Unsigned bigint overflow problem when using an index

When using an index a query may present the following strange behaviour:

1) A constant value is wrongly returned

2) Results are not found
2.b) Using >= =< instead of BETWEEN returns the results, but still constant is wrongly returned

3) ERROR 1690 (22003): BIGINT value is out of range is not consistent

- select count(*),9223372036854775807+4 from t1  where b>1;  ERROR

- select count(*),9223372036854775808+4 from t1  where b>1;  OK

And I think there are many other related side effects.

Test case attached.