/* $OpenBSD: invctrig_test.c,v 1.3 2021/12/13 18:04:28 deraadt Exp $ */ /*- * Copyright (c) 2008-2013 David Schultz * 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. */ #include "macros.h" /* * Tests for casin[h](), cacos[h](), and catan[h](). */ #include #include #include #include #include #include #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)); \ ATF_REQUIRE_EQ(0, feclearexcept(FE_ALL_EXCEPT)); \ CHECK_CFPEQUAL_CS((func)(_d), (result), (checksign)); \ CHECK_FP_EXCEPTIONS_MSG(excepts, exceptmask, "for %s(%s)", \ #func, #z); \ } while (0) /* * Test within a given tolerance. The tolerance indicates relative error * in ulps. */ #define test_p_tol(func, z, result, tol) do { \ debug(" testing %s(%Lg + %Lg I) ~= %Lg + %Lg I\n", #func, \ creall(z), cimagl(z), creall(result), cimagl(result)); \ CHECK_CFPEQUAL_TOL((func)(z), (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 */ ATF_TC_WITHOUT_HEAD(zero); ATF_TC_BODY(zero, tc) { 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. */ ATF_TC_WITHOUT_HEAD(nan); ATF_TC_BODY(nan, tc) { 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); } ATF_TC_WITHOUT_HEAD(inf); ATF_TC_BODY(inf, tc) { 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. */ ATF_TC_WITHOUT_HEAD(axes); ATF_TC_BODY(axes, tc) { static const long double nums[] = { -2, -1, -0.5, 0.5, 1, 2 }; long double complex z; unsigned i; for (i = 0; i < nitems(nums); i++) { /* Real axis */ z = CMPLXL(nums[i], 0.0); if (fabsl(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(fabsl(nums[i])), (nums[i] < 0) ? pi : 0), 1); testall_tol(cacos, z, CMPLXL((nums[i] < 0) ? pi : 0, -acosh(fabsl(nums[i]))), 1); testall_tol(casin, z, CMPLXL(copysign(pi / 2, nums[i]), acosh(fabsl(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. */ } } ATF_TC_WITHOUT_HEAD(small); ATF_TC_BODY(small, tc) { /* * 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 */ complex long double z; complex long double acos_z; complex long double asin_z; complex long double atan_z; z = CMPLXL(0.75L, 0.25L); acos_z = CMPLXL(pi / 4, -0.34657359027997265470861606072908828L); asin_z = CMPLXL(pi / 4, 0.34657359027997265470861606072908828L); atan_z = CMPLXL(0.66290883183401623252961960521423782L, 0.15899719167999917436476103600701878L); testall_tol(cacos, z, acos_z, 2); testall_odd_tol(casin, z, asin_z, 2); testall_odd_tol(catan, z, atan_z, 2); } /* Test inputs that might cause overflow in a sloppy implementation. */ ATF_TC_WITHOUT_HEAD(large); ATF_TC_BODY(large, tc) { /* TODO: Write these tests */ } ATF_TP_ADD_TCS(tp) { ATF_TP_ADD_TC(tp, zero); ATF_TP_ADD_TC(tp, nan); ATF_TP_ADD_TC(tp, inf); ATF_TP_ADD_TC(tp, axes); ATF_TP_ADD_TC(tp, small); ATF_TP_ADD_TC(tp, large); return (atf_no_error()); }