[Numpy-discussion] bug in round with negative number of decimals
Paulo J. S. Silva
pjssilva at ime.usp.br
Mon Sep 4 10:08:28 CDT 2006
Interesting, I was just reading about the round rule in IEEE standard
last Friday.
What numpy's "around" function does is called "round to even" (round is
take to make the next digit even), instead of "round up". According to
"What every computer scientist should know about floating-point
arithmetic" (do a Google search), the reason to prefer "round to even"
is exemplified by the following result from Reiser and Knuth:
Theorem
Let x and y be floating-point numbers, and define x0 = x, x1 = (x0 - y)
+ y, ..., xn = (xn-1 - y) + y. If + and - are exactly rounded using
round to even, then either xn = x for all n or xn = x1 for all n >= 1.
If you use "round up" the sequence xn can start increasing slowly "for
ever", and as the paper says:
"...This example suggests that when using the round up rule,
computations can gradually drift upward, whereas when using round to
even the theorem says this cannot happen."
Best,
Paulo
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