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/*-
* Copyright (c) 2008-2013 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 casin[h](), cacos[h](), and catan[h]().
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
#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.
*
* 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_p(func, z, result, exceptmask, excepts, checksign) do { \
volatile long double complex _d = z; \
debug(" testing %s(%Lg + %Lg I) == %Lg + %Lg I\n", #func, \
creall(_d), cimagl(_d), creall(result), cimagl(result)); \
assert(feclearexcept(FE_ALL_EXCEPT) == 0); \
assert(cfpequal_cs((func)(_d), (result), (checksign))); \
assert(((void)(func), fetestexcept(exceptmask) == (excepts))); \
} while (0)
/*
* Test within a given tolerance. The tolerance indicates relative error
* in ulps.
*/
#define test_p_tol(func, z, result, tol) do { \
volatile long double complex _d = z; \
debug(" testing %s(%Lg + %Lg I) ~= %Lg + %Lg I\n", #func, \
creall(_d), cimagl(_d), creall(result), cimagl(result)); \
assert(cfpequal_tol((func)(_d), (result), (tol), CS_BOTH)); \
} while (0)
/* These wrappers apply the identities f(conj(z)) = conj(f(z)). */
#define test(func, z, result, exceptmask, excepts, checksign) do { \
test_p(func, z, result, exceptmask, excepts, checksign); \
test_p(func, conjl(z), conjl(result), exceptmask, excepts, checksign); \
} while (0)
#define test_tol(func, z, result, tol) do { \
test_p_tol(func, z, result, tol); \
test_p_tol(func, conjl(z), conjl(result), tol); \
} while (0)
/* Test the given function in all precisions. */
#define testall(func, x, result, exceptmask, excepts, checksign) do { \
test(func, x, result, exceptmask, excepts, checksign); \
test(func##f, x, result, exceptmask, excepts, checksign); \
} while (0)
#define testall_odd(func, x, result, exceptmask, excepts, checksign) do { \
testall(func, x, result, exceptmask, excepts, checksign); \
testall(func, -(x), -result, exceptmask, excepts, checksign); \
} while (0)
#define testall_even(func, x, result, exceptmask, excepts, checksign) do { \
testall(func, x, result, exceptmask, excepts, checksign); \
testall(func, -(x), result, exceptmask, excepts, checksign); \
} while (0)
/*
* Test the given function in all precisions, within a given tolerance.
* The tolerance is specified in ulps.
*/
#define testall_tol(func, x, result, tol) do { \
test_tol(func, x, result, (tol) * DBL_ULP()); \
test_tol(func##f, x, result, (tol) * FLT_ULP()); \
} while (0)
#define testall_odd_tol(func, x, result, tol) do { \
testall_tol(func, x, result, tol); \
testall_tol(func, -(x), -result, tol); \
} while (0)
#define testall_even_tol(func, x, result, tol) do { \
testall_tol(func, x, result, tol); \
testall_tol(func, -(x), result, tol); \
} while (0)
static const long double
pi = 3.14159265358979323846264338327950280L,
c3pi = 9.42477796076937971538793014983850839L;
/* Tests for 0 */
void
test_zero(void)
{
long double complex zero = CMPLXL(0.0, 0.0);
testall_tol(cacosh, zero, CMPLXL(0.0, pi / 2), 1);
testall_tol(cacosh, -zero, CMPLXL(0.0, -pi / 2), 1);
testall_tol(cacos, zero, CMPLXL(pi / 2, -0.0), 1);
testall_tol(cacos, -zero, CMPLXL(pi / 2, 0.0), 1);
testall_odd(casinh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
testall_odd(casin, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
testall_odd(catanh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
testall_odd(catan, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
}
/*
* Tests for NaN inputs.
*/
void
test_nan()
{
long double complex nan_nan = CMPLXL(NAN, NAN);
long double complex z;
/*
* IN CACOSH CACOS CASINH CATANH
* NaN,NaN NaN,NaN NaN,NaN NaN,NaN NaN,NaN
* finite,NaN NaN,NaN* NaN,NaN* NaN,NaN* NaN,NaN*
* NaN,finite NaN,NaN* NaN,NaN* NaN,NaN* NaN,NaN*
* NaN,Inf Inf,NaN NaN,-Inf ?Inf,NaN ?0,pi/2
* +-Inf,NaN Inf,NaN NaN,?Inf +-Inf,NaN +-0,NaN
* +-0,NaN NaN,NaN* pi/2,NaN NaN,NaN* +-0,NaN
* NaN,0 NaN,NaN* NaN,NaN* NaN,0 NaN,NaN*
*
* * = raise invalid
*/
z = nan_nan;
testall(cacosh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
testall(cacos, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
testall(casinh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
testall(casin, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
testall(catanh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
testall(catan, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
z = CMPLXL(0.5, NAN);
testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0);
testall(cacos, z, nan_nan, OPT_INVALID, 0, 0);
testall(casinh, z, nan_nan, OPT_INVALID, 0, 0);
testall(casin, z, nan_nan, OPT_INVALID, 0, 0);
testall(catanh, z, nan_nan, OPT_INVALID, 0, 0);
testall(catan, z, nan_nan, OPT_INVALID, 0, 0);
z = CMPLXL(NAN, 0.5);
testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0);
testall(cacos, z, nan_nan, OPT_INVALID, 0, 0);
testall(casinh, z, nan_nan, OPT_INVALID, 0, 0);
testall(casin, z, nan_nan, OPT_INVALID, 0, 0);
testall(catanh, z, nan_nan, OPT_INVALID, 0, 0);
testall(catan, z, nan_nan, OPT_INVALID, 0, 0);
z = CMPLXL(NAN, INFINITY);
testall(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
testall(cacosh, -z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
testall(cacos, z, CMPLXL(NAN, -INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG);
testall(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 0);
testall(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG);
testall_tol(catanh, z, CMPLXL(0.0, pi / 2), 1);
testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, CS_IMAG);
z = CMPLXL(INFINITY, NAN);
testall_even(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0,
CS_REAL);
testall_even(cacos, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0);
testall_odd(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0,
CS_REAL);
testall_odd(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0);
testall_odd(catanh, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
testall_odd_tol(catan, z, CMPLXL(pi / 2, 0.0), 1);
z = CMPLXL(0.0, NAN);
/* XXX We allow a spurious inexact exception here. */
testall_even(cacosh, z, nan_nan, OPT_INVALID & ~FE_INEXACT, 0, 0);
testall_even_tol(cacos, z, CMPLXL(pi / 2, NAN), 1);
testall_odd(casinh, z, nan_nan, OPT_INVALID, 0, 0);
testall_odd(casin, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
testall_odd(catanh, z, CMPLXL(0.0, NAN), OPT_INVALID, 0, CS_REAL);
testall_odd(catan, z, nan_nan, OPT_INVALID, 0, 0);
z = CMPLXL(NAN, 0.0);
testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0);
testall(cacos, z, nan_nan, OPT_INVALID, 0, 0);
testall(casinh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, CS_IMAG);
testall(casin, z, nan_nan, OPT_INVALID, 0, 0);
testall(catanh, z, nan_nan, OPT_INVALID, 0, CS_IMAG);
testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, 0);
}
void
test_inf(void)
{
long double complex z;
/*
* IN CACOSH CACOS CASINH CATANH
* Inf,Inf Inf,pi/4 pi/4,-Inf Inf,pi/4 0,pi/2
* -Inf,Inf Inf,3pi/4 3pi/4,-Inf --- ---
* Inf,finite Inf,0 0,-Inf Inf,0 0,pi/2
* -Inf,finite Inf,pi pi,-Inf --- ---
* finite,Inf Inf,pi/2 pi/2,-Inf Inf,pi/2 0,pi/2
*/
z = CMPLXL(INFINITY, INFINITY);
testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 4), 1);
testall_tol(cacosh, -z, CMPLXL(INFINITY, -c3pi / 4), 1);
testall_tol(cacos, z, CMPLXL(pi / 4, -INFINITY), 1);
testall_tol(cacos, -z, CMPLXL(c3pi / 4, INFINITY), 1);
testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 4), 1);
testall_odd_tol(casin, z, CMPLXL(pi / 4, INFINITY), 1);
testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1);
testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1);
z = CMPLXL(INFINITY, 0.5);
/* XXX We allow a spurious inexact exception here. */
testall(cacosh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH);
testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi), 1);
testall(cacos, z, CMPLXL(0, -INFINITY), OPT_INEXACT, 0, CS_BOTH);
testall_tol(cacos, -z, CMPLXL(pi, INFINITY), 1);
testall_odd(casinh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH);
testall_odd_tol(casin, z, CMPLXL(pi / 2, INFINITY), 1);
testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1);
testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1);
z = CMPLXL(0.5, INFINITY);
testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 2), 1);
testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi / 2), 1);
testall_tol(cacos, z, CMPLXL(pi / 2, -INFINITY), 1);
testall_tol(cacos, -z, CMPLXL(pi / 2, INFINITY), 1);
testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 2), 1);
/* XXX We allow a spurious inexact exception here. */
testall_odd(casin, z, CMPLXL(0.0, INFINITY), OPT_INEXACT, 0, CS_BOTH);
testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1);
testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1);
}
/* Tests along the real and imaginary axes. */
void
test_axes(void)
{
static const long double nums[] = {
-2, -1, -0.5, 0.5, 1, 2
};
long double complex z;
int i;
for (i = 0; i < sizeof(nums) / sizeof(nums[0]); i++) {
/* Real axis */
z = CMPLXL(nums[i], 0.0);
if (fabs(nums[i]) <= 1) {
testall_tol(cacosh, z, CMPLXL(0.0, acos(nums[i])), 1);
testall_tol(cacos, z, CMPLXL(acosl(nums[i]), -0.0), 1);
testall_tol(casin, z, CMPLXL(asinl(nums[i]), 0.0), 1);
testall_tol(catanh, z, CMPLXL(atanh(nums[i]), 0.0), 1);
} else {
testall_tol(cacosh, z,
CMPLXL(acosh(fabs(nums[i])),
(nums[i] < 0) ? pi : 0), 1);
testall_tol(cacos, z,
CMPLXL((nums[i] < 0) ? pi : 0,
-acosh(fabs(nums[i]))), 1);
testall_tol(casin, z,
CMPLXL(copysign(pi / 2, nums[i]),
acosh(fabs(nums[i]))), 1);
testall_tol(catanh, z,
CMPLXL(atanh(1 / nums[i]), pi / 2), 1);
}
testall_tol(casinh, z, CMPLXL(asinh(nums[i]), 0.0), 1);
testall_tol(catan, z, CMPLXL(atan(nums[i]), 0), 1);
/* TODO: Test the imaginary axis. */
}
}
void
test_small(void)
{
/*
* z = 0.75 + i 0.25
* acos(z) = Pi/4 - i ln(2)/2
* asin(z) = Pi/4 + i ln(2)/2
* atan(z) = atan(4)/2 + i ln(17/9)/4
*/
static const struct {
complex long double z;
complex long double acos_z;
complex long double asin_z;
complex long double atan_z;
} tests[] = {
{ CMPLXL(0.75L, 0.25L),
CMPLXL(pi / 4, -0.34657359027997265470861606072908828L),
CMPLXL(pi / 4, 0.34657359027997265470861606072908828L),
CMPLXL(0.66290883183401623252961960521423782L,
0.15899719167999917436476103600701878L) },
};
int i;
for (i = 0; i < sizeof(tests) / sizeof(tests[0]); i++) {
testall_tol(cacos, tests[i].z, tests[i].acos_z, 2);
testall_odd_tol(casin, tests[i].z, tests[i].asin_z, 2);
testall_odd_tol(catan, tests[i].z, tests[i].atan_z, 2);
}
}
/* Test inputs that might cause overflow in a sloppy implementation. */
void
test_large(void)
{
/* TODO: Write these tests */
}
int
main(int argc, char *argv[])
{
printf("1..6\n");
test_zero();
printf("ok 1 - invctrig zero\n");
test_nan();
printf("ok 2 - invctrig nan\n");
test_inf();
printf("ok 3 - invctrig inf\n");
test_axes();
printf("ok 4 - invctrig axes\n");
test_small();
printf("ok 5 - invctrig small\n");
test_large();
printf("ok 6 - invctrig large\n");
return (0);
}
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