ross, I read your tutorial when I was doing my Compression project. The only thing I didn't know was how many decimil places the calc holds, and there is really no call to use something like that in this game.
Here is what I did to make it fast:
the game's graphics are not tiled, so drawing each screen is fast.
even though the graphics are not tiled the position of the character is, every 5 pixels you move you go into a diffrent cell of a matrix, but you move 2 pixels at a time.
the matrix contains info about the place where you are standing, it is possible to make the character walk on air or fall through a apparently solid floor.
if the matrix does not say otherwise then climping/falling/jumping are all determined by a pixel test of the space right below you, if nothing is there you fall.
movement inside buildings is purely tiled, allowing you to move about quickly, and allowing me to enable talking with NPCs.
The battle system:
a 10x10 arena setup.
random battle maps and a few templates.
up to 5 enemys at a time.
up to 2 teammates, plus yourself.
various floors (ex: grass, dirt, wood, stone, lava, empty (hole))
various objects on each floor (ex: bushes, Boulders, treasure chests)
each character has a set number of movement points which they use to attack/move plus they can get a team bonus which can be used with any team member.
more later, I got to go.
==========EDIT==========
more on the battle system:
at the start of each battle traps are placed at random places on the map, these traps go off when anything steps on them.
traps include damage, recovery, warps, stats ailments, and widespread damage.
some characters will not be able to use magic, they will make up for this by having other abilities, such as the ability to set traps.
these same characters, and mabey others will also be able to detect traps and tell you what they do.
each stage can also have places with raised or lowered elevation, increasing or desceasing the range of your weapon.
Im sure that other things will arise as developement progresses.
by the way, I am about 55% done with the demo version.