If this is your entering in hardfault, I think the PSP may not what is active in your code(instead the msp is), since the PC and some important message must be saved in stack before hardfault. First you can check the some special register:

To help detect what type of error was encountered in the fault handler, the Cortex®-M3 and Cortex®-M4 processors also have a number Fault Status Registers (FSRs) and Fault Address Registers (FARs) that are used for fault analysis.​ (from stm32 blog)

And from your infos I guess that It may be because of some instructions that are not supported on cortexM4 as the memory consumption there seems not so expensive.(so you can go on check the special register above and improve you description)