Pixel shader instructions per clock

[bver78]

So for the newest generation of GPUs, how many pixel shader operations can they execute per clock cycle, and would that be considered a pass (like if your ps requires that number + 1 ops, it would require 2 passesin the traditional sense)?

[Hyp-X]

So for the newest generation of GPUs, how many pixel shader operations can they execute per clock cycle,

Assuming you mean PS2.0:

R300/R350 - at least 8 arithmetic ops - sometimes 16 if you have a pairable vec3 and scalar op and 8 texture ops.
RV350 - at least 4 arithmetic ops - sometimes 8 is you have a pairable vec3 and scalar op and 4 texture ops.

NV30 - 4 arithmetic ops or 8 texture ops.
NV31 - (IIRC) 2 arithmetic ops or 4 texture ops.
NV34 - (IIRC) 1 arithmetic ops or 4 texture ops.

and would that be considered a pass (like if your ps requires that number + 1 ops, it would require 2 passesin the traditional sense)?

No it wouldn't.