Fix fma (a, b, c) for small a * b (bugs 14784, 14785).

diff --git a/ChangeLog b/ChangeLog
index b205a57..a042ebf 100644 (file)
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,16 @@
+2012-11-01  Joseph Myers  <joseph@codesourcery.com>
+
+       [BZ #14784]
+       [BZ #14785]
+       * sysdeps/ieee754/dbl-64/s_fma.c (__fma): Handle cases with small
+       x * y using scaling, not as x * y + z.
+       * sysdeps/ieee754/ldbl-128/s_fmal.c (__fmal): Likewise.
+       * sysdeps/ieee754/ldbl-96/s_fmal.c (__fmal): Likewise.
+       * math/libm-test.inc (fma_test): Add more tests.
+       (fma_test_towardzero): Likewise.
+       (fma_test_downward): Likewise.
+       (fma_test_upward): Likewise.
+
 2012-11-01  Thomas Schwinge  <thomas@codesourcery.com>
 
        * sysdeps/mach/hurd/bits/param.h: Remove stray #endif.

diff --git a/NEWS b/NEWS
index 8b691e5..12184f8 100644 (file)
--- a/NEWS
+++ b/NEWS
@@ -17,7 +17,7 @@ Version 2.17
   14459, 14476, 14477, 14505, 14510, 14516, 14518, 14519, 14530, 14532,
   14538, 14543, 14544, 14545, 14557, 14562, 14568, 14576, 14579, 14583,
   14587, 14595, 14602, 14610, 14621, 14638, 14645, 14648, 14652, 14660,
-  14661, 14683, 14694, 14716, 14743, 14767, 14783.
+  14661, 14683, 14694, 14716, 14743, 14767, 14783, 14784, 14785.
 
 * Support for STT_GNU_IFUNC symbols added for s390 and s390x.
   Optimized versions of memcpy, memset, and memcmp added for System z10 and

diff --git a/math/libm-test.inc b/math/libm-test.inc
index 9c77392..258c960 100644 (file)
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -4633,6 +4633,22 @@ fma_test (void)
   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);
+  TEST_fff_f (fma, 0x1p-149, 0x1p-149, 0x1p127, 0x1p127);
+  TEST_fff_f (fma, 0x1p-149, -0x1p-149, 0x1p127, 0x1p127);
+  TEST_fff_f (fma, 0x1p-149, 0x1p-149, -0x1p127, -0x1p127);
+  TEST_fff_f (fma, 0x1p-149, -0x1p-149, -0x1p127, -0x1p127);
+  TEST_fff_f (fma, 0x1p-149, 0x1p-149, 0x1p-126, 0x1p-126);
+  TEST_fff_f (fma, 0x1p-149, -0x1p-149, 0x1p-126, 0x1p-126, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+  TEST_fff_f (fma, 0x1p-149, 0x1p-149, -0x1p-126, -0x1p-126, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+  TEST_fff_f (fma, 0x1p-149, -0x1p-149, -0x1p-126, -0x1p-126);
+  TEST_fff_f (fma, 0x1p-149, 0x1p-149, 0x0.fffffep-126, 0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-149, -0x1p-149, 0x0.fffffep-126, 0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-149, 0x1p-149, -0x0.fffffep-126, -0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-149, -0x1p-149, -0x0.fffffep-126, -0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-149, 0x1p-149, 0x1p-149, 0x1p-149, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-149, -0x1p-149, 0x1p-149, 0x1p-149, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-149, 0x1p-149, -0x1p-149, -0x1p-149, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-149, -0x1p-149, -0x1p-149, -0x1p-149, 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);
@@ -4663,6 +4679,22 @@ fma_test (void)
   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);
+  TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, 0x1p1023, 0x1p1023);
+  TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, 0x1p1023, 0x1p1023);
+  TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, -0x1p1023, -0x1p1023);
+  TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, -0x1p1023, -0x1p1023);
+  TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, 0x1p-1022, 0x1p-1022);
+  TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, 0x1p-1022, 0x1p-1022, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+  TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, -0x1p-1022, -0x1p-1022, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+  TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, -0x1p-1022, -0x1p-1022);
+  TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, 0x0.fffffffffffffp-1022, 0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, 0x0.fffffffffffffp-1022, 0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, -0x0.fffffffffffffp-1022, -0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, -0x0.fffffffffffffp-1022, -0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, 0x1p-1074, 0x1p-1074, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, 0x1p-1074, 0x1p-1074, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, -0x1p-1074, -0x1p-1074, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, -0x1p-1074, -0x1p-1074, 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);
@@ -4679,6 +4711,22 @@ fma_test (void)
   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);
+  TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, 0x1p16383L, 0x1p16383L);
+  TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, 0x1p16383L, 0x1p16383L);
+  TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, -0x1p16383L, -0x1p16383L);
+  TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, -0x1p16383L, -0x1p16383L);
+  TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, 0x1p-16382L, 0x1p-16382L);
+  TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, 0x1p-16382L, 0x1p-16382L, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+  TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, -0x1p-16382L, -0x1p-16382L, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+  TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, -0x1p-16382L, -0x1p-16382L);
+  TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, 0x0.fffffffffffffffep-16382L, 0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, 0x0.fffffffffffffffep-16382L, 0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, -0x0.fffffffffffffffep-16382L, -0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, -0x0.fffffffffffffffep-16382L, -0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, 0x1p-16445L, 0x1p-16445L, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, 0x1p-16445L, 0x1p-16445L, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, -0x1p-16445L, -0x1p-16445L, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, -0x1p-16445L, -0x1p-16445L, 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);
@@ -4702,6 +4750,22 @@ fma_test (void)
   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);
+  TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, 0x1p16383L, 0x1p16383L);
+  TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, 0x1p16383L, 0x1p16383L);
+  TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, -0x1p16383L, -0x1p16383L);
+  TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, -0x1p16383L, -0x1p16383L);
+  TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, 0x1p-16382L, 0x1p-16382L);
+  TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, 0x1p-16382L, 0x1p-16382L, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+  TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, -0x1p-16382L, -0x1p-16382L, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+  TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, -0x1p-16382L, -0x1p-16382L);
+  TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, 0x0.ffffffffffffffffffffffffffffp-16382L, 0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, 0x0.ffffffffffffffffffffffffffffp-16382L, 0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, -0x0.ffffffffffffffffffffffffffffp-16382L, -0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, -0x0.ffffffffffffffffffffffffffffp-16382L, -0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, 0x1p-16494L, 0x1p-16494L, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, 0x1p-16494L, 0x1p-16494L, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, -0x1p-16494L, -0x1p-16494L, UNDERFLOW_EXCEPTION);
+  TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, -0x1p-16494L, -0x1p-16494L, UNDERFLOW_EXCEPTION);
 #endif
 
   END (fma);
@@ -4766,6 +4830,22 @@ fma_test_towardzero (void)
       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);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, 0x1p127, 0x1p127);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, 0x1p127, 0x0.ffffffp127);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, -0x1p127, -0x0.ffffffp127);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, -0x1p127, -0x1p127);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, 0x1p-126, 0x1p-126);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, 0x1p-126, 0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, -0x1p-126, -0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, -0x1p-126, -0x1p-126);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, 0x0.fffffep-126, 0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, 0x0.fffffep-126, 0x0.fffffcp-126, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, -0x0.fffffep-126, -0x0.fffffcp-126, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, -0x0.fffffep-126, -0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, 0x1p-149, 0x1p-149, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, 0x1p-149, plus_zero, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, -0x1p-149, minus_zero, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, -0x1p-149, -0x1p-149, 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);
@@ -4776,6 +4856,22 @@ fma_test_towardzero (void)
       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);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, 0x1p1023, 0x1p1023);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, 0x1p1023, 0x0.fffffffffffff8p1023);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, -0x1p1023, -0x0.fffffffffffff8p1023);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, -0x1p1023, -0x1p1023);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, 0x1p-1022, 0x1p-1022);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, 0x1p-1022, 0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, -0x1p-1022, -0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, -0x1p-1022, -0x1p-1022);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, 0x0.fffffffffffffp-1022, 0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, 0x0.fffffffffffffp-1022, 0x0.ffffffffffffep-1022, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, -0x0.fffffffffffffp-1022, -0x0.ffffffffffffep-1022, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, -0x0.fffffffffffffp-1022, -0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, 0x1p-1074, 0x1p-1074, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, 0x1p-1074, plus_zero, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, -0x1p-1074, minus_zero, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, -0x1p-1074, -0x1p-1074, 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);
@@ -4786,6 +4882,22 @@ fma_test_towardzero (void)
       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);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, 0x1p16383L, 0x1p16383L);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, 0x1p16383L, 0x0.ffffffffffffffffp16383L);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, -0x1p16383L, -0x0.ffffffffffffffffp16383L);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, -0x1p16383L, -0x1p16383L);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, 0x1p-16382L, 0x1p-16382L);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, 0x1p-16382L, 0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, -0x1p-16382L, -0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, -0x1p-16382L, -0x1p-16382L);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, 0x0.fffffffffffffffep-16382L, 0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, 0x0.fffffffffffffffep-16382L, 0x0.fffffffffffffffcp-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, -0x0.fffffffffffffffep-16382L, -0x0.fffffffffffffffcp-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, -0x0.fffffffffffffffep-16382L, -0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, 0x1p-16445L, 0x1p-16445L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, 0x1p-16445L, plus_zero, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, -0x1p-16445L, minus_zero, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, -0x1p-16445L, -0x1p-16445L, 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);
@@ -4796,6 +4908,22 @@ fma_test_towardzero (void)
       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);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, 0x1p16383L, 0x1p16383L);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, 0x1p16383L, 0x0.ffffffffffffffffffffffffffff8p16383L);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, -0x1p16383L, -0x0.ffffffffffffffffffffffffffff8p16383L);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, -0x1p16383L, -0x1p16383L);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, 0x1p-16382L, 0x1p-16382L);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, 0x1p-16382L, 0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, -0x1p-16382L, -0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, -0x1p-16382L, -0x1p-16382L);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, 0x0.ffffffffffffffffffffffffffffp-16382L, 0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, 0x0.ffffffffffffffffffffffffffffp-16382L, 0x0.fffffffffffffffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, -0x0.ffffffffffffffffffffffffffffp-16382L, -0x0.fffffffffffffffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, -0x0.ffffffffffffffffffffffffffffp-16382L, -0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, 0x1p-16494L, 0x1p-16494L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, 0x1p-16494L, plus_zero, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, -0x1p-16494L, minus_zero, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, -0x1p-16494L, -0x1p-16494L, UNDERFLOW_EXCEPTION);
 #endif
     }
 
@@ -4863,6 +4991,22 @@ fma_test_downward (void)
       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);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, 0x1p127, 0x1p127);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, 0x1p127, 0x0.ffffffp127);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, -0x1p127, -0x1p127);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, -0x1p127, -0x1.000002p127);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, 0x1p-126, 0x1p-126);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, 0x1p-126, 0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, -0x1p-126, -0x1p-126, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, -0x1p-126, -0x1.000002p-126);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, 0x0.fffffep-126, 0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, 0x0.fffffep-126, 0x0.fffffcp-126, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, -0x0.fffffep-126, -0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, -0x0.fffffep-126, -0x1p-126, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, 0x1p-149, 0x1p-149, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, 0x1p-149, plus_zero, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, -0x1p-149, -0x1p-149, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, -0x1p-149, -0x1p-148, 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);
@@ -4873,6 +5017,22 @@ fma_test_downward (void)
       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);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, 0x1p1023, 0x1p1023);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, 0x1p1023, 0x0.fffffffffffff8p1023);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, -0x1p1023, -0x1p1023);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, -0x1p1023, -0x1.0000000000001p1023);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, 0x1p-1022, 0x1p-1022);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, 0x1p-1022, 0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, -0x1p-1022, -0x1p-1022, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, -0x1p-1022, -0x1.0000000000001p-1022);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, 0x0.fffffffffffffp-1022, 0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, 0x0.fffffffffffffp-1022, 0x0.ffffffffffffep-1022, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, -0x0.fffffffffffffp-1022, -0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, -0x0.fffffffffffffp-1022, -0x1p-1022, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, 0x1p-1074, 0x1p-1074, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, 0x1p-1074, plus_zero, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, -0x1p-1074, -0x1p-1074, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, -0x1p-1074, -0x1p-1073, 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);
@@ -4883,6 +5043,22 @@ fma_test_downward (void)
       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);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, 0x1p16383L, 0x1p16383L);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, 0x1p16383L, 0x0.ffffffffffffffffp16383L);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, -0x1p16383L, -0x1p16383L);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, -0x1p16383L, -0x1.0000000000000002p16383L);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, 0x1p-16382L, 0x1p-16382L);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, 0x1p-16382L, 0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, -0x1p-16382L, -0x1p-16382L, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, -0x1p-16382L, -0x1.0000000000000002p-16382L);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, 0x0.fffffffffffffffep-16382L, 0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, 0x0.fffffffffffffffep-16382L, 0x0.fffffffffffffffcp-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, -0x0.fffffffffffffffep-16382L, -0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, -0x0.fffffffffffffffep-16382L, -0x1p-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, 0x1p-16445L, 0x1p-16445L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, 0x1p-16445L, plus_zero, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, -0x1p-16445L, -0x1p-16445L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, -0x1p-16445L, -0x1p-16444L, 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);
@@ -4893,6 +5069,22 @@ fma_test_downward (void)
       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);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, 0x1p16383L, 0x1p16383L);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, 0x1p16383L, 0x0.ffffffffffffffffffffffffffff8p16383L);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, -0x1p16383L, -0x1p16383L);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, -0x1p16383L, -0x1.0000000000000000000000000001p16383L);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, 0x1p-16382L, 0x1p-16382L);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, 0x1p-16382L, 0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, -0x1p-16382L, -0x1p-16382L, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, -0x1p-16382L, -0x1.0000000000000000000000000001p-16382L);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, 0x0.ffffffffffffffffffffffffffffp-16382L, 0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, 0x0.ffffffffffffffffffffffffffffp-16382L, 0x0.fffffffffffffffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, -0x0.ffffffffffffffffffffffffffffp-16382L, -0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, -0x0.ffffffffffffffffffffffffffffp-16382L, -0x1p-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, 0x1p-16494L, 0x1p-16494L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, 0x1p-16494L, plus_zero, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, -0x1p-16494L, -0x1p-16494L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, -0x1p-16494L, -0x1p-16493L, UNDERFLOW_EXCEPTION);
 #endif
     }
 
@@ -4960,6 +5152,22 @@ fma_test_upward (void)
       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);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, 0x1p127, 0x1.000002p127);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, 0x1p127, 0x1p127);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, -0x1p127, -0x0.ffffffp127);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, -0x1p127, -0x1p127);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, 0x1p-126, 0x1.000002p-126);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, 0x1p-126, 0x1p-126, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, -0x1p-126, -0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, -0x1p-126, -0x1p-126);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, 0x0.fffffep-126, 0x1p-126, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, 0x0.fffffep-126, 0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, -0x0.fffffep-126, -0x0.fffffcp-126, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, -0x0.fffffep-126, -0x0.fffffep-126, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, 0x1p-149, 0x1p-148, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, 0x1p-149, 0x1p-149, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, 0x1p-149, -0x1p-149, minus_zero, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-149, -0x1p-149, -0x1p-149, -0x1p-149, 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);
@@ -4970,6 +5178,22 @@ fma_test_upward (void)
       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);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, 0x1p1023, 0x1.0000000000001p1023);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, 0x1p1023, 0x1p1023);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, -0x1p1023, -0x0.fffffffffffff8p1023);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, -0x1p1023, -0x1p1023);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, 0x1p-1022, 0x1.0000000000001p-1022);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, 0x1p-1022, 0x1p-1022, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, -0x1p-1022, -0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, -0x1p-1022, -0x1p-1022);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, 0x0.fffffffffffffp-1022, 0x1p-1022, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, 0x0.fffffffffffffp-1022, 0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, -0x0.fffffffffffffp-1022, -0x0.ffffffffffffep-1022, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, -0x0.fffffffffffffp-1022, -0x0.fffffffffffffp-1022, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, 0x1p-1074, 0x1p-1073, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, 0x1p-1074, 0x1p-1074, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, 0x1p-1074, -0x1p-1074, minus_zero, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-1074, -0x1p-1074, -0x1p-1074, -0x1p-1074, 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);
@@ -4980,6 +5204,22 @@ fma_test_upward (void)
       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);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, 0x1p16383L, 0x1.0000000000000002p16383L);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, 0x1p16383L, 0x1p16383L);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, -0x1p16383L, -0x0.ffffffffffffffffp16383L);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, -0x1p16383L, -0x1p16383L);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, 0x1p-16382L, 0x1.0000000000000002p-16382L);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, 0x1p-16382L, 0x1p-16382L, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, -0x1p-16382L, -0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, -0x1p-16382L, -0x1p-16382L);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, 0x0.fffffffffffffffep-16382L, 0x1p-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, 0x0.fffffffffffffffep-16382L, 0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, -0x0.fffffffffffffffep-16382L, -0x0.fffffffffffffffcp-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, -0x0.fffffffffffffffep-16382L, -0x0.fffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, 0x1p-16445L, 0x1p-16444L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, 0x1p-16445L, 0x1p-16445L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, 0x1p-16445L, -0x1p-16445L, minus_zero, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16445L, -0x1p-16445L, -0x1p-16445L, -0x1p-16445L, 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);
@@ -4990,6 +5230,22 @@ fma_test_upward (void)
       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);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, 0x1p16383L, 0x1.0000000000000000000000000001p16383L);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, 0x1p16383L, 0x1p16383L);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, -0x1p16383L, -0x0.ffffffffffffffffffffffffffff8p16383L);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, -0x1p16383L, -0x1p16383L);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, 0x1p-16382L, 0x1.0000000000000000000000000001p-16382L);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, 0x1p-16382L, 0x1p-16382L, UNDERFLOW_EXCEPTION_BEFORE_ROUNDING);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, -0x1p-16382L, -0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, -0x1p-16382L, -0x1p-16382L);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, 0x0.ffffffffffffffffffffffffffffp-16382L, 0x1p-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, 0x0.ffffffffffffffffffffffffffffp-16382L, 0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, -0x0.ffffffffffffffffffffffffffffp-16382L, -0x0.fffffffffffffffffffffffffffep-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, -0x0.ffffffffffffffffffffffffffffp-16382L, -0x0.ffffffffffffffffffffffffffffp-16382L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, 0x1p-16494L, 0x1p-16493L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, 0x1p-16494L, 0x1p-16494L, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, 0x1p-16494L, -0x1p-16494L, minus_zero, UNDERFLOW_EXCEPTION);
+      TEST_fff_f (fma, 0x1p-16494L, -0x1p-16494L, -0x1p-16494L, -0x1p-16494L, UNDERFLOW_EXCEPTION);
 #endif
     }
 

diff --git a/sysdeps/ieee754/dbl-64/s_fma.c b/sysdeps/ieee754/dbl-64/s_fma.c
index 155a773..68c63a1 100644 (file)
--- a/sysdeps/ieee754/dbl-64/s_fma.c
+++ b/sysdeps/ieee754/dbl-64/s_fma.c
@@ -56,16 +56,44 @@ __fma (double x, double y, double z)
       if (z == 0 && x != 0 && y != 0)
        return x * y;
       /* If x or y or z is Inf/NaN, or if fma will certainly overflow,
-        or if x * y is less than half of DBL_DENORM_MIN,
-        compute as x * y + z.  */
+        or if x * y is zero, compute as x * y + z.  */
       if (u.ieee.exponent == 0x7ff
          || v.ieee.exponent == 0x7ff
          || w.ieee.exponent == 0x7ff
          || u.ieee.exponent + v.ieee.exponent
             > 0x7ff + IEEE754_DOUBLE_BIAS
-         || u.ieee.exponent + v.ieee.exponent
-            < IEEE754_DOUBLE_BIAS - DBL_MANT_DIG - 2)
+         || x == 0
+         || y == 0)
        return x * y + z;
+      /* If x * y is less than 1/4 of DBL_DENORM_MIN, neither the
+        result nor whether there is underflow depends on its exact
+        value, only on its sign.  */
+      if (u.ieee.exponent + v.ieee.exponent
+         < IEEE754_DOUBLE_BIAS - DBL_MANT_DIG - 2)
+       {
+         int neg = u.ieee.negative ^ v.ieee.negative;
+         double tiny = neg ? -0x1p-1074 : 0x1p-1074;
+         if (w.ieee.exponent >= 3)
+           return tiny + z;
+         /* Scaling up, adding TINY and scaling down produces the
+            correct result, because in round-to-nearest mode adding
+            TINY has no effect and in other modes double rounding is
+            harmless.  But it may not produce required underflow
+            exceptions.  */
+         v.d = z * 0x1p54 + tiny;
+         if (TININESS_AFTER_ROUNDING
+             ? v.ieee.exponent < 55
+             : (w.ieee.exponent == 0
+                || (w.ieee.exponent == 1
+                    && w.ieee.negative != neg
+                    && w.ieee.mantissa1 == 0
+                    && w.ieee.mantissa0 == 0)))
+           {
+             volatile double force_underflow = x * y;
+             (void) force_underflow;
+           }
+         return v.d * 0x1p-54;
+       }
       if (u.ieee.exponent + v.ieee.exponent
          >= 0x7ff + IEEE754_DOUBLE_BIAS - DBL_MANT_DIG)
        {

diff --git a/sysdeps/ieee754/ldbl-128/s_fmal.c b/sysdeps/ieee754/ldbl-128/s_fmal.c
index 201bff9..c6a3d71 100644 (file)
--- a/sysdeps/ieee754/ldbl-128/s_fmal.c
+++ b/sysdeps/ieee754/ldbl-128/s_fmal.c
@@ -57,16 +57,46 @@ __fmal (long double x, long double y, long double z)
       if (z == 0 && x != 0 && y != 0)
        return x * y;
       /* If x or y or z is Inf/NaN, or if fma will certainly overflow,
-        or if x * y is less than half of LDBL_DENORM_MIN,
-        compute as x * y + z.  */
+        or if x * y is zero, compute as x * y + z.  */
       if (u.ieee.exponent == 0x7fff
          || v.ieee.exponent == 0x7fff
          || w.ieee.exponent == 0x7fff
          || u.ieee.exponent + v.ieee.exponent
             > 0x7fff + IEEE854_LONG_DOUBLE_BIAS
-         || u.ieee.exponent + v.ieee.exponent
-            < IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG - 2)
+         || x == 0
+         || y == 0)
        return x * y + z;
+      /* If x * y is less than 1/4 of LDBL_DENORM_MIN, neither the
+        result nor whether there is underflow depends on its exact
+        value, only on its sign.  */
+      if (u.ieee.exponent + v.ieee.exponent
+         < IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG - 2)
+       {
+         int neg = u.ieee.negative ^ v.ieee.negative;
+         long double tiny = neg ? -0x1p-16494L : 0x1p-16494L;
+         if (w.ieee.exponent >= 3)
+           return tiny + z;
+         /* Scaling up, adding TINY and scaling down produces the
+            correct result, because in round-to-nearest mode adding
+            TINY has no effect and in other modes double rounding is
+            harmless.  But it may not produce required underflow
+            exceptions.  */
+         v.d = z * 0x1p114L + tiny;
+         if (TININESS_AFTER_ROUNDING
+             ? v.ieee.exponent < 115
+             : (w.ieee.exponent == 0
+                || (w.ieee.exponent == 1
+                    && w.ieee.negative != neg
+                    && w.ieee.mantissa3 == 0
+                    && w.ieee.mantissa2 == 0
+                    && w.ieee.mantissa1 == 0
+                    && w.ieee.mantissa0 == 0)))
+           {
+             volatile long double force_underflow = x * y;
+             (void) force_underflow;
+           }
+         return v.d * 0x1p-114L;
+       }
       if (u.ieee.exponent + v.ieee.exponent
          >= 0x7fff + IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG)
        {

diff --git a/sysdeps/ieee754/ldbl-96/s_fmal.c b/sysdeps/ieee754/ldbl-96/s_fmal.c
index 91333af..b5fdcba 100644 (file)
--- a/sysdeps/ieee754/ldbl-96/s_fmal.c
+++ b/sysdeps/ieee754/ldbl-96/s_fmal.c
@@ -57,16 +57,44 @@ __fmal (long double x, long double y, long double z)
       if (z == 0 && x != 0 && y != 0)
        return x * y;
       /* If x or y or z is Inf/NaN, or if fma will certainly overflow,
-        or if x * y is less than half of LDBL_DENORM_MIN,
-        compute as x * y + z.  */
+        or if x * y is zero, compute as x * y + z.  */
       if (u.ieee.exponent == 0x7fff
          || v.ieee.exponent == 0x7fff
          || w.ieee.exponent == 0x7fff
          || u.ieee.exponent + v.ieee.exponent
             > 0x7fff + IEEE854_LONG_DOUBLE_BIAS
-         || u.ieee.exponent + v.ieee.exponent
-            < IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG - 2)
+         || x == 0
+         || y == 0)
        return x * y + z;
+      /* If x * y is less than 1/4 of LDBL_DENORM_MIN, neither the
+        result nor whether there is underflow depends on its exact
+        value, only on its sign.  */
+      if (u.ieee.exponent + v.ieee.exponent
+         < IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG - 2)
+       {
+         int neg = u.ieee.negative ^ v.ieee.negative;
+         long double tiny = neg ? -0x1p-16445L : 0x1p-16445L;
+         if (w.ieee.exponent >= 3)
+           return tiny + z;
+         /* Scaling up, adding TINY and scaling down produces the
+            correct result, because in round-to-nearest mode adding
+            TINY has no effect and in other modes double rounding is
+            harmless.  But it may not produce required underflow
+            exceptions.  */
+         v.d = z * 0x1p65L + tiny;
+         if (TININESS_AFTER_ROUNDING
+             ? v.ieee.exponent < 66
+             : (w.ieee.exponent == 0
+                || (w.ieee.exponent == 1
+                    && w.ieee.negative != neg
+                    && w.ieee.mantissa1 == 0
+                    && w.ieee.mantissa0 == 0x80000000)))
+           {
+             volatile long double force_underflow = x * y;
+             (void) force_underflow;
+           }
+         return v.d * 0x1p-65L;
+       }
       if (u.ieee.exponent + v.ieee.exponent
          >= 0x7fff + IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG)
        {