One small intervention. The haste spell double the number of attacks you make on a particular round. It does not increase your attack rate. The fighter will not go from 3/2 to 3/1 . He will do 2 attacks one round, and the next he will do four. Which might look like 3/1 but it is not. The difference is a slim one, but it can mean a lot with certain magical items.
Well, I highly suggest reading the excerpt I just quoted from the DMG, and taking it up with Gygax. Here's the relevant portions for you with regard to TWF and haste:
When one or more creatures involved in combat are permitted to use their attack routines twice or more often during the round, then the following initiative determinants are employed. When the attack routine may be used twice, then allow the side with this advantage to attack FIRST and LAST with those members of its group who have this advantage. If it is possessed by both parties, the initiative roll determines which group strikes FIRST and THIRD, which group strikes SECOND and LAST. If one or both groups have members allowed only one attack routine, it will always fall in the middle of the other attacks, the order determined by dicing for initiative, when necessary. If one party has the ability to employ its attack routines thrice, then the other party dices for initiative to see if it, or the multi-routine group, strikes first in the mid-point of the round. Extrapolate for routines which occur four or more times in a round by following the method above. Note that a routine is the attack or attacks usual to the creature concerned, i.e. a weapon (or weapons) for a character, a claw/claw/bite routine for a bear (with incidental; damage assessed as it occurs - the hug, for exomple). A 12th level fighter is allowed attack routines twice in every odd numbered melee round, for example, and this moves up to three per round if a haste spell is cast upon the fighter. Damage from successful attacks is assessed when the "to hit" score is made and damage determined, the creature so taking damage having to survive it in order to follow its attack routine.