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Fix fma underflow exceptions in after-rounding edge cases
- From: "Joseph S. Myers" <joseph at codesourcery dot com>
- To: <libc-alpha at sourceware dot org>
- Date: Wed, 31 Oct 2012 01:35:14 +0000
- Subject: Fix fma underflow exceptions in after-rounding edge cases
As promised in
<http://sourceware.org/ml/libc-alpha/2012-10/msg00836.html>, this
patch fixes issues where the fma implementations after that patch
could introduce spurious underflow exceptions in cases where underflow
exceptions should only occur on machines detecting underflow before
rounding. These cases are very limited and all the information is
readily available at the relevant point in the code to determine
whether the result is tiny, in the after-rounding sense, or not (and
exact results have already been dealt with at this point, so if tiny,
underflow exceptions are correct), so this patch inserts such a check
on such systems. (No corresponding bug is filed in Bugzilla since I
don't think these corner cases would have given any exceptions,
whether correct or incorrect, in previous releases.)
Tested x86_64 (multi-arch both enabled and disabled) and x86, and
powerpc to verify the before-rounding case of the tests for float and
double.
2012-10-31 Joseph Myers <joseph@codesourcery.com>
* sysdeps/ieee754/dbl-64/s_fma.c: Include <tininess.h>.
(__fma): Do not extract and scale down low bits on after-rounding
systems when result rounded to normal precision would have normal
exponent.
* sysdeps/ieee754/ldbl-128/s_fmal.c: Include <tininess.h>.
(__fmal): Do not extract and scale down low bits on after-rounding
systems when result rounded to normal precision would have normal
exponent.
* sysdeps/ieee754/ldbl-96/s_fmal.c: Include <tininess.h>.
(__fmal): Do not extract and scale down low bits on after-rounding
systems when result rounded to normal precision would have normal
exponent.
* math/libm-test.inc (UNDERFLOW_EXCEPTION_BEFORE_ROUNDING): New
macro.
(fma_test): Add more tests.
(fma_test_towardzero): Likewise.
(fma_test_downward): Likewise.
(fma_test_upward): Likewise.
diff --git a/math/libm-test.inc b/math/libm-test.inc
index 1e067fe..91019a1 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -132,6 +132,7 @@
#include <stdio.h>
#include <string.h>
#include <argp.h>
+#include <tininess.h>
/* Allow platforms without all rounding modes to test properly,
assuming they provide an __FE_UNDEFINED in <bits/fenv.h> which
@@ -187,6 +188,11 @@
#else
# define UNDERFLOW_EXCEPTION_LDOUBLE_IBM 0
#endif
+/* Values underflowing on architectures detecting tininess before
+ rounding, but not on those detecting tininess after rounding. */
+#define UNDERFLOW_EXCEPTION_BEFORE_ROUNDING (TININESS_AFTER_ROUNDING \
+ ? 0 \
+ : UNDERFLOW_EXCEPTION)
/* Various constants (we must supply them precalculated for accuracy). */
#define M_PI_6l .52359877559829887307710723054658383L
@@ -4618,6 +4624,12 @@ fma_test (void)
TEST_fff_f (fma, 0x1.fffffep+127, 2.0, -0x1.fffffep+127, 0x1.fffffep+127);
TEST_fff_f (fma, 0x1.4p-126, 0x1.000004p-1, 0x1p-128, 0x1.c00004p-127, UNDERFLOW_EXCEPTION);
TEST_fff_f (fma, -0x1.4p-126, 0x1.000004p-1, -0x1p-128, -0x1.c00004p-127, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1.fffff8p-126, 0x1.000002p-1, 0x1p-149, 0x1p-126, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+ TEST_fff_f (fma, -0x1.fffff8p-126, 0x1.000002p-1, -0x1p-149, -0x1p-126, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+ TEST_fff_f (fma, 0x1p-149, 0x1p-1, 0x0.fffffep-126, 0x1p-126, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-149, 0x1p-1, -0x0.fffffep-126, -0x1p-126, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-149, 0x1.1p-1, 0x0.fffffep-126, 0x1p-126, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-149, 0x1.1p-1, -0x0.fffffep-126, -0x1p-126, UNDERFLOW_EXCEPTION);
#endif
#if defined (TEST_DOUBLE) && DBL_MANT_DIG == 53
TEST_fff_f (fma, 0x1.7fp+13, 0x1.0000000000001p+0, 0x1.ffep-48, 0x1.7f00000000001p+13);
@@ -4642,6 +4654,12 @@ fma_test (void)
TEST_fff_f (fma, -0x1.fffffffffffffp-711, 0x1.fffffffffffffp-275, 0x1.fffffe00007ffp-983, 0x1.7ffffe00007ffp-983);
TEST_fff_f (fma, 0x1.4p-1022, 0x1.0000000000002p-1, 0x1p-1024, 0x1.c000000000002p-1023, UNDERFLOW_EXCEPTION);
TEST_fff_f (fma, -0x1.4p-1022, 0x1.0000000000002p-1, -0x1p-1024, -0x1.c000000000002p-1023, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1.ffffffffffffcp-1022, 0x1.0000000000001p-1, 0x1p-1074, 0x1p-1022, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+ TEST_fff_f (fma, -0x1.ffffffffffffcp-1022, 0x1.0000000000001p-1, -0x1p-1074, -0x1p-1022, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+ TEST_fff_f (fma, 0x1p-1074, 0x1p-1, 0x0.fffffffffffffp-1022, 0x1p-1022, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-1074, 0x1p-1, -0x0.fffffffffffffp-1022, -0x1p-1022, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-1074, 0x1.1p-1, 0x0.fffffffffffffp-1022, 0x1p-1022, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-1074, 0x1.1p-1, -0x0.fffffffffffffp-1022, -0x1p-1022, UNDERFLOW_EXCEPTION);
#endif
#if defined (TEST_LDOUBLE) && LDBL_MANT_DIG == 64
TEST_fff_f (fma, -0x8.03fcp+3696L, 0xf.fffffffffffffffp-6140L, 0x8.3ffffffffffffffp-2450L, -0x8.01ecp-2440L);
@@ -4652,6 +4670,12 @@ fma_test (void)
TEST_fff_f (fma, 0xb.ffffp-4777L, 0x8.000000fffffffffp-11612L, -0x0.3800fff8p-16385L, 0x5.c7fe80c7ffeffffp-16385L, UNDERFLOW_EXCEPTION);
TEST_fff_f (fma, 0x1.4p-16382L, 0x1.0000000000000004p-1L, 0x1p-16384L, 0x1.c000000000000004p-16383L, UNDERFLOW_EXCEPTION);
TEST_fff_f (fma, -0x1.4p-16382L, 0x1.0000000000000004p-1L, -0x1p-16384L, -0x1.c000000000000004p-16383L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1.fffffffffffffff8p-16382L, 0x1.0000000000000002p-1L, 0x1p-16445L, 0x1p-16382L, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+ TEST_fff_f (fma, -0x1.fffffffffffffff8p-16382L, 0x1.0000000000000002p-1L, -0x1p-16445L, -0x1p-16382L, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+ TEST_fff_f (fma, 0x1p-16445L, 0x1p-1L, 0x0.fffffffffffffffep-16382L, 0x1p-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-16445L, 0x1p-1L, -0x0.fffffffffffffffep-16382L, -0x1p-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-16445L, 0x1.1p-1L, 0x0.fffffffffffffffep-16382L, 0x1p-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-16445L, 0x1.1p-1L, -0x0.fffffffffffffffep-16382L, -0x1p-16382L, UNDERFLOW_EXCEPTION);
#endif
#if defined (TEST_LDOUBLE) && LDBL_MANT_DIG == 113
TEST_fff_f (fma, 0x1.bb2de33e02ccbbfa6e245a7c1f71p-2584L, -0x1.6b500daf0580d987f1bc0cadfcddp-13777L, 0x1.613cd91d9fed34b33820e5ab9d8dp-16378L, -0x1.3a79fb50eb9ce887cffa0f09bd9fp-16360L);
@@ -4669,6 +4693,12 @@ fma_test (void)
TEST_fff_f (fma, 0x1.801181509c03bdbef10d6165588cp-15131L, 0x1.ad86f8e57d3d40bfa8007780af63p-368L, -0x1.6e9df0dab1c9f1d7a6043c390741p-15507L, 0x1.417c9b2b15e2ad57dc9e0e920844p-15498L);
TEST_fff_f (fma, 0x1.4p-16382L, 0x1.0000000000000000000000000002p-1L, 0x1p-16384L, 0x1.c000000000000000000000000002p-16383L, UNDERFLOW_EXCEPTION);
TEST_fff_f (fma, -0x1.4p-16382L, 0x1.0000000000000000000000000002p-1L, -0x1p-16384L, -0x1.c000000000000000000000000002p-16383L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1.fffffffffffffffffffffffffffcp-16382L, 0x1.0000000000000000000000000001p-1L, 0x1p-16494L, 0x1p-16382L, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+ TEST_fff_f (fma, -0x1.fffffffffffffffffffffffffffcp-16382L, 0x1.0000000000000000000000000001p-1L, -0x1p-16494L, -0x1p-16382L, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+ TEST_fff_f (fma, 0x1p-16494L, 0x1p-1L, 0x0.ffffffffffffffffffffffffffffp-16382L, 0x1p-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-16494L, 0x1p-1L, -0x0.ffffffffffffffffffffffffffffp-16382L, -0x1p-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-16494L, 0x1.1p-1L, 0x0.ffffffffffffffffffffffffffffp-16382L, 0x1p-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-16494L, 0x1.1p-1L, -0x0.ffffffffffffffffffffffffffffp-16382L, -0x1p-16382L, UNDERFLOW_EXCEPTION);
#endif
END (fma);
@@ -4727,18 +4757,42 @@ fma_test_towardzero (void)
#if defined (TEST_FLOAT) && FLT_MANT_DIG == 24
TEST_fff_f (fma, 0x1.4p-126, 0x1.000004p-1, 0x1p-128, 0x1.c00004p-127, UNDERFLOW_EXCEPTION);
TEST_fff_f (fma, -0x1.4p-126, 0x1.000004p-1, -0x1p-128, -0x1.c00004p-127, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1.fffff8p-126, 0x1.000002p-1, 0x1p-149, 0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1.fffff8p-126, 0x1.000002p-1, -0x1p-149, -0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-149, 0x1p-1, 0x0.fffffep-126, 0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-149, 0x1p-1, -0x0.fffffep-126, -0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-149, 0x1.1p-1, 0x0.fffffep-126, 0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-149, 0x1.1p-1, -0x0.fffffep-126, -0x0.fffffep-126, UNDERFLOW_EXCEPTION);
#endif
#if defined (TEST_DOUBLE) && DBL_MANT_DIG == 53
TEST_fff_f (fma, 0x1.4p-1022, 0x1.0000000000002p-1, 0x1p-1024, 0x1.c000000000002p-1023, UNDERFLOW_EXCEPTION);
TEST_fff_f (fma, -0x1.4p-1022, 0x1.0000000000002p-1, -0x1p-1024, -0x1.c000000000002p-1023, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1.ffffffffffffcp-1022, 0x1.0000000000001p-1, 0x1p-1074, 0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1.ffffffffffffcp-1022, 0x1.0000000000001p-1, -0x1p-1074, -0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-1074, 0x1p-1, 0x0.fffffffffffffp-1022, 0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-1074, 0x1p-1, -0x0.fffffffffffffp-1022, -0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-1074, 0x1.1p-1, 0x0.fffffffffffffp-1022, 0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-1074, 0x1.1p-1, -0x0.fffffffffffffp-1022, -0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
#endif
#if defined (TEST_LDOUBLE) && LDBL_MANT_DIG == 64
TEST_fff_f (fma, 0x1.4p-16382L, 0x1.0000000000000004p-1L, 0x1p-16384L, 0x1.c000000000000004p-16383L, UNDERFLOW_EXCEPTION);
TEST_fff_f (fma, -0x1.4p-16382L, 0x1.0000000000000004p-1L, -0x1p-16384L, -0x1.c000000000000004p-16383L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1.fffffffffffffff8p-16382L, 0x1.0000000000000002p-1L, 0x1p-16445L, 0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1.fffffffffffffff8p-16382L, 0x1.0000000000000002p-1L, -0x1p-16445L, -0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-16445L, 0x1p-1L, 0x0.fffffffffffffffep-16382L, 0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-16445L, 0x1p-1L, -0x0.fffffffffffffffep-16382L, -0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-16445L, 0x1.1p-1L, 0x0.fffffffffffffffep-16382L, 0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-16445L, 0x1.1p-1L, -0x0.fffffffffffffffep-16382L, -0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
#endif
#if defined (TEST_LDOUBLE) && LDBL_MANT_DIG == 113
TEST_fff_f (fma, 0x1.4p-16382L, 0x1.0000000000000000000000000002p-1L, 0x1p-16384L, 0x1.c000000000000000000000000002p-16383L, UNDERFLOW_EXCEPTION);
TEST_fff_f (fma, -0x1.4p-16382L, 0x1.0000000000000000000000000002p-1L, -0x1p-16384L, -0x1.c000000000000000000000000002p-16383L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1.fffffffffffffffffffffffffffcp-16382L, 0x1.0000000000000000000000000001p-1L, 0x1p-16494L, 0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1.fffffffffffffffffffffffffffcp-16382L, 0x1.0000000000000000000000000001p-1L, -0x1p-16494L, -0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-16494L, 0x1p-1L, 0x0.ffffffffffffffffffffffffffffp-16382L, 0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-16494L, 0x1p-1L, -0x0.ffffffffffffffffffffffffffffp-16382L, -0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-16494L, 0x1.1p-1L, 0x0.ffffffffffffffffffffffffffffp-16382L, 0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-16494L, 0x1.1p-1L, -0x0.ffffffffffffffffffffffffffffp-16382L, -0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
#endif
}
@@ -4800,18 +4854,42 @@ fma_test_downward (void)
#if defined (TEST_FLOAT) && FLT_MANT_DIG == 24
TEST_fff_f (fma, 0x1.4p-126, 0x1.000004p-1, 0x1p-128, 0x1.c00004p-127, UNDERFLOW_EXCEPTION);
TEST_fff_f (fma, -0x1.4p-126, 0x1.000004p-1, -0x1p-128, -0x1.c00008p-127, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1.fffff8p-126, 0x1.000002p-1, 0x1p-149, 0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1.fffff8p-126, 0x1.000002p-1, -0x1p-149, -0x1p-126, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+ TEST_fff_f (fma, 0x1p-149, 0x1p-1, 0x0.fffffep-126, 0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-149, 0x1p-1, -0x0.fffffep-126, -0x1p-126, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-149, 0x1.1p-1, 0x0.fffffep-126, 0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-149, 0x1.1p-1, -0x0.fffffep-126, -0x1p-126, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
#endif
#if defined (TEST_DOUBLE) && DBL_MANT_DIG == 53
TEST_fff_f (fma, 0x1.4p-1022, 0x1.0000000000002p-1, 0x1p-1024, 0x1.c000000000002p-1023, UNDERFLOW_EXCEPTION);
TEST_fff_f (fma, -0x1.4p-1022, 0x1.0000000000002p-1, -0x1p-1024, -0x1.c000000000004p-1023, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1.ffffffffffffcp-1022, 0x1.0000000000001p-1, 0x1p-1074, 0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1.ffffffffffffcp-1022, 0x1.0000000000001p-1, -0x1p-1074, -0x1p-1022, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+ TEST_fff_f (fma, 0x1p-1074, 0x1p-1, 0x0.fffffffffffffp-1022, 0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-1074, 0x1p-1, -0x0.fffffffffffffp-1022, -0x1p-1022, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-1074, 0x1.1p-1, 0x0.fffffffffffffp-1022, 0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-1074, 0x1.1p-1, -0x0.fffffffffffffp-1022, -0x1p-1022, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
#endif
#if defined (TEST_LDOUBLE) && LDBL_MANT_DIG == 64
TEST_fff_f (fma, 0x1.4p-16382L, 0x1.0000000000000004p-1L, 0x1p-16384L, 0x1.c000000000000004p-16383L, UNDERFLOW_EXCEPTION);
TEST_fff_f (fma, -0x1.4p-16382L, 0x1.0000000000000004p-1L, -0x1p-16384L, -0x1.c000000000000008p-16383L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1.fffffffffffffff8p-16382L, 0x1.0000000000000002p-1L, 0x1p-16445L, 0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1.fffffffffffffff8p-16382L, 0x1.0000000000000002p-1L, -0x1p-16445L, -0x1p-16382L, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+ TEST_fff_f (fma, 0x1p-16445L, 0x1p-1L, 0x0.fffffffffffffffep-16382L, 0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-16445L, 0x1p-1L, -0x0.fffffffffffffffep-16382L, -0x1p-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-16445L, 0x1.1p-1L, 0x0.fffffffffffffffep-16382L, 0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-16445L, 0x1.1p-1L, -0x0.fffffffffffffffep-16382L, -0x1p-16382L, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
#endif
#if defined (TEST_LDOUBLE) && LDBL_MANT_DIG == 113
TEST_fff_f (fma, 0x1.4p-16382L, 0x1.0000000000000000000000000002p-1L, 0x1p-16384L, 0x1.c000000000000000000000000002p-16383L, UNDERFLOW_EXCEPTION);
TEST_fff_f (fma, -0x1.4p-16382L, 0x1.0000000000000000000000000002p-1L, -0x1p-16384L, -0x1.c000000000000000000000000004p-16383L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1.fffffffffffffffffffffffffffcp-16382L, 0x1.0000000000000000000000000001p-1L, 0x1p-16494L, 0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1.fffffffffffffffffffffffffffcp-16382L, 0x1.0000000000000000000000000001p-1L, -0x1p-16494L, -0x1p-16382L, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+ TEST_fff_f (fma, 0x1p-16494L, 0x1p-1L, 0x0.ffffffffffffffffffffffffffffp-16382L, 0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-16494L, 0x1p-1L, -0x0.ffffffffffffffffffffffffffffp-16382L, -0x1p-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-16494L, 0x1.1p-1L, 0x0.ffffffffffffffffffffffffffffp-16382L, 0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-16494L, 0x1.1p-1L, -0x0.ffffffffffffffffffffffffffffp-16382L, -0x1p-16382L, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
#endif
}
@@ -4873,18 +4951,42 @@ fma_test_upward (void)
#if defined (TEST_FLOAT) && FLT_MANT_DIG == 24
TEST_fff_f (fma, 0x1.4p-126, 0x1.000004p-1, 0x1p-128, 0x1.c00008p-127, UNDERFLOW_EXCEPTION);
TEST_fff_f (fma, -0x1.4p-126, 0x1.000004p-1, -0x1p-128, -0x1.c00004p-127, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1.fffff8p-126, 0x1.000002p-1, 0x1p-149, 0x1p-126, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+ TEST_fff_f (fma, -0x1.fffff8p-126, 0x1.000002p-1, -0x1p-149, -0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-149, 0x1p-1, 0x0.fffffep-126, 0x1p-126, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-149, 0x1p-1, -0x0.fffffep-126, -0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-149, 0x1.1p-1, 0x0.fffffep-126, 0x1p-126, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+ TEST_fff_f (fma, -0x1p-149, 0x1.1p-1, -0x0.fffffep-126, -0x0.fffffep-126, UNDERFLOW_EXCEPTION);
#endif
#if defined (TEST_DOUBLE) && DBL_MANT_DIG == 53
TEST_fff_f (fma, 0x1.4p-1022, 0x1.0000000000002p-1, 0x1p-1024, 0x1.c000000000004p-1023, UNDERFLOW_EXCEPTION);
TEST_fff_f (fma, -0x1.4p-1022, 0x1.0000000000002p-1, -0x1p-1024, -0x1.c000000000002p-1023, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1.ffffffffffffcp-1022, 0x1.0000000000001p-1, 0x1p-1074, 0x1p-1022, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+ TEST_fff_f (fma, -0x1.ffffffffffffcp-1022, 0x1.0000000000001p-1, -0x1p-1074, -0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-1074, 0x1p-1, 0x0.fffffffffffffp-1022, 0x1p-1022, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-1074, 0x1p-1, -0x0.fffffffffffffp-1022, -0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-1074, 0x1.1p-1, 0x0.fffffffffffffp-1022, 0x1p-1022, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+ TEST_fff_f (fma, -0x1p-1074, 0x1.1p-1, -0x0.fffffffffffffp-1022, -0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
#endif
#if defined (TEST_LDOUBLE) && LDBL_MANT_DIG == 64
TEST_fff_f (fma, 0x1.4p-16382L, 0x1.0000000000000004p-1L, 0x1p-16384L, 0x1.c000000000000008p-16383L, UNDERFLOW_EXCEPTION);
TEST_fff_f (fma, -0x1.4p-16382L, 0x1.0000000000000004p-1L, -0x1p-16384L, -0x1.c000000000000004p-16383L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1.fffffffffffffff8p-16382L, 0x1.0000000000000002p-1L, 0x1p-16445L, 0x1p-16382L, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+ TEST_fff_f (fma, -0x1.fffffffffffffff8p-16382L, 0x1.0000000000000002p-1L, -0x1p-16445L, -0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-16445L, 0x1p-1L, 0x0.fffffffffffffffep-16382L, 0x1p-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-16445L, 0x1p-1L, -0x0.fffffffffffffffep-16382L, -0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-16445L, 0x1.1p-1L, 0x0.fffffffffffffffep-16382L, 0x1p-16382L, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+ TEST_fff_f (fma, -0x1p-16445L, 0x1.1p-1L, -0x0.fffffffffffffffep-16382L, -0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
#endif
#if defined (TEST_LDOUBLE) && LDBL_MANT_DIG == 113
TEST_fff_f (fma, 0x1.4p-16382L, 0x1.0000000000000000000000000002p-1L, 0x1p-16384L, 0x1.c000000000000000000000000004p-16383L, UNDERFLOW_EXCEPTION);
TEST_fff_f (fma, -0x1.4p-16382L, 0x1.0000000000000000000000000002p-1L, -0x1p-16384L, -0x1.c000000000000000000000000002p-16383L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1.fffffffffffffffffffffffffffcp-16382L, 0x1.0000000000000000000000000001p-1L, 0x1p-16494L, 0x1p-16382L, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+ TEST_fff_f (fma, -0x1.fffffffffffffffffffffffffffcp-16382L, 0x1.0000000000000000000000000001p-1L, -0x1p-16494L, -0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-16494L, 0x1p-1L, 0x0.ffffffffffffffffffffffffffffp-16382L, 0x1p-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, -0x1p-16494L, 0x1p-1L, -0x0.ffffffffffffffffffffffffffffp-16382L, -0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+ TEST_fff_f (fma, 0x1p-16494L, 0x1.1p-1L, 0x0.ffffffffffffffffffffffffffffp-16382L, 0x1p-16382L, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+ TEST_fff_f (fma, -0x1p-16494L, 0x1.1p-1L, -0x0.ffffffffffffffffffffffffffffp-16382L, -0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
#endif
}
diff --git a/sysdeps/ieee754/dbl-64/s_fma.c b/sysdeps/ieee754/dbl-64/s_fma.c
index 108fd66..155a773 100644
--- a/sysdeps/ieee754/dbl-64/s_fma.c
+++ b/sysdeps/ieee754/dbl-64/s_fma.c
@@ -22,6 +22,7 @@
#include <fenv.h>
#include <ieee754.h>
#include <math_private.h>
+#include <tininess.h>
/* This implementation uses rounding to odd to avoid problems with
double rounding. See a paper by Boldo and Melquiond:
@@ -208,6 +209,17 @@ __fma (double x, double y, double z)
for proper rounding. */
if (v.ieee.exponent == 106)
{
+ /* If the exponent would be in the normal range when
+ rounding to normal precision with unbounded exponent
+ range, the exact result is known and spurious underflows
+ must be avoided on systems detecting tininess after
+ rounding. */
+ if (TININESS_AFTER_ROUNDING)
+ {
+ w.d = a1 + u.d;
+ if (w.ieee.exponent == 107)
+ return w.d * 0x1p-106;
+ }
/* v.ieee.mantissa1 & 2 is LSB bit of the result before rounding,
v.ieee.mantissa1 & 1 is the round bit and j is our sticky
bit. */
diff --git a/sysdeps/ieee754/ldbl-128/s_fmal.c b/sysdeps/ieee754/ldbl-128/s_fmal.c
index 7fb9856..201bff9 100644
--- a/sysdeps/ieee754/ldbl-128/s_fmal.c
+++ b/sysdeps/ieee754/ldbl-128/s_fmal.c
@@ -22,6 +22,7 @@
#include <fenv.h>
#include <ieee754.h>
#include <math_private.h>
+#include <tininess.h>
/* This implementation uses rounding to odd to avoid problems with
double rounding. See a paper by Boldo and Melquiond:
@@ -209,6 +210,17 @@ __fmal (long double x, long double y, long double z)
for proper rounding. */
if (v.ieee.exponent == 226)
{
+ /* If the exponent would be in the normal range when
+ rounding to normal precision with unbounded exponent
+ range, the exact result is known and spurious underflows
+ must be avoided on systems detecting tininess after
+ rounding. */
+ if (TININESS_AFTER_ROUNDING)
+ {
+ w.d = a1 + u.d;
+ if (w.ieee.exponent == 227)
+ return w.d * 0x1p-226L;
+ }
/* v.ieee.mantissa3 & 2 is LSB bit of the result before rounding,
v.ieee.mantissa3 & 1 is the round bit and j is our sticky
bit. */
diff --git a/sysdeps/ieee754/ldbl-96/s_fmal.c b/sysdeps/ieee754/ldbl-96/s_fmal.c
index 7310491..91333af 100644
--- a/sysdeps/ieee754/ldbl-96/s_fmal.c
+++ b/sysdeps/ieee754/ldbl-96/s_fmal.c
@@ -22,6 +22,7 @@
#include <fenv.h>
#include <ieee754.h>
#include <math_private.h>
+#include <tininess.h>
/* This implementation uses rounding to odd to avoid problems with
double rounding. See a paper by Boldo and Melquiond:
@@ -209,6 +210,17 @@ __fmal (long double x, long double y, long double z)
for proper rounding. */
if (v.ieee.exponent == 128)
{
+ /* If the exponent would be in the normal range when
+ rounding to normal precision with unbounded exponent
+ range, the exact result is known and spurious underflows
+ must be avoided on systems detecting tininess after
+ rounding. */
+ if (TININESS_AFTER_ROUNDING)
+ {
+ w.d = a1 + u.d;
+ if (w.ieee.exponent == 129)
+ return w.d * 0x1p-128L;
+ }
/* v.ieee.mantissa1 & 2 is LSB bit of the result before rounding,
v.ieee.mantissa1 & 1 is the round bit and j is our sticky
bit. */
--
Joseph S. Myers
joseph@codesourcery.com