Earlier quoted context omitted.
I've given a bit more background to the fast JPEG codec on my engineering blog: http://www.snappylabs.com/blog/snappycam/2013/07/31/iphone-k... If you like signal processing, fixed point arithmetic, SIMD cores, and assembly, then this is for you. :-)
So the summary is "JPEG encoder written in assembly with NEON instructions saves images faster than Apple's encoder." That's a cool feat and is a little damning for Accelerate.framework, although the way techcrunch writes it I expected a new kind of fast cosine transform.
The actual DCT algorithm created and used in the app is different to the typical AAN (Arai, Agui, Nakajima) DCT algorithm that's used in JPEG codecs, at least all the ones I've seen.
It's all about doing as little work as possible to achieve the end result. That's why there's so much asm implementation, with carefully chosen NEON instructions for each step.
Think of it as a cross-layer optimization between algorithm and implementation... done by hand. :-)