How did he calculate 5,800 petaflops? Bitcoincharts.com shows we are at 500 giga hashes per second as an entire network. Isn't a hash roughly ~5 flops? Which would put us at about 2.5 tera flops.
I would say a hash is more like in the low 4 digits (thousand(s)) of ops, just seeing the code. Definitely not 5 or anything similar.
Hashing is mostly elementary integer ops like bit shifts, and are hardly as meaty as floating point ops. Here might be a helpful relation though: for each cluster of 5 alus on a 5970, four mainly do integer ops and simple float ops, and the fifth can do both integer and full floating point including transcendentals (sin,cos,log,exp,etc.) So in the context of 5970s, integer ops and flops may be different. But by no more than a ratio of 5 to 1.