/*
 *  unate.c -- routines for dealing with unate functions
 */

#include "espresso.h"

static pset_family abs_covered(pset_family A, register int pick);
static pset_family abs_covered_many(pset_family A, register pset pick_set);
static int abs_select_restricted(pset_family A, pset esp_restrict);

pcover map_cover_to_unate(pset *T)
{
    register unsigned int word_test, word_set, bit_test, bit_set;
    register pcube p, pA;
    pset_family A;
    pcube *T1;
    int ncol, i;

    A = sf_new(CUBELISTSIZE(T), cdata.vars_unate);
    A->count = CUBELISTSIZE(T);
    foreachi_set(A, i, p) {
	(void) set_clear(p, A->sf_size);
    }
    ncol = 0;

    for(i = 0; i < cube.size; i++) {
	if (cdata.part_zeros[i] > 0) {
	    assert(ncol <= cdata.vars_unate);

	    /* Copy a column from T to A */
	    word_test = WHICH_WORD(i);
	    bit_test = 1 << WHICH_BIT(i);
	    word_set = WHICH_WORD(ncol);
	    bit_set = 1 << WHICH_BIT(ncol);

	    pA = A->data;
	    for(T1 = T+2; (p = *T1++) != 0; ) {
		if ((p[word_test] & bit_test) == 0) {
		    pA[word_set] |= bit_set;
		}
		pA += A->wsize;
	    }

	    ncol++;
	}
    }

    return A;
}

pcover map_unate_to_cover(pset_family A)
{
    register int i, ncol, lp;
    register pcube p, pB;
    int var, nunate, *unate;
    pcube last;
    pset_family B;

    B = sf_new(A->count, cube.size);
    B->count = A->count;

    /* Find the unate variables */
    unate = ALLOC(int, cube.num_vars);
    nunate = 0;
    for(var = 0; var < cube.num_vars; var++) {
	if (cdata.is_unate[var]) {
	    unate[nunate++] = var;
	}
    }

    /* Loop for each set of A */
    pB = B->data;
    foreach_set(A, last, p) {

	/* Initialize this set of B */
	INLINEset_fill(pB, cube.size);

	/* Now loop for the unate variables; if the part is in A,
	 * then this variable of B should be a single 1 in the unate
	 * part.
	 */
	for(ncol = 0; ncol < nunate; ncol++) {
	    if (is_in_set(p, ncol)) {
		lp = cube.last_part[unate[ncol]];
		for(i = cube.first_part[unate[ncol]]; i <= lp; i++) {
		    if (cdata.part_zeros[i] == 0) {
			set_remove(pB, i);
		    }
		}
	    }
	}
	pB += B->wsize;
    }

    FREE(unate);
    return B;
}

/*
 *  unate_compl
 */

pset_family unate_compl(pset_family A)
{
    register pset p, last;

    /* Make sure A is single-cube containment minimal */
/*    A = sf_rev_contain(A);*/

    foreach_set(A, last, p) {
	PUTSIZE(p, set_ord(p));
    }

    /* Recursively find the complement */
    A = unate_complement(A);

    /* Now, we can guarantee a minimal result by containing the result */
    A = sf_rev_contain(A);
    return A;
}


/*
 *  Assume SIZE(p) records the size of each set
 */
pset_family unate_complement(pset_family A)
              			/* disposes of A */
{
    pset_family Abar;
    register pset p, p1, esp_restrict;
    register int i;
    int max_i, min_set_ord, j;

    /* Check for no sets in the matrix -- complement is the universe */
    if (A->count == 0) {
	sf_free(A);
	Abar = sf_new(1, A->sf_size);
	(void) set_clear(GETSET(Abar, Abar->count++), A->sf_size);

    /* Check for a single set in the maxtrix -- compute de Morgan complement */
    } else if (A->count == 1) {
	p = A->data;
	Abar = sf_new(A->sf_size, A->sf_size);
	for(i = 0; i < A->sf_size; i++) {
	    if (is_in_set(p, i)) {
		p1 = set_clear(GETSET(Abar, Abar->count++), A->sf_size);
		set_insert(p1, i);
	    }
	}
	sf_free(A);

    } else {

	/* Select splitting variable as the variable which belongs to a set
	 * of the smallest size, and which has greatest column count
	 */
	esp_restrict = set_new(A->sf_size);
	min_set_ord = A->sf_size + 1;
	foreachi_set(A, i, p) {
	    if (SIZE(p) < min_set_ord) {
		set_copy(esp_restrict, p);
		min_set_ord = SIZE(p);
	    } else if (SIZE(p) == min_set_ord) {
		set_or(esp_restrict, esp_restrict, p);
	    }
	}

	/* Check for no data (shouldn't happen ?) */
	if (min_set_ord == 0) {
	    A->count = 0;
	    Abar = A;

	/* Check for "essential" columns */
	} else if (min_set_ord == 1) {
	    Abar = unate_complement(abs_covered_many(A, esp_restrict));
	    sf_free(A);
	    foreachi_set(Abar, i, p) {
		set_or(p, p, esp_restrict);
	    }

	/* else, recur as usual */
	} else {
	    max_i = abs_select_restricted(A, esp_restrict);

	    /* Select those rows of A which are not covered by max_i,
	     * recursively find all minimal covers of these rows, and
	     * then add back in max_i
	     */
	    Abar = unate_complement(abs_covered(A, max_i));
	    foreachi_set(Abar, i, p) {
		set_insert(p, max_i);
	    }

	    /* Now recur on A with all zero's on column max_i */
	    foreachi_set(A, i, p) {
		if (is_in_set(p, max_i)) {
		    set_remove(p, max_i);
		    j = SIZE(p) - 1;
		    PUTSIZE(p, j);
		}
	    }

	    Abar = sf_append(Abar, unate_complement(A));
	}
	set_free(esp_restrict);
    }

    return Abar;
}

pset_family exact_minimum_cover(pset_family T)
{
    register pset p, last, p1;
    register int i, n;
    int lev, lvl;
    pset nlast;
    pset_family temp;
    long start = ptime();
    struct {
	pset_family sf;
	int level;
    } stack[32];                /* 32 suffices for 2 ** 32 cubes ! */

    if (T->count <= 0)
	return sf_new(1, T->sf_size);
    for(n = T->count, lev = 0; n != 0; n >>= 1, lev++)   ;

    /* A simple heuristic ordering */
    T = lex_sort(sf_save(T));

    /* Push a full set on the stack to get things started */
    n = 1;
    stack[0].sf = sf_new(1, T->sf_size);
    stack[0].level = lev;
    set_fill(GETSET(stack[0].sf, stack[0].sf->count++), T->sf_size);

    nlast = GETSET(T, T->count - 1);
    foreach_set(T, last, p) {

	/* "unstack" the set into a family */
	temp = sf_new(set_ord(p), T->sf_size);
	for(i = 0; i < T->sf_size; i++)
	    if (is_in_set(p, i)) {
		p1 = set_fill(GETSET(temp, temp->count++), T->sf_size);
		set_remove(p1, i);
	    }
	stack[n].sf = temp;
	stack[n++].level = lev;

	/* Pop the stack and perform (leveled) intersections */
	while (n > 1 && (stack[n-1].level==stack[n-2].level || p == nlast)) {
	    temp = unate_intersect(stack[n-1].sf, stack[n-2].sf, FALSE);
	    lvl = MIN(stack[n-1].level, stack[n-2].level) - 1;
	    if (debug & MINCOV && lvl < 10) {
		printf("# EXACT_MINCOV[%d]: %4d = %4d x %4d, time = %s\n",
		    lvl, temp->count, stack[n-1].sf->count,
		    stack[n-2].sf->count, print_time(ptime() - start));
		(void) fflush(stdout);
	    }
	    sf_free(stack[n-2].sf);
	    sf_free(stack[n-1].sf);
	    stack[n-2].sf = temp;
	    stack[n-2].level = lvl;
	    n--;
	}
    }

    temp = stack[0].sf;
    p1 = set_fill(set_new(T->sf_size), T->sf_size);
    foreach_set(temp, last, p)
	INLINEset_diff(p, p1, p);
    set_free(p1);
    if (debug & MINCOV1) {
	printf("MINCOV: family of all minimal coverings is\n");
	sf_print(temp);
    }
    sf_free(T);         /* this is the copy of T we made ... */
    return temp;
}

/*
 *  unate_intersect -- intersect two unate covers
 *
 *  If largest_only is TRUE, then only the largest cube(s) are returned
 */

#define MAGIC 500               /* save 500 cubes before containment */

pset_family unate_intersect(pset_family A, pset_family B, int largest_only)
{
    register pset pi, pj, lasti, lastj, pt;
    pset_family T, Tsave;
    bool save;
    int maxord, ord;

    /* How large should each temporary result cover be ? */
    T = sf_new(MAGIC, A->sf_size);
    Tsave = NULL;
    maxord = 0;
    pt = T->data;

    /* Form pairwise intersection of each set of A with each cube of B */
    foreach_set(A, lasti, pi) {

	foreach_set(B, lastj, pj) {

	    save = set_andp(pt, pi, pj);

	    /* Check if we want the largest only */
	    if (save && largest_only) {
		if ((ord = set_ord(pt)) > maxord) {
		    /* discard Tsave and T */
		    if (Tsave != NULL) {
			sf_free(Tsave);
			Tsave = NULL;
		    }
		    pt = T->data;
		    T->count = 0;
		    /* Re-create pt (which was just thrown away) */
		    (void) set_and(pt, pi, pj);
		    maxord = ord;
		} else if (ord < maxord) {
		    save = FALSE;
		}
	    }

	    if (save) {
		if (++T->count >= T->capacity) {
		    T = sf_contain(T);
		    Tsave = (Tsave == NULL) ? T : sf_union(Tsave, T);
		    T = sf_new(MAGIC, A->sf_size);
		    pt = T->data;
		} else {
		    pt += T->wsize;
		}
	    }
	}
    }


    /* Contain the final result and merge it into Tsave */
    T = sf_contain(T);
    Tsave = (Tsave == NULL) ? T : sf_union(Tsave, T);

    return Tsave;
}

/*
 *  abs_covered -- after selecting a new column for the selected set,
 *  create a new matrix which is only those rows which are still uncovered
 */
static pset_family
abs_covered(pset_family A, register int pick)
{
    register pset last, p, pdest;
    register pset_family Aprime;

    Aprime = sf_new(A->count, A->sf_size);
    pdest = Aprime->data;
    foreach_set(A, last, p)
	if (! is_in_set(p, pick)) {
	    INLINEset_copy(pdest, p);
	    Aprime->count++;
	    pdest += Aprime->wsize;
	}
    return Aprime;
}


/*
 *  abs_covered_many -- after selecting many columns for ther selected set,
 *  create a new matrix which is only those rows which are still uncovered
 */
static pset_family
abs_covered_many(pset_family A, register pset pick_set)
{
    register pset last, p, pdest;
    register pset_family Aprime;

    Aprime = sf_new(A->count, A->sf_size);
    pdest = Aprime->data;
    foreach_set(A, last, p)
	if (setp_disjoint(p, pick_set)) {
	    INLINEset_copy(pdest, p);
	    Aprime->count++;
	    pdest += Aprime->wsize;
	}
    return Aprime;
}


/*
 *  abs_select_restricted -- select the column of maximum column count which
 *  also belongs to the set "restrict"; weight each column of a set as
 *  1 / (set_ord(p) - 1).
 */
static int
abs_select_restricted(pset_family A, pset esp_restrict)
{
    register int i, best_var, best_count, *count;

    /* Sum the elements in these columns */
    count = sf_count_restricted(A, esp_restrict);

    /* Find which variable has maximum weight */
    best_var = -1;
    best_count = 0;
    for(i = 0; i < A->sf_size; i++) {
	if (count[i] > best_count) {
	    best_var = i;
	    best_count = count[i];
	}
    }
    FREE(count);

    if (best_var == -1)
	fatal("abs_select_restricted: should not have best_var == -1");

    return best_var;
}
