/*- * 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. * * $FreeBSD: src/tools/regression/lib/msun/test-ctrig.c,v 1.1 2011/10/21 06:34:38 das Exp $ */ /* * Tests for csin[h](), ccos[h](), and ctan[h](). */ #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); }