Initial formula solver
This commit is contained in:
Álvaro González
parent
fe666fdcd6
commit
bc38acbff6
3 changed files with 162 additions and 47 deletions
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@ -7,7 +7,7 @@ Calculates the magnitude of the electrostatic force between two point charges.
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Formula: $F = k \dfrac{q_1 q_2}{r^2}$ where $k = 8.9875517923\times10^9\ \mathrm{N\,m^2/C^2}$.
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Inputs: `q1`, `q2` in coulombs; `r` in meters.
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Inputs: $q_1$, $q_2$ in coulombs; $r$ in meters.
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Output: Force `F` in newtons (N).""",
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"input": [
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{"name": "q1", "unit": "coulomb"},
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@ -7,11 +7,6 @@ import 'formula_models.dart';
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import 'error_handler.dart';
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import 'd4rt_bridge.dart';
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/// Exception thrown when formula evaluation fails
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class FormulaEvaluationException implements Exception {
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final String message;
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@ -20,26 +15,30 @@ class FormulaEvaluationException implements Exception {
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const FormulaEvaluationException(this.message, [this.cause]);
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@override
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String toString() => 'FormulaEvaluationException: $message'
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String toString() =>
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'FormulaEvaluationException: $message'
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'${cause != null ? ' (caused by: $cause)' : ''}';
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}
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class MyMath{
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class MyMath {
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static Number myLog(Number x) => Math.log(x);
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static Number myPow(Number b, Number e) => Math.pow(b,e) as Number;
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static Number myPow(Number b, Number e) => Math.pow(b, e) as Number;
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}
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class FormulaResult{
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class FormulaResult {
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const FormulaResult();
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}
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class StringResult extends FormulaResult{
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class StringResult extends FormulaResult {
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final String value;
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const StringResult(this.value);
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}
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class NumberResult extends FormulaResult{
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class NumberResult extends FormulaResult {
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final Number value;
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const NumberResult(this.value);
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}
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@ -48,39 +47,44 @@ class FormulaEvaluator {
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static D4rt createDefaultInterpreter() => D4rt();
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FormulaEvaluator([D4rt? interpreter]) : _interpreter = interpreter ?? createDefaultInterpreter(){
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FormulaEvaluator([D4rt? interpreter])
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: _interpreter = interpreter ?? createDefaultInterpreter() {
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prepareInterpreter(_interpreter);
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}
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static Number _getNumberValueOf(String s){
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static Number _getNumberValueOf(String s) {
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return double.parse(s);
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}
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static void prepareInterpreter(D4rt interpreter){
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static void prepareInterpreter(D4rt interpreter) {
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final myMathDefinition = BridgedClass(
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nativeType: MyMath,
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name: 'MyMath',
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staticMethods: {
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'myPow': (visitor, positionalArgs, namedArgs) {
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final Number base = _getNumberValueOf( positionalArgs[0].toString() );
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final Number exp = _getNumberValueOf( positionalArgs[1].toString() );
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return MyMath.myPow(base,exp);
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final Number base = _getNumberValueOf(positionalArgs[0].toString());
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final Number exp = _getNumberValueOf(positionalArgs[1].toString());
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return MyMath.myPow(base, exp);
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},
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'myLog': (visitor, positionalArgs, namedArgs) {
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final Number x = _getNumberValueOf( positionalArgs[0].toString() );
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final Number x = _getNumberValueOf(positionalArgs[0].toString());
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return MyMath.myLog(x);
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},
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}
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},
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);
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interpreter.registerBridgedClass(myMathDefinition, "package:d4rt_formulas.dart");
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interpreter.registerBridgedClass(
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myMathDefinition,
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"package:d4rt_formulas.dart",
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);
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registerD4rtBridgeBridges(interpreter);
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}
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static FormulaResult evaluateExpression(String code, [D4rt? interpreter]) {
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final d4rtInterpreter = interpreter ?? createDefaultInterpreter();
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prepareInterpreter(d4rtInterpreter);
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final d4rtCode = """
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final d4rtCode =
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"""
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$preamble
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main()
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{
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@ -90,7 +94,7 @@ class FormulaEvaluator {
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}""";
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print("evaluateExpression:\n$d4rtCode");
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final result = d4rtInterpreter.execute(source: d4rtCode);
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switch ( result ){
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switch (result) {
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case int value:
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return NumberResult(value.toDouble());
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case Number value:
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@ -98,7 +102,9 @@ class FormulaEvaluator {
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case String value:
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return StringResult(value);
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default:
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throw FormulaEvaluationException( "Unexpected result type: ${result.runtimeType} -- $result" );
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throw FormulaEvaluationException(
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"Unexpected result type: ${result.runtimeType} -- $result",
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);
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}
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}
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@ -108,13 +114,12 @@ class FormulaEvaluator {
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try {
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final result = _interpreter.execute(source: completeSource);
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return result;
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}
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catch (e, stack) {
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} catch (e, stack) {
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// SPECIAL CASE: If the error message starts with signalMagicString, treat it as a signal message and return it instead of throwing an exception
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// SEE signal() function in the generated d4rt code above for how this is used
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print( "#######################");
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if(e.toString().contains(signalMagicString)){
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print( "***********************");
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print("#######################");
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if (e.toString().contains(signalMagicString)) {
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print("***********************");
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final signalMessage = e.toString().split(signalMagicString).last.trim();
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return signalMessage;
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}
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@ -151,7 +156,9 @@ class FormulaEvaluator {
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if (inputValue != null) {
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// Convert input value to string for comparison since allowed values are stored as strings
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final inputValueAsString = inputValue.toString();
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final containsValue = values.any((allowedValue) => allowedValue.toString() == inputValueAsString);
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final containsValue = values.any(
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(allowedValue) => allowedValue.toString() == inputValueAsString,
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);
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if (!containsValue) {
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throw FormulaEvaluationException(
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@ -164,15 +171,14 @@ class FormulaEvaluator {
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}
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}
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List<String> getInputVariableOrder(Formula formula) {
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return formula.inputVarNames()..sort();
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}
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static final String signalMagicString = "###";
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static final String preamble = """
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static final String preamble =
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"""
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import 'dart:math';
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import "package:d4rt_formulas.dart";
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import "package:formulas/runtime_bridge.dart";
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@ -181,18 +187,23 @@ class FormulaEvaluator {
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""";
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static const reservedVariableNames = { "variableValues", "indexOf", "variableAllowedValues"} ;
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static const reservedVariableNames = {
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"variableValues",
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"indexOf",
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"variableAllowedValues",
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};
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String _buildCompleteSource(Formula formula, Map<String, dynamic> inputValues) {
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String _buildCompleteSource(
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Formula formula,
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Map<String, dynamic> inputValues,
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) {
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final buffer = StringBuffer();
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buffer.writeln("""
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$preamble
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main()
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{
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"""
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);
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""");
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for (final entry in inputValues.entries) {
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final varName = entry.key;
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@ -241,13 +252,17 @@ class FormulaEvaluator {
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for (final vs in formula.input) {
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final values = vs.values;
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if (values != null && values.isNotEmpty) {
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variableValuesMap[vs.name] = values.map((v) => v.toString()).toList(growable: false);
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variableValuesMap[vs.name] = values
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.map((v) => v.toString())
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.toList(growable: false);
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}
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}
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// Explicitly include the output VariableSpec if it has allowed values
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final outValues = formula.output.values;
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if (outValues != null && outValues.isNotEmpty) {
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variableValuesMap[formula.output.name] = outValues.map((v) => v.toString()).toList(growable: false);
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variableValuesMap[formula.output.name] = outValues
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.map((v) => v.toString())
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.toList(growable: false);
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}
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// Write the variableValues map into the generated source without escaping names/values
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@ -276,6 +291,80 @@ class FormulaEvaluator {
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}
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""");
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return buffer.toString();
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}
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}
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return buffer.toString();
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}
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}
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class NoSolutionException implements Exception {
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final String message;
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const NoSolutionException(this.message);
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@override
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String toString() => 'NoSolutionException: $message';
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}
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Number functionSolver(
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Number Function(Number) f, {
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Number hint = 0,
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Number step = 10,
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Number maxDelta = 0.01,
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int maxTries = 100,
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}) {
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Number sign(Number x) => switch (x) {
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> 0 => 1,
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< 0 => -1,
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_ => 0,
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};
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Number binarySearch(Number low, Number high) {
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var yLow = f(low);
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var yHigh = f(high);
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assert(sign(yLow) != sign(yHigh));
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int count = 0;
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while ((high - low).abs() > maxDelta) {
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count += 1;
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if (count > maxTries) {
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throw NoSolutionException("Failed to find a root after $maxTries tries.");
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}
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var mid = (low + high) / 2;
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var yMid = f(mid);
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if (sign(yMid) == sign(f(low))) {
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low = mid;
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yLow = yMid;
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} else {
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high = mid;
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yHigh = yMid;
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}
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}
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return (low + high) / 2;
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}
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List<Number> searchApproximately(Number x1, Number x2) {
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var y1 = f(x1);
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var y2 = f(x2);
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int count = 0;
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while (sign(y1) == sign(y2)) {
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count += 1;
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if (count > maxTries) {
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throw NoSolutionException("Failed to find a root after $maxTries tries.");
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}
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if (y1.abs() < y2.abs()) {
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x2 = x1;
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x1 = x1 - step;
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y2 = y1;
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y1 = f(x1);
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} else {
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x1 = x2;
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x2 = x2 + step;
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y1 = y2;
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y2 = f(x2);
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}
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}
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return [x1, x2];
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}
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var approx = searchApproximately(hint, hint + step);
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return binarySearch(approx[0], approx[1]);
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}
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26
test/formula_solver_test.dart
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26
test/formula_solver_test.dart
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@ -0,0 +1,26 @@
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import 'package:d4rt_formulas/formula_evaluator.dart';
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import 'package:d4rt_formulas/formula_models.dart';
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import 'package:flutter_test/flutter_test.dart';
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void main() {
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test("Solve x^2", () {
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Number f(Number x) => x*x;
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var root = functionSolver(f, hint: 10, step: 1);
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expect(root, closeTo(0, 0.1));
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});
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test("Solve x^2 + 1", () {
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Number f(Number x) => x*x+1;
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expect(()=> functionSolver(f, hint: 10, step: 1), throwsA(isA<NoSolutionException>()));
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});
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test("Solve (x-2)(x-10", () {
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Number f(Number x) => (x-2)*(x-10);
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expect( functionSolver(f, hint: 10, step: 1), closeTo(10, 0.1));
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});
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}
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