Prelookup — Control Systems/Lookup Tables

Prelookup

Control Systems / Lookup Tables

Finds where the input sits on a breakpoint axis and publishes the position as a pair, without consulting any table: the index k of the interval the input falls in, and the fraction f of the way across that interval it sits, so that u ≈ bp[k] + f·(bp[k+1] − bp[k]).

Splitting the search from the table is the point of the block: several tables sharing one axis do the search once here and feed Interpolation Using Prelookup, instead of each repeating it.

Ports

• Input – the value u to locate, of any size [m,n]. Each entry is searched independently.
• Output k – the interval index, of the SAME size [m,n]. A whole number carried as a double, counted from zero, and never larger than n−2 – see the note below.
• Output f – the fraction, same size again. Inside the table it lies in [0,1]; outside it, under Linear extrapolation, it deliberately does not.

Parameters

• Breakpoints – the axis, as a row or column vector; both spell the same list. It must hold at least two strictly increasing values: a repeated breakpoint is a zero-width interval whose fraction is a division by zero, and a decreasing one describes no axis at all.
• Extrapolation Method – what to report for an input outside the axis.
  • Linear – the fraction continues past the end interval, so it goes negative below the first breakpoint and above 1 past the last. That is what lets a downstream interpolator extrapolate.
  • Clip – the fraction is held in [0,1], pinning an out-of-range input to the nearer end of the axis.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

The index stops at n−2

The last breakpoint reports k = n−2 and f = 1, not k = n−1 and f = 0. Both name the same point, but only the first leaves an interval [k, k+1] for an interpolator to stand in – a k of n−1 would send it off the end of the table. This is Simulink's behaviour (verified against the R2026a block with breakpoints [−2 −0.5 0.3 1.4 2.6], where an input of 2.6 returns index 3, fraction 1) rather than a choice made here, and it is the difference that catches people comparing the two.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text. The axis is baked into the arithmetic at export time rather than exposed as a tunable parameter, and it has to be: the number of breakpoints decides how many branches the generated code has, so the axis and the structure of the code cannot be separated. The search is emitted as a chain of comparisons, which is the one shape all ten targets agree on.

The three HDL targets are not simulation-only. No divider is emitted: each interval's width is known at export time, so the fraction is a multiply by a constant reciprocal. The HDL caveat is range rather than accuracy – a signal is carried in Q16.16 there, so a breakpoint outside ±32767 cannot be represented.

Simulink bridge

Import and export, mapped to simulink/Lookup Tables/Prelookup. "Breakpoints" to BreakpointsData and "Extrapolation Method" to ExtrapMethod – the two values are Simulink's own strings, so that mapping is 1:1 and lossless both ways. The block always writes OutputSelection = Index and fraction, which is what having two output ports means; Simulink's other two selections (index only, and the pair as a bus) have no counterpart here. "Sampling Time (s)" goes to SampleTime, as on every block.

Simulink's index output is an integer type (uint32 by default) while every ICore signal is a double. The values agree exactly – the index is a whole number on both sides – but a Simulink model reading the exported index alongside doubles may need a Data Type Conversion, which is why the parity testbench inserts one.

Notes

• Algebraic, with no state.
• Elementwise: both outputs carry the input's size, and each entry is searched on its own.
• Not linear, and so deliberately carries no state space – model reduction reports it as unmergeable rather than absorbing a chain of comparisons.
• See Interpolation Using Prelookup for the block that consumes this pair, and 1-D Lookup Table for the two steps done together in one block.