2013-01-14T13:42:33Z Photos, electronics, cnc, and more Jeff Eplerjepler@unpythonic.net 2013-01-14T13:42:33Z 2013-01-14T13:42:33Z https://gamma.unpythonic.net/01358170953 In the quest to &quot;prove&quot; the quality of the numbers output by my <a href="https://gamma.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. 2012-03-07T15:42:39Z 2012-03-07T15:42:39Z https://gamma.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">