diff --git a/gcc/testsuite/gcc.dg/torture/bitint-53.c b/gcc/testsuite/gcc.dg/torture/bitint-53.c
new file mode 100644
index 0000000000000000000000000000000000000000..8ead40e450ba89ccc16dbb54e92cd788c57bed59
--- /dev/null
+++ b/gcc/testsuite/gcc.dg/torture/bitint-53.c
@@ -0,0 +1,26 @@
+/* PR libgcc/113604 */
+/* { dg-do run { target bitint } } */
+/* { dg-options "-std=c23 -pedantic-errors" } */
+/* { dg-skip-if "" { ! run_expensive_tests }  { "*" } { "-O0" "-O2" } } */
+/* { dg-skip-if "" { ! run_expensive_tests } { "-flto" } { "" } } */
+
+#if __BITINT_MAXWIDTH__ >= 256
+unsigned _BitInt (256) x;
+
+void
+foo (unsigned _BitInt (256) a, unsigned _BitInt (128) b)
+{
+  x = a / b;
+}
+#endif
+
+int
+main ()
+{
+#if __BITINT_MAXWIDTH__ >= 256
+  foo (0xfffffffffffffffffffffc0000000000000000000004uwb, 0x7ffffffffffffffffffffffffffuwb);
+  if (x != 0x1fffffffffffffffffuwb)
+    __builtin_abort ();
+#endif
+  return 0;
+}
diff --git a/gcc/testsuite/gcc.dg/torture/bitint-55.c b/gcc/testsuite/gcc.dg/torture/bitint-55.c
new file mode 100644
index 0000000000000000000000000000000000000000..7d4bff3fd1296d9208a71a60634bd7a12d6dddf7
--- /dev/null
+++ b/gcc/testsuite/gcc.dg/torture/bitint-55.c
@@ -0,0 +1,66 @@
+/* PR libgcc/113604 */
+/* { dg-do run { target bitint } } */
+/* { dg-options "-std=c23 -pedantic-errors" } */
+/* { dg-skip-if "" { ! run_expensive_tests }  { "*" } { "-O0" "-O2" } } */
+/* { dg-skip-if "" { ! run_expensive_tests } { "-flto" } { "" } } */
+
+#if __BITINT_MAXWIDTH__ >= 513
+signed _BitInt(513)
+foo (signed _BitInt(513) x, signed _BitInt(513) y)
+{
+  return x % y;
+}
+#endif
+
+#if __BITINT_MAXWIDTH__ >= 512
+unsigned _BitInt(512)
+bar (unsigned _BitInt(512) x, unsigned _BitInt(512) y)
+{
+  return x % y;
+}
+#endif
+
+#if __BITINT_MAXWIDTH__ >= 256
+unsigned _BitInt(256)
+baz (unsigned _BitInt(256) x, unsigned _BitInt(256) y)
+{
+  return x % y;
+}
+#endif
+
+int
+main ()
+{
+#if __BITINT_MAXWIDTH__ >= 513
+  if (foo (11155754932722990178552651944728825929130437979239421228991532051555943675wb,
+	   32783817256434357484609367438786815wb) != 0wb)
+    __builtin_abort ();
+  if (foo (542904728531209767665756029992981529373473101602268731408384wb,
+	   235447394450476261134537147263765988105wb)
+      != 235447394450476261116090403190056436489wb)
+    __builtin_abort ();
+  if (foo (542904728531209767665690117878483036079552477922114364506112wb,
+	   235447394450476261134537147263765988105wb)
+      != 169535279951982967195466723035689534217wb)
+    __builtin_abort ();
+  if (foo (542904728531209767665690117878483036079534031178040654954496wb,
+	   235447394450476261134537147263765988105wb)
+      != 169535279951982967177019978961979982601wb)
+    __builtin_abort ();
+  if (foo (542904728531209767665454670484032559818581851459155356811264wb,
+	   235447394450476261134537147263765988105wb)
+      != 169535279951982967359377407340447827474wb)
+    __builtin_abort ();
+#endif
+#if __BITINT_MAXWIDTH__ >= 512
+  if (bar (6703903964971298549787012499102923063739682910296196688861780721860882015036773488400937149083451713845015929093243025426876941405973284973216824503042048uwb,
+	   170141183460469231731687303715884105735uwb) != 19208uwb)
+    __builtin_abort ();
+#endif
+#if __BITINT_MAXWIDTH__ >= 256
+  if (baz (115792089237316195423570985008687907853269984665640564039457584007913129639926uwb,
+	   68056473384187692692674921486353642292uwb) != 6uwb)
+    __builtin_abort ();
+#endif
+  return 0;
+}
diff --git a/libgcc/libgcc2.c b/libgcc/libgcc2.c
index e04d169f888a6c47a33551f7a4d81e8eb0d07a5c..ef46153731fd619f9869ff9d21e1df43858349a7 100644
--- a/libgcc/libgcc2.c
+++ b/libgcc/libgcc2.c
@@ -1863,12 +1863,46 @@ __divmodbitint4 (UBILtype *q, SItype qprec,
 	      if (uv1 >= vv1)
 		{
 		  /* udiv_qrnnd doesn't support quotients which don't
-		     fit into UWtype, so subtract from uv1:uv0 vv1
-		     first.  */
-		  uv1 -= vv1 + __builtin_sub_overflow (uv0, vv1, &uv0);
-		  udiv_qrnnd (qhat, rhat, uv1, uv0, vv1);
-		  if (!__builtin_add_overflow (rhat, vv1, &rhat))
-		    goto again;
+		     fit into UWtype, while Knuth's algorithm originally
+		     uses a double-word by word to double-word division.
+		     Fortunately, the algorithm guarantees that uv1 <= vv1,
+		     because if uv1 > vv1, then even if v would have all
+		     bits in all words below vv1 set, the previous iteration
+		     would be supposed to use qhat larger by 1 and subtract
+		     v.  With uv1 == vv1 and uv0 >= vv1 the double-word
+		     qhat in Knuth's algorithm would be 1 in the upper word
+		     and 1 in the lower word, say for
+		     uv1 0x8000000000000000ULL
+		     uv0 0xffffffffffffffffULL
+		     vv1 0x8000000000000000ULL
+		     0x8000000000000000ffffffffffffffffuwb
+		     / 0x8000000000000000uwb == 0x10000000000000001uwb, and
+		     exactly like that also for any other value
+		     > 0x8000000000000000ULL in uv1 and vv1 and uv0 >= uv1.
+		     So we need to subtract one or at most two vv1s from
+		     uv1:uv0 (qhat because of that decreases by 1 or 2 and
+		     is then representable in UWtype) and need to increase
+		     rhat by vv1 once or twice because of that.  Now, if
+		     we need to subtract 2 vv1s, i.e. if
+		     uv1 == vv1 && uv0 >= vv1, then rhat (which is uv0 - vv1)
+		     + vv1 computation can't overflow, because it is equal
+		     to uv0 and therefore the original algorithm in that case
+		     performs goto again, but the second vv1 addition must
+		     overflow already because vv1 has msb set from the
+		     canonicalization.  */
+		  uv1 -= __builtin_sub_overflow (uv0, vv1, &uv0);
+		  if (uv1 >= vv1)
+		    {
+		      uv1 -= __builtin_sub_overflow (uv0, vv1, &uv0);
+		      udiv_qrnnd (qhat, rhat, uv1, uv0, vv1);
+		      rhat += 2 * vv1;
+		    }
+		  else
+		    {
+		      udiv_qrnnd (qhat, rhat, uv1, uv0, vv1);
+		      if (!__builtin_add_overflow (rhat, vv1, &rhat))
+			goto again;
+		    }
 		}
 	      else
 		{