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| Current File : //usr/src/tools/regression/lib/msun/test-cexp.c |
/*-
* 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: release/9.1.0/tools/regression/lib/msun/test-cexp.c 219362 2011-03-07 03:15:49Z das $");
#include <assert.h>
#include <complex.h>
#include <fenv.h>
#include <float.h>
#include <math.h>
#include <stdio.h>
#define ALL_STD_EXCEPT (FE_DIVBYZERO | FE_INEXACT | FE_INVALID | \
FE_OVERFLOW | FE_UNDERFLOW)
#define FLT_ULP() ldexpl(1.0, 1 - FLT_MANT_DIG)
#define DBL_ULP() ldexpl(1.0, 1 - DBL_MANT_DIG)
#define LDBL_ULP() ldexpl(1.0, 1 - LDBL_MANT_DIG)
#define N(i) (sizeof(i) / sizeof((i)[0]))
#pragma STDC FENV_ACCESS ON
#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);
}
/*
* 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(func, z, result, exceptmask, excepts, checksign) do { \
volatile long double complex _d = z; \
assert(feclearexcept(FE_ALL_EXCEPT) == 0); \
assert(cfpequal((func)(_d), (result), (checksign))); \
assert(((func), fetestexcept(exceptmask) == (excepts))); \
} while (0)
/* 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))); \
} 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(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 };
/*
* Determine whether x and y are equal, with two special rules:
* +0.0 != -0.0
* NaN == NaN
* If checksign is 0, we compare the absolute values instead.
*/
static int
fpequal(long double x, long double y, int checksign)
{
if (isnan(x) || isnan(y))
return (1);
if (checksign)
return (x == y && !signbit(x) == !signbit(y));
else
return (fabsl(x) == fabsl(y));
}
static int
fpequal_tol(long double x, long double y, long double tol)
{
fenv_t env;
int ret;
if (isnan(x) && isnan(y))
return (1);
if (!signbit(x) != !signbit(y))
return (0);
if (x == y)
return (1);
if (tol == 0)
return (0);
/* Hard case: need to check the tolerance. */
feholdexcept(&env);
/*
* For our purposes here, if y=0, we interpret tol as an absolute
* tolerance. This is to account for roundoff in the input, e.g.,
* cos(Pi/2) ~= 0.
*/
if (y == 0.0)
ret = fabsl(x - y) <= fabsl(tol);
else
ret = fabsl(x - y) <= fabsl(y * tol);
fesetenv(&env);
return (ret);
}
static int
cfpequal(long double complex x, long double complex y, int checksign)
{
return (fpequal(creal(x), creal(y), checksign)
&& fpequal(cimag(x), cimag(y), checksign));
}
static int
cfpequal_tol(long double complex x, long double complex y, long double tol)
{
return (fpequal_tol(creal(x), creal(y), tol)
&& fpequal_tol(cimag(x), cimag(y), tol));
}
/* Tests for 0 */
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(cpackl(0.0, -0.0), cpackl(1.0, -0.0), ALL_STD_EXCEPT, 0, 1);
testall(cpackl(-0.0, -0.0), cpackl(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.
*/
void
test_nan()
{
int 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 < N(finites); i++) {
testall(cpackl(finites[i], NAN), cpackl(NAN, NAN),
ALL_STD_EXCEPT & ~FE_INVALID, 0, 0);
if (finites[i] == 0.0)
continue;
/* XXX FE_INEXACT shouldn't be raised here */
testall(cpackl(NAN, finites[i]), cpackl(NAN, NAN),
ALL_STD_EXCEPT & ~(FE_INVALID | FE_INEXACT), 0, 0);
}
/* cexp(NaN +- 0i) = NaN +- 0i */
testall(cpackl(NAN, 0.0), cpackl(NAN, 0.0), ALL_STD_EXCEPT, 0, 1);
testall(cpackl(NAN, -0.0), cpackl(NAN, -0.0), ALL_STD_EXCEPT, 0, 1);
/* cexp(inf + NaN i) = inf + nan i */
testall(cpackl(INFINITY, NAN), cpackl(INFINITY, NAN),
ALL_STD_EXCEPT, 0, 0);
/* cexp(-inf + NaN i) = 0 */
testall(cpackl(-INFINITY, NAN), cpackl(0.0, 0.0),
ALL_STD_EXCEPT, 0, 0);
/* cexp(NaN + NaN i) = NaN + NaN i */
testall(cpackl(NAN, NAN), cpackl(NAN, NAN),
ALL_STD_EXCEPT, 0, 0);
}
void
test_inf(void)
{
int i;
/* cexp(x + inf i) = NaN + NaNi and raises invalid */
/* cexp(inf + yi) = 0 + 0yi */
/* cexp(-inf + yi) = inf + inf yi (except y=0) */
for (i = 0; i < N(finites); i++) {
testall(cpackl(finites[i], INFINITY), cpackl(NAN, NAN),
ALL_STD_EXCEPT, FE_INVALID, 1);
/* XXX shouldn't raise an inexact exception */
testall(cpackl(-INFINITY, finites[i]),
cpackl(0.0, 0.0 * finites[i]),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
if (finites[i] == 0)
continue;
testall(cpackl(INFINITY, finites[i]),
cpackl(INFINITY, INFINITY * finites[i]),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
}
testall(cpackl(INFINITY, 0.0), cpackl(INFINITY, 0.0),
ALL_STD_EXCEPT, 0, 1);
testall(cpackl(INFINITY, -0.0), cpackl(INFINITY, -0.0),
ALL_STD_EXCEPT, 0, 1);
}
void
test_reals(void)
{
int i;
for (i = 0; i < N(finites); i++) {
/* XXX could check exceptions more meticulously */
test(cexp, cpackl(finites[i], 0.0),
cpackl(exp(finites[i]), 0.0),
FE_INVALID | FE_DIVBYZERO, 0, 1);
test(cexp, cpackl(finites[i], -0.0),
cpackl(exp(finites[i]), -0.0),
FE_INVALID | FE_DIVBYZERO, 0, 1);
test(cexpf, cpackl(finites[i], 0.0),
cpackl(expf(finites[i]), 0.0),
FE_INVALID | FE_DIVBYZERO, 0, 1);
test(cexpf, cpackl(finites[i], -0.0),
cpackl(expf(finites[i]), -0.0),
FE_INVALID | FE_DIVBYZERO, 0, 1);
}
}
void
test_imaginaries(void)
{
int i;
for (i = 0; i < N(finites); i++) {
test(cexp, cpackl(0.0, finites[i]),
cpackl(cos(finites[i]), sin(finites[i])),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
test(cexp, cpackl(-0.0, finites[i]),
cpackl(cos(finites[i]), sin(finites[i])),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
test(cexpf, cpackl(0.0, finites[i]),
cpackl(cosf(finites[i]), sinf(finites[i])),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
test(cexpf, cpackl(-0.0, finites[i]),
cpackl(cosf(finites[i]), sinf(finites[i])),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
}
}
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;
int i;
for (i = 0; i < N(tests); i += 4) {
a = tests[i];
b = tests[i + 1];
x = tests[i + 2];
y = tests[i + 3];
test_tol(cexp, cpackl(a, b), cpackl(x, y), 3 * DBL_ULP());
/* float doesn't have enough precision to pass these tests */
if (x == 0 || y == 0)
continue;
test_tol(cexpf, cpackl(a, b), cpackl(x, y), 1 * FLT_ULP());
}
}
/* Test inputs with a real part r that would overflow exp(r). */
void
test_large(void)
{
test_tol(cexp, cpackl(709.79, 0x1p-1074),
cpackl(INFINITY, 8.94674309915433533273e-16), DBL_ULP());
test_tol(cexp, cpackl(1000, 0x1p-1074),
cpackl(INFINITY, 9.73344457300016401328e+110), DBL_ULP());
test_tol(cexp, cpackl(1400, 0x1p-1074),
cpackl(INFINITY, 5.08228858149196559681e+284), DBL_ULP());
test_tol(cexp, cpackl(900, 0x1.23456789abcdep-1020),
cpackl(INFINITY, 7.42156649354218408074e+83), DBL_ULP());
test_tol(cexp, cpackl(1300, 0x1.23456789abcdep-1020),
cpackl(INFINITY, 3.87514844965996756704e+257), DBL_ULP());
test_tol(cexpf, cpackl(88.73, 0x1p-149),
cpackl(INFINITY, 4.80265603e-07), 2 * FLT_ULP());
test_tol(cexpf, cpackl(90, 0x1p-149),
cpackl(INFINITY, 1.7101492622e-06f), 2 * FLT_ULP());
test_tol(cexpf, cpackl(192, 0x1p-149),
cpackl(INFINITY, 3.396809344e+38f), 2 * FLT_ULP());
test_tol(cexpf, cpackl(120, 0x1.234568p-120),
cpackl(INFINITY, 1.1163382522e+16f), 2 * FLT_ULP());
test_tol(cexpf, cpackl(170, 0x1.234568p-120),
cpackl(INFINITY, 5.7878851079e+37f), 2 * FLT_ULP());
}
int
main(int argc, char *argv[])
{
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);
}