2012-03-07T15:42:39Z Photos, electronics, cnc, and more Jeff Eplerjepler@unpythonic.net 2012-03-07T15:42:39Z 2012-03-07T15:42:39Z https://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">