Fix fma underflow exceptions in after-rounding edge cases.

diff --git a/ChangeLog b/ChangeLog
index 970cbc1..d5eefa6 100644 (file)
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,24 @@
+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.
+
 2012-10-30  H.J. Lu  <hongjiu.lu@intel.com>
 
        * sysdeps/i386/tininess.h: Renamed to ...

diff --git a/math/libm-test.inc b/math/libm-test.inc
index 1e067fe..91019a1 100644 (file)
--- 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 (file)
--- 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 (file)
--- 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 (file)
--- 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.  */