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Diffstat (limited to 'test/math/libm-test.inc')
| -rw-r--r-- | test/math/libm-test.inc | 4521 |
1 files changed, 4521 insertions, 0 deletions
diff --git a/test/math/libm-test.inc b/test/math/libm-test.inc new file mode 100644 index 000000000..a0d08cefb --- /dev/null +++ b/test/math/libm-test.inc @@ -0,0 +1,4521 @@ +/* Copyright (C) 1997, 1998, 1999, 2000, 2001 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Andreas Jaeger <aj@arthur.rhein-neckar.de>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, write to the Free + Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA + 02111-1307 USA. */ + +/* Part of testsuite for libm. + + This file is processed by a perl script. The resulting file has to + be included by a master file that defines: + + Makros: + FUNC(function): converts general function name (like cos) to + name with correct suffix (e.g. cosl or cosf) + MATHCONST(x): like FUNC but for constants (e.g convert 0.0 to 0.0L) + FLOAT: floating point type to test + - TEST_MSG: informal message to be displayed + CHOOSE(Clongdouble,Cdouble,Cfloat,Cinlinelongdouble,Cinlinedouble,Cinlinefloat): + chooses one of the parameters as delta for testing + equality + PRINTF_EXPR Floating point conversion specification to print a variable + of type FLOAT with printf. PRINTF_EXPR just contains + the specifier, not the percent and width arguments, + e.g. "f". + PRINTF_XEXPR Like PRINTF_EXPR, but print in hexadecimal format. + PRINTF_NEXPR Like PRINTF_EXPR, but print nice. */ + +/* This testsuite has currently tests for: + acos, acosh, asin, asinh, atan, atan2, atanh, + cbrt, ceil, copysign, cos, cosh, erf, erfc, exp, exp10, exp2, expm1, + fabs, fdim, floor, fma, fmax, fmin, fmod, fpclassify, + frexp, gamma, hypot, + ilogb, isfinite, isinf, isnan, isnormal, + isless, islessequal, isgreater, isgreaterequal, islessgreater, isunordered, + j0, j1, jn, + ldexp, lgamma, log, log10, log1p, log2, logb, + modf, nearbyint, nextafter, + pow, remainder, remquo, rint, lrint, llrint, + round, lround, llround, + scalb, scalbn, scalbln, signbit, sin, sincos, sinh, sqrt, tan, tanh, tgamma, trunc, + y0, y1, yn + + and for the following complex math functions: + cabs, cacos, cacosh, carg, casin, casinh, catan, catanh, + ccos, ccosh, cexp, clog, cpow, cproj, csin, csinh, csqrt, ctan, ctanh. + + At the moment the following functions aren't tested: + drem, significand, nan + + Parameter handling is primitive in the moment: + --verbose=[0..3] for different levels of output: + 0: only error count + 1: basic report on failed tests (default) + 2: full report on all tests + -v for full output (equals --verbose=3) + -u for generation of an ULPs file + */ + +/* "Philosophy": + + This suite tests some aspects of the correct implementation of + mathematical functions in libm. Some simple, specific parameters + are tested for correctness but there's no exhaustive + testing. Handling of specific inputs (e.g. infinity, not-a-number) + is also tested. Correct handling of exceptions is checked + against. These implemented tests should check all cases that are + specified in ISO C99. + + Exception testing: At the moment only divide-by-zero and invalid + exceptions are tested. Overflow/underflow and inexact exceptions + aren't checked at the moment. + + NaN values: There exist signalling and quiet NaNs. This implementation + only uses signalling NaN as parameter but does not differenciate + between the two kinds of NaNs as result. + + Inline functions: Inlining functions should give an improvement in + speed - but not in precission. The inlined functions return + reasonable values for a reasonable range of input values. The + result is not necessarily correct for all values and exceptions are + not correctly raised in all cases. Problematic input and return + values are infinity, not-a-number and minus zero. This suite + therefore does not check these specific inputs and the exception + handling for inlined mathematical functions - just the "reasonable" + values are checked. + + Beware: The tests might fail for any of the following reasons: + - Tests are wrong + - Functions are wrong + - Floating Point Unit not working properly + - Compiler has errors + + With e.g. gcc 2.7.2.2 the test for cexp fails because of a compiler error. + + + To Do: All parameter should be numbers that can be represented as + exact floating point values. Currently some values cannot be represented + exactly and therefore the result is not the expected result. +*/ + +#ifndef _GNU_SOURCE +# define _GNU_SOURCE +#endif + +#include "libm-test-ulps.h" +#include <complex.h> +#include <math.h> +#include <float.h> +#include <limits.h> + +#include <errno.h> +#include <stdlib.h> +#include <stdio.h> +#include <string.h> +#include <getopt.h> + +//#include <fenv.h> +#define feclearexcept(X) +#define fetestexcept(X) 0 + +/* Possible exceptions */ +#define NO_EXCEPTION 0x0 +#define INVALID_EXCEPTION 0x1 +#define DIVIDE_BY_ZERO_EXCEPTION 0x2 +/* The next flags signals that those exceptions are allowed but not required. */ +#define INVALID_EXCEPTION_OK 0x4 +#define DIVIDE_BY_ZERO_EXCEPTION_OK 0x8 +#define EXCEPTIONS_OK INVALID_EXCEPTION_OK+DIVIDE_BY_ZERO_EXCEPTION_OK +/* Some special test flags, passed togther with exceptions. */ +#define IGNORE_ZERO_INF_SIGN 0x10 + +/* Various constants (we must supply them precalculated for accuracy). */ +#define M_PI_6l .52359877559829887307710723054658383L +#define M_E2l 7.389056098930650227230427460575008L +#define M_E3l 20.085536923187667740928529654581719L +#define M_2_SQRT_PIl 3.5449077018110320545963349666822903L /* 2 sqrt (M_PIl) */ +#define M_SQRT_PIl 1.7724538509055160272981674833411451L /* sqrt (M_PIl) */ +#define M_LOG_SQRT_PIl 0.57236494292470008707171367567652933L /* log(sqrt(M_PIl)) */ +#define M_LOG_2_SQRT_PIl 1.265512123484645396488945797134706L /* log(2*sqrt(M_PIl)) */ +#define M_PI_34l (M_PIl - M_PI_4l) /* 3*pi/4 */ +#define M_PI_34_LOG10El (M_PIl - M_PI_4l) * M_LOG10El +#define M_PI2_LOG10El M_PI_2l * M_LOG10El +#define M_PI4_LOG10El M_PI_4l * M_LOG10El +#define M_PI_LOG10El M_PIl * M_LOG10El + +static FILE *ulps_file; /* File to document difference. */ +static int output_ulps; /* Should ulps printed? */ + +static int noErrors; /* number of errors */ +static int noTests; /* number of tests (without testing exceptions) */ +static int noExcTests; /* number of tests for exception flags */ +static int noXFails; /* number of expected failures. */ +static int noXPasses; /* number of unexpected passes. */ + +static int verbose; +static int output_max_error; /* Should the maximal errors printed? */ +static int output_points; /* Should the single function results printed? */ +static int ignore_max_ulp; /* Should we ignore max_ulp? */ + +static FLOAT minus_zero, plus_zero; +static FLOAT plus_infty, minus_infty, nan_value; + +static FLOAT max_error, real_max_error, imag_max_error; + + +#define BUILD_COMPLEX(real, imag) \ + ({ __complex__ FLOAT __retval; \ + __real__ __retval = (real); \ + __imag__ __retval = (imag); \ + __retval; }) + +#define BUILD_COMPLEX_INT(real, imag) \ + ({ __complex__ int __retval; \ + __real__ __retval = (real); \ + __imag__ __retval = (imag); \ + __retval; }) + + +#define MANT_DIG CHOOSE ((LDBL_MANT_DIG-1), (DBL_MANT_DIG-1), (FLT_MANT_DIG-1), \ + (LDBL_MANT_DIG-1), (DBL_MANT_DIG-1), (FLT_MANT_DIG-1)) + +static void +init_max_error (void) +{ + max_error = 0; + real_max_error = 0; + imag_max_error = 0; + feclearexcept (FE_ALL_EXCEPT); +} + +static void +set_max_error (FLOAT current, FLOAT *curr_max_error) +{ + if (current > *curr_max_error) + *curr_max_error = current; +} + + +/* Should the message print to screen? This depends on the verbose flag, + and the test status. */ +static int +print_screen (int ok, int xfail) +{ + if (output_points + && (verbose > 1 + || (verbose == 1 && ok == xfail))) + return 1; + return 0; +} + + +/* Should the message print to screen? This depends on the verbose flag, + and the test status. */ +static int +print_screen_max_error (int ok, int xfail) +{ + if (output_max_error + && (verbose > 1 + || ((verbose == 1) && (ok == xfail)))) + return 1; + return 0; +} + +/* Update statistic counters. */ +static void +update_stats (int ok, int xfail) +{ + ++noTests; + if (ok && xfail) + ++noXPasses; + else if (!ok && xfail) + ++noXFails; + else if (!ok && !xfail) + ++noErrors; +} + +static void +print_ulps (const char *test_name, FLOAT ulp) +{ + if (output_ulps) + { + fprintf (ulps_file, "Test \"%s\":\n", test_name); + fprintf (ulps_file, "%s: %.0" PRINTF_NEXPR "\n", + CHOOSE("ldouble", "double", "float", + "ildouble", "idouble", "ifloat"), + FUNC(ceil) (ulp)); + } +} + +static void +print_function_ulps (const char *function_name, FLOAT ulp) +{ + if (output_ulps) + { + fprintf (ulps_file, "Function: \"%s\":\n", function_name); + fprintf (ulps_file, "%s: %.0" PRINTF_NEXPR "\n", + CHOOSE("ldouble", "double", "float", + "ildouble", "idouble", "ifloat"), + FUNC(ceil) (ulp)); + } +} + + +static void +print_complex_function_ulps (const char *function_name, FLOAT real_ulp, + FLOAT imag_ulp) +{ + if (output_ulps) + { + if (real_ulp != 0.0) + { + fprintf (ulps_file, "Function: Real part of \"%s\":\n", function_name); + fprintf (ulps_file, "%s: %.0" PRINTF_NEXPR "\n", + CHOOSE("ldouble", "double", "float", + "ildouble", "idouble", "ifloat"), + FUNC(ceil) (real_ulp)); + } + if (imag_ulp != 0.0) + { + fprintf (ulps_file, "Function: Imaginary part of \"%s\":\n", function_name); + fprintf (ulps_file, "%s: %.0" PRINTF_NEXPR "\n", + CHOOSE("ldouble", "double", "float", + "ildouble", "idouble", "ifloat"), + FUNC(ceil) (imag_ulp)); + } + + + } +} + + + +/* Test if Floating-Point stack hasn't changed */ +static void +fpstack_test (const char *test_name) +{ +#ifdef i386 + static int old_stack; + int sw; + + asm ("fnstsw" : "=a" (sw)); + sw >>= 11; + sw &= 7; + + if (sw != old_stack) + { + printf ("FP-Stack wrong after test %s (%d, should be %d)\n", + test_name, sw, old_stack); + ++noErrors; + old_stack = sw; + } +#endif +} + + +static void +print_max_error (const char *func_name, FLOAT allowed, int xfail) +{ + int ok = 0; + + if (max_error == 0.0 || (max_error <= allowed && !ignore_max_ulp)) + { + ok = 1; + } + + if (!ok) + print_function_ulps (func_name, max_error); + + + if (print_screen_max_error (ok, xfail)) + { + printf ("Maximal error of `%s'\n", func_name); + printf (" is : %.0" PRINTF_NEXPR " ulp\n", FUNC(ceil) (max_error)); + printf (" accepted: %.0" PRINTF_NEXPR " ulp\n", FUNC(ceil) (allowed)); + } + + update_stats (ok, xfail); +} + + +static void +print_complex_max_error (const char *func_name, __complex__ FLOAT allowed, + __complex__ int xfail) +{ + int ok = 0; + + if ((real_max_error == 0 && imag_max_error == 0) + || (real_max_error <= __real__ allowed + && imag_max_error <= __imag__ allowed + && !ignore_max_ulp)) + { + ok = 1; + } + + if (!ok) + print_complex_function_ulps (func_name, real_max_error, imag_max_error); + + + if (print_screen_max_error (ok, xfail)) + { + printf ("Maximal error of real part of: %s\n", func_name); + printf (" is : %.0" PRINTF_NEXPR " ulp\n", + FUNC(ceil) (real_max_error)); + printf (" accepted: %.0" PRINTF_NEXPR " ulp\n", + FUNC(ceil) (__real__ allowed)); + printf ("Maximal error of imaginary part of: %s\n", func_name); + printf (" is : %.0" PRINTF_NEXPR " ulp\n", + FUNC(ceil) (imag_max_error)); + printf (" accepted: %.0" PRINTF_NEXPR " ulp\n", + FUNC(ceil) (__imag__ allowed)); + } + + update_stats (ok, xfail); +} + + +/* Test whether a given exception was raised. */ +static void +test_single_exception (const char *test_name, + int exception, + int exc_flag, + int fe_flag, + const char *flag_name) +{ +#ifndef TEST_INLINE + int ok = 1; + if (exception & exc_flag) + { + if (fetestexcept (fe_flag)) + { + if (print_screen (1, 0)) + printf ("Pass: %s: Exception \"%s\" set\n", test_name, flag_name); + } + else + { + ok = 0; + if (print_screen (0, 0)) + printf ("Failure: %s: Exception \"%s\" not set\n", + test_name, flag_name); + } + } + else + { + if (fetestexcept (fe_flag)) + { + ok = 0; + if (print_screen (0, 0)) + printf ("Failure: %s: Exception \"%s\" set\n", + test_name, flag_name); + } + else + { + if (print_screen (1, 0)) + printf ("%s: Exception \"%s\" not set\n", test_name, + flag_name); + } + } + if (!ok) + ++noErrors; + +#endif +} + + +/* Test whether exceptions given by EXCEPTION are raised. Ignore thereby + allowed but not required exceptions. +*/ +static void +test_exceptions (const char *test_name, int exception) +{ + ++noExcTests; +#ifdef FE_DIVBYZERO + if ((exception & DIVIDE_BY_ZERO_EXCEPTION_OK) == 0) + test_single_exception (test_name, exception, + DIVIDE_BY_ZERO_EXCEPTION, FE_DIVBYZERO, + "Divide by zero"); +#endif +#ifdef FE_INVALID + if ((exception & INVALID_EXCEPTION_OK) == 0) + test_single_exception (test_name, exception, INVALID_EXCEPTION, FE_INVALID, + "Invalid operation"); +#endif + feclearexcept (FE_ALL_EXCEPT); +} + + +static void +check_float_internal (const char *test_name, FLOAT computed, FLOAT expected, + FLOAT max_ulp, int xfail, int exceptions, + FLOAT *curr_max_error) +{ + int ok = 0; + int print_diff = 0; + FLOAT diff = 0; + FLOAT ulp = 0; + + test_exceptions (test_name, exceptions); + if (isnan (computed) && isnan (expected)) + ok = 1; + else if (isinf (computed) && isinf (expected)) + { + /* Test for sign of infinities. */ + if ((exceptions & IGNORE_ZERO_INF_SIGN) == 0 + && signbit (computed) != signbit (expected)) + { + ok = 0; + printf ("infinity has wrong sign.\n"); + } + else + ok = 1; + } + /* Don't calc ulp for NaNs or infinities. */ + else if (isinf (computed) || isnan (computed) || isinf (expected) || isnan (expected)) + ok = 0; + else + { + diff = FUNC(fabs) (computed - expected); + /* ilogb (0) isn't allowed. */ + if (expected == 0.0) + ulp = diff / FUNC(ldexp) (1.0, - MANT_DIG); + else + ulp = diff / FUNC(ldexp) (1.0, FUNC(ilogb) (expected) - MANT_DIG); + set_max_error (ulp, curr_max_error); + print_diff = 1; + if ((exceptions & IGNORE_ZERO_INF_SIGN) == 0 + && computed == 0.0 && expected == 0.0 + && signbit(computed) != signbit (expected)) + ok = 0; + else if (ulp == 0.0 || (ulp <= max_ulp && !ignore_max_ulp)) + ok = 1; + else + { + ok = 0; + print_ulps (test_name, ulp); + } + + } + if (print_screen (ok, xfail)) + { + if (!ok) + printf ("Failure: "); + printf ("Test: %s\n", test_name); + printf ("Result:\n"); + printf (" is: % .20" PRINTF_EXPR " % .20" PRINTF_XEXPR "\n", + computed, computed); + printf (" should be: % .20" PRINTF_EXPR " % .20" PRINTF_XEXPR "\n", + expected, expected); + if (print_diff) + { + printf (" difference: % .20" PRINTF_EXPR " % .20" PRINTF_XEXPR + "\n", diff, diff); + printf (" ulp : % .4" PRINTF_NEXPR "\n", ulp); + printf (" max.ulp : % .4" PRINTF_NEXPR "\n", max_ulp); + } + } + update_stats (ok, xfail); + + fpstack_test (test_name); +} + + +static void +check_float (const char *test_name, FLOAT computed, FLOAT expected, + FLOAT max_ulp, int xfail, int exceptions) +{ + check_float_internal (test_name, computed, expected, max_ulp, xfail, + exceptions, &max_error); +} + + +static void +check_complex (const char *test_name, __complex__ FLOAT computed, + __complex__ FLOAT expected, + __complex__ FLOAT max_ulp, __complex__ int xfail, + int exception) +{ + FLOAT part_comp, part_exp, part_max_ulp; + int part_xfail; + char str[200]; + + sprintf (str, "Real part of: %s", test_name); + part_comp = __real__ computed; + part_exp = __real__ expected; + part_max_ulp = __real__ max_ulp; + part_xfail = __real__ xfail; + + check_float_internal (str, part_comp, part_exp, part_max_ulp, part_xfail, + exception, &real_max_error); + + sprintf (str, "Imaginary part of: %s", test_name); + part_comp = __imag__ computed; + part_exp = __imag__ expected; + part_max_ulp = __imag__ max_ulp; + part_xfail = __imag__ xfail; + + /* Don't check again for exceptions, just pass through the + zero/inf sign test. */ + check_float_internal (str, part_comp, part_exp, part_max_ulp, part_xfail, + exception & IGNORE_ZERO_INF_SIGN, + &imag_max_error); +} + + +/* Check that computed and expected values are equal (int values). */ +static void +check_int (const char *test_name, int computed, int expected, int max_ulp, + int xfail, int exceptions) +{ + int diff = computed - expected; + int ok = 0; + + test_exceptions (test_name, exceptions); + noTests++; + if (abs (diff) <= max_ulp) + ok = 1; + + if (!ok) + print_ulps (test_name, diff); + + if (print_screen (ok, xfail)) + { + if (!ok) + printf ("Failure: "); + printf ("Test: %s\n", test_name); + printf ("Result:\n"); + printf (" is: %d\n", computed); + printf (" should be: %d\n", expected); + } + + update_stats (ok, xfail); + fpstack_test (test_name); +} + + +/* Check that computed and expected values are equal (long int values). */ +static void +check_long (const char *test_name, long int computed, long int expected, + long int max_ulp, int xfail, int exceptions) +{ + long int diff = computed - expected; + int ok = 0; + + test_exceptions (test_name, exceptions); + noTests++; + if (labs (diff) <= max_ulp) + ok = 1; + + if (!ok) + print_ulps (test_name, diff); + + if (print_screen (ok, xfail)) + { + if (!ok) + printf ("Failure: "); + printf ("Test: %s\n", test_name); + printf ("Result:\n"); + printf (" is: %ld\n", computed); + printf (" should be: %ld\n", expected); + } + + update_stats (ok, xfail); + fpstack_test (test_name); +} + + +/* Check that computed value is true/false. */ +static void +check_bool (const char *test_name, int computed, int expected, + long int max_ulp, int xfail, int exceptions) +{ + int ok = 0; + + test_exceptions (test_name, exceptions); + noTests++; + if ((computed == 0) == (expected == 0)) + ok = 1; + + if (print_screen (ok, xfail)) + { + if (!ok) + printf ("Failure: "); + printf ("Test: %s\n", test_name); + printf ("Result:\n"); + printf (" is: %d\n", computed); + printf (" should be: %d\n", expected); + } + + update_stats (ok, xfail); + fpstack_test (test_name); +} + + +/* check that computed and expected values are equal (long int values) */ +static void +check_longlong (const char *test_name, long long int computed, + long long int expected, + long long int max_ulp, int xfail, + int exceptions) +{ + long long int diff = computed - expected; + int ok = 0; + + test_exceptions (test_name, exceptions); + noTests++; + if (llabs (diff) <= max_ulp) + ok = 1; + + if (!ok) + print_ulps (test_name, diff); + + if (print_screen (ok, xfail)) + { + if (!ok) + printf ("Failure:"); + printf ("Test: %s\n", test_name); + printf ("Result:\n"); + printf (" is: %lld\n", computed); + printf (" should be: %lld\n", expected); + } + + update_stats (ok, xfail); + fpstack_test (test_name); +} + + + +/* This is to prevent messages from the SVID libm emulation. */ +int +matherr (struct exception *x __attribute__ ((unused))) +{ + return 1; +} + + +/**************************************************************************** + Tests for single functions of libm. + Please keep them alphabetically sorted! +****************************************************************************/ + +static void +acos_test (void) +{ + errno = 0; + FUNC(acos) (0); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + START (acos); + + TEST_f_f (acos, plus_infty, nan_value, INVALID_EXCEPTION); + TEST_f_f (acos, minus_infty, nan_value, INVALID_EXCEPTION); + TEST_f_f (acos, nan_value, nan_value); + + /* |x| > 1: */ + TEST_f_f (acos, 1.1L, nan_value, INVALID_EXCEPTION); + TEST_f_f (acos, -1.1L, nan_value, INVALID_EXCEPTION); + + TEST_f_f (acos, 0, M_PI_2l); + TEST_f_f (acos, minus_zero, M_PI_2l); + TEST_f_f (acos, 1, 0); + TEST_f_f (acos, -1, M_PIl); + TEST_f_f (acos, 0.5, M_PI_6l*2.0); + TEST_f_f (acos, -0.5, M_PI_6l*4.0); + TEST_f_f (acos, 0.7L, 0.79539883018414355549096833892476432L); + + END (acos); +} + +static void +acosh_test (void) +{ + errno = 0; + FUNC(acosh) (7); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + START (acosh); + + TEST_f_f (acosh, plus_infty, plus_infty); + TEST_f_f (acosh, minus_infty, nan_value, INVALID_EXCEPTION); + + /* x < 1: */ + TEST_f_f (acosh, -1.1L, nan_value, INVALID_EXCEPTION); + + TEST_f_f (acosh, 1, 0); + TEST_f_f (acosh, 7, 2.633915793849633417250092694615937L); + + END (acosh); +} + +static void +asin_test (void) +{ + errno = 0; + FUNC(asin) (0); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + START (asin); + + TEST_f_f (asin, plus_infty, nan_value, INVALID_EXCEPTION); + TEST_f_f (asin, minus_infty, nan_value, INVALID_EXCEPTION); + TEST_f_f (asin, nan_value, nan_value); + + /* asin x == NaN plus invalid exception for |x| > 1. */ + TEST_f_f (asin, 1.1L, nan_value, INVALID_EXCEPTION); + TEST_f_f (asin, -1.1L, nan_value, INVALID_EXCEPTION); + + TEST_f_f (asin, 0, 0); + TEST_f_f (asin, minus_zero, minus_zero); + TEST_f_f (asin, 0.5, M_PI_6l); + TEST_f_f (asin, -0.5, -M_PI_6l); + TEST_f_f (asin, 1.0, M_PI_2l); + TEST_f_f (asin, -1.0, -M_PI_2l); + TEST_f_f (asin, 0.7L, 0.77539749661075306374035335271498708L); + + END (asin); +} + +static void +asinh_test (void) +{ + errno = 0; + FUNC(asinh) (0.7L); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + START (asinh); + + TEST_f_f (asinh, 0, 0); + TEST_f_f (asinh, minus_zero, minus_zero); +#ifndef TEST_INLINE + TEST_f_f (asinh, plus_infty, plus_infty); + TEST_f_f (asinh, minus_infty, minus_infty); +#endif + TEST_f_f (asinh, nan_value, nan_value); + TEST_f_f (asinh, 0.7L, 0.652666566082355786L); + + END (asinh); +} + +static void +atan_test (void) +{ + errno = 0; + FUNC(atan) (0); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + START (atan); + + TEST_f_f (atan, 0, 0); + TEST_f_f (atan, minus_zero, minus_zero); + + TEST_f_f (atan, plus_infty, M_PI_2l); + TEST_f_f (atan, minus_infty, -M_PI_2l); + TEST_f_f (atan, nan_value, nan_value); + + TEST_f_f (atan, 1, M_PI_4l); + TEST_f_f (atan, -1, -M_PI_4l); + + TEST_f_f (atan, 0.7L, 0.61072596438920861654375887649023613L); + + END (atan); +} + + + +static void +atanh_test (void) +{ + errno = 0; + FUNC(atanh) (0.7L); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + START (atanh); + + + TEST_f_f (atanh, 0, 0); + TEST_f_f (atanh, minus_zero, minus_zero); + + TEST_f_f (atanh, 1, plus_infty, DIVIDE_BY_ZERO_EXCEPTION); + TEST_f_f (atanh, -1, minus_infty, DIVIDE_BY_ZERO_EXCEPTION); + TEST_f_f (atanh, nan_value, nan_value); + + /* atanh (x) == NaN plus invalid exception if |x| > 1. */ + TEST_f_f (atanh, 1.1L, nan_value, INVALID_EXCEPTION); + TEST_f_f (atanh, -1.1L, nan_value, INVALID_EXCEPTION); + + TEST_f_f (atanh, 0.7L, 0.8673005276940531944L); + + END (atanh); +} + +static void +atan2_test (void) +{ + errno = 0; + FUNC(atan2) (-0, 1); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + START (atan2); + + /* atan2 (0,x) == 0 for x > 0. */ + TEST_ff_f (atan2, 0, 1, 0); + + /* atan2 (-0,x) == -0 for x > 0. */ + TEST_ff_f (atan2, minus_zero, 1, minus_zero); + + TEST_ff_f (atan2, 0, 0, 0); + TEST_ff_f (atan2, minus_zero, 0, minus_zero); + + /* atan2 (+0,x) == +pi for x < 0. */ + TEST_ff_f (atan2, 0, -1, M_PIl); + + /* atan2 (-0,x) == -pi for x < 0. */ + TEST_ff_f (atan2, minus_zero, -1, -M_PIl); + + TEST_ff_f (atan2, 0, minus_zero, M_PIl); + TEST_ff_f (atan2, minus_zero, minus_zero, -M_PIl); + + /* atan2 (y,+0) == pi/2 for y > 0. */ + TEST_ff_f (atan2, 1, 0, M_PI_2l); + + /* atan2 (y,-0) == pi/2 for y > 0. */ + TEST_ff_f (atan2, 1, minus_zero, M_PI_2l); + + /* atan2 (y,+0) == -pi/2 for y < 0. */ + TEST_ff_f (atan2, -1, 0, -M_PI_2l); + + /* atan2 (y,-0) == -pi/2 for y < 0. */ + TEST_ff_f (atan2, -1, minus_zero, -M_PI_2l); + + /* atan2 (y,inf) == +0 for finite y > 0. */ + TEST_ff_f (atan2, 1, plus_infty, 0); + + /* atan2 (y,inf) == -0 for finite y < 0. */ + TEST_ff_f (atan2, -1, plus_infty, minus_zero); + + /* atan2(+inf, x) == pi/2 for finite x. */ + TEST_ff_f (atan2, plus_infty, -1, M_PI_2l); + + /* atan2(-inf, x) == -pi/2 for finite x. */ + TEST_ff_f (atan2, minus_infty, 1, -M_PI_2l); + + /* atan2 (y,-inf) == +pi for finite y > 0. */ + TEST_ff_f (atan2, 1, minus_infty, M_PIl); + + /* atan2 (y,-inf) == -pi for finite y < 0. */ + TEST_ff_f (atan2, -1, minus_infty, -M_PIl); + + TEST_ff_f (atan2, plus_infty, plus_infty, M_PI_4l); + TEST_ff_f (atan2, minus_infty, plus_infty, -M_PI_4l); + TEST_ff_f (atan2, plus_infty, minus_infty, M_PI_34l); + TEST_ff_f (atan2, minus_infty, minus_infty, -M_PI_34l); + TEST_ff_f (atan2, nan_value, nan_value, nan_value); + + TEST_ff_f (atan2, 0.7L, 1, 0.61072596438920861654375887649023613L); + TEST_ff_f (atan2, -0.7L, 1.0L, -0.61072596438920861654375887649023613L); + TEST_ff_f (atan2, 0.7L, -1.0L, 2.530866689200584621918884506789267L); + TEST_ff_f (atan2, -0.7L, -1.0L, -2.530866689200584621918884506789267L); + TEST_ff_f (atan2, 0.4L, 0.0003L, 1.5700463269355215717704032607580829L); + TEST_ff_f (atan2, 1.4L, -0.93L, 2.1571487668237843754887415992772736L); + + END (atan2); +} + + +static void +cabs_test (void) +{ + errno = 0; + FUNC(cabs) (BUILD_COMPLEX (0.7L, 12.4L)); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + START (cabs); + + /* cabs (x + iy) is specified as hypot (x,y) */ + + /* cabs (+inf + i x) == +inf. */ + TEST_c_f (cabs, plus_infty, 1.0, plus_infty); + /* cabs (-inf + i x) == +inf. */ + TEST_c_f (cabs, minus_infty, 1.0, plus_infty); + + TEST_c_f (cabs, minus_infty, nan_value, plus_infty); + TEST_c_f (cabs, minus_infty, nan_value, plus_infty); + + TEST_c_f (cabs, nan_value, nan_value, nan_value); + + /* cabs (x,y) == cabs (y,x). */ + TEST_c_f (cabs, 0.7L, 12.4L, 12.419742348374220601176836866763271L); + /* cabs (x,y) == cabs (-x,y). */ + TEST_c_f (cabs, -12.4L, 0.7L, 12.419742348374220601176836866763271L); + /* cabs (x,y) == cabs (-y,x). */ + TEST_c_f (cabs, -0.7L, 12.4L, 12.419742348374220601176836866763271L); + /* cabs (x,y) == cabs (-x,-y). */ + TEST_c_f (cabs, -12.4L, -0.7L, 12.419742348374220601176836866763271L); + /* cabs (x,y) == cabs (-y,-x). */ + TEST_c_f (cabs, -0.7L, -12.4L, 12.419742348374220601176836866763271L); + /* cabs (x,0) == fabs (x). */ + TEST_c_f (cabs, -0.7L, 0, 0.7L); + TEST_c_f (cabs, 0.7L, 0, 0.7L); + TEST_c_f (cabs, -1.0L, 0, 1.0L); + TEST_c_f (cabs, 1.0L, 0, 1.0L); + TEST_c_f (cabs, -5.7e7L, 0, 5.7e7L); + TEST_c_f (cabs, 5.7e7L, 0, 5.7e7L); + + TEST_c_f (cabs, 0.7L, 1.2L, 1.3892443989449804508432547041028554L); + + END (cabs); +} + +#if 0 +static void +cacos_test (void) +{ + errno = 0; + FUNC(cacos) (BUILD_COMPLEX (0.7L, 1.2L)); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + START (cacos); + + + TEST_c_c (cacos, 0, 0, M_PI_2l, minus_zero); + TEST_c_c (cacos, minus_zero, 0, M_PI_2l, minus_zero); + TEST_c_c (cacos, minus_zero, minus_zero, M_PI_2l, 0.0); + TEST_c_c (cacos, 0, minus_zero, M_PI_2l, 0.0); + + TEST_c_c (cacos, minus_infty, plus_infty, M_PI_34l, minus_infty); + TEST_c_c (cacos, minus_infty, minus_infty, M_PI_34l, plus_infty); + + TEST_c_c (cacos, plus_infty, plus_infty, M_PI_4l, minus_infty); + TEST_c_c (cacos, plus_infty, minus_infty, M_PI_4l, plus_infty); + + TEST_c_c (cacos, -10.0, plus_infty, M_PI_2l, minus_infty); + TEST_c_c (cacos, -10.0, minus_infty, M_PI_2l, plus_infty); + TEST_c_c (cacos, 0, plus_infty, M_PI_2l, minus_infty); + TEST_c_c (cacos, 0, minus_infty, M_PI_2l, plus_infty); + TEST_c_c (cacos, 0.1L, plus_infty, M_PI_2l, minus_infty); + TEST_c_c (cacos, 0.1L, minus_infty, M_PI_2l, plus_infty); + + TEST_c_c (cacos, minus_infty, 0, M_PIl, minus_infty); + TEST_c_c (cacos, minus_infty, minus_zero, M_PIl, plus_infty); + TEST_c_c (cacos, minus_infty, 100, M_PIl, minus_infty); + TEST_c_c (cacos, minus_infty, -100, M_PIl, plus_infty); + + TEST_c_c (cacos, plus_infty, 0, 0.0, minus_infty); + TEST_c_c (cacos, plus_infty, minus_zero, 0.0, plus_infty); + TEST_c_c (cacos, plus_infty, 0.5, 0.0, minus_infty); + TEST_c_c (cacos, plus_infty, -0.5, 0.0, plus_infty); + + TEST_c_c (cacos, plus_infty, nan_value, nan_value, plus_infty, IGNORE_ZERO_INF_SIGN); + TEST_c_c (cacos, minus_infty, nan_value, nan_value, plus_infty, IGNORE_ZERO_INF_SIGN); + + TEST_c_c (cacos, 0, nan_value, M_PI_2l, nan_value); + TEST_c_c (cacos, minus_zero, nan_value, M_PI_2l, nan_value); + + TEST_c_c (cacos, nan_value, plus_infty, nan_value, minus_infty); + TEST_c_c (cacos, nan_value, minus_infty, nan_value, plus_infty); + + TEST_c_c (cacos, 10.5, nan_value, nan_value, nan_value, INVALID_EXCEPTION_OK); + TEST_c_c (cacos, -10.5, nan_value, nan_value, nan_value, INVALID_EXCEPTION_OK); + + TEST_c_c (cacos, nan_value, 0.75, nan_value, nan_value, INVALID_EXCEPTION_OK); + TEST_c_c (cacos, nan_value, -0.75, nan_value, nan_value, INVALID_EXCEPTION_OK); + + TEST_c_c (cacos, nan_value, nan_value, nan_value, nan_value); + + TEST_c_c (cacos, 0.7L, 1.2L, 1.1351827477151551088992008271819053L, -1.0927647857577371459105272080819308L); + TEST_c_c (cacos, -2, -3, 2.1414491111159960199416055713254211L, 1.9833870299165354323470769028940395L); + + END (cacos, complex); +} + + +static void +cacosh_test (void) +{ + errno = 0; + FUNC(cacosh) (BUILD_COMPLEX (0.7L, 1.2L)); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + START (cacosh); + + + TEST_c_c (cacosh, 0, 0, 0.0, M_PI_2l); + TEST_c_c (cacosh, minus_zero, 0, 0.0, M_PI_2l); + TEST_c_c (cacosh, 0, minus_zero, 0.0, -M_PI_2l); + TEST_c_c (cacosh, minus_zero, minus_zero, 0.0, -M_PI_2l); + TEST_c_c (cacosh, minus_infty, plus_infty, plus_infty, M_PI_34l); + TEST_c_c (cacosh, minus_infty, minus_infty, plus_infty, -M_PI_34l); + + TEST_c_c (cacosh, plus_infty, plus_infty, plus_infty, M_PI_4l); + TEST_c_c (cacosh, plus_infty, minus_infty, plus_infty, -M_PI_4l); + + TEST_c_c (cacosh, -10.0, plus_infty, plus_infty, M_PI_2l); + TEST_c_c (cacosh, -10.0, minus_infty, plus_infty, -M_PI_2l); + TEST_c_c (cacosh, 0, plus_infty, plus_infty, M_PI_2l); + TEST_c_c (cacosh, 0, minus_infty, plus_infty, -M_PI_2l); + TEST_c_c (cacosh, 0.1L, plus_infty, plus_infty, M_PI_2l); + TEST_c_c (cacosh, 0.1L, minus_infty, plus_infty, -M_PI_2l); + + TEST_c_c (cacosh, minus_infty, 0, plus_infty, M_PIl); + TEST_c_c (cacosh, minus_infty, minus_zero, plus_infty, -M_PIl); + TEST_c_c (cacosh, minus_infty, 100, plus_infty, M_PIl); + TEST_c_c (cacosh, minus_infty, -100, plus_infty, -M_PIl); + + TEST_c_c (cacosh, plus_infty, 0, plus_infty, 0.0); + TEST_c_c (cacosh, plus_infty, minus_zero, plus_infty, minus_zero); + TEST_c_c (cacosh, plus_infty, 0.5, plus_infty, 0.0); + TEST_c_c (cacosh, plus_infty, -0.5, plus_infty, minus_zero); + + TEST_c_c (cacosh, plus_infty, nan_value, plus_infty, nan_value); + TEST_c_c (cacosh, minus_infty, nan_value, plus_infty, nan_value); + + TEST_c_c (cacosh, 0, nan_value, nan_value, nan_value); + TEST_c_c (cacosh, minus_zero, nan_value, nan_value, nan_value); + + TEST_c_c (cacosh, nan_value, plus_infty, plus_infty, nan_value); + TEST_c_c (cacosh, nan_value, minus_infty, plus_infty, nan_value); + + TEST_c_c (cacosh, 10.5, nan_value, nan_value, nan_value, INVALID_EXCEPTION_OK); + TEST_c_c (cacosh, -10.5, nan_value, nan_value, nan_value, INVALID_EXCEPTION_OK); + + TEST_c_c (cacosh, nan_value, 0.75, nan_value, nan_value, INVALID_EXCEPTION_OK); + TEST_c_c (cacosh, nan_value, -0.75, nan_value, nan_value, INVALID_EXCEPTION_OK); + + TEST_c_c (cacosh, nan_value, nan_value, nan_value, nan_value); + + TEST_c_c (cacosh, 0.7L, 1.2L, 1.0927647857577371459105272080819308L, 1.1351827477151551088992008271819053L); + TEST_c_c (cacosh, -2, -3, -1.9833870299165354323470769028940395L, 2.1414491111159960199416055713254211L); + + END (cacosh, complex); +} + +static void +carg_test (void) +{ + START (carg); + + /* carg (x + iy) is specified as atan2 (y, x) */ + + /* carg (x + i 0) == 0 for x > 0. */ + TEST_c_f (carg, 2.0, 0, 0); + /* carg (x - i 0) == -0 for x > 0. */ + TEST_c_f (carg, 2.0, minus_zero, minus_zero); + + TEST_c_f (carg, 0, 0, 0); + TE |