1049 lines
42 KiB
TypeScript
1049 lines
42 KiB
TypeScript
import { createResource, Resource } from "features/resources/resource";
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import Formula, {
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calculateCost,
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calculateMaxAffordable,
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unrefFormulaSource
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} from "game/formulas/formulas";
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import type { GenericFormula, InvertibleFormula } from "game/formulas/types";
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import Decimal, { DecimalSource } from "util/bignum";
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import { beforeAll, describe, expect, test } from "vitest";
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import { ref } from "vue";
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import "../utils";
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type FormulaFunctions = keyof GenericFormula & keyof typeof Formula & keyof typeof Decimal;
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const testValues = [-1, "0", Decimal.dOne] as const;
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const invertibleZeroParamFunctionNames = [
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"neg",
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"recip",
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"log10",
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"log2",
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"ln",
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"pow10",
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"exp",
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"sqr",
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"sqrt",
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"cube",
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"cbrt",
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"lambertw",
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"ssqrt",
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"sin",
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"cos",
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"tan",
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"asin",
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"acos",
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"atan",
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"sinh",
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"cosh",
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"tanh",
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"asinh",
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"acosh",
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"atanh",
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"slog",
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"tetrate",
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"iteratedexp"
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] as const;
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const nonInvertibleZeroParamFunctionNames = [
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"abs",
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"sign",
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"round",
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"floor",
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"ceil",
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"trunc",
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"pLog10",
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"absLog10",
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"factorial",
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"gamma",
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"lngamma"
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] as const;
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const integrableZeroParamFunctionNames = [
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"neg",
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"recip",
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"log10",
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"log2",
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"ln",
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"pow10",
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"exp",
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"sqr",
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"sqrt",
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"cube",
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"cbrt",
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"sin",
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"cos",
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"tan",
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"asin",
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"acos",
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"atan",
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"sinh",
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"cosh",
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"tanh",
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"asinh",
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"acosh",
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"atanh"
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] as const;
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const nonIntegrableZeroParamFunctionNames = [
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...nonInvertibleZeroParamFunctionNames,
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"lambertw",
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"ssqrt"
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] as const;
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const invertibleIntegralZeroPramFunctionNames = [
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"recip",
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"log10",
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"log2",
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"ln",
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"pow10",
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"sqr",
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"sqrt",
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"cube",
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"cbrt"
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] as const;
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const nonInvertibleIntegralZeroPramFunctionNames = [
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...nonIntegrableZeroParamFunctionNames,
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"neg",
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"exp",
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"sin",
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"cos",
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"tan",
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"asin",
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"acos",
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"atan",
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"sinh",
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"cosh",
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"tanh",
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"asinh",
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"acosh",
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"atanh"
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] as const;
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const invertibleOneParamFunctionNames = [
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"add",
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"sub",
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"mul",
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"div",
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"log",
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"pow",
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"root",
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"layeradd"
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] as const;
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const nonInvertibleOneParamFunctionNames = ["layeradd10"] as const;
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const integrableOneParamFunctionNames = ["add", "sub", "mul", "div", "log", "pow", "root"] as const;
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const nonIntegrableOneParamFunctionNames = [...nonInvertibleOneParamFunctionNames, "slog"] as const;
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const invertibleIntegralOneParamFunctionNames = integrableOneParamFunctionNames;
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const nonInvertibleIntegralOneParamFunctionNames = nonIntegrableOneParamFunctionNames;
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const nonInvertibleTwoParamFunctionNames = ["iteratedlog", "pentate"] as const;
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const nonIntegrableTwoParamFunctionNames = nonInvertibleTwoParamFunctionNames;
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const nonInvertibleIntegralTwoParamFunctionNames = nonIntegrableTwoParamFunctionNames;
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describe("Formula Equality Checking", () => {
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describe("Equality Checks", () => {
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test("Equals", () => expect(Formula.add(1, 1).equals(Formula.add(1, 1))).toBe(true));
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test("Not Equals due to inputs", () =>
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expect(Formula.add(1, 1).equals(Formula.add(1, 0))).toBe(false));
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test("Not Equals due to functions", () =>
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expect(Formula.add(1, 1).equals(Formula.sub(1, 1))).toBe(false));
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test("Not Equals due to hasVariable", () =>
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expect(Formula.constant(1).equals(Formula.variable(1))).toBe(false));
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});
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describe("Formula aliases", () => {
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function testAliases<T extends FormulaFunctions>(
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aliases: T[],
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args: Parameters<typeof Formula[T]>
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) {
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describe(aliases[0], () => {
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let formula: GenericFormula;
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beforeAll(() => {
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// eslint-disable-next-line @typescript-eslint/ban-ts-comment
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// @ts-ignore
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formula = Formula[aliases[0]](...args);
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});
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aliases.slice(1).forEach(alias => {
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// eslint-disable-next-line @typescript-eslint/ban-ts-comment
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// @ts-ignore
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test(alias, () => expect(Formula[alias](...args).equals(formula)).toBe(true));
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});
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});
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}
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testAliases(["neg", "negate", "negated"], [1]);
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testAliases(["recip", "reciprocal", "reciprocate"], [1]);
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testAliases(["sign", "sgn"], [1]);
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testAliases(["add", "plus"], [1, 1]);
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testAliases(["sub", "subtract", "minus"], [1, 1]);
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testAliases(["mul", "multiply", "times"], [1, 1]);
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testAliases(["div", "divide"], [1, 1]);
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testAliases(["log", "logarithm"], [1, 1]);
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});
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describe("Instance vs Static methods", () => {
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let formula: GenericFormula;
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beforeAll(() => {
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formula = Formula.constant(10);
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});
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[...invertibleZeroParamFunctionNames, ...nonInvertibleZeroParamFunctionNames].forEach(
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name => {
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test(name, () => {
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const instanceFormula = formula[name]();
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const staticFormula = Formula[name](formula);
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expect(instanceFormula.equals(staticFormula)).toBe(true);
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});
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}
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);
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[...invertibleOneParamFunctionNames, ...nonInvertibleOneParamFunctionNames].forEach(
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name => {
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test(name, () => {
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const instanceFormula = formula[name](10);
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const staticFormula = Formula[name](formula, 10);
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expect(instanceFormula.equals(staticFormula)).toBe(true);
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});
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}
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);
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});
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});
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describe("Creating Formulas", () => {
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describe("Constants", () => {
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function testConstant(
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desc: string,
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formulaFunc: () => InvertibleFormula,
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expectedValue: DecimalSource = 10
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) {
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describe(desc, () => {
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let formula: GenericFormula;
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beforeAll(() => {
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formula = formulaFunc();
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});
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test("Is not invertible", () => expect(formula.isInvertible()).toBe(false));
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test("Is not integrable", () => expect(formula.isIntegrable()).toBe(false));
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test("Integral is not invertible", () =>
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expect(formula.isIntegralInvertible()).toBe(false));
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test("Is not marked as having a variable", () =>
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expect(formula.hasVariable()).toBe(false));
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test("Evaluates correctly", () =>
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expect(formula.evaluate()).compare_tolerance(expectedValue));
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test("Invert throws", () => expect(() => formula.invert(25)).toThrow());
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test("Integrate throws", () => expect(() => formula.evaluateIntegral()).toThrow());
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test("Invert integral throws", () =>
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expect(() => formula.invertIntegral(25)).toThrow());
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});
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}
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testConstant("number", () => Formula.constant(10));
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testConstant("string", () => Formula.constant("10"));
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testConstant("decimal", () => Formula.constant(new Decimal("1e400")), "1e400");
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testConstant("ref", () => Formula.constant(ref(10)));
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});
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function checkFormula<T extends FormulaFunctions>(
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functionName: T,
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args: Readonly<Parameters<typeof Formula[T]>>
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) {
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let formula: GenericFormula;
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beforeAll(() => {
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// eslint-disable-next-line @typescript-eslint/ban-ts-comment
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// @ts-ignore
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formula = Formula[functionName](...args);
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});
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// None of these formulas have variables, so they should all behave the same
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test("Is not marked as having a variable", () => expect(formula.hasVariable()).toBe(false));
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test("Is not invertible", () => expect(formula.isInvertible()).toBe(false));
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test(`Formula throws if trying to invert`, () =>
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expect(() => formula.invert(10)).toThrow());
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test("Is not integrable", () => expect(formula.isIntegrable()).toBe(false));
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test("Has a non-invertible integral", () =>
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expect(formula.isIntegralInvertible()).toBe(false));
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}
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// Utility function that will test all the different
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// It's a lot of tests, but I'd rather be exhaustive
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function testFormulaCall<T extends FormulaFunctions>(
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functionName: T,
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args: Readonly<Parameters<typeof Formula[T]>>
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) {
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let testName = functionName + "(";
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for (let i = 0; i < args.length; i++) {
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if (i !== 0) {
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testName += ", ";
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}
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testName += args[i];
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}
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testName += ") evaluates correctly";
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test(testName, () => {
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// eslint-disable-next-line @typescript-eslint/ban-ts-comment
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// @ts-ignore
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const formula = Formula[functionName](...args);
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try {
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const expectedEvaluation = Decimal[functionName](
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// eslint-disable-next-line @typescript-eslint/ban-ts-comment
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// @ts-ignore
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...args.map(i => unrefFormulaSource(i))
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);
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if (expectedEvaluation != null) {
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expect(formula.evaluate()).compare_tolerance(expectedEvaluation);
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}
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} catch {
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// If this is an invalid Decimal operation, then ignore this test case
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}
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});
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}
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describe("0-param", () => {
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[...invertibleZeroParamFunctionNames, ...nonInvertibleZeroParamFunctionNames].forEach(
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names =>
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describe(names, () => {
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checkFormula(names, [0] as const);
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testValues.forEach(i => testFormulaCall(names, [i] as const));
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})
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);
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});
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describe("1-param", () => {
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(
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[
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...invertibleOneParamFunctionNames,
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...nonInvertibleOneParamFunctionNames,
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"max",
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"min",
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"maxabs",
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"minabs",
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"clampMin",
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"clampMax"
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] as const
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).forEach(names =>
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describe(names, () => {
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checkFormula(names, [0, 0] as const);
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testValues.forEach(i =>
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testValues.forEach(j => testFormulaCall(names, [i, j] as const))
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);
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})
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);
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});
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describe("2-param", () => {
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([...nonInvertibleTwoParamFunctionNames, "clamp"] as const).forEach(names =>
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describe(names, () => {
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checkFormula(names, [0, 0, 0] as const);
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testValues.forEach(i =>
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testValues.forEach(j =>
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testValues.forEach(k => testFormulaCall(names, [i, j, k] as const))
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)
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);
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})
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);
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});
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});
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describe("Variables", () => {
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let variable: GenericFormula;
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let constant: GenericFormula;
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beforeAll(() => {
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variable = Formula.variable(10);
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constant = Formula.constant(10);
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});
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test("Created variable is marked as a variable", () =>
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expect(variable.hasVariable()).toBe(true));
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test("evaluate() returns variable's value", () =>
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expect(variable.evaluate()).compare_tolerance(10));
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test("evaluate(variable) overrides variable value", () =>
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expect(variable.add(10).evaluate(20)).compare_tolerance(30));
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test("Nested variable is marked as having a variable", () =>
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expect(variable.add(10).div(3).pow(2).hasVariable()).toBe(true));
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test("Nested non-variable is marked as not having a variable", () =>
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expect(constant.add(10).div(3).pow(2).hasVariable()).toBe(false));
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});
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describe("Inverting", () => {
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let variable: GenericFormula;
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let constant: GenericFormula;
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beforeAll(() => {
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variable = Formula.variable(10);
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constant = Formula.constant(10);
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});
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test("variable.invert() is pass-through", () =>
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expect(variable.invert(100)).compare_tolerance(100));
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describe("Invertible Formulas correctly calculate when they contain a variable", () => {
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function checkFormula(formula: GenericFormula, expectedBool = true) {
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expect(formula.isInvertible()).toBe(expectedBool);
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expect(formula.hasVariable()).toBe(expectedBool);
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}
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invertibleZeroParamFunctionNames.forEach(name => {
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describe(name, () => {
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test(`${name}(var) is marked as invertible and having a variable`, () =>
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checkFormula(Formula[name](variable)));
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});
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});
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invertibleOneParamFunctionNames.forEach(name => {
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describe(name, () => {
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test(`${name}(var, const) is marked as invertible and having a variable`, () =>
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checkFormula(Formula[name](variable, constant)));
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test(`${name}(const, var) is marked as invertible and having a variable`, () =>
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checkFormula(Formula[name](constant, variable)));
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test(`${name}(var, var) is marked as not invertible and not having a variable`, () =>
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checkFormula(Formula[name](variable, variable), false));
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});
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});
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});
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describe("Non-invertible formulas marked as such", () => {
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function checkFormula(formula: GenericFormula) {
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expect(formula.isInvertible()).toBe(false);
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expect(formula.isIntegrable()).toBe(false);
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expect(formula.isIntegralInvertible()).toBe(false);
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}
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nonInvertibleZeroParamFunctionNames.forEach(name => {
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describe(name, () => {
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test(`${name}(var) is marked as not invertible`, () =>
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checkFormula(Formula[name](variable)));
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});
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});
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nonInvertibleOneParamFunctionNames.forEach(name => {
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describe(name, () => {
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test(`${name}(var, const) is marked as not invertible`, () =>
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checkFormula(Formula[name](variable, constant)));
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test(`${name}(const, var) is marked as not invertible`, () =>
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checkFormula(Formula[name](constant, variable)));
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test(`${name}(var, var) is marked as not invertible`, () =>
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checkFormula(Formula[name](variable, variable)));
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});
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});
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nonInvertibleTwoParamFunctionNames.forEach(name => {
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describe(name, () => {
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test(`${name}(var, const, const) is marked as not invertible`, () =>
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checkFormula(Formula[name](variable, constant, constant)));
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test(`${name}(const, var, const) is marked as not invertible`, () =>
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checkFormula(Formula[name](constant, variable, constant)));
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test(`${name}(const, const, var) is marked as not invertible`, () =>
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checkFormula(Formula[name](constant, constant, variable)));
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test(`${name}(var, var, const) is marked as not invertible`, () =>
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checkFormula(Formula[name](variable, variable, constant)));
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test(`${name}(var, const, var) is marked as not invertible`, () =>
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checkFormula(Formula[name](variable, constant, variable)));
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test(`${name}(const, var, var) is marked as not invertible`, () =>
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checkFormula(Formula[name](constant, variable, variable)));
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test(`${name}(var, var, var) is marked as not invertible`, () =>
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checkFormula(Formula[name](variable, variable, variable)));
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});
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});
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});
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|
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describe("Inverting calculates the value of the variable", () => {
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let variable: GenericFormula;
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let constant: GenericFormula;
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beforeAll(() => {
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variable = Formula.variable(2);
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constant = Formula.constant(3);
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});
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invertibleOneParamFunctionNames.forEach(name =>
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describe(name, () => {
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test(`${name}(var, const).invert()`, () => {
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const formula = Formula[name](variable, constant);
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const result = formula.evaluate();
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expect(formula.invert(result)).compare_tolerance(2);
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});
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if (name !== "layeradd") {
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test(`${name}(const, var).invert()`, () => {
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const formula = Formula[name](constant, variable);
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const result = formula.evaluate();
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expect(formula.invert(result)).compare_tolerance(2);
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});
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}
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})
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);
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});
|
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describe("Inverting pass-throughs", () => {
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test("max", () => expect(Formula.max(variable, constant).invert(10)).compare_tolerance(10));
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test("min", () => expect(Formula.min(variable, constant).invert(10)).compare_tolerance(10));
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test("minabs", () =>
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expect(Formula.minabs(variable, constant).invert(10)).compare_tolerance(10));
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|
test("maxabs", () =>
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expect(Formula.maxabs(variable, constant).invert(10)).compare_tolerance(10));
|
|
test("clampMax", () =>
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expect(Formula.clampMax(variable, constant).invert(10)).compare_tolerance(10));
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test("clampMin", () =>
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expect(Formula.clampMin(variable, constant).invert(10)).compare_tolerance(10));
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test("clamp", () =>
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expect(Formula.clamp(variable, constant, constant).invert(10)).compare_tolerance(10));
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});
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test("Inverting nested formulas", () => {
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const formula = Formula.add(variable, constant).times(constant);
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expect(formula.invert(100)).compare_tolerance(0);
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});
|
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|
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test("Inverting with non-invertible sections", () => {
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const formula = Formula.add(variable, constant.ceil());
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expect(formula.isInvertible()).toBe(true);
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expect(formula.invert(10)).compare_tolerance(0);
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});
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});
|
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|
|
describe("Integrating", () => {
|
|
let variable: GenericFormula;
|
|
let constant: GenericFormula;
|
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beforeAll(() => {
|
|
variable = Formula.variable(ref(10));
|
|
constant = Formula.constant(10);
|
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});
|
|
|
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test("evaluateIntegral() returns variable's value", () =>
|
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expect(variable.evaluate()).compare_tolerance(10));
|
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test("evaluateIntegral(variable) overrides variable value", () =>
|
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expect(variable.add(10).evaluateIntegral(20)).compare_tolerance(400));
|
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|
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describe("Integrable functions marked as such", () => {
|
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function checkFormula(formula: GenericFormula) {
|
|
expect(formula.isIntegrable()).toBe(true);
|
|
expect(() => formula.evaluateIntegral()).to.not.throw();
|
|
}
|
|
integrableZeroParamFunctionNames.forEach(name => {
|
|
describe(name, () => {
|
|
test(`${name}(var) is marked as integrable`, () =>
|
|
checkFormula(Formula[name](variable)));
|
|
});
|
|
});
|
|
integrableOneParamFunctionNames.forEach(name => {
|
|
describe(name, () => {
|
|
test(`${name}(var, const) is marked as integrable`, () =>
|
|
checkFormula(Formula[name](variable, constant)));
|
|
if (name !== "log" && name !== "root") {
|
|
test(`${name}(const, var) is marked as integrable`, () =>
|
|
checkFormula(Formula[name](constant, variable)));
|
|
}
|
|
test(`${name}(var, var) is marked as not integrable`, () =>
|
|
expect(Formula[name](variable, variable).isIntegrable()).toBe(false));
|
|
});
|
|
});
|
|
});
|
|
|
|
describe("Non-Integrable functions marked as such", () => {
|
|
function checkFormula(formula: GenericFormula) {
|
|
expect(formula.isIntegrable()).toBe(false);
|
|
}
|
|
nonIntegrableZeroParamFunctionNames.forEach(name => {
|
|
describe(name, () => {
|
|
test(`${name}(var) is marked as not integrable`, () =>
|
|
checkFormula(Formula[name](variable)));
|
|
});
|
|
});
|
|
nonIntegrableOneParamFunctionNames.forEach(name => {
|
|
describe(name, () => {
|
|
test(`${name}(var, const) is marked as not integrable`, () =>
|
|
checkFormula(Formula[name](variable, constant)));
|
|
test(`${name}(const, var) is marked as not integrable`, () =>
|
|
checkFormula(Formula[name](constant, variable)));
|
|
test(`${name}(var, var) is marked as not integrable`, () =>
|
|
checkFormula(Formula[name](variable, variable)));
|
|
});
|
|
});
|
|
nonIntegrableTwoParamFunctionNames.forEach(name => {
|
|
describe(name, () => {
|
|
test(`${name}(var, const, const) is marked as not integrable`, () =>
|
|
checkFormula(Formula[name](variable, constant, constant)));
|
|
test(`${name}(const, var, const) is marked as not integrable`, () =>
|
|
checkFormula(Formula[name](constant, variable, constant)));
|
|
test(`${name}(const, const, var) is marked as not integrable`, () =>
|
|
checkFormula(Formula[name](constant, constant, variable)));
|
|
test(`${name}(var, var, const) is marked as not integrable`, () =>
|
|
checkFormula(Formula[name](variable, variable, constant)));
|
|
test(`${name}(var, const, var) is marked as not integrable`, () =>
|
|
checkFormula(Formula[name](variable, constant, variable)));
|
|
test(`${name}(const, var, var) is marked as not integrable`, () =>
|
|
checkFormula(Formula[name](constant, variable, variable)));
|
|
test(`${name}(var, var, var) is marked as not integrable`, () =>
|
|
checkFormula(Formula[name](variable, variable, variable)));
|
|
});
|
|
});
|
|
});
|
|
|
|
// TODO I think these tests will require writing at least one known example for every function
|
|
describe.todo("Integrable formulas integrate correctly");
|
|
|
|
test("Integrating nested formulas", () => {
|
|
const formula = Formula.add(variable, constant).times(constant).pow(2).times(30);
|
|
const actualCost = new Array(10)
|
|
.fill(null)
|
|
.reduce((acc, _, i) => acc.add(formula.evaluate(i)), new Decimal(0));
|
|
const calculatedCost = Decimal.add(
|
|
formula.evaluateIntegral(),
|
|
formula.calculateConstantOfIntegration()
|
|
);
|
|
// Check if the calculated cost is within 10% of the actual cost,
|
|
// because this is an approximation
|
|
expect(
|
|
Decimal.sub(actualCost, calculatedCost).abs().div(actualCost).toNumber()
|
|
).toBeLessThan(0.1);
|
|
});
|
|
|
|
test("Integrating nested complex formulas", () => {
|
|
const formula = Formula.pow(1.05, variable).times(100).pow(0.5);
|
|
expect(() => formula.evaluateIntegral()).toThrow();
|
|
});
|
|
});
|
|
|
|
describe("Inverting integrals", () => {
|
|
let variable: GenericFormula;
|
|
let constant: GenericFormula;
|
|
beforeAll(() => {
|
|
variable = Formula.variable(10);
|
|
constant = Formula.constant(10);
|
|
});
|
|
|
|
test("variable.invertIntegral() is pass-through", () =>
|
|
expect(variable.invertIntegral(20)).compare_tolerance(20));
|
|
|
|
describe("Invertible Integral functions marked as such", () => {
|
|
function checkFormula(formula: GenericFormula) {
|
|
expect(formula.isIntegralInvertible()).toBe(true);
|
|
expect(() => formula.invertIntegral(10)).to.not.throw();
|
|
}
|
|
invertibleIntegralZeroPramFunctionNames.forEach(name => {
|
|
describe(name, () => {
|
|
test(`${name}(var) is marked as having an invertible integral`, () =>
|
|
checkFormula(Formula[name](variable)));
|
|
});
|
|
});
|
|
invertibleIntegralOneParamFunctionNames.forEach(name => {
|
|
describe(name, () => {
|
|
test(`${name}(var, const) is marked as having an invertible integral`, () =>
|
|
checkFormula(Formula[name](variable, constant)));
|
|
if (name !== "log" && name !== "root") {
|
|
test(`${name}(const, var) is marked as having an invertible integral`, () =>
|
|
checkFormula(Formula[name](constant, variable)));
|
|
}
|
|
test(`${name}(var, var) is marked as not having an invertible integral`, () => {
|
|
const formula = Formula[name](variable, variable);
|
|
expect(formula.isIntegralInvertible()).toBe(false);
|
|
expect(() => formula.invertIntegral(10)).to.throw();
|
|
});
|
|
});
|
|
});
|
|
});
|
|
|
|
describe("Non-Invertible integral functions marked as such", () => {
|
|
function checkFormula(formula: GenericFormula) {
|
|
expect(formula.isIntegralInvertible()).toBe(false);
|
|
}
|
|
nonInvertibleIntegralZeroPramFunctionNames.forEach(name => {
|
|
describe(name, () => {
|
|
test(`${name}(var) is marked as not having an invertible integral`, () =>
|
|
checkFormula(Formula[name](variable)));
|
|
});
|
|
});
|
|
nonInvertibleIntegralOneParamFunctionNames.forEach(name => {
|
|
describe(name, () => {
|
|
test(`${name}(var, const) is marked as not having an invertible integral`, () =>
|
|
checkFormula(Formula[name](variable, constant)));
|
|
test(`${name}(const, var) is marked as not having an invertible integral`, () =>
|
|
checkFormula(Formula[name](constant, variable)));
|
|
test(`${name}(var, var) is marked as not having an invertible integral`, () =>
|
|
checkFormula(Formula[name](variable, variable)));
|
|
});
|
|
});
|
|
nonInvertibleIntegralTwoParamFunctionNames.forEach(name => {
|
|
describe(name, () => {
|
|
test(`${name}(var, const, const) is marked as not having an invertible integral`, () =>
|
|
checkFormula(Formula[name](variable, constant, constant)));
|
|
test(`${name}(const, var, const) is marked as not having an invertible integral`, () =>
|
|
checkFormula(Formula[name](constant, variable, constant)));
|
|
test(`${name}(const, const, var) is marked as not having an invertible integral`, () =>
|
|
checkFormula(Formula[name](constant, constant, variable)));
|
|
test(`${name}(var, var, const) is marked as not having an invertible integral`, () =>
|
|
checkFormula(Formula[name](variable, variable, constant)));
|
|
test(`${name}(var, const, var) is marked as not having an invertible integral`, () =>
|
|
checkFormula(Formula[name](variable, constant, variable)));
|
|
test(`${name}(const, var, var) is marked as not having an invertible integral`, () =>
|
|
checkFormula(Formula[name](constant, variable, variable)));
|
|
test(`${name}(var, var, var) is marked as not having an invertible integral`, () =>
|
|
checkFormula(Formula[name](variable, variable, variable)));
|
|
});
|
|
});
|
|
});
|
|
|
|
// TODO I think these tests will require writing at least one known example for every function
|
|
describe.todo("Invertible Integral formulas invert correctly");
|
|
|
|
test("Inverting integral of nested formulas", () => {
|
|
const formula = Formula.add(variable, constant).times(constant).pow(2).times(30);
|
|
expect(formula.invertIntegral(7000000)).compare_tolerance(10);
|
|
});
|
|
|
|
test("Inverting integral of nested complex formulas", () => {
|
|
const formula = Formula.pow(1.05, variable).times(100).pow(0.5);
|
|
expect(() => formula.invertIntegral(100)).toThrow();
|
|
});
|
|
|
|
describe("Inverting integral pass-throughs", () => {
|
|
test("max", () =>
|
|
expect(Formula.max(variable, constant).invertIntegral(10)).compare_tolerance(10));
|
|
test("min", () =>
|
|
expect(Formula.min(variable, constant).invertIntegral(10)).compare_tolerance(10));
|
|
test("minabs", () =>
|
|
expect(Formula.minabs(variable, constant).invertIntegral(10)).compare_tolerance(10));
|
|
test("maxabs", () =>
|
|
expect(Formula.maxabs(variable, constant).invertIntegral(10)).compare_tolerance(10));
|
|
test("clampMax", () =>
|
|
expect(Formula.clampMax(variable, constant).invertIntegral(10)).compare_tolerance(10));
|
|
test("clampMin", () =>
|
|
expect(Formula.clampMin(variable, constant).invertIntegral(10)).compare_tolerance(10));
|
|
test("clamp", () =>
|
|
expect(
|
|
Formula.clamp(variable, constant, constant).invertIntegral(10)
|
|
).compare_tolerance(10));
|
|
});
|
|
});
|
|
|
|
describe("Step-wise", () => {
|
|
let variable: GenericFormula;
|
|
let constant: GenericFormula;
|
|
beforeAll(() => {
|
|
variable = Formula.variable(10);
|
|
constant = Formula.constant(10);
|
|
});
|
|
|
|
test("Formula without variable is marked as such", () => {
|
|
expect(Formula.step(constant, 10, value => Formula.sqrt(value)).isInvertible()).toBe(false);
|
|
expect(Formula.step(constant, 10, value => Formula.sqrt(value)).hasVariable()).toBe(false);
|
|
});
|
|
|
|
test("Formula with variable is marked as such", () => {
|
|
expect(Formula.step(variable, 10, value => Formula.sqrt(value)).isInvertible()).toBe(true);
|
|
expect(Formula.step(variable, 10, value => Formula.sqrt(value)).hasVariable()).toBe(true);
|
|
});
|
|
|
|
test("Non-invertible formula modifier marks formula as such", () => {
|
|
expect(Formula.step(constant, 10, value => Formula.abs(value)).isInvertible()).toBe(false);
|
|
expect(Formula.step(constant, 10, value => Formula.abs(value)).hasVariable()).toBe(false);
|
|
});
|
|
|
|
test("Formula never marked integrable", () => {
|
|
expect(Formula.step(constant, 10, value => Formula.add(value, 10)).isIntegrable()).toBe(
|
|
false
|
|
);
|
|
expect(() =>
|
|
Formula.step(constant, 10, value => Formula.add(value, 10)).evaluateIntegral()
|
|
).toThrow();
|
|
});
|
|
|
|
test("Formula never marked as having an invertible integral", () => {
|
|
expect(
|
|
Formula.step(constant, 10, value => Formula.add(value, 10)).isIntegralInvertible()
|
|
).toBe(false);
|
|
expect(() =>
|
|
Formula.step(constant, 10, value => Formula.add(value, 10)).invertIntegral(10)
|
|
).toThrow();
|
|
});
|
|
|
|
test("Formula modifiers with variables mark formula as non-invertible", () => {
|
|
expect(
|
|
Formula.step(constant, 10, value => Formula.add(value, variable)).isInvertible()
|
|
).toBe(false);
|
|
expect(
|
|
Formula.step(constant, 10, value => Formula.add(value, variable)).hasVariable()
|
|
).toBe(false);
|
|
});
|
|
|
|
describe("Pass-through underneath start", () => {
|
|
test("Evaluates correctly", () =>
|
|
expect(
|
|
Formula.step(constant, 20, value => Formula.sqrt(value)).evaluate()
|
|
).compare_tolerance(10));
|
|
test("Inverts correctly with variable in input", () =>
|
|
expect(
|
|
Formula.step(variable, 20, value => Formula.sqrt(value)).invert(10)
|
|
).compare_tolerance(10));
|
|
});
|
|
|
|
describe("Pass-through at boundary", () => {
|
|
test("Evaluates correctly", () =>
|
|
expect(
|
|
Formula.step(constant, 10, value => Formula.sqrt(value)).evaluate()
|
|
).compare_tolerance(10));
|
|
test("Inverts correctly with variable in input", () =>
|
|
expect(
|
|
Formula.step(variable, 10, value => Formula.sqrt(value)).invert(10)
|
|
).compare_tolerance(10));
|
|
});
|
|
|
|
describe("Evaluates correctly beyond start", () => {
|
|
test("Evaluates correctly", () =>
|
|
expect(
|
|
Formula.step(variable, 8, value => Formula.add(value, 2)).evaluate()
|
|
).compare_tolerance(12));
|
|
test("Inverts correctly", () =>
|
|
expect(
|
|
Formula.step(variable, 8, value => Formula.add(value, 2)).invert(12)
|
|
).compare_tolerance(10));
|
|
});
|
|
|
|
describe("Evaluates correctly when nested", () => {
|
|
test("Evaluates correctly", () =>
|
|
expect(
|
|
Formula.add(variable, constant)
|
|
.step(10, value => Formula.mul(value, 2))
|
|
.sub(10)
|
|
.evaluate()
|
|
).compare_tolerance(20));
|
|
test("Inverts correctly", () =>
|
|
expect(
|
|
Formula.add(variable, constant)
|
|
.step(10, value => Formula.mul(value, 2))
|
|
.sub(10)
|
|
.invert(30)
|
|
).compare_tolerance(15));
|
|
});
|
|
});
|
|
|
|
describe("Conditionals", () => {
|
|
let variable: GenericFormula;
|
|
let constant: GenericFormula;
|
|
beforeAll(() => {
|
|
variable = Formula.variable(10);
|
|
constant = Formula.constant(10);
|
|
});
|
|
|
|
test("Formula without variable is marked as such", () => {
|
|
expect(Formula.if(constant, true, value => Formula.sqrt(value)).isInvertible()).toBe(false);
|
|
expect(Formula.if(constant, true, value => Formula.sqrt(value)).hasVariable()).toBe(false);
|
|
});
|
|
|
|
test("Formula with variable is marked as such", () => {
|
|
expect(Formula.if(variable, true, value => Formula.sqrt(value)).isInvertible()).toBe(true);
|
|
expect(Formula.if(variable, true, value => Formula.sqrt(value)).hasVariable()).toBe(true);
|
|
});
|
|
|
|
test("Non-invertible formula modifier marks formula as such", () => {
|
|
expect(Formula.if(constant, true, value => Formula.abs(value)).isInvertible()).toBe(false);
|
|
expect(Formula.if(constant, true, value => Formula.abs(value)).hasVariable()).toBe(false);
|
|
});
|
|
|
|
test("Formula never marked integrable", () => {
|
|
expect(Formula.if(constant, true, value => Formula.add(value, 10)).isIntegrable()).toBe(
|
|
false
|
|
);
|
|
expect(() =>
|
|
Formula.if(constant, true, value => Formula.add(value, 10)).evaluateIntegral()
|
|
).toThrow();
|
|
});
|
|
|
|
test("Formula never marked as having an invertible integral", () => {
|
|
expect(
|
|
Formula.if(constant, true, value => Formula.add(value, 10)).isIntegralInvertible()
|
|
).toBe(false);
|
|
expect(() =>
|
|
Formula.if(constant, true, value => Formula.add(value, 10)).invertIntegral(10)
|
|
).toThrow();
|
|
});
|
|
|
|
test("Formula modifiers with variables mark formula as non-invertible", () => {
|
|
expect(
|
|
Formula.if(constant, true, value => Formula.add(value, variable)).isInvertible()
|
|
).toBe(false);
|
|
expect(
|
|
Formula.if(constant, true, value => Formula.add(value, variable)).hasVariable()
|
|
).toBe(false);
|
|
});
|
|
|
|
describe("Pass-through with condition false", () => {
|
|
test("Evaluates correctly", () =>
|
|
expect(
|
|
Formula.if(constant, false, value => Formula.sqrt(value)).evaluate()
|
|
).compare_tolerance(10));
|
|
test("Inverts correctly with variable in input", () =>
|
|
expect(
|
|
Formula.if(variable, false, value => Formula.sqrt(value)).invert(10)
|
|
).compare_tolerance(10));
|
|
});
|
|
|
|
describe("Evaluates correctly with condition true", () => {
|
|
test("Evaluates correctly", () =>
|
|
expect(
|
|
Formula.if(variable, true, value => Formula.add(value, 2)).evaluate()
|
|
).compare_tolerance(12));
|
|
test("Inverts correctly", () =>
|
|
expect(
|
|
Formula.if(variable, true, value => Formula.add(value, 2)).invert(12)
|
|
).compare_tolerance(10));
|
|
});
|
|
|
|
describe("Evaluates correctly when nested", () => {
|
|
test("Evaluates correctly", () =>
|
|
expect(
|
|
Formula.add(variable, constant)
|
|
.if(true, value => Formula.add(value, 2))
|
|
.div(2)
|
|
.evaluate()
|
|
).compare_tolerance(11));
|
|
test("Inverts correctly", () =>
|
|
expect(
|
|
Formula.add(variable, constant)
|
|
.if(true, value => Formula.add(value, 2))
|
|
.div(2)
|
|
.invert(12)
|
|
).compare_tolerance(12));
|
|
});
|
|
});
|
|
|
|
describe("Custom Formulas", () => {
|
|
let variable: GenericFormula;
|
|
beforeAll(() => {
|
|
variable = Formula.variable(1);
|
|
});
|
|
|
|
describe("Formula with evaluate", () => {
|
|
test("Zero input evaluates correctly", () =>
|
|
expect(new Formula({ inputs: [], evaluate: () => 10 }).evaluate()).compare_tolerance(
|
|
10
|
|
));
|
|
test("One input evaluates correctly", () =>
|
|
expect(
|
|
new Formula({ inputs: [1], evaluate: value => value }).evaluate()
|
|
).compare_tolerance(1));
|
|
test("Two inputs evaluates correctly", () =>
|
|
expect(
|
|
new Formula({ inputs: [1, 2], evaluate: (v1, v2) => v1 }).evaluate()
|
|
).compare_tolerance(1));
|
|
});
|
|
|
|
describe("Formula with invert", () => {
|
|
test("Zero input does not invert", () =>
|
|
expect(() =>
|
|
new Formula({
|
|
inputs: [],
|
|
evaluate: () => 6,
|
|
invert: value => value,
|
|
hasVariable: true
|
|
}).invert(10)
|
|
).toThrow());
|
|
test("One input inverts correctly", () =>
|
|
expect(
|
|
new Formula({
|
|
inputs: [variable],
|
|
evaluate: () => 10,
|
|
invert: (value, v1) => v1.evaluate(),
|
|
hasVariable: true
|
|
}).invert(10)
|
|
).compare_tolerance(1));
|
|
test("Two inputs inverts correctly", () =>
|
|
expect(
|
|
new Formula({
|
|
inputs: [variable, 2],
|
|
evaluate: () => 10,
|
|
invert: (value, v1, v2) => v2,
|
|
hasVariable: true
|
|
}).invert(10)
|
|
).compare_tolerance(2));
|
|
});
|
|
|
|
describe("Formula with integrate", () => {
|
|
test("Zero input integrates correctly", () =>
|
|
expect(
|
|
new Formula({
|
|
inputs: [],
|
|
evaluate: () => 10,
|
|
integrate: () => 20
|
|
}).evaluateIntegral()
|
|
).compare_tolerance(20));
|
|
test("One input integrates correctly", () =>
|
|
expect(
|
|
new Formula({
|
|
inputs: [variable],
|
|
evaluate: () => 10,
|
|
integrate: (val, stack, v1) => val ?? 20
|
|
}).evaluateIntegral()
|
|
).compare_tolerance(20));
|
|
test("Two inputs integrates correctly", () =>
|
|
expect(
|
|
new Formula({
|
|
inputs: [variable, 2],
|
|
evaluate: (v1, v2) => 10,
|
|
integrate: (v1, v2) => 3
|
|
}).evaluateIntegral()
|
|
).compare_tolerance(3));
|
|
});
|
|
|
|
describe("Formula with invertIntegral", () => {
|
|
test("Zero input does not invert integral", () =>
|
|
expect(() =>
|
|
new Formula({
|
|
inputs: [],
|
|
evaluate: () => 10,
|
|
invertIntegral: () => 1,
|
|
hasVariable: true
|
|
}).invertIntegral(8)
|
|
).toThrow());
|
|
test("One input inverts integral correctly", () =>
|
|
expect(
|
|
new Formula({
|
|
inputs: [variable],
|
|
evaluate: () => 10,
|
|
invertIntegral: (val, v1) => 1,
|
|
hasVariable: true
|
|
}).invertIntegral(8)
|
|
).compare_tolerance(1));
|
|
test("Two inputs inverts integral correctly", () =>
|
|
expect(
|
|
new Formula({
|
|
inputs: [variable, 2],
|
|
evaluate: (v1, v2) => 10,
|
|
invertIntegral: (v1, v2) => 1,
|
|
hasVariable: true
|
|
}).invertIntegral(8)
|
|
).compare_tolerance(1));
|
|
});
|
|
|
|
describe.todo("Formula as input");
|
|
|
|
describe.todo("Determines invertibility etc. correctly");
|
|
});
|
|
|
|
describe("Buy Max", () => {
|
|
let resource: Resource;
|
|
beforeAll(() => {
|
|
resource = createResource(ref(1000));
|
|
});
|
|
describe("Without spending", () => {
|
|
test("Throws on formula with non-invertible integral", () => {
|
|
const maxAffordable = calculateMaxAffordable(Formula.neg(10), resource, false);
|
|
expect(() => maxAffordable.value).toThrow();
|
|
});
|
|
// https://www.desmos.com/calculator/7ffthe7wi8
|
|
test("Calculates max affordable and cost correctly", () => {
|
|
const variable = Formula.variable(0);
|
|
const formula = Formula.pow(1.05, variable).times(100);
|
|
const maxAffordable = calculateMaxAffordable(formula, resource, false);
|
|
expect(maxAffordable.value).compare_tolerance(47);
|
|
expect(calculateCost(formula, maxAffordable.value, false)).compare_tolerance(
|
|
Decimal.pow(1.05, 47).times(100)
|
|
);
|
|
});
|
|
});
|
|
describe("With spending", () => {
|
|
test("Throws on non-invertible formula", () => {
|
|
const maxAffordable = calculateMaxAffordable(Formula.abs(10), resource);
|
|
expect(() => maxAffordable.value).toThrow();
|
|
});
|
|
// https://www.desmos.com/calculator/7ffthe7wi8
|
|
test("Calculates max affordable and cost correctly", () => {
|
|
const variable = Formula.variable(0);
|
|
const formula = Formula.pow(1.05, variable).times(100);
|
|
const maxAffordable = calculateMaxAffordable(formula, resource);
|
|
expect(maxAffordable.value).compare_tolerance(7);
|
|
|
|
const actualCost = new Array(7)
|
|
.fill(null)
|
|
.reduce((acc, _, i) => acc.add(formula.evaluate(i)), new Decimal(0));
|
|
const calculatedCost = calculateCost(formula, maxAffordable.value);
|
|
// Check if the calculated cost is within 10% of the actual cost,
|
|
// because this is an approximation
|
|
expect(
|
|
Decimal.sub(actualCost, calculatedCost).abs().div(actualCost).toNumber()
|
|
).toBeLessThan(0.1);
|
|
});
|
|
});
|
|
});
|