there's actually a pretty broud spectrum of procedures referred to as female circumcision. most of them are far more extreme than male circumcision, but type 1a is basically equivalent, though by far a minority. other forms are even worse than you've described.

but i've also got to point out that male circumcision is also explicitely a method of sexual control, among other excuses. a major reason it ever caught on in america was in an effort to prevent masturbation.