Huh. Didn't think you needed room for Tumbling. I always thought it was like, mid air flips and such, tuck into a ball and roll. Ah well. I learned something today!
The rules don't say one way or the other, but that's the way I see it (If you've played Ocriana of Time, think of how you roll to reduce falls there. That's the way I see it, and the hole's not big enough for that.) Either way, you're fine since you can Feather Fall.
Completely random question: Have any of you signed up for the D&D Next public playtest?