);
+ free_cubelist(T);
+ return TRUE;
+ }
+ }
+
+ /* Check for a column of all 0's which can be factored out */
+ ceil = set_save(cof);
+ for(T1 = T+2; (p = *T1++) != NULL; ) {
+ INLINEset_or(ceil, ceil, p);
+ }
+ if (! setp_equal(ceil, cube.fullset)) {
+ p = new_cube();
+ (void) set_diff(p, cube.fullset, ceil);
+ (void) set_or(cof, cof, p);
+ set_free(p);
+ simp_comp(T, Tnew, Tbar);
+
+ /* Adjust the ON-set */
+ A = *Tnew;
+ foreach_set(A, last, p) {
+ INLINEset_and(p, p, ceil);
+ }
+
+ /* Compute the new complement */
+ *Tbar = sf_append(*Tbar, compl_cube(ceil));
+ set_free(ceil);
+ return TRUE;
+ }
+ set_free(ceil);
+
+ /* Collect column counts, determine unate variables, etc. */
+ massive_count(T);
+
+ /* If single active variable not factored out above, then tautology ! */
+ if (cdata.vars_active == 1) {
+ *Tnew = sf_addset(new_cover(1), cube.fullset);
+ *Tbar = new_cover(1);
+ free_cubelist(T);
+ return TRUE;
+
+ /* Check for unate cover */
+ } else if (cdata.vars_unate == cdata.vars_active) {
+ /* Make the cover minimum by single-cube containment */
+ A = cubeunlist(T);
+ *Tnew = sf_contain(A);
+
+ /* Now form a minimum representation of the complement */
+ A = map_cover_to_unate(T);
+ A = unate_compl(A);
+ *Tbar = map_unate_to_cover(A);
+ sf_free(A);
+ free_cubelist(T);
+ return TRUE;
+
+ /* Not much we can do about it */
+ } else {
+ return MAYBE;
+ }
+}
+
+/* simplify -- quick simplification of T */
+pcover simplify(T)
+pcube *T; /* T will be disposed of */
+{
+ register pcube cl, cr;
+ register int best;
+ pcover Tbar, Tl, Tr;
+ int lifting;
+ static int simplify_level = 0;
+
+ if (debug & COMPL) {
+ debug_print(T, "SIMPLIFY", simplify_level++);
+ }
+
+ if (simplify_special_cases(T, &Tbar) == MAYBE) {
+
+ /* Allocate space for the partition cubes */
+ cl = new_cube();
+ cr = new_cube();
+
+ best = binate_split_select(T, cl, cr, COMPL);
+
+ /* Complement the left and right halves */
+ Tl = simplify(scofactor(T, cl, best));
+ Tr = simplify(scofactor(T, cr, best));
+
+ lifting = USE_COMPL_LIFT;
+ Tbar = compl_merge(T, Tl, Tr, cl, cr, best, lifting);
+
+ /* All of this work for nothing ? Let's hope not ... */
+ if (Tbar->count > CUBELISTSIZE(T)) {
+ sf_free(Tbar);
+ Tbar = cubeunlist(T);
+ }
+
+ free_cube(cl);
+ free_cube(cr);
+ free_cubelist(T);
+ }
+
+ if (debug & COMPL) {
+ debug1_print(Tbar, "exit SIMPLIFY", --simplify_level);
+ }
+ return Tbar;
+}
+
+static bool simplify_special_cases(T, Tnew)
+pcube *T; /* will be disposed if answer is determined */
+pcover *Tnew; /* returned only if answer determined */
+{
+ register pcube *T1, p, ceil, cof=T[0];
+ pcube last;
+ pcover A;
+
+ /* Check for no cubes in the cover */
+ if (T[2] == NULL) {
+ *Tnew = new_cover(0);
+ free_cubelist(T);
+ return TRUE;
+ }
+
+ /* Check for only a single cube in the cover */
+ if (T[3] == NULL) {
+ *Tnew = sf_addset(new_cover(1), set_or(cof, cof, T[2]));
+ free_cubelist(T);
+ return TRUE;
+ }
+
+ /* Check for a row of all 1's (implies function is a tautology) */
+ for(T1 = T+2; (p = *T1++) != NULL; ) {
+ if (full_row(p, cof)) {
+ *Tnew = sf_addset(new_cover(1), cube.fullset);
+ free_cubelist(T);
+ return TRUE;
+ }
+ }
+
+ /* Check for a column of all 0's which can be factored out */
+ ceil = set_save(cof);
+ for(T1 = T+2; (p = *T1++) != NULL; ) {
+ INLINEset_or(ceil, ceil, p);
+ }
+ if (! setp_equal(ceil, cube.fullset)) {
+ p = new_cube();
+ (void) set_diff(p, cube.fullset, ceil);
+ (void) set_or(cof, cof, p);
+ free_cube(p);
+
+ A = simplify(T);
+ foreach_set(A, last, p) {
+ INLINEset_and(p, p, ceil);
+ }
+ *Tnew = A;
+ set_free(ceil);
+ return TRUE;
+ }
+ set_free(ceil);
+
+ /* Collect column counts, determine unate variables, etc. */
+ massive_count(T);
+
+ /* If single active variable not factored out above, then tautology ! */
+ if (cdata.vars_active == 1) {
+ *Tnew = sf_addset(new_cover(1), cube.fullset);
+ free_cubelist(T);
+ return TRUE;
+
+ /* Check for unate cover */
+ } else if (cdata.vars_unate == cdata.vars_active) {
+ A = cubeunlist(T);
+ *Tnew = sf_contain(A);
+ free_cubelist(T);
+ return TRUE;
+
+ /* Not much we can do about it */
+ } else {
+ return MAYBE;
+ }
+}
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