Fast and lightweight computation of AUC metric for the binary case (1 positive and 0 negative) is offered by lightAUC package. The algorithm used is a fast implementation from algorithm of Fawcett (2006).
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For parallel calculations use:
# E.g. 2 cores (you can use cores = parallel::detectCores() for your case)
probs <- c(1, 0.4, 0.8)
actuals <- c(0, 0, 1)
lightAUC(probs, actuals, parallel = TRUE, cores = 2)
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Fawcett, T. (2006). An
introduction to ROC analysis.