Both Channelled Spells and DoT's are changing so that they are benefit from Haste without shortening the duration by half, and to prevent clipping. This is my attempt at an explanation. Don't worry, the changes are GOOD.
HASTE:
Haste will be calculated as it is now for hasted spells, but if there is suddenly room for another tick, the spell expands to allow that extra tick. This means that with sufficient haste, you will be casting 4 ticks of Mind Flay or 6 shots of Arcane Missiles in the period you previously shot 3 or 5. The last tick will always occur when the spell expires, as it does now.
Example 1:
Assume you have 30% haste on a Mind Flay (works for any spell, dots included)
Take the time between ticks, for Mind Flay this is 1s.
Apply haste: 1s / 1.3 = .7692s
How many of these fit into the base duration? For Mind Flay, this is 3 seconds.
3 / .7692 = 3.9
We always round down, so 3
Your new mind flay will have 3 ticks every .7692s for a total duration of 2.3 seconds.
Example 2:
Assume you have 40% haste on a Mind Flay
Take the time between ticks, for Mind Flay this is 1s.
Apply haste: 1s / 1.4 = .7143s
How many of these fit into the base duration? For Mind Flay, this is 3 seconds.
3 / .7143 = 4.2
We always round down, so 4
Your new mind flay will have 4 ticks every .7143s for a total duration of 2.86 seconds.
Example 3:
Assume you have 20% haste + Eradication + Heroism + Aura on a Unstable Affliction (15s duration, 5 ticks every 3 seconds)
This is 1.2 x 1.2 x 1.3 x 1.03 = 92.8% Haste
Apply haste: 3s / 1.928 = 1.556s
How many of these fit into the base duration?
15 / 1.556 = 9.64
We always round down, so 9
Your new UA will have 9 ticks every 1.556s for a total duration of 14.004 seconds.
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CLIPPING:
You will no longer be able to clip your spells and have a period of no damage from the dot. In WOTLK, if you recast a DoT with .1 seconds remaining, the tick that would have happened in .1 seconds is essentially deleted. You get nothing. In Cataclysm, if you recast a DoT with .1 seconds remaining, the next tick will still occur in .1 seconds and the duration of the DoT will adjust to fit. For example, if you sat still and spammed the crap out of your Corruption spell, it would actually do damage in Cataclysm. Would it be smart to do so? Not really, you're not casting any other spells and uselessly maintaining 100% uptime on corruption.
Sometimes you will in fact lose a tick (damage done) due to haste and the moment you clipped, but you will not lose DPS from that particular spell. Sometimes you will not lose the tick. Here is what I mean.
Let's use example 3:
Your new UA will have 9 ticks every 1.556s for a total duration of 14.004 seconds.
This means that you can refresh the old one with less than .996 seconds remaining (base - hasted duration). The duration of the new spell will be 14.004 + duration remaining. It will have 10 ticks instead of 9. Cool, hey? Here's the logic
Refresh at .5 seconds remaining:
A) New spell = 14.504s duration.
B) Is this under max duration (15s)?
D) Yes: 14.504s duration with the next tick occuring at 14.004s and every 1.556s after that.
If you refresh with more than .996 seconds remaining, the duration of the new spell will be greater than 15 seconds. In this case you lose a tick of the new spell
Refresh at 1.5 seconds remaining
A) New spell = 15.504s duration.
B) Is this under max duration (15s)?
C) No: Minus a tick 15.504 - 1.556 = 13.948s duration
B) Is this under max duration (15s)?
D) Yes: 13.948s duration with the next tick occuring at 12.448s and every 1.556s after that.
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IMPACT ON US AS DPS:
Gameplay remains unchanged. You should never clip a spell, intentional or not. Intentional clipping just causes you to cast more spells to maintain the exact same 100% uptime. This results in fewer GCD's in which to use filler spells. Overall, the clipping change is good for people learning to play without being overly punished. Over a 5 minute fight, clipping 10 times, you will lose 2 filler spells total. Currently, you would lose 10 ticks which are valued much more than 2 fillers, and it would not be easy to detect from a log parse or recount. This is bad and the fix is good.
However.
There is the possibility of using an addon to calculate optimal refresh time. Due to the mechanics of haste and dot clipping, there may be times where you have a choice to clip or cast a filler spell, and the clip will result in more dps. If your haste + remaining duration is such that it appends the duration to a fresh cast and does not result in a lost tick, it will be more beneficial to clip. However, the window for this is exceptionally small - less than 1 second in most cases. I expect that at some point there will be a mod for this, but the capability to make full use of it will depend on the ability of the mod to forecast your dps rotation. It would have to think ahead 2 spells in order to tell you when it is optimal to clip.