ALU,RAM and ROM test for LPC 1778
What are you afraid of? That an internal route between gates within the chip be broken or shorted? If it was the case, it would certainly mean the chip was physically broken. I mean, broken as in "split in two halves because of some thermal stress". In which case it wouldn't work at all. What you are trying to test here isn't worth it, the probability that one internal trace is wrong is more than unlikely.

What would be more likely are single event upset, which you can't prevent by prior testing (and which is very difficult to handle anyway, you'd need probably some lock-step core and ECC memory).

Eventually, use some CRC for critical data in memory, to react in case it gets corrupted. That is the best you can do.