Comparing fields in 2 large files

I am new to perl and would appreciate any suggestions as to how to do
the following.

I have two files, one with 3.5 million records, the other with almost a
million records.   Basically here's what I need to do.

See if field_1 in file_a is part of field_1 in file_b
If so, see if field_2 in file_a is part of field_1 in file_b
If so, see if field_3 in file_a is equal to field_2 in file_b
If not equal, write out field_4 in file_a plus field_3 in file_b

I have written a script that will do this, but it runs literally for
days.   I'm guessing my method is not the most efficient.   I do not
have enough memory to read the files at one time into an array.

Thanks in advance for ideas.

Craig