On a machine recorded as Laptop A (a quad-core laptop CPU with two populated…

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Scientific Computing for Physicists, Ch Arrays in memory: layout, cost and the data structures of physical problems

Problem

On a machine recorded as Laptop A (a quad-core laptop CPU with two populated DDR4-3200 channels, commit and lockfile as usual), you measure the memory-bandwidth triad np.add(b, c, out=a), one operation with no temporary, on three float64 arrays of

N = 5\times10^{7}

elements each, following twenty measured repeats after warm-up: the median time is

45\,\mathrm{ms}

(interquartile range

2\,\mathrm{ms}

). ((a)) State the bytes the triad must move and estimate the sustained bandwidth

\beta_{\rm mem}

of Laptop A. ((b)) Using this

\beta_{\rm mem}

, estimate the lower bound on the time for one step of the explicit two-dimensional diffusion stencil on a

4000\times4000

grid, assuming perfect cache reuse (one read and one write per grid point). ((c)) The same machine executes one such stencil step with a measured median time of

52\,\mathrm{ms}

(twenty repeats). Give the ratio of the measured time to the lower bound, to one significant figure, and say what the ratio shows.

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