A graphics-processor molecular-dynamics code stores a particle's velocity component…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Numerical and computational mathematics · Numerical and computational mathematics

Error, Chance and the Machine, Ch Rounding, backward error and the sensitivity of a computation

Problem

A graphics-processor molecular-dynamics code stores a particle's velocity component

v = -850.0\ \mathrm{m\,s^{-1}}

in the half-precision format, whose significand (including the implicit leading bit) has

t = 11

bits. ((a)) State

\epsilon_{\rm M}

and

u

for half precision. ((b)) Give the bound on the absolute error committed in storing

v

that follows from the rounding model

\mathrm{fl}(v) = v(1+\delta)

|\delta|\le u

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