Lets start by defining what each of these functions does:

Short Term Fuel Trim (STFT): A rapid, non-stored fuel adjustment described by percent fuel error.

Long Term Fuel Trim (LTFT): A slow, averaged, stored fuel adjustment described by percent fuel error. Can be modified or reset to zero by firmware or reset to zero by user action (VCM Controls, removing battery power).

Fuel Trim Cell (FTC): A pointer to the FTC matrix (array) described by the LTFT boundaries of MAP & RPM and stored in RAM. Also includes cells for Idle, canister purge, WOT, transmission selection (P/N, gear) and AC on/off. See the help file for more definitions of FTC per vehicle type.

How it works (Closed Loop only!):
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The PCM reads the o2 sensor value and compares it with the last reading to see if it switched from rich to lean or lean to rich. If it hasn't switched, it averages that value with the last and uses the proportional o2 error tables to determine how much the pulsewidth needs to be changed to make the o2 switch.

This averaged value (filtered) is then turned into the STFT value. If the o2 has been rich for a while (filtered, averaged) the STFT goes negative, pulsewidth drops, and vice versus.

Now, if the STFT goes above/below a preset limit over a period of time (~450msec), the LTFT will be Incremented (if STFT+) or Decremented (if STFT-) accordingly. If STFT is *way out of whack*, LTFT will Increment or Decrement more rapidly based on filter values in the closed loop control.

When the engine operating conditions cause the FTC to change, the last LTFT value from the current FTC is stored in RAM to be retrieved the next time the engine returns to that particular FTC. The LTFT value for the current FTC is then loaded from RAM and the process repeats.