On OpenBSD 5.1/SPARC64, the sqrtl() function returns values that have a
relative error > 50000000 ulp. Obviously unusable. Witness:
#include <math.h>
#include <stdio.h>
int main ()
{
volatile long double a = 8.1974099812331540680810141969554806865L;
volatile long double b = sqrtl (a);
volatile long double c = b * b;
printf ("%.36Lg\n%.36Lg\n%.36Lg\n%.36Lg\n", a, b, c, c-a);
return 0;
}
prints
8.1974099812331540680810141969554800813
2.863111940045861080044397012682076147
8.1974099812331744117149208728836063001
2.0343633906675928126218841258144957861e-14
Here's the workaround:
2012-03-13 Bruno Haible <br...@clisp.org>
sqrtl: Bypass broken implementation in OpenBSD 5.1/SPARC.
* lib/math.in.h (sqrtl): Replace it if REPLACE_SQRTL is 1.
* m4/sqrtl.m4 (gl_FUNC_SQRTL_WORKS): New macro.
(gl_FUNC_SQRTL): Invoke it. Set REPLACE_SQRTL to 1 if sqrtl() produces
too big rounding errors.
* m4/math_h.m4 (gl_MATH_H_DEFAULTS): Initialize REPLACE_SQRTL.
* modules/math (Makefile.am): Substitute REPLACE_SQRTL.
* modules/sqrtl (configure.ac): Consider REPLACE_SQRTL.
(Depends-on): Update conditions.
* tests/test-sqrtl.c (my_ldexpl): New function.
(main): Add test of a particular value.
* doc/posix-functions/sqrtl.texi: Mention the OpenBSD 5.1/SPARC bug.
--- doc/posix-functions/sqrtl.texi.orig Wed Mar 14 01:45:33 2012
+++ doc/posix-functions/sqrtl.texi Wed Mar 14 01:13:59 2012
@@ -17,6 +17,9 @@
@item
This function is not declared on some platforms:
MacOS X 10.3.
+@item
+This function produces very imprecise results on some platforms:
+OpenBSD 5.1/SPARC.
@end itemize
Portability problems not fixed by Gnulib:
--- lib/math.in.h.orig Wed Mar 14 01:45:33 2012
+++ lib/math.in.h Wed Mar 14 01:12:33 2012
@@ -1698,11 +1698,20 @@
#endif
#if @GNULIB_SQRTL@
-# if !@HAVE_SQRTL@ || !@HAVE_DECL_SQRTL@
-# undef sqrtl
+# if @REPLACE_SQRTL@
+# if !(defined __cplusplus && defined GNULIB_NAMESPACE)
+# undef sqrtl
+# define sqrtl rpl_sqrtl
+# endif
+_GL_FUNCDECL_RPL (sqrtl, long double, (long double x));
+_GL_CXXALIAS_RPL (sqrtl, long double, (long double x));
+# else
+# if !@HAVE_SQRTL@ || !@HAVE_DECL_SQRTL@
+# undef sqrtl
_GL_FUNCDECL_SYS (sqrtl, long double, (long double x));
-# endif
+# endif
_GL_CXXALIAS_SYS (sqrtl, long double, (long double x));
+# endif
_GL_CXXALIASWARN (sqrtl);
#elif defined GNULIB_POSIXCHECK
# undef sqrtl
--- m4/math_h.m4.orig Wed Mar 14 01:45:33 2012
+++ m4/math_h.m4 Wed Mar 14 01:13:01 2012
@@ -1,4 +1,4 @@
-# math_h.m4 serial 103
+# math_h.m4 serial 104
dnl Copyright (C) 2007-2012 Free Software Foundation, Inc.
dnl This file is free software; the Free Software Foundation
dnl gives unlimited permission to copy and/or distribute it,
@@ -295,6 +295,7 @@
REPLACE_ROUNDL=0; AC_SUBST([REPLACE_ROUNDL])
REPLACE_SIGNBIT=0; AC_SUBST([REPLACE_SIGNBIT])
REPLACE_SIGNBIT_USING_GCC=0; AC_SUBST([REPLACE_SIGNBIT_USING_GCC])
+ REPLACE_SQRTL=0; AC_SUBST([REPLACE_SQRTL])
REPLACE_TRUNC=0; AC_SUBST([REPLACE_TRUNC])
REPLACE_TRUNCF=0; AC_SUBST([REPLACE_TRUNCF])
REPLACE_TRUNCL=0; AC_SUBST([REPLACE_TRUNCL])
--- m4/sqrtl.m4.orig Wed Mar 14 01:45:33 2012
+++ m4/sqrtl.m4 Wed Mar 14 01:34:41 2012
@@ -1,4 +1,4 @@
-# sqrtl.m4 serial 7
+# sqrtl.m4 serial 8
dnl Copyright (C) 2010-2012 Free Software Foundation, Inc.
dnl This file is free software; the Free Software Foundation
dnl gives unlimited permission to copy and/or distribute it,
@@ -58,9 +58,20 @@
dnl Also check whether it's declared.
dnl MacOS X 10.3 has sqrtl() in libc but doesn't declare it in <math.h>.
AC_CHECK_DECL([sqrtl], , [HAVE_DECL_SQRTL=0], [[#include <math.h>]])
+
+ save_LIBS="$LIBS"
+ LIBS="$LIBS $SQRTL_LIBM"
+ gl_FUNC_SQRTL_WORKS
+ LIBS="$save_LIBS"
+ case "$gl_cv_func_sqrtl_works" in
+ *yes) ;;
+ *) REPLACE_SQRTL=1 ;;
+ esac
else
HAVE_DECL_SQRTL=0
HAVE_SQRTL=0
+ fi
+ if test $HAVE_SQRTL = 0 || test $REPLACE_SQRTL = 1; then
dnl Find libraries needed to link lib/sqrtl.c.
if test $HAVE_SAME_LONG_DOUBLE_AS_DOUBLE = 1; then
AC_REQUIRE([gl_FUNC_SQRT])
@@ -94,3 +105,56 @@
fi
AC_SUBST([SQRTL_LIBM])
])
+
+dnl Test whether sqrtl() works.
+dnl On OpenBSD 5.1/SPARC, sqrtl(8.1974099812331540680810141969554806865L) has
+dnl rounding errors that eat up the last 8 to 9 decimal digits.
+AC_DEFUN([gl_FUNC_SQRTL_WORKS],
+[
+ AC_REQUIRE([AC_PROG_CC])
+ AC_REQUIRE([AC_CANONICAL_HOST]) dnl for cross-compiles
+ AC_CACHE_CHECK([whether sqrtl works], [gl_cv_func_sqrtl_works],
+ [
+ AC_RUN_IFELSE(
+ [AC_LANG_SOURCE([[
+#include <float.h>
+#include <math.h>
+extern
+#ifdef __cplusplus
+"C"
+#endif
+long double sqrtl (long double);
+static long double
+my_ldexpl (long double x, int d)
+{
+ for (; d > 0; d--)
+ x *= 2.0L;
+ for (; d < 0; d++)
+ x *= 0.5L;
+ return x;
+}
+volatile long double x;
+volatile long double y;
+long double z;
+int main ()
+{
+ x = 8.1974099812331540680810141969554806865L;
+ y = sqrtl (x);
+ z = y * y - x;
+ z = my_ldexpl (z, LDBL_MANT_DIG);
+ if (z < 0)
+ z = - z;
+ if (z > 100.0L)
+ return 1;
+ return 0;
+}
+]])],
+ [gl_cv_func_sqrtl_works=yes],
+ [gl_cv_func_sqrtl_works=no],
+ [case "$host_os" in
+ osf*) gl_cv_func_sqrtl_works="guessing no";;
+ *) gl_cv_func_sqrtl_works="guessing yes";;
+ esac
+ ])
+ ])
+])
--- modules/math.orig Wed Mar 14 01:45:33 2012
+++ modules/math Wed Mar 14 01:13:28 2012
@@ -262,6 +262,7 @@
-e 's|@''REPLACE_ROUNDL''@|$(REPLACE_ROUNDL)|g' \
-e 's|@''REPLACE_SIGNBIT''@|$(REPLACE_SIGNBIT)|g' \
-e
's|@''REPLACE_SIGNBIT_USING_GCC''@|$(REPLACE_SIGNBIT_USING_GCC)|g' \
+ -e 's|@''REPLACE_SQRTL''@|$(REPLACE_SQRTL)|g' \
-e 's|@''REPLACE_TRUNC''@|$(REPLACE_TRUNC)|g' \
-e 's|@''REPLACE_TRUNCF''@|$(REPLACE_TRUNCF)|g' \
-e 's|@''REPLACE_TRUNCL''@|$(REPLACE_TRUNCL)|g' \
--- modules/sqrtl.orig Wed Mar 14 01:45:33 2012
+++ modules/sqrtl Wed Mar 14 01:15:15 2012
@@ -8,15 +8,15 @@
Depends-on:
math
extensions
-sqrt [test $HAVE_SQRTL = 0]
-float [test $HAVE_SQRTL = 0 && test $HAVE_SAME_LONG_DOUBLE_AS_DOUBLE
= 0]
-isnanl [test $HAVE_SQRTL = 0 && test $HAVE_SAME_LONG_DOUBLE_AS_DOUBLE
= 0]
-frexpl [test $HAVE_SQRTL = 0 && test $HAVE_SAME_LONG_DOUBLE_AS_DOUBLE
= 0]
-ldexpl [test $HAVE_SQRTL = 0 && test $HAVE_SAME_LONG_DOUBLE_AS_DOUBLE
= 0]
+sqrt [{ test $HAVE_SQRTL = 0 || test $REPLACE_SQRTL = 1; }]
+float [{ test $HAVE_SQRTL = 0 || test $REPLACE_SQRTL = 1; } && test
$HAVE_SAME_LONG_DOUBLE_AS_DOUBLE = 0]
+isnanl [{ test $HAVE_SQRTL = 0 || test $REPLACE_SQRTL = 1; } && test
$HAVE_SAME_LONG_DOUBLE_AS_DOUBLE = 0]
+frexpl [{ test $HAVE_SQRTL = 0 || test $REPLACE_SQRTL = 1; } && test
$HAVE_SAME_LONG_DOUBLE_AS_DOUBLE = 0]
+ldexpl [{ test $HAVE_SQRTL = 0 || test $REPLACE_SQRTL = 1; } && test
$HAVE_SAME_LONG_DOUBLE_AS_DOUBLE = 0]
configure.ac:
gl_FUNC_SQRTL
-if test $HAVE_SQRTL = 0; then
+if test $HAVE_SQRTL = 0 || test $REPLACE_SQRTL = 1; then
AC_LIBOBJ([sqrtl])
fi
gl_MATH_MODULE_INDICATOR([sqrtl])
--- tests/test-sqrtl.c.orig Wed Mar 14 01:45:33 2012
+++ tests/test-sqrtl.c Wed Mar 14 01:32:13 2012
@@ -35,6 +35,16 @@
#define RANDOM randoml
#include "test-sqrt.h"
+static long double
+my_ldexpl (long double x, int d)
+{
+ for (; d > 0; d--)
+ x *= 2.0L;
+ for (; d < 0; d++)
+ x *= 0.5L;
+ return x;
+}
+
int
main ()
{
@@ -47,6 +57,20 @@
y = sqrtl (x);
ASSERT (y >= 0.7745966692L && y <= 0.7745966693L);
+ /* Another particular value. */
+ {
+ long double z;
+ long double err;
+
+ x = 8.1974099812331540680810141969554806865L;
+ y = sqrtl (x);
+ z = y * y - x;
+ err = my_ldexpl (z, LDBL_MANT_DIG);
+ if (err < 0)
+ err = - err;
+ ASSERT (err <= 100.0L);
+ }
+
test_function ();
return 0;
