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-rw-r--r--math/libm-test-support.c1209
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diff --git a/math/libm-test-support.c b/math/libm-test-support.c
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+/* Support code for testing libm functions (compiled once per type).
+   Copyright (C) 1997-2017 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   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, see
+   <http://www.gnu.org/licenses/>.  */
+
+/* Part of testsuite for libm.
+
+   libm-test-support.c contains functions shared by tests of different
+   libm functions and types; it is compiled once per type.
+   libm-test-driver.c defines the main function, and various variables
+   that are used to configure the code in libm-test-support.c for
+   different types and for variants such as testing inline functions.
+
+   The tests of individual functions are in .inc files processed by
+   gen-libm-test.pl, with the resulting files included together with
+   libm-test-driver.c.
+
+   The per-type headers included both before libm-test-support.c and
+   for the tests of individual functions must define the following
+   macros:
+
+   FUNC(function): Convert general function name (like cos) to name
+   with correct suffix (e.g. cosl or cosf).
+
+   FLOAT: Floating-point type to test.
+
+   BUILD_COMPLEX(real, imag): Create a complex number by calling a
+   macro such as CMPLX.
+
+   PREFIX: The prefix for <float.h> macros for the type (e.g. LDBL,
+   DBL, or FLT).
+
+   TYPE_STR: The name of the type as used in ulps files, as a string.
+
+   LIT: Append the correct suffix to a literal.
+
+   LITM: Append the correct suffix to an M_* macro name.
+
+   FTOSTR: A function similar in type to strfromf which converts a
+   FLOAT to a string.
+
+   snan_value_MACRO: The macro such as SNAN for a signaling NaN for
+   the type.
+
+*/
+
+/* 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.
+
+   NaN values: The payload of NaNs is set in inputs for functions
+   where it is significant, and is examined in the outputs of some
+   functions.
+
+   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.  */
+
+#include "libm-test-support.h"
+
+#include <argp.h>
+#include <errno.h>
+#include <string.h>
+
+/* This header defines func_ulps, func_real_ulps and func_imag_ulps
+   arrays.  */
+#include "libm-test-ulps.h"
+
+/* Maximum character buffer to store a stringitized FLOAT value.  */
+#define FSTR_MAX (128)
+
+#define ulps_file_name "ULPs"	/* Name of the ULPs file.  */
+static FILE *ulps_file;		/* File to document difference.  */
+static int output_ulps;		/* Should ulps printed?  */
+static char *output_dir;	/* Directory where generated files will be written.  */
+
+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 noErrnoTests;/* number of tests for errno values */
+
+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 max_error, real_max_error, imag_max_error;
+
+static FLOAT prev_max_error, prev_real_max_error, prev_imag_max_error;
+
+static FLOAT max_valid_error;
+
+/* Sufficient numbers of digits to represent any floating-point value
+   unambiguously (for any choice of the number of bits in the first
+   hex digit, in the case of TYPE_HEX_DIG).  When used with printf
+   formats where the precision counts only digits after the point, 1
+   is subtracted from these values. */
+#define TYPE_DECIMAL_DIG __CONCATX (PREFIX, _DECIMAL_DIG)
+#define TYPE_HEX_DIG ((MANT_DIG + 6) / 4)
+
+/* Converts VALUE (a floating-point number) to string and writes it to DEST.
+   PRECISION specifies the number of fractional digits that should be printed.
+   CONVERSION is the conversion specifier, such as in printf, e.g. 'f' or 'a'.
+   The output is prepended with an empty space if VALUE is non-negative.  */
+static void
+fmt_ftostr (char *dest, size_t size, int precision, const char *conversion,
+	    FLOAT value)
+{
+  char format[64];
+  char *ptr_format;
+  int ret;
+
+  /* Generate the format string.  */
+  ptr_format = stpcpy (format, "%.");
+  ret = sprintf (ptr_format, "%d", precision);
+  ptr_format += ret;
+  ptr_format = stpcpy (ptr_format, conversion);
+
+  /* Add a space to the beginning of the output string, if the floating-point
+     number is non-negative.  This mimics the behavior of the space (' ') flag
+     in snprintf, which is not available on strfrom.  */
+  if (! signbit (value))
+    {
+      *dest = ' ';
+      dest++;
+      size--;
+    }
+
+  /* Call the float to string conversion function, e.g.: strfromd.  */
+  FTOSTR (dest, size, format, value);
+}
+
+/* Compare KEY (a string, with the name of a function) with ULP (a
+   pointer to a struct ulp_data structure), returning a value less
+   than, equal to or greater than zero for use in bsearch.  */
+
+static int
+compare_ulp_data (const void *key, const void *ulp)
+{
+  const char *keystr = key;
+  const struct ulp_data *ulpdat = ulp;
+  return strcmp (keystr, ulpdat->name);
+}
+
+static const int ulp_i_idx = __CONCATX (ULP_I_, PREFIX);
+static const int ulp_idx = __CONCATX (ULP_, PREFIX);
+
+/* Return the ulps for NAME in array DATA with NMEMB elements, or 0 if
+   no ulps listed.  */
+
+static FLOAT
+find_ulps (const char *name, const struct ulp_data *data, size_t nmemb)
+{
+  const struct ulp_data *entry = bsearch (name, data, nmemb, sizeof (*data),
+					  compare_ulp_data);
+  if (entry == NULL)
+    return 0;
+  else
+    return entry->max_ulp[(flag_test_inline ? ulp_i_idx : ulp_idx)];
+}
+
+void
+init_max_error (const char *name, int exact)
+{
+  max_error = 0;
+  real_max_error = 0;
+  imag_max_error = 0;
+  prev_max_error = find_ulps (name, func_ulps,
+			      sizeof (func_ulps) / sizeof (func_ulps[0]));
+  prev_real_max_error = find_ulps (name, func_real_ulps,
+				   (sizeof (func_real_ulps)
+				    / sizeof (func_real_ulps[0])));
+  prev_imag_max_error = find_ulps (name, func_imag_ulps,
+				   (sizeof (func_imag_ulps)
+				    / sizeof (func_imag_ulps[0])));
+#if TEST_COND_ibm128
+  /* The documented accuracy of IBM long double division is 3ulp (see
+     libgcc/config/rs6000/ibm-ldouble-format), so do not require
+     better accuracy for libm functions that are exactly defined for
+     other formats.  */
+  max_valid_error = exact ? 3 : 16;
+#else
+  max_valid_error = exact ? 0 : 9;
+#endif
+  prev_max_error = (prev_max_error <= max_valid_error
+		    ? prev_max_error
+		    : max_valid_error);
+  prev_real_max_error = (prev_real_max_error <= max_valid_error
+			 ? prev_real_max_error
+			 : max_valid_error);
+  prev_imag_max_error = (prev_imag_max_error <= max_valid_error
+			 ? prev_imag_max_error
+			 : max_valid_error);
+  feclearexcept (FE_ALL_EXCEPT);
+  errno = 0;
+}
+
+static void
+set_max_error (FLOAT current, FLOAT *curr_max_error)
+{
+  if (current > *curr_max_error && current <= max_valid_error)
+    *curr_max_error = current;
+}
+
+
+/* Print a FLOAT.  */
+static void
+print_float (FLOAT f)
+{
+  /* As printf doesn't differ between a sNaN and a qNaN, do this manually.  */
+  if (issignaling (f))
+    printf ("sNaN\n");
+  else if (isnan (f))
+    printf ("qNaN\n");
+  else
+    {
+      char fstrn[FSTR_MAX], fstrx[FSTR_MAX];
+      fmt_ftostr (fstrn, FSTR_MAX, TYPE_DECIMAL_DIG - 1, "e", f);
+      fmt_ftostr (fstrx, FSTR_MAX, TYPE_HEX_DIG - 1, "a", f);
+      printf ("%s  %s\n", fstrn, fstrx);
+    }
+}
+
+/* Should the message print to screen?  This depends on the verbose flag,
+   and the test status.  */
+static int
+print_screen (int ok)
+{
+  if (output_points
+      && (verbose > 1
+	  || (verbose == 1 && ok == 0)))
+    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)
+{
+  if (output_max_error
+      && (verbose > 1
+	  || ((verbose == 1) && (ok == 0))))
+    return 1;
+  return 0;
+}
+
+/* Update statistic counters.  */
+static void
+update_stats (int ok)
+{
+  ++noTests;
+  if (!ok)
+    ++noErrors;
+}
+
+static void
+print_function_ulps (const char *function_name, FLOAT ulp)
+{
+  if (output_ulps)
+    {
+      char ustrn[FSTR_MAX];
+      FTOSTR (ustrn, FSTR_MAX, "%.0f", FUNC (ceil) (ulp));
+      fprintf (ulps_file, "Function: \"%s\":\n", function_name);
+      fprintf (ulps_file, "%s: %s\n", qtype_str, ustrn);
+    }
+}
+
+
+static void
+print_complex_function_ulps (const char *function_name, FLOAT real_ulp,
+			     FLOAT imag_ulp)
+{
+  if (output_ulps)
+    {
+      char fstrn[FSTR_MAX];
+      if (real_ulp != 0.0)
+	{
+	  FTOSTR (fstrn, FSTR_MAX, "%.0f", FUNC (ceil) (real_ulp));
+	  fprintf (ulps_file, "Function: Real part of \"%s\":\n", function_name);
+	  fprintf (ulps_file, "%s: %s\n", qtype_str, fstrn);
+	}
+      if (imag_ulp != 0.0)
+	{
+	  FTOSTR (fstrn, FSTR_MAX, "%.0f", FUNC (ceil) (imag_ulp));
+	  fprintf (ulps_file, "Function: Imaginary part of \"%s\":\n", function_name);
+	  fprintf (ulps_file, "%s: %s\n", qtype_str, fstrn);
+	}
+
+
+    }
+}
+
+
+
+/* Test if Floating-Point stack hasn't changed */
+static void
+fpstack_test (const char *test_name)
+{
+#if defined (__i386__) || defined (__x86_64__)
+  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
+}
+
+
+void
+print_max_error (const char *func_name)
+{
+  int ok = 0;
+
+  if (max_error == 0.0 || (max_error <= prev_max_error && !ignore_max_ulp))
+    {
+      ok = 1;
+    }
+
+  if (!ok)
+    print_function_ulps (func_name, max_error);
+
+
+  if (print_screen_max_error (ok))
+    {
+      char mestr[FSTR_MAX], pmestr[FSTR_MAX];
+      FTOSTR (mestr, FSTR_MAX, "%.0f", FUNC (ceil) (max_error));
+      FTOSTR (pmestr, FSTR_MAX, "%.0f", FUNC (ceil) (prev_max_error));
+      printf ("Maximal error of `%s'\n", func_name);
+      printf (" is      : %s ulp\n", mestr);
+      printf (" accepted: %s ulp\n", pmestr);
+    }
+
+  update_stats (ok);
+}
+
+
+void
+print_complex_max_error (const char *func_name)
+{
+  int real_ok = 0, imag_ok = 0, ok;
+
+  if (real_max_error == 0
+      || (real_max_error <= prev_real_max_error && !ignore_max_ulp))
+    {
+      real_ok = 1;
+    }
+
+  if (imag_max_error == 0
+      || (imag_max_error <= prev_imag_max_error && !ignore_max_ulp))
+    {
+      imag_ok = 1;
+    }
+
+  ok = real_ok && imag_ok;
+
+  if (!ok)
+    print_complex_function_ulps (func_name,
+				 real_ok ? 0 : real_max_error,
+				 imag_ok ? 0 : imag_max_error);
+
+  if (print_screen_max_error (ok))
+    {
+      char rmestr[FSTR_MAX], prmestr[FSTR_MAX];
+      char imestr[FSTR_MAX], pimestr[FSTR_MAX];
+      FTOSTR (rmestr, FSTR_MAX, "%.0f", FUNC (ceil) (real_max_error));
+      FTOSTR (prmestr, FSTR_MAX, "%.0f", FUNC (ceil) (prev_real_max_error));
+      FTOSTR (imestr, FSTR_MAX, "%.0f", FUNC (ceil) (imag_max_error));
+      FTOSTR (pimestr, FSTR_MAX, "%.0f", FUNC (ceil) (prev_imag_max_error));
+      printf ("Maximal error of real part of: %s\n", func_name);
+      printf (" is      : %s ulp\n", rmestr);
+      printf (" accepted: %s ulp\n", prmestr);
+      printf ("Maximal error of imaginary part of: %s\n", func_name);
+      printf (" is      : %s ulp\n", imestr);
+      printf (" accepted: %s ulp\n", pimestr);
+    }
+
+  update_stats (ok);
+}
+
+
+#if FE_ALL_EXCEPT
+/* 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)
+{
+  int ok = 1;
+  if (exception & exc_flag)
+    {
+      if (fetestexcept (fe_flag))
+	{
+	  if (print_screen (1))
+	    printf ("Pass: %s: Exception \"%s\" set\n", test_name, flag_name);
+	}
+      else
+	{
+	  ok = 0;
+	  if (print_screen (0))
+	    printf ("Failure: %s: Exception \"%s\" not set\n",
+		    test_name, flag_name);
+	}
+    }
+  else
+    {
+      if (fetestexcept (fe_flag))
+	{
+	  ok = 0;
+	  if (print_screen (0))
+	    printf ("Failure: %s: Exception \"%s\" set\n",
+		    test_name, flag_name);
+	}
+      else
+	{
+	  if (print_screen (1))
+	    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)
+{
+  if (flag_test_exceptions && EXCEPTION_TESTS (FLOAT))
+    {
+      ++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
+#ifdef FE_OVERFLOW
+      if ((exception & OVERFLOW_EXCEPTION_OK) == 0)
+	test_single_exception (test_name, exception, OVERFLOW_EXCEPTION,
+			       FE_OVERFLOW, "Overflow");
+#endif
+      /* Spurious "underflow" and "inexact" exceptions are always
+	 allowed for IBM long double, in line with the underlying
+	 arithmetic.  */
+#ifdef FE_UNDERFLOW
+      if ((exception & UNDERFLOW_EXCEPTION_OK) == 0
+	  && !(TEST_COND_ibm128
+	       && (exception & UNDERFLOW_EXCEPTION) == 0))
+	test_single_exception (test_name, exception, UNDERFLOW_EXCEPTION,
+			       FE_UNDERFLOW, "Underflow");
+#endif
+#ifdef FE_INEXACT
+      if ((exception & (INEXACT_EXCEPTION | NO_INEXACT_EXCEPTION)) != 0
+	  && !(TEST_COND_ibm128
+	       && (exception & NO_INEXACT_EXCEPTION) != 0))
+	test_single_exception (test_name, exception, INEXACT_EXCEPTION,
+			       FE_INEXACT, "Inexact");
+#endif
+    }
+  feclearexcept (FE_ALL_EXCEPT);
+}
+
+/* Test whether errno for TEST_NAME, set to ERRNO_VALUE, has value
+   EXPECTED_VALUE (description EXPECTED_NAME).  */
+static void
+test_single_errno (const char *test_name, int errno_value,
+		   int expected_value, const char *expected_name)
+{
+  if (errno_value == expected_value)
+    {
+      if (print_screen (1))
+	printf ("Pass: %s: errno set to %d (%s)\n", test_name, errno_value,
+		expected_name);
+    }
+  else
+    {
+      ++noErrors;
+      if (print_screen (0))
+	printf ("Failure: %s: errno set to %d, expected %d (%s)\n",
+		test_name, errno_value, expected_value, expected_name);
+    }
+}
+
+/* Test whether errno (value ERRNO_VALUE) has been for TEST_NAME set
+   as required by EXCEPTIONS.  */
+static void
+test_errno (const char *test_name, int errno_value, int exceptions)
+{
+  if (flag_test_errno)
+    {
+      ++noErrnoTests;
+      if (exceptions & ERRNO_UNCHANGED)
+	test_single_errno (test_name, errno_value, 0, "unchanged");
+      if (exceptions & ERRNO_EDOM)
+	test_single_errno (test_name, errno_value, EDOM, "EDOM");
+      if (exceptions & ERRNO_ERANGE)
+	test_single_errno (test_name, errno_value, ERANGE, "ERANGE");
+    }
+}
+
+/* Returns the number of ulps that GIVEN is away from EXPECTED.  */
+#define ULPDIFF(given, expected) \
+	(FUNC(fabs) ((given) - (expected)) / ulp (expected))
+
+/* Returns the size of an ulp for VALUE.  */
+static FLOAT
+ulp (FLOAT value)
+{
+  FLOAT ulp;
+
+  switch (fpclassify (value))
+    {
+      case FP_ZERO:
+	/* We compute the distance to the next FP which is the same as the
+	   value of the smallest subnormal number. Previously we used
+	   2^-(MANT_DIG - 1) which is too large a value to be useful. Note that we
+	   can't use ilogb(0), since that isn't a valid thing to do. As a point
+	   of comparison Java's ulp returns the next normal value e.g.
+	   2^(1 - MAX_EXP) for ulp(0), but that is not what we want for
+	   glibc.  */
+	/* Fall through...  */
+      case FP_SUBNORMAL:
+        /* The next closest subnormal value is a constant distance away.  */
+	ulp = FUNC(ldexp) (1.0, MIN_EXP - MANT_DIG);
+	break;
+
+      case FP_NORMAL:
+	ulp = FUNC(ldexp) (1.0, FUNC(ilogb) (value) - MANT_DIG + 1);
+	break;
+
+      default:
+	/* It should never happen. */
+	abort ();
+	break;
+    }
+  return ulp;
+}
+
+static void
+check_float_internal (const char *test_name, FLOAT computed, FLOAT expected,
+		      int exceptions,
+		      FLOAT *curr_max_error, FLOAT max_ulp)
+{
+  int ok = 0;
+  int print_diff = 0;
+  FLOAT diff = 0;
+  FLOAT ulps = 0;
+  int errno_value = errno;
+
+  test_exceptions (test_name, exceptions);
+  test_errno (test_name, errno_value, exceptions);
+  if (exceptions & IGNORE_RESULT)
+    goto out;
+  if (issignaling (computed) && issignaling (expected))
+    {
+      if ((exceptions & TEST_NAN_SIGN) != 0
+	  && signbit (computed) != signbit (expected))
+	{
+	  ok = 0;
+	  printf ("signaling NaN has wrong sign.\n");
+	}
+      else if ((exceptions & TEST_NAN_PAYLOAD) != 0
+	       && (FUNC (getpayload) (&computed)
+		   != FUNC (getpayload) (&expected)))
+	{
+	  ok = 0;
+	  printf ("signaling NaN has wrong payload.\n");
+	}
+      else
+	ok = 1;
+    }
+  else if (issignaling (computed) || issignaling (expected))
+    ok = 0;
+  else if (isnan (computed) && isnan (expected))
+    {
+      if ((exceptions & TEST_NAN_SIGN) != 0
+	  && signbit (computed) != signbit (expected))
+	{
+	  ok = 0;
+	  printf ("quiet NaN has wrong sign.\n");
+	}
+      else if ((exceptions & TEST_NAN_PAYLOAD) != 0
+	       && (FUNC (getpayload) (&computed)
+		   != FUNC (getpayload) (&expected)))
+	{
+	  ok = 0;
+	  printf ("quiet NaN has wrong payload.\n");
+	}
+      else
+	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 calculate ULPs for infinities or any kind of NaNs.  */
+  else if (isinf (computed) || isnan (computed)
+	   || isinf (expected) || isnan (expected))
+    ok = 0;
+  else
+    {
+      diff = FUNC(fabs) (computed - expected);
+      ulps = ULPDIFF (computed, expected);
+      set_max_error (ulps, 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 (ulps <= max_ulp && !ignore_max_ulp)
+	ok = 1;
+      else
+	ok = 0;
+    }
+  if (print_screen (ok))
+    {
+      if (!ok)
+	printf ("Failure: ");
+      printf ("Test: %s\n", test_name);
+      printf ("Result:\n");
+      printf (" is:         ");
+      print_float (computed);
+      printf (" should be:  ");
+      print_float (expected);
+      if (print_diff)
+	{
+	  char dstrn[FSTR_MAX], dstrx[FSTR_MAX];
+	  char ustrn[FSTR_MAX], mustrn[FSTR_MAX];
+	  fmt_ftostr (dstrn, FSTR_MAX, TYPE_DECIMAL_DIG - 1, "e", diff);
+	  fmt_ftostr (dstrx, FSTR_MAX, TYPE_HEX_DIG - 1, "a", diff);
+	  fmt_ftostr (ustrn, FSTR_MAX, 4, "f", ulps);
+	  fmt_ftostr (mustrn, FSTR_MAX, 4, "f", max_ulp);
+	  printf (" difference: %s  %s\n", dstrn, dstrx);
+	  printf (" ulp       : %s\n", ustrn);
+	  printf (" max.ulp   : %s\n", mustrn);
+	}
+    }
+  update_stats (ok);
+
+ out:
+  fpstack_test (test_name);
+  errno = 0;
+}
+
+
+void
+check_float (const char *test_name, FLOAT computed, FLOAT expected,
+	     int exceptions)
+{
+  check_float_internal (test_name, computed, expected,
+			exceptions, &max_error, prev_max_error);
+}
+
+
+void
+check_complex (const char *test_name, __complex__ FLOAT computed,
+	       __complex__ FLOAT expected,
+	       int exception)
+{
+  FLOAT part_comp, part_exp;
+  char *str;
+
+  if (asprintf (&str, "Real part of: %s", test_name) == -1)
+    abort ();
+
+  part_comp = __real__ computed;
+  part_exp = __real__ expected;
+
+  check_float_internal (str, part_comp, part_exp,
+			exception, &real_max_error, prev_real_max_error);
+  free (str);
+
+  if (asprintf (&str, "Imaginary part of: %s", test_name) == -1)
+    abort ();
+
+  part_comp = __imag__ computed;
+  part_exp = __imag__ expected;
+
+  /* Don't check again for exceptions or errno, just pass through the
+     other relevant flags.  */
+  check_float_internal (str, part_comp, part_exp,
+			exception & (IGNORE_ZERO_INF_SIGN
+				     | TEST_NAN_SIGN
+				     | IGNORE_RESULT),
+			&imag_max_error, prev_imag_max_error);
+  free (str);
+}
+
+
+/* Check that computed and expected values are equal (int values).  */
+void
+check_int (const char *test_name, int computed, int expected,
+	   int exceptions)
+{
+  int ok = 0;
+  int errno_value = errno;
+
+  test_exceptions (test_name, exceptions);
+  test_errno (test_name, errno_value, exceptions);
+  if (exceptions & IGNORE_RESULT)
+    goto out;
+  noTests++;
+  if (computed == expected)
+    ok = 1;
+
+  if (print_screen (ok))
+    {
+      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);
+ out:
+  fpstack_test (test_name);
+  errno = 0;
+}
+
+
+/* Check that computed and expected values are equal (long int values).  */
+void
+check_long (const char *test_name, long int computed, long int expected,
+	    int exceptions)
+{
+  int ok = 0;
+  int errno_value = errno;
+
+  test_exceptions (test_name, exceptions);
+  test_errno (test_name, errno_value, exceptions);
+  if (exceptions & IGNORE_RESULT)
+    goto out;
+  noTests++;
+  if (computed == expected)
+    ok = 1;
+
+  if (print_screen (ok))
+    {
+      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);
+ out:
+  fpstack_test (test_name);
+  errno = 0;
+}
+
+
+/* Check that computed value is true/false.  */
+void
+check_bool (const char *test_name, int computed, int expected,
+	    int exceptions)
+{
+  int ok = 0;
+  int errno_value = errno;
+
+  test_exceptions (test_name, exceptions);
+  test_errno (test_name, errno_value, exceptions);
+  if (exceptions & IGNORE_RESULT)
+    goto out;
+  noTests++;
+  if ((computed == 0) == (expected == 0))
+    ok = 1;
+
+  if (print_screen (ok))
+    {
+      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);
+ out:
+  fpstack_test (test_name);
+  errno = 0;
+}
+
+
+/* check that computed and expected values are equal (long int values) */
+void
+check_longlong (const char *test_name, long long int computed,
+		long long int expected,
+		int exceptions)
+{
+  int ok = 0;
+  int errno_value = errno;
+
+  test_exceptions (test_name, exceptions);
+  test_errno (test_name, errno_value, exceptions);
+  if (exceptions & IGNORE_RESULT)
+    goto out;
+  noTests++;
+  if (computed == expected)
+    ok = 1;
+
+  if (print_screen (ok))
+    {
+      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);
+ out:
+  fpstack_test (test_name);
+  errno = 0;
+}
+
+
+/* Check that computed and expected values are equal (intmax_t values).  */
+void
+check_intmax_t (const char *test_name, intmax_t computed,
+		intmax_t expected, int exceptions)
+{
+  int ok = 0;
+  int errno_value = errno;
+
+  test_exceptions (test_name, exceptions);
+  test_errno (test_name, errno_value, exceptions);
+  if (exceptions & IGNORE_RESULT)
+    goto out;
+  noTests++;
+  if (computed == expected)
+    ok = 1;
+
+  if (print_screen (ok))
+    {
+      if (!ok)
+	printf ("Failure:");
+      printf ("Test: %s\n", test_name);
+      printf ("Result:\n");
+      printf (" is:         %jd\n", computed);
+      printf (" should be:  %jd\n", expected);
+    }
+
+  update_stats (ok);
+ out:
+  fpstack_test (test_name);
+  errno = 0;
+}
+
+
+/* Check that computed and expected values are equal (uintmax_t values).  */
+void
+check_uintmax_t (const char *test_name, uintmax_t computed,
+		 uintmax_t expected, int exceptions)
+{
+  int ok = 0;
+  int errno_value = errno;
+
+  test_exceptions (test_name, exceptions);
+  test_errno (test_name, errno_value, exceptions);
+  if (exceptions & IGNORE_RESULT)
+    goto out;
+  noTests++;
+  if (computed == expected)
+    ok = 1;
+
+  if (print_screen (ok))
+    {
+      if (!ok)
+	printf ("Failure:");
+      printf ("Test: %s\n", test_name);
+      printf ("Result:\n");
+      printf (" is:         %ju\n", computed);
+      printf (" should be:  %ju\n", expected);
+    }
+
+  update_stats (ok);
+ out:
+  fpstack_test (test_name);
+  errno = 0;
+}
+
+/* Return whether a test with flags EXCEPTIONS should be run.  */
+int
+enable_test (int exceptions)
+{
+  if (exceptions & XFAIL_TEST)
+    return 0;
+  if (flag_test_inline && (exceptions & NO_TEST_INLINE))
+    return 0;
+  if (flag_test_finite && (exceptions & NON_FINITE) != 0)
+    return 0;
+  if (!SNAN_TESTS (FLOAT) && (exceptions & TEST_SNAN) != 0)
+    return 0;
+  if (flag_test_mathvec && (exceptions & NO_TEST_MATHVEC) != 0)
+    return 0;
+
+  return 1;
+}
+
+/* This is to prevent messages from the SVID libm emulation.  */
+int
+matherr (struct exception *x __attribute__ ((unused)))
+{
+  return 1;
+}
+
+static void
+initialize (void)
+{
+  fpstack_test ("start *init*");
+
+  /* Clear all exceptions.  From now on we must not get random exceptions.  */
+  feclearexcept (FE_ALL_EXCEPT);
+  errno = 0;
+
+  /* Test to make sure we start correctly.  */
+  fpstack_test ("end *init*");
+}
+
+/* Definitions of arguments for argp functions.  */
+static const struct argp_option options[] =
+{
+  { "verbose", 'v', "NUMBER", 0, "Level of verbosity (0..3)"},
+  { "ulps-file", 'u', NULL, 0, "Output ulps to file ULPs"},
+  { "no-max-error", 'f', NULL, 0,
+    "Don't output maximal errors of functions"},
+  { "no-points", 'p', NULL, 0,
+    "Don't output results of functions invocations"},
+  { "ignore-max-ulp", 'i', "yes/no", 0,
+    "Ignore given maximal errors"},
+  { "output-dir", 'o', "DIR", 0,
+    "Directory where generated files will be placed"},
+  { NULL, 0, NULL, 0, NULL }
+};
+
+/* Prototype for option handler.  */
+static error_t parse_opt (int key, char *arg, struct argp_state *state);
+
+/* Data structure to communicate with argp functions.  */
+static struct argp argp =
+{
+  options, parse_opt, NULL, doc,
+};
+
+
+/* Handle program arguments.  */
+static error_t
+parse_opt (int key, char *arg, struct argp_state *state)
+{
+  switch (key)
+    {
+    case 'f':
+      output_max_error = 0;
+      break;
+    case 'i':
+      if (strcmp (arg, "yes") == 0)
+	ignore_max_ulp = 1;
+      else if (strcmp (arg, "no") == 0)
+	ignore_max_ulp = 0;
+      break;
+    case 'o':
+      output_dir = (char *) malloc (strlen (arg) + 1);
+      if (output_dir != NULL)
+	strcpy (output_dir, arg);
+      else
+        return errno;
+      break;
+    case 'p':
+      output_points = 0;
+      break;
+    case 'u':
+      output_ulps = 1;
+      break;
+    case 'v':
+      if (optarg)
+	verbose = (unsigned int) strtoul (optarg, NULL, 0);
+      else
+	verbose = 3;
+      break;
+    default:
+      return ARGP_ERR_UNKNOWN;
+    }
+  return 0;
+}
+
+/* Verify that our ulp () implementation is behaving as expected
+   or abort.  */
+static void
+check_ulp (void)
+{
+   FLOAT ulps, ulpx, value;
+   int i;
+   /* Check ulp of zero is a subnormal value...  */
+   ulps = ulp (0x0.0p0);
+   if (fpclassify (ulps) != FP_SUBNORMAL)
+     {
+       fprintf (stderr, "ulp (0x0.0p0) is not FP_SUBNORMAL!\n");
+       exit (EXIT_FAILURE);
+     }
+   /* Check that the ulp of one is a normal value... */
+   ulps = ulp (1.0L);
+   if (fpclassify (ulps) != FP_NORMAL)
+     {
+       fprintf (stderr, "ulp (1.0L) is not FP_NORMAL\n");
+       exit (EXIT_FAILURE);
+     }
+
+   /* Compute the next subnormal value using nextafter to validate ulp.
+      We allow +/- 1 ulp around the represented value.  */
+   value = FUNC(nextafter) (0, 1);
+   ulps = ULPDIFF (value, 0);
+   ulpx = ulp (1.0L);
+   if (ulps < (1.0L - ulpx) || ulps > (1.0L + ulpx))
+     {
+       fprintf (stderr, "Value outside of 1 +/- 1ulp.\n");
+       exit (EXIT_FAILURE);
+     }
+   /* Compute the nearest representable number from 10 towards 20.
+      The result is 10 + 1ulp.  We use this to check the ulp function.
+      We allow +/- 1 ulp around the represented value.  */
+   value = FUNC(nextafter) (10, 20);
+   ulps = ULPDIFF (value, 10);
+   ulpx = ulp (1.0L);
+   if (ulps < (1.0L - ulpx) || ulps > (1.0L + ulpx))
+     {
+       fprintf (stderr, "Value outside of 1 +/- 1ulp.\n");
+       exit (EXIT_FAILURE);
+     }
+   /* This gives one more ulp.  */
+   value = FUNC(nextafter) (value, 20);
+   ulps = ULPDIFF (value, 10);
+   ulpx = ulp (2.0L);
+   if (ulps < (2.0L - ulpx) || ulps > (2.0L + ulpx))
+     {
+       fprintf (stderr, "Value outside of 2 +/- 1ulp.\n");
+       exit (EXIT_FAILURE);
+     }
+   /* And now calculate 100 ulp.  */
+   for (i = 2; i < 100; i++)
+     value = FUNC(nextafter) (value, 20);
+   ulps = ULPDIFF (value, 10);
+   ulpx = ulp (100.0L);
+   if (ulps < (100.0L - ulpx) || ulps > (100.0L + ulpx))
+     {
+       fprintf (stderr, "Value outside of 100 +/- 1ulp.\n");
+       exit (EXIT_FAILURE);
+     }
+}
+
+/* Do all initialization for a test run with arguments given by ARGC
+   and ARGV.  */
+void
+libm_test_init (int argc, char **argv)
+{
+  int remaining;
+  char *ulps_file_path;
+  size_t dir_len = 0;
+
+  verbose = 1;
+  output_ulps = 0;
+  output_max_error = 1;
+  output_points = 1;
+  output_dir = NULL;
+  /* XXX set to 0 for releases.  */
+  ignore_max_ulp = 0;
+
+  /* Parse and process arguments.  */
+  argp_parse (&argp, argc, argv, 0, &remaining, NULL);
+
+  if (remaining != argc)
+    {
+      fprintf (stderr, "wrong number of arguments");
+      argp_help (&argp, stdout, ARGP_HELP_SEE, program_invocation_short_name);
+      exit (EXIT_FAILURE);
+    }
+
+  if (output_ulps)
+    {
+      if (output_dir != NULL)
+	dir_len = strlen (output_dir);
+      ulps_file_path = (char *) malloc (dir_len + strlen (ulps_file_name) + 1);
+      if (ulps_file_path == NULL)
+        {
+	  perror ("can't allocate path for `ULPs' file: ");
+	  exit (1);
+        }
+      sprintf (ulps_file_path, "%s%s", output_dir == NULL ? "" : output_dir, ulps_file_name);
+      ulps_file = fopen (ulps_file_path, "a");
+      if (ulps_file == NULL)
+	{
+	  perror ("can't open file `ULPs' for writing: ");
+	  exit (1);
+	}
+    }
+
+
+  initialize ();
+  fputs (test_msg, stdout);
+
+  INIT_ARCH_EXT;
+
+  check_ulp ();
+}
+
+/* Process the test results, returning the exit status.  */
+int
+libm_test_finish (void)
+{
+  if (output_ulps)
+    fclose (ulps_file);
+
+  printf ("\nTest suite completed:\n");
+  printf ("  %d test cases plus %d tests for exception flags and\n"
+	  "    %d tests for errno executed.\n",
+	  noTests, noExcTests, noErrnoTests);
+  if (noErrors)
+    {
+      printf ("  %d errors occurred.\n", noErrors);
+      return 1;
+    }
+  printf ("  All tests passed successfully.\n");
+
+  return 0;
+}