prelookup

Computes the interval index k and fraction f for a shared breakpoint search.

📝Syntax

Block type: prelookup

📥Input Arguments

Parameter	Description
input ports	1 input port(s) declared.

📤Output Arguments

Parameter	Description
output ports	1 output port(s) declared.

📄Description

Computes the interval index k and fraction f for a shared breakpoint search.

Module	`nflow_blocks`
Library	Lookup Tables
Type	`prelookup`
Label	Prelookup

Description

Given a scalar input u and the strictly increasing BreakpointsForDimension1 vector, computes the interval index k with bp[k] <= u < bp[k+1] and the fraction f = (u - bp[k]) / (bp[k+1] - bp[k]). The output is the 2-element vector [k, f], which one or more interpolationPrelookup blocks can reuse to interpolate several tables without repeating the interval search.

Out-of-range inputs are clipped: below the first breakpoint gives [0, 0]; at or above the last gives [N-2, 1]. Code generation is supported for C and Rust (the vector-expansion pass lowers the block into scalar helpers).

Ports

Input(s)

Port	Role	Side	Position
Port_1	Numeric signal read by the block.	left	x=0, y=40

Output(s)

Port	Role	Side	Position
Port_1	Numeric signal produced by the block.	right	x=90, y=40

Parameters

Parameter	Default value
`BreakpointsForDimension1`	[0 1 2 3 4]

Block Characteristics

Block type	prelookup
Family	Lookup Tables
Rendered size	90 x 80
Phases	ALGEBRAIC
Internal state or history	no
Signal data type	double numeric values

Algorithms

ALGEBRAIC: locate k, compute f, output [k, f].

Equation or Rule

$$k : b_k \le u < b_{k+1},\quad f = \frac{u - b_k}{b_{k+1} - b_k}$$

Extended Capabilities

Code generation: supported for C and Rust.

Implementation Sources

Manifestmodules/nflow_blocks/libraries/lookup/library.json

{
  "id": "builtin.lookup",
  "title": "Lookup Tables",
  "version": "0.1.0",
  "format": "nflow-2",
  "builtin": true,
  "blocks": [
    {
      "type": "lookup1D",
      "label": "1-D Lookup Table",
      "icon": "lookup1D.svg",
      "phases": [
        "ALGEBRAIC"
      ],
      "width": 90,
      "height": 80,
      "inputs": [
        {
          "x": 0,
          "y": 40,
          "side": "left"
        }
      ],
      "outputs": [
        {
          "x": 90,
          "y": 40,
          "side": "right"
        }
      ],
      "defaultParams": {
        "BreakpointsForDimension1": [
          0,
          1,
          2,
          3,
          4
        ],
        "Table": [
          0,
          1,
          4,
          9,
          16
        ],
        "InterpMethod": "Linear point-slope",
        "ExtrapMethod": "Linear"
      },
      "render": {
        "type": "image",
        "src": "exports/lookup1D.svg",
        "svgMode": "element",
        "preserveAspectRatio": "none",
        "x": 0,
        "y": 0,
        "width": 90,
        "height": 80
      }
    },
    {
      "type": "lookup2D",
      "label": "2-D Lookup Table",
      "icon": "lookup2D.svg",
      "phases": [
        "ALGEBRAIC"
      ],
      "width": 90,
      "height": 80,
      "inputs": [
        {
          "x": 0,
          "y": 30,
          "side": "left"
        },
        {
          "x": 0,
          "y": 50,
          "side": "left"
        }
      ],
      "outputs": [
        {
          "x": 90,
          "y": 40,
          "side": "right"
        }
      ],
      "defaultParams": {
        "BreakpointsForDimension1": [
          1,
          2,
          3
        ],
        "BreakpointsForDimension2": [
          1,
          2,
          3
        ],
        "Table": [
          4,
          5,
          6,
          5,
          7,
          8,
          6,
          8,
          10
        ],
        "InterpMethod": "Linear point-slope",
        "ExtrapMethod": "Linear"
      },
      "render": {
        "type": "image",
        "src": "exports/lookup2D.svg",
        "svgMode": "element",
        "preserveAspectRatio": "none",
        "x": 0,
        "y": 0,
        "width": 90,
        "height": 80
      }
    },
    {
      "type": "lookupND",
      "label": "n-D Lookup Table",
      "icon": "lookupND.svg",
      "phases": [
        "ALGEBRAIC"
      ],
      "width": 90,
      "height": 80,
      "inputs": [
        {
          "x": 0,
          "y": 30,
          "side": "left"
        },
        {
          "x": 0,
          "y": 50,
          "side": "left"
        }
      ],
      "outputs": [
        {
          "x": 90,
          "y": 40,
          "side": "right"
        }
      ],
      "defaultParams": {
        "NumberOfTableDimensions": 2,
        "BreakpointsForDimension1": [
          1,
          2,
          3
        ],
        "BreakpointsForDimension2": [
          1,
          2,
          3
        ],
        "Table": [
          4,
          5,
          6,
          5,
          7,
          8,
          6,
          8,
          10
        ],
        "InterpMethod": "Linear point-slope",
        "ExtrapMethod": "Linear"
      },
      "render": {
        "type": "image",
        "src": "exports/lookupND.svg",
        "svgMode": "element",
        "preserveAspectRatio": "none",
        "x": 0,
        "y": 0,
        "width": 90,
        "height": 80
      }
    },
    {
      "type": "directLookup",
      "label": "Direct Lookup Table (n-D)",
      "icon": "directLookup.svg",
      "phases": [
        "ALGEBRAIC"
      ],
      "width": 90,
      "height": 80,
      "inputs": [
        {
          "x": 0,
          "y": 30,
          "side": "left"
        },
        {
          "x": 0,
          "y": 50,
          "side": "left"
        }
      ],
      "outputs": [
        {
          "x": 90,
          "y": 40,
          "side": "right"
        }
      ],
      "defaultParams": {
        "NumberOfTableDimensions": 2,
        "TableDimensions": [
          2,
          3
        ],
        "Table": [
          0,
          1,
          10,
          11,
          20,
          21
        ]
      },
      "render": {
        "type": "image",
        "src": "exports/directLookup.svg",
        "svgMode": "element",
        "preserveAspectRatio": "none",
        "x": 0,
        "y": 0,
        "width": 90,
        "height": 80
      }
    },
    {
      "type": "prelookup",
      "label": "Prelookup",
      "icon": "prelookup.svg",
      "phases": [
        "ALGEBRAIC"
      ],
      "width": 90,
      "height": 80,
      "inputs": [
        {
          "x": 0,
          "y": 40,
          "side": "left"
        }
      ],
      "outputs": [
        {
          "x": 90,
          "y": 30,
          "side": "right"
        },
        {
          "x": 90,
          "y": 50,
          "side": "right"
        }
      ],
      "defaultParams": {
        "BreakpointsForDimension1": [
          0,
          1,
          2,
          3,
          4
        ]
      },
      "render": {
        "type": "image",
        "src": "exports/prelookup.svg",
        "svgMode": "element",
        "preserveAspectRatio": "none",
        "x": 0,
        "y": 0,
        "width": 90,
        "height": 80
      }
    },
    {
      "type": "interpolationPrelookup",
      "label": "Interpolation Using Prelookup",
      "icon": "interpolationPrelookup.svg",
      "phases": [
        "ALGEBRAIC"
      ],
      "width": 90,
      "height": 80,
      "inputs": [
        {
          "x": 0,
          "y": 30,
          "side": "left"
        },
        {
          "x": 0,
          "y": 50,
          "side": "left"
        }
      ],
      "outputs": [
        {
          "x": 90,
          "y": 40,
          "side": "right"
        }
      ],
      "defaultParams": {
        "Table": [
          0,
          1,
          4,
          9,
          16
        ]
      },
      "render": {
        "type": "image",
        "src": "exports/interpolationPrelookup.svg",
        "svgMode": "element",
        "preserveAspectRatio": "none",
        "x": 0,
        "y": 0,
        "width": 90,
        "height": 80
      }
    },
    {
      "type": "lookupDynamic",
      "label": "Lookup Table Dynamic",
      "icon": "lookupDynamic.svg",
      "phases": [
        "ALGEBRAIC"
      ],
      "width": 90,
      "height": 80,
      "inputs": [
        {
          "x": 0,
          "y": 20,
          "side": "left"
        },
        {
          "x": 0,
          "y": 40,
          "side": "left"
        },
        {
          "x": 0,
          "y": 60,
          "side": "left"
        }
      ],
      "outputs": [
        {
          "x": 90,
          "y": 40,
          "side": "right"
        }
      ],
      "defaultParams": {},
      "render": {
        "type": "image",
        "src": "exports/lookupDynamic.svg",
        "svgMode": "element",
        "preserveAspectRatio": "none",
        "x": 0,
        "y": 0,
        "width": 90,
        "height": 80
      }
    }
  ]
}

Runtimemodules/nflow_blocks/src/cpp/lookup/prelookup.cpp

//=============================================================================
// Copyright (c) 2016-present Allan CORNET (Nelson)
//=============================================================================
// This file is part of Nelson.
//=============================================================================
// LICENCE_BLOCK_BEGIN
// SPDX-License-Identifier: LGPL-3.0-or-later
// LICENCE_BLOCK_END
//=============================================================================
// prelookup (Prelookup): computes the interval index k and the fraction f for a
// scalar input over a strictly increasing breakpoint vector, so several tables
// can share one interval search via interpolationPrelookup. The output is the
// 2-element vector [k, f] where bp[k] <= u < bp[k+1] and f = (u - bp[k]) /
// (bp[k+1] - bp[k]). Out-of-range inputs are clipped: below the first
// breakpoint -> [0, 0]; at/above the last -> [N-2, 1]. Feedthrough (ALGEBRAIC),
// real double, no state. Native runtime (the 2-vector output is a follow-up for
// code generation).
//=============================================================================
#include "SimEngineTypes.hpp"
#include "BlockRegistry.hpp"
#include "FieldNames.hpp"
#include "NFlowBlockDescriptor.hpp"
#include "lookup_blocks.hpp"
#include <string>
#include <vector>
//=============================================================================
namespace Nelson {
namespace NFlow {
    //=============================================================================
    namespace {
        int
        preFindInterval(const std::vector<double>& bp, double u)
        {
            const int n = (int)bp.size();
            for (int i = n - 2; i >= 0; --i) {
                if (u >= bp[i]) {
                    return i;
                }
            }
            return 0;
        }

        bool
        preIsStrictlyIncreasing(const std::vector<double>& v)
        {
            for (size_t i = 1; i < v.size(); ++i) {
                if (!(v[i] > v[i - 1])) {
                    return false;
                }
            }
            return true;
        }
    } // namespace
    //=============================================================================
    bool
    handlePrelookup(SimCtx& ctx, const Block& b, Phase phase)
    {
        if (phase != Phase::ALGEBRAIC) {
            return false;
        }
        if (!hasInput(ctx, b.nid, 0)) {
            return false;
        }
        nflow::BlockDescriptor bd(b, ctx.variables);
        const std::vector<double> bp = bd.paramList("BreakpointsForDimension1");
        const double u = getInput(ctx, b.nid, 0, 0.0);
        const int n = (int)bp.size();
        double k = 0.0, f = 0.0;
        if (n >= 2) {
            if (u <= bp[0]) {
                k = 0.0;
                f = 0.0;
            } else if (u >= bp[n - 1]) {
                k = (double)(n - 2);
                f = 1.0;
            } else {
                const int i = preFindInterval(bp, u);
                k = (double)i;
                const double d = bp[i + 1] - bp[i];
                f = (d != 0.0) ? (u - bp[i]) / d : 0.0;
            }
        }
        // Index and fraction leave on two ports, the way the pair is wired: the
        // index on port 0, the fraction on port 1. They used to share one
        // two-wide port, which no other block reads that way.
        setOutput(ctx, b.nid, k);
        if (numOutputs(ctx, b.nid) > 1) {
            double* f1 = outputSlice(ctx, b.nid, 1);
            if (f1 != nullptr) {
                f1[0] = f;
            }
        }
        return false;
    }
    //=============================================================================
    // Scalar input; the index and the fraction leave on their own ports.
    bool
    resolvePrelookupDims(const Block& b, const ValMap& vars, const std::vector<PortSig>&,
        std::vector<PortSig>& outSigs, std::string& err)
    {
        nflow::BlockDescriptor bd(b, vars);
        const std::vector<double> bp = bd.paramList("BreakpointsForDimension1");
        if (bp.size() < 2) {
            err = "prelookup requires at least 2 breakpoints";
            return false;
        }
        if (!preIsStrictlyIncreasing(bp)) {
            err = "prelookup breakpoints must be strictly increasing";
            return false;
        }
        for (size_t i = 0; i < outSigs.size() && i < 2; ++i) {
            outSigs[i].setVector(1);
            outSigs[i].type = SigType::Double;
        }
        return true;
    }
    //=============================================================================
} // namespace NFlow
} // namespace Nelson
//=============================================================================

💡Examples

Prelookup u = 2.5 over [0 1 2 3 4], then interpolate table [0 1 4 9 16] -> 6.5.

d.blocks={ struct('id','c','type','constant','inputs',0,'outputs',1,'params',struct('Value',2.5)), struct('id','pl','type','prelookup','inputs',1,'outputs',1,'params',struct('BreakpointsForDimension1',[0 1 2 3 4])), struct('id','ip','type','interpolationPrelookup','inputs',1,'outputs',1,'params',struct('Table',[0 1 4 9 16])), struct('id','w','type','toWorkspace','inputs',1,'outputs',0,'params',struct('VariableName','y','SaveFormat','Array')) };
d.connections={ struct('from','c','to','pl','fromIndex',0,'toIndex',0), struct('from','pl','to','ip','fromIndex',0,'toIndex',0), struct('from','ip','to','w','fromIndex',0,'toIndex',0) };
d.sampleTime=0.1; d.duration=0.2; d.solver='discrete'; d.variables=struct();
r=jsondecode(__nflow_simulate__(jsonencode(d)));

🔗See Also

interpolationPrelookup lookup1D

🕔Version History

Version	Description
1.0.0	initial version

Edit this page on GitHub