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45de1d006d
because different tests have different ideas about what it means to be "close enough" to the right answer, depending on the properties of the function being tested. In the process, I fixed some warnings and added a few more 'volatile' hacks, which are sufficient to make all the tests pass at -O2 with clang.
372 lines
13 KiB
C
372 lines
13 KiB
C
/*-
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* Copyright (c) 2008-2013 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 casin[h](), cacos[h](), and catan[h]().
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*/
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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#include <assert.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.
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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_p(func, z, result, exceptmask, excepts, checksign) do { \
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volatile long double complex _d = z; \
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debug(" testing %s(%Lg + %Lg I) == %Lg + %Lg I\n", #func, \
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creall(_d), cimagl(_d), creall(result), cimagl(result)); \
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assert(feclearexcept(FE_ALL_EXCEPT) == 0); \
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assert(cfpequal_cs((func)(_d), (result), (checksign))); \
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assert(((void)(func), fetestexcept(exceptmask) == (excepts))); \
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} while (0)
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/*
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* Test within a given tolerance. The tolerance indicates relative error
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* in ulps.
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*/
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#define test_p_tol(func, z, result, tol) do { \
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volatile long double complex _d = z; \
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debug(" testing %s(%Lg + %Lg I) ~= %Lg + %Lg I\n", #func, \
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creall(_d), cimagl(_d), creall(result), cimagl(result)); \
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assert(cfpequal_tol((func)(_d), (result), (tol), CS_BOTH)); \
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} while (0)
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/* These wrappers apply the identities f(conj(z)) = conj(f(z)). */
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#define test(func, z, result, exceptmask, excepts, checksign) do { \
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test_p(func, z, result, exceptmask, excepts, checksign); \
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test_p(func, conjl(z), conjl(result), exceptmask, excepts, checksign); \
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} while (0)
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#define test_tol(func, z, result, tol) do { \
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test_p_tol(func, z, result, tol); \
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test_p_tol(func, conjl(z), conjl(result), tol); \
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} while (0)
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/* Test the given function in all precisions. */
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#define testall(func, x, result, exceptmask, excepts, checksign) do { \
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test(func, x, result, exceptmask, excepts, checksign); \
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test(func##f, x, result, exceptmask, excepts, checksign); \
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} while (0)
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#define testall_odd(func, x, result, exceptmask, excepts, checksign) do { \
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testall(func, x, result, exceptmask, excepts, checksign); \
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testall(func, -(x), -result, exceptmask, excepts, checksign); \
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} while (0)
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#define testall_even(func, x, result, exceptmask, excepts, checksign) do { \
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testall(func, x, result, exceptmask, excepts, checksign); \
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testall(func, -(x), result, exceptmask, excepts, checksign); \
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} while (0)
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/*
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* Test the given function in all precisions, 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(func, x, result, tol) do { \
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test_tol(func, x, result, (tol) * DBL_ULP()); \
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test_tol(func##f, x, result, (tol) * FLT_ULP()); \
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} while (0)
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#define testall_odd_tol(func, x, result, tol) do { \
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testall_tol(func, x, result, tol); \
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testall_tol(func, -(x), -result, tol); \
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} while (0)
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#define testall_even_tol(func, x, result, tol) do { \
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testall_tol(func, x, result, tol); \
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testall_tol(func, -(x), result, tol); \
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} while (0)
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static const long double
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pi = 3.14159265358979323846264338327950280L,
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c3pi = 9.42477796076937971538793014983850839L;
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/* Tests for 0 */
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void
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test_zero(void)
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{
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long double complex zero = CMPLXL(0.0, 0.0);
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testall_tol(cacosh, zero, CMPLXL(0.0, pi / 2), 1);
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testall_tol(cacosh, -zero, CMPLXL(0.0, -pi / 2), 1);
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testall_tol(cacos, zero, CMPLXL(pi / 2, -0.0), 1);
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testall_tol(cacos, -zero, CMPLXL(pi / 2, 0.0), 1);
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testall_odd(casinh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
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testall_odd(casin, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
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testall_odd(catanh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
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testall_odd(catan, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
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}
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/*
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* Tests for NaN inputs.
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*/
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void
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test_nan()
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{
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long double complex nan_nan = CMPLXL(NAN, NAN);
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long double complex z;
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/*
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* IN CACOSH CACOS CASINH CATANH
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* NaN,NaN NaN,NaN NaN,NaN NaN,NaN NaN,NaN
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* finite,NaN NaN,NaN* NaN,NaN* NaN,NaN* NaN,NaN*
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* NaN,finite NaN,NaN* NaN,NaN* NaN,NaN* NaN,NaN*
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* NaN,Inf Inf,NaN NaN,-Inf ?Inf,NaN ?0,pi/2
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* +-Inf,NaN Inf,NaN NaN,?Inf +-Inf,NaN +-0,NaN
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* +-0,NaN NaN,NaN* pi/2,NaN NaN,NaN* +-0,NaN
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* NaN,0 NaN,NaN* NaN,NaN* NaN,0 NaN,NaN*
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*
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* * = raise invalid
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*/
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z = nan_nan;
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testall(cacosh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
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testall(cacos, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
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testall(casinh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
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testall(casin, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
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testall(catanh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
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testall(catan, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
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z = CMPLXL(0.5, NAN);
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testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0);
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testall(cacos, z, nan_nan, OPT_INVALID, 0, 0);
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testall(casinh, z, nan_nan, OPT_INVALID, 0, 0);
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testall(casin, z, nan_nan, OPT_INVALID, 0, 0);
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testall(catanh, z, nan_nan, OPT_INVALID, 0, 0);
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testall(catan, z, nan_nan, OPT_INVALID, 0, 0);
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z = CMPLXL(NAN, 0.5);
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testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0);
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testall(cacos, z, nan_nan, OPT_INVALID, 0, 0);
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testall(casinh, z, nan_nan, OPT_INVALID, 0, 0);
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testall(casin, z, nan_nan, OPT_INVALID, 0, 0);
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testall(catanh, z, nan_nan, OPT_INVALID, 0, 0);
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testall(catan, z, nan_nan, OPT_INVALID, 0, 0);
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z = CMPLXL(NAN, INFINITY);
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testall(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
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testall(cacosh, -z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
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testall(cacos, z, CMPLXL(NAN, -INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG);
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testall(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 0);
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testall(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG);
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testall_tol(catanh, z, CMPLXL(0.0, pi / 2), 1);
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testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, CS_IMAG);
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z = CMPLXL(INFINITY, NAN);
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testall_even(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0,
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CS_REAL);
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testall_even(cacos, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0);
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testall_odd(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0,
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CS_REAL);
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testall_odd(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0);
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testall_odd(catanh, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
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testall_odd_tol(catan, z, CMPLXL(pi / 2, 0.0), 1);
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z = CMPLXL(0.0, NAN);
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/* XXX We allow a spurious inexact exception here. */
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testall_even(cacosh, z, nan_nan, OPT_INVALID & ~FE_INEXACT, 0, 0);
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testall_even_tol(cacos, z, CMPLXL(pi / 2, NAN), 1);
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testall_odd(casinh, z, nan_nan, OPT_INVALID, 0, 0);
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testall_odd(casin, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
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testall_odd(catanh, z, CMPLXL(0.0, NAN), OPT_INVALID, 0, CS_REAL);
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testall_odd(catan, z, nan_nan, OPT_INVALID, 0, 0);
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z = CMPLXL(NAN, 0.0);
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testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0);
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testall(cacos, z, nan_nan, OPT_INVALID, 0, 0);
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testall(casinh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, CS_IMAG);
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testall(casin, z, nan_nan, OPT_INVALID, 0, 0);
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testall(catanh, z, nan_nan, OPT_INVALID, 0, CS_IMAG);
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testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, 0);
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}
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void
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test_inf(void)
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{
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long double complex z;
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/*
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* IN CACOSH CACOS CASINH CATANH
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* Inf,Inf Inf,pi/4 pi/4,-Inf Inf,pi/4 0,pi/2
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* -Inf,Inf Inf,3pi/4 3pi/4,-Inf --- ---
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* Inf,finite Inf,0 0,-Inf Inf,0 0,pi/2
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* -Inf,finite Inf,pi pi,-Inf --- ---
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* finite,Inf Inf,pi/2 pi/2,-Inf Inf,pi/2 0,pi/2
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*/
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z = CMPLXL(INFINITY, INFINITY);
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testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 4), 1);
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testall_tol(cacosh, -z, CMPLXL(INFINITY, -c3pi / 4), 1);
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testall_tol(cacos, z, CMPLXL(pi / 4, -INFINITY), 1);
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testall_tol(cacos, -z, CMPLXL(c3pi / 4, INFINITY), 1);
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testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 4), 1);
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testall_odd_tol(casin, z, CMPLXL(pi / 4, INFINITY), 1);
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testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1);
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testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1);
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z = CMPLXL(INFINITY, 0.5);
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/* XXX We allow a spurious inexact exception here. */
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testall(cacosh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH);
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testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi), 1);
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testall(cacos, z, CMPLXL(0, -INFINITY), OPT_INEXACT, 0, CS_BOTH);
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testall_tol(cacos, -z, CMPLXL(pi, INFINITY), 1);
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testall_odd(casinh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH);
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testall_odd_tol(casin, z, CMPLXL(pi / 2, INFINITY), 1);
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testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1);
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testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1);
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z = CMPLXL(0.5, INFINITY);
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testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 2), 1);
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testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi / 2), 1);
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testall_tol(cacos, z, CMPLXL(pi / 2, -INFINITY), 1);
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testall_tol(cacos, -z, CMPLXL(pi / 2, INFINITY), 1);
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testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 2), 1);
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/* XXX We allow a spurious inexact exception here. */
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testall_odd(casin, z, CMPLXL(0.0, INFINITY), OPT_INEXACT, 0, CS_BOTH);
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testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1);
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testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1);
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}
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/* Tests along the real and imaginary axes. */
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void
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test_axes(void)
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{
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static const long double nums[] = {
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-2, -1, -0.5, 0.5, 1, 2
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};
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long double complex z;
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int i;
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for (i = 0; i < sizeof(nums) / sizeof(nums[0]); i++) {
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/* Real axis */
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z = CMPLXL(nums[i], 0.0);
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if (fabs(nums[i]) <= 1) {
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testall_tol(cacosh, z, CMPLXL(0.0, acos(nums[i])), 1);
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testall_tol(cacos, z, CMPLXL(acosl(nums[i]), -0.0), 1);
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testall_tol(casin, z, CMPLXL(asinl(nums[i]), 0.0), 1);
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testall_tol(catanh, z, CMPLXL(atanh(nums[i]), 0.0), 1);
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} else {
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testall_tol(cacosh, z,
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CMPLXL(acosh(fabs(nums[i])),
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(nums[i] < 0) ? pi : 0), 1);
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testall_tol(cacos, z,
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CMPLXL((nums[i] < 0) ? pi : 0,
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-acosh(fabs(nums[i]))), 1);
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testall_tol(casin, z,
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CMPLXL(copysign(pi / 2, nums[i]),
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acosh(fabs(nums[i]))), 1);
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testall_tol(catanh, z,
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CMPLXL(atanh(1 / nums[i]), pi / 2), 1);
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}
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testall_tol(casinh, z, CMPLXL(asinh(nums[i]), 0.0), 1);
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testall_tol(catan, z, CMPLXL(atan(nums[i]), 0), 1);
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/* TODO: Test the imaginary axis. */
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}
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}
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void
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test_small(void)
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{
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/*
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* z = 0.75 + i 0.25
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* acos(z) = Pi/4 - i ln(2)/2
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* asin(z) = Pi/4 + i ln(2)/2
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* atan(z) = atan(4)/2 + i ln(17/9)/4
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*/
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static const struct {
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complex long double z;
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complex long double acos_z;
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complex long double asin_z;
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complex long double atan_z;
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} tests[] = {
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{ CMPLXL(0.75L, 0.25L),
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CMPLXL(pi / 4, -0.34657359027997265470861606072908828L),
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CMPLXL(pi / 4, 0.34657359027997265470861606072908828L),
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CMPLXL(0.66290883183401623252961960521423782L,
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0.15899719167999917436476103600701878L) },
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};
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int i;
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for (i = 0; i < sizeof(tests) / sizeof(tests[0]); i++) {
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testall_tol(cacos, tests[i].z, tests[i].acos_z, 2);
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testall_odd_tol(casin, tests[i].z, tests[i].asin_z, 2);
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testall_odd_tol(catan, tests[i].z, tests[i].atan_z, 2);
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}
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}
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/* Test inputs that might cause overflow in a sloppy implementation. */
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void
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test_large(void)
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{
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/* TODO: Write these tests */
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}
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int
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main(int argc, char *argv[])
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{
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printf("1..6\n");
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test_zero();
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printf("ok 1 - invctrig zero\n");
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test_nan();
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printf("ok 2 - invctrig nan\n");
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test_inf();
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printf("ok 3 - invctrig inf\n");
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test_axes();
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printf("ok 4 - invctrig axes\n");
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test_small();
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printf("ok 5 - invctrig small\n");
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test_large();
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printf("ok 6 - invctrig large\n");
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return (0);
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}
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