Makoto Kobayashi and Myron H. MacDougall. The Stack Growth Function: Cache Line Reference Models. IEEE Transactions on Computers, 38(6):798--805, June 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....u ns While our previous analysis used a fixed value of u ns for each time quantum, considerable amount of empirical evidence indicates that u ns diminishes with time. Several studies have found that the cumulative number of unique blocks accessed by a program grows less than linearly with time [12, 13, 14, 6]. Specifically, Belady and Kuehner [12] Kobayashi and MacDougall [13] and Thiebaut [14] have suggested that the total number of unique data blocks referenced by a program grows as some power function of time. If r denotes the time since the program started executing, the total number of unique ....

....considerable amount of empirical evidence indicates that u ns diminishes with time. Several studies have found that the cumulative number of unique blocks accessed by a program grows less than linearly with time [12, 13, 14, 6] Specifically, Belady and Kuehner [12] Kobayashi and MacDougall [13], and Thiebaut [14] have suggested that the total number of unique data blocks referenced by a program grows as some power function of time. If r denotes the time since the program started executing, the total number of unique blocks can be represented as ar b where a and b are some constants. ....

Makoto Kobayashi and Myron H. MacDougall. The Stack Growth Function: Cache Line Reference Models. IEEE Transactions on Computers, 38(6):798--805, June 1989.

....parameters from the trace and use them to estimate misses on a range of cache configurations. For instance, models for fully associative caches employ an exponential or power function model for the change in working set over time. These models have been extended to account for a range of line sizes[4, 5]. Other models have been developed for direct mapped caches [6] instruction caches [7] 8] multi level memory hierarchies [9] and multiprocessor caches [10] The analytic cache model by Agarwal et al., referred to subsequently as the AHH model, estimates the miss rate of setassociative caches ....

M. Kobayashi and M. H. Macdougall, "The Stack Growth Function: Cache Line Reference Models," IEEE Transactions on Computers, vol. 38, pp. 798--805, 1989.

....misses disappear when cache size is increased, rather than modelling true conflict misses. Other models are based on the property that the number of unique referenced blocks grows almost like a power law with the number of references [20] Several cache models are based on this observation [10, 12, 15]. However, none of these models allow the set index functions to be varied. On the other hand, our estimates of conflict misses are only valid for direct mapped caches of a fixed size and block size. There are some pending issues involved when implementing set index functions in a physically ....

M. Kobayashi and M. MacDougall. The stack growth function: Cache line reference models. IEEE Transactions on Computers, 38(6):798--805, June 1991.

.... elements are distinct addresses generated during a period [t #,t) i.e. t #,t # 1, t 1 ) In case for # 0, the period is (t, t #] working set size: w(t, #) Size of a working set W (t, #) i.e. the number of elements of W (t, #) inverse stack growth function (ISGF) [8]: f(t) Expectation value of the number of distinct addresses generated during a period (t, t #] f(t, #) E[w(t, #) 1) In addition, stack growth function (SGF) g(t,k ) denotes the expectation value of the number of accesses such that the number of distinct addresses isk , i.e. ....

....of the number of accesses such that the number of distinct addresses isk , i.e. f(t, #) k # g(t,k ) #, or (2) g = f 1 . 3) Note that because ISGF f is defined only on integer, SGF g cannot be defined directly. The consistent way to obtain the relation between ISGF and SGF is shown in [8]. Hereafter, we regard ISGF and SGF as functions defined on the real number with respect to # andk , respectively. B. Reference Models for Computer Memory In computer memory references, it is well known that the concept about locality of a reference pattern appears. The locality (especially, ....

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M. Kobayashi and M.H. MacDougall, "The stack growth function: Cache line reference models," IEEE Trans. Comput., vol. 38, no. 6, 1989.

....capture the behavior of real programs. Others [32] have argued that the ability of synthetic traces to capture a wide range of possible behaviors (such as different degrees of locality in the LRU stack model) still makes them a useful workload. A large literature exists on program behavior models [8, 33, 34, 35]. 2.2 Inclusion and Related Concepts Many of the techniques for trace storage and use are based on a set of results initiated by the work of Mattson, et al. 14] In this subsection we introduce the basic concepts involved. A replacement algorithm is said to have the inclusion property if after ....

M. Kobayashi and M. H. MacDougall, "The stack growth function: Cache line reference models, " IEEE Transactions on Computers, vol. C-38, pp. 798--804, June 1989.

....set size, spatial locality, temporal locality, and interactions between spatial and temporal locality, respectively, of the intervening processing. The fact that u(R(x i ) L) is a power function of R(x i ) for fixed L was observed independently by Thiebaut [23, 24] and Kobayashi and MacDougall [11]. In [20] the authors show equation (1) to be consistent with data given by Smith [21] and Agarwal, Horowitz and Hennessy [1] They also demonstrate its accuracy through detailed validation on segments of a 200 millionreference trace of a multiprogrammed IBM 370 MVS workload, consisting of a ....

M. Kobayashi and M. MacDougall. The stack growth function: Cache line reference models. IEEE Transactions on Computers, 38(6):798--805, June 1989.

....nature: the working set is closed in the sense that same fixed number of frames are used over a long interval of time. The range of power constants for GAMTEB, from 0.45 to 0.71, overlap the values found in conventional architectures, which range from 0.484 to 0.544 [16] and from 0.43 to 0. 75 [17]. This suggests that the amount of locality in frame memory references may be similar to memory references in conventional architectures at least for LIFO scheduling. This is a nice result if holds true for most multithreaded applications because it suggests that the local memory systems designed ....

Makoto Kobayashi, Myron MacDougall. The Stack Growth Function: Cache Line Reference Models. IEEE Transactions of computers, Vol. 38, No. 6, June 1989, pages 798-805.

....set size, spatial locality, temporal locality, and interactions between spatial and temporal locality, respectively, of the intervening processing. The fact that u(R(x i ) L) is a power function of R(x i ) for fixed L was observed independently by Thiebaut [31, 32] and Kobayashi and MacDougall [16]. In [28] the authors show equation (1) to be consistent with data given by Smith [29] and Agarwal, Horowitz and Hennessy [1] They also demonstrate its accuracy through detailed validation on segments of a 200 millionreference trace of a multiprogrammed IBM 370 MVS workload, consisting of a ....

M. Kobayashi and M. MacDougall. The stack growth function: Cache line reference models. IEEE Transactions on Computers, 38(6):798--805, June 1989.

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Kobayashi, M. and MacDougall, M. H., "The stack growth function: Cache line reference models," IEEE Transactions on Computers, vol. 38, no. 6, pp. 798--805, June 1989.

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