  A new deterministic floating-point arithmetic called precision arithmetic is
developed to track precision for arithmetic calculations. It uses a novel
rounding scheme to avoid excessive rounding error propagation of conventional
floating-point arithmetic. Unlike interval arithmetic, its uncertainty tracking
is based on statistics and the central limit theorem, with a much tighter
bounding range. Its stable rounding error distribution is approximated by a
truncated normal distribution. Generic standards and systematic methods for
validating uncertainty-bearing arithmetics are discussed. The precision
arithmetic is found to be better than interval arithmetic in both
uncertainty-tracking and uncertainty-bounding for normal usages.
  The precision arithmetic is available publicly at
http://precisionarithm.sourceforge.net.
