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Diffstat (limited to 'lib/msun/tests/invtrig_test.c')
| -rw-r--r-- | lib/msun/tests/invtrig_test.c | 479 |
1 files changed, 479 insertions, 0 deletions
diff --git a/lib/msun/tests/invtrig_test.c b/lib/msun/tests/invtrig_test.c new file mode 100644 index 0000000..01b0379 --- /dev/null +++ b/lib/msun/tests/invtrig_test.c @@ -0,0 +1,479 @@ +/*- + * Copyright (c) 2008 David Schultz <das@FreeBSD.org> + * 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 <sys/cdefs.h> +__FBSDID("$FreeBSD$"); + +#include <assert.h> +#include <fenv.h> +#include <float.h> +#include <math.h> +#include <stdio.h> + +#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); \ + assert(feclearexcept(FE_ALL_EXCEPT) == 0); \ + assert(fpequal_tol(func(_in), _out, (tol), CS_BOTH)); \ + assert(((void)func, fetestexcept(ALL_STD_EXCEPT) == (excepts))); \ +} 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 +#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); \ + assert(feclearexcept(FE_ALL_EXCEPT) == 0); \ + assert(fpequal_tol(func(_iny, _inx), _out, (tol), CS_BOTH)); \ + assert(((void)func, fetestexcept(ALL_STD_EXCEPT) == (excepts))); \ +} 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 +#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)) + +long double +pi = 3.14159265358979323846264338327950280e+00L, +pio3 = 1.04719755119659774615421446109316766e+00L, +c3pi = 9.42477796076937971538793014983850839e+00L, +c5pi = 1.57079632679489661923132169163975140e+01L, +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. + */ +static void +test_special(void) +{ + + 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. + */ +static void +test_special_atan2(void) +{ + 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. + */ +static void +test_accuracy(void) +{ + + /* 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. + */ +static void +test_p2x_atan2(void) +{ + + 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. + */ +static void +test_tiny(void) +{ + 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(). + */ +static void +test_atan_huge(void) +{ + 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))); +} + +static long double +sinasinl(long double x) +{ + + return (sinl(asinl(x))); +} + +static long double +cosacosf(float x) +{ + + return (cosl(acosf(x))); +} + +static long double +cosacos(double x) +{ + + return (cosl(acos(x))); +} + +static long double +cosacosl(long double x) +{ + + return (cosl(acosl(x))); +} + +static long double +tanatanf(float x) +{ + + return (tanl(atanf(x))); +} + +static long double +tanatan(double x) +{ + + return (tanl(atan(x))); +} + +static long double +tanatanl(long double x) +{ + + return (tanl(atanl(x))); +} + +static void +test_inverse(void) +{ + 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); + } +} + +int +main(int argc, char *argv[]) +{ + +#if defined(__i386__) + printf("1..0 # SKIP fails all assertions on i386\n"); + return (0); +#endif + + printf("1..7\n"); + + test_special(); + printf("ok 1 - special\n"); + + test_special_atan2(); + printf("ok 2 - atan2 special\n"); + + test_accuracy(); + printf("ok 3 - accuracy\n"); + + test_p2x_atan2(); + printf("ok 4 - atan2 p2x\n"); + + test_tiny(); + printf("ok 5 - tiny inputs\n"); + + test_atan_huge(); + printf("ok 6 - atan huge inputs\n"); + + test_inverse(); + printf("ok 7 - inverse\n"); + + return (0); +} |
