/*-
* 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("$FreeBSD$");
#include <sys/param.h>
#include <assert.h>
#include <complex.h>
#include <float.h>
#include <math.h>
#include <stdio.h>
#include "test-utils.h"
/*
* 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.
*/
static 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
/*
* 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)
{
assert(cfpequal(d1, 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(void)
{
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;
unsigned i, j;
for (i = 0; i < nitems(tests); i += 4) {
for (j = 0; j < nitems(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(CMPLXL(a, b)) == CMPLXL(x, y));
}
}
}
/*
* Test the handling of +/- 0.
*/
static void
test_zeros(void)
{
assert_equal(t_csqrt(CMPLXL(0.0, 0.0)), CMPLXL(0.0, 0.0));
assert_equal(t_csqrt(CMPLXL(-0.0, 0.0)), CMPLXL(0.0, 0.0));
assert_equal(t_csqrt(CMPLXL(0.0, -0.0)), CMPLXL(0.0, -0.0));
assert_equal(t_csqrt(CMPLXL(-0.0, -0.0)), CMPLXL(0.0, -0.0));
}
/*
* Test the handling of infinities when the other argument is not NaN.
*/
static void
test_infinities(void)
{
static const double vals[] = {
0.0,
-0.0,
42.0,
-42.0,
INFINITY,
-INFINITY,
};
unsigned i;
for (i = 0; i < nitems(vals); i++) {
if (isfinite(vals[i])) {
assert_equal(t_csqrt(CMPLXL(-INFINITY, vals[i])),
CMPLXL(0.0, copysignl(INFINITY, vals[i])));
assert_equal(t_csqrt(CMPLXL(INFINITY, vals[i])),
CMPLXL(INFINITY, copysignl(0.0, vals[i])));
}
assert_equal(t_csqrt(CMPLXL(vals[i], INFINITY)),
CMPLXL(INFINITY, INFINITY));
assert_equal(t_csqrt(CMPLXL(vals[i], -INFINITY)),
CMPLXL(INFINITY, -INFINITY));
}
}
/*
* Test the handling of NaNs.
*/
static void
test_nans(void)
{
assert(creall(t_csqrt(CMPLXL(INFINITY, NAN))) == INFINITY);
assert(isnan(cimagl(t_csqrt(CMPLXL(INFINITY, NAN)))));
assert(isnan(creall(t_csqrt(CMPLXL(-INFINITY, NAN)))));
assert(isinf(cimagl(t_csqrt(CMPLXL(-INFINITY, NAN)))));
assert_equal(t_csqrt(CMPLXL(NAN, INFINITY)),
CMPLXL(INFINITY, INFINITY));
assert_equal(t_csqrt(CMPLXL(NAN, -INFINITY)),
CMPLXL(INFINITY, -INFINITY));
assert_equal(t_csqrt(CMPLXL(0.0, NAN)), CMPLXL(NAN, NAN));
assert_equal(t_csqrt(CMPLXL(-0.0, NAN)), CMPLXL(NAN, NAN));
assert_equal(t_csqrt(CMPLXL(42.0, NAN)), CMPLXL(NAN, NAN));
assert_equal(t_csqrt(CMPLXL(-42.0, NAN)), CMPLXL(NAN, NAN));
assert_equal(t_csqrt(CMPLXL(NAN, 0.0)), CMPLXL(NAN, NAN));
assert_equal(t_csqrt(CMPLXL(NAN, -0.0)), CMPLXL(NAN, NAN));
assert_equal(t_csqrt(CMPLXL(NAN, 42.0)), CMPLXL(NAN, NAN));
assert_equal(t_csqrt(CMPLXL(NAN, -42.0)), CMPLXL(NAN, NAN));
assert_equal(t_csqrt(CMPLXL(NAN, NAN)), CMPLXL(NAN, NAN));
}
/*
* Test whether csqrt(a + bi) works for inputs that are large enough to
* cause overflow in hypot(a, b) + a. Each of the tests is scaled up to
* near MAX_EXP.
*/
static void
test_overflow(int maxexp)
{
long double a, b;
long double complex result;
int exp, i;
assert(maxexp > 0 && maxexp % 2 == 0);
for (i = 0; i < 4; i++) {
exp = maxexp - 2 * i;
/* csqrt(115 + 252*I) == 14 + 9*I */
a = ldexpl(115 * 0x1p-8, exp);
b = ldexpl(252 * 0x1p-8, exp);
result = t_csqrt(CMPLXL(a, b));
assert(creall(result) == ldexpl(14 * 0x1p-4, exp / 2));
assert(cimagl(result) == ldexpl(9 * 0x1p-4, exp / 2));
/* csqrt(-11 + 60*I) = 5 + 6*I */
a = ldexpl(-11 * 0x1p-6, exp);
b = ldexpl(60 * 0x1p-6, exp);
result = t_csqrt(CMPLXL(a, b));
assert(creall(result) == ldexpl(5 * 0x1p-3, exp / 2));
assert(cimagl(result) == ldexpl(6 * 0x1p-3, exp / 2));
/* csqrt(225 + 0*I) == 15 + 0*I */
a = ldexpl(225 * 0x1p-8, exp);
b = 0;
result = t_csqrt(CMPLXL(a, b));
assert(creall(result) == ldexpl(15 * 0x1p-4, exp / 2));
assert(cimagl(result) == 0);
}
}
/*
* Test that precision is maintained for some large squares. Set all or
* some bits in the lower mantdig/2 bits, square the number, and try to
* recover the sqrt. Note:
* (x + xI)**2 = 2xxI
*/
static void
test_precision(int maxexp, int mantdig)
{
long double b, x;
long double complex result;
uint64_t mantbits, sq_mantbits;
int exp, i;
assert(maxexp > 0 && maxexp % 2 == 0);
assert(mantdig <= 64);
mantdig = rounddown(mantdig, 2);
for (exp = 0; exp <= maxexp; exp += 2) {
mantbits = ((uint64_t)1 << (mantdig / 2 )) - 1;
for (i = 0;
i < 100 && mantbits > ((uint64_t)1 << (mantdig / 2 - 1));
i++, mantbits--) {
sq_mantbits = mantbits * mantbits;
/*
* sq_mantibts is a mantdig-bit number. Divide by
* 2**mantdig to normalize it to [0.5, 1), where,
* note, the binary power will be -1. Raise it by
* 2**exp for the test. exp is even. Lower it by
* one to reach a final binary power which is also
* even. The result should be exactly
* representable, given that mantdig is less than or
* equal to the available precision.
*/
b = ldexpl((long double)sq_mantbits,
exp - 1 - mantdig);
x = ldexpl(mantbits, (exp - 2 - mantdig) / 2);
assert(b == x * x * 2);
result = t_csqrt(CMPLXL(0, b));
assert(creall(result) == x);
assert(cimagl(result) == x);
}
}
}
int
main(void)
{
printf("1..18\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");
test_precision(DBL_MAX_EXP, DBL_MANT_DIG);
printf("ok 6 - csqrt\n");
/* Now test csqrtf() */
t_csqrt = _csqrtf;
test_finite();
printf("ok 7 - csqrt\n");
test_zeros();
printf("ok 8 - csqrt\n");
test_infinities();
printf("ok 9 - csqrt\n");
test_nans();
printf("ok 10 - csqrt\n");
test_overflow(FLT_MAX_EXP);
printf("ok 11 - csqrt\n");
test_precision(FLT_MAX_EXP, FLT_MANT_DIG);
printf("ok 12 - csqrt\n");
/* Now test csqrtl() */
t_csqrt = csqrtl;
test_finite();
printf("ok 13 - csqrt\n");
test_zeros();
printf("ok 14 - csqrt\n");
test_infinities();
printf("ok 15 - csqrt\n");
test_nans();
printf("ok 16 - csqrt\n");
test_overflow(LDBL_MAX_EXP);
printf("ok 17 - csqrt\n");
test_precision(LDBL_MAX_EXP,
#ifndef __i386__
LDBL_MANT_DIG
#else
DBL_MANT_DIG
#endif
);
printf("ok 18 - csqrt\n");
return (0);
}