ack/util/ncgg/hall.c

/*
 * (c) copyright 1987 by the Vrije Universiteit, Amsterdam, The Netherlands.
 * See the copyright notice in the ACK home directory, in the file "Copyright".
 */
#ifndef NORCSID
static char rcsid[] = "$Id$";
#endif

#include <assert.h>
#include "param.h"
#include "set.h"
#include "extern.h"
#include "hall.h"
#include <stdio.h>

/*
 * This file implements the marriage thesis from Hall.
 * The thesis says that givoid hallverbose(void)ven a number, say N, of subsets from
 * a finite set, it is possible to create a set with cardinality N,
 * that contains one member for each of the subsets,
 * iff for each number, say M, of subsets from 2 to N the union of
 * each M-tuple sets has cardinality >= M.
 *
 * So what, you might say. As indeed I did.
 * But this is actually used here to check the possibility of each
 * code rule. If a code rule has a number of token_sets in the with
 * clause and a number of properties in the uses rule it must be
 * possible to do this from an empty fakestack. Hall helps.
 */

#define MAXHALL (TOKPATMAX+MAXALLREG)
short hallsets[MAXHALL][SETSIZE];
int nhallsets = -1;
int hallfreq[MAXHALL][2];

int recurhall(int, short [][SETSIZE]);
void unite(register short *, short *);


void hallverbose(void)
{
	register int i;
	register int max;

	fprintf(stderr, "Table of hall frequencies\n   #   pre   post\n");
	for (max = MAXHALL - 1; hallfreq[max][0] == 0 && hallfreq[max][1] == 0;
			max--)
		;
	for (i = 0; i <= max; i++)
		fprintf(stderr, "%3d%6d%6d\n", i, hallfreq[i][0], hallfreq[i][1]);
}

void inithall(void)
{

	assert(nhallsets == -1);
	nhallsets = 0;
}

void nexthall(register short *sp)
{
	register int i;

	assert(nhallsets >= 0);
	for (i = 0; i < SETSIZE; i++)
		hallsets[nhallsets][i] = sp[i];
	nhallsets++;
}

int card(register short *sp)
{
	register int sum, i;

	sum = 0;
	for (i = 0; i < 8 * sizeof(short) * SETSIZE; i++)
		if (BIT(sp, i))
			sum++;
	return (sum);
}

void checkhall(void)
{
	assert(nhallsets >= 0);
	if (!hall())
		error("Hall says: \"You can't have those registers\"");
}

int hall(void)
{
	register int i, j, k;
	int ok;

	hallfreq[nhallsets][0]++;
	/*
	 * If a set has cardinality >= nhallsets it can never be the cause
	 * of the hall algorithm failing. So it can be thrown away.
	 * But then nhallsets is less, so this step can be re-applied.
	 */

	do
	{
		ok = 0;
		for (i = 0; i < nhallsets; i++)
			if (card(hallsets[i]) >= nhallsets)
			{
				for (j = i + 1; j < nhallsets; j++)
					for (k = 0; k < SETSIZE; k++)
						hallsets[j - 1][k] = hallsets[j][k];
				nhallsets--;
				ok = 1;
				break;
			}
	} while (ok);

	/*
	 * Now all sets have cardinality < nhallsets
	 */

	hallfreq[nhallsets][1]++;
	ok = recurhall(nhallsets, hallsets);
	nhallsets = -1;
	return (ok);
}

int recurhall(int nhallsets, short hallsets[][SETSIZE])
{
	short copysets[MAXHALL][SETSIZE];
	short setsum[SETSIZE];
	register int i, j, k, ncopys;

	/*
	 * First check cardinality of union of all
	 */
	for (k = 0; k < SETSIZE; k++)
		setsum[k] = 0;
	for (i = 0; i < nhallsets; i++)
		unite(hallsets[i], setsum);
	if (card(setsum) < nhallsets)
		return (0);
	/*
	 * Now check the hall property of everything but one set,
	 * for all sets
	 */
	for (i = 0; i < nhallsets; i++)
	{
		ncopys = 0;
		for (j = 0; j < nhallsets; j++)
			if (j != i)
			{
				for (k = 0; k < SETSIZE; k++)
					copysets[ncopys][k] = hallsets[j][k];
				ncopys++;
			}
		assert(ncopys == nhallsets - 1);
		if (!recurhall(ncopys, copysets))
			return (0);
	}
	return (1);
}

void unite(register short *sp, short *into)
{
	register int i;

	for (i = 0; i < SETSIZE; i++)
		into[i] |= sp[i];
}

/*
 * Limerick (rot13)
 *
 * N zngurzngvpvna anzrq Unyy
 * Unf n urknurqebavpny onyy,
 * 	Naq gur phor bs vgf jrvtug
 * 	Gvzrf uvf crpxre'f, cyhf rvtug
 * Vf uvf cubar ahzore -- tvir uvz n pnyy..
 */