Build most libm-test support code once per type.

libm-test-driver.c contains various functions used in the course of
libm testing, which are built as part of each test using this
machinery.

Currently, these functions get built for three tests for each type
(e.g. test-float, test-ifloat, test-float-finite), plus the vector
function tests.  All these tests are huge and thus slow to build; the
output of gen-libm-test.pl totals around 40 MB across all functions.
To make the individual tests built from the Makefile smaller, it makes
sense to split these tests up so the tests for each function are built
separately (thus, three tests for each (function, type) pair, plus
vector tests built only for functions that actually have vector
versions).  This improves parallelism and means that if tests fail,
the summary of failed tests makes it more obvious where the problem
might be without needing to look in the .out files to see which
functions' tests failed (though architecture maintainers still need to
keep libm-test-ulps up to date to avoid spurious failures of little
interest).

Simply including libm-test-driver.c as-is in such individual-function
tests does not work because of unused static check_* functions (those
functions only being used for the types of the outputs of the function
under test).  It also means the common code gets built over 1000 times
instead of nine (plus vector tests).  To avoid that issue, this patch
splits out the bulk of the libm-test-driver.c code into a separate
file libm-test-support.c (with a few functions made non-static).  That
separate file is built only once for each floating-point type (so at
present three times, or twice on architectures with long double =
double).  Definitions needed in both libm-test-support.c and
libm-test-driver.c go in libm-test-support.h (it's possible some of
those are in fact only needed in one of the two files).
libm-test-driver.c keeps definitions of a limited number of variables
used to configure how libm-test-support.c behaves, various macros and
structures needed by individual-function tests, and the main function.

This move is also consistent in spirit with the move away from
test-skeleton.c having all the test support code, to a small
support/test-driver.c included in individual tests with most of the
code built separately.

Tested for x86_64 and x86.

	* math/libm-test-support.c: New file.  Content from
	math/libm-test-driver.c.
	* math/libm-test-support.h: Likewise.
	* math/libm-test-support-double.c: New file.
	* math/libm-test-support-float.c: Likewise.
	* math/libm-test-support-ldouble.c: Likewise.
	* math/libm-test-driver.c: Remove main comment and header
	includes.  Include libm-test-support.h.
	[!_GNU_SOURCE] (_GNU_SOURCE): Do not define.
	(flag_test_errno): Remove static.
	(flag_test_exceptions): Likewise.
	(flag_test_finite): Likewise.
	(flag_test_inline): Likewise.
	(flag_test_mathvec): Likewise.
	(test_msg): Likewise.
	(NO_EXCEPTION): Remove.
	(INVALID_EXCEPTION): Likewise.
	(DIVIDE_BY_ZERO_EXCEPTION): Likewise.
	(OVERFLOW_EXCEPTION): Likewise.
	(UNDERFLOW_EXCEPTION): Likewise.
	(INEXACT_EXCEPTION): Likewise.
	(INVALID_EXCEPTION_OK): Likewise.
	(DIVIDE_BY_ZERO_EXCEPTION_OK): Likewise.
	(OVERFLOW_EXCEPTION_OK): Likewise.
	(UNDERFLOW_EXCEPTION_OK): Likewise.
	(NO_INEXACT_EXCEPTION): Likewise.
	(EXCEPTIONS_OK): Likewise.
	(IGNORE_ZERO_INF_SIGN): Likewise.
	(TEST_NAN_SIGN): Likewise.
	(TEST_NAN_PAYLOAD): Likewise.
	(NO_TEST_INLINE): Likewise.
	(XFAIL_TEST): Likewise.
	(ERRNO_UNCHANGED): Likewise.
	(ERRNO_EDOM): Likewise.
	(ERRNO_ERANGE): Likewise.
	(IGNORE_RESULT): Likewise.
	(NON_FINITE): Likewise.
	(TEST_SNAN): Likewise.
	(NO_TEST_MATHVEC): Likewise.
	(__CONCATX): Likewise.
	(TYPE_MIN): Likewise.
	(TYPE_TRUE_MIN): Likewise.
	(TYPE_MAX): Likewise.
	(MIN_EXP): Likewise.
	(MAX_EXP): Likewise.
	(MANT_DIG): Likewise.
	(FSTR_MAX): Likewise.
	(ulp_idx): Likewise.
	(qtype_str): Remove static.
	(TEST_COND_binary32): Remove.
	(TEST_COND_binary64): Likewise.
	(TEST_COND_binary128): Likewise.
	(TEST_COND_ibm128): Likewise.
	(TEST_COND_intel96): Likewise.
	(TEST_COND_m68k96): Likewise.
	(TEST_COND_ibm128_libgcc): Likewise.
	(XFAIL_IBM128_LIBGCC): Likewise.
	(PAYLOAD_DIG): Likewise.
	(UNDERFLOW_EXCEPTION_FLOAT): Likewise.
	(UNDERFLOW_EXCEPTION_OK_FLOAT): Likewise.
	(UNDERFLOW_EXCEPTION_DOUBLE): Likewise.
	(UNDERFLOW_EXCEPTION_OK_DOUBLE): Likewise.
	(UNDERFLOW_EXCEPTION_LDOUBLE_IBM): Likewise.
	(UNDERFLOW_EXCEPTION_BEFORE_ROUNDING): Likewise.
	(TEST_COND_long32): Likewise.
	(TEST_COND_long64): Likewise.
	(TEST_COND_before_rounding): Likewise.
	(TEST_COND_after_rounding): Likewise.
	(ulps_file_name): Likewise.
	(ulps_file): Likewise.
	(output_ulps): Likewise.
	(output_dir): Likewise.
	(noErrors): Likewise.
	(noTests): Likewise.
	(noExcTests): Likewise.
	(noErrnoTests): Likewise.
	(verbose): Likewise.
	(output_max_error): Likewise.
	(output_points): Likewise.
	(ignore_max_ulp): Likewise.
	(max_error): Likewise.
	(real_max_error): Likewise.
	(imag_max_error): Likewise.
	(prev_max_error): Likewise.
	(prev_real_max_error): Likewise.
	(prev_imag_max_error): Likewise.
	(max_valid_error): Likewise.
	(TYPE_DECIMAL_DIG): Likewise.
	(TYPE_HEX_DIG): Likewise.
	(fmt_ftostr): Likewise.
	(compare_ulp_data): Likewise.
	(find_ulps): Likewise.
	(init_max_error): Likewise.
	(set_max_error): Likewise.
	(print_float): Likewise.
	(print_screen): Likewise.
	(print_screen_max_error): Likewise.
	(update_stats): Likewise.
	(print_function_ulps): Likewise.
	(print_complex_function_ulps): Likewise.
	(fpstack_test): Likewise.
	(print_max_error): Likewise.
	(print_complex_max_error): Likewise.
	(test_single_exception): Likewise.
	(test_exceptions): Likewise.
	(test_single_errno): Likewise.
	(test_errno): Likewise.
	(ULPDIFF): Likewise.
	(ulp): Likewise.
	(check_float_internal): Likewise.
	(check_float): Likewise.
	(check_complex): Likewise.
	(check_int): Likewise.
	(check_long): Likewise.
	(check_bool): Likewise.
	(check_longlong): Likewise.
	(check_intmax_t): Likewise.
	(check_uintmax_t): Likewise.
	(enable_test): Likewise.
	(matherr): Likewise.
	(initialize): Likewise.
	(options): Likewise.
	(doc): Remove static.
	(argp): Likewise.
	(parse_opt): Remove.
	(check_ulp): Likewise.
	(libm_test_init): Likewise.
	(libm_test_finish): Likewise.
	* math/Makefile (libm-test-support): New variable.
	(test-extras): Add libm-test-support files.
	(extra-test-objs): Likewise.
	(CFLAGS-libm-test-support-float.c): New variable.
	(CFLAGS-libm-test-support-double.c): Likewise.
	(CFLAGS-libm-test-support-ldouble.c): Likewise.
	($(addprefix $(objpfx),$(libm-tests)): Depend on appropriate
	libm-test-support objects.

1 files changed, 1209 insertions, 0 deletions

diff --git a/math/libm-test-support.c b/math/libm-test-support.c
new file mode 100644
index 0000000000..d387f813d0
--- /dev/null
+++ b/math/libm-test-support.c
@@ -0,0 +1,1209 @@
+/* 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;
+}