/*- * 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 corner cases in cexp*(). */ #include __FBSDID("$FreeBSD$"); #include #include #include #include #include #include #define ALL_STD_EXCEPT (FE_DIVBYZERO | FE_INEXACT | FE_INVALID | \ FE_OVERFLOW | FE_UNDERFLOW) #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) #define N(i) (sizeof(i) / sizeof((i)[0])) #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); } /* * 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. In some cases, * whether cexp() raises an invalid exception is unspecified. * * 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(func, z, result, exceptmask, excepts, checksign) do { \ volatile long double complex _d = z; \ assert(feclearexcept(FE_ALL_EXCEPT) == 0); \ assert(cfpequal((func)(_d), (result), (checksign))); \ assert(((func), fetestexcept(exceptmask) == (excepts))); \ } while (0) /* Test within a given tolerance. */ #define test_tol(func, z, result, tol) do { \ volatile long double complex _d = z; \ assert(cfpequal_tol((func)(_d), (result), (tol))); \ } while (0) /* Test all the functions that compute cexp(x). */ #define testall(x, result, exceptmask, excepts, checksign) do { \ test(cexp, x, result, exceptmask, excepts, checksign); \ test(cexpf, x, result, exceptmask, excepts, checksign); \ } while (0) /* * Test all the functions that compute cexp(x), within a given tolerance. * The tolerance is specified in ulps. */ #define testall_tol(x, result, tol) do { \ test_tol(cexp, x, result, tol * DBL_ULP()); \ test_tol(cexpf, x, result, tol * FLT_ULP()); \ } while (0) /* Various finite non-zero numbers to test. */ static const float finites[] = { -42.0e20, -1.0 -1.0e-10, -0.0, 0.0, 1.0e-10, 1.0, 42.0e20 }; /* * 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) 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) && fpequal(cimag(x), cimag(y), checksign)); } 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) { /* cexp(0) = 1, no exceptions raised */ testall(0.0, 1.0, ALL_STD_EXCEPT, 0, 1); testall(-0.0, 1.0, ALL_STD_EXCEPT, 0, 1); testall(cpackl(0.0, -0.0), cpackl(1.0, -0.0), ALL_STD_EXCEPT, 0, 1); testall(cpackl(-0.0, -0.0), cpackl(1.0, -0.0), ALL_STD_EXCEPT, 0, 1); } /* * Tests for NaN. The signs of the results are indeterminate unless the * imaginary part is 0. */ void test_nan() { int i; /* cexp(x + NaNi) = NaN + NaNi and optionally raises invalid */ /* cexp(NaN + yi) = NaN + NaNi and optionally raises invalid (|y|>0) */ for (i = 0; i < N(finites); i++) { testall(cpackl(finites[i], NAN), cpackl(NAN, NAN), ALL_STD_EXCEPT & ~FE_INVALID, 0, 0); if (finites[i] == 0.0) continue; /* XXX FE_INEXACT shouldn't be raised here */ testall(cpackl(NAN, finites[i]), cpackl(NAN, NAN), ALL_STD_EXCEPT & ~(FE_INVALID | FE_INEXACT), 0, 0); } /* cexp(NaN +- 0i) = NaN +- 0i */ testall(cpackl(NAN, 0.0), cpackl(NAN, 0.0), ALL_STD_EXCEPT, 0, 1); testall(cpackl(NAN, -0.0), cpackl(NAN, -0.0), ALL_STD_EXCEPT, 0, 1); /* cexp(inf + NaN i) = inf + nan i */ testall(cpackl(INFINITY, NAN), cpackl(INFINITY, NAN), ALL_STD_EXCEPT, 0, 0); /* cexp(-inf + NaN i) = 0 */ testall(cpackl(-INFINITY, NAN), cpackl(0.0, 0.0), ALL_STD_EXCEPT, 0, 0); /* cexp(NaN + NaN i) = NaN + NaN i */ testall(cpackl(NAN, NAN), cpackl(NAN, NAN), ALL_STD_EXCEPT, 0, 0); } void test_inf(void) { int i; /* cexp(x + inf i) = NaN + NaNi and raises invalid */ /* cexp(inf + yi) = 0 + 0yi */ /* cexp(-inf + yi) = inf + inf yi (except y=0) */ for (i = 0; i < N(finites); i++) { testall(cpackl(finites[i], INFINITY), cpackl(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 1); /* XXX shouldn't raise an inexact exception */ testall(cpackl(-INFINITY, finites[i]), cpackl(0.0, 0.0 * finites[i]), ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); if (finites[i] == 0) continue; testall(cpackl(INFINITY, finites[i]), cpackl(INFINITY, INFINITY * finites[i]), ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); } testall(cpackl(INFINITY, 0.0), cpackl(INFINITY, 0.0), ALL_STD_EXCEPT, 0, 1); testall(cpackl(INFINITY, -0.0), cpackl(INFINITY, -0.0), ALL_STD_EXCEPT, 0, 1); } void test_reals(void) { int i; for (i = 0; i < N(finites); i++) { /* XXX could check exceptions more meticulously */ test(cexp, cpackl(finites[i], 0.0), cpackl(exp(finites[i]), 0.0), FE_INVALID | FE_DIVBYZERO, 0, 1); test(cexp, cpackl(finites[i], -0.0), cpackl(exp(finites[i]), -0.0), FE_INVALID | FE_DIVBYZERO, 0, 1); test(cexpf, cpackl(finites[i], 0.0), cpackl(expf(finites[i]), 0.0), FE_INVALID | FE_DIVBYZERO, 0, 1); test(cexpf, cpackl(finites[i], -0.0), cpackl(expf(finites[i]), -0.0), FE_INVALID | FE_DIVBYZERO, 0, 1); } } void test_imaginaries(void) { int i; for (i = 0; i < N(finites); i++) { test(cexp, cpackl(0.0, finites[i]), cpackl(cos(finites[i]), sin(finites[i])), ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); test(cexp, cpackl(-0.0, finites[i]), cpackl(cos(finites[i]), sin(finites[i])), ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); test(cexpf, cpackl(0.0, finites[i]), cpackl(cosf(finites[i]), sinf(finites[i])), ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); test(cexpf, cpackl(-0.0, finites[i]), cpackl(cosf(finites[i]), sinf(finites[i])), ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); } } void test_small(void) { static const double tests[] = { /* csqrt(a + bI) = x + yI */ /* a b x y */ 1.0, M_PI_4, M_SQRT2 * 0.5 * M_E, M_SQRT2 * 0.5 * M_E, -1.0, M_PI_4, M_SQRT2 * 0.5 / M_E, M_SQRT2 * 0.5 / M_E, 2.0, M_PI_2, 0.0, M_E * M_E, M_LN2, M_PI, -2.0, 0.0, }; double a, b; double x, y; int i; for (i = 0; i < N(tests); i += 4) { a = tests[i]; b = tests[i + 1]; x = tests[i + 2]; y = tests[i + 3]; test_tol(cexp, cpackl(a, b), cpackl(x, y), 3 * DBL_ULP()); /* float doesn't have enough precision to pass these tests */ if (x == 0 || y == 0) continue; test_tol(cexpf, cpackl(a, b), cpackl(x, y), 1 * FLT_ULP()); } } /* Test inputs with a real part r that would overflow exp(r). */ void test_large(void) { test_tol(cexp, cpackl(709.79, 0x1p-1074), cpackl(INFINITY, 8.94674309915433533273e-16), DBL_ULP()); test_tol(cexp, cpackl(1000, 0x1p-1074), cpackl(INFINITY, 9.73344457300016401328e+110), DBL_ULP()); test_tol(cexp, cpackl(1400, 0x1p-1074), cpackl(INFINITY, 5.08228858149196559681e+284), DBL_ULP()); test_tol(cexp, cpackl(900, 0x1.23456789abcdep-1020), cpackl(INFINITY, 7.42156649354218408074e+83), DBL_ULP()); test_tol(cexp, cpackl(1300, 0x1.23456789abcdep-1020), cpackl(INFINITY, 3.87514844965996756704e+257), DBL_ULP()); test_tol(cexpf, cpackl(88.73, 0x1p-149), cpackl(INFINITY, 4.80265603e-07), 2 * FLT_ULP()); test_tol(cexpf, cpackl(90, 0x1p-149), cpackl(INFINITY, 1.7101492622e-06f), 2 * FLT_ULP()); test_tol(cexpf, cpackl(192, 0x1p-149), cpackl(INFINITY, 3.396809344e+38f), 2 * FLT_ULP()); test_tol(cexpf, cpackl(120, 0x1.234568p-120), cpackl(INFINITY, 1.1163382522e+16f), 2 * FLT_ULP()); test_tol(cexpf, cpackl(170, 0x1.234568p-120), cpackl(INFINITY, 5.7878851079e+37f), 2 * FLT_ULP()); } int main(int argc, char *argv[]) { printf("1..7\n"); test_zero(); printf("ok 1 - cexp zero\n"); test_nan(); printf("ok 2 - cexp nan\n"); test_inf(); printf("ok 3 - cexp inf\n"); test_reals(); printf("ok 4 - cexp reals\n"); test_imaginaries(); printf("ok 5 - cexp imaginaries\n"); test_small(); printf("ok 6 - cexp small\n"); test_large(); printf("ok 7 - cexp large\n"); return (0); }