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301 lines
10 KiB
C
301 lines
10 KiB
C
/*-
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* Copyright (c) 2008-2011 David Schultz <das@FreeBSD.org>
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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/*
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* Tests for corner cases in cexp*().
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*/
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#include <sys/param.h>
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#include <complex.h>
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#include <fenv.h>
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#include <float.h>
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#include <math.h>
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#include <stdio.h>
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#include "test-utils.h"
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#pragma STDC FENV_ACCESS ON
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#pragma STDC CX_LIMITED_RANGE OFF
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/*
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* Test that a function returns the correct value and sets the
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* exception flags correctly. The exceptmask specifies which
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* exceptions we should check. We need to be lenient for several
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* reasons, but mainly because on some architectures it's impossible
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* to raise FE_OVERFLOW without raising FE_INEXACT. In some cases,
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* whether cexp() raises an invalid exception is unspecified.
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*
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* These are macros instead of functions so that assert provides more
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* meaningful error messages.
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*
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* XXX The volatile here is to avoid gcc's bogus constant folding and work
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* around the lack of support for the FENV_ACCESS pragma.
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*/
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#define test_t(type, func, z, result, exceptmask, excepts, checksign) \
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do { \
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volatile long double complex _d = z; \
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volatile type complex _r = result; \
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ATF_REQUIRE_EQ(0, feclearexcept(FE_ALL_EXCEPT)); \
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CHECK_CFPEQUAL_CS((func)(_d), (_r), (checksign)); \
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CHECK_FP_EXCEPTIONS_MSG(excepts, exceptmask, "for %s(%s)", \
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#func, #z); \
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} while (0)
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#define test(func, z, result, exceptmask, excepts, checksign) \
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test_t(double, func, z, result, exceptmask, excepts, checksign)
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#define test_f(func, z, result, exceptmask, excepts, checksign) \
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test_t(float, func, z, result, exceptmask, excepts, checksign)
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/* Test within a given tolerance. */
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#define test_tol(func, z, result, tol) do { \
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CHECK_CFPEQUAL_TOL((func)(z), (result), (tol), \
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FPE_ABS_ZERO | CS_BOTH); \
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} while (0)
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/* Test all the functions that compute cexp(x). */
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#define testall(x, result, exceptmask, excepts, checksign) do { \
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test(cexp, x, result, exceptmask, excepts, checksign); \
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test_f(cexpf, x, result, exceptmask, excepts, checksign); \
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} while (0)
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/*
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* Test all the functions that compute cexp(x), within a given tolerance.
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* The tolerance is specified in ulps.
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*/
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#define testall_tol(x, result, tol) do { \
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test_tol(cexp, x, result, tol * DBL_ULP()); \
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test_tol(cexpf, x, result, tol * FLT_ULP()); \
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} while (0)
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/* Various finite non-zero numbers to test. */
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static const float finites[] =
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{ -42.0e20, -1.0, -1.0e-10, -0.0, 0.0, 1.0e-10, 1.0, 42.0e20 };
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/* Tests for 0 */
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ATF_TC_WITHOUT_HEAD(zero);
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ATF_TC_BODY(zero, tc)
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{
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/* cexp(0) = 1, no exceptions raised */
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testall(0.0, 1.0, ALL_STD_EXCEPT, 0, 1);
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testall(-0.0, 1.0, ALL_STD_EXCEPT, 0, 1);
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testall(CMPLXL(0.0, -0.0), CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, 1);
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testall(CMPLXL(-0.0, -0.0), CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, 1);
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}
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/*
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* Tests for NaN. The signs of the results are indeterminate unless the
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* imaginary part is 0.
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*/
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ATF_TC_WITHOUT_HEAD(nan);
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ATF_TC_BODY(nan, tc)
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{
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unsigned i;
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/* cexp(x + NaNi) = NaN + NaNi and optionally raises invalid */
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/* cexp(NaN + yi) = NaN + NaNi and optionally raises invalid (|y|>0) */
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for (i = 0; i < nitems(finites); i++) {
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testall(CMPLXL(finites[i], NAN), CMPLXL(NAN, NAN),
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ALL_STD_EXCEPT & ~FE_INVALID, 0, 0);
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if (finites[i] == 0.0)
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continue;
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/* XXX FE_INEXACT shouldn't be raised here */
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testall(CMPLXL(NAN, finites[i]), CMPLXL(NAN, NAN),
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ALL_STD_EXCEPT & ~(FE_INVALID | FE_INEXACT), 0, 0);
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}
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/* cexp(NaN +- 0i) = NaN +- 0i */
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testall(CMPLXL(NAN, 0.0), CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, 1);
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testall(CMPLXL(NAN, -0.0), CMPLXL(NAN, -0.0), ALL_STD_EXCEPT, 0, 1);
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/* cexp(inf + NaN i) = inf + nan i */
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testall(CMPLXL(INFINITY, NAN), CMPLXL(INFINITY, NAN),
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ALL_STD_EXCEPT, 0, 0);
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/* cexp(-inf + NaN i) = 0 */
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testall(CMPLXL(-INFINITY, NAN), CMPLXL(0.0, 0.0),
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ALL_STD_EXCEPT, 0, 0);
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/* cexp(NaN + NaN i) = NaN + NaN i */
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testall(CMPLXL(NAN, NAN), CMPLXL(NAN, NAN),
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ALL_STD_EXCEPT, 0, 0);
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}
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ATF_TC_WITHOUT_HEAD(inf);
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ATF_TC_BODY(inf, tc)
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{
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unsigned i;
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/* cexp(x + inf i) = NaN + NaNi and raises invalid */
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for (i = 0; i < nitems(finites); i++) {
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testall(CMPLXL(finites[i], INFINITY), CMPLXL(NAN, NAN),
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ALL_STD_EXCEPT, FE_INVALID, 1);
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}
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/* cexp(-inf + yi) = 0 * (cos(y) + sin(y)i) */
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/* XXX shouldn't raise an inexact exception */
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testall(CMPLXL(-INFINITY, M_PI_4), CMPLXL(0.0, 0.0),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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testall(CMPLXL(-INFINITY, 3 * M_PI_4), CMPLXL(-0.0, 0.0),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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testall(CMPLXL(-INFINITY, 5 * M_PI_4), CMPLXL(-0.0, -0.0),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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testall(CMPLXL(-INFINITY, 7 * M_PI_4), CMPLXL(0.0, -0.0),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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testall(CMPLXL(-INFINITY, 0.0), CMPLXL(0.0, 0.0),
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ALL_STD_EXCEPT, 0, 1);
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testall(CMPLXL(-INFINITY, -0.0), CMPLXL(0.0, -0.0),
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ALL_STD_EXCEPT, 0, 1);
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/* cexp(inf + yi) = inf * (cos(y) + sin(y)i) (except y=0) */
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/* XXX shouldn't raise an inexact exception */
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testall(CMPLXL(INFINITY, M_PI_4), CMPLXL(INFINITY, INFINITY),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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testall(CMPLXL(INFINITY, 3 * M_PI_4), CMPLXL(-INFINITY, INFINITY),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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testall(CMPLXL(INFINITY, 5 * M_PI_4), CMPLXL(-INFINITY, -INFINITY),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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testall(CMPLXL(INFINITY, 7 * M_PI_4), CMPLXL(INFINITY, -INFINITY),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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/* cexp(inf + 0i) = inf + 0i */
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testall(CMPLXL(INFINITY, 0.0), CMPLXL(INFINITY, 0.0),
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ALL_STD_EXCEPT, 0, 1);
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testall(CMPLXL(INFINITY, -0.0), CMPLXL(INFINITY, -0.0),
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ALL_STD_EXCEPT, 0, 1);
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}
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ATF_TC_WITHOUT_HEAD(reals);
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ATF_TC_BODY(reals, tc)
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{
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unsigned i;
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for (i = 0; i < nitems(finites); i++) {
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/* XXX could check exceptions more meticulously */
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test(cexp, CMPLXL(finites[i], 0.0),
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CMPLXL(exp(finites[i]), 0.0),
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FE_INVALID | FE_DIVBYZERO, 0, 1);
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test(cexp, CMPLXL(finites[i], -0.0),
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CMPLXL(exp(finites[i]), -0.0),
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FE_INVALID | FE_DIVBYZERO, 0, 1);
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test_f(cexpf, CMPLXL(finites[i], 0.0),
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CMPLXL(expf(finites[i]), 0.0),
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FE_INVALID | FE_DIVBYZERO, 0, 1);
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test_f(cexpf, CMPLXL(finites[i], -0.0),
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CMPLXL(expf(finites[i]), -0.0),
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FE_INVALID | FE_DIVBYZERO, 0, 1);
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}
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}
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ATF_TC_WITHOUT_HEAD(imaginaries);
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ATF_TC_BODY(imaginaries, tc)
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{
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unsigned i;
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for (i = 0; i < nitems(finites); i++) {
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test(cexp, CMPLXL(0.0, finites[i]),
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CMPLXL(cos(finites[i]), sin(finites[i])),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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test(cexp, CMPLXL(-0.0, finites[i]),
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CMPLXL(cos(finites[i]), sin(finites[i])),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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test_f(cexpf, CMPLXL(0.0, finites[i]),
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CMPLXL(cosf(finites[i]), sinf(finites[i])),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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test_f(cexpf, CMPLXL(-0.0, finites[i]),
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CMPLXL(cosf(finites[i]), sinf(finites[i])),
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ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
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}
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}
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ATF_TC_WITHOUT_HEAD(small);
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ATF_TC_BODY(small, tc)
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{
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static const double tests[] = {
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/* csqrt(a + bI) = x + yI */
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/* a b x y */
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1.0, M_PI_4, M_SQRT2 * 0.5 * M_E, M_SQRT2 * 0.5 * M_E,
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-1.0, M_PI_4, M_SQRT2 * 0.5 / M_E, M_SQRT2 * 0.5 / M_E,
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2.0, M_PI_2, 0.0, M_E * M_E,
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M_LN2, M_PI, -2.0, 0.0,
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};
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double a, b;
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double x, y;
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unsigned i;
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for (i = 0; i < nitems(tests); i += 4) {
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a = tests[i];
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b = tests[i + 1];
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x = tests[i + 2];
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y = tests[i + 3];
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test_tol(cexp, CMPLXL(a, b), CMPLXL(x, y), 3 * DBL_ULP());
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/* float doesn't have enough precision to pass these tests */
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if (x == 0 || y == 0)
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continue;
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test_tol(cexpf, CMPLXL(a, b), CMPLXL(x, y), 1 * FLT_ULP());
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}
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}
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/* Test inputs with a real part r that would overflow exp(r). */
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ATF_TC_WITHOUT_HEAD(large);
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ATF_TC_BODY(large, tc)
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{
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test_tol(cexp, CMPLXL(709.79, 0x1p-1074),
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CMPLXL(INFINITY, 8.94674309915433533273e-16), DBL_ULP());
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test_tol(cexp, CMPLXL(1000, 0x1p-1074),
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CMPLXL(INFINITY, 9.73344457300016401328e+110), DBL_ULP());
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test_tol(cexp, CMPLXL(1400, 0x1p-1074),
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CMPLXL(INFINITY, 5.08228858149196559681e+284), DBL_ULP());
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test_tol(cexp, CMPLXL(900, 0x1.23456789abcdep-1020),
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CMPLXL(INFINITY, 7.42156649354218408074e+83), DBL_ULP());
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test_tol(cexp, CMPLXL(1300, 0x1.23456789abcdep-1020),
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CMPLXL(INFINITY, 3.87514844965996756704e+257), DBL_ULP());
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test_tol(cexpf, CMPLXL(88.73, 0x1p-149),
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CMPLXL(INFINITY, 4.80265603e-07), 2 * FLT_ULP());
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test_tol(cexpf, CMPLXL(90, 0x1p-149),
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CMPLXL(INFINITY, 1.7101492622e-06f), 2 * FLT_ULP());
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test_tol(cexpf, CMPLXL(192, 0x1p-149),
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CMPLXL(INFINITY, 3.396809344e+38f), 2 * FLT_ULP());
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test_tol(cexpf, CMPLXL(120, 0x1.234568p-120),
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CMPLXL(INFINITY, 1.1163382522e+16f), 2 * FLT_ULP());
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test_tol(cexpf, CMPLXL(170, 0x1.234568p-120),
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CMPLXL(INFINITY, 5.7878851079e+37f), 2 * FLT_ULP());
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}
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ATF_TP_ADD_TCS(tp)
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{
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ATF_TP_ADD_TC(tp, zero);
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ATF_TP_ADD_TC(tp, nan);
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ATF_TP_ADD_TC(tp, inf);
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ATF_TP_ADD_TC(tp, reals);
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ATF_TP_ADD_TC(tp, imaginaries);
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ATF_TP_ADD_TC(tp, small);
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ATF_TP_ADD_TC(tp, large);
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return (atf_no_error());
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}
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