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Fix IBM long double division inaccuracy (glibc bug 15396)
- From: "Joseph S. Myers" <joseph at codesourcery dot com>
- To: <gcc-patches at gcc dot gnu dot org>
- Cc: <dje dot gcc at gmail dot com>, Adhemerval Zanella <azanella at linux dot vnet dot ibm dot com>
- Date: Thu, 2 Jan 2014 21:46:56 +0000
- Subject: Fix IBM long double division inaccuracy (glibc bug 15396)
- Authentication-results: sourceware.org; auth=none
This patch fixes inaccuracy of IBM long double division that causes
large errors in glibc testing
<https://sourceware.org/bugzilla/show_bug.cgi?id=15396>. The
implementation computes a first approximation to the result as t = a /
c, dividing the high parts of the arguments, then does adjustments
involving calculating c * t as the exact sum of two double values. In
the problem cases, the low part of c * t underflows, so resulting in
loss of precision compared to the precision available for a number
with the exponent of the final result. This patch scales the
arguments up in the problem case.
Tested with no regressions for cross to powerpc-linux-gnu. OK to
commit?
(Note that there remain other bugs in the IBM long double code, some
causing glibc test failures, at least (a) invalid results in rounding
modes other than FE_TONEAREST, (b) spurious overflow and underflow
exceptions, mainly but not entirely where discontiguous mantissa bits
are involved.)
libgcc:
2014-01-02 Joseph Myers <joseph@codesourcery.com>
* config/rs6000/ibm-ldouble.c (__gcc_qdiv): Scale up arguments in
case of small numerator and finite nonzero result.
gcc/testsuite:
2014-01-02 Joseph Myers <joseph@codesourcery.com>
* gcc.target/powerpc/rs6000-ldouble-3.c: New test.
Index: gcc/testsuite/gcc.target/powerpc/rs6000-ldouble-3.c
===================================================================
--- gcc/testsuite/gcc.target/powerpc/rs6000-ldouble-3.c (revision 0)
+++ gcc/testsuite/gcc.target/powerpc/rs6000-ldouble-3.c (revision 0)
@@ -0,0 +1,21 @@
+/* Test accuracy of long double division (glibc bug 15396). */
+/* { dg-do run { target powerpc*-*-linux* powerpc*-*-darwin* powerpc*-*-aix* rs6000-*-* } } */
+/* { dg-options "-mlong-double-128" } */
+
+extern void exit (int);
+extern void abort (void);
+
+volatile long double a = 0x1p-1024L;
+volatile long double b = 0x3p-53L;
+volatile long double r;
+volatile long double expected = 0x1.55555555555555555555555555p-973L;
+
+int
+main (void)
+{
+ r = a / b;
+ /* Allow error up to 2ulp. */
+ if (__builtin_fabsl (r - expected) > 0x1p-1073L)
+ abort ();
+ exit (0);
+}
Index: libgcc/config/rs6000/ibm-ldouble.c
===================================================================
--- libgcc/config/rs6000/ibm-ldouble.c (revision 206280)
+++ libgcc/config/rs6000/ibm-ldouble.c (working copy)
@@ -190,7 +190,16 @@ __gcc_qdiv (double a, double b, double c, double d
|| nonfinite (t))
return t;
- /* Finite nonzero result requires corrections to the highest order term. */
+ /* Finite nonzero result requires corrections to the highest order
+ term. These corrections require the low part of c * t to be
+ exactly represented in double. */
+ if (fabs (a) <= 0x1p-969)
+ {
+ a *= 0x1p106;
+ b *= 0x1p106;
+ c *= 0x1p106;
+ d *= 0x1p106;
+ }
s = c * t; /* (s,sigma) = c*t exactly. */
w = -(-b + d * t); /* Written to get fnmsub for speed, but not
--
Joseph S. Myers
joseph@codesourcery.com