The Importance of Arbitrary Precision
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Two photon paths are simulated in this animation. The only
difference is that the paths are initialized with different precision.
The gray path starts with machine precision. The orange path starts
with 120 digits of precision using Mathematica's arbitrary
precision. At each step in the algorithm, precision is lost. In the
case of the gray photon, all precision is lost and the resulting path
can no longer be trusted and deviates significantly from the orange path.
The orange path ends with 62 digits of precision still remaining.
Check out the Wolfram
Technology Guide for more on this technology as well as other
technology used in Mathematica.
This animation was generating using code supplied by Jeff Bryant
and Jeremy Davis. The underlying math was orginally obtained from
one of the Hundred-Dollar, Hundred-Digit Challenge Problems published in SIAM News.