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.

Enigma: The Battle for the Code[0] is a very good read. It details the Polish achievements, the rush to save the Polish cryptographers out of France as the it was collapsing in 1940, and then goes into details with the many more details that gone into the cracking effort, besides Turing's team. Eg. tt shows the importance of weather report patterns in finding cribs that short-circuited the decryption (known clear text headers) and the importance of the submarine captured Enigma machines that showed the disk settings in the Navy setup (the Navy machine was much harder to crack than the Army ones). Not only a good read, but also very educating for anyone using cryptography today!

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

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.)