diff --git a/numeric.c b/numeric.c
index a7769ca255..1e38cdee99 100644
--- a/numeric.c
+++ b/numeric.c
@@ -4793,7 +4793,7 @@ rb_fix_digits(VALUE fix, long base)
 static VALUE
 rb_int_digits_bigbase(VALUE num, VALUE base)
 {
-    VALUE digits;
+    VALUE digits, bases;
 
     assert(!rb_num_negative_p(num));
 
@@ -4811,13 +4811,33 @@ rb_int_digits_bigbase(VALUE num, VALUE base)
     if (FIXNUM_P(num))
         return rb_ary_new_from_args(1, num);
 
-    digits = rb_ary_new();
-    while (!FIXNUM_P(num) || FIX2LONG(num) > 0) {
-        VALUE qr = rb_int_divmod(num, base);
-        rb_ary_push(digits, RARRAY_AREF(qr, 1));
-        num = RARRAY_AREF(qr, 0);
+    if (int_lt(rb_int_div(rb_int_bit_length(num), rb_int_bit_length(base)), INT2FIX(50))) {
+	digits = rb_ary_new();
+	while (!FIXNUM_P(num) || FIX2LONG(num) > 0) {
+	    VALUE qr = rb_int_divmod(num, base);
+	    rb_ary_push(digits, RARRAY_AREF(qr, 1));
+	    num = RARRAY_AREF(qr, 0);
+	}
+	return digits;
+    }
+
+    bases = rb_ary_new();
+    for (VALUE b = base; int_lt(b, num) == Qtrue; b = rb_int_mul(b, b)) {
+	rb_ary_push(bases, b);
+    }
+    digits = rb_ary_new_from_args(1, num);
+    while (RARRAY_LEN(bases)) {
+	VALUE b = rb_ary_pop(bases);
+	long i, last_idx = RARRAY_LEN(digits) - 1;
+	for(i = last_idx; i >= 0; i--) {
+	    VALUE n = RARRAY_AREF(digits, i);
+	    VALUE divmod = rb_int_divmod(n, b);
+	    VALUE div = RARRAY_AREF(divmod, 0);
+	    VALUE mod = RARRAY_AREF(divmod, 1);
+	    if (i != last_idx || div != INT2FIX(0)) rb_ary_store(digits, 2 * i + 1,  div);
+	    rb_ary_store(digits, 2 * i, mod);
+	}
     }
-
     return digits;
 }
 
diff --git a/test/ruby/test_integer.rb b/test/ruby/test_integer.rb
index 1b485760e3..ac5bdfdddf 100644
--- a/test/ruby/test_integer.rb
+++ b/test/ruby/test_integer.rb
@@ -444,6 +444,8 @@ def test_digits
     assert_equal([0, 9, 8, 7, 6, 5, 4, 3, 2, 1], 1234567890.digits)
     assert_equal([90, 78, 56, 34, 12], 1234567890.digits(100))
     assert_equal([10, 5, 6, 8, 0, 10, 8, 6, 1], 1234567890.digits(13))
+    assert_equal((2 ** 1024).to_s(7).chars.map(&:to_i).reverse, (2 ** 1024).digits(7))
+    assert_equal([0] * 100 + [1], (2 ** (128 * 100)).digits(2 ** 128))
   end
 
   def test_digits_for_negative_numbers