Where EBP records EDI ESI are used

For the architecture x86 - 64bits there are the following registers:

General Registers [GPR]
As the name says, they are records of general use. They serve to do most common operations.

• Accumulator register RAX
• Base registration RBX
• Accountant Record RCX
• Data Registration RDX

All these registers allow access to sections of themselves, for this we must refer to them as RAX for 64 bits; EAX for 32 bits; AX for the first 16 bits; AH for the second half of the first 16 bits; AL for the first 8 bits. This applies to all other general records (and also for indexes and pointers). To understand how they are distributed you can see the following scheme:

[ 64 bits = 8 Bytes RAX ]
[ 32 bits = 4 Bytes | EAX ]
[ | | AX ]
[ | | AH | AL ]

Indexes and pointers
This keeps indexes and pointers (memory addresses).

• Destination index record [Destination index] RDI
• Source index record [Source index] RSI
  Used to maintain the address of destination and origin (respectively) in copy operations of arrays (vectors) and text strings.
• Pointer to stack origin record [Stack Base pointer] RBP
  This record maintains the address of the origin of the stack.
• Pointer to stack log [Stack pointer] RSP
  This record keeps the address of the most recent element in the stack.
• Pointer record to instruction EIP This record maintains the address of the following instruction.

As in the general registers, portions of these registers can be accessed with RSI , ESI and SI . (also applies for other records eg: RDI , EDI , DI ).

You can see more information about the missing record at X86 architecture.