# MMIX

MMIX is a 64-bit RISC virtual machine designed by Donald Knuth, with significant contributions by John Hennessy (who designed the MIPS chip) and Dick Sites (who was the architect of the Alpha chip). Knuth will be using MMIX in all future editions of his epic masterpiece The Art of Computer Programming (TAoCP) to illustrate machine-level aspects of programming, especially in relation to the analysis of algorithms. It is pronounced 'emmix.

MMIX's predecessor, MIX, is used in current and earlier editions of TAoCP. MMIX is a completely new design, conforming to modern ideas about computer design, and is to replace the now thoroughly archaic MIX.

 Contents

## Architecture

MMIX is a binary computer with a 64-bit virtual address space and 32-bit instructions which uses the big-endian convention.

### Instructions

All instructions have an associated mnemonic. For example instruction 32 is associated to ADD. Most instructions have the symbolic form "OP, X, Y, Z", where OP specifies the sort of instruction, X specifies the register used to store the result of the instruction and the rest specify the operands of the instruction. Each of these fields is eight bits wide. For example the instruction "ADD \$0, \$1, 3", will add the contents of register 1 and the immediate value 3 and store the result in register 0. MMIX programs are typically constructed using the MMIXAL assembly language. For an example see the Hello world page.

### Registers

There are 256 general purpose architectural registers in an MMIX chip, designated by \$0 through \$255 and 32 special physical architectural registers. They are implemented by 256-32 global physical registers and 512 local physical registers. If X is a number from 0 to 255 inclusive, then special registers rL and rG determine whether register \$X refers to a local or a global physical register.

#### Local Register Stack

The local register stack provides each subroutine with its own rL local registers, designated by \$0 through \$(rL-1). Whenever a subroutine is called, a number of local registers is pushed down the stack. The arguments of the called subroutine are left in the remaining local registers. When a subroutine finishes it pops the previously pushed registers. Because there are only 512 local physical registers, it may be necessary to store a part of the stack in memory. This is implemented with the special registers rO and rS which record which part of the local register stack is in memory and which part is still in local physical registers. The register stack provides for fast subroutine linkage.

#### Special Registers

The 32 special physical architectural registers are:

1. rB, the bootstrap register (trip)
When tripping, rB <- \$255 and \$255 <- rJ. Thus saving rJ in a general register.
2. rD, the dividend register
Unsigned integer divide uses this as the left half of the 128-bit input that is to be divided by the other operand.
3. rE, the epsilon register
Used for floating comparisons with respect to epsilon.
4. rH, the himult register
Used to store the left half of the 128-bit result of unsigned integer multiplication.
5. rJ, the return-jump register
Used to save the address of the next instruction by PUSHes and by POP to return from a PUSH.
6. rM, the multiplex mask register
Used by the multiplex instruction.
7. rR, the remainder register
Is set to the remainder of integer division.
8. rBB, the bootstrap register (trap)
When trapping, rBB <- \$255 and \$255 <- rJ. Thus saving rJ in a general register
9. rC, the cycle counter
Incremented every cycle.
10. rN, the serial number
A constant identifying this particular MMIX processor.
11. rO, the register stack offset
Used to implement the register stack.
12. rS, the register stack pointer
Used to implement the register stack.
13. rI, the interval counter
Decremented every cycle. Causes an interrupt when zero.
14. rT, the trap address register
Used to store the address of the trip vector.
15. rTT, the dynamic trap address register
Used to store the address of the trap vector.
16. rK, the interrupt mask register
Used to enable and disable specific interrupts.
17. rQ, the interrupt request register
Used to record interrupts as they occur.
18. rU, the usage counter
Used to keep a count of executed instructions.
19. rV, the virtual translation register
Used to translate virtual addresses to physical addresses. Contains the size and number of segments, the root location of the page table and the address space number.
20. rG, the global threshold register
All general registers references with a number greater or equal to rG refer to global registers.
21. rL, the local threshold register
All general registers references with a number smaller than rL refer to local registers.
22. rA, the arithmetic status register
Used to record, enable and disable arithmetic exception like overflow and divide by zero.
23. rF, the failure location register
Used to store the address of the instruction that caused a failure.
24. rP, the prediction register
Used by conditional swap (CSWAP).
25. rW, the where-interrupted register (trip)
Used, when tripping, to store the address of the instruction after the one that was interrupted.
26. rX, the execution register (trip)
Used, when tripping, to store the instruction that was interrupted.
27. rY, the Y operand (trip)
Used, when tripping, to store the Y operand of the interrupted instruction.
28. rZ, the Z operand (trip)
Used, when tripping, to store the Z operand of the interrupted instruction.
29. rWW, the where-interrupted register (trap)
Used, when trapping, to store the address of the instruction after the one that was interrupted.
30. rXX, the execution register (trap)
Used, when trapping, to store the instruction that was interrupted.
31. rYY, the Y operand (trap)
Used, when trapping, to store the Y operand of the interrupted instruction.
32. rZZ, the Z operand (trap)
Used, when trapping, to store the Z operand of the interrupted instruction.

## References

• Donald E. Knuth (1999). MMIXware: A RISC Computer for the Third Millennium. Heidelberg: Springer-Verlag. ISBN 3-540-66938-8 (errata) (http://www-cs-faculty.stanford.edu/~knuth/mmixware.html)

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