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Method for definition of lookup tables
Overview
A lookup table may be viewed as a set of of parallelized truth tables receiving the same inputs and providing collectively a vector of outputs instead of a single one. In this sense m constraints would be needed to model m outputs. A more efficient and expandable approach however would be to model the lookup table as a memory element with k inputs (address) and m outputs (memory word).
Applicability
Lookup tables are appropiate for functions which outputs depend on a combination of values of the inputs. Lookup tables map input value (ranges) to output values.
Examples
The following lookup table relates the brake distance and brake time dependent on the train velocity where the standstill corresponds to row #1 (this is simplified because this mapping depends on several other aspects).
row | input (train velocity) | input (estimated brake distance) | output (estimated brake time) |
---|---|---|---|
#1 | 0 km/h | 0 m | 0 s |
#2 | <= 20 km/h | 28 m | 9 s |
#3 | <= 40 km/h | 99 m | 17 s |
#4 | <= 60 km/h | 215 m | 24 s |
#5 | <= 80 kn/h | 375 m | 32 s |
#6 | <= 100 km/h | 579 m | 40 s |
#7 | <= 120 km/h | 827 m | 48 s |