Formulas for the gravity potential, eld, eld-gradient,<br>magnetic potential and eld of a polyhedral target<br>of spatially uniform density or magnetization su er<br>asymptotic rounding error that grows proportionally to a<br>power of the dimensionless target distance. The form of<br>the error growth can be speci ed by universal templates<br>that are applicable to a very wide class of targets and<br>arbitrary floating point precision, and hold for all the<br>standard gravimetric anomaly calculations.<br>A compact form of the anomaly formulas allows the theoretical<br>a priori templates to be be derived, depending<br>only on the presence or absence of foreshortening in the<br>observed anomaly, and class of anomaly formula used,<br>of which three kinds are found in the literature. Computational<br>results, con rming this claim, demonstrate<br>automatic method selection to accomplish maintenance<br>of rounding error to a speci ed level in magnetic eld<br>computations.


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