Overlapping intervals¶

Checking if two intervals overlap is covered on this page:

which shows intervals

$(s_1, e_1) (s_2, e_2)$

overlap if

$(s_2 < e_1) \wedge (s_1 < e_2)$

If the intervals are specified by a width

$(s_1, (s_1+w_1)) (s_2, (s_2+w_2))$

then the overlap test is

$(s_2 < (s_1 + w_1)) \wedge (s_1 < (s_2 + w_2))$

and the expression

$a < (b + c)$

is equivalent to evaluating

$a - b - c$

then checking that the result is negative by examining the sign bit.