This is a PM I sent to Violent by Design, who was trying to eke decent speed out of an i7 using onboard graphics. The bottleneck in his case was the IGP, but some of the settings might apply for people that just want to find out what some of the settings do:
1. Config > Emulation Settings > EE/IOP: Emotion Engine and iOP should be set to Recompiler, EE Cache should be disabled/Unchecked. set EE/FPU Advanced Recompiler to Chop/Zero, Clamping mode to None (or Normal, it's only a minor speed hit).
2. Config > Emulation Settings > VUs: VU0 and VU1 should be set to microVU recompiler (superVU used to be faster and less accurate, but recent changes added a few optimization tricks to microVU, according to the devs, making the superVU useless nowadays). Advanced Recompiler options are again Chop/Zero, and Clamping mode to Normal (setting it to none is faster, but there are some games that need it e.g. FFX will have characters facing the wrong way in some instances if it is set to none)
3. Config > Emulation Settings > GS: Ignore everything. The defaults should be fine (in my case, everything is disabled as most of the options in there will slow down emulation and meant only for debugging/testing)
4. Config > Emulation Settings > GS Window: Same as above. The options here have no bearing on speed, except for the vsync option (will slow down the emu a bit, as expected of vsync)
5. Config > Emulation Settings > Speedhacks: Enable speedhacks, but set the EE Cyclerate to 1 (Default cyclerate. It's meant to downclock the emulated CPU, which is bad if the game you're playing uses the Emotion Engine heavily. It will choke and you'll end up with either slow motion gameplay or frameskips, depending on the game. FMVs in particular will skip and stutter on the 3rd setting).
VU Cycle Stealing should be 0 (disabled, it "steals" gpu cycles in order to lighten the load. It works on some games, but majority of games are also dependent on the PS2's vu, so starving them results in 60 fps but slow motion gameplay).
Enable INTC Spin Detection should be Checked, as well as Enable Wait Loop Detection. MVu Flag Hack is safe as well. MTVU will give you the biggest speedboost here, but some games crash with it enabled (e.g. Dragonball Z Budokai Tenkaichi 3), so try it at first. If it works, leave it on for that game.
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Sound part (use SPU2-X):
1. Config > Audio > Plugin Settings: put a check on Disable Effects Processing, and set interpolation to 0 (Nearest). The rest can be left alone on their default settings
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Graphics part - Use GSDx. Use either the 4.1 version or the AVx one if your CPU supports those extensions, both of them take advantage of said instruction sets to speed up some drawing functions.
1. Config > Video > Plugin Settings: for Renderer, choose Direct3D9 (Hardware). Your video supports DX11 (I think) but like most onboards, it's not very good at it. DX9 is faster in your case. Then make sure "Original PS2 resolution: Native" is checked.
Texture Filtering should be left at the default setting (blue box instead of check or blank), Logarithmic Z and Alpha Correction come with a speed hit, but you need them enabled in order to get proper sprite priorities and transparencies. Allow 8-bit textures should be unchecked (it's only useful for videocards that have little RAM but a decent amount of ROPs). Enable HW Hacks should be disabled.
Alternatively, you can choose Direct3D11 (Software) or Direct3D9 (Software) and then set the Extra Rendering Threads to 2 or 3 (i7s are all quad cores, right? I haven't touched one of them so I'm not sure.) In some cases this will be faster than if you were using Hardware, given your beefy CPU.
Some games will work faster in D3D11 than D3D9, and some will go the other way around (in my experience, DBZ Budokai Tenkaichi 3 works faster in D3D9 but DBZ: Infinite World works faster in D3D11. I dunno why.)
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....aaand that's it. Beyond that, it's usually up to the game you are playing. Different PS2 games treat the PS2 hardware differently. Kingdom Hearts, Marvel vs. Capcom, and Final Fantasy X are some of the easiest as they're not hard on the PS2, but there are some really heavy games like Shadow of the Collossus and MGS2 that even people with high end PCs have trouble emulating. The rest fall in between. And there are edge cases like WWE Smackdown vs. Raw 2006, which is easy to emulate when you're only playing the normal modes and Royal Rumble, but once you run an elimination chamber match, it starts lagging.