hypotl on OpenBSD 5.1/SPARC

[Bruno Haible]

> On OpenBSD 5.1/SPARC64, the sqrtl() function returns values that have a
> relative error > 50000000 ulp. Obviously unusable.

Likewise for the hypotl() function. Witness:

#include <math.h>
#include <stdio.h>
#include <float.h>
volatile long double x;
volatile long double y;
volatile long double z;
int main ()
{
  x = 2.5541394760659556563446062497337725156L;
  y = 7.7893454113437840832487794525518765265L;
  z = hypotl (x, y);
  long double err = (z * z - (x * x + y * y));
  int i;
  for (i = 1; i <= LDBL_MANT_DIG; i++)
    err = err * 2.0L;
  printf ("%.36Lf\n%.36Lf\n%.36Lf\n%Lg\n", x, y, z, err);
  return 0;
}

prints

2.554139476065955656344606249733772516
7.789345411343784083248779452551876527
8.197409981233154068081014187198178182
-1.66122e+09

So this is an error of ca. 200 million ulps! Here's the workaround:


2012-03-13  Bruno Haible  <address@hidden>

        hypotl: Bypass broken implementation in OpenBSD 5.1/SPARC.
        * m4/hypotl.m4 (gl_FUNC_HYPOTL_WORKS): New macro.
        (gl_FUNC_HYPOTL): Invoke it. If the function does not work, set
        REPLACE_HYPOTL to 1.
        * doc/posix-functions/hypotl.texi: Mention the OpenBSD 5.1/SPARC bug.

--- doc/posix-functions/hypotl.texi.orig        Wed Mar 14 03:23:54 2012
+++ doc/posix-functions/hypotl.texi     Wed Mar 14 02:58:39 2012
@@ -11,6 +11,9 @@
 @item
 This function is missing on some platforms:
 FreeBSD 6.0, NetBSD 5.0, OpenBSD 3.8, Minix 3.1.8, AIX 5.1, HP-UX 11, IRIX 
6.5, Solaris 9, Cygwin, MSVC 9, Interix 3.5, BeOS.
address@hidden
+This function produces very imprecise results on some platforms:
+OpenBSD 5.1/SPARC.
 @end itemize
 
 Portability problems fixed by Gnulib module @code{hypotl-ieee}:
--- m4/hypotl.m4.orig   Wed Mar 14 03:23:54 2012
+++ m4/hypotl.m4        Wed Mar 14 03:16:44 2012
@@ -1,4 +1,4 @@
-# hypotl.m4 serial 3
+# hypotl.m4 serial 4
 dnl Copyright (C) 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,
@@ -21,6 +21,16 @@
   LIBS="$save_LIBS"
   if test $ac_cv_func_hypotl = yes; then
     HYPOTL_LIBM="$HYPOT_LIBM"
+
+    save_LIBS="$LIBS"
+    LIBS="$LIBS $HYPOTL_LIBM"
+    gl_FUNC_HYPOTL_WORKS
+    LIBS="$save_LIBS"
+    case "$gl_cv_func_hypotl_works" in
+      *yes) ;;
+      *) REPLACE_HYPOTL=1 ;;
+    esac
+
     m4_ifdef([gl_FUNC_HYPOTL_IEEE], [
       if test $gl_hypotl_required = ieee && test $REPLACE_HYPOTL = 0; then
         AC_CACHE_CHECK([whether hypotl works according to ISO C 99 with IEC 
60559],
@@ -105,3 +115,55 @@
   fi
   AC_SUBST([HYPOTL_LIBM])
 ])
+
+dnl Test whether hypotl() works.
+dnl On OpenBSD 5.1/SPARC,
+dnl hypotl (2.5541394760659556563446062497337725156L, 
7.7893454113437840832487794525518765265L)
+dnl has rounding errors that eat up the last 8 to 9 decimal digits.
+AC_DEFUN([gl_FUNC_HYPOTL_WORKS],
+[
+  AC_REQUIRE([AC_PROG_CC])
+  AC_REQUIRE([AC_CANONICAL_HOST]) dnl for cross-compiles
+  AC_CACHE_CHECK([whether hypotl works], [gl_cv_func_hypotl_works],
+    [
+      AC_RUN_IFELSE(
+        [AC_LANG_SOURCE([[
+#include <float.h>
+#include <math.h>
+static long double
+my_ldexpl (long double x, int d)
+{
+  for (; d > 0; d--)
+    x *= 2.0L;
+  for (; d < 0; d++)
+    x *= 0.5L;
+  return x;
+}
+volatile long double x;
+volatile long double y;
+volatile long double z;
+int main ()
+{
+  long double err;
+
+  x = 2.5541394760659556563446062497337725156L;
+  y = 7.7893454113437840832487794525518765265L;
+  z = hypotl (x, y);
+  err = z * z - (x * x + y * y);
+  err = my_ldexpl (err, LDBL_MANT_DIG);
+  if (err < 0)
+    err = - err;
+  if (err > 1000.0L)
+    return 1;
+  return 0;
+}
+]])],
+        [gl_cv_func_hypotl_works=yes],
+        [gl_cv_func_hypotl_works=no],
+        [case "$host_os" in
+           openbsd*) gl_cv_func_hypotl_works="guessing no";;
+           *)        gl_cv_func_hypotl_works="guessing yes";;
+         esac
+        ])
+    ])
+])