In this exercise we look at memory locality properties of matrix computation. The following code is written in C, where elements within the same row are stored contiguously. Assume each word is a 64-bit integer. for (I = 0; I < 8; I++) for (J = 0; J < 8000; J++) A[I][J] = B[I][0] + A[J][I]; (a) How many 64-bit integers can be stored in a 16-byte cache block? (b) Which variable references exhibit temporal locality? (c) Which variable references exhibit spatial locality? (d) Locality is affected by both the reference order and data layout. The same computation can also be written below in Matlab, which differs from C in that it stores matrix elements within the same column contiguously in memory. for I 1:8 for J 1:8000 A(I,J) = B(1,0) + A(J,I); end end (e) Which variable references exhibit temporal locality? (f) Which variable references exhibit spatial locality? (g) How many 16-byte cache blocks are needed to store all 64-bit matrix elements being referenced using Matlab's matrix storage? How many using C's matrix storage? (Assume each row contains more than one element.)

In this exercise we look at memory locality properties of matrix computation. The following code is written in C, where elements within the same row are stored contiguously. Assume each word is a 64-bit integer. for (I = 0; I < 8; I++) for (J = 0; J < 8000; J++) A[I][J] = B[I][0] + A[J][I]; (a) How many 64-bit integers can be stored in a 16-byte cache block? (b) Which variable references exhibit temporal locality? (c) Which variable references exhibit spatial locality? (d) Locality is affected by both the reference order and data layout. The same computation can also be written below in Matlab, which differs from C in that it stores matrix elements within the same column contiguously in memory. for I 1:8 for J 1:8000 A(I,J) = B(1,0) + A(J,I); end end (e) Which variable references exhibit temporal locality? (f) Which variable references exhibit spatial locality? (g) How many 16-byte cache blocks are needed to store all 64-bit matrix elements being referenced using Matlab's matrix storage? How many using C's matrix storage? (Assume each row contains more than one element.)

Systems Architecture

7th Edition

ISBN:9781305080195

Author:Stephen D. Burd

Publisher:Stephen D. Burd

Chapter3: Data Representation

Section: Chapter Questions

Problem 1PE

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