When hooking 64-bit functions with a 5-byte JMP (E9 xx xx xx xx):

Formula for the 32-bit signed relative displacement:

int32_t displacement = (int32_t)((uintptr_t)pDestination - ((uintptr_t)pSource + 5));

If the trampoline distance exceeds 2GB (|pDestination - pSource| > 0x7FFFFFFF):
Use an indirect 64-bit jump without registers:

FF 25 00 00 00 00 [8-byte absolute address]

This reads the 64-bit address from RIP + 0 and jumps directly without clobbering RAX/RCX/RDX!

FF 25 00 00 00 00 (jmp [rip+0]) is the cleanest 14-byte absolute jump on x64 because it preserves all GPRs.

Always remember to subtract 5 (the length of the jmp instruction) when computing relative E9 displacements.