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+/*
+ * Revision Control Information
+ *
+ * $Source$
+ * $Author$
+ * $Revision$
+ * $Date$
+ *
+ */
+#include "espresso.h"
+
+/*
+ * Phase assignment technique (T. Sasao):
+ *
+ * 1. create a function with 2*m outputs which implements the
+ * original function and its complement for each output
+ *
+ * 2. minimize this function
+ *
+ * 3. choose the minimum number of prime implicants from the
+ * result of step 2 which are needed to realize either a function
+ * or its complement for each output
+ *
+ * Step 3 is performed in a rather crude way -- by simply multiplying
+ * out a large expression of the form:
+ *
+ * I = (ab + cdef)(acd + bgh) ...
+ *
+ * which is a product of m expressions where each expression has two
+ * product terms -- one representing which primes are needed for the
+ * function, and one representing which primes are needed for the
+ * complement. The largest product term resulting shows which primes
+ * to keep to implement one function or the other for each output.
+ * For problems with many outputs, this may grind to a
+ * halt.
+ *
+ * Untried: form complement of I and use unate_complement ...
+ *
+ * I have unsuccessfully tried several modifications to the basic
+ * algorithm. The first is quite simple: use Sasao's technique, but
+ * only commit to a single output at a time (rather than all
+ * outputs). The goal would be that the later minimizations can "take
+ * into account" the partial assignment at each step. This is
+ * expensive (m+1 minimizations rather than 2), and the results are
+ * discouraging.
+ *
+ * The second modification is rather complicated. The result from the
+ * minimization in step 2 is guaranteed to be minimal. Hence, for
+ * each output, the set of primes with a 1 in that output are both
+ * necessary and sufficient to implement the function. Espresso
+ * achieves the minimality using the routine MAKE_SPARSE. The
+ * modification is to prevent MAKE_SPARSE from running. Hence, there
+ * are potentially many subsets of the set of primes with a 1 in a
+ * column which can be used to implement that output. We use
+ * IRREDUNDANT to enumerate all possible subsets and then proceed as
+ * before.
+ */
+
+static int opo_no_make_sparse;
+static int opo_repeated;
+static int opo_exact;
+static void minimize();
+
+void phase_assignment(PLA, opo_strategy)
+pPLA PLA;
+int opo_strategy;
+{
+ opo_no_make_sparse = opo_strategy % 2;
+ skip_make_sparse = opo_no_make_sparse;
+ opo_repeated = (opo_strategy / 2) % 2;
+ opo_exact = (opo_strategy / 4) % 2;
+
+ /* Determine a phase assignment */
+ if (PLA->phase != NULL) {
+ FREE(PLA->phase);
+ }
+
+ if (opo_repeated) {
+ PLA->phase = set_save(cube.fullset);
+ repeated_phase_assignment(PLA);
+ } else {
+ PLA->phase = find_phase(PLA, 0, (pcube) NULL);
+ }
+
+ /* Now minimize with this assignment */
+ skip_make_sparse = FALSE;
+ (void) set_phase(PLA);
+ minimize(PLA);
+}
+
+/*
+ * repeated_phase_assignment -- an alternate strategy which commits
+ * to a single phase assignment a step at a time. Performs m + 1
+ * minimizations !
+ */
+void repeated_phase_assignment(PLA)
+pPLA PLA;
+{
+ int i;
+ pcube phase;
+
+ for(i = 0; i < cube.part_size[cube.output]; i++) {
+
+ /* Find best assignment for all undecided outputs */
+ phase = find_phase(PLA, i, PLA->phase);
+
+ /* Commit for only a single output ... */
+ if (! is_in_set(phase, cube.first_part[cube.output] + i)) {
+ set_remove(PLA->phase, cube.first_part[cube.output] + i);
+ }
+
+ if (trace || summary) {
+ printf("\nOPO loop for output #%d\n", i);
+ printf("PLA->phase is %s\n", pc1(PLA->phase));
+ printf("phase is %s\n", pc1(phase));
+ }
+ set_free(phase);
+ }
+}
+
+
+/*
+ * find_phase -- find a phase assignment for the PLA for all outputs starting
+ * with output number first_output.
+ */
+pcube find_phase(PLA, first_output, phase1)
+pPLA PLA;
+int first_output;
+pcube phase1;
+{
+ pcube phase;
+ pPLA PLA1;
+
+ phase = set_save(cube.fullset);
+
+ /* setup the double-phase characteristic function, resize the cube */
+ PLA1 = new_PLA();
+ PLA1->F = sf_save(PLA->F);
+ PLA1->R = sf_save(PLA->R);
+ PLA1->D = sf_save(PLA->D);
+ if (phase1 != NULL) {
+ PLA1->phase = set_save(phase1);
+ (void) set_phase(PLA1);
+ }
+ EXEC_S(output_phase_setup(PLA1, first_output), "OPO-SETUP ", PLA1->F);
+
+ /* minimize the double-phase function */
+ minimize(PLA1);
+
+ /* set the proper phases according to what gives a minimum solution */
+ EXEC_S(PLA1->F = opo(phase, PLA1->F, PLA1->D, PLA1->R, first_output),
+ "OPO ", PLA1->F);
+ free_PLA(PLA1);
+
+ /* set the cube structure to reflect the old size */
+ setdown_cube();
+ cube.part_size[cube.output] -=
+ (cube.part_size[cube.output] - first_output) / 2;
+ cube_setup();
+
+ return phase;
+}
+
+/*
+ * opo -- multiply the expression out to determine a minimum subset of
+ * primes.
+ */
+
+/*ARGSUSED*/
+pcover opo(phase, T, D, R, first_output)
+pcube phase;
+pcover T, D, R;
+int first_output;
+{
+ int offset, output, i, last_output, ind;
+ pset pdest, select, p, p1, last, last1, not_covered, tmp;
+ pset_family temp, T1, T2;
+
+ /* must select all primes for outputs [0 .. first_output-1] */
+ select = set_full(T->count);
+ for(output = 0; output < first_output; output++) {
+ ind = cube.first_part[cube.output] + output;
+ foreachi_set(T, i, p) {
+ if (is_in_set(p, ind)) {
+ set_remove(select, i);
+ }
+ }
+ }
+
+ /* Recursively perform the intersections */
+ offset = (cube.part_size[cube.output] - first_output) / 2;
+ last_output = first_output + offset - 1;
+ temp = opo_recur(T, D, select, offset, first_output, last_output);
+
+ /* largest set is on top -- select primes which are inferred from it */
+ pdest = temp->data;
+ T1 = new_cover(T->count);
+ foreachi_set(T, i, p) {
+ if (! is_in_set(pdest, i)) {
+ T1 = sf_addset(T1, p);
+ }
+ }
+
+ set_free(select);
+ sf_free(temp);
+
+ /* finding phases is difficult -- see which functions are not covered */
+ T2 = complement(cube1list(T1));
+ not_covered = new_cube();
+ tmp = new_cube();
+ foreach_set(T, last, p) {
+ foreach_set(T2, last1, p1) {
+ if (cdist0(p, p1)) {
+ (void) set_or(not_covered, not_covered, set_and(tmp, p, p1));
+ }
+ }
+ }
+ free_cover(T);
+ free_cover(T2);
+ set_free(tmp);
+
+ /* Now reflect the phase choice in a single cube */
+ for(output = first_output; output <= last_output; output++) {
+ ind = cube.first_part[cube.output] + output;
+ if (is_in_set(not_covered, ind)) {
+ if (is_in_set(not_covered, ind + offset)) {
+ fatal("error in output phase assignment");
+ } else {
+ set_remove(phase, ind);
+ }
+ }
+ }
+ set_free(not_covered);
+ return T1;
+}
+
+pset_family opo_recur(T, D, select, offset, first, last)
+pcover T, D;
+pcube select;
+int offset, first, last;
+{
+ static int level = 0;
+ int middle;
+ pset_family sl, sr, temp;
+
+ level++;
+ if (first == last) {
+#if 0
+ if (opo_no_make_sparse) {
+ temp = form_cover_table(T, D, select, first, first + offset);
+ } else {
+ temp = opo_leaf(T, select, first, first + offset);
+ }
+#else
+ temp = opo_leaf(T, select, first, first + offset);
+#endif
+ } else {
+ middle = (first + last) / 2;
+ sl = opo_recur(T, D, select, offset, first, middle);
+ sr = opo_recur(T, D, select, offset, middle+1, last);
+ temp = unate_intersect(sl, sr, level == 1);
+ if (trace) {
+ printf("# OPO[%d]: %4d = %4d x %4d, time = %s\n", level - 1,
+ temp->count, sl->count, sr->count, print_time(ptime()));
+ (void) fflush(stdout);
+ }
+ free_cover(sl);
+ free_cover(sr);
+ }
+ level--;
+ return temp;
+}
+
+
+pset_family opo_leaf(T, select, out1, out2)
+register pcover T;
+pset select;
+int out1, out2;
+{
+ register pset_family temp;
+ register pset p, pdest;
+ register int i;
+
+ out1 += cube.first_part[cube.output];
+ out2 += cube.first_part[cube.output];
+
+ /* Allocate space for the result */
+ temp = sf_new(2, T->count);
+
+ /* Find which primes are needed for the ON-set of this fct */
+ pdest = GETSET(temp, temp->count++);
+ (void) set_copy(pdest, select);
+ foreachi_set(T, i, p) {
+ if (is_in_set(p, out1)) {
+ set_remove(pdest, i);
+ }
+ }
+
+ /* Find which primes are needed for the OFF-set of this fct */
+ pdest = GETSET(temp, temp->count++);
+ (void) set_copy(pdest, select);
+ foreachi_set(T, i, p) {
+ if (is_in_set(p, out2)) {
+ set_remove(pdest, i);
+ }
+ }
+
+ return temp;
+}
+
+#if 0
+pset_family form_cover_table(F, D, select, f, fbar)
+pcover F, D;
+pset select;
+int f, fbar; /* indices of f and fbar in the output part */
+{
+ register int i;
+ register pcube p;
+ pset_family f_table, fbar_table;
+
+ /* setup required for fcube_is_covered */
+ Rp_size = F->count;
+ Rp_start = set_new(Rp_size);
+ foreachi_set(F, i, p) {
+ PUTSIZE(p, i);
+ }
+ foreachi_set(D, i, p) {
+ RESET(p, REDUND);
+ }
+
+ f_table = find_covers(F, D, select, f);
+ fbar_table = find_covers(F, D, select, fbar);
+ f_table = sf_append(f_table, fbar_table);
+
+ set_free(Rp_start);
+ return f_table;
+}
+
+
+pset_family find_covers(F, D, select, n)
+pcover F, D;
+register pset select;
+int n;
+{
+ register pset p, last, new;
+ pcover F1;
+ pcube *Flist;
+ pset_family f_table, table;
+ int i;
+
+ n += cube.first_part[cube.output];
+
+ /* save cubes in this output, and remove the output variable */
+ F1 = new_cover(F->count);
+ foreach_set(F, last, p)
+ if (is_in_set(p, n)) {
+ new = GETSET(F1, F1->count++);
+ set_or(new, p, cube.var_mask[cube.output]);
+ PUTSIZE(new, SIZE(p));
+ SET(new, REDUND);
+ }
+
+ /* Find ways (sop form) to fail to cover output indexed by n */
+ Flist = cube2list(F1, D);
+ table = sf_new(10, Rp_size);
+ foreach_set(F1, last, p) {
+ set_fill(Rp_start, Rp_size);
+ set_remove(Rp_start, SIZE(p));
+ table = sf_append(table, fcube_is_covered(Flist, p));
+ RESET(p, REDUND);
+ }
+ set_fill(Rp_start, Rp_size);
+ foreach_set(table, last, p) {
+ set_diff(p, Rp_start, p);
+ }
+
+ /* complement this to get possible ways to cover the function */
+ for(i = 0; i < Rp_size; i++) {
+ if (! is_in_set(select, i)) {
+ p = set_new(Rp_size);
+ set_insert(p, i);
+ table = sf_addset(table, p);
+ set_free(p);
+ }
+ }
+ f_table = unate_compl(table);
+
+ /* what a pain, but we need bitwise complement of this */
+ set_fill(Rp_start, Rp_size);
+ foreach_set(f_table, last, p) {
+ set_diff(p, Rp_start, p);
+ }
+
+ free_cubelist(Flist);
+ sf_free(F1);
+ return f_table;
+}
+#endif
+
+/*
+ * Take a PLA (ON-set, OFF-set and DC-set) and create the
+ * "double-phase characteristic function" which is merely a new
+ * function which has twice as many outputs and realizes both the
+ * function and the complement.
+ *
+ * The cube structure is assumed to represent the PLA upon entering.
+ * It will be modified to represent the double-phase function upon
+ * exit.
+ *
+ * Only the outputs numbered starting with "first_output" are
+ * duplicated in the output part
+ */
+
+output_phase_setup(PLA, first_output)
+INOUT pPLA PLA;
+int first_output;
+{
+ pcover F, R, D;
+ pcube mask, mask1, last;
+ int first_part, offset;
+ bool save;
+ register pcube p, pr, pf;
+ register int i, last_part;
+
+ if (cube.output == -1)
+ fatal("output_phase_setup: must have an output");
+
+ F = PLA->F;
+ D = PLA->D;
+ R = PLA->R;
+ first_part = cube.first_part[cube.output] + first_output;
+ last_part = cube.last_part[cube.output];
+ offset = cube.part_size[cube.output] - first_output;
+
+ /* Change the output size, setup the cube structure */
+ setdown_cube();
+ cube.part_size[cube.output] += offset;
+ cube_setup();
+
+ /* Create a mask to select that part of the cube which isn't changing */
+ mask = set_save(cube.fullset);
+ for(i = first_part; i < cube.size; i++)
+ set_remove(mask, i);
+ mask1 = set_save(mask);
+ for(i = cube.first_part[cube.output]; i < first_part; i++) {
+ set_remove(mask1, i);
+ }
+
+ PLA->F = new_cover(F->count + R->count);
+ PLA->R = new_cover(F->count + R->count);
+ PLA->D = new_cover(D->count);
+
+ foreach_set(F, last, p) {
+ pf = GETSET(PLA->F, (PLA->F)->count++);
+ pr = GETSET(PLA->R, (PLA->R)->count++);
+ INLINEset_and(pf, mask, p);
+ INLINEset_and(pr, mask1, p);
+ for(i = first_part; i <= last_part; i++)
+ if (is_in_set(p, i))
+ set_insert(pf, i);
+ save = FALSE;
+ for(i = first_part; i <= last_part; i++)
+ if (is_in_set(p, i))
+ save = TRUE, set_insert(pr, i+offset);
+ if (! save) PLA->R->count--;
+ }
+
+ foreach_set(R, last, p) {
+ pf = GETSET(PLA->F, (PLA->F)->count++);
+ pr = GETSET(PLA->R, (PLA->R)->count++);
+ INLINEset_and(pf, mask1, p);
+ INLINEset_and(pr, mask, p);
+ save = FALSE;
+ for(i = first_part; i <= last_part; i++)
+ if (is_in_set(p, i))
+ save = TRUE, set_insert(pf, i+offset);
+ if (! save) PLA->F->count--;
+ for(i = first_part; i <= last_part; i++)
+ if (is_in_set(p, i))
+ set_insert(pr, i);
+ }
+
+ foreach_set(D, last, p) {
+ pf = GETSET(PLA->D, (PLA->D)->count++);
+ INLINEset_and(pf, mask, p);
+ for(i = first_part; i <= last_part; i++)
+ if (is_in_set(p, i)) {
+ set_insert(pf, i);
+ set_insert(pf, i+offset);
+ }
+ }
+
+ free_cover(F);
+ free_cover(D);
+ free_cover(R);
+ set_free(mask);
+ set_free(mask1);
+}
+
+/*
+ * set_phase -- given a "cube" which describes which phases of the output
+ * are to be implemented, compute the appropriate on-set and off-set
+ */
+pPLA set_phase(PLA)
+INOUT pPLA PLA;
+{
+ pcover F1, R1;
+ register pcube last, p, outmask;
+ register pcube temp=cube.temp[0], phase=PLA->phase, phase1=cube.temp[1];
+
+ outmask = cube.var_mask[cube.num_vars - 1];
+ set_diff(phase1, outmask, phase);
+ set_or(phase1, set_diff(temp, cube.fullset, outmask), phase1);
+ F1 = new_cover((PLA->F)->count + (PLA->R)->count);
+ R1 = new_cover((PLA->F)->count + (PLA->R)->count);
+
+ foreach_set(PLA->F, last, p) {
+ if (! setp_disjoint(set_and(temp, p, phase), outmask))
+ set_copy(GETSET(F1, F1->count++), temp);
+ if (! setp_disjoint(set_and(temp, p, phase1), outmask))
+ set_copy(GETSET(R1, R1->count++), temp);
+ }
+ foreach_set(PLA->R, last, p) {
+ if (! setp_disjoint(set_and(temp, p, phase), outmask))
+ set_copy(GETSET(R1, R1->count++), temp);
+ if (! setp_disjoint(set_and(temp, p, phase1), outmask))
+ set_copy(GETSET(F1, F1->count++), temp);
+ }
+ free_cover(PLA->F);
+ free_cover(PLA->R);
+ PLA->F = F1;
+ PLA->R = R1;
+ return PLA;
+}
+
+#define POW2(x) (1 << (x))
+
+void opoall(PLA, first_output, last_output, opo_strategy)
+pPLA PLA;
+int first_output, last_output;
+int opo_strategy;
+{
+ pcover F, D, R, best_F, best_D, best_R;
+ int i, j, ind, num;
+ pcube bestphase;
+
+ opo_exact = opo_strategy;
+
+ if (PLA->phase != NULL) {
+ set_free(PLA->phase);
+ }
+
+ bestphase = set_save(cube.fullset);
+ best_F = sf_save(PLA->F);
+ best_D = sf_save(PLA->D);
+ best_R = sf_save(PLA->R);
+
+ for(i = 0; i < POW2(last_output - first_output + 1); i++) {
+
+ /* save the initial PLA covers */
+ F = sf_save(PLA->F);
+ D = sf_save(PLA->D);
+ R = sf_save(PLA->R);
+
+ /* compute the phase cube for this iteration */
+ PLA->phase = set_save(cube.fullset);
+ num = i;
+ for(j = last_output; j >= first_output; j--) {
+ if (num % 2 == 0) {
+ ind = cube.first_part[cube.output] + j;
+ set_remove(PLA->phase, ind);
+ }
+ num /= 2;
+ }
+
+ /* set the phase and minimize */
+ (void) set_phase(PLA);
+ printf("# phase is %s\n", pc1(PLA->phase));
+ summary = TRUE;
+ minimize(PLA);
+
+ /* see if this is the best so far */
+ if (PLA->F->count < best_F->count) {
+ /* save new best solution */
+ set_copy(bestphase, PLA->phase);
+ sf_free(best_F);
+ sf_free(best_D);
+ sf_free(best_R);
+ best_F = PLA->F;
+ best_D = PLA->D;
+ best_R = PLA->R;
+ } else {
+ /* throw away the solution */
+ free_cover(PLA->F);
+ free_cover(PLA->D);
+ free_cover(PLA->R);
+ }
+ set_free(PLA->phase);
+
+ /* restore the initial PLA covers */
+ PLA->F = F;
+ PLA->D = D;
+ PLA->R = R;
+ }
+
+ /* one more minimization to restore the best answer */
+ PLA->phase = bestphase;
+ sf_free(PLA->F);
+ sf_free(PLA->D);
+ sf_free(PLA->R);
+ PLA->F = best_F;
+ PLA->D = best_D;
+ PLA->R = best_R;
+}
+
+static void minimize(PLA)
+pPLA PLA;
+{
+ if (opo_exact) {
+ EXEC_S(PLA->F = minimize_exact(PLA->F,PLA->D,PLA->R,1), "EXACT", PLA->F);
+ } else {
+ EXEC_S(PLA->F = espresso(PLA->F, PLA->D, PLA->R), "ESPRESSO ",PLA->F);
+ }
+}
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