Why reversible architectures? What about automatic emulation algorithms? E.g.: Ben73, Ben89, LMT, Frank02. Transform an irreversible alg. to an equiv. revble one. But, these do not yield the most cost-efficient reversible
algorithms for all problems! E.g., log(RE(i./r)/Ron/off) may be only 0.4 rather than 0.5. Finding the best reversible algorithm requires a creative algorithm discovery process! An optimally cost-efficient general-purpose architecture must allow the programmer to specify a custom
reversible algorithm that is specific to his problem. Reversibility Affects All Levels As Ron/off increases & cost of device manuf. declines (while the cost of energy stays high), Maximizing overall cost-efficiency requires an increasingly
large fraction of all bit-ops be done adiabatically. Maximizing the efficiency of the resulting algorithms, in turn, requires reversibility in:
Pro- gramming model
Logic design Functional units Instruction set architectures (unless a perfect emulator is found) Programming languages Increasing requirement High-level algorithms for degree of
reversibility All Known Reversible Architectures Ed Barton (MIT class project, 1978) Conservative logic, w. garbage stack Andrew Ressler (MIT bachelors thesis, 1979; MIT masters thesis, 1981) Like Bartons, but more detailed. Paired branches.
Henry Baker (1992) Reversible pointer automaton machine instructions. J. Storrs JoSH Hall (1994) Retractile-cascade-based PDP-10-like architecture. Carlin Vieri (MIT masters thesis, 1995) Early Pendulum ISA, irrev. impl., full VHDL detail. Frank & Rixner (MIT class project, 1996)
Tick: VLSI schematics & layout of Pendulum subset, w. paired branches Frank & Love (MIT class project, 1996) FlatTop: Adiabatic VLSI impl. of programmable reversible gate array Vieri (MIT Ph.D. thesis, 1999) Fully adiabatic VLSI implementation of Pendulum w. paired branches Reversible Programmable GateArray Architectures
(as of May 99) Photo of packaged FlatTop chip A Bouncing BBMCA Ball
A BBMCA Fredkin Gate Reversible von Neumann Architectures Reversible Architecture Issues Instruction-Set Architecture (ISA) Issues:
How to define irrev. ops (AND, etc.) reversibly? How to do jumps/branches reversibly? What kind of memory interface to have? What about I/O? How to permit efficient reversible algorithms? Should the hardware guarantee reversibility?
Reversible ALU operations Shared buses Program counter control The Trivial Cases Many typical instructions already reversible:
NOT a Set register a to its bitwise logical complement, a := ~a NEG a Set a to its twos complement negation
a := -a INC a or a := ~a + 1
Increment a by 1 (modulo 2). ADD a b Add register b into register a
(a := (a + b) mod 2) Exclusive-or b into a (a := a b) XOR a b
ROL a b Rotate bits in register a left by # positions given by b. The Nontrivial Cases Other common instructions are not reversible CLR a
Clear register a to 0. LD a b Load register a from addr. pointed to by b.
LDI a 3 Load immediate value 3 into register a. AND a b Set a to the bitwise AND of a and b
JMP a Jump to the instruction pointed to by a. SLL a b
Shift the bits in a left by b bits, filling with 0s on right. Irreversible Data Operations How to do expanding ops reversibly? E.g., AND a b - Prior value of a is lost. Approach #1: Garbage Stack approach.
Based on Landauers embedding. Push all data that would otherwise be destroyed onto a special garbage stack hidden from pgmr. Can unwind computation when finished to recover stack space. (Lecerf 63/Bennett 73 approach)
Problems: Large garbage stack memory needed. Limits computation length. Leaves programmer no opportunity to choose a more efficient reversible algorithm! Illustrating Garbage Stack
Let mean reversible move, mean reversible copy, a reversible uncopy. AND a b Garbage Stack Memory (GSM)
implemented by... 1. t a 2. a t & b 3. t GSM[GSP++] Garbage Stack
Pointer (GSP) 3 230 0 46 1 17 2 0 3
0 4 ... Programmer-Controlled Garbage Put extra data in a programmer-manipulable location.
What if destination location isnt empty? Signal an error, or Use an op that does something reversible anyway Provide undo operations to accomplish unexpanding inverses of expanding ops.
1st method: Errors on non-empty destination: AND A B C -If (A=0) AB&C else error UNAND A B C -If (A=B&C) AB&C else error 2nd method: Use always-reversible store ops.
ANDX A B C - A A (B & C) (self-undoing!) Pendulum - packaged chip photo
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