Fastest method to compute an AUC

Context: AUC is an acronym for "Area Under the (ROC) Curve". If you are not familiar with the ROC curve and AUC, I suggest reading this blog post before to continuing further. For several projects, I needed to compute a large number of AUC. It started with 25,000, increased to 230,000 and now I need to compute 1,500,000 AUC. With so many AUC, the time to compute each one becomes critical. On the web, I don't find much information about this specific [...]