Elliptic Curve operations in Bitcoin

[missfox]

Hello,

I have got a question: Bitcoin uses Elliptic Curves maths for several reasons. But my question is: How does it work in reality?

Of course in every book you find the "normal" addition and point doubling formulas in every book, such as:

http://patentimages.storage.googleapis.com/EP1653428A1/imgf0001.png

This is nice to see, but is is "standard theory", these computations are very expensive; there are much more efficient algorithms. Especially, Renes, Costello and Batina showed "complete addition formulas" (see https://eprint.iacr.org/2015/1060.pdf), where one calculates in the projective plane. 

So, does anyone know how ECC is used in Bitcoin? Is there a possibility where I can find the code in the Bitcoin protocol?

I also read that Bitcoin chose Secp256k1 because of efficiency reasons, so I cannot believe that they use "standard" formulas for calculating.