xref: /freebsd-11.0-release/lib/msun/tests/csqrt_test.c

/*-
 * Copyright (c) 2007 David Schultz <das@FreeBSD.org>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 */

/*
 * Tests for csqrt{,f}()
 */

#include <sys/cdefs.h>
__FBSDID("$FreeBSD: head/tools/regression/lib/msun/test-csqrt.c 177763 2008-03-30 20:09:51Z das $");

#include <assert.h>
#include <complex.h>
#include <float.h>
#include <math.h>
#include <stdio.h>

#define	N(i)	(sizeof(i) / sizeof((i)[0]))

/*
 * This is a test hook that can point to csqrtl(), _csqrt(), or to _csqrtf().
 * The latter two convert to float or double, respectively, and test csqrtf()
 * and csqrt() with the same arguments.
 */
long double complex (*t_csqrt)(long double complex);

static long double complex
_csqrtf(long double complex d)
{

	return (csqrtf((float complex)d));
}

static long double complex
_csqrt(long double complex d)
{

	return (csqrt((double complex)d));
}

#pragma	STDC CX_LIMITED_RANGE	off

/*
 * XXX gcc implements complex multiplication incorrectly. In
 * particular, it implements it as if the CX_LIMITED_RANGE pragma
 * were ON. Consequently, we need this function to form numbers
 * such as x + INFINITY * I, since gcc evalutes INFINITY * I as
 * NaN + INFINITY * I.
 */
static inline long double complex
cpackl(long double x, long double y)
{
	long double complex z;

	__real__ z = x;
	__imag__ z = y;
	return (z);
}

/*
 * Compare d1 and d2 using special rules: NaN == NaN and +0 != -0.
 * Fail an assertion if they differ.
 */
static void
assert_equal(long double complex d1, long double complex d2)
{

	if (isnan(creall(d1))) {
		assert(isnan(creall(d2)));
	} else {
		assert(creall(d1) == creall(d2));
		assert(copysignl(1.0, creall(d1)) ==
		       copysignl(1.0, creall(d2)));
	}
	if (isnan(cimagl(d1))) {
		assert(isnan(cimagl(d2)));
	} else {
		assert(cimagl(d1) == cimagl(d2));
		assert(copysignl(1.0, cimagl(d1)) ==
		       copysignl(1.0, cimagl(d2)));
	}
}

/*
 * Test csqrt for some finite arguments where the answer is exact.
 * (We do not test if it produces correctly rounded answers when the
 * result is inexact, nor do we check whether it throws spurious
 * exceptions.)
 */
static void
test_finite()
{
	static const double tests[] = {
	     /* csqrt(a + bI) = x + yI */
	     /* a	b	x	y */
		0,	8,	2,	2,
		0,	-8,	2,	-2,
		4,	0,	2,	0,
		-4,	0,	0,	2,
		3,	4,	2,	1,
		3,	-4,	2,	-1,
		-3,	4,	1,	2,
		-3,	-4,	1,	-2,
		5,	12,	3,	2,
		7,	24,	4,	3,
		9,	40,	5,	4,
		11,	60,	6,	5,
		13,	84,	7,	6,
		33,	56,	7,	4,
		39,	80,	8,	5,
		65,	72,	9,	4,
		987,	9916,	74,	67,
		5289,	6640,	83,	40,
		460766389075.0, 16762287900.0, 678910, 12345
	};
	/*
	 * We also test some multiples of the above arguments. This
	 * array defines which multiples we use. Note that these have
	 * to be small enough to not cause overflow for float precision
	 * with all of the constants in the above table.
	 */
	static const double mults[] = {
		1,
		2,
		3,
		13,
		16,
		0x1.p30,
		0x1.p-30,
	};

	double a, b;
	double x, y;
	int i, j;

	for (i = 0; i < N(tests); i += 4) {
		for (j = 0; j < N(mults); j++) {
			a = tests[i] * mults[j] * mults[j];
			b = tests[i + 1] * mults[j] * mults[j];
			x = tests[i + 2] * mults[j];
			y = tests[i + 3] * mults[j];
			assert(t_csqrt(cpackl(a, b)) == cpackl(x, y));
		}
	}

}

/*
 * Test the handling of +/- 0.
 */
static void
test_zeros()
{

	assert_equal(t_csqrt(cpackl(0.0, 0.0)), cpackl(0.0, 0.0));
	assert_equal(t_csqrt(cpackl(-0.0, 0.0)), cpackl(0.0, 0.0));
	assert_equal(t_csqrt(cpackl(0.0, -0.0)), cpackl(0.0, -0.0));
	assert_equal(t_csqrt(cpackl(-0.0, -0.0)), cpackl(0.0, -0.0));
}

/*
 * Test the handling of infinities when the other argument is not NaN.
 */
static void
test_infinities()
{
	static const double vals[] = {
		0.0,
		-0.0,
		42.0,
		-42.0,
		INFINITY,
		-INFINITY,
	};

	int i;

	for (i = 0; i < N(vals); i++) {
		if (isfinite(vals[i])) {
			assert_equal(t_csqrt(cpackl(-INFINITY, vals[i])),
			    cpackl(0.0, copysignl(INFINITY, vals[i])));
			assert_equal(t_csqrt(cpackl(INFINITY, vals[i])),
			    cpackl(INFINITY, copysignl(0.0, vals[i])));
		}
		assert_equal(t_csqrt(cpackl(vals[i], INFINITY)),
		    cpackl(INFINITY, INFINITY));
		assert_equal(t_csqrt(cpackl(vals[i], -INFINITY)),
		    cpackl(INFINITY, -INFINITY));
	}
}

/*
 * Test the handling of NaNs.
 */
static void
test_nans()
{

	assert(creall(t_csqrt(cpackl(INFINITY, NAN))) == INFINITY);
	assert(isnan(cimagl(t_csqrt(cpackl(INFINITY, NAN)))));

	assert(isnan(creall(t_csqrt(cpackl(-INFINITY, NAN)))));
	assert(isinf(cimagl(t_csqrt(cpackl(-INFINITY, NAN)))));

	assert_equal(t_csqrt(cpackl(NAN, INFINITY)),
		     cpackl(INFINITY, INFINITY));
	assert_equal(t_csqrt(cpackl(NAN, -INFINITY)),
		     cpackl(INFINITY, -INFINITY));

	assert_equal(t_csqrt(cpackl(0.0, NAN)), cpackl(NAN, NAN));
	assert_equal(t_csqrt(cpackl(-0.0, NAN)), cpackl(NAN, NAN));
	assert_equal(t_csqrt(cpackl(42.0, NAN)), cpackl(NAN, NAN));
	assert_equal(t_csqrt(cpackl(-42.0, NAN)), cpackl(NAN, NAN));
	assert_equal(t_csqrt(cpackl(NAN, 0.0)), cpackl(NAN, NAN));
	assert_equal(t_csqrt(cpackl(NAN, -0.0)), cpackl(NAN, NAN));
	assert_equal(t_csqrt(cpackl(NAN, 42.0)), cpackl(NAN, NAN));
	assert_equal(t_csqrt(cpackl(NAN, -42.0)), cpackl(NAN, NAN));
	assert_equal(t_csqrt(cpackl(NAN, NAN)), cpackl(NAN, NAN));
}

/*
 * Test whether csqrt(a + bi) works for inputs that are large enough to
 * cause overflow in hypot(a, b) + a. In this case we are using
 *	csqrt(115 + 252*I) == 14 + 9*I
 * scaled up to near MAX_EXP.
 */
static void
test_overflow(int maxexp)
{
	long double a, b;
	long double complex result;

	a = ldexpl(115 * 0x1p-8, maxexp);
	b = ldexpl(252 * 0x1p-8, maxexp);
	result = t_csqrt(cpackl(a, b));
	assert(creall(result) == ldexpl(14 * 0x1p-4, maxexp / 2));
	assert(cimagl(result) == ldexpl(9 * 0x1p-4, maxexp / 2));
}

int
main(int argc, char *argv[])
{

	printf("1..15\n");

	/* Test csqrt() */
	t_csqrt = _csqrt;

	test_finite();
	printf("ok 1 - csqrt\n");

	test_zeros();
	printf("ok 2 - csqrt\n");

	test_infinities();
	printf("ok 3 - csqrt\n");

	test_nans();
	printf("ok 4 - csqrt\n");

	test_overflow(DBL_MAX_EXP);
	printf("ok 5 - csqrt\n");

	/* Now test csqrtf() */
	t_csqrt = _csqrtf;

	test_finite();
	printf("ok 6 - csqrt\n");

	test_zeros();
	printf("ok 7 - csqrt\n");

	test_infinities();
	printf("ok 8 - csqrt\n");

	test_nans();
	printf("ok 9 - csqrt\n");

	test_overflow(FLT_MAX_EXP);
	printf("ok 10 - csqrt\n");

	/* Now test csqrtl() */
	t_csqrt = csqrtl;

	test_finite();
	printf("ok 11 - csqrt\n");

	test_zeros();
	printf("ok 12 - csqrt\n");

	test_infinities();
	printf("ok 13 - csqrt\n");

	test_nans();
	printf("ok 14 - csqrt\n");

	test_overflow(LDBL_MAX_EXP);
	printf("ok 15 - csqrt\n");

	return (0);
}