what your dram power models are not telling you...1. real dram power varies widely from idd values...
TRANSCRIPT
![Page 1: What Your DRAM Power Models Are Not Telling You...1. Real DRAM Power Varies Widely from IDD Values Different vendors have very different margins (i.e., guardbands)Low variance among](https://reader034.vdocuments.net/reader034/viewer/2022042017/5e74fb6016013a184d52a97e/html5/thumbnails/1.jpg)
What Your DRAM Power ModelsAre Not Telling You:
Lessons from a Detailed Experimental Study
Saugata Ghose, A. Giray Yağlıkçı, Raghav Gupta, Donghyuk Lee, Kais Kudrolli, William X. Liu, Hasan Hassan, Kevin K. Chang,
Niladrish Chatterjee, Aditya Agrawal, Mike O’Connor, Onur Mutlu
June 21, 2018
![Page 2: What Your DRAM Power Models Are Not Telling You...1. Real DRAM Power Varies Widely from IDD Values Different vendors have very different margins (i.e., guardbands)Low variance among](https://reader034.vdocuments.net/reader034/viewer/2022042017/5e74fb6016013a184d52a97e/html5/thumbnails/2.jpg)
DRAM Power Is Becoming a Major Design Concern
Main memory in computersconsists of DRAM modules
DRAM consumes up to halfof total system power
State-of-the-art DRAM power models are not adequate• Based on IDD values: standard current measurements provided by vendors• Often have a high mean absolute percentage error
» 32% for DRAMPower» 161% for Micron power model
Page 2 of 20
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OUR GOAL
Measure and analyze the power used by real DRAM, and build an accurate DRAM power model
Frac
tion
ofTo
tal S
yste
m E
nerg
y
![Page 3: What Your DRAM Power Models Are Not Telling You...1. Real DRAM Power Varies Widely from IDD Values Different vendors have very different margins (i.e., guardbands)Low variance among](https://reader034.vdocuments.net/reader034/viewer/2022042017/5e74fb6016013a184d52a97e/html5/thumbnails/3.jpg)
Background: DRAM Organization & Operation
Characterization Methodology
New Findings on DRAM Power Consumption
VAMPIRE: A Variation-Aware DRAM Power Model
Conclusion
Page 3 of 20
Outline
![Page 4: What Your DRAM Power Models Are Not Telling You...1. Real DRAM Power Varies Widely from IDD Values Different vendors have very different margins (i.e., guardbands)Low variance among](https://reader034.vdocuments.net/reader034/viewer/2022042017/5e74fb6016013a184d52a97e/html5/thumbnails/4.jpg)
Simplified DRAM Organization and Operation
Fundamental DRAM commands: activate, read, write, precharge
Page 4 of 20
DRAM ChipBank 0 . . .
Processor ChipDRAM
Cell Array
Bank 7
Core . . . Core
Shared Last-Level Cache
![Page 5: What Your DRAM Power Models Are Not Telling You...1. Real DRAM Power Varies Widely from IDD Values Different vendors have very different margins (i.e., guardbands)Low variance among](https://reader034.vdocuments.net/reader034/viewer/2022042017/5e74fb6016013a184d52a97e/html5/thumbnails/5.jpg)
Simplified DRAM Organization and Operation
Fundamental DRAM commands: activate, read, write, prechargeOne row of DRAM: 8 kBOne cache line of data: 64 B
Page 4 of 20
DRAM ChipBank 0 . . .
. . .
Processor Chip
Memory Controller
Column Select
Bank Select
I/O DriversI/O Drivers
memory channel
DRAMCell Array
Row Buffer
Bank 7
activationCore . . . Core
Shared Last-Level Cache
![Page 6: What Your DRAM Power Models Are Not Telling You...1. Real DRAM Power Varies Widely from IDD Values Different vendors have very different margins (i.e., guardbands)Low variance among](https://reader034.vdocuments.net/reader034/viewer/2022042017/5e74fb6016013a184d52a97e/html5/thumbnails/6.jpg)
Simplified DRAM Organization and Operation
Fundamental DRAM commands: activate, read, write, prechargeOne row of DRAM: 8 kBOne cache line of data: 64 B
Page 4 of 20
DRAM ChipBank 0 . . .
. . .
Processor Chip
Memory Controller
Column Select
Bank Select
I/O DriversI/O Drivers
memory channel
DRAMCell Array
Row Buffer
Bank 7
Core . . . Core
Shared Last-Level Cache
![Page 7: What Your DRAM Power Models Are Not Telling You...1. Real DRAM Power Varies Widely from IDD Values Different vendors have very different margins (i.e., guardbands)Low variance among](https://reader034.vdocuments.net/reader034/viewer/2022042017/5e74fb6016013a184d52a97e/html5/thumbnails/7.jpg)
Background: DRAM Organization & Operation
Characterization Methodology
New Findings on DRAM Power Consumption
VAMPIRE: A Variation-Aware DRAM Power Model
Conclusion
Page 5 of 20
Outline
![Page 8: What Your DRAM Power Models Are Not Telling You...1. Real DRAM Power Varies Widely from IDD Values Different vendors have very different margins (i.e., guardbands)Low variance among](https://reader034.vdocuments.net/reader034/viewer/2022042017/5e74fb6016013a184d52a97e/html5/thumbnails/8.jpg)
Keysight 34134A DC Current Probe
DDR3L SO-DIMM
JET-5467A Riser Board
Virtex 6FPGA
Power Measurement Platform
Page 6 of 20
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Methodology Details
SoftMC: an FPGA-based memory controller [Hassan+ HPCA ’17]
• Modified to repeatedly loop commands• Open-source: https://github.com/CMU-SAFARI/SoftMC
Measure current consumed by a module during a SoftMC test
Tested 50 DDR3L DRAM modules (200 DRAM chips)• Supply voltage: 1.35 V• Three major vendors: A, B, C• Manufactured between 2014 and 2016
For each experimental test that we perform• 10 runs of each test per module• At least 10 current samples per run
Page 7 of 20
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Background: DRAM Organization & Operation
Characterization Methodology
New Findings on DRAM Power Consumption
VAMPIRE: A Variation-Aware DRAM Power Model
Conclusion
Page 8 of 20
Outline
![Page 11: What Your DRAM Power Models Are Not Telling You...1. Real DRAM Power Varies Widely from IDD Values Different vendors have very different margins (i.e., guardbands)Low variance among](https://reader034.vdocuments.net/reader034/viewer/2022042017/5e74fb6016013a184d52a97e/html5/thumbnails/11.jpg)
1. Real DRAM Power Varies Widely from IDD Values
Different vendors have very different margins (i.e., guardbands)Low variance among different modules from same vendor
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0
20
40
60
80
100
Curr
ent (
mA)
DatasheetMeasured
A B C0
50
100
150
200
Curr
ent(
mA)
A B C 0
200
400
600
800
Curr
ent(
mA)
DatasheetCorrected
A B C
IDD2NIdle
IDD0Activate–Precharge
IDD4RRead
Current consumed by real DRAM modulesvaries significantly for all IDD values that we measure
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2. DRAM Power is Dependent on Data Values
Some variation due to infrastructure – can be subtractedWithout infrastructure variation: up to 230 mA of changeToggle affects power consumption, but < 0.15 mA per bit
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0
200
400
600
800
0 128 256 384 512
Read
Cur
rent
(mA)
Number of Ones in a Cache Line
Vendor AVendor BVendor C
0
200
400
600
800
0 128 256 384 512
Writ
e Cu
rren
t(m
A)
Number of Ones in a Cache Line
Vendor AVendor BVendor C
DRAM power consumption depends stronglyon the data value, but not on bit toggling
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3. Structural Variation Affects DRAM Power Usage
Vendor C: variation in idle current across banks
All vendors: variation in read current across banks
All vendors: variation in activation based onrow address
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0.81.01.21.4
Vendor A Vendor B Vendor C0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7No
rmal
ized
Idle
Cur
rent
0.80.91.01.1
Vendor A Vendor B Vendor C0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7No
rmal
ized
Read
Cur
rent
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Norm
alize
d M
easu
red
Curr
ent
Number of Ones in Row Address
Vendor A Vendor B Vendor C1.201.151.101.051.000.95
Significant structural variation: DRAM power varies systematically by bank and row
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4. Generational Savings Are Smaller Than Expected
Similar trends for idle and read currents
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IDD0Activate–Precharge
IDD4WWrite
Actual power savings of newer DRAM is much lowerthan the savings indicated in the datasheets
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Summary of New Observations on DRAM Power
1. Real DRAM modules often consume less powerthan vendor-provided IDD values state
2. DRAM power consumption is dependent on the data value that is read/written
3. Across banks and rows, structural variation affects powerconsumption of DRAM
4. Newer DRAM modules save less power than indicated in datasheets by vendors
Detailed observations and analyses in the paper
Page 13 of 20
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Background: DRAM Organization & Operation
Characterization Methodology
New Findings on DRAM Power Consumption
VAMPIRE: A Variation-Aware DRAM Power Model
Conclusion
Page 14 of 20
Outline
![Page 17: What Your DRAM Power Models Are Not Telling You...1. Real DRAM Power Varies Widely from IDD Values Different vendors have very different margins (i.e., guardbands)Low variance among](https://reader034.vdocuments.net/reader034/viewer/2022042017/5e74fb6016013a184d52a97e/html5/thumbnails/17.jpg)
A New Variation-Aware DRAM Power Model
VAMPIRE: Variation-Aware model of Memory PowerInformed by Real Experiments
VAMPIRE and raw characterization data will be open-source:https://github.com/CMU-SAFARI/VAMPIRE (August 2018)
Page 15 of 20
VAMPIRERead/Write andData-DependentPower Modeling
Idle/Activate/PrechargePower Modeling
Structural Variation AwarePower Modeling
Inputs(from memory system
simulator)
Trace of DRAM commands, timing
Data that isbeing written
Outputs
Per-vendorpower
consumption
Range foreach vendor
(optional)
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VAMPIRE Has Lower Error Than Existing Models
Validated using new power measurements: details in the paper
Page 16 of 20
VAMPIRE has very low error for all vendors: 6.8%Much more accurate than prior models
160.6%
32.4%6.8%
0%
50%
100%
150%
200%
250%
Vendor A Vendor B Vendor C GMean
Mea
n Ab
solu
tePe
rcen
tage
Err
or Micron Model DRAMPower VAMPIRE
(8 modules) (7 modules) (7 modules)
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VAMPIRE Enables Several New Studies
Taking advantage of structural variation to perform variation-aware physical page allocation to reduce power
Smarter DRAM power-down scheduling
Reducing DRAM energy with data-dependency-awarecache line encodings• 23 applications from
the SPEC 2006 benchmark suite
• Traces collected usingPin and Ramulator
We expect there to be many other new studies in the futurePage 17 of 20
0.70.80.91.01.11.2
Vendor A Vendor B Vendor C GMean
Norm
alize
dDR
AM E
nerg
y Baseline BDI Optimized OWI-12.2%
![Page 20: What Your DRAM Power Models Are Not Telling You...1. Real DRAM Power Varies Widely from IDD Values Different vendors have very different margins (i.e., guardbands)Low variance among](https://reader034.vdocuments.net/reader034/viewer/2022042017/5e74fb6016013a184d52a97e/html5/thumbnails/20.jpg)
Background: DRAM Organization & Operation
Characterization Methodology
New Findings on DRAM Power Consumption
VAMPIRE: A Variation-Aware DRAM Power Model
Conclusion
Page 18 of 20
Outline
![Page 21: What Your DRAM Power Models Are Not Telling You...1. Real DRAM Power Varies Widely from IDD Values Different vendors have very different margins (i.e., guardbands)Low variance among](https://reader034.vdocuments.net/reader034/viewer/2022042017/5e74fb6016013a184d52a97e/html5/thumbnails/21.jpg)
Conclusion
DRAM consumes up to half of total system power:need to develop new low-power solutions
State-of-the-art DRAM power models are based only onIDD values, and have a high error
We make four new observations on DRAM power consumption using 50 real DRAM modules from three major vendors• Real DRAM modules often consume less power than IDD values state• Power consumption is dependent on the data value being read/written• Across banks and rows, structural variation affects power consumption• Newer DRAM modules save less power than indicated in datasheets
VAMPIRE: a new DRAM power model built on our observations• Mean absolute percentage error of only 6.8%• Case study: dependency-aware data encoding reduces DRAM power by 12%
Page 19 of 20
More information: https://github.com/CMU-SAFARI/VAMPIRE
![Page 22: What Your DRAM Power Models Are Not Telling You...1. Real DRAM Power Varies Widely from IDD Values Different vendors have very different margins (i.e., guardbands)Low variance among](https://reader034.vdocuments.net/reader034/viewer/2022042017/5e74fb6016013a184d52a97e/html5/thumbnails/22.jpg)
What Your DRAM Power ModelsAre Not Telling You:
Lessons from a Detailed Experimental Study
Saugata Ghose, A. Giray Yağlıkçı, Raghav Gupta, Donghyuk Lee, Kais Kudrolli, William X. Liu, Hasan Hassan, Kevin K. Chang,
Niladrish Chatterjee, Aditya Agrawal, Mike O’Connor, Onur Mutlu
More information: https://github.com/CMU-SAFARI/VAMPIRE
![Page 23: What Your DRAM Power Models Are Not Telling You...1. Real DRAM Power Varies Widely from IDD Values Different vendors have very different margins (i.e., guardbands)Low variance among](https://reader034.vdocuments.net/reader034/viewer/2022042017/5e74fb6016013a184d52a97e/html5/thumbnails/23.jpg)
Backup Slides
Page 21 of 20
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More Information in the Paper…
Full characterization analysis
Application-level comparison to existing power models
Case study: dependency-aware data encoding
Paper available at https://github.com/CMU-SAFARI/VAMPIRE
Page 22 of 20
0.8
0.9
1.0
1.1
Vendor A Vendor B Vendor C
Norm
alize
dEn
ergy
Baseline BDI Optimized OWI
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Today’s Models Leave a Lot to Be Desired
Most models reliant on JEDEC-based IDD values• Micron power calculator• DRAMPower• gem5/GPGPU-Sim
Some rely on circuit-level models• Vogelsang model for memory scaling• CACTI
None are all that accurate• One value for each DRAM• Does not capture any inherent variation (e.g., data, structure)
Page 23 of 20
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VDD
FPGA
SoftMC [1]
PCI-e IF
HostPC
PCI-e
How Do We Measure Current?
Page 24 of 20
DRAM Module
Rank. . .
Chip Chipmemorychannel
USB Probe
Cmd Buffer
Hassan et al. “SoftMC: A Flexible and Practical Open-Source Infrastructure for Enabling Experimental DRAM Studies,” HPCA, 2017.
[1]
![Page 27: What Your DRAM Power Models Are Not Telling You...1. Real DRAM Power Varies Widely from IDD Values Different vendors have very different margins (i.e., guardbands)Low variance among](https://reader034.vdocuments.net/reader034/viewer/2022042017/5e74fb6016013a184d52a97e/html5/thumbnails/27.jpg)
Foundation of Current Power Models
Just how bad are current models?
JEDEC defines a set of IDD values
Page 25 of 20
IDD0 Activation and Precharge
IDD1 Activation – 1 Column Read – Precharge
IDD2N Precharge Standby (all banks are precharged/closed) ✔ clk enabled
IDD3N Active Standby (all banks are active/opened) ✔ clk enabled
IDD2P Precharge Power-Down (all banks are precharged/closed) ✘clk disabled
IDD3P Active Power-Down (all banks are active/opened) ✘clk disabled
IDD4R/W Burst mode Read/Write
IDD5B Burst mode Refresh
IDD7 Activate – Column Read w/ Auto Precharge
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What’s So Bad About That?
JEDEC defined IDD measurement loops cover:• Average power consumption of all banks
» missing variation across banks• Average power consumption of only two rows: 00 and F0
» missing variation across rows in a subarray» missing variation across subarrays
• Average power consumption of only two data patterns: 00 and 33» missing effect of number of ones/zeros in data» missing effect of toggling bits
Page 26 of 20
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IDD0: Activation and Precharge Energy
Page 27 of 20
A B C
Norm
alize
dM
easu
red
Curr
ent 0.50
0.45
0.40
0.35
0.300
50
100
150
200
Curr
ent(
mA)
DatasheetMeasured
Vendor A VendorB VendorC
time
ACT PRE ACTtRAS tRP PREtRASDRAM Array
Row Buffer0x00
0xF0
![Page 30: What Your DRAM Power Models Are Not Telling You...1. Real DRAM Power Varies Widely from IDD Values Different vendors have very different margins (i.e., guardbands)Low variance among](https://reader034.vdocuments.net/reader034/viewer/2022042017/5e74fb6016013a184d52a97e/html5/thumbnails/30.jpg)
IDD1: Activation, Read, and Precharge Energy
Page 28 of 20
A B C
Norm
alize
dM
easu
red
Curr
ent
0.70
0.60
0.50
0.40
0.20
0.300
50100150200250300350
Curr
ent(
mA)
DatasheetMeasured
Vendor A Vendor B Vendor C
Row Buffer
DRAM Array
0x00
0xF0
time
ACT PRE ACTtRCD tRP
RDtRAS
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IDD2N: Precharged Standby
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A B C
Norm
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dM
easu
red
Curr
ent
1.00
0.80
0.60
0.40
0.200
20
40
60
80
100
Curr
ent(
mA)
DatasheetMeasured
Vendor A Vendor B Vendor C
Row Buffer
DRAM ArrayBank 0 Bank 1 Bank 7
(1) Precharge All Banks(Close Row Buffers)
(2) WaitRow Buffer
DRAM Array
Row Buffer
DRAM Array
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IDD3N: Active Standby
Page 30 of 20A B C
Norm
alize
dM
easu
red
Curr
ent
0.70
0.500.40
0.200.10
0.60
0.30
0
50
100
150
200
Curr
ent(
mA)
DatasheetMeasured
Vendor A Vendor B Vendor C
Row Buffer
DRAM Array
Row Buffer
DRAM Array
Row Buffer
DRAM ArrayBank 0 Bank 1 Bank 7
(1) Activate All Banks(Open Row Buffers)
(2) Wait
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IDD2P: Precharged Power Down
Page 31 of 20
A B C
Norm
alize
dM
easu
red
Curr
ent
1.20
0.800.60
0.200.00
1.00
0.40
0
20
40
60
80
Curr
ent(
mA)
DatasheetMeasured
Vendor A Vendor B Vendor C
Row Buffer
DRAM ArrayBank 0 Bank 1 Bank 7
(1) Precharge All Banks(Close Row Buffers)
(2) WaitRow Buffer
DRAM Array
Row Buffer
DRAM Array
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IDD4R: Burst Read Current
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0
200
400
600
800
Curr
ent(
mA)
Datasheet Measured Corrected
Vendor A Vendor B Vendor C
Row Buffer
DRAM Array
Row Buffer
DRAM Array
Row Buffer
DRAM ArrayBank 0 Bank 1 Bank 7
(1) Activate All Banks(Open Row Buffers)
(2) Read one column at a time
(3) Interleave across banks after each read
0 1 78 9 150x00 0x33 0x00 0x33 0x00 0x33
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IDD4W: Burst Write Current
Page 33 of 20
0
200
400
600
Curr
ent(
mA)
DatasheetMeasured
Vendor A Vendor B Vendor C
Row Buffer
DRAM Array
Row Buffer
DRAM Array
Row Buffer
DRAM ArrayBank 0 Bank 1 Bank 7
(1) Activate All Banks(Open Row Buffers)
(2) Write one column at a time
(3) Interleave across banks after each read
0 1 78 9 150x00 0x33 0x00 0x33 0x00 0x33
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IDD5B: Refresh in Burst Mode
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tREFI(64ms)
tRFC
time
REF REFtRFC
Burst Mode:
0
200
400
600
800
1000
Curr
ent(
mA)
DatasheetMeasured
Vendor A Vendor B Vendor C A B C
Norm
alize
dM
easu
red
Curr
ent
1.00
0.90
0.80
0.70
0.50
0.60
REFtRFC
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ACT-RDA
IDD7: Read, Auto-Precharge
Page 35 of 20
time
ACT-RDA tRRD tRRD ACT-RDA tRRD
0
200
400
600
800
Curr
ent(
mA)
DatasheetMeasured
Vendor A VendorB VendorC A B C
Norm
alize
dM
easu
red
Curr
ent
0.650.60
0.500.45
0.350.40
0.55
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Impact of Bit Toggling on DRAM Power
Page 36 of 20
0000 1010 1111 … 0011
Bank 0 Row Buffer0 1
columnnumber 2 c – 1
1011 0010 1011 … 0110
Bank 1 Row Buffer0 1 2 c – 1
1011 0010 1011 … 0110
Bank 7 Row Buffer0 1 2 c – 1
1
2
. . .
. . .
. . .
. . .
. . . . . . . . .
Column Select Column Select Column Select
Bank Selectglobal bitlines
peripheral busto I/O drivers
global bitlines
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Data Dependency Model
Page 37 of 20
Read WriteF (mA) G (mA) H (mA) F (mA) G (mA) H (mA)
Vendor A 246.44 0.433 0.0515 531.18 -0.246 0.0461
Vendor B 217.42 0.157 0.0947 466.84 -0.215 0.0166
Vendor C 234.42 0.154 0.0856 368.29 -0.116 0.0229
Additional current per bit toggleAdditional current per logic-1
0
200
400
600
800
0 128 256 384 512
Read
Cur
rent
(mA)
Number of Ones in a Cache Line
0
200
400
600
800
0 128 256 384 512
Writ
e Cu
rren
t(m
A)
Number of Ones in a Cache Line
Vendor AVendor BVendor C
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Models
Page 38 of 20https://github.com/CMU-SAFARI/VAMPIRE
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Structural Variation
Page 39 of 20
Normalized Read Burst Energy across Banks
0.80.91.01.1
Vendor A Vendor B Vendor C
Norm
alize
d Cu
rren
t
0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
0.81.01.21.4
Vendor A Vendor B Vendor C
Norm
alize
d Cu
rren
t
0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
Normalized Active Standby Energyacross Banks
0.80.91.01.1
Vendor A Vendor B Vendor C0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
Norm
alize
dW
rite
Curr
ent
Normalized Write Burst Energy across Banks
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Evaluated System Configuration
Application traces collected using Pin
DRAM command timings generated using Ramulator:https://github.com/CMU-SAFARI/ramulator
Page 40 of 20
Processor x86-64 ISA, one core 3.2 GHz, 128-entry instruction window
Cache L1: 64 kB, 4-way associative; L2: 2 MB, 16-way associative
Memory Controller
64/64-entry read/write request queues, FR-FCFS [119, 149]
DRAM DDR3L-800 [57], 1 channel, 1 rank/8 banks per channel
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0
100
200
300
400
2010 2011 2012 2013 2014 2015
Curr
ent(
mA)
Year Manufactured
Datasheet Measured
-192.1mA
-64.0mA0
50
100
150
200
2010 2011 2012 2013 2014 2015Cu
rren
t(m
A)Year Manufactured
Datasheet Measured
-112.1mA
-53.7mA
0100200300400500600700
2010 2011 2012 2013 2014 2015
Curr
ent(
mA)
Year Manufactured
Datasheet Measured
-212.2mA-140.6mA
0100200300400500600700
2010 2011 2012 2013 2014 2015
Curr
ent(
mA)
Year Manufactured
Datasheet Measured
-200.2mA
-147.4mA
Trends Across Generations
Basically, if you’re building a system, you aren’t getting the kinds of savings you were promised
Page 41 of 20
Activation Energy Precharge Standby Energy
Read Energy Write Energy
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Data Encoding
Baseline: No codingBDI: Base Delta ImmediateOptimized: Minimize the number of ones OWI: Minimize ones for reads, maximize ones for writes
Page 42 of 20
0.6
0.8
1.0
1.2
Vendor A Vendor B Vendor C
Norm
alize
d En
ergy
Baseline BDI Optimized OWI
12.5% Energy Reduction
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Validating Our DRAM Power Models
New tests run on 22 of our DDR3L DRAM SO-DIMMsValidation command sequence
• Activate• n reads
» Sweep n from 0 to 764»All reads contain data value 0xAA»All reads to Bank 0, Row 128»Column interleaved
• Precharge
Error metric: mean absolute percentage error (MAPE)
Best prior model (DRAMPower): 32.4% MAPEVAMPIRE: 6.8% MAPE
Page 43 of 20