Archive for June 2011  Stata 12 Announced   Here are the
highlights of what’s new:    Precision (yet again), Part II  In
part I, I wrote about precision issues in English. If you
enjoyed that, you may want to stop reading now, because I’m
about to go into the technical details. Actually, these details
are pretty interesting.  For instance, I offered the following
formula for calculating error due to float precision:
maximum_error = 2-24 X  I later mentioned that the formula is an
approximation, and said that the true formula is,  maximum_error
= 2-24 2floor(log2 X)  I didn’t explain how I got either
formula.  I need to be more precise today than I was in my
previous posting. For instance, I previously used x for two
concepts, the true value and the rounded-after-storage value.
Today I need to distinguish those concepts.  X is the true
value.  x is the value after rounding due to storage.  The issue
is the difference between x and X when X is stored in 24-binary-
digit float precision.  Base 10  Although I har