From 680c716ea62c69d5b6dd3d39c1529a6fa1bb2119 Mon Sep 17 00:00:00 2001 From: ngie Date: Sun, 27 Dec 2015 21:39:28 +0000 Subject: [PATCH] MFstable/10 r226603,r251119: r226603 (by das): Tests for complex trig and hyperbolic functions. r251119 (by das): Basic tests for complex inverse trig and hyperbolic functions. git-svn-id: svn://svn.freebsd.org/base/stable/9@292803 ccf9f872-aa2e-dd11-9fc8-001c23d0bc1f --- tools/regression/lib/msun/Makefile | 6 +- tools/regression/lib/msun/test-ctrig.c | 540 ++++++++++++++++++++++ tools/regression/lib/msun/test-ctrig.t | 10 + tools/regression/lib/msun/test-invctrig.c | 442 ++++++++++++++++++ 4 files changed, 996 insertions(+), 2 deletions(-) create mode 100644 tools/regression/lib/msun/test-ctrig.c create mode 100644 tools/regression/lib/msun/test-ctrig.t create mode 100644 tools/regression/lib/msun/test-invctrig.c diff --git a/tools/regression/lib/msun/Makefile b/tools/regression/lib/msun/Makefile index 155fd314e..9559bb175 100644 --- a/tools/regression/lib/msun/Makefile +++ b/tools/regression/lib/msun/Makefile @@ -1,7 +1,9 @@ # $FreeBSD$ -TESTS= test-cexp test-conj test-csqrt test-exponential test-fenv test-fma \ - test-fmaxmin test-ilogb test-invtrig test-logarithm test-lrint \ +TESTS= test-cexp test-conj test-csqrt test-ctrig \ + test-exponential test-fenv test-fma \ + test-fmaxmin test-ilogb test-invtrig test-invctrig \ + test-logarithm test-lrint \ test-lround test-nan test-nearbyint test-next test-rem test-trig CFLAGS+= -O0 -lm diff --git a/tools/regression/lib/msun/test-ctrig.c b/tools/regression/lib/msun/test-ctrig.c new file mode 100644 index 000000000..ed7866184 --- /dev/null +++ b/tools/regression/lib/msun/test-ctrig.c @@ -0,0 +1,540 @@ +/*- + * Copyright (c) 2008-2011 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. + */ + +/* + * Tests for csin[h](), ccos[h](), and ctan[h](). + */ + +#include +__FBSDID("$FreeBSD$"); + +#include +#include +#include +#include +#include +#include + +#define ALL_STD_EXCEPT (FE_DIVBYZERO | FE_INEXACT | FE_INVALID | \ + FE_OVERFLOW | FE_UNDERFLOW) +#define OPT_INVALID (ALL_STD_EXCEPT & ~FE_INVALID) +#define OPT_INEXACT (ALL_STD_EXCEPT & ~FE_INEXACT) +#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) + +#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); +} + +/* Flags that determine whether to check the signs of the result. */ +#define CS_REAL 1 +#define CS_IMAG 2 +#define CS_BOTH (CS_REAL | CS_IMAG) + +#ifdef DEBUG +#define debug(...) printf(__VA_ARGS__) +#else +#define debug(...) (void)0 +#endif + +/* + * 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((func)(_d), (result), (checksign))); \ + assert(((func), fetestexcept(exceptmask) == (excepts))); \ +} while (0) + +/* + * Test within a given tolerance. The tolerance indicates relative error + * in ulps. If result is 0, however, it measures absolute error in units + * of _EPSILON. + */ +#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))); \ +} 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 { \ + test_tol(func, x, result, tol * DBL_ULP()); \ + test_tol(func, -x, -result, tol * DBL_ULP()); \ +} while (0) +#define testall_even_tol(func, x, result, tol) do { \ + test_tol(func, x, result, tol * DBL_ULP()); \ + test_tol(func, -x, result, tol * DBL_ULP()); \ +} while (0) + +/* + * 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) && tol == 0) + 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 & CS_REAL) + && fpequal(cimag(x), cimag(y), checksign & CS_IMAG)); +} + +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) +{ + long double complex zero = cpackl(0.0, 0.0); + + /* csinh(0) = ctanh(0) = 0; ccosh(0) = 1 (no exceptions raised) */ + testall_odd(csinh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); + testall_odd(csin, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); + testall_even(ccosh, zero, 1.0, ALL_STD_EXCEPT, 0, CS_BOTH); + testall_even(ccos, zero, cpackl(1.0, -0.0), ALL_STD_EXCEPT, 0, CS_BOTH); + testall_odd(ctanh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); + testall_odd(ctan, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); +} + +/* + * Tests for NaN inputs. + */ +void +test_nan() +{ + long double complex nan_nan = cpackl(NAN, NAN); + long double complex z; + + /* + * IN CSINH CCOSH CTANH + * NaN,NaN NaN,NaN NaN,NaN NaN,NaN + * finite,NaN NaN,NaN [inval] NaN,NaN [inval] NaN,NaN [inval] + * NaN,finite NaN,NaN [inval] NaN,NaN [inval] NaN,NaN [inval] + * NaN,Inf NaN,NaN [inval] NaN,NaN [inval] NaN,NaN [inval] + * Inf,NaN +-Inf,NaN Inf,NaN 1,+-0 + * 0,NaN +-0,NaN NaN,+-0 NaN,NaN [inval] + * NaN,0 NaN,0 NaN,+-0 NaN,0 + */ + z = nan_nan; + testall_odd(csinh, z, nan_nan, ALL_STD_EXCEPT, 0, 0); + testall_even(ccosh, z, nan_nan, ALL_STD_EXCEPT, 0, 0); + testall_odd(ctanh, z, nan_nan, ALL_STD_EXCEPT, 0, 0); + testall_odd(csin, z, nan_nan, ALL_STD_EXCEPT, 0, 0); + testall_even(ccos, z, nan_nan, ALL_STD_EXCEPT, 0, 0); + testall_odd(ctan, z, nan_nan, ALL_STD_EXCEPT, 0, 0); + + z = cpackl(42, NAN); + testall_odd(csinh, z, nan_nan, OPT_INVALID, 0, 0); + testall_even(ccosh, z, nan_nan, OPT_INVALID, 0, 0); + /* XXX We allow a spurious inexact exception here. */ + testall_odd(ctanh, z, nan_nan, OPT_INVALID & ~FE_INEXACT, 0, 0); + testall_odd(csin, z, nan_nan, OPT_INVALID, 0, 0); + testall_even(ccos, z, nan_nan, OPT_INVALID, 0, 0); + testall_odd(ctan, z, nan_nan, OPT_INVALID, 0, 0); + + z = cpackl(NAN, 42); + testall_odd(csinh, z, nan_nan, OPT_INVALID, 0, 0); + testall_even(ccosh, z, nan_nan, OPT_INVALID, 0, 0); + testall_odd(ctanh, z, nan_nan, OPT_INVALID, 0, 0); + testall_odd(csin, z, nan_nan, OPT_INVALID, 0, 0); + testall_even(ccos, z, nan_nan, OPT_INVALID, 0, 0); + /* XXX We allow a spurious inexact exception here. */ + testall_odd(ctan, z, nan_nan, OPT_INVALID & ~FE_INEXACT, 0, 0); + + z = cpackl(NAN, INFINITY); + testall_odd(csinh, z, nan_nan, OPT_INVALID, 0, 0); + testall_even(ccosh, z, nan_nan, OPT_INVALID, 0, 0); + testall_odd(ctanh, z, nan_nan, OPT_INVALID, 0, 0); + testall_odd(csin, z, cpackl(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0); + testall_even(ccos, z, cpackl(INFINITY, NAN), ALL_STD_EXCEPT, 0, + CS_IMAG); + testall_odd(ctan, z, cpackl(0, 1), ALL_STD_EXCEPT, 0, CS_IMAG); + + z = cpackl(INFINITY, NAN); + testall_odd(csinh, z, cpackl(INFINITY, NAN), ALL_STD_EXCEPT, 0, 0); + testall_even(ccosh, z, cpackl(INFINITY, NAN), ALL_STD_EXCEPT, 0, + CS_REAL); + testall_odd(ctanh, z, cpackl(1, 0), ALL_STD_EXCEPT, 0, CS_REAL); + testall_odd(csin, z, nan_nan, OPT_INVALID, 0, 0); + testall_even(ccos, z, nan_nan, OPT_INVALID, 0, 0); + testall_odd(ctan, z, nan_nan, OPT_INVALID, 0, 0); + + z = cpackl(0, NAN); + testall_odd(csinh, z, cpackl(0, NAN), ALL_STD_EXCEPT, 0, 0); + testall_even(ccosh, z, cpackl(NAN, 0), ALL_STD_EXCEPT, 0, 0); + testall_odd(ctanh, z, nan_nan, OPT_INVALID, 0, 0); + testall_odd(csin, z, cpackl(0, NAN), ALL_STD_EXCEPT, 0, CS_REAL); + testall_even(ccos, z, cpackl(NAN, 0), ALL_STD_EXCEPT, 0, 0); + testall_odd(ctan, z, cpackl(0, NAN), ALL_STD_EXCEPT, 0, CS_REAL); + + z = cpackl(NAN, 0); + testall_odd(csinh, z, cpackl(NAN, 0), ALL_STD_EXCEPT, 0, CS_IMAG); + testall_even(ccosh, z, cpackl(NAN, 0), ALL_STD_EXCEPT, 0, 0); + testall_odd(ctanh, z, cpackl(NAN, 0), ALL_STD_EXCEPT, 0, CS_IMAG); + testall_odd(csin, z, cpackl(NAN, 0), ALL_STD_EXCEPT, 0, 0); + testall_even(ccos, z, cpackl(NAN, 0), ALL_STD_EXCEPT, 0, 0); + testall_odd(ctan, z, nan_nan, OPT_INVALID, 0, 0); +} + +void +test_inf(void) +{ + static const long double finites[] = { + 0, M_PI / 4, 3 * M_PI / 4, 5 * M_PI / 4, + }; + long double complex z, c, s; + int i; + + /* + * IN CSINH CCOSH CTANH + * Inf,Inf +-Inf,NaN inval +-Inf,NaN inval 1,+-0 + * Inf,finite Inf cis(finite) Inf cis(finite) 1,0 sin(2 finite) + * 0,Inf +-0,NaN inval NaN,+-0 inval NaN,NaN inval + * finite,Inf NaN,NaN inval NaN,NaN inval NaN,NaN inval + */ + z = cpackl(INFINITY, INFINITY); + testall_odd(csinh, z, cpackl(INFINITY, NAN), + ALL_STD_EXCEPT, FE_INVALID, 0); + testall_even(ccosh, z, cpackl(INFINITY, NAN), + ALL_STD_EXCEPT, FE_INVALID, 0); + testall_odd(ctanh, z, cpackl(1, 0), ALL_STD_EXCEPT, 0, CS_REAL); + testall_odd(csin, z, cpackl(NAN, INFINITY), + ALL_STD_EXCEPT, FE_INVALID, 0); + testall_even(ccos, z, cpackl(INFINITY, NAN), + ALL_STD_EXCEPT, FE_INVALID, 0); + testall_odd(ctan, z, cpackl(0, 1), ALL_STD_EXCEPT, 0, CS_REAL); + + /* XXX We allow spurious inexact exceptions here (hard to avoid). */ + for (i = 0; i < sizeof(finites) / sizeof(finites[0]); i++) { + z = cpackl(INFINITY, finites[i]); + c = INFINITY * cosl(finites[i]); + s = finites[i] == 0 ? finites[i] : INFINITY * sinl(finites[i]); + testall_odd(csinh, z, cpackl(c, s), OPT_INEXACT, 0, CS_BOTH); + testall_even(ccosh, z, cpackl(c, s), OPT_INEXACT, 0, CS_BOTH); + testall_odd(ctanh, z, cpackl(1, 0 * sin(finites[i] * 2)), + OPT_INEXACT, 0, CS_BOTH); + z = cpackl(finites[i], INFINITY); + testall_odd(csin, z, cpackl(s, c), OPT_INEXACT, 0, CS_BOTH); + testall_even(ccos, z, cpackl(c, -s), OPT_INEXACT, 0, CS_BOTH); + testall_odd(ctan, z, cpackl(0 * sin(finites[i] * 2), 1), + OPT_INEXACT, 0, CS_BOTH); + } + + z = cpackl(0, INFINITY); + testall_odd(csinh, z, cpackl(0, NAN), ALL_STD_EXCEPT, FE_INVALID, 0); + testall_even(ccosh, z, cpackl(NAN, 0), ALL_STD_EXCEPT, FE_INVALID, 0); + testall_odd(ctanh, z, cpackl(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0); + z = cpackl(INFINITY, 0); + testall_odd(csin, z, cpackl(NAN, 0), ALL_STD_EXCEPT, FE_INVALID, 0); + testall_even(ccos, z, cpackl(NAN, 0), ALL_STD_EXCEPT, FE_INVALID, 0); + testall_odd(ctan, z, cpackl(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0); + + z = cpackl(42, INFINITY); + testall_odd(csinh, z, cpackl(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0); + testall_even(ccosh, z, cpackl(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0); + /* XXX We allow a spurious inexact exception here. */ + testall_odd(ctanh, z, cpackl(NAN, NAN), OPT_INEXACT, FE_INVALID, 0); + z = cpackl(INFINITY, 42); + testall_odd(csin, z, cpackl(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0); + testall_even(ccos, z, cpackl(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0); + /* XXX We allow a spurious inexact exception here. */ + testall_odd(ctan, z, cpackl(NAN, NAN), OPT_INEXACT, FE_INVALID, 0); +} + +/* Tests along the real and imaginary axes. */ +void +test_axes(void) +{ + static const long double nums[] = { + M_PI / 4, M_PI / 2, 3 * M_PI / 4, + 5 * M_PI / 4, 3 * M_PI / 2, 7 * M_PI / 4, + }; + long double complex z; + int i; + + for (i = 0; i < sizeof(nums) / sizeof(nums[0]); i++) { + /* Real axis */ + z = cpackl(nums[i], 0.0); + testall_odd_tol(csinh, z, cpackl(sinh(nums[i]), 0), 0); + testall_even_tol(ccosh, z, cpackl(cosh(nums[i]), 0), 0); + testall_odd_tol(ctanh, z, cpackl(tanh(nums[i]), 0), 1); + testall_odd_tol(csin, z, cpackl(sin(nums[i]), + copysign(0, cos(nums[i]))), 0); + testall_even_tol(ccos, z, cpackl(cos(nums[i]), + -copysign(0, sin(nums[i]))), 0); + testall_odd_tol(ctan, z, cpackl(tan(nums[i]), 0), 1); + + /* Imaginary axis */ + z = cpackl(0.0, nums[i]); + testall_odd_tol(csinh, z, cpackl(copysign(0, cos(nums[i])), + sin(nums[i])), 0); + testall_even_tol(ccosh, z, cpackl(cos(nums[i]), + copysign(0, sin(nums[i]))), 0); + testall_odd_tol(ctanh, z, cpackl(0, tan(nums[i])), 1); + testall_odd_tol(csin, z, cpackl(0, sinh(nums[i])), 0); + testall_even_tol(ccos, z, cpackl(cosh(nums[i]), -0.0), 0); + testall_odd_tol(ctan, z, cpackl(0, tanh(nums[i])), 1); + } +} + +void +test_small(void) +{ + /* + * z = 0.5 + i Pi/4 + * sinh(z) = (sinh(0.5) + i cosh(0.5)) * sqrt(2)/2 + * cosh(z) = (cosh(0.5) + i sinh(0.5)) * sqrt(2)/2 + * tanh(z) = (2cosh(0.5)sinh(0.5) + i) / (2 cosh(0.5)**2 - 1) + * z = -0.5 + i Pi/2 + * sinh(z) = cosh(0.5) + * cosh(z) = -i sinh(0.5) + * tanh(z) = -coth(0.5) + * z = 1.0 + i 3Pi/4 + * sinh(z) = (-sinh(1) + i cosh(1)) * sqrt(2)/2 + * cosh(z) = (-cosh(1) + i sinh(1)) * sqrt(2)/2 + * tanh(z) = (2cosh(1)sinh(1) - i) / (2cosh(1)**2 - 1) + */ + static const struct { + long double a, b; + long double sinh_a, sinh_b; + long double cosh_a, cosh_b; + long double tanh_a, tanh_b; + } tests[] = { + { 0.5L, + 0.78539816339744830961566084581987572L, + 0.36847002415910435172083660522240710L, + 0.79735196663945774996093142586179334L, + 0.79735196663945774996093142586179334L, + 0.36847002415910435172083660522240710L, + 0.76159415595576488811945828260479359L, + 0.64805427366388539957497735322615032L }, + { -0.5L, + 1.57079632679489661923132169163975144L, + 0.0L, + 1.12762596520638078522622516140267201L, + 0.0L, + -0.52109530549374736162242562641149156L, + -2.16395341373865284877000401021802312L, + 0.0L }, + { 1.0L, + 2.35619449019234492884698253745962716L, + -0.83099273328405698212637979852748608L, + 1.09112278079550143030545602018565236L, + -1.09112278079550143030545602018565236L, + 0.83099273328405698212637979852748609L, + 0.96402758007581688394641372410092315L, + -0.26580222883407969212086273981988897L } + }; + long double complex z; + int i; + + for (i = 0; i < sizeof(tests) / sizeof(tests[0]); i++) { + z = cpackl(tests[i].a, tests[i].b); + testall_odd_tol(csinh, z, + cpackl(tests[i].sinh_a, tests[i].sinh_b), 1.1); + testall_even_tol(ccosh, z, + cpackl(tests[i].cosh_a, tests[i].cosh_b), 1.1); + testall_odd_tol(ctanh, z, + cpackl(tests[i].tanh_a, tests[i].tanh_b), 1.1); + } +} + +/* Test inputs that might cause overflow in a sloppy implementation. */ +void +test_large(void) +{ + long double complex z; + + /* tanh() uses a threshold around x=22, so check both sides. */ + z = cpackl(21, 0.78539816339744830961566084581987572L); + testall_odd_tol(ctanh, z, + cpackl(1.0, 1.14990445285871196133287617611468468e-18L), 1); + z++; + testall_odd_tol(ctanh, z, + cpackl(1.0, 1.55622644822675930314266334585597964e-19L), 1); + + z = cpackl(355, 0.78539816339744830961566084581987572L); + testall_odd_tol(ctanh, z, + cpackl(1.0, 8.95257245135025991216632140458264468e-309L), 1); + z = cpackl(30, 0x1p1023L); + testall_odd_tol(ctanh, z, + cpackl(1.0, -1.62994325413993477997492170229268382e-26L), 1); + z = cpackl(1, 0x1p1023L); + testall_odd_tol(ctanh, z, + cpackl(0.878606311888306869546254022621986509L, + -0.225462792499754505792678258169527424L), 1); + + z = cpackl(710.6, 0.78539816339744830961566084581987572L); + testall_odd_tol(csinh, z, + cpackl(1.43917579766621073533185387499658944e308L, + 1.43917579766621073533185387499658944e308L), 1); + testall_even_tol(ccosh, z, + cpackl(1.43917579766621073533185387499658944e308L, + 1.43917579766621073533185387499658944e308L), 1); + + z = cpackl(1500, 0.78539816339744830961566084581987572L); + testall_odd(csinh, z, cpackl(INFINITY, INFINITY), OPT_INEXACT, + FE_OVERFLOW, CS_BOTH); + testall_even(ccosh, z, cpackl(INFINITY, INFINITY), OPT_INEXACT, + FE_OVERFLOW, CS_BOTH); +} + +int +main(int argc, char *argv[]) +{ + + printf("1..6\n"); + + test_zero(); + printf("ok 1 - ctrig zero\n"); + + test_nan(); + printf("ok 2 - ctrig nan\n"); + + test_inf(); + printf("ok 3 - ctrig inf\n"); + + test_axes(); + printf("ok 4 - ctrig axes\n"); + + test_small(); + printf("ok 5 - ctrig small\n"); + + test_large(); + printf("ok 6 - ctrig large\n"); + + return (0); +} diff --git a/tools/regression/lib/msun/test-ctrig.t b/tools/regression/lib/msun/test-ctrig.t new file mode 100644 index 000000000..8bdfd03be --- /dev/null +++ b/tools/regression/lib/msun/test-ctrig.t @@ -0,0 +1,10 @@ +#!/bin/sh +# $FreeBSD$ + +cd `dirname $0` + +executable=`basename $0 .t` + +make $executable 2>&1 > /dev/null + +exec ./$executable diff --git a/tools/regression/lib/msun/test-invctrig.c b/tools/regression/lib/msun/test-invctrig.c new file mode 100644 index 000000000..6f0fe58a5 --- /dev/null +++ b/tools/regression/lib/msun/test-invctrig.c @@ -0,0 +1,442 @@ +/*- + * 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. + */ + +/* + * Tests for casin[h](), cacos[h](), and catan[h](). + */ + +#include +__FBSDID("$FreeBSD$"); + +#include +#include +#include +#include +#include +#include + +#define ALL_STD_EXCEPT (FE_DIVBYZERO | FE_INEXACT | FE_INVALID | \ + FE_OVERFLOW | FE_UNDERFLOW) +#define OPT_INVALID (ALL_STD_EXCEPT & ~FE_INVALID) +#define OPT_INEXACT (ALL_STD_EXCEPT & ~FE_INEXACT) +#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) + +#pragma STDC FENV_ACCESS ON +#pragma STDC CX_LIMITED_RANGE OFF + +/* Flags that determine whether to check the signs of the result. */ +#define CS_REAL 1 +#define CS_IMAG 2 +#define CS_BOTH (CS_REAL | CS_IMAG) + +#ifdef DEBUG +#define debug(...) printf(__VA_ARGS__) +#else +#define debug(...) (void)0 +#endif + +/* + * 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((func)(_d), (result), (checksign))); \ + assert(((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))); \ +} 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; + +/* + * 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 || y == 0.0) + return (0); + + /* Hard case: need to check the tolerance. */ + feholdexcept(&env); + 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 & CS_REAL) + && fpequal(cimag(x), cimag(y), checksign & CS_IMAG)); +} + +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) +{ + 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); +} -- 2.45.0