My first post here, I've been reading the forum a while but now I decided to show myself.
The LM4F120 indeed does not have the hardware QEI modules available on the higher-end models. So you'll need a pure software solution.
I'm currently working on a final year mechatronics project at Aalto University (in Finland), and the device I'm building has three quadrature encoders. I'm using the SLaunchPad as the controller and am now writing my own support libraries on top of StellarisWare. One such library module is a software QEI, having most of the features that the hardware API has, excluding velocity measurement.
Just a fair warning; you can't run a very fast encoder on a software QEI, let alone multiple encoders. I have a 1000 ppr encoder which I spun at increasing speeds until the software reported an error condition (both channels having an active interrupt at the same time). I got to around 2000-3000 rpm, and the decoding was done in 4x mode, so both edges on both channels were counted. Using an idle-while loop counter, I estimated the CPU usage at that point to be around 50%.
I'm not yet publish-confident with the library, but if you give me your email address, I'll send you the source code. The library supports counting in 1x, 2x and 4x modes, has optional support for Z channel and autoconfiguration for the pins.
I am working on porting eLua to the Stellaris and Tiva Launchpad.
eLua is a version of Lua (a scripting language) for microcontrollers. Main eLua web site http://www.eluaproject.net/ eLua works as an interpreter running on the virtual serial port. eLua already runs on several of the Stellaris LM3 development kits.
Source code for my port is available on Github https://github.com/ecdr/elua
in the LM4 branch
It compiles (using codesourcery) and runs (i.e. hello world and blinking led work).
It is integer only (may not be enough memory for floating point). Several peripherals are turned off (no CAN, no I2C).
[Edit: CAN now turned on]