Behavioral thermal modeling for quad-core microprocessors

Transcription

1 Behavioral thermal modeling for quad-core microproceor Duo Li and Sheldon X.-D. Tan Department of Electrical Engineering Univerity of California, Riveride, CA Murli Tirumala Intel Corporation

2 Outline Introduction and Motivation The need for dynamic thermal management (DTM) Why oftware thermal enor Power etimation for functional unit Architecture level thermal modeling Summary

3 Outline Introduction and Motivation Architecture level thermal modeling Intel quad-core tructure Tranfer function General pencil of function method Log-ale ampling and tabilization Simulation reult Summary

4 Top view: quad core 1 cm Lateral view die:3 1 cm die:2 die:1 die:0 die:4 CACHE Heat ink TIM2 Heat preader TIM1 DIE Temperature reported are on the die bottom face and centered with each die region

5 Active core 0 at 20 W: T ditribution Temperature (deg C) E time ()

6 Quad-core core0 core1 core2 core3 cache c1 c0 c2 c3 c4 ytem t0 t1 t2 t3 t4

7 Tranfer function LTI (linear, time-invariant ytem) input ignal x (t) and output y(t) Y ( ) = H ( ) X ( ) or H ( ) = Y ( ) X ( ) where H() i the tranfer function of the LTI ytem

8 Impule repone and polereidue repreentation Pole-zero n n m m a a b b b H = ) ( ) )...( ( ) ( ) )...( ( ) ( ) ( n m p p p z z z K H = ) exp( ) ( ) ( 1 i i n i i i tp k t h p k H = = = Pole-reidue and impule repone in time domain

9 Concept of Matrix Pencil Matrix pencil M ( z) = Y zy 1 2 where z i a calar valuable, Y1 and Y2 are two (quare or rectangular ) matrice. M(z) decreae it rank by one if only if z i the generalized eigenvalue of M, which contain the deired information about the ytem like direction of the wave arrival and the ignal pole (thu the pole of the ytem, which generate the ignal). Pencil-of-function f ( t, z) = g( t) + zh( t)

10 General pencil-of-function method Ued for extracting pole and reidue from tranient ignal. y k = M i= 1 r i exp( p Δtk) k = 0, 1,, N-1, r i are the complex reidue, p i are the complex pole, i N: # of ample L: window ize for GPOF,. i.e. number of ample ued in GPOF. M: # of pole ued in the model. t i the ampling interval.

11 General pencil-of-function method Define following pof a y0 λy1, y1 λy2,..., Define Y 1 and Y 2 a y M 1 λy M Then, we have So, the rank of matrix pencil reduce one when become z i, which i the pole in the z-domain ( zi = exp( Δtpi )) a Y1 and Y2 pan the ame Subpace of ampled ignal. λ

12 General Pencil of Function Method

13 How to chooe M and L M i model order number. L i ampling window ize. N i the number of total ampled point. For GPOF, M L N-M. Allow different window ize and pole number. Typically, chooing L = N/2 and M = L can yield better reult.

14 Sampling iue Traditional MP uing contant interval time for ampling. Temperature increae dramatically fat in the firt few econd. Log-cale ampling i a good way. Numerical differentiation for computing impule repone. Need to compute the impule repone intead of tep repone, which are given.

15 Linear v Log-cale

16 Numerical Differential and Stabilization (1) Stable pole extraction

17 Numerical Differential and Stabilization (2) Stabilizing the tarting repone Impule and tep repone without tarting time truncation. Impule and tep repone with tarting time truncation.

18 Training Extracting 5 group of pole and reidue uing matrix pencil method. Obtaining the tranfer function of the ytem. Simulating the output of the ytem (thermal imulation). Linear combination

19 Simulation reult (1) Core0 temperature increae curve, when all the core and cache are active (driven by 20W power).

20 Simulation reult (2) Cache temperature increae curve, when all the core and cache are active (driven by 20W power).

21 Simulation reult (3)

22 Simulation reult (4) The maximum difference i le than 0.5 o C and 1 % for all the core. The average difference i le than 0.3 o C and 0.3 % for all the core.

23 Concluion Efficient on-chip thermal analyi technique i required for on-chip dynamic thermal management tudy and run-timing DTM. Developed a new etimation method to compute real microproceor Function Unit power. Developed behavioral thermal modeling technique baed on general pencil-offunction method.