[math-fun] Current state of "Spigot" algorithms ?

What is the current state of "spigot" (Borwein-type) algorithms for transcendental numbers? Are there only a handful of such algorithms for specific numbers, or are there some classes of numbers -- e.g., log(some-expression), sin(some-expression) -- which have "parameterized" spigot algorithms? I'm looking for a relatively short (1-2 sentences) and/or links that might have the answer. I want to mention "spigots" in passing while talking about random number generators.