Dividing Negative integer ranges
Redundant check

If xiExistingRangeStart is greater than xiExistingRangeEnd, then you only have to verify that xiExistingRangeStart is not greater than zero to know that xiExistingRangeEnd can't be.

Parameters + Error messages

I would prefer your exception messages to be more explicit.   Rather than:


  "The SMALLER value MUST be provided first. Note that since values are negative, this first value will have the larger ABSOLUTE value!"); }


I think it would be better to refer to 'Start' rather than 'first' value.  This may seem pedantic but consistency between the error name and the parameter name make it easier to resolve issues.

Similarly, when I think of negative numbers, I tend to think of numbers &lt; 0, not &lt;= zero which seems to be what your code suggests.  So again, I'd tend to be more explicit.