diff --git a/stdlib/strtod_l.c b/stdlib/strtod_l.c
index be515ce659..beb97b3d0c 100644
--- a/stdlib/strtod_l.c
+++ b/stdlib/strtod_l.c
@@ -222,6 +222,7 @@ round_and_return (mp_limb_t *retval, intmax_t exponent, int negative,
 
       mp_size_t shift = MIN_EXP - 1 - exponent;
       bool is_tiny = true;
+      bool old_half_bit = (round_limb & (((mp_limb_t) 1) << round_bit)) != 0;
 
       more_bits |= (round_limb & ((((mp_limb_t) 1) << round_bit) - 1)) != 0;
       if (shift == MANT_DIG)
@@ -292,6 +293,7 @@ round_and_return (mp_limb_t *retval, intmax_t exponent, int negative,
 	  round_bit = shift - 1;
 	  (void) __mpn_rshift (retval, retval, RETURN_LIMB_SIZE, shift);
 	}
+      more_bits |= old_half_bit;
       /* This is a hook for the m68k long double format, where the
 	 exponent bias is the same for normalized and denormalized
 	 numbers.  */
diff --git a/stdlib/tst-strtod-round-data b/stdlib/tst-strtod-round-data
index 84ab705709..9489fbcc9c 100644
--- a/stdlib/tst-strtod-round-data
+++ b/stdlib/tst-strtod-round-data
@@ -265,3 +265,15 @@
 1.000000000000000000000000000000000385185988877447170611195588516985463707620329643077639047987759113311767578125
 1.0000000000000000000000000000000001925929944387235853055977942584927318538101648215388195239938795566558837890625
 1.00000000000000000000000000000000009629649721936179265279889712924636592690508241076940976199693977832794189453125
+0x30000002222225p-1077
+0x0.7fffffffffffeap-1022
+0x0.7fffffffffffe9p-1022
+0x0.7ffffd4p-126
+0x0.7ffffffffffffffd4p-16382
+0x0.7ffffffffffffffd4p-16383
+0x0.7ffffffffffffffffffffffffffeap-16382
+0x0.7000004p-126
+0x0.70000000000002p-1022
+0x0.70000000000000004p-16382
+0x0.70000000000000004p-16383
+0x0.70000000000000000000000000002p-16382
diff --git a/stdlib/tst-strtod-round-data.h b/stdlib/tst-strtod-round-data.h
index 13e62dd2b0..ed50eb2537 100644
--- a/stdlib/tst-strtod-round-data.h
+++ b/stdlib/tst-strtod-round-data.h
@@ -15437,4 +15437,376 @@ static const struct test tests[] = {
 	0x1p+0, false, false,
 	0x1p+0, false, false,
 	0x1.0000000000000000000000000001p+0, false, false),
+  TEST ("0x30000002222225p-1077",
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x8p-152, false, true,
+	false,
+	0x1.800000111111p-1024, false, true,
+	0x1.8000001111114p-1024, false, true,
+	0x1.800000111111p-1024, false, true,
+	0x1.8000001111114p-1024, false, true,
+	true,
+	0x1.80000011111128p-1024, false, false,
+	0x1.80000011111128p-1024, false, false,
+	0x1.80000011111128p-1024, false, false,
+	0x1.80000011111128p-1024, false, false,
+	true,
+	0x1.80000011111128p-1024, false, false,
+	0x1.80000011111128p-1024, false, false,
+	0x1.80000011111128p-1024, false, false,
+	0x1.80000011111128p-1024, false, false,
+	false,
+	0x1.800000111111p-1024, false, true,
+	0x1.8000001111114p-1024, false, true,
+	0x1.800000111111p-1024, false, true,
+	0x1.8000001111114p-1024, false, true,
+	true,
+	0x1.80000011111128p-1024, false, false,
+	0x1.80000011111128p-1024, false, false,
+	0x1.80000011111128p-1024, false, false,
+	0x1.80000011111128p-1024, false, false),
+  TEST ("0x0.7fffffffffffeap-1022",
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x8p-152, false, true,
+	false,
+	0x1.ffffffffffff8p-1024, false, true,
+	0x1.ffffffffffffcp-1024, false, true,
+	0x1.ffffffffffff8p-1024, false, true,
+	0x1.ffffffffffffcp-1024, false, true,
+	true,
+	0x1.ffffffffffffa8p-1024, false, false,
+	0x1.ffffffffffffa8p-1024, false, false,
+	0x1.ffffffffffffa8p-1024, false, false,
+	0x1.ffffffffffffa8p-1024, false, false,
+	true,
+	0x1.ffffffffffffa8p-1024, false, false,
+	0x1.ffffffffffffa8p-1024, false, false,
+	0x1.ffffffffffffa8p-1024, false, false,
+	0x1.ffffffffffffa8p-1024, false, false,
+	false,
+	0x1.ffffffffffff8p-1024, false, true,
+	0x1.ffffffffffffcp-1024, false, true,
+	0x1.ffffffffffff8p-1024, false, true,
+	0x1.ffffffffffffcp-1024, false, true,
+	true,
+	0x1.ffffffffffffa8p-1024, false, false,
+	0x1.ffffffffffffa8p-1024, false, false,
+	0x1.ffffffffffffa8p-1024, false, false,
+	0x1.ffffffffffffa8p-1024, false, false),
+  TEST ("0x0.7fffffffffffe9p-1022",
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x8p-152, false, true,
+	false,
+	0x1.ffffffffffff8p-1024, false, true,
+	0x1.ffffffffffffcp-1024, false, true,
+	0x1.ffffffffffff8p-1024, false, true,
+	0x1.ffffffffffffcp-1024, false, true,
+	true,
+	0x1.ffffffffffffa4p-1024, false, false,
+	0x1.ffffffffffffa4p-1024, false, false,
+	0x1.ffffffffffffa4p-1024, false, false,
+	0x1.ffffffffffffa4p-1024, false, false,
+	true,
+	0x1.ffffffffffffa4p-1024, false, false,
+	0x1.ffffffffffffa4p-1024, false, false,
+	0x1.ffffffffffffa4p-1024, false, false,
+	0x1.ffffffffffffa4p-1024, false, false,
+	false,
+	0x1.ffffffffffff8p-1024, false, true,
+	0x1.ffffffffffffcp-1024, false, true,
+	0x1.ffffffffffff8p-1024, false, true,
+	0x1.ffffffffffffcp-1024, false, true,
+	true,
+	0x1.ffffffffffffa4p-1024, false, false,
+	0x1.ffffffffffffa4p-1024, false, false,
+	0x1.ffffffffffffa4p-1024, false, false,
+	0x1.ffffffffffffa4p-1024, false, false),
+  TEST ("0x0.7ffffd4p-126",
+	false,
+	0x1.fffffp-128, false, true,
+	0x1.fffff8p-128, false, true,
+	0x1.fffffp-128, false, true,
+	0x1.fffff8p-128, false, true,
+	true,
+	0x1.fffff5p-128, false, false,
+	0x1.fffff5p-128, false, false,
+	0x1.fffff5p-128, false, false,
+	0x1.fffff5p-128, false, false,
+	true,
+	0x1.fffff5p-128, false, false,
+	0x1.fffff5p-128, false, false,
+	0x1.fffff5p-128, false, false,
+	0x1.fffff5p-128, false, false,
+	true,
+	0x1.fffff5p-128, false, false,
+	0x1.fffff5p-128, false, false,
+	0x1.fffff5p-128, false, false,
+	0x1.fffff5p-128, false, false,
+	true,
+	0x1.fffff5p-128, false, false,
+	0x1.fffff5p-128, false, false,
+	0x1.fffff5p-128, false, false,
+	0x1.fffff5p-128, false, false,
+	true,
+	0x1.fffff5p-128, false, false,
+	0x1.fffff5p-128, false, false,
+	0x1.fffff5p-128, false, false,
+	0x1.fffff5p-128, false, false),
+  TEST ("0x0.7ffffffffffffffd4p-16382",
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x8p-152, false, true,
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x4p-1076, false, true,
+	false,
+	0x1.fffffffffffffffp-16384, false, true,
+	0x1.fffffffffffffff8p-16384, false, true,
+	0x1.fffffffffffffffp-16384, false, true,
+	0x1.fffffffffffffff8p-16384, false, true,
+	false,
+	0x1.fffffffffffffff4p-16384, false, true,
+	0x1.fffffffffffffff4p-16384, false, true,
+	0x1.fffffffffffffff4p-16384, false, true,
+	0x1.fffffffffffffff8p-16384, false, true,
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x4p-1076, false, true,
+	true,
+	0x1.fffffffffffffff5p-16384, false, false,
+	0x1.fffffffffffffff5p-16384, false, false,
+	0x1.fffffffffffffff5p-16384, false, false,
+	0x1.fffffffffffffff5p-16384, false, false),
+  TEST ("0x0.7ffffffffffffffd4p-16383",
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x8p-152, false, true,
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x4p-1076, false, true,
+	false,
+	0xf.ffffffffffffff8p-16388, false, true,
+	0xf.ffffffffffffff8p-16388, false, true,
+	0xf.ffffffffffffff8p-16388, false, true,
+	0x1p-16384, false, true,
+	false,
+	0xf.ffffffffffffff8p-16388, false, true,
+	0xf.ffffffffffffffcp-16388, false, true,
+	0xf.ffffffffffffff8p-16388, false, true,
+	0xf.ffffffffffffffcp-16388, false, true,
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x4p-1076, false, true,
+	true,
+	0xf.ffffffffffffffa8p-16388, false, false,
+	0xf.ffffffffffffffa8p-16388, false, false,
+	0xf.ffffffffffffffa8p-16388, false, false,
+	0xf.ffffffffffffffa8p-16388, false, false),
+  TEST ("0x0.7ffffffffffffffffffffffffffeap-16382",
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x8p-152, false, true,
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x4p-1076, false, true,
+	false,
+	0x1.fffffffffffffff8p-16384, false, true,
+	0x2p-16384, false, true,
+	0x1.fffffffffffffff8p-16384, false, true,
+	0x2p-16384, false, true,
+	false,
+	0x1.fffffffffffffffcp-16384, false, true,
+	0x2p-16384, false, true,
+	0x1.fffffffffffffffcp-16384, false, true,
+	0x2p-16384, false, true,
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x4p-1076, false, true,
+	false,
+	0x1.fffffffffffffffffffffffffff8p-16384, false, true,
+	0x1.fffffffffffffffffffffffffffcp-16384, false, true,
+	0x1.fffffffffffffffffffffffffff8p-16384, false, true,
+	0x1.fffffffffffffffffffffffffffcp-16384, false, true),
+  TEST ("0x0.7000004p-126",
+	false,
+	0x1.cp-128, false, true,
+	0x1.cp-128, false, true,
+	0x1.cp-128, false, true,
+	0x1.c00008p-128, false, true,
+	true,
+	0x1.c00001p-128, false, false,
+	0x1.c00001p-128, false, false,
+	0x1.c00001p-128, false, false,
+	0x1.c00001p-128, false, false,
+	true,
+	0x1.c00001p-128, false, false,
+	0x1.c00001p-128, false, false,
+	0x1.c00001p-128, false, false,
+	0x1.c00001p-128, false, false,
+	true,
+	0x1.c00001p-128, false, false,
+	0x1.c00001p-128, false, false,
+	0x1.c00001p-128, false, false,
+	0x1.c00001p-128, false, false,
+	true,
+	0x1.c00001p-128, false, false,
+	0x1.c00001p-128, false, false,
+	0x1.c00001p-128, false, false,
+	0x1.c00001p-128, false, false,
+	true,
+	0x1.c00001p-128, false, false,
+	0x1.c00001p-128, false, false,
+	0x1.c00001p-128, false, false,
+	0x1.c00001p-128, false, false),
+  TEST ("0x0.70000000000002p-1022",
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x8p-152, false, true,
+	false,
+	0x1.cp-1024, false, true,
+	0x1.cp-1024, false, true,
+	0x1.cp-1024, false, true,
+	0x1.c000000000004p-1024, false, true,
+	true,
+	0x1.c0000000000008p-1024, false, false,
+	0x1.c0000000000008p-1024, false, false,
+	0x1.c0000000000008p-1024, false, false,
+	0x1.c0000000000008p-1024, false, false,
+	true,
+	0x1.c0000000000008p-1024, false, false,
+	0x1.c0000000000008p-1024, false, false,
+	0x1.c0000000000008p-1024, false, false,
+	0x1.c0000000000008p-1024, false, false,
+	false,
+	0x1.cp-1024, false, true,
+	0x1.cp-1024, false, true,
+	0x1.cp-1024, false, true,
+	0x1.c000000000004p-1024, false, true,
+	true,
+	0x1.c0000000000008p-1024, false, false,
+	0x1.c0000000000008p-1024, false, false,
+	0x1.c0000000000008p-1024, false, false,
+	0x1.c0000000000008p-1024, false, false),
+  TEST ("0x0.70000000000000004p-16382",
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x8p-152, false, true,
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x4p-1076, false, true,
+	false,
+	0x1.cp-16384, false, true,
+	0x1.cp-16384, false, true,
+	0x1.cp-16384, false, true,
+	0x1.c000000000000008p-16384, false, true,
+	false,
+	0x1.cp-16384, false, true,
+	0x1.cp-16384, false, true,
+	0x1.cp-16384, false, true,
+	0x1.c000000000000004p-16384, false, true,
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x4p-1076, false, true,
+	true,
+	0x1.c000000000000001p-16384, false, false,
+	0x1.c000000000000001p-16384, false, false,
+	0x1.c000000000000001p-16384, false, false,
+	0x1.c000000000000001p-16384, false, false),
+  TEST ("0x0.70000000000000004p-16383",
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x8p-152, false, true,
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x4p-1076, false, true,
+	false,
+	0xep-16388, false, true,
+	0xep-16388, false, true,
+	0xep-16388, false, true,
+	0xe.000000000000008p-16388, false, true,
+	false,
+	0xep-16388, false, true,
+	0xep-16388, false, true,
+	0xep-16388, false, true,
+	0xe.000000000000004p-16388, false, true,
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x4p-1076, false, true,
+	true,
+	0xe.0000000000000008p-16388, false, false,
+	0xe.0000000000000008p-16388, false, false,
+	0xe.0000000000000008p-16388, false, false,
+	0xe.0000000000000008p-16388, false, false),
+  TEST ("0x0.70000000000000000000000000002p-16382",
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x8p-152, false, true,
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x4p-1076, false, true,
+	false,
+	0x1.cp-16384, false, true,
+	0x1.cp-16384, false, true,
+	0x1.cp-16384, false, true,
+	0x1.c000000000000008p-16384, false, true,
+	false,
+	0x1.cp-16384, false, true,
+	0x1.cp-16384, false, true,
+	0x1.cp-16384, false, true,
+	0x1.c000000000000004p-16384, false, true,
+	false,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x0p+0, false, true,
+	0x4p-1076, false, true,
+	false,
+	0x1.cp-16384, false, true,
+	0x1.cp-16384, false, true,
+	0x1.cp-16384, false, true,
+	0x1.c000000000000000000000000004p-16384, false, true),
 };