Jeff Epler's blog2013-01-14T13:42:33ZPhotos, electronics, cnc, and moreJeff Eplerjepler@unpythonic.netHash saturation calculator2013-01-14T13:42:33Z2013-01-14T13:42:33Zhttps://emergent.unpythonic.net/01358170953
In the quest to "prove" the quality of the numbers output by my <a href="https://emergent.unpythonic.net/01257868826">Arduino Random Number Generator</a>, I've come across
the concept of <a href="http://www.av8n.com/turbid/paper/turbid.htm#sec-saturation">hash
saturation</a> while reading about the <a href="http://www.av8n.com/turbid">turbid</a> random number generator which uses
noise plus hash to give high quality random numbers. Implicitly I've
relied on hash saturation all along, but now I have is a mathematical
basis for this reliance.Cancellation error2012-03-07T15:42:39Z2012-03-07T15:42:39Zhttps://emergent.unpythonic.net/01331134959
I was recently reminded of the importance of choosing numeric algorithms that
don't behave catastrophically for certain inputs. One example is the
calculation of 1-cos(θ) for small θ. In this case, cos(θ) is very close to 1,
leading to a <a href="http://en.wikipedia.org/wiki/Loss_of_significance">large
cancellation error</a> in the subtraction step.
<p><img src="https://media.unpythonic.net/emergent-files/01331134959/cancelerr.png">