General Computer Science 320201 GenCS I & II Lecture ... - Kwarc

the L(VM) program store: P (2 24 ) to P (2 32 − 1)
We represent the virtual program counter VPC by the index register IN1 and the stack
pointer by the index register IN2 (with offset 8).
We will use P (0) as an argument store.
choose a numerical representation for the L(VM) instructions: (have lots of space)
halt ↦→ 0, add ↦→ 1, sub ↦→ 2, . . .
c○: Michael Kohlhase 287
Recall that the virtual machine VM is a ASM program, so it will reside in the REMA program store.
This is the program executed by the register machine. So both the VM stack and the L(VM) program
have to be stored in the REMA data store (therefore we treat L(VM) programs as sequences of words
and have to do counting acrobatics for instructions of differing length). We somewhat arbitrarily
fix a boundary in the data store of REMA at cell number 2 24 − 1. We will also need a little piece
of scratch-pad memory, which we locate at cells 0-7 for convenience (then we can simply address
with absolute numbers as addresses).
Memory Layout for the Virtual Machine
Program Store
Operation Argument
2n−bit Cells
CPU
ACC (accumulator)
IN1 (VM prog. cnt.)
IN2 (stack pointer)
IN3 (frame pointer)
PC (program counter)
ASM Program
for VM
Program
Stack
Scratch Area
c○: Michael Kohlhase 288
Data Store
n−bit Cells
To make our implementation of the virtual more convenient, we will extend ASM with a couple of
convenience features. Note that these features do not extend the theoretical expressivity of ASM
(i.e. they do not extend the range of programs that ASM), since all new commands can be replaced
by regular language constructs.
Extending REMA and ASM
Give ourselves another register IN3 (and LOADIN 3, STOREIN 3, MOVE ∗ IN3, MOVE IN3 ∗)
We will use a syntactic variant of ASM for transparency
JUMP and JUMPR with labels of the form 〈foo〉
(compute relative jump distances automatically)
inc R for MOVE R ACC, ADDI 1, MOVE ACC R (dec R similar)
note that inc R and dec R overwrite the current ACC (take care of it)
All additions can be eliminated by substitution.
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