/*-
* Copyright (c) 2008-2011 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 corner cases in cexp*().
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
#include <sys/param.h>
#include <assert.h>
#include <complex.h>
#include <fenv.h>
#include <float.h>
#include <math.h>
#include <stdio.h>
#include "test-utils.h"
#pragma STDC FENV_ACCESS ON
#pragma STDC CX_LIMITED_RANGE OFF
/*
* Test that a function returns the correct value and sets the
* exception flags correctly. The exceptmask specifies which
* exceptions we should check. We need to be lenient for several
* reasons, but mainly because on some architectures it's impossible
* to raise FE_OVERFLOW without raising FE_INEXACT. In some cases,
* whether cexp() raises an invalid exception is unspecified.
*
* These are macros instead of functions so that assert provides more
* meaningful error messages.
*
* XXX The volatile here is to avoid gcc's bogus constant folding and work
* around the lack of support for the FENV_ACCESS pragma.
*/
#define test_t(type, func, z, result, exceptmask, excepts, checksign) \
do { \
volatile long double complex _d = z; \
volatile type complex _r = result; \
assert(feclearexcept(FE_ALL_EXCEPT) == 0); \
assert(cfpequal_cs((func)(_d), (_r), (checksign))); \
assert(((void)(func), fetestexcept(exceptmask) == (excepts))); \
} while (0)
#define test(func, z, result, exceptmask, excepts, checksign) \
test_t(double, func, z, result, exceptmask, excepts, checksign)
#define test_f(func, z, result, exceptmask, excepts, checksign) \
test_t(float, func, z, result, exceptmask, excepts, checksign)
/* Test within a given tolerance. */
#define test_tol(func, z, result, tol) do { \
volatile long double complex _d = z; \
assert(cfpequal_tol((func)(_d), (result), (tol), \
FPE_ABS_ZERO | CS_BOTH)); \
} while (0)
/* Test all the functions that compute cexp(x). */
#define testall(x, result, exceptmask, excepts, checksign) do { \
test(cexp, x, result, exceptmask, excepts, checksign); \
test_f(cexpf, x, result, exceptmask, excepts, checksign); \
} while (0)
/*
* Test all the functions that compute cexp(x), within a given tolerance.
* The tolerance is specified in ulps.
*/
#define testall_tol(x, result, tol) do { \
test_tol(cexp, x, result, tol * DBL_ULP()); \
test_tol(cexpf, x, result, tol * FLT_ULP()); \
} while (0)
/* Various finite non-zero numbers to test. */
static const float finites[] =
{ -42.0e20, -1.0, -1.0e-10, -0.0, 0.0, 1.0e-10, 1.0, 42.0e20 };
/* Tests for 0 */
static void
test_zero(void)
{
/* cexp(0) = 1, no exceptions raised */
testall(0.0, 1.0, ALL_STD_EXCEPT, 0, 1);
testall(-0.0, 1.0, ALL_STD_EXCEPT, 0, 1);
testall(CMPLXL(0.0, -0.0), CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, 1);
testall(CMPLXL(-0.0, -0.0), CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, 1);
}
/*
* Tests for NaN. The signs of the results are indeterminate unless the
* imaginary part is 0.
*/
static void
test_nan(void)
{
unsigned i;
/* cexp(x + NaNi) = NaN + NaNi and optionally raises invalid */
/* cexp(NaN + yi) = NaN + NaNi and optionally raises invalid (|y|>0) */
for (i = 0; i < nitems(finites); i++) {
printf("# Run %d..\n", i);
testall(CMPLXL(finites[i], NAN), CMPLXL(NAN, NAN),
ALL_STD_EXCEPT & ~FE_INVALID, 0, 0);
if (finites[i] == 0.0)
continue;
/* XXX FE_INEXACT shouldn't be raised here */
testall(CMPLXL(NAN, finites[i]), CMPLXL(NAN, NAN),
ALL_STD_EXCEPT & ~(FE_INVALID | FE_INEXACT), 0, 0);
}
/* cexp(NaN +- 0i) = NaN +- 0i */
testall(CMPLXL(NAN, 0.0), CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, 1);
testall(CMPLXL(NAN, -0.0), CMPLXL(NAN, -0.0), ALL_STD_EXCEPT, 0, 1);
/* cexp(inf + NaN i) = inf + nan i */
testall(CMPLXL(INFINITY, NAN), CMPLXL(INFINITY, NAN),
ALL_STD_EXCEPT, 0, 0);
/* cexp(-inf + NaN i) = 0 */
testall(CMPLXL(-INFINITY, NAN), CMPLXL(0.0, 0.0),
ALL_STD_EXCEPT, 0, 0);
/* cexp(NaN + NaN i) = NaN + NaN i */
testall(CMPLXL(NAN, NAN), CMPLXL(NAN, NAN),
ALL_STD_EXCEPT, 0, 0);
}
static void
test_inf(void)
{
unsigned i;
/* cexp(x + inf i) = NaN + NaNi and raises invalid */
for (i = 0; i < nitems(finites); i++) {
printf("# Run %d..\n", i);
testall(CMPLXL(finites[i], INFINITY), CMPLXL(NAN, NAN),
ALL_STD_EXCEPT, FE_INVALID, 1);
}
/* cexp(-inf + yi) = 0 * (cos(y) + sin(y)i) */
/* XXX shouldn't raise an inexact exception */
testall(CMPLXL(-INFINITY, M_PI_4), CMPLXL(0.0, 0.0),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
testall(CMPLXL(-INFINITY, 3 * M_PI_4), CMPLXL(-0.0, 0.0),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
testall(CMPLXL(-INFINITY, 5 * M_PI_4), CMPLXL(-0.0, -0.0),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
testall(CMPLXL(-INFINITY, 7 * M_PI_4), CMPLXL(0.0, -0.0),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
testall(CMPLXL(-INFINITY, 0.0), CMPLXL(0.0, 0.0),
ALL_STD_EXCEPT, 0, 1);
testall(CMPLXL(-INFINITY, -0.0), CMPLXL(0.0, -0.0),
ALL_STD_EXCEPT, 0, 1);
/* cexp(inf + yi) = inf * (cos(y) + sin(y)i) (except y=0) */
/* XXX shouldn't raise an inexact exception */
testall(CMPLXL(INFINITY, M_PI_4), CMPLXL(INFINITY, INFINITY),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
testall(CMPLXL(INFINITY, 3 * M_PI_4), CMPLXL(-INFINITY, INFINITY),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
testall(CMPLXL(INFINITY, 5 * M_PI_4), CMPLXL(-INFINITY, -INFINITY),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
testall(CMPLXL(INFINITY, 7 * M_PI_4), CMPLXL(INFINITY, -INFINITY),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
/* cexp(inf + 0i) = inf + 0i */
testall(CMPLXL(INFINITY, 0.0), CMPLXL(INFINITY, 0.0),
ALL_STD_EXCEPT, 0, 1);
testall(CMPLXL(INFINITY, -0.0), CMPLXL(INFINITY, -0.0),
ALL_STD_EXCEPT, 0, 1);
}
static void
test_reals(void)
{
unsigned i;
for (i = 0; i < nitems(finites); i++) {
/* XXX could check exceptions more meticulously */
printf("# Run %d..\n", i);
test(cexp, CMPLXL(finites[i], 0.0),
CMPLXL(exp(finites[i]), 0.0),
FE_INVALID | FE_DIVBYZERO, 0, 1);
test(cexp, CMPLXL(finites[i], -0.0),
CMPLXL(exp(finites[i]), -0.0),
FE_INVALID | FE_DIVBYZERO, 0, 1);
test_f(cexpf, CMPLXL(finites[i], 0.0),
CMPLXL(expf(finites[i]), 0.0),
FE_INVALID | FE_DIVBYZERO, 0, 1);
test_f(cexpf, CMPLXL(finites[i], -0.0),
CMPLXL(expf(finites[i]), -0.0),
FE_INVALID | FE_DIVBYZERO, 0, 1);
}
}
static void
test_imaginaries(void)
{
unsigned i;
for (i = 0; i < nitems(finites); i++) {
printf("# Run %d..\n", i);
test(cexp, CMPLXL(0.0, finites[i]),
CMPLXL(cos(finites[i]), sin(finites[i])),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
test(cexp, CMPLXL(-0.0, finites[i]),
CMPLXL(cos(finites[i]), sin(finites[i])),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
test_f(cexpf, CMPLXL(0.0, finites[i]),
CMPLXL(cosf(finites[i]), sinf(finites[i])),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
test_f(cexpf, CMPLXL(-0.0, finites[i]),
CMPLXL(cosf(finites[i]), sinf(finites[i])),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
}
}
static void
test_small(void)
{
static const double tests[] = {
/* csqrt(a + bI) = x + yI */
/* a b x y */
1.0, M_PI_4, M_SQRT2 * 0.5 * M_E, M_SQRT2 * 0.5 * M_E,
-1.0, M_PI_4, M_SQRT2 * 0.5 / M_E, M_SQRT2 * 0.5 / M_E,
2.0, M_PI_2, 0.0, M_E * M_E,
M_LN2, M_PI, -2.0, 0.0,
};
double a, b;
double x, y;
unsigned i;
for (i = 0; i < nitems(tests); i += 4) {
printf("# Run %d..\n", i);
a = tests[i];
b = tests[i + 1];
x = tests[i + 2];
y = tests[i + 3];
test_tol(cexp, CMPLXL(a, b), CMPLXL(x, y), 3 * DBL_ULP());
/* float doesn't have enough precision to pass these tests */
if (x == 0 || y == 0)
continue;
test_tol(cexpf, CMPLXL(a, b), CMPLXL(x, y), 1 * FLT_ULP());
}
}
/* Test inputs with a real part r that would overflow exp(r). */
static void
test_large(void)
{
test_tol(cexp, CMPLXL(709.79, 0x1p-1074),
CMPLXL(INFINITY, 8.94674309915433533273e-16), DBL_ULP());
test_tol(cexp, CMPLXL(1000, 0x1p-1074),
CMPLXL(INFINITY, 9.73344457300016401328e+110), DBL_ULP());
test_tol(cexp, CMPLXL(1400, 0x1p-1074),
CMPLXL(INFINITY, 5.08228858149196559681e+284), DBL_ULP());
test_tol(cexp, CMPLXL(900, 0x1.23456789abcdep-1020),
CMPLXL(INFINITY, 7.42156649354218408074e+83), DBL_ULP());
test_tol(cexp, CMPLXL(1300, 0x1.23456789abcdep-1020),
CMPLXL(INFINITY, 3.87514844965996756704e+257), DBL_ULP());
test_tol(cexpf, CMPLXL(88.73, 0x1p-149),
CMPLXL(INFINITY, 4.80265603e-07), 2 * FLT_ULP());
test_tol(cexpf, CMPLXL(90, 0x1p-149),
CMPLXL(INFINITY, 1.7101492622e-06f), 2 * FLT_ULP());
test_tol(cexpf, CMPLXL(192, 0x1p-149),
CMPLXL(INFINITY, 3.396809344e+38f), 2 * FLT_ULP());
test_tol(cexpf, CMPLXL(120, 0x1.234568p-120),
CMPLXL(INFINITY, 1.1163382522e+16f), 2 * FLT_ULP());
test_tol(cexpf, CMPLXL(170, 0x1.234568p-120),
CMPLXL(INFINITY, 5.7878851079e+37f), 2 * FLT_ULP());
}
int
main(void)
{
printf("1..7\n");
test_zero();
printf("ok 1 - cexp zero\n");
test_nan();
printf("ok 2 - cexp nan\n");
test_inf();
printf("ok 3 - cexp inf\n");
test_reals();
printf("ok 4 - cexp reals\n");
test_imaginaries();
printf("ok 5 - cexp imaginaries\n");
test_small();
printf("ok 6 - cexp small\n");
test_large();
printf("ok 7 - cexp large\n");
return (0);
}