Transcript ppt

ESE370:
Circuit-Level
Modeling, Design, and Optimization
for Digital Systems
Day 38: December 10, 2010
Energy and Computation
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Penn ESE370 Fall2010 -- DeHon
Question
• Do we have to spend energy in order to
compute?
– What is the lower-bound on energy
required to perform a computation?
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Day 32
Minimum Energy
• Single bit gate output
– Set from previous value to 0 or 1
– Reduce state space by factor of 2
– Entropy: S= k×ln(before/after)=k×ln2
– Energy=T S=kT×ln(2)
• Setting a bit costs at least kT×ln(2)
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Today
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Thermodynamics
Information and Energy
Reversibility
Adiabatic Logic
Adiabatic Pipelines
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Second Law of
Thermodynamics
• Entropy in closed system increases:
 S≥0
– Entropy is a measure of disorder
– Move from order to disorder
• Heat does not move from cold areas to
hot areas
– Systems tend to equilibrium
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Entropy
• Measure of disorder of a system
• Proportional to
– logarithm of
• the number of microscope states
(arrangements of atoms, electrons…) that can
give rise to macroscopic observation of state
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Example
• 2 electrons
• Attached to any of 128 atoms
– (e.g. conduction band)
• Equilibrium:
– States each could be in any of 128
positions (128*127/2)=8128
– log2(8128)=13
• Constrain both to be on left 64
– States both on left (64*63/2)=2116
– Smaller Entropy  more order
– log2(2116)=11
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Information
• Information standpoint
– knowing both on left 64
– provides 2 bits of information
• 6 bits = log(64) to describe each position
instead of log(128)=7
• In fact we quantify how unknown a
bitstream as information entropy
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Entropy & Information
• Entropy proportional to Information Content
– Pun?
• Thermodyanic Entropy vs. Information Entropy
– Both defined as log(possibilities)
• If equally likely
• Reducing the information content
– Reduces entropy
 requires energy proporational to change in
entropy
Penn ESE370 Fall2010 -- DeHon
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Computation
• Creates order
• Take an output at any value and set it
to a specific value
– Decreases entropy
• Bit set costs at least kT×ln(2)
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Discard Information
More specifically:
• Discarding Information is what must
cost thermodynamic energy
S proportional to change in information
content
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Idea
• Don’t discard information
• Make changes that preserve the size of
the state space
– Preserve information
• All state transforms must be reversible
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Scale Change
• Going to change scale
– From configuration of atoms
– To configurations of bits
• Macroscale information
• Necessary that macroscale information
preservation hold
– For microstate information not to shrink
• Not sufficient by itself
• Our concern is lower bounds
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Idea
• Don’t discard information
• Make changes that preserve the size of
the state space
– Preserve information
• All state transforms must be reversible
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Reversible Operation
• Irreversible
– C=AND(A,B)
• 4 states collapse to 2
• Reversible
– C=XOR(A,B), with D=A
– AB: 00  CD: 00
– AB: 01  CD: 10
– AB: 10  CD: 11
– AB: 11  CD: 01
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Reversible Operation
• Irreversible
– C=AND(A,B) with D=A
• Only 3 states
– (C=0,D=1) (C=1,D=1) (C=0,D=0)
– C=1,D=0 cannot happen
• Given C=0, D=0, cannot reconstruct B
• Reversible
– C=/A
– C=XOR(A,B), with D=A
– D=XOR(A&B,C) with E=A, F=B
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Computational State Transform
• Need to look at larger state than single
result bit
– To assess information preservation
• Typical operations are not information
preserving
– Group common cases together
• E.g. AND(A,B), OR(A,B)
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Three Reversible
Logic Primitives
Controlled NOT
Controlled Controlled NOT
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Universal Primitives
• These primitives
– Universal
– Reversible
• If keep all the intermediates they
produce
– Discard no information
– Can run computation in reverse
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Reversible Half Adder
A
A
B
XOR(A,B)
0
A&B
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Cleaning Up
• Can keep “erase” unwanted
intermediates with reverse circuit
– Must “uncompute” the value
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Reversible Computing
• In principal
– Reversible operations do not need to discard
energy
• Does not violate necessary conditions for energy
consumption in thermodynamics
• Restricting ourselves to reversible operations
– Does not limit what we can compute
• FYI
– Reversibility required for Quantum Computing 22
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Adiabatic
• Adiabatic – a thermodynamic process
without heat transfer
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Adiabatic Logic
SCRL
Split-Level Charge Recovery Logic
(Younis and Knight – ISLPED 1994)
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SCRL Inverter
 F’s, nodes, at Vdd/2
• P1 at ground
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Slowly turn on P1
Slow split F’s
Slow turn off P1’s
Slow return F’s to
Vdd/2
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SCRL Inverter
• Basic operation
– Set inputs
– Split rails to compute output
adiabatically
– Isolate output
– Bring rails back together
• Have transferred input
(logic) to output
• Still need to worry about
resetting output adiabatically
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SCRL Controlled NOT
• Same basic idea works for any gate
– Set inputs
– Adiabatically switch output
– Isolate output
– Reset power rails
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SCRL Cascade
• Cascade like domino logic
– Compute phase 1
– Compute phase 2 from phase 1…
– Control Clock/power phases
• How do we restore the output?
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SCRL Pipeline
• We must uncompute the logic
– Forward gates compute output
– Reverse gate restore to Vdd/2
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SCRL Pipeline
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P1 high (F1 on; F1 reset (F2-1) off)
F1 split: a=F1(a0)
F2 split: b=F2(F1(a0))
F2-1(F2(F1(a0))=a
P1 low – now F2-1 drives a
– But to same value already set
• no voltage difference
• F1 restore by F1 converge
• …restore F2
• Use F2-1 to restore a to Vdd/2 adiabatically
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Adiabatic Pipeline
• Drive Forward
• Hand off control of node to reverse
computation from forward path
• Allows earlier gates to reset for next
operation
– So can insert next value into pipeline
– While previous value still traversing pipe
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SCRL Pipeline
b
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SCRL Rail Timing
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SCRL
• Requires Reversible Gates to
uncompute each intermediate
– Macroscopic energy saving does require
reversibility we derived for microscale
thermodynamics
• All switching (except IO) is adiabatic
• Dissipate energy proportional to
– Bits discarded at pipeline I/O
– Speed of operation
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Reversible Processor
• Pendulum (Vieri) at MIT
• Preserves enough information so every
instruction reversible
– E.g.
• Memory operation is an exchange
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Critical Questions
• Same as adiabatic switching
– Can contain losses enough to come out
ahead?
• Leakage
• Resistive losses
– High enough Q resonators?
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Ideas
• In principal, can compute without energy
• Costs energy to discard information
– So don’t do that
– …or do as little as possible
• Demands reversibility
• Reversible computation can be universal
• Can apply idea to CMOS
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Final
• Comprehensive – everything
• Specific things you might expect
– Energy and Delay estimation
• Logic and interconnect
• Elmore and wire delay
– Driving RC wires and C loads
– Precharge and Clocking
– Memories
– Crosstalk and Noise
– Variation
– Transmission Lines
Penn ESE370 Fall2010 -- DeHon
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Admin
• Review Monday
– Select Time
• Monday 5—7pm (likely in Ketterer)
• Andre office hours Tuesday
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Feedback
• Topics
– Omitted (hoped to see)
– Should have spent more time on
– Should have spent less time on
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