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feat: Interval evaluator for expressions
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‎lib/src/evaluator.dart

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@@ -474,3 +474,127 @@ class RealEvaluator extends ExpressionEvaluator<num> {
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push1(product);
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}
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}
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class IntervalEvaluator extends ExpressionEvaluator<Interval> {
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/// Create a new evaluator with the given context.
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IntervalEvaluator([ContextModel? context])
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: super(EvaluationType.INTERVAL, context ?? ContextModel());
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@override
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void visitNumber(Number literal) {
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if (literal.value is num) {
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push1(Interval(literal.value, literal.value));
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} else if (literal.value is Interval) {
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push1(literal.value);
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} else {
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throw UnsupportedError(
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'Number $literal with type ${literal.value.runtimeType} can not be interpreted as: $type');
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}
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}
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@override
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void visitInterval(IntervalLiteral literal) {
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var (max, min) = pop2();
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// Expect min and max expressions to evaluate to real numbers,
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// i.e. an interval with min == max.
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assert(min.min == min.max);
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assert(max.min == max.max);
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push1(Interval(min.min, max.min));
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}
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@override
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void visitUnaryPlus(UnaryPlus op) {
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// no-op
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}
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@override
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void visitUnaryMinus(UnaryMinus op) {
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var (val,) = pop1();
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push1(-val);
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}
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@override
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void visitPlus(Plus op) {
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var (addend, augend) = pop2();
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push1(augend + addend);
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}
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@override
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void visitMinus(Minus op) {
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var (subtrahend, minuend) = pop2();
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push1(minuend - subtrahend);
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}
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@override
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void visitTimes(Times op) {
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var (multiplicand, multiplier) = pop2();
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push1(multiplier * multiplicand);
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}
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@override
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void visitDivide(Divide op) {
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var (divisor, dividend) = pop2();
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push1(dividend / divisor);
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}
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@override
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void visitModulo(Modulo op) {
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throw UnimplementedError(
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'Evaluate Modulo with type $type not supported yet.');
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}
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@override
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void visitPower(Power op) {
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// Expect base to be interval.
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var (exp, base) = pop2();
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// Expect exponent to be a natural number.
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int exponent = exp.min.toInt();
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num evalMin, evalMax;
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// Distinction of cases depending on oddity of exponent.
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if (exponent.isOdd) {
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// [x, y]^n = [x^n, y^n] for n = odd
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evalMin = math.pow(base.min, exponent);
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evalMax = math.pow(base.max, exponent);
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} else {
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// [x, y]^n = [x^n, y^n] for x >= 0
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if (base.min >= 0) {
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// Positive interval.
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evalMin = math.pow(base.min, exponent);
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evalMax = math.pow(base.max, exponent);
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}
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// [x, y]^n = [y^n, x^n] for y < 0
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if (base.min >= 0) {
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// Positive interval.
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evalMin = math.pow(base.max, exponent);
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evalMax = math.pow(base.min, exponent);
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}
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// [x, y]^n = [0, max(x^n, y^n)] otherwise
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evalMin = 0;
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evalMax =
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math.max(math.pow(base.min, exponent), math.pow(base.min, exponent));
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}
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assert(evalMin <= evalMax);
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push1(Interval(evalMin, evalMax));
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}
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@override
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void visitFunction(MathFunction func) {
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if (func is! Exponential) {
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throw UnimplementedError();
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}
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}
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@override
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void visitExponential(Exponential func) {
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var (val,) = pop1();
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// Special case of a^[x, y] = [a^x, a^y] for a > 1 (with a = e)
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// Expect exponent to be interval.
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push1(Interval(math.exp(val.min), math.exp(val.max)));
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}
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}

‎test/evaluator_interval_test_set.dart

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@@ -0,0 +1,131 @@
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part of 'math_expressions_test.dart';
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class IntervalEvaluatorTests extends TestSet {
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@override
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String get name => 'Interval evaluation';
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@override
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String get tags => 'evaluator';
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@override
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Map<String, Function> get testGroups => {
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// Literals
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'Number': evaluateNumber,
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'Vector': evaluateVector,
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'Interval': evaluateInterval,
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'Variable': evaluateVariable,
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'BoundVariable': evaluateBoundVariable,
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// Operators: generic cases
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'UnaryOperator': evaluateUnaryOperator,
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'BinaryOperator': evaluateBinaryOperator,
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// Default functions
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'Exponential': evaluateExponential,
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};
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final evaluator = IntervalEvaluator();
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final zero = Number(0);
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final one = Number(1);
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final two = Number(2);
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void parameterized(Map<Expression, dynamic> cases,
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{ExpressionEvaluator? evaluator}) {
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evaluator ??= this.evaluator;
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cases.forEach((key, value) {
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if (value is Throws) {
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test('$key -> $value',
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() => expect(() => evaluator!.evaluate(key), value));
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} else {
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test('$key -> $value', () => expect(evaluator!.evaluate(key), value));
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}
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});
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}
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void evaluateNumber() {
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var cases = {
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zero: Interval(0.0, 0.0),
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one: Interval(1.0, 1.0),
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Number(0.5): Interval(0.5, 0.5),
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// max precision 15 digits
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Number(999999999999999): Interval(999999999999999, 999999999999999)
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};
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parameterized(cases);
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}
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void evaluateVector() {
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var cases = {
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Vector([Number(1.0), Number(2.0)]): throwsA(isUnsupportedError),
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};
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parameterized(cases);
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}
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void evaluateInterval() {
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var cases = {IntervalLiteral(Number(1.0), Number(2.0)): Interval(1.0, 2.0)};
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parameterized(cases);
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}
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void evaluateVariable() {
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var cases = <Expression, Interval>{
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Variable('x'): Interval(12, 12),
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Variable('y'): Interval(24, 24),
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Variable('∞'): Interval(double.infinity, double.infinity),
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};
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var evaluator = IntervalEvaluator(ContextModel()
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..bindVariableName('x', Number(12))
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..bindVariableName('y', two * Variable('x'))
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..bindVariableName('∞', Number(double.infinity)));
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parameterized(cases, evaluator: evaluator);
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}
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void evaluateBoundVariable() {
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var cases = <Expression, Interval>{
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BoundVariable(IntervalLiteral(Number(9), Number(9))): Interval(9.0, 9.0)
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};
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parameterized(cases);
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}
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void evaluateUnaryOperator() {
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final num1 = 2.25;
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final num2 = 5.0;
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var interval = IntervalLiteral(Number(num1), Number(num2));
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var cases = {
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UnaryPlus(interval): Interval(num1, num2),
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UnaryMinus(interval): -Interval(num1, num2),
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UnaryMinus(UnaryMinus(interval)): Interval(num1, num2),
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};
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parameterized(cases);
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}
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void evaluateBinaryOperator() {
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final num1 = 2.25;
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final num2 = 5.0;
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final num3 = 199.9999999;
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var int1 = Interval(num1, num2), int2 = Interval(num2, num3);
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var n1 = Number(num1), n2 = Number(num2), n3 = Number(num3);
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var i1 = IntervalLiteral(n1, n2), i2 = IntervalLiteral(n2, n3);
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var cases = {
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i1 + i2: int1 + int2,
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i1 - i2: int1 - int2,
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i1 * i2: int1 * int2,
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i1 / i2: int1 / int2,
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i1 % i2: throwsA(isUnimplementedError),
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i1 ^ i2: Interval(57.6650390625, 3125.0),
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};
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parameterized(cases);
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}
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void evaluateExponential() {
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var cases = {
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// e(0) -> 1
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Exponential(IntervalLiteral(zero, zero)): Interval(1.0, 1.0),
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};
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parameterized(cases);
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}
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}

‎test/math_expressions_test.dart

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@@ -15,6 +15,7 @@ part 'lexer_test_set.dart';
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part 'parser_test_set.dart';
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part 'parser_petit_test_set.dart';
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part 'evaluator_test_set.dart';
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part 'evaluator_interval_test_set.dart';
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/// relative accuracy for floating-point calculations
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const num EPS = 0.00001;
@@ -28,6 +29,7 @@ void main() {
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PetitParserTests(),
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ExpressionTests(),
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RealEvaluatorTests(),
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IntervalEvaluatorTests(),
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];
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TestExecutor.initWith(testSets).runTests();

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