MMIX

MMIX also refers to the year 2009, in Roman numerals.

MMIX (pronounced em-mix) is a 64-bit RISC instruction set architecture (ISA) designed by Donald Knuth, with significant contributions by John L. Hennessy (who contributed to the design of the MIPS ISA) and Richard L. Sites (who was an architect of the Alpha ISA). In Knuth’s own words:

MMIX is a computer intended to illustrate machine-level aspects of programming. In my books The Art of Computer Programming, it replaces MIX, the 1960s-style machine that formerly played such a role... I strove to design MMIX so that its machine language would be simple, elegant, and easy to learn. At the same time I was careful to include all of the complexities needed to achieve high performance in practice, so that MMIX could in principle be built and even perhaps be competitive with some of the fastest general-purpose computers in the marketplace.

Its purpose for education is quite similar to John L. Hennessy's and David A. Patterson's DLX architecture, from Computer Architecture: A Quantitative Approach.

Architecture

MMIX is a 64-bit RISC computer, with 256 64-bit general-purpose registers and 32 64-bit special-purpose registers. MMIX is a big-endian machine with 32-bit instructions and a 64-bit virtual address space. The MMIX instruction set comprises 256 opcodes, one of which is reserved for future expansion.

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.

Most instructions can take either immediate values or register contents; thus a single instruction mnemonic may correspond to one of two opcodes.

MMIX programs are typically constructed using the MMIXAL assembly language. The below is a simple MMIXAL program, which prints Hello, world:

string BYTE  "Hello, world!",#a,0  'string to be printed (#a is newline and 0 terminates the string)
Main   GETA  $255,string           'get the address of the string in register 255
       TRAP  0,Fputs,StdOut        'put the string pointed to by register 255 to file StdOut
       TRAP  0,Halt,0              'end process

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 $256-32=224$ 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 as follows:

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.

Hardware implementations

As of 2008, the MMIX instruction set architecture has not yet been implemented in hardware.

Software tools

The MMIX instruction set architecture is supported by a number of software tools for computer architecture research and software development.

Simulators and assembler

• MMIXware (version 20090205) – Donald Knuth’s MMIX-SIM simple (behavioral) simulator, MMIXAL assembler, test suite, sample programs, full documentation, and MMMIX architectural (pipeline) simulator (gzipped tar file.)
• MMIXX – An X11-based graphics package contributed by Andrew Pochinsky of MIT’s Center for Theoretical Physics which, when combined with the MMIXware sources above, augments the MMIX virtual machine with a VGA-resolution, true-color ‘virtual display’ (for UNIX/Linux.)

Compiler

The GNU Compiler Collection includes an MMIX back-end for its C/C++ compilers, contributed by Hans-Peter Nilsson and part of the main GCC distribution since late 2001.

• Installation instructions for GCC + MMIX tools by Hans-Peter Nilsson.

References

• Errata to above book.
• Donald E. Knuth (2005). The Art of Computer Programming Volume 1 Fascicle 1: MMIX A RISC Computer for the New Millennium. Addison-Wesley. ISBN 0-201-85392-2 (errata)

External links

• Donald Knuth's MMIX page — A brief introduction to MMIX, and Knuth's reasons for using a hypothetical assembly language in TAoCP.
• Donald Knuth's MMIX news page — An open-source simulator written in CWEB, a programmer's manual, and example programs.
• MMIXmasters web site A web site for the volunteers (MMIXmasters) who are converting all of the programs in TAOCP, Volumes 1 - 3, from the old language MIX to the new language MMIX.