I have Enigma by Hugh Sebag-Montefiore (https://www.amazon.com/Enigma-Battle-Code-Hugh-Sebag-Montefi...) except in incredibly nice Folio Society edition. It is meticulously researched and covers all the fun parts of Bombes and programming. The appendixes do step by step algorithm explanation of how this work. Tons of unsung heroism in the seas with the capture of various machines from U boats and ships.

The American Black Chamber (there's some controversy surrounding the author, too)

https://en.wikipedia.org/wiki/The_American_Black_Chamber

Enigma: The Battle for the Code (I think that's the one I read)

http://www.amazon.com/Enigma-Battle-Code-Hugh-Sebag-Montefio...

I know I read one specifically about breaking Purple, but can't seem to track it down (I don't believe it's the William F. Friedman bio).

I haven't read this one, but it also seems to be what you're looking for (and has a decent rating):

http://www.amazon.com/Code-Book-Secret-History-Code-breaking...

(You might check a public/university library for these and related titles--that's where I found them.)