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libm-test.inc
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/* Copyright (C) 1997-2006, 2007, 2009, 2010, 2011 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Andreas Jaeger <aj@suse.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:
Macros:
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, significand
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, 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 quiet 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. For this we will use 36 digits so that numbers can be
represented exactly. */
#ifndef _GNU_SOURCE
# define _GNU_SOURCE
#endif
#include "libm-test-ulps.h"
#include <complex.h>
#include <math.h>
#include <float.h>
#include <fenv.h>
#include <limits.h>
#include <errno.h>
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <argp.h>
/* 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
#define M_SQRT_2_2 0.70710678118654752440084436210484903L /* sqrt (2) / 2 */
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, max_value, min_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);
switch (fpclassify (expected))
{
case FP_ZERO:
/* ilogb (0) isn't allowed. */
ulp = diff / FUNC(ldexp) (1.0, - MANT_DIG);
break;
case FP_NORMAL:
ulp = diff / FUNC(ldexp) (1.0, FUNC(ilogb) (expected) - MANT_DIG);
break;
case FP_SUBNORMAL:
ulp = (FUNC(ldexp) (diff, MANT_DIG)
/ FUNC(ldexp) (1.0, FUNC(ilogb) (expected)));
break;
default:
/* It should never happen. */
abort ();
break;
}
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 <= 0.5 || (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, 1.125L, nan_value, INVALID_EXCEPTION);
TEST_f_f (acos, -1.125L, 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, 0.75L, 0.722734247813415611178377352641333362L);
TEST_f_f (acos, 2e-17L, 1.57079632679489659923132169163975144L);
TEST_f_f (acos, 0.0625L, 1.50825556499840522843072005474337068L);
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, -1.125L, nan_value, INVALID_EXCEPTION);
TEST_f_f (acosh, 1, 0);
TEST_f_f (acosh, 7, 2.63391579384963341725009269461593689L);
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, 1.125L, nan_value, INVALID_EXCEPTION);
TEST_f_f (asin, -1.125L, 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, 0.75L, 0.848062078981481008052944338998418080L);
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, 0.75L, 0.693147180559945309417232121458176568L);
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, 0.75L, 0.643501108793284386802809228717322638L);
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, 1.125L, nan_value, INVALID_EXCEPTION);
TEST_f_f (atanh, -1.125L, nan_value, INVALID_EXCEPTION);
TEST_f_f (atanh, 0.75L, 0.972955074527656652552676371721589865L);
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, 0.75L, 1, 0.643501108793284386802809228717322638L);
TEST_ff_f (atan2, -0.75L, 1.0L, -0.643501108793284386802809228717322638L);
TEST_ff_f (atan2, 0.75L, -1.0L, 2.49809154479650885165983415456218025L);
TEST_ff_f (atan2, -0.75L, -1.0L, -2.49809154479650885165983415456218025L);
TEST_ff_f (atan2, 0.390625L, .00029L, 1.57005392693128974780151246612928941L);
TEST_ff_f (atan2, 1.390625L, 0.9296875L, 0.981498387184244311516296577615519772L);
TEST_ff_f (atan2, -0.00756827042671106339L, -.001792735857538728036L, -1.80338464113663849327153994379639112L);
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, 0.75L, 12.390625L, 12.4133028598606664302388810868156657L);
/* cabs (x,y) == cabs (-x,y). */
TEST_c_f (cabs, -12.390625L, 0.75L, 12.4133028598606664302388810868156657L);
/* cabs (x,y) == cabs (-y,x). */
TEST_c_f (cabs, -0.75L, 12.390625L, 12.4133028598606664302388810868156657L);
/* cabs (x,y) == cabs (-x,-y). */
TEST_c_f (cabs, -12.390625L, -0.75L, 12.4133028598606664302388810868156657L);
/* cabs (x,y) == cabs (-y,-x). */
TEST_c_f (cabs, -0.75L, -12.390625L, 12.4133028598606664302388810868156657L);
/* cabs (x,0) == fabs (x). */
TEST_c_f (cabs, -0.75L, 0, 0.75L);
TEST_c_f (cabs, 0.75L, 0, 0.75L);