glibc/math/libm-test.c

/* Copyright (C) 1997 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Contributed by Andreas Jaeger <aj@arthur.pfalz.de>, 1997.

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Library General Public License as
   published by the Free Software Foundation; either version 2 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
   Library General Public License for more details.

   You should have received a copy of the GNU Library General Public
   License along with the GNU C Library; see the file COPYING.LIB.  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 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)
   MATHTYPE:       floating point type to test
   TEST_MSG:       informal message to be displayed
   CHOOSE(Clongdouble,Cdouble,Cfloat):
   chooses one of the parameters as epsilon for testing
   equality
   PRINTF_EXPR     Floating point conversion specification to print a variable
   of type MATHTYPE with printf. PRINTF_EXPR just contains
   the specifier, not the percent and width arguments,
   e.g. "f"
 */

/* This program isn't finished yet.
   It has tests for acos, acosh, asin, asinh, atan, atan2, atanh,
   cbrt, ceil, cos, cosh, exp, exp2, expm1, fabs, floor, fpclassify,
   frexp, hypot, ldexp,
   log, log10, log1p, log2, logb, modf,
   pow, sin, sinh, tan, tanh.
   Tests for the other libm-functions will come later.

   The routines using random variables are still under construction. I don't
   like it the way it's working now and will change it.

   Exception handling has not been implemented so far so don't get fooled
   that these tests pass.

   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
   2: full report on failed tests
   3: full report on failed and passed tests (default)
   -v for full output (equals --verbose=3)
   -s,--silent outputs only the error count (equals --verbose=0)
 */

/* Define if the following ISO C 9X functions are implemented: exp2,
   log2.  */
#undef ISO_9X_IMPLEMENTED

#ifndef _GNU_SOURCE
# define _GNU_SOURCE
#endif

#include <math.h>
#include <float.h>

#include <errno.h>
#include <stdlib.h>
#include <stdio.h>
#include <time.h>
#include <getopt.h>

/* TEST_EXCEPTION: tests if an exception as occured */
/* for the moment: does nothing */
/* Possible exceptions */
#define NO_EXCEPTION             0x0
#define INVALID_EXCEPTION        0x1
#define DIVIDE_BY_ZERO_EXCEPTION 0x2

#define PRINT 1
#define NO_PRINT 0

#define TEST_EXCEPTION(test) do {} while (0);
/* As long as no exception code is available prevent warnings.  */
#define UNUSED __attribute__ ((unused))

static int noErrors;

static int verbose = 3;
static MATHTYPE minus_zero, plus_zero;
static MATHTYPE plus_infty, minus_infty, nan_value;

typedef MATHTYPE (*mathfunc) (MATHTYPE);


#define ISINF(x)                                \
(sizeof (x) == sizeof (float) ?                 \
 isinff (x)                                   \
 : sizeof (x) == sizeof (double) ?              \
 isinf (x) : isinfl (x))


     /*
        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\n", test_name);
      if (verbose > 2)
	printf ("=======> stack = %d\n", sw);
      ++noErrors;
      old_stack = sw;
    }
#endif
}


/*
   Call to an external function so that floating point registers
   get moved to memory
 */
static void
this_does_nothing (void)
{
  clock_t dummy;

  dummy = clock ();
}

/*
   Get a random value x with min_value < x < max_value
   and min_value, max_value finite,
   max_value and min_value shouldn't be too close together
 */
static MATHTYPE
random_value (MATHTYPE min_value, MATHTYPE max_value)
{
  int r;
  MATHTYPE x;

  r = rand ();

  x = (max_value - min_value) / RAND_MAX * (MATHTYPE) r + min_value;

  if ((x <= min_value) || (x >= max_value) || !isfinite (x))
    x = (max_value - min_value) / 2 + min_value;

  return x;
}

/* Get a random value x with x > min_value.  */
static MATHTYPE
random_greater (MATHTYPE min_value)
{
  return random_value (min_value, 1e6);		/* CHOOSE (LDBL_MAX, DBL_MAX, FLT_MAX) */
}

/* Get a random value x with x < max_value.  */
static MATHTYPE
random_less (MATHTYPE max_value)
{
  return random_value (-1e6, max_value);
}


/* Test if two floating point numbers are equal.  */
static int
check_equal (MATHTYPE computed, MATHTYPE supplied, MATHTYPE eps, MATHTYPE * diff)
{
  /* Both plus Infinity or both minus infinity.  */
  if (ISINF (computed) && (ISINF (computed) == ISINF (supplied)))
    return 1;

  if (isnan (computed) && isnan (supplied))	/* isnan works for all types */
    return 1;

  *diff = FUNC(fabs) (computed - supplied);

  if (*diff <= eps && (signbit (computed) == signbit (supplied) || eps != 0.0))
    return 1;

  return 0;
}


static void
output_result_bool (const char *test_name, int result)
{
  if (result)
    {
      if (verbose > 2)
	printf ("Pass: %s\n", test_name);
    }
  else
    {
      if (verbose)
	printf ("Fail: %s\n", test_name);
      ++noErrors;
    }

  fpstack_test (test_name);
}


static void
output_isvalue (const char *test_name, int result,
		MATHTYPE value)
{
  if (result)
    {
      if (verbose > 2)
	printf ("Pass: %s\n", test_name);
    }
  else
    {
      if (verbose)
	printf ("Fail: %s\n", test_name);
      if (verbose > 1)
	printf (" Value: %.20" PRINTF_EXPR "\n", value);
      noErrors++;
    }

  fpstack_test (test_name);
}


static void
output_isvalue_ext (const char *test_name, int result,
		    MATHTYPE value, MATHTYPE parameter)
{
  if (result)
    {
      if (verbose > 2)
	printf ("Pass: %s\n", test_name);
    }
  else
    {
      if (verbose)
	printf ("Fail: %s\n", test_name);
      if (verbose > 1)
	{
	  printf (" Value:     %.20" PRINTF_EXPR "\n", value);
	  printf (" Parameter: %.20" PRINTF_EXPR "\n", parameter);
	}
      noErrors++;
    }

  fpstack_test (test_name);
}


static void
output_result (const char *test_name, int result,
	       MATHTYPE computed, MATHTYPE expected,
	       MATHTYPE difference,
	       int print_values, int print_diff)
{
  if (result)
    {
      if (verbose > 2)
	printf ("Pass: %s\n", test_name);
    }
  else
    {
      if (verbose)
	printf ("Fail: %s\n", test_name);
      if (verbose > 1 && print_values)
	{
	  printf ("Result:\n");
	  printf (" is:         %.20" PRINTF_EXPR "\n", computed);
	  printf (" should be:  %.20" PRINTF_EXPR "\n", expected);
	  if (print_diff)
	    printf (" difference: %.20" PRINTF_EXPR "\n", difference);
	}
      noErrors++;
    }

  fpstack_test (test_name);
}


static void
output_result_ext (const char *test_name, int result,
		   MATHTYPE computed, MATHTYPE expected,
		   MATHTYPE difference,
		   MATHTYPE parameter,
		   int print_values, int print_diff)
{
  if (result)
    {
      if (verbose > 2)
	printf ("Pass: %s\n", test_name);
    }
  else
    {
      if (verbose)
	printf ("Fail: %s\n", test_name);
      if (verbose > 1 && print_values)
	{
	  printf ("Result:\n");
	  printf (" is:         %.20" PRINTF_EXPR "\n", computed);
	  printf (" should be:  %.20" PRINTF_EXPR "\n", expected);
	  if (print_diff)
	    printf (" difference: %.20" PRINTF_EXPR "\n", difference);
	  printf ("Parameter:   %.20" PRINTF_EXPR "\n", parameter);
	}
      noErrors++;
    }

  fpstack_test (test_name);
}


static void
check (const char *test_name, MATHTYPE computed, MATHTYPE expected)
{
  MATHTYPE diff;
  int result;

  result = check_equal (computed, expected, 0, &diff);
  output_result (test_name, result,
		 computed, expected, diff, PRINT, PRINT);
}


static void
check_ext (const char *test_name, MATHTYPE computed, MATHTYPE expected,
	   MATHTYPE parameter)
{
  MATHTYPE diff;
  int result;

  result = check_equal (computed, expected, 0, &diff);
  output_result_ext (test_name, result,
		     computed, expected, diff, parameter, PRINT, PRINT);
}


static void
check_eps (const char *test_name, MATHTYPE computed, MATHTYPE expected,
	   MATHTYPE epsilon)
{
  MATHTYPE diff;
  int result;

  result = check_equal (computed, expected, epsilon, &diff);
  output_result (test_name, result,
		 computed, expected, diff, PRINT, PRINT);
}


static void
check_bool (const char *test_name, int computed)
{
  output_result_bool (test_name, computed);
}


static void
check_isnan (const char *test_name, MATHTYPE computed)
{
  output_isvalue (test_name, isnan (computed), computed);
}


static void
check_isnan_exc (const char *test_name, MATHTYPE computed,
		 short exception UNUSED)
{
  output_isvalue (test_name, isnan (computed), computed);
}


static void
check_isnan_ext (const char *test_name, MATHTYPE computed,
		 MATHTYPE parameter)
{
  output_isvalue_ext (test_name, isnan (computed), computed, parameter);
}


/* Tests if computed is +Inf */
static void
check_isinfp (const char *test_name, MATHTYPE computed)
{
  output_isvalue (test_name, (ISINF (computed) == +1), computed);
}


static void
check_isinfp_ext (const char *test_name, MATHTYPE computed,
		  MATHTYPE parameter)
{
  output_isvalue_ext (test_name, (ISINF (computed) == +1), computed, parameter);
}


/* Tests if computed is +Inf */
static void
check_isinfp_exc (const char *test_name, MATHTYPE computed,
		  int exception UNUSED)
{
  output_isvalue (test_name, (ISINF (computed) == +1), computed);
}

/* Tests if computed is -Inf */
static void
check_isinfn (const char *test_name, MATHTYPE computed)
{
  output_isvalue (test_name, (ISINF (computed) == -1), computed);
}


static void
check_isinfn_ext (const char *test_name, MATHTYPE computed,
		  MATHTYPE parameter)
{
  output_isvalue_ext (test_name, (ISINF (computed) == -1), computed, parameter);
}


/* Tests if computed is -Inf */
static void
check_isinfn_exc (const char *test_name, MATHTYPE computed,
		  int exception UNUSED)
{
  output_isvalue (test_name, (ISINF (computed) == -1), computed);
}


/****************************************************************************
  Test for single functions of libm
****************************************************************************/

static void
acos_test (void)
{
  MATHTYPE x;

  check ("acos (1) == 0", FUNC(acos) (1), 0);

  x = random_greater (1);
  check_isnan_exc ("acos (x) == NaN + invalid exception for |x| > 1",
		   FUNC(acos) (x),
		   INVALID_EXCEPTION);
}

static void
acosh_test (void)
{
  MATHTYPE x;

  check ("acosh(1) == 0", FUNC(acosh) (1), 0);
  check_isinfp ("acosh(+inf) == +inf", FUNC(acosh) (plus_infty));

  x = random_less (1);
  check_isnan_exc ("acosh(x) == NaN plus invalid exception if x < 1",
		   FUNC(acosh) (x), INVALID_EXCEPTION);
}


static void
asin_test (void)
{
  MATHTYPE x;
  check ("asin (0) == 0", FUNC(asin) (0), 0);

  x = random_greater (1);
  check_isnan_exc ("asin x == NaN + invalid exception for |x| > 1",
		   FUNC(asin) (x),
		   INVALID_EXCEPTION);
}

static void
asinh_test (void)
{

  check ("asinh(+0) == +0", FUNC(asinh) (0), 0);
  check ("asinh(-0) == -0", FUNC(asinh) (minus_zero), minus_zero);
}


static void
atan_test (void)
{
  check ("atan (0) == 0", FUNC(atan) (0), 0);
  check ("atan (-0) == -0", FUNC(atan) (minus_zero), minus_zero);

  check ("atan (+inf) == pi/2", FUNC(atan) (plus_infty), M_PI_2);
  check ("atan (-inf) == -pi/2", FUNC(atan) (minus_infty), -M_PI_2);

}

static void
atan2_test (void)
{
  MATHTYPE x;

  x = random_greater (0);
  check ("atan2 (0,x) == 0 for x > 0",
	 FUNC(atan2) (0, x), 0);
  x = random_greater (0);
  check ("atan2 (-0,x) == -0 for x > 0",
	 FUNC(atan2) (minus_zero, x), minus_zero);

  check ("atan2 (+0,+0) == +0", FUNC(atan2) (0, 0), 0);
  check ("atan2 (-0,+0) == -0", FUNC(atan2) (minus_zero, 0), minus_zero);

  x = -random_greater (0);
  check ("atan2 (+0,x) == +pi for x < 0", FUNC(atan2) (0, x), M_PI);

  x = -random_greater (0);
  check ("atan2 (-0,x) == -pi for x < 0", FUNC(atan2) (minus_zero, x), -M_PI);

  check ("atan2 (+0,-0) == +pi", FUNC(atan2) (0, minus_zero), M_PI);
  check ("atan2 (-0,-0) == -pi", FUNC(atan2) (minus_zero, minus_zero), -M_PI);

  x = random_greater (0);
  check ("atan2 (y,+0) == pi/2 for y > 0", FUNC(atan2) (x, 0), M_PI_2);

  x = random_greater (0);
  check ("atan2 (y,-0) == pi/2 for y > 0", FUNC(atan2) (x, minus_zero), M_PI_2);

  x = random_greater (0);
  check ("atan2 (y,-inf) == +pi for finite y > 0",
	 FUNC(atan2) (x, minus_infty), M_PI);

  x = -random_greater (0);
  check ("atan2 (y,-inf) == -pi for finite y < 0",
	 FUNC(atan2) (x, minus_infty), -M_PI);

  check ("atan2 (+inf,+inf) == +pi/4",
	 FUNC(atan2) (plus_infty, plus_infty), M_PI_4);

  check ("atan2 (-inf,+inf) == -pi/4",
	 FUNC(atan2) (minus_infty, plus_infty), -M_PI_4);

  check ("atan2 (+inf,-inf) == +3*pi/4",
	 FUNC(atan2) (plus_infty, minus_infty), 3 * M_PI_4);

  check ("atan2 (-inf,-inf) == -3*pi/4",
	 FUNC(atan2) (minus_infty, minus_infty), -3 * M_PI_4);
}


static void
atanh_test (void)
{

  check ("atanh(+0) == +0", FUNC(atanh) (0), 0);
  check ("atanh(-0) == -0", FUNC(atanh) (minus_zero), minus_zero);
  check_isinfp_exc ("atanh(+1) == +inf plus divide-by-zero exception",
		    FUNC(atanh) (1), DIVIDE_BY_ZERO_EXCEPTION);
  check_isinfn_exc ("atanh(-1) == -inf plus divide-by-zero exception",
		    FUNC(atanh) (-1), DIVIDE_BY_ZERO_EXCEPTION);
}


static void
cbrt_test (void)
{
  check ("cbrt (+0) == +0", FUNC(cbrt) (0.0), 0.0);
  check ("cbrt (-0) == -0", FUNC(cbrt) (minus_zero), minus_zero);

  check ("cbrt (8) == 2", FUNC(cbrt) (8), 2);
  check ("cbrt (-27) == -3", FUNC(cbrt) (-27.0), -3.0);
}


static void
ceil_test (void)
{
  check ("ceil (+0) == +0", FUNC(ceil) (0.0), 0.0);
  check ("ceil (-0) == -0", FUNC(ceil) (minus_zero), minus_zero);
  check_isinfp ("ceil (+inf) == +inf", FUNC(ceil) (plus_infty));
  check_isinfn ("ceil (-inf) == -inf", FUNC(ceil) (minus_infty));

  check ("ceil (pi) == 4", FUNC(ceil) (M_PI), 4.0);
  check ("ceil (-pi) == -3", FUNC(ceil) (-M_PI), -3.0);
}


static void
cos_test (void)
{

  check ("cos (+0) == 1", FUNC(cos) (0), 1);
  check ("cos (-0) == 1", FUNC(cos) (minus_zero), 1);
  check_isnan_exc ("cos (+inf) == NaN plus invalid exception",
		   FUNC(cos) (plus_infty),
		   INVALID_EXCEPTION);
  check_isnan_exc ("cos (-inf) == NaN plus invalid exception",
		   FUNC(cos) (minus_infty),
		   INVALID_EXCEPTION);

  check_eps ("cos (pi/3) == 0.5", FUNC(cos) (M_PI / 3.0),
	     0.5, CHOOSE (0, 1e-15L, 1e-7L));
  check_eps ("cos (pi/2) == 0.5", FUNC(cos) (M_PI_2),
	     0, CHOOSE (1e-19L, 1e-16L, 1e-7L));

}

static void
cosh_test (void)
{
  check ("cosh (+0) == 1", FUNC(cosh) (0), 1);
  check ("cosh (-0) == 1", FUNC(cosh) (minus_zero), 1);

  check_isinfp ("cosh (+inf) == +inf", FUNC(cosh) (plus_infty));
  check_isinfp ("cosh (-inf) == +inf", FUNC(cosh) (minus_infty));
}


static void
exp_test (void)
{
  check ("exp (+0) == 1", FUNC(exp) (0), 1);
  check ("exp (-0) == 1", FUNC(exp) (minus_zero), 1);

  check_isinfp ("exp (+inf) == +inf", FUNC(exp) (plus_infty));
  check ("exp (-inf) == 0", FUNC(exp) (minus_infty), 0);

  check ("exp (1) == e", FUNC(exp) (1), M_E);
}


#ifdef ISO_9X_IMPLEMENTED
static void
exp2_test (void)
{
  check ("exp2 (+0) == 1", FUNC(exp2) (0), 1);
  check ("exp2 (-0) == 1", FUNC(exp2) (minus_zero), 1);

  check_isinfp ("exp2 (+inf) == +inf", FUNC(exp2) (plus_infty));
  check ("exp2 (-inf) == 0", FUNC(exp2) (minus_infty), 0);
  check ("exp2 (10) == 1024", FUNC(exp2) (10), 1024);
}
#endif


static void
expm1_test (void)
{
  check ("expm1 (+0) == 0", FUNC(expm1) (0), 0);
  check ("expm1 (-0) == -0", FUNC(expm1) (minus_zero), minus_zero);

  check_isinfp ("expm1 (+inf) == +inf", FUNC(expm1) (plus_infty));
  check ("expm1 (-inf) == -1", FUNC(expm1) (minus_infty), -1);

  check ("expm1 (1) == e-1", FUNC(expm1) (1), M_E - 1.0);
}




static void
check_frexp (const char *test_name, MATHTYPE computed, MATHTYPE expected,
	     int comp_int, int exp_int)
{
  MATHTYPE diff;
  int result;

  result = (check_equal (computed, expected, 0, &diff)
	    && (comp_int == exp_int));

  if (result)
    {
      if (verbose > 2)
	printf ("Pass: %s\n", test_name);
    }
  else
    {
      if (verbose)
	printf ("Fail: %s\n", test_name);
      if (verbose > 1)
	{
	  printf ("Result:\n");
	  printf (" is:         %.20" PRINTF_EXPR " *2^%d\n", computed, comp_int);
	  printf (" should be:  %.20" PRINTF_EXPR " *2^%d\n", expected, exp_int);
	  printf (" difference: %.20" PRINTF_EXPR "\n", diff);
	}
      noErrors++;
    }
  fpstack_test (test_name);
  output_result (test_name, result,
		 computed, expected, diff, PRINT, PRINT);
}


static void
frexp_test (void)
{
  int x_int;
  MATHTYPE result;

  result = FUNC(frexp) (plus_infty, &x_int);
  check_isinfp ("frexp (+inf, expr) == +inf", result);

  result = FUNC(frexp) (minus_infty, &x_int);
  check_isinfn ("frexp (-inf, expr) == -inf", result);

  result = FUNC(frexp) (nan_value, &x_int);
  check_isnan ("frexp (Nan, expr) == NaN", result);

  result = FUNC(frexp) (0, &x_int);
  check_frexp ("frexp: +0 == 0 * 2^0", result, 0, x_int, 0);

  result = FUNC(frexp) (minus_zero, &x_int);
  check_frexp ("frexp: -0 == -0 * 2^0", result, minus_zero, x_int, 0);

  result = FUNC(frexp) (12.8L, &x_int);
  check_frexp ("frexp: 12.8 == 0.8 * 2^4", result, 0.8L, x_int, 4);

  result = FUNC(frexp) (-27.34L, &x_int);
  check_frexp ("frexp: -27.34 == -0.854375 * 2^5", result, -0.854375L, x_int, 5);

}


#if __GLIBC__ < 2 || (__GLIBC__ == 2 && __GLIBC_MINOR__ < 1)
/* All floating-point numbers can be put in one of these categories.  */
enum
{
  FP_NAN,
#define FP_NAN FP_NAN
  FP_INFINITE,
#define FP_INFINITE FP_INFINITE
  FP_ZERO,
#define FP_ZERO FP_ZERO
  FP_SUBNORMAL,
#define FP_SUBNORMAL FP_SUBNORMAL
  FP_NORMAL
#define FP_NORMAL FP_NORMAL
};
#endif


static void
fpclassify_test (void)
{
  MATHTYPE x;

  /* fpclassify is a macro, don't give it constants as parameter */
  check_bool ("fpclassify (NaN) == FP_NAN", fpclassify (nan_value) == FP_NAN);
  check_bool ("fpclassify (+inf) == FP_INFINITE",
	      fpclassify (plus_infty) == FP_INFINITE);
  check_bool ("fpclassify (-inf) == FP_INFINITE",
	      fpclassify (minus_infty) == FP_INFINITE);
  check_bool ("fpclassify (+0) == FP_ZERO",
	      fpclassify (plus_zero) == FP_ZERO);
  check_bool ("fpclassify (-0) == FP_ZERO",
	      fpclassify (minus_zero) == FP_ZERO);

  x = 1000.0;
  check_bool ("fpclassify (1000) == FP_NORMAL",
	      fpclassify (x) == FP_NORMAL);
}


static void
ldexp_test (void)
{
  check ("ldexp (0, 0) == 0", FUNC(ldexp) (0, 0), 0);

  check_isinfp ("ldexp (+inf, 1) == +inf", FUNC(ldexp) (plus_infty, 1));
  check_isinfn ("ldexp (-inf, 1) == -inf", FUNC(ldexp) (minus_infty, 1));
  check_isnan ("ldexp (NaN, 1) == NaN", FUNC(ldexp) (nan_value, 1));

  check ("ldexp (0.8, 4) == 12.8", FUNC(ldexp) (0.8L, 4), 12.8L);
  check ("ldexp (-0.854375, 5) == -27.34", FUNC(ldexp) (-0.854375L, 5), -27.34L);
}


static void
log_test (void)
{
  check_isinfn_exc ("log (+0) == -inf", FUNC(log) (0),
		    DIVIDE_BY_ZERO_EXCEPTION);
  check_isinfn_exc ("log (-0) == -inf", FUNC(log) (minus_zero),
		    DIVIDE_BY_ZERO_EXCEPTION);

  check ("log (1) == 0", FUNC(log) (1), 0);

  check_isnan_exc ("log (x) == NaN plus divide-by-zero exception if x < 0",
		   FUNC(log) (-1), INVALID_EXCEPTION);
  check_isinfp ("log (+inf) == +inf", FUNC(log) (plus_infty));

  check_eps ("log (e) == 1", FUNC(log) (M_E), 1, CHOOSE (0, 0, 9e-8L));
  check ("log (1/e) == -1", FUNC(log) (1.0 / M_E), -1);
  check ("log (2) == M_LN2", FUNC(log) (2), M_LN2);
  check ("log (10) == M_LN10", FUNC(log) (10), M_LN10);
}


static void
log10_test (void)
{
  check_isinfn_exc ("log10 (+0) == -inf", FUNC(log10) (0),
		    DIVIDE_BY_ZERO_EXCEPTION);
  check_isinfn_exc ("log10 (-0) == -inf", FUNC(log10) (minus_zero),
		    DIVIDE_BY_ZERO_EXCEPTION);

  check ("log10 (1) == +0", FUNC(log10) (1), 0);

  check_isnan_exc ("log10 (x) == NaN plus divide-by-zero exception if x < 0",
		   FUNC(log10) (-1), INVALID_EXCEPTION);

  check_isinfp ("log10 (+inf) == +inf", FUNC(log10) (plus_infty));

  check ("log10 (0.1) == -1", FUNC(log10) (0.1L), -1);
  check ("log10 (10) == 1", FUNC(log10) (10.0), 1);
  check ("log10 (100) == 2", FUNC(log10) (100.0), 2);
  check ("log10 (10000) == 4", FUNC(log10) (10000.0), 4);
  check_eps ("log10 (e) == M_LOG10E", FUNC(log10) (M_E), M_LOG10E,
	     CHOOSE (9e-20, 0, 9e-8));
}


static void
log1p_test (void)
{
  check ("log1p (+0) == +0", FUNC(log1p) (0), 0);
  check ("log1p (-0) == -0", FUNC(log1p) (minus_zero), minus_zero);

  check_isinfn_exc ("log1p (-1) == -inf", FUNC(log1p) (-1),
		    DIVIDE_BY_ZERO_EXCEPTION);
  check_isnan_exc ("log1p (x) == NaN plus divide-by-zero exception if x < -1",
		   FUNC(log1p) (-2), INVALID_EXCEPTION);

  check_isinfp ("log1p (+inf) == +inf", FUNC(log1p) (plus_infty));

  check ("log1p (e-1) == 1", FUNC(log1p) (M_E - 1.0), 1);

}


#ifdef ISO_9X_IMPLEMENTED
static void
log2_test (void)
{
  check_isinfn_exc ("log2 (+0) == -inf", FUNC(log2) (0),
		    DIVIDE_BY_ZERO_EXCEPTION);
  check_isinfn_exc ("log2 (-0) == -inf", FUNC(log2) (minus_zero),
		    DIVIDE_BY_ZERO_EXCEPTION);

  check ("log2 (1) == +0", FUNC(log2) (1), 0);

  check_isnan_exc ("log2 (x) == NaN plus divide-by-zero exception if x < 0",
		   FUNC(log2) (-1), INVALID_EXCEPTION);

  check_isinfp ("log2 (+inf) == +inf", FUNC(log2) (plus_infty));

  check ("log2 (e) == M_LOG2E", FUNC(log2) (M_E), M_LOG2E);
  check ("log2 (2) == 1", FUNC(log2) (2.0), 1);
  check ("log2 (16) == 4", FUNC(log2) (16.0), 4);
  check ("log2 (256) == 8", FUNC(log2) (256.0), 8);

}
#endif


static void
logb_test (void)
{
  check_isinfp ("logb (+inf) == +inf", FUNC(logb) (plus_infty));
  check_isinfp ("logb (-inf) == +inf", FUNC(logb) (minus_infty));

  check_isinfn_exc ("logb (+0) == -inf plus divide-by-zero exception",
		    FUNC(logb) (0), DIVIDE_BY_ZERO_EXCEPTION);

  check_isinfn_exc ("logb (-0) == -inf plus divide-by-zero exception",
		    FUNC(logb) (minus_zero), DIVIDE_BY_ZERO_EXCEPTION);

  check ("logb (1) == 0", FUNC(logb) (1), 0);
  check ("logb (e) == 1", FUNC(logb) (M_E), 1);
  check ("logb (1024) == 10", FUNC(logb) (1024), 10);
  check ("logb (-2000) == 10", FUNC(logb) (-2000), 10);

}


static void
modf_test (void)
{
  MATHTYPE result, intpart;

  result = FUNC(modf) (plus_infty, &intpart);
  check ("modf (+inf, &x) returns +0", result, 0);
  check_isinfp ("modf (+inf, &x) set x to +inf", intpart);

  result = FUNC(modf) (minus_infty, &intpart);
  check ("modf (-inf, &x) returns -0", result, minus_zero);
  check_isinfn ("modf (-inf, &x) sets x to -inf", intpart);

  result = FUNC(modf) (nan_value, &intpart);
  check_isnan ("modf (NaN, &x) returns NaN", result);
  check_isnan ("modf (-inf, &x) sets x to NaN", intpart);

  result = FUNC(modf) (0, &intpart);
  check ("modf (0, &x) returns 0", result, 0);
  check ("modf (0, &x) sets x to 0", intpart, 0);

  result = FUNC(modf) (minus_zero, &intpart);
  check ("modf (-0, &x) returns -0", result, minus_zero);
  check ("modf (-0, &x) sets x to -0", intpart, minus_zero);

  result = FUNC(modf) (2.5, &intpart);
  check ("modf (2.5, &x) returns 0.5", result, 0.5);
  check ("modf (2.5, &x) sets x to 2", intpart, 2);

  result = FUNC(modf) (-2.5, &intpart);
  check ("modf (-2.5, &x) returns -0.5", result, -0.5);
  check ("modf (-2.5, &x) sets x to -2", intpart, -2);

}


static void
sin_test (void)
{
  check ("sin (+0) == +0", FUNC(sin) (0), 0);
  check ("sin (-0) == -0", FUNC(sin) (minus_zero), minus_zero);
  check_isnan_exc ("sin (+inf) == NaN plus invalid exception",
		   FUNC(sin) (plus_infty),
		   INVALID_EXCEPTION);
  check_isnan_exc ("sin (-inf) == NaN plus invalid exception",
		   FUNC(sin) (minus_infty),
		   INVALID_EXCEPTION);

  check ("sin (pi/6) == 0.5", FUNC(sin) (M_PI / 6.0), 0.5);
  check ("sin (pi/2) == 1", FUNC(sin) (M_PI_2), 1);
}


static void
sinh_test (void)
{
  check ("sinh (+0) == +0", FUNC(sinh) (0), 0);
  check ("sinh (-0) == -0", FUNC(sinh) (minus_zero), minus_zero);

  check_isinfp ("sinh (+inf) == +inf", FUNC(sinh) (plus_infty));
  check_isinfn ("sinh (-inf) == -inf", FUNC(sinh) (minus_infty));
}


static void
tan_test (void)
{
  check ("tan (+0) == -0", FUNC(tan) (0), 0);
  check ("tan (-0) == -0", FUNC(tan) (minus_zero), minus_zero);
  check_isnan_exc ("tan (+inf) == NaN plus invalid exception",
		   FUNC(tan) (plus_infty), INVALID_EXCEPTION);
  check_isnan_exc ("tan (-inf) == NaN plus invalid exception",
		   FUNC(tan) (minus_infty), INVALID_EXCEPTION);

  check_eps ("tan (pi/4) == 1", FUNC(tan) (M_PI_4), 1, CHOOSE (0, 1e-15L, 0));
}


static void
tanh_test (void)
{
  check ("tanh (+0) == +0", FUNC(tanh) (0), 0);
  check ("tanh (-0) == -0", FUNC(tanh) (minus_zero), minus_zero);

  check ("tanh (+inf) == +1", FUNC(tanh) (plus_infty), 1);
  check ("tanh (-inf) == -1", FUNC(tanh) (minus_infty), -1);
}


static void
fabs_test (void)
{
  check ("fabs (+0) == +0", FUNC(fabs) (0), 0);
  check ("fabs (-0) == +0", FUNC(fabs) (minus_zero), 0);

  check_isinfp ("fabs (+inf) == +inf", FUNC(fabs) (plus_infty));
  check_isinfp ("fabs (-inf) == +inf", FUNC(fabs) (minus_infty));

  check ("fabs (+38) == 38", FUNC(fabs) (38.0), 38.0);
  check ("fabs (-e) == e", FUNC(fabs) (-M_E), M_E);
}


static void
floor_test (void)
{
  check ("floor (+0) == +0", FUNC(floor) (0.0), 0.0);
  check ("floor (-0) == -0", FUNC(floor) (minus_zero), minus_zero);
  check_isinfp ("floor (+inf) == +inf", FUNC(floor) (plus_infty));
  check_isinfn ("floor (-inf) == -inf", FUNC(floor) (minus_infty));

  check ("floor (pi) == 3", FUNC(floor) (M_PI), 3.0);
  check ("floor (-pi) == -4", FUNC(floor) (-M_PI), -4.0);
}


static void
hypot_test (void)
{
  MATHTYPE a;

  a = random_greater (0);
  check_isinfp_ext ("hypot (+inf, x) == +inf", FUNC(hypot) (plus_infty, a), a);
  check_isinfp_ext ("hypot (-inf, x) == +inf", FUNC(hypot) (minus_infty, a), a);

  check_isnan ("hypot (NaN, NaN) == NaN", FUNC(hypot) (nan_value, nan_value));

  a = FUNC(hypot) (12.4L, 0.7L);
  check ("hypot (x,y) == hypot (y,x)", FUNC(hypot) (0.7L, 12.4L), a);
  check ("hypot (x,y) == hypot (-x,y)", FUNC(hypot) (-12.4L, 0.7L), a);
  check ("hypot (x,y) == hypot (-y,x)", FUNC(hypot) (-0.7L, 12.4L), a);
  check ("hypot (x,y) == hypot (-x,-y)", FUNC(hypot) (-12.4L, -0.7L), a);
  check ("hypot (x,y) == hypot (-y,-x)", FUNC(hypot) (-0.7L, -12.4L), a);
  check ("hypot (x,0) == fabs (x)", FUNC(hypot) (-0.7L, 0), 0.7L);
  check ("hypot (x,0) == fabs (x)", FUNC(hypot) (0.7L, 0), 0.7L);
  check ("hypot (x,0) == fabs (x)", FUNC(hypot) (-1.0L, 0), 1.0L);
  check ("hypot (x,0) == fabs (x)", FUNC(hypot) (1.0L, 0), 1.0L);
  check ("hypot (x,0) == fabs (x)", FUNC(hypot) (-5.7e7L, 0), 5.7e7L);
  check ("hypot (x,0) == fabs (x)", FUNC(hypot) (5.7e7L, 0), 5.7e7L);
}


static void
pow_test (void)
{
  MATHTYPE x;

  check ("pow (+0, +0) == 1", FUNC(pow) (0, 0), 1);
  check ("pow (+0, -0) == 1", FUNC(pow) (0, minus_zero), 1);
  check ("pow (-0, +0) == 1", FUNC(pow) (minus_zero, 0), 1);
  check ("pow (-0, -0) == 1", FUNC(pow) (minus_zero, minus_zero), 1);

  check ("pow (+10, +0) == 1", FUNC(pow) (10, 0), 1);
  check ("pow (+10, -0) == 1", FUNC(pow) (10, minus_zero), 1);
  check ("pow (-10, +0) == 1", FUNC(pow) (-10, 0), 1);
  check ("pow (-10, -0) == 1", FUNC(pow) (-10, minus_zero), 1);

  check ("pow (NaN, +0) == 1", FUNC(pow) (nan_value, 0), 1);
  check ("pow (NaN, -0) == 1", FUNC(pow) (nan_value, minus_zero), 1);

  check_isinfp ("pow (+1.1, +inf) == +inf", FUNC(pow) (1.1, plus_infty));
  check_isinfp ("pow (+inf, +inf) == +inf", FUNC(pow) (plus_infty, plus_infty));
  check_isinfp ("pow (-1.1, +inf) == +inf", FUNC(pow) (-1.1, plus_infty));
  check_isinfp ("pow (-inf, +inf) == +inf", FUNC(pow) (minus_infty, plus_infty));

  check ("pow (0.9, +inf) == +0", FUNC(pow) (0.9L, plus_infty), 0);
  check ("pow (1e-7, +inf) == +0", FUNC(pow) (1e-7L, plus_infty), 0);
  check ("pow (-0.9, +inf) == +0", FUNC(pow) (-0.9L, plus_infty), 0);
  check ("pow (-1e-7, +inf) == +0", FUNC(pow) (-1e-7L, plus_infty), 0);

  check ("pow (+1.1, -inf) == +inf", FUNC(pow) (1.1, minus_infty), 0);
  check ("pow (+inf, -inf) == +inf", FUNC(pow) (plus_infty, minus_infty), 0);
  check ("pow (-1.1, -inf) == +inf", FUNC(pow) (-1.1, minus_infty), 0);
  check ("pow (-inf, -inf) == +inf", FUNC(pow) (minus_infty, minus_infty), 0);

  check_isinfp ("pow (0.9, -inf) == +0", FUNC(pow) (0.9L, minus_infty));
  check_isinfp ("pow (1e-7, -inf) == +0", FUNC(pow) (1e-7L, minus_infty));
  check_isinfp ("pow (-0.9, -inf) == +0", FUNC(pow) (-0.9L, minus_infty));
  check_isinfp ("pow (-1e-7, -inf) == +0", FUNC(pow) (-1e-7L, minus_infty));

  check_isinfp ("pow (+inf, 1e-7) == +inf", FUNC(pow) (plus_infty, 1e-7L));
  check_isinfp ("pow (+inf, 1) == +inf", FUNC(pow) (plus_infty, 1));
  check_isinfp ("pow (+inf, 1e7) == +inf", FUNC(pow) (plus_infty, 1e7L));

  check ("pow (+inf, -1e-7) == 0", FUNC(pow) (plus_infty, -1e-7L), 0);
  check ("pow (+inf, -1) == 0", FUNC(pow) (plus_infty, -1), 0);
  check ("pow (+inf, -1e7) == 0", FUNC(pow) (plus_infty, -1e7L), 0);

  check_isinfn ("pow (-inf, 1) == -inf", FUNC(pow) (minus_infty, 1));
  check_isinfn ("pow (-inf, 11) == -inf", FUNC(pow) (minus_infty, 11));
  check_isinfn ("pow (-inf, 1001) == -inf", FUNC(pow) (minus_infty, 1001));

  check_isinfp ("pow (-inf, 2) == +inf", FUNC(pow) (minus_infty, 2));
  check_isinfp ("pow (-inf, 12) == +inf", FUNC(pow) (minus_infty, 12));
  check_isinfp ("pow (-inf, 1002) == +inf", FUNC(pow) (minus_infty, 1002));
  check_isinfp ("pow (-inf, 0.1) == +inf", FUNC(pow) (minus_infty, 0.1));
  check_isinfp ("pow (-inf, 1.1) == +inf", FUNC(pow) (minus_infty, 1.1));
  check_isinfp ("pow (-inf, 11.1) == +inf", FUNC(pow) (minus_infty, 11.1));
  check_isinfp ("pow (-inf, 1001.1) == +inf", FUNC(pow) (minus_infty, 1001.1));

  check ("pow (-inf, -1) == -0", FUNC(pow) (minus_infty, -1), minus_zero);
  check ("pow (-inf, -11) == -0", FUNC(pow) (minus_infty, -11), minus_zero);
  check ("pow (-inf, -1001) == -0", FUNC(pow) (minus_infty, -1001), minus_zero);

  check ("pow (-inf, -2) == +0", FUNC(pow) (minus_infty, -2), 0);
  check ("pow (-inf, -12) == +0", FUNC(pow) (minus_infty, -12), 0);
  check ("pow (-inf, -1002) == +0", FUNC(pow) (minus_infty, -1002), 0);
  check ("pow (-inf, -0.1) == +0", FUNC(pow) (minus_infty, -0.1), 0);
  check ("pow (-inf, -1.1) == +0", FUNC(pow) (minus_infty, -1.1), 0);
  check ("pow (-inf, -11.1) == +0", FUNC(pow) (minus_infty, -11.1), 0);
  check ("pow (-inf, -1001.1) == +0", FUNC(pow) (minus_infty, -1001.1), 0);

  check_isnan ("pow (NaN, NaN) == NaN", FUNC(pow) (nan_value, nan_value));
  check_isnan ("pow (0, NaN) == NaN", FUNC(pow) (0, nan_value));
  check_isnan ("pow (1, NaN) == NaN", FUNC(pow) (1, nan_value));
  check_isnan ("pow (-1, NaN) == NaN", FUNC(pow) (-1, nan_value));
  check_isnan ("pow (NaN, 1) == NaN", FUNC(pow) (nan_value, 1));
  check_isnan ("pow (NaN, -1) == NaN", FUNC(pow) (nan_value, -1));

  x = random_greater (0.0);
  check_isnan_ext ("pow (x, NaN) == NaN", FUNC(pow) (x, nan_value), x);

  check_isnan_exc ("pow (+1, +inf) == NaN", FUNC(pow) (1, plus_infty),
		   INVALID_EXCEPTION);
  check_isnan_exc ("pow (-1, +inf) == NaN", FUNC(pow) (1, plus_infty),
		   INVALID_EXCEPTION);
  check_isnan_exc ("pow (+1, -inf) == NaN", FUNC(pow) (1, plus_infty),
		   INVALID_EXCEPTION);
  check_isnan_exc ("pow (-1, -inf) == NaN", FUNC(pow) (1, plus_infty),
		   INVALID_EXCEPTION);

  check_isnan_exc ("pow (-0.1, 1.1) == NaN", FUNC(pow) (-0.1, 1.1),
		   INVALID_EXCEPTION);
  check_isnan_exc ("pow (-0.1, -1.1) == NaN", FUNC(pow) (-0.1, -1.1),
		   INVALID_EXCEPTION);
  check_isnan_exc ("pow (-10.1, 1.1) == NaN", FUNC(pow) (-10.1, 1.1),
		   INVALID_EXCEPTION);
  check_isnan_exc ("pow (-10.1, -1.1) == NaN", FUNC(pow) (-10.1, -1.1),
		   INVALID_EXCEPTION);

  check_isinfp_exc ("pow (+0, -1) == +inf", FUNC(pow) (0, -1),
		    DIVIDE_BY_ZERO_EXCEPTION);
  check_isinfp_exc ("pow (+0, -11) == +inf", FUNC(pow) (0, -11),
		    DIVIDE_BY_ZERO_EXCEPTION);
  check_isinfn_exc ("pow (-0, -1) == -inf", FUNC(pow) (minus_zero, -1),
		    DIVIDE_BY_ZERO_EXCEPTION);
  check_isinfn_exc ("pow (-0, -11) == -inf", FUNC(pow) (minus_zero, -11),
		    DIVIDE_BY_ZERO_EXCEPTION);

  check_isinfp_exc ("pow (+0, -2) == +inf", FUNC(pow) (0, -2),
		    DIVIDE_BY_ZERO_EXCEPTION);
  check_isinfp_exc ("pow (+0, -11.1) == +inf", FUNC(pow) (0, -11.1),
		    DIVIDE_BY_ZERO_EXCEPTION);
  check_isinfp_exc ("pow (-0, -2) == +inf", FUNC(pow) (minus_zero, -2),
		    DIVIDE_BY_ZERO_EXCEPTION);
  check_isinfp_exc ("pow (-0, -11.1) == +inf", FUNC(pow) (minus_zero, -11.1),
		    DIVIDE_BY_ZERO_EXCEPTION);

  check ("pow (+0, 1) == +0", FUNC(pow) (0, 1), 0);
  check ("pow (+0, 11) == +0", FUNC(pow) (0, 11), 0);
  check ("pow (-0, 1) == -0", FUNC(pow) (minus_zero, 1), minus_zero);
  check ("pow (-0, 11) == -0", FUNC(pow) (minus_zero, 11), minus_zero);

  check ("pow (+0, 2) == +0", FUNC(pow) (0, 2), 0);
  check ("pow (+0, 11.1) == +0", FUNC(pow) (0, 11.1), 0);
  check ("pow (-0, 2) == +0", FUNC(pow) (minus_zero, 2), 0);
  check ("pow (-0, 11.1) == +0", FUNC(pow) (minus_zero, 11.1), 0);

  x = random_greater (0.0);
  check_isinfp_ext ("pow (x, +inf) == +inf for |x| > 1",
		    FUNC(pow) (x, plus_infty), x);

  x = random_value (-1.0, 1.0);
  check_ext ("pow (x, +inf) == +0 for |x| < 1",
	     FUNC(pow) (x, plus_infty), 0.0, x);

  x = random_greater (0.0);
  check_ext ("pow (x, -inf) == +0 for |x| > 1",
	     FUNC(pow) (x, minus_infty), 0.0, x);

  x = random_value (-1.0, 1.0);
  check_isinfp_ext ("pow (x, -inf) == +inf for |x| < 1",
		    FUNC(pow) (x, minus_infty), x);

  x = random_greater (0.0);
  check_isinfp_ext ("pow (+inf, y) == +inf for y > 0",
		    FUNC(pow) (plus_infty, x), x);

  x = random_less (0.0);
  check_ext ("pow (+inf, y) == +0 for y < 0",
	     FUNC(pow) (plus_infty, x), 0.0, x);

  x = (rand () % 1000000) * 2.0 + 1;	/* Get random odd integer > 0 */
  check_isinfn_ext ("pow (-inf, y) == -inf for y an odd integer > 0",
		    FUNC(pow) (minus_infty, x), x);

  x = ((rand () % 1000000) + 1) * 2.0;	/* Get random even integer > 1 */
  check_isinfp_ext ("pow (-inf, y) == +inf for y > 0 and not an odd integer",
		    FUNC(pow) (minus_infty, x), x);

  x = -((rand () % 1000000) * 2.0 + 1);	/* Get random odd integer < 0 */
  check_ext ("pow (-inf, y) == -0 for y an odd integer < 0",
	     FUNC(pow) (minus_infty, x), minus_zero, x);

  x = ((rand () % 1000000) + 1) * -2.0;	/* Get random even integer < 0 */
  check_ext ("pow (-inf, y) == 0 for y < 0 and not an odd integer",
	     FUNC(pow) (minus_infty, x), 0.0, x);

  x = (rand () % 1000000) * 2.0 + 1;	/* Get random odd integer > 0 */
  check_ext ("pow (+0, y) == +0 for y an odd integer > 0",
	     FUNC(pow) (0.0, x), 0.0, x);
  x = (rand () % 1000000) * 2.0 + 1;	/* Get random odd integer > 0 */
  check_ext ("pow (-0, y) == -0 for y an odd integer > 0",
	     FUNC(pow) (minus_zero, x), minus_zero, x);

  x = ((rand () % 1000000) + 1) * 2.0;	/* Get random even integer > 1 */
  check_ext ("pow (+0, y) == +0 for y > 0 and not an odd integer",
	     FUNC(pow) (0.0, x), 0.0, x);

  x = ((rand () % 1000000) + 1) * 2.0;	/* Get random even integer > 1 */
  check_ext ("pow (-0, y) == +0 for y > 0 and not an odd integer",
	     FUNC(pow) (minus_zero, x), 0.0, x);
}


static void
inverse_func_pair_test (const char *test_name,
			mathfunc f1, mathfunc inverse,
			MATHTYPE x, MATHTYPE epsilon)
{
  MATHTYPE a, b, difference;
  int result;

  a = f1 (x);
  this_does_nothing ();
  b = inverse (a);
  this_does_nothing ();

  result = check_equal (b, x, epsilon, &difference);
  output_result (test_name, result,
		 b, x, difference, PRINT, PRINT);
}


static void
inverse_functions (void)
{
  inverse_func_pair_test ("(asin(sin(x)) == x",
			FUNC(sin), FUNC(asin), 1.0, CHOOSE (0, 0, 1e-7L));
  inverse_func_pair_test ("(sin(asin(x)) == x",
			  FUNC(asin), FUNC(sin), 1.0, 0.0);

  inverse_func_pair_test ("(acos(cos(x)) == x",
		       FUNC(cos), FUNC(acos), 1.0, CHOOSE (0, 1e-15L, 0));
  inverse_func_pair_test ("(cos(acos(x)) == x",
			  FUNC(acos), FUNC(cos), 1.0, 0.0);
  inverse_func_pair_test ("(atan(tan(x)) == x",
			  FUNC(tan), FUNC(atan), 1.0, 0.0);
  inverse_func_pair_test ("(tan(atan(x)) == x",
		       FUNC(atan), FUNC(tan), 1.0, CHOOSE (0, 1e-15L, 0));

  inverse_func_pair_test ("(asinh(sinh(x)) == x",
		     FUNC(sinh), FUNC(asinh), 1.0, CHOOSE (1e-18L, 0, 0));
  inverse_func_pair_test ("(sinh(asinh(x)) == x",
			  FUNC(asinh), FUNC(sinh), 1.0, 0.0);

  inverse_func_pair_test ("(acosh(cosh(x)) == x",
		FUNC(cosh), FUNC(acosh), 1.0, CHOOSE (1e-18L, 1e-15L, 0));
  inverse_func_pair_test ("(cosh(acosh(x)) == x",
			  FUNC(acosh), FUNC(cosh), 1.0, 0.0);

  inverse_func_pair_test ("(atanh(tanh(x)) == x",
		     FUNC(tanh), FUNC(atanh), 1.0, CHOOSE (0, 1e-15L, 0));
  inverse_func_pair_test ("(tanh(atanh(x)) == x",
			  FUNC(atanh), FUNC(tanh), 1.0, 0.0);

}

/* Test sin and cos with the identity: sin(x)^2 + cos(x)^2 = 1.  */
static void
identities1_test (MATHTYPE x, MATHTYPE epsilon)
{
  MATHTYPE res1, res2, res3, diff;
  int result;

  res1 = FUNC(sin) (x);
  this_does_nothing ();
  res2 = FUNC(cos) (x);
  this_does_nothing ();
  res3 = res1 * res1 + res2 * res2;
  this_does_nothing ();

  result = check_equal (res3, 1.0, epsilon, &diff);
  output_result_ext ("sin^2 + cos^2 == 1", result,
		     res3, 1.0, diff, x, PRINT, PRINT);
}


/* Test sin, cos, tan with the following relation: tan = sin/cos.  */
static void
identities2_test (MATHTYPE x, MATHTYPE epsilon)
{
  MATHTYPE res1, res2, res3, res4, diff;
  int result;

  res1 = FUNC(sin) (x);
  this_does_nothing ();
  res2 = FUNC(cos) (x);
  this_does_nothing ();
  res3 = FUNC(tan) (x);
  this_does_nothing ();
  res4 = res1 / res2;
  this_does_nothing ();

  result = check_equal (res4, res3, epsilon, &diff);
  output_result_ext ("sin/cos == tan", result,
		     res4, res3, diff, x, PRINT, PRINT);
}


/* Test cosh and sinh with the identity cosh^2 - sinh^2 = 1.  */
static void
identities3_test (MATHTYPE x, MATHTYPE epsilon)
{
  MATHTYPE res1, res2, res3, diff;
  int result;

  res1 = FUNC(sinh) (x);
  this_does_nothing ();
  res2 = FUNC(cosh) (x);
  this_does_nothing ();
  res3 = res2 * res2 - res1 * res1;
  this_does_nothing ();

  result = check_equal (res3, 1.0, epsilon, &diff);
  output_result_ext ("cosh^2 - sinh^2 == 1", result,
		     res3, 1.0, diff, x, PRINT, PRINT);
}


static void
identities (void)
{
  identities1_test (0.2L, CHOOSE (1e-19L, 0, 0));
  identities1_test (0.9L, 0);
  identities1_test (0, 0);
  identities1_test (-1, CHOOSE (0, 0, 1e-7));

  identities2_test (0.2L, CHOOSE (0, 1e-16, 0));
  identities2_test (0.9L, CHOOSE (0, 1e-15, 0));
  identities2_test (0, 0);
  identities2_test (-1, CHOOSE (1e-18L, 1e-15, 0));

  identities3_test (0.2L, CHOOSE (0, 0, 1e-7));
  identities3_test (0.9L, CHOOSE (1e-18L, 1e-15, 1e-6));
  identities3_test (0, CHOOSE (0, 0, 1e-6));
  identities3_test (-1, CHOOSE (1e-18L, 0, 1e-6));
}


/*
   Let's test that basic arithmetic is working
   tests: Infinity and NaN
 */
static void
basic_tests (void)
{
  /* variables are declared volatile to forbid some compiler
     optimizations */
  volatile MATHTYPE Inf_var, NaN_var, zero_var, one_var;
  MATHTYPE x1, x2;

  zero_var = 0.0;
  one_var = 1.0;
  NaN_var = nan_value;
  Inf_var = one_var / zero_var;

  this_does_nothing ();

  check_isinfp ("isinf (1/0) == +1", Inf_var);
  check_isinfn ("isinf (-1/0) == -1", -Inf_var);
  check_bool ("!isinf (1)", !(FUNC(isinf) (one_var)));
  check_bool ("!isinf (0/0)", !(FUNC(isinf) (NaN_var)));

  check_isnan ("isnan (0/0)", NaN_var);
  check_isnan ("isnan (-(0/0))", -NaN_var);
  check_bool ("!isnan (1)", !(FUNC(isnan) (one_var)));
  check_bool ("!isnan (0/0)", !(FUNC(isnan) (Inf_var)));

  check_bool ("inf == inf", Inf_var == Inf_var);
  check_bool ("-inf == -inf", -Inf_var == -Inf_var);
  check_bool ("inf != -inf", Inf_var != -Inf_var);
  check_bool ("NaN != NaN", NaN_var != NaN_var);

  /*
     the same tests but this time with NAN from <nan.h>
     NAN is a double const
   */
  check_bool ("isnan (NAN)", isnan (NAN));
  check_bool ("isnan (-NAN)", isnan (-NAN));
  check_bool ("!isinf (NAN)", !(isinf (NAN)));
  check_bool ("!isinf (-NAN)", !(isinf (-NAN)));
  check_bool ("NAN != NAN", NAN != NAN);

  /* test if EPSILON is ok */
  x1 = MATHCONST (1.0);
  x2 = x1 + CHOOSE (LDBL_EPSILON, DBL_EPSILON, FLT_EPSILON);
  check_bool ("1 != 1+EPSILON", x1 != x2);

  x1 = MATHCONST (1.0);
  x2 = x1 - CHOOSE (LDBL_EPSILON, DBL_EPSILON, FLT_EPSILON);
  check_bool ("1 != 1-EPSILON", x1 != x2);

  /* test if HUGE_VALx is ok */
  x1 = CHOOSE (HUGE_VALL, HUGE_VAL, HUGE_VALF);
  check_bool ("isinf (HUGE_VALx) == +1", ISINF (x1) == +1);
  x1 = -CHOOSE (HUGE_VALL, HUGE_VAL, HUGE_VALF);
  check_bool ("isinf (-HUGE_VALx) == -1", ISINF (x1) == -1);

}


static void
initialize (void)
{
  plus_zero = 0.0;
  nan_value = plus_zero / plus_zero;	/* Suppress GCC warning */

  minus_zero = copysign (0.0, -1.0);
  plus_infty = CHOOSE (HUGE_VALL, HUGE_VAL, HUGE_VALF);
  minus_infty = -CHOOSE (HUGE_VALL, HUGE_VAL, HUGE_VALF);

  /* Test to make sure we start correctly.  */
  fpstack_test ("*init*");
}


static struct option long_options[] =
{
  {"verbose", optional_argument, NULL, 'v'},
  {"silent", no_argument, NULL, 's'},
  {0, 0, 0, 0}
};


static void
parse_options (int argc, char *argv[])
{
  int c;
  int option_index;

  verbose = 1;

  while (1)
    {
      c = getopt_long (argc, argv, "vs",
		       long_options, &option_index);

      /* Detect the end of the options. */
      if (c == -1)
	break;

      switch (c)
	{
	case 'v':
	  if (optarg)
	    verbose = (unsigned int) strtoul (optarg, NULL, 0);
	  else
	    verbose = 3;
	  break;
	case 's':
	  verbose = 0;
	default:
	  break;
	}
    }
}


int
main (int argc, char *argv[])
{
  parse_options (argc, argv);

  initialize ();
  printf (TEST_MSG);
  basic_tests ();

  acos_test ();
  acosh_test ();
  asin_test ();
  asinh_test ();
  atan_test ();
  atanh_test ();
  atan2_test ();
  cbrt_test ();
  ceil_test ();
  cos_test ();
  cosh_test ();
  exp_test ();
#ifdef ISO_9X_IMPLEMENTED
  exp2_test ();
#endif
  expm1_test ();
  frexp_test ();
  ldexp_test ();
  log_test ();
  log10_test ();
  log1p_test ();
#ifdef ISO_9X_IMPLEMENTED
  log2_test ();
#endif
  logb_test ();
  modf_test ();
  sin_test ();
  sinh_test ();
  tan_test ();
  tanh_test ();
  fabs_test ();
  floor_test ();
  fpclassify_test ();
  hypot_test ();
  pow_test ();

  identities ();
  inverse_functions ();

  if (noErrors)
    {
      printf ("\n%d errors occured.\n", noErrors);
      exit (1);
    }
  printf ("\n All tests passed sucessfully.\n");
  exit (0);
}