Video here:
http://www.youtube.com/watch?v=tJXtFpeKmRQ
Looking at videos, pictures and consulting my books on bow-making, I've come to these conclusions.
The giants stormig the wall seem to be even bigger as the one Jon saw in the camp, about 3 times the size of a man, 5.5 to 6m.
The bow was 3.5 to 4m long, and compared to other things nearby, it seems to have about 4 to 5 inches wide (It's almost as wide as a human's head, accordin to the video). The wrapping and recurves seems to indicate it's a composite of horn and sinew - a wooden bow would be worse if wrapped. (probably mammoth, if we keep the giant's theme...) The fact the wildlings use these bow type as well, and that it was quite usual makes me quite confident of this.
The Wildling archer used a composite bow, and his arrow reached up to about 600feet (just shy of the 700 feet the wall is), or about 200m - indicating a good average 80-90 lbs draw weight of a strong hunting/standard war bow. Draw weights like this are more than adequate for war when using composite bows, allowing for about 400+ meters range with about 70-80m/s speed. (I've lately had the pleasure to shoot one of 75lbs draw weight, and that thing sent the arrows 330 to 350m downrange. Rule of thumb: you can shoot about half as high up as you can shoot them far at optimum angle.)
The giant's bow was about 4 times as wide as the wildling's - means as a low end, it's about 4 times as strong (the arrow was the size of a spear - and since the arrow and draw lenght are increased as well, there is no reduced efficiency due to longer limbs): ~360lbs -NO WAY!
High end, we must assume that it's also 4 times as thick, which would mean that it's 64 times stronger (doubling the thickness means an 8-fold increase in draw weight), and then times four for the width increase: 23000 lbs draw weight. 10.5 metric tons. This claim seems outrageous, but remember that one of these guys lifted that gate up over his head - the gate is about 8x8m in size, and 9 inches thick which means about 8-9 metric tons in wood alone, ignoring the wrought iron reinforcements, resistance of the gate mechanism, and stuff (probably frozen shut).
Let's check against the visuals - if we only went by double thickness, this would give it a total of (8x4) 32 times the wildling's bow's strenght- about 2900 pounds draw weight. People used crossbows of such draw weights, and they didn't do anything like that, so we must be somewhere much closer to high end.
The arrow hit the man at 700feet height in (less than, it seems) a second, and took him for a 20 m flight before it ran out of energy and they dropped. That means a velocity of at least 700 fps(or km/h, they are almost identical).
World records are about 600fps for 150lbs bows, so an arrow certainly can get that fast, it's just a question of the weight of that damn thing.
I'm going with 2kg for the ~6 foot/1.5 inches diam. shaft with that huge stone tip, and 210m/s - 44000 joules, enough to send a 100 kg (strong and armored) man flying at 30m/s after getting stuck in said armor. The man seemed to fly much slower, but there whould be a lot of energy lost in such an event, so I guess it's probably a good ballpark value.
Given that you need a 150lbs bow to send an 30gram arrow that fast, we need at least 10000 lbs draw weigth if we assume a linear correllation. (which would be another low- end value).
Conclusio: That giant archer pulled a frickin catapult-sized bow with a draw weight between 10000 and 23000 lbs.
A minute's thought suggests that the very idea of this is stupid. A more detailed examination raises the possibility that it might be an answer to the question "how could the Germans win the war after the US gets involved?" - Captain Seafort, in a thread proposing a 1942 'D-Day' in Quiberon Bay
I do archery skeet. With a Trebuchet.