An evaluation of HotSpot-3.0 block-based temperature model Damien Fetis, Pierre Michaud June 2006.
An evaluation of HotSpot-3.0 block-based temperature model
Transcript of An evaluation of HotSpot-3.0 block-based temperature model
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Temperature: an important constraint
Technology Scale down
Power must be decreased to prevent temperature from increasing
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HotSpot: a thermal model for temperature-aware microarchitecture
• http://lava.cs.virginia.edu/HotSpot/
• Based on thermal resistances and capacitances
• It is becoming a standard tool in the computer architecture community
• Several tens of works based on HotSpot have been published so far
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Outline
1. Short tutorial on temperature modeling 2. Short description of HotSpot block model 3. Some limitations of HotSpot
Conclusion: be careful when using HotSpot
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Processor temperature model
Material characteristics, heat-sink thermal resistance, etc…
Power-density map q(x,y,t)
Temperature model
Ambient temperature
processor temperature
T(x,y,t)
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Qualitative accuracy
• Accurate temperature number ? forget it ! – If the conclusions of your research depend on precise parameter values, what
you are proposing probably has little value
• What we need for research: qualitative accuracy – Model can tell whether an idea is worth or not
• We would like to be consistent with physics
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Heat conduction theory
Tkq ∇−=Fourier’s law: heat flux (W/m2)
proportional to temperature gradient
thermal conductivity
tTCqg∂
∂=⋅∇−
Heat equation
heat capacity per unit volume
3D power density
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Solving the heat equation • Analytical method
– Exact solution – Possible only for simple geometries
• Finite methods
– Search (xn) that makes T’ “close” to the actual solution • solve a system of equations
– Finite differences – Finite elements – Spectral methods – …
),,,(),,,('0
tzyxxtzyxT n
N
nnφ∑
=
=
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1D thermal resistance
Thermally-insulated side
Uniform power P over area A
L
• Right cylinder – Length = L – Cross section area = A – Thermal conductivity = k
T1
T2
LTTk
AP 21 −=
Uniform power over cross section
uniform temperature over cross section
PRTT ×=− 21
Define thermal “resistance” AkLR×
=
Silicon die Interface material
Copper heat spreader
Copper heat sink base
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What HotSpot models
Power sources
ambient air
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How HotSpot “solves” the heat equation
Model power generation as current sources
Model ambient as ground
Thermal resistances
Instead of using formal methods, solve an “electrical” network
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HotSpot block model
• Thermal “resistances” simulate Fourier’s law
• Thermal “capacitances” simulate transients
• Network consists of few layers – “horizontal” resistances within layers – “vertical” resistances between layers
• Single layer for the silicon die
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Compute resistance between block center and block edge
R
πLZa =
W
H L
Z=silicon die thickness
πHZb =
ba
=εkHZW2
=θ
πεπλ
1+=
θπkbB 1=
bW2
=τ
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
+
+−+=
B
Bka
Rλ
λτ
λλτ
εετπ )tanh(1
)tanh(11
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Each block is connected to adjacent blocks through a resistance
1R
2R
RRR111
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=+
Thermal conductance proportional to shared edge length
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HotSpot is empirical
• Not based on mathematical foundations – Resistance formula applied without justification
• Was derived for definite boundary conditions that do not apply here
• Coarse “vertical” space discretization
• Problem with empirical models: more difficult to validate – Require extensive validation
• Not sufficient to validate a few points in the parameter space – Error may vary significantly with parameter values
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Evaluation
• We are not validating HotSpot – We are just highlighting some of its limitations – deliberate focus on problematic cases
• Compare HotSpot block model with finite-element solver FF3D – Model same physical system as HotSpot
• Two versions of HotSpot – The original one – Our modified version with simple 1D resistance formula
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05
101520253035404550
Bpred IntReg IntExec
cels
ius
(rela
tive
to a
mbi
ent)
FF3DHOTSPOTHOTSPOT mod
Steady-state temperature
EV6 floorplan, default HotSpot configuration
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Let’s take a better interface material
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Bpred IntReg IntExec
cels
ius
(rela
tive
to a
mbi
ent)
FF3DHOTSPOTHOTSPOT mod
Interface material with ~6x higher thermal conductivity
emphasizes “horizontal” heat conduction through copper
Even the modified HotSpot is inaccurate
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Single square source
A
B
• Model the same square source with two different floorplans (default HotSpot parameters)
• Power = 10 W
mm 21
0
50
100
150
200
250
0.001 0.003 0.005source side (meters)
cels
ius
(rel
ativ
e to
am
bien
t)
ff3dHotSpot AHotSpot BHotSpot mod AHotSpot mod B
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What do we learn ?
• In some cases, HotSpot may be significantly inaccurate
• The usefulness of the complicated thermal resistance formula is not obvious
• HotSpot documentation indicates that mixing small and large blocks may be source of inaccuracy we confirm
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Point source: transient temperature
α4
2dt =
d
0=t
opposite side starts heating
)4
erfc(2
),(t
rkrPtru
απ=
Ck
=αThermal diffusivity
Example: silicon die
d=0.5 mm
sm / 10.7 25−≈α
s 9004
2
µα≈
d HotSpot miss this behavior
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Volume vs. surface power sources
Sources spread in bulk silicon Sources concentrated in thin layer
time t
temperature
time t
temperature
t~ t~
HotSpot behavior Close to actual behavior
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What this implies for HotSpot
• HotSpot block-model considers a single network layer for the silicon die
• cannot produce correct behavior for small times
• Underestimates slope of temperature transient – E.g., how long does it take to get a 1°C increase ?
• HotSpot may be wrong by orders of magnitude
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1 mm square source dissipating 10 W
0
5
10
15
20
25
30
0 0.0002 0.0004 0.0006 0.0008 0.001
seconds
cels
ius
(rela
tive
to a
mbi
ent)
HotSpot AHotSpot BFF3D
Problem: insufficient “vertical” discretization in silicon
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Conclusion
• Be careful when using HotSpot – Good to read a little heat conduction theory before …
• Heat conduction ≠ electric conduction
• Ok to use HotSpot for confirming a priori intuitions
• Draw qualitative conclusions, not quantitative ones
• In case of doubt, check with formal methods that HotSpot is correctly calibrated for a particular use
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HotSpot still evolving
• This study was only for HotSpot block model
• Version 3.0 features a new grid mode – Discretization is automatic (but “vertically”) – Permits defining multiple silicon layers – must be validated
• HotSpot will probably continue to evolve – Will end up resembling finite differences ?