A 16-bit floating-point format

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

Mathematical Methods for Physics, Ch Floating-point arithmetic, conditioning and numerical stability

Problem

A 16-bit floating-point format, used on some graphics hardware, keeps

p = 11

bits in its mantissa. Two readings,

1001.3

and

1000.9

, are stored in this format and then subtracted; the true difference is

0.4

. ((a)) Find

\epsilon_{\mathrm{M}}

for this format. ((b)) Find the spacing between neighbouring representable numbers near

1000

. ((c)) Predict how many significant figures of the difference survive. Then find the two stored readings and their stored difference, and check the prediction against the true

0.4

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