regress.cal

Calc Software Package for Number Calc

/*
 * test_config - test config control
 */
define test_config()
{
	local callcfg;		/* caller configuration value */
	local oldcfg;		/* caller configuration value */
	local newcfg;		/* caller configuration value */

	print '500: Beginning test_config';

	/* check the set and return of all config */
	callcfg = config("all");
	print				'501: callcfg = config("all")';
	vrfy(callcfg == startcfg,	'502: callcfg == startcfg');

	callcfg = config("all", "oldstd");
	print				'503: callcfg = config("all","oldstd")';
	vrfy(callcfg == startcfg,	'504: callcfg == startcfg');
	oldcfg = config("all");
	print				'505: oldcfg = config("all");';
	vrfy(config("all") == oldcfg,	'506: config("all") == oldcfg');
	vrfy(oldcfg==config("all","newstd"),
					'507: oldcfg==config("all","newstd")');
	vrfy(defcfg == config("all"),	'508: defcfg == config("all")');

	/* vrfy the state of the default config */
	vrfy(config("mode") == "real",
					'509: config("mode") == "real"');
	vrfy(config("display") == 20,
					'510: config("display") == 20');
	vrfy(config("epsilon") == 1e-20,
					'511: config("epsilon") == 1e-20');
	vrfy(config("trace") == 0,
					'512: config("trace") == 0');
	vrfy(config("maxprint") == 16,
					'513: config("maxprint") == 16');
	vrfy(config("mul2") == 1780,
					'514: config("mul2") == 1780');
	vrfy(config("sq2") == 3388,
					'515: config("sq2") == 3388');
	vrfy(config("pow2") == 176,
					'516: config("pow2") == 176');
	vrfy(config("redc2") == 220,
					'517: config("redc2") == 220');
	vrfy(config("tilde"),
					'518: config("tilde")');
	vrfy(config("tab"),
					'519: config("tab")');
	vrfy(config("quomod") == 0,
					'520: config("quomod") == 0');
	vrfy(config("quo") == 2,
					'521: config("quo") == 2');
	vrfy(config("mod") == 0,
					'522: config("mod") == 0');
	vrfy(config("sqrt") == 24,
					'523: config("sqrt") == 24');
	vrfy(config("appr") == 24,
					'524: config("appr") == 24');
	vrfy(config("cfappr") == 0,
					'525: config("cfappr") == 0');
	vrfy(config("cfsim") == 8,
					'526: config("cfsim") == 8');
	vrfy(config("outround") == 24,
					'527: config("outround") == 24');
	vrfy(config("round") == 24,
					'528: config("round") == 24');
	vrfy(config("leadzero") == 1,
					'529: config("leadzero") == 1');
	vrfy(config("fullzero") == 0,
					'530: config("fullzero") == 0');
	vrfy(config("maxscan") == 20,
					'531: config("maxscan") == 20');
	vrfy(config("prompt") == "; ",
					'532: config("prompt") == "; "');
	vrfy(config("more") == ";; ",
					'533: config("more") == ";; "');

	/* convert to "oldstd" config by individual changes */
	print				'534: test unused';
	vrfy(config("outround", 2) == 24,
					'535: config("outround", 2) == 24');
	vrfy(config("leadzero","n") == 1,
					'536: config("leadzero","n") == 1');
	print				'537: test unused';
	vrfy(config("prompt", "> ") == "; ",
					'538: config("prompt", "> ") == "; "');
	vrfy(config("more", ">> ") == ";; ",
					'539: config("more", ">> ") == ";; "');
	vrfy(config("all") == oldcfg,	'540: config("all") == oldcfg');

	/* restore the configation at the start of this function */
	vrfy(config("all",callcfg) == oldcfg,
					'541: config("all",callcfg) == oldcfg');

	/* display and fullzero tests */
	vrfy(config("display",2) == 20,
					'542: config("display",2) == 20');
	vrfy(config("leadzero",0) == 1,
					'543: config("leadzero",0) == 1');
	vrfy(config("fullzero",1) == 0,
					'544: config("fullzero",1) == 0');
	vrfy(strprintf("%d %d %d", 0, 1, 2) == ".00 1.00 2.00",
		'545: strprintf("%d %d %d", 0, 1, 2) == ".00 1.00 2.00"');
	vrfy(config("display",20) == 2,
					'546: config("display",20) == 2');
	vrfy(config("leadzero",1) == 0,
					'547: config("leadzero",1) == 0');
	vrfy(config("fullzero",0) == 1,
					'548: config("fullzero",0) == 1');
	vrfy(strprintf("%d %d %d", 0, 1, 2) == "0 1 2",
		'549: strprintf("%d %d %d", 0, 1, 2) == "0 1 2"');

	/* restore calling config */
	vrfy(config("all",callcfg) == startcfg,
		'550: config("all",callcfg) == startcfg');
	vrfy(config("all") == callcfg,	'551: config("all") == callcfg');
	vrfy(config("all") == startcfg, '552: config("all") == startcfg');

	/* check read-only config values */
	vrfy(strlen(config("program")) > 0,
					'553: strlen(config("program")) > 0');
	vrfy(strlen(config("basename")) > 0,
					'554: strlen(config("basename")) > 0');
	vrfy(strlen(config("version")) > 0,
					'555: strlen(config("version")) > 0');

	/* mode2 is off by default */
	vrfy(config("mode2") == "off",
					'556: config("mode2") == "off"');

	/* hz is numeric */
	vrfy(isint(config("hz")),	'557: isint(config("hz"))');

	/* compile_custom is simple */
	vrfy(issimple(config("compile_custom")),
		'558: issimple(config("compile_custom"))');

	/* allow_custom is simple */
	vrfy(issimple(config("allow_custom")),
		'559: issimple(config("allow_custom"))');

	/* allow_custom is simple */
	vrfy(issimple(config("allow_custom")),
		'559: issimple(config("allow_custom"))');

	/* baseb is numeric */
	vrfy(isint(config("baseb")),	'560: isint(config("baseb"))');

	/* redecl_warn is simple */
	vrfy(issimple(config("redecl_warn")),
		'561: issimple(config("redecl_warn"))');

	/* dupvar_warn is simple */
	vrfy(issimple(config("dupvar_warn")),
		'562: issimple(config("rdupvar_warn"))');

	print '563: Ending test_config';
}
print '010: parsed test_config()';



/*
 * Do multiplication and division on three numbers in various ways
 * and vrfy the results agree.
 */
define muldivcheck(a, b, c, str)
{
	local	abc, acb, bac, bca, cab, cba;

	abc = (a * b) * c;
	acb = (a * c) * b;
	bac = (b * a) * c;
	bca = (b * c) * a;
	cab = (c * a) * b;
	cba = (c * b) * a;

	if (abc != acb) {print '**** abc != acb:', str; ++prob;}
	if (acb != bac) {print '**** acb != bac:', str; ++prob;}
	if (bac != bca) {print '**** bac != bca:', str; ++prob;}
	if (bca != cab) {print '**** bca != cab:', str; ++prob;}
	if (cab != cba) {print '**** cab != cba:', str; ++prob;}
	if (abc/a != b*c) {print '**** abc/a != bc:', str; ++prob;}
	if (abc/b != a*c) {print '**** abc/b != ac:', str; ++prob;}
	if (abc/c != a*b) {print '**** abc/c != ab:', str; ++prob;}
	print str;
}
print '011: parsed muldivcheck(a, b, c, str)';


/*
 * Use the identity for squaring the sum of two squares to check
 * multiplication and squaring.
 */
define squarecheck(a, b, str)
{
	local	a2, b2, tab, apb, apb2, t;

	a2 = a^2;
	b2 = b^2;
	tab = a * b * 2;
	apb = a + b;
	apb2 = apb^2;
	if (a2 != a*a) {print '**** a^2 != a*a:', str; ++prob;}
	if (b2 != b*b) {print '**** b^2 != b*b:', str; ++prob;}
	if (apb2 != apb*apb) {
		print '**** (a+b)^2 != (a+b)*(a+b):', str;
		++prob;
	}
	if (a2+tab+b2 != apb2) {
		print '**** (a+b)^2 != a^2 + 2ab + b^2:', str;
		++prob;
	}
	if (a2/a != a) {print '**** a^2/a != a:', str; ++prob;}
	if (b2/b != b) {print '**** b^2/b != b:', str; ++prob;}
	if (apb2/apb != apb) {print '**** (a+b)^2/(a+b) != a+b:', str; ++prob;}
	if (a2*b2 != (a*b)^2) {print '**** a^2*b^2 != (ab)^2:', str; ++prob;}
	print str;
}
print '012: parsed squarecheck(a, b, str)';


/*
 * Use the raising of numbers to large powers to check multiplication
 * and exponentiation.
 */
define powercheck(a, p1, p2, str)
{
	local	a1, a2, a3;

	a1 = (a^p1)^p2;
	a2 = (a^p2)^p1;
	a3 = a^(p1*p2);
	if (a1 != a2) {print '**** (a^p1)^p2 != (a^p2)^p1:', str; ++prob;}
	if (a1 != a3) {print '**** (a^p1)^p2 != a^(p1*p2):', str; ++prob;}
	print str;
}
print '013: parsed powercheck(a, p1, p2, str)';


/*
 * Test fraction reductions.
 * Arguments MUST be relatively prime.
 */
define fraccheck(a, b, c, str)
{
	local	ab, bc, ca, aoc, boc, aob;

	ab = a * b;
	bc = b * c;
	ca = c * a;
	aoc = ab / bc;
	if (num(aoc) != a) {print '**** num(aoc) != a:', str; ++prob;}
	if (den(aoc) != c) {print '**** den(aoc) != c:', str; ++prob;}
	boc = ab / ca;
	if (num(boc) != b) {print '**** num(boc) != b:', str; ++prob;}
	if (den(boc) != c) {print '**** den(boc) != c:', str; ++prob;}
	aob = ca / bc;
	if (num(aob) != a) {print '**** num(aob) != a:', str; ++prob;}
	if (den(aob) != b) {print '**** den(aob) != b:', str; ++prob;}
	if (aob*boc != aoc) {print '**** aob*boc != aoc;', str; ++prob;}
	print str;
}
print '014: parsed fraccheck(a, b, c, str)';


/*
 * Test multiplication and squaring algorithms.
 */
define algcheck(a, b, str)
{
	local	ss, ms, t1, t2, t3, t4, t5, t6, t7;
	local	a1, a2, a3, a4, a5, a6, a7;
	local	oldmul2, oldsq2;

	oldmul2 = config("mul2", 2);
	oldsq2 = config("sq2", 2);
	a1 = a * b;
	a2 = a * a;
	a3 = b * b;
	a4 = a^2;
	a5 = b^2;
	a6 = a2^2;
	a7 = pmod(3,a-1,a);
	for (ms = 2; ms < 20; ms++) {
		for (ss = 2; ss < 20; ss++) {
			config("mul2", ms);
			config("sq2", ss);
			t1 = a * b;
			t2 = a * a;
			t3 = b * b;
			t4 = a^2;
			t5 = b^2;
			t6 = t2^2;
			if (((ms + ss) % 37) == 4)
				t7 = pmod(3,a-1,a);
			if (t1 != a1) {print '**** t1 != a1:', str; ++prob;}
			if (t2 != a2) {print '**** t2 != a2:', str; ++prob;}
			if (t3 != a3) {print '**** t3 != a3:', str; ++prob;}
			if (t4 != a4) {print '**** t4 != a4:', str; ++prob;}
			if (t5 != a5) {print '**** t5 != a5:', str; ++prob;}
			if (t6 != a6) {print '**** t6 != a6:', str; ++prob;}
			if (t7 != a7) {print '**** t7 != a7:', str; ++prob;}
		}
	}
	config("mul2", oldmul2);
	config("sq2", oldsq2);
	print str;
}
print '015: parsed algcheck(a, b, str)';


/*
 * Test big numbers using some identities.
 */
define test_bignums()
{
	local	a, b, c, d;

	print '600: Beginning test_bignums';

	a = 64357824568234938591;
	b = 12764632632458756817;
	c = 43578234973856347982;
	muldivcheck(a, b, c, '601: muldivcheck 1');
	a = 3^100;
	b = 5^97;
	c = 7^88;
	muldivcheck(a, b, c, '602: muldivcheck 2');
	a = 2^160 - 1;
	b = 2^161 - 1;
	c = 2^162 - 1;
	muldivcheck(a, b, c, '603: muldivcheck 3');
	a = 3^35 / 5^35;
	b = 7^35 / 11^35;
	c = 13^35 / 17^35;
	muldivcheck(a, b, c, '604: muldivcheck 4');
	a = (10^97-1) / 9;
	b = (10^53-1) / 9;
	c = (10^37-1) / 9;
	muldivcheck(a, b, c, '605: muldivcheck 5');
	a = 17^50;
	b = 19^47;
	squarecheck(a, b, '606: squarecheck 1');
	a = 2^111-1;
	b = 2^17;
	squarecheck(a, b, '607: squarecheck 2');
	a = 23^43 / 29^43;
	b = 31^42 / 37^29;
	squarecheck(a, b, '608: squarecheck 3');
	a = 4657892345743659834657238947854639;
	b = 43784356784365893467659347867689;
	squarecheck(a, b, '609: squarecheck 4');
	a = (10^80-1) / 9;
	b = (10^50-1) / 9;
	squarecheck(a, b, '610: squarecheck 5');
	a = 101^99;
	b = 2 * a;
	squarecheck(a, b, '611: squarecheck 6');
	a = (10^19-1) / 9;
	vrfy(ptest(a, 20), '612: primetest R19');
	a = (10^23-1) / 9;
	vrfy(ptest(a, 20), '613: primetest R23');
	a = 2^127 - 1;
	vrfy(ptest(a, 1), '614: primetest M127');