diff --git a/lib/msun/tests/invtrig_test.c b/lib/msun/tests/invtrig_test.c index 7dd8b26f652f..90ebcc5dfdad 100644 --- a/lib/msun/tests/invtrig_test.c +++ b/lib/msun/tests/invtrig_test.c @@ -1,457 +1,463 @@ /*- * Copyright (c) 2008 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 the inverse trigonometric functions. Some * accuracy tests are included as well, but these are very basic * sanity checks, not intended to be comprehensive. */ #include __FBSDID("$FreeBSD$"); #include #include #include #include #include "test-utils.h" #pragma STDC FENV_ACCESS ON /* * Test that a function returns the correct value and sets the * exception flags correctly. A tolerance specifying the maximum * relative error allowed may be specified. For the 'testall' * functions, the tolerance is specified in ulps. * * These are macros instead of functions so that assert provides more * meaningful error messages. */ #define test_tol(func, x, result, tol, excepts) do { \ volatile long double _in = (x), _out = (result); \ ATF_REQUIRE_EQ(0, feclearexcept(FE_ALL_EXCEPT)); \ CHECK_FPEQUAL_TOL(func(_in), _out, (tol), CS_BOTH); \ CHECK_FP_EXCEPTIONS_MSG(excepts, ALL_STD_EXCEPT, "for %s(%s)", \ #func, #x); \ } while (0) #define test(func, x, result, excepts) \ test_tol(func, (x), (result), 0, (excepts)) #define _testall_tol(prefix, x, result, tol, excepts) do { \ test_tol(prefix, (double)(x), (double)(result), \ (tol) * ldexp(1.0, 1 - DBL_MANT_DIG), (excepts)); \ test_tol(prefix##f, (float)(x), (float)(result), \ (tol) * ldexpf(1.0, 1 - FLT_MANT_DIG), (excepts)); \ } while (0) -#if LDBL_PREC == 53 +#ifdef __i386__ #define testall_tol _testall_tol #else #define testall_tol(prefix, x, result, tol, excepts) do { \ _testall_tol(prefix, x, result, tol, excepts); \ test_tol(prefix##l, (x), (result), \ (tol) * ldexpl(1.0, 1 - LDBL_MANT_DIG), (excepts)); \ } while (0) #endif #define testall(prefix, x, result, excepts) \ testall_tol(prefix, (x), (result), 0, (excepts)) #define test2_tol(func, y, x, result, tol, excepts) do { \ volatile long double _iny = (y), _inx = (x), _out = (result); \ ATF_REQUIRE_EQ(0, feclearexcept(FE_ALL_EXCEPT)); \ CHECK_FPEQUAL_TOL(func(_iny, _inx), _out, (tol), CS_BOTH); \ CHECK_FP_EXCEPTIONS_MSG(excepts, ALL_STD_EXCEPT, "for %s(%s)", \ #func, #x); \ } while (0) #define test2(func, y, x, result, excepts) \ test2_tol(func, (y), (x), (result), 0, (excepts)) #define _testall2_tol(prefix, y, x, result, tol, excepts) do { \ test2_tol(prefix, (double)(y), (double)(x), (double)(result), \ (tol) * ldexp(1.0, 1 - DBL_MANT_DIG), (excepts)); \ test2_tol(prefix##f, (float)(y), (float)(x), (float)(result), \ (tol) * ldexpf(1.0, 1 - FLT_MANT_DIG), (excepts)); \ } while (0) -#if LDBL_PREC == 53 +#ifdef __i386__ #define testall2_tol _testall2_tol #else #define testall2_tol(prefix, y, x, result, tol, excepts) do { \ _testall2_tol(prefix, y, x, result, tol, excepts); \ test2_tol(prefix##l, (y), (x), (result), \ (tol) * ldexpl(1.0, 1 - LDBL_MANT_DIG), (excepts)); \ } while (0) #endif #define testall2(prefix, y, x, result, excepts) \ testall2_tol(prefix, (y), (x), (result), 0, (excepts)) static long double pi = 3.14159265358979323846264338327950280e+00L, pio3 = 1.04719755119659774615421446109316766e+00L, c3pi = 9.42477796076937971538793014983850839e+00L, c7pi = 2.19911485751285526692385036829565196e+01L, c5pio3 = 5.23598775598298873077107230546583851e+00L, sqrt2m1 = 4.14213562373095048801688724209698081e-01L; /* * Test special case inputs in asin(), acos() and atan(): signed * zeroes, infinities, and NaNs. */ ATF_TC_WITHOUT_HEAD(special); ATF_TC_BODY(special, tc) { testall(asin, 0.0, 0.0, 0); testall(acos, 0.0, pi / 2, FE_INEXACT); testall(atan, 0.0, 0.0, 0); testall(asin, -0.0, -0.0, 0); testall(acos, -0.0, pi / 2, FE_INEXACT); testall(atan, -0.0, -0.0, 0); testall(asin, INFINITY, NAN, FE_INVALID); testall(acos, INFINITY, NAN, FE_INVALID); testall(atan, INFINITY, pi / 2, FE_INEXACT); testall(asin, -INFINITY, NAN, FE_INVALID); testall(acos, -INFINITY, NAN, FE_INVALID); testall(atan, -INFINITY, -pi / 2, FE_INEXACT); testall(asin, NAN, NAN, 0); testall(acos, NAN, NAN, 0); testall(atan, NAN, NAN, 0); } /* * Test special case inputs in atan2(), where the exact value of y/x is * zero or non-finite. */ ATF_TC_WITHOUT_HEAD(special_atan2); ATF_TC_BODY(special_atan2, tc) { long double z; int e; testall2(atan2, 0.0, -0.0, pi, FE_INEXACT); testall2(atan2, -0.0, -0.0, -pi, FE_INEXACT); testall2(atan2, 0.0, 0.0, 0.0, 0); testall2(atan2, -0.0, 0.0, -0.0, 0); testall2(atan2, INFINITY, -INFINITY, c3pi / 4, FE_INEXACT); testall2(atan2, -INFINITY, -INFINITY, -c3pi / 4, FE_INEXACT); testall2(atan2, INFINITY, INFINITY, pi / 4, FE_INEXACT); testall2(atan2, -INFINITY, INFINITY, -pi / 4, FE_INEXACT); /* Tests with one input in the range (0, Inf]. */ z = 1.23456789L; for (e = FLT_MIN_EXP - FLT_MANT_DIG; e <= FLT_MAX_EXP; e++) { test2(atan2f, 0.0, ldexpf(z, e), 0.0, 0); test2(atan2f, -0.0, ldexpf(z, e), -0.0, 0); test2(atan2f, 0.0, ldexpf(-z, e), (float)pi, FE_INEXACT); test2(atan2f, -0.0, ldexpf(-z, e), (float)-pi, FE_INEXACT); test2(atan2f, ldexpf(z, e), 0.0, (float)pi / 2, FE_INEXACT); test2(atan2f, ldexpf(z, e), -0.0, (float)pi / 2, FE_INEXACT); test2(atan2f, ldexpf(-z, e), 0.0, (float)-pi / 2, FE_INEXACT); test2(atan2f, ldexpf(-z, e), -0.0, (float)-pi / 2, FE_INEXACT); } for (e = DBL_MIN_EXP - DBL_MANT_DIG; e <= DBL_MAX_EXP; e++) { test2(atan2, 0.0, ldexp(z, e), 0.0, 0); test2(atan2, -0.0, ldexp(z, e), -0.0, 0); test2(atan2, 0.0, ldexp(-z, e), (double)pi, FE_INEXACT); test2(atan2, -0.0, ldexp(-z, e), (double)-pi, FE_INEXACT); test2(atan2, ldexp(z, e), 0.0, (double)pi / 2, FE_INEXACT); test2(atan2, ldexp(z, e), -0.0, (double)pi / 2, FE_INEXACT); test2(atan2, ldexp(-z, e), 0.0, (double)-pi / 2, FE_INEXACT); test2(atan2, ldexp(-z, e), -0.0, (double)-pi / 2, FE_INEXACT); } for (e = LDBL_MIN_EXP - LDBL_MANT_DIG; e <= LDBL_MAX_EXP; e++) { test2(atan2l, 0.0, ldexpl(z, e), 0.0, 0); test2(atan2l, -0.0, ldexpl(z, e), -0.0, 0); test2(atan2l, 0.0, ldexpl(-z, e), pi, FE_INEXACT); test2(atan2l, -0.0, ldexpl(-z, e), -pi, FE_INEXACT); test2(atan2l, ldexpl(z, e), 0.0, pi / 2, FE_INEXACT); test2(atan2l, ldexpl(z, e), -0.0, pi / 2, FE_INEXACT); test2(atan2l, ldexpl(-z, e), 0.0, -pi / 2, FE_INEXACT); test2(atan2l, ldexpl(-z, e), -0.0, -pi / 2, FE_INEXACT); } /* Tests with one input in the range (0, Inf). */ for (e = FLT_MIN_EXP - FLT_MANT_DIG; e <= FLT_MAX_EXP - 1; e++) { test2(atan2f, ldexpf(z, e), INFINITY, 0.0, 0); test2(atan2f, ldexpf(-z,e), INFINITY, -0.0, 0); test2(atan2f, ldexpf(z, e), -INFINITY, (float)pi, FE_INEXACT); test2(atan2f, ldexpf(-z,e), -INFINITY, (float)-pi, FE_INEXACT); test2(atan2f, INFINITY, ldexpf(z,e), (float)pi/2, FE_INEXACT); test2(atan2f, INFINITY, ldexpf(-z,e), (float)pi/2, FE_INEXACT); test2(atan2f, -INFINITY, ldexpf(z,e), (float)-pi/2,FE_INEXACT); test2(atan2f, -INFINITY, ldexpf(-z,e),(float)-pi/2,FE_INEXACT); } for (e = DBL_MIN_EXP - DBL_MANT_DIG; e <= DBL_MAX_EXP - 1; e++) { test2(atan2, ldexp(z, e), INFINITY, 0.0, 0); test2(atan2, ldexp(-z,e), INFINITY, -0.0, 0); test2(atan2, ldexp(z, e), -INFINITY, (double)pi, FE_INEXACT); test2(atan2, ldexp(-z,e), -INFINITY, (double)-pi, FE_INEXACT); test2(atan2, INFINITY, ldexp(z,e), (double)pi/2, FE_INEXACT); test2(atan2, INFINITY, ldexp(-z,e), (double)pi/2, FE_INEXACT); test2(atan2, -INFINITY, ldexp(z,e), (double)-pi/2,FE_INEXACT); test2(atan2, -INFINITY, ldexp(-z,e),(double)-pi/2,FE_INEXACT); } for (e = LDBL_MIN_EXP - LDBL_MANT_DIG; e <= LDBL_MAX_EXP - 1; e++) { test2(atan2l, ldexpl(z, e), INFINITY, 0.0, 0); test2(atan2l, ldexpl(-z,e), INFINITY, -0.0, 0); test2(atan2l, ldexpl(z, e), -INFINITY, pi, FE_INEXACT); test2(atan2l, ldexpl(-z,e), -INFINITY, -pi, FE_INEXACT); test2(atan2l, INFINITY, ldexpl(z, e), pi / 2, FE_INEXACT); test2(atan2l, INFINITY, ldexpl(-z, e), pi / 2, FE_INEXACT); test2(atan2l, -INFINITY, ldexpl(z, e), -pi / 2, FE_INEXACT); test2(atan2l, -INFINITY, ldexpl(-z, e), -pi / 2, FE_INEXACT); } } /* * Test various inputs to asin(), acos() and atan() and verify that the * results are accurate to within 1 ulp. */ ATF_TC_WITHOUT_HEAD(accuracy); ATF_TC_BODY(accuracy, tc) { /* We expect correctly rounded results for these basic cases. */ testall(asin, 1.0, pi / 2, FE_INEXACT); testall(acos, 1.0, 0, 0); testall(atan, 1.0, pi / 4, FE_INEXACT); testall(asin, -1.0, -pi / 2, FE_INEXACT); testall(acos, -1.0, pi, FE_INEXACT); testall(atan, -1.0, -pi / 4, FE_INEXACT); /* * Here we expect answers to be within 1 ulp, although inexactness * in the input, combined with double rounding, could cause larger * errors. */ testall_tol(asin, sqrtl(2) / 2, pi / 4, 1, FE_INEXACT); testall_tol(acos, sqrtl(2) / 2, pi / 4, 1, FE_INEXACT); testall_tol(asin, -sqrtl(2) / 2, -pi / 4, 1, FE_INEXACT); testall_tol(acos, -sqrtl(2) / 2, c3pi / 4, 1, FE_INEXACT); testall_tol(asin, sqrtl(3) / 2, pio3, 1, FE_INEXACT); testall_tol(acos, sqrtl(3) / 2, pio3 / 2, 1, FE_INEXACT); testall_tol(atan, sqrtl(3), pio3, 1, FE_INEXACT); testall_tol(asin, -sqrtl(3) / 2, -pio3, 1, FE_INEXACT); testall_tol(acos, -sqrtl(3) / 2, c5pio3 / 2, 1, FE_INEXACT); testall_tol(atan, -sqrtl(3), -pio3, 1, FE_INEXACT); testall_tol(atan, sqrt2m1, pi / 8, 1, FE_INEXACT); testall_tol(atan, -sqrt2m1, -pi / 8, 1, FE_INEXACT); } /* * Test inputs to atan2() where x is a power of 2. These are easy cases * because y/x is exact. */ ATF_TC_WITHOUT_HEAD(p2x_atan2); ATF_TC_BODY(p2x_atan2, tc) { testall2(atan2, 1.0, 1.0, pi / 4, FE_INEXACT); testall2(atan2, 1.0, -1.0, c3pi / 4, FE_INEXACT); testall2(atan2, -1.0, 1.0, -pi / 4, FE_INEXACT); testall2(atan2, -1.0, -1.0, -c3pi / 4, FE_INEXACT); testall2_tol(atan2, sqrt2m1 * 2, 2.0, pi / 8, 1, FE_INEXACT); testall2_tol(atan2, sqrt2m1 * 2, -2.0, c7pi / 8, 1, FE_INEXACT); testall2_tol(atan2, -sqrt2m1 * 2, 2.0, -pi / 8, 1, FE_INEXACT); testall2_tol(atan2, -sqrt2m1 * 2, -2.0, -c7pi / 8, 1, FE_INEXACT); testall2_tol(atan2, sqrtl(3) * 0.5, 0.5, pio3, 1, FE_INEXACT); testall2_tol(atan2, sqrtl(3) * 0.5, -0.5, pio3 * 2, 1, FE_INEXACT); testall2_tol(atan2, -sqrtl(3) * 0.5, 0.5, -pio3, 1, FE_INEXACT); testall2_tol(atan2, -sqrtl(3) * 0.5, -0.5, -pio3 * 2, 1, FE_INEXACT); } /* * Test inputs very close to 0. */ ATF_TC_WITHOUT_HEAD(tiny); ATF_TC_BODY(tiny, tc) { float tiny = 0x1.23456p-120f; testall(asin, tiny, tiny, FE_INEXACT); testall(acos, tiny, pi / 2, FE_INEXACT); testall(atan, tiny, tiny, FE_INEXACT); testall(asin, -tiny, -tiny, FE_INEXACT); testall(acos, -tiny, pi / 2, FE_INEXACT); testall(atan, -tiny, -tiny, FE_INEXACT); /* Test inputs to atan2() that would cause y/x to underflow. */ test2(atan2f, 0x1.0p-100, 0x1.0p100, 0.0, FE_INEXACT | FE_UNDERFLOW); test2(atan2, 0x1.0p-1000, 0x1.0p1000, 0.0, FE_INEXACT | FE_UNDERFLOW); test2(atan2l, ldexpl(1.0, 100 - LDBL_MAX_EXP), ldexpl(1.0, LDBL_MAX_EXP - 100), 0.0, FE_INEXACT | FE_UNDERFLOW); test2(atan2f, -0x1.0p-100, 0x1.0p100, -0.0, FE_INEXACT | FE_UNDERFLOW); test2(atan2, -0x1.0p-1000, 0x1.0p1000, -0.0, FE_INEXACT | FE_UNDERFLOW); test2(atan2l, -ldexpl(1.0, 100 - LDBL_MAX_EXP), ldexpl(1.0, LDBL_MAX_EXP - 100), -0.0, FE_INEXACT | FE_UNDERFLOW); test2(atan2f, 0x1.0p-100, -0x1.0p100, (float)pi, FE_INEXACT); test2(atan2, 0x1.0p-1000, -0x1.0p1000, (double)pi, FE_INEXACT); test2(atan2l, ldexpl(1.0, 100 - LDBL_MAX_EXP), -ldexpl(1.0, LDBL_MAX_EXP - 100), pi, FE_INEXACT); test2(atan2f, -0x1.0p-100, -0x1.0p100, (float)-pi, FE_INEXACT); test2(atan2, -0x1.0p-1000, -0x1.0p1000, (double)-pi, FE_INEXACT); test2(atan2l, -ldexpl(1.0, 100 - LDBL_MAX_EXP), -ldexpl(1.0, LDBL_MAX_EXP - 100), -pi, FE_INEXACT); } /* * Test very large inputs to atan(). */ ATF_TC_WITHOUT_HEAD(atan_huge); ATF_TC_BODY(atan_huge, tc) { float huge = 0x1.23456p120; testall(atan, huge, pi / 2, FE_INEXACT); testall(atan, -huge, -pi / 2, FE_INEXACT); /* Test inputs to atan2() that would cause y/x to overflow. */ test2(atan2f, 0x1.0p100, 0x1.0p-100, (float)pi / 2, FE_INEXACT); test2(atan2, 0x1.0p1000, 0x1.0p-1000, (double)pi / 2, FE_INEXACT); test2(atan2l, ldexpl(1.0, LDBL_MAX_EXP - 100), ldexpl(1.0, 100 - LDBL_MAX_EXP), pi / 2, FE_INEXACT); test2(atan2f, -0x1.0p100, 0x1.0p-100, (float)-pi / 2, FE_INEXACT); test2(atan2, -0x1.0p1000, 0x1.0p-1000, (double)-pi / 2, FE_INEXACT); test2(atan2l, -ldexpl(1.0, LDBL_MAX_EXP - 100), ldexpl(1.0, 100 - LDBL_MAX_EXP), -pi / 2, FE_INEXACT); test2(atan2f, 0x1.0p100, -0x1.0p-100, (float)pi / 2, FE_INEXACT); test2(atan2, 0x1.0p1000, -0x1.0p-1000, (double)pi / 2, FE_INEXACT); test2(atan2l, ldexpl(1.0, LDBL_MAX_EXP - 100), -ldexpl(1.0, 100 - LDBL_MAX_EXP), pi / 2, FE_INEXACT); test2(atan2f, -0x1.0p100, -0x1.0p-100, (float)-pi / 2, FE_INEXACT); test2(atan2, -0x1.0p1000, -0x1.0p-1000, (double)-pi / 2, FE_INEXACT); test2(atan2l, -ldexpl(1.0, LDBL_MAX_EXP - 100), -ldexpl(1.0, 100 - LDBL_MAX_EXP), -pi / 2, FE_INEXACT); } /* * Test that sin(asin(x)) == x, and similarly for acos() and atan(). * You need to have a working sinl(), cosl(), and tanl() for these * tests to pass. */ static long double sinasinf(float x) { return (sinl(asinf(x))); } static long double sinasin(double x) { return (sinl(asin(x))); } +#ifndef __i386__ static long double sinasinl(long double x) { return (sinl(asinl(x))); } +#endif static long double cosacosf(float x) { return (cosl(acosf(x))); } static long double cosacos(double x) { return (cosl(acos(x))); } +#ifndef __i386__ static long double cosacosl(long double x) { return (cosl(acosl(x))); } +#endif static long double tanatanf(float x) { return (tanl(atanf(x))); } static long double tanatan(double x) { return (tanl(atan(x))); } +#ifndef __i386__ static long double tanatanl(long double x) { return (tanl(atanl(x))); } +#endif ATF_TC_WITHOUT_HEAD(inverse); ATF_TC_BODY(inverse, tc) { float i; for (i = -1; i <= 1; i += 0x1.0p-12f) { testall_tol(sinasin, i, i, 2, i == 0 ? 0 : FE_INEXACT); /* The relative error for cosacos is very large near x=0. */ if (fabsf(i) > 0x1.0p-4f) testall_tol(cosacos, i, i, 16, i == 1 ? 0 : FE_INEXACT); testall_tol(tanatan, i, i, 2, i == 0 ? 0 : FE_INEXACT); } } ATF_TP_ADD_TCS(tp) { ATF_TP_ADD_TC(tp, special); ATF_TP_ADD_TC(tp, special_atan2); ATF_TP_ADD_TC(tp, accuracy); ATF_TP_ADD_TC(tp, p2x_atan2); ATF_TP_ADD_TC(tp, tiny); ATF_TP_ADD_TC(tp, atan_huge); ATF_TP_ADD_TC(tp, inverse); return (atf_no_error()); }