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Planar-Pioneers/tests/game/formulas.test.ts

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import { createResource, Resource } from "features/resources/resource";
import Formula, {
calculateCost,
calculateMaxAffordable,
unrefFormulaSource
} from "game/formulas/formulas";
import type { GenericFormula, IntegrableFormula, InvertibleFormula } from "game/formulas/types";
import Decimal, { DecimalSource } from "util/bignum";
import { beforeAll, describe, expect, test } from "vitest";
import { ref } from "vue";
import "../utils";
import { InvertibleIntegralFormula } from "game/formulas/types";
type FormulaFunctions = keyof GenericFormula & keyof typeof Formula & keyof typeof Decimal;
const testValues = [-1, "0", Decimal.dOne] as const;
const invertibleZeroParamFunctionNames = [
"neg",
"recip",
"log10",
"log2",
"ln",
"pow10",
"exp",
"sqr",
"sqrt",
"cube",
"cbrt",
"lambertw",
"ssqrt",
"sin",
"cos",
"tan",
"asin",
"acos",
"atan",
"sinh",
"cosh",
"tanh",
"asinh",
"acosh",
"atanh",
"slog",
"tetrate",
"iteratedexp"
] as const;
const nonInvertibleZeroParamFunctionNames = [
"abs",
"sign",
"round",
"floor",
"ceil",
"trunc",
"pLog10",
"absLog10",
"factorial",
"gamma",
"lngamma"
] as const;
const integrableZeroParamFunctionNames = [
"neg",
"recip",
"log10",
"log2",
"ln",
"pow10",
"exp",
"sqr",
"sqrt",
"cube",
"cbrt",
"sin",
"cos",
"tan",
"asin",
"acos",
"atan",
"sinh",
"cosh",
"tanh",
"asinh",
"acosh",
"atanh"
] as const;
const nonIntegrableZeroParamFunctionNames = [
...nonInvertibleZeroParamFunctionNames,
"lambertw",
"ssqrt"
] as const;
const invertibleIntegralZeroPramFunctionNames = [
"recip",
"log10",
"log2",
"ln",
"pow10",
"sqr",
"sqrt",
"cube",
"cbrt",
"neg",
"exp",
"sin",
"cos",
"tan",
"sinh",
"cosh",
"tanh"
] as const;
const nonInvertibleIntegralZeroPramFunctionNames = [
...nonIntegrableZeroParamFunctionNames,
"asin",
"acos",
"atan",
"asinh",
"acosh",
"atanh"
] as const;
const invertibleOneParamFunctionNames = [
"add",
"sub",
"mul",
"div",
"log",
"pow",
"root",
"layeradd"
] as const;
const nonInvertibleOneParamFunctionNames = ["layeradd10"] as const;
const integrableOneParamFunctionNames = ["add", "sub", "mul", "div", "log", "pow", "root"] as const;
const nonIntegrableOneParamFunctionNames = [...nonInvertibleOneParamFunctionNames, "slog"] as const;
const invertibleIntegralOneParamFunctionNames = integrableOneParamFunctionNames;
const nonInvertibleIntegralOneParamFunctionNames = nonIntegrableOneParamFunctionNames;
const nonInvertibleTwoParamFunctionNames = ["iteratedlog", "pentate"] as const;
const nonIntegrableTwoParamFunctionNames = nonInvertibleTwoParamFunctionNames;
const nonInvertibleIntegralTwoParamFunctionNames = nonIntegrableTwoParamFunctionNames;
describe("Formula Equality Checking", () => {
describe("Equality Checks", () => {
test("Equals", () => expect(Formula.add(1, 1).equals(Formula.add(1, 1))).toBe(true));
test("Not Equals due to inputs", () =>
expect(Formula.add(1, 1).equals(Formula.add(1, 0))).toBe(false));
test("Not Equals due to functions", () =>
expect(Formula.add(1, 1).equals(Formula.sub(1, 1))).toBe(false));
test("Not Equals due to hasVariable", () =>
expect(Formula.constant(1).equals(Formula.variable(1))).toBe(false));
});
describe("Formula aliases", () => {
function testAliases<T extends FormulaFunctions>(
aliases: T[],
args: Parameters<(typeof Formula)[T]>
) {
describe(aliases[0], () => {
let formula: GenericFormula;
beforeAll(() => {
// eslint-disable-next-line @typescript-eslint/ban-ts-comment
// @ts-ignore
formula = Formula[aliases[0]](...args);
});
aliases.slice(1).forEach(alias => {
// eslint-disable-next-line @typescript-eslint/ban-ts-comment
// @ts-ignore
test(alias, () => expect(Formula[alias](...args).equals(formula)).toBe(true));
});
});
}
testAliases(["neg", "negate", "negated"], [1]);
testAliases(["recip", "reciprocal", "reciprocate"], [1]);
testAliases(["sign", "sgn"], [1]);
testAliases(["add", "plus"], [1, 1]);
testAliases(["sub", "subtract", "minus"], [1, 1]);
testAliases(["mul", "multiply", "times"], [1, 1]);
testAliases(["div", "divide"], [1, 1]);
testAliases(["log", "logarithm"], [1, 1]);
});
describe("Instance vs Static methods", () => {
let formula: GenericFormula;
beforeAll(() => {
formula = Formula.constant(10);
});
[...invertibleZeroParamFunctionNames, ...nonInvertibleZeroParamFunctionNames].forEach(
name => {
test(name, () => {
const instanceFormula = formula[name]();
const staticFormula = Formula[name](formula);
expect(instanceFormula.equals(staticFormula)).toBe(true);
});
}
);
[...invertibleOneParamFunctionNames, ...nonInvertibleOneParamFunctionNames].forEach(
name => {
test(name, () => {
const instanceFormula = formula[name](10);
const staticFormula = Formula[name](formula, 10);
expect(instanceFormula.equals(staticFormula)).toBe(true);
});
}
);
});
});
describe("Creating Formulas", () => {
describe("Constants", () => {
function testConstant(
desc: string,
formulaFunc: () => InvertibleFormula,
expectedValue: DecimalSource = 10
) {
describe(desc, () => {
let formula: GenericFormula;
beforeAll(() => {
formula = formulaFunc();
});
test("Is not invertible", () => expect(formula.isInvertible()).toBe(false));
test("Is not integrable", () => expect(formula.isIntegrable()).toBe(false));
test("Integral is not invertible", () =>
expect(formula.isIntegralInvertible()).toBe(false));
test("Is not marked as having a variable", () =>
expect(formula.hasVariable()).toBe(false));
test("Evaluates correctly", () =>
expect(formula.evaluate()).compare_tolerance(expectedValue));
// eslint-disable-next-line @typescript-eslint/ban-ts-comment
/* @ts-ignore */
test("Invert throws", () => expect(() => formula.invert(25)).toThrow());
// eslint-disable-next-line @typescript-eslint/ban-ts-comment
/* @ts-ignore */
test("Integrate throws", () => expect(() => formula.evaluateIntegral()).toThrow());
test("Invert integral throws", () =>
// eslint-disable-next-line @typescript-eslint/ban-ts-comment
/* @ts-ignore */
expect(() => formula.invertIntegral(25)).toThrow());
});
}
testConstant("number", () => Formula.constant(10));
testConstant("string", () => Formula.constant("10"));
testConstant("decimal", () => Formula.constant(new Decimal("1e400")), "1e400");
testConstant("ref", () => Formula.constant(ref(10)));
});
function checkFormula<T extends FormulaFunctions>(
functionName: T,
args: Readonly<Parameters<(typeof Formula)[T]>>
) {
let formula: GenericFormula;
beforeAll(() => {
// eslint-disable-next-line @typescript-eslint/ban-ts-comment
// @ts-ignore
formula = Formula[functionName](...args);
});
// None of these formulas have variables, so they should all behave the same
test("Is not marked as having a variable", () => expect(formula.hasVariable()).toBe(false));
test("Is not invertible", () => expect(formula.isInvertible()).toBe(false));
test(`Formula throws if trying to invert`, () =>
// eslint-disable-next-line @typescript-eslint/ban-ts-comment
/* @ts-ignore */
expect(() => formula.invert(10)).toThrow());
test("Is not integrable", () => expect(formula.isIntegrable()).toBe(false));
test("Has a non-invertible integral", () =>
expect(formula.isIntegralInvertible()).toBe(false));
}
// Utility function that will test all the different
// It's a lot of tests, but I'd rather be exhaustive
function testFormulaCall<T extends FormulaFunctions>(
functionName: T,
args: Readonly<Parameters<(typeof Formula)[T]>>
) {
if ((functionName === "slog" || functionName === "layeradd") && args[0] === -1) {
// These cases in particular take a long time, so skip them
// We still have plenty of coverage
return;
}
let testName = functionName + "(";
for (let i = 0; i < args.length; i++) {
if (i !== 0) {
testName += ", ";
}
testName += args[i];
}
testName += ") evaluates correctly";
test(testName, () => {
// eslint-disable-next-line @typescript-eslint/ban-ts-comment
// @ts-ignore
const formula = Formula[functionName](...args);
try {
const expectedEvaluation = Decimal[functionName](
// eslint-disable-next-line @typescript-eslint/ban-ts-comment
// @ts-ignore
...args.map(i => unrefFormulaSource(i))
);
if (expectedEvaluation != null) {
expect(formula.evaluate()).compare_tolerance(expectedEvaluation);
}
} catch {
// If this is an invalid Decimal operation, then ignore this test case
}
});
}
describe("0-param", () => {
[...invertibleZeroParamFunctionNames, ...nonInvertibleZeroParamFunctionNames].forEach(
names =>
describe(names, () => {
checkFormula(names, [0] as const);
testValues.forEach(i => testFormulaCall(names, [i] as const));
})
);
});
describe("1-param", () => {
(
[
...invertibleOneParamFunctionNames,
...nonInvertibleOneParamFunctionNames,
"max",
"min",
"maxabs",
"minabs",
"clampMin",
"clampMax"
] as const
).forEach(names =>
describe(names, () => {
checkFormula(names, [0, 0] as const);
testValues.forEach(i =>
testValues.forEach(j => testFormulaCall(names, [i, j] as const))
);
})
);
});
describe("2-param", () => {
([...nonInvertibleTwoParamFunctionNames, "clamp"] as const).forEach(names =>
describe(names, () => {
checkFormula(names, [0, 0, 0] as const);
testValues.forEach(i =>
testValues.forEach(j =>
testValues.forEach(k => testFormulaCall(names, [i, j, k] as const))
)
);
})
);
});
});
describe("Variables", () => {
let variable: GenericFormula;
let constant: GenericFormula;
beforeAll(() => {
variable = Formula.variable(10);
constant = Formula.constant(10);
});
test("Created variable is marked as a variable", () =>
expect(variable.hasVariable()).toBe(true));
test("evaluate() returns variable's value", () =>
expect(variable.evaluate()).compare_tolerance(10));
test("evaluate(variable) overrides variable value", () =>
expect(variable.add(10).evaluate(20)).compare_tolerance(30));
test("Nested variable is marked as having a variable", () =>
expect(variable.add(10).div(3).pow(2).hasVariable()).toBe(true));
test("Nested non-variable is marked as not having a variable", () =>
expect(constant.add(10).div(3).pow(2).hasVariable()).toBe(false));
});
describe("Inverting", () => {
let variable: IntegrableFormula;
let constant: GenericFormula;
beforeAll(() => {
variable = Formula.variable(10);
constant = Formula.constant(10);
});
test("variable.invert() is pass-through", () =>
expect(variable.invert(100)).compare_tolerance(100));
describe("Invertible Formulas correctly calculate when they contain a variable", () => {
function checkFormula(formula: GenericFormula, expectedBool = true) {
expect(formula.isInvertible()).toBe(expectedBool);
expect(formula.hasVariable()).toBe(expectedBool);
}
invertibleZeroParamFunctionNames.forEach(name => {
describe(name, () => {
test(`${name}(var) is marked as invertible and having a variable`, () =>
checkFormula(Formula[name](variable)));
});
});
invertibleOneParamFunctionNames.forEach(name => {
describe(name, () => {
test(`${name}(var, const) is marked as invertible and having a variable`, () =>
checkFormula(Formula[name](variable, constant)));
test(`${name}(const, var) is marked as invertible and having a variable`, () =>
checkFormula(Formula[name](constant, variable)));
test(`${name}(var, var) is marked as not invertible and not having a variable`, () =>
checkFormula(Formula[name](variable, variable), false));
});
});
});
describe("Non-invertible formulas marked as such", () => {
function checkFormula(formula: GenericFormula) {
expect(formula.isInvertible()).toBe(false);
expect(formula.isIntegrable()).toBe(false);
expect(formula.isIntegralInvertible()).toBe(false);
}
nonInvertibleZeroParamFunctionNames.forEach(name => {
describe(name, () => {
test(`${name}(var) is marked as not invertible`, () =>
checkFormula(Formula[name](variable)));
});
});
nonInvertibleOneParamFunctionNames.forEach(name => {
describe(name, () => {
test(`${name}(var, const) is marked as not invertible`, () =>
checkFormula(Formula[name](variable, constant)));
test(`${name}(const, var) is marked as not invertible`, () =>
checkFormula(Formula[name](constant, variable)));
test(`${name}(var, var) is marked as not invertible`, () =>
checkFormula(Formula[name](variable, variable)));
});
});
nonInvertibleTwoParamFunctionNames.forEach(name => {
describe(name, () => {
test(`${name}(var, const, const) is marked as not invertible`, () =>
checkFormula(Formula[name](variable, constant, constant)));
test(`${name}(const, var, const) is marked as not invertible`, () =>
checkFormula(Formula[name](constant, variable, constant)));
test(`${name}(const, const, var) is marked as not invertible`, () =>
checkFormula(Formula[name](constant, constant, variable)));
test(`${name}(var, var, const) is marked as not invertible`, () =>
checkFormula(Formula[name](variable, variable, constant)));
test(`${name}(var, const, var) is marked as not invertible`, () =>
checkFormula(Formula[name](variable, constant, variable)));
test(`${name}(const, var, var) is marked as not invertible`, () =>
checkFormula(Formula[name](constant, variable, variable)));
test(`${name}(var, var, var) is marked as not invertible`, () =>
checkFormula(Formula[name](variable, variable, variable)));
});
});
});
describe("Inverting calculates the value of the variable", () => {
let variable: IntegrableFormula;
let constant: IntegrableFormula;
beforeAll(() => {
variable = Formula.variable(2);
constant = Formula.constant(3);
});
invertibleOneParamFunctionNames.forEach(name =>
describe(name, () => {
test(`${name}(var, const).invert()`, () => {
const formula = Formula[name](variable, constant);
const result = formula.evaluate();
// eslint-disable-next-line @typescript-eslint/no-non-null-assertion
expect(formula.invert!(result)).compare_tolerance(2);
});
if (name !== "layeradd") {
test(`${name}(const, var).invert()`, () => {
const formula = Formula[name](constant, variable);
const result = formula.evaluate();
expect(formula.invert(result)).compare_tolerance(2);
});
}
})
);
});
describe("Inverting pass-throughs", () => {
test("max", () => expect(Formula.max(variable, constant).invert(10)).compare_tolerance(10));
test("min", () => expect(Formula.min(variable, constant).invert(10)).compare_tolerance(10));
test("minabs", () =>
expect(Formula.minabs(variable, constant).invert(10)).compare_tolerance(10));
test("maxabs", () =>
expect(Formula.maxabs(variable, constant).invert(10)).compare_tolerance(10));
test("clampMax", () =>
expect(Formula.clampMax(variable, constant).invert(10)).compare_tolerance(10));
test("clampMin", () =>
expect(Formula.clampMin(variable, constant).invert(10)).compare_tolerance(10));
test("clamp", () =>
expect(Formula.clamp(variable, constant, constant).invert(10)).compare_tolerance(10));
});
test("Inverting nested formulas", () => {
const formula = Formula.add(variable, constant).times(constant);
expect(formula.invert(100)).compare_tolerance(0);
});
test("Inverting with non-invertible sections", () => {
const formula = Formula.add(variable, constant.ceil());
expect(formula.isInvertible()).toBe(true);
expect(formula.invert(10)).compare_tolerance(0);
});
});
describe("Integrating", () => {
let variable: IntegrableFormula;
let constant: IntegrableFormula;
beforeAll(() => {
variable = Formula.variable(ref(10));
constant = Formula.constant(10);
});
test("variable.evaluateIntegral() calculates correctly", () =>
expect(variable.evaluateIntegral()).compare_tolerance(Decimal.pow(10, 2).div(2)));
test("variable.evaluateIntegral(variable) overrides variable value", () =>
expect(variable.evaluateIntegral(20)).compare_tolerance(Decimal.pow(20, 2).div(2)));
describe("Integrable functions marked as such", () => {
function checkFormula(formula: IntegrableFormula) {
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).add(10);
const actualCost = new Array(10)
.fill(null)
.reduce((acc, _, i) => acc.add(formula.evaluate(i)), new Decimal(0));
// Check if the calculated cost is within 10% of the actual cost,
// because this is an approximation
expect(
Decimal.sub(
actualCost,
Decimal.add(formula.evaluateIntegral(), formula.calculateConstantOfIntegration())
)
.abs()
.div(actualCost)
.toNumber()
).toBeLessThan(0.1);
});
test("Integrating nested formulas with overidden variable", () => {
const formula = Formula.add(variable, constant).times(constant).pow(2).times(30).add(10);
const actualCost = new Array(20)
.fill(null)
.reduce((acc, _, i) => acc.add(formula.evaluate(i)), new Decimal(0));
// Check if the calculated cost is within 10% of the actual cost,
// because this is an approximation
expect(
Decimal.sub(
actualCost,
Decimal.add(formula.evaluateIntegral(20), formula.calculateConstantOfIntegration())
)
.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: InvertibleIntegralFormula;
let constant: InvertibleIntegralFormula;
beforeAll(() => {
variable = Formula.variable(10);
constant = Formula.constant(10);
});
test("variable.invertIntegral() calculates correctly", () =>
expect(variable.invertIntegral(20)).compare_tolerance(
Decimal.sqrt(20).times(Decimal.sqrt(2))
));
describe("Invertible Integral functions marked as such", () => {
function checkFormula(formula: InvertibleIntegralFormula) {
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(formula.evaluateIntegral())).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("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 false and else statement", () => {
test("Evaluates correctly", () =>
expect(
Formula.if(
constant,
false,
value => Formula.sqrt(value),
value => value.times(2)
).evaluate()
).compare_tolerance(20));
test("Inverts correctly with variable in input", () =>
expect(
Formula.if(
variable,
false,
value => Formula.sqrt(value),
value => value.times(2)
).invert(20)
).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: InvertibleIntegralFormula;
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
}).invert(10)
).toThrow());
test("One input inverts correctly", () =>
expect(
new Formula({
inputs: [variable],
evaluate: () => 10,
invert: (value, v1) => v1.evaluate()
}).invert(10)
).compare_tolerance(1));
test("Two inputs inverts correctly", () =>
expect(
new Formula({
inputs: [variable, 2],
evaluate: () => 10,
invert: (value, v1, v2) => v2
}).invert(10)
).compare_tolerance(2));
});
describe("Formula with integrate", () => {
test("Zero input cannot integrate", () =>
expect(() =>
new Formula({
inputs: [],
evaluate: () => 0,
integrate: stack => variable
}).evaluateIntegral()
).toThrow());
test("One input integrates correctly", () =>
expect(
new Formula({
inputs: [variable],
evaluate: v1 => Decimal.add(v1, 10),
integrate: (stack, v1) => Formula.add(v1, 10)
}).evaluateIntegral()
).compare_tolerance(11));
test("Two inputs integrates correctly", () =>
expect(
new Formula({
inputs: [variable, 10],
evaluate: (v1, v2) => Decimal.add(v1, v2),
integrate: (stack, v1, v2) => Formula.add(v1, v2)
}).evaluateIntegral()
).compare_tolerance(11));
});
describe("Formula with invertIntegral", () => {
test("Zero input does not invert integral", () =>
expect(() =>
new Formula({
inputs: [],
evaluate: () => 0,
integrate: stack => variable
}).invertIntegral(20)
).toThrow());
test("One input inverts integral correctly", () =>
expect(
new Formula({
inputs: [variable],
evaluate: v1 => Decimal.add(v1, 10),
integrate: (stack, v1) => Formula.add(v1, 10)
}).invertIntegral(20)
).compare_tolerance(10));
test("Two inputs inverts integral correctly", () =>
expect(
new Formula({
inputs: [variable, 10],
evaluate: (v1, v2) => Decimal.add(v1, v2),
integrate: (stack, v1, v2) => Formula.add(v1, v2)
}).invertIntegral(20)
).compare_tolerance(10));
});
describe("Formula as input", () => {
let customFormula: InvertibleIntegralFormula;
beforeAll(() => {
customFormula = new Formula({
inputs: [variable],
evaluate: v1 => v1,
invert: value => value,
integrate: (stack, v1) => v1.getIntegralFormula(stack)
});
});
test("Evaluate correctly", () =>
expect(customFormula.add(10).evaluate()).compare_tolerance(11));
test("Invert correctly", () =>
expect(customFormula.add(10).invert(20)).compare_tolerance(10));
test("Integrate correctly", () =>
expect(customFormula.add(10).evaluateIntegral(10)).compare_tolerance(20));
});
});
describe("Buy Max", () => {
let resource: Resource;
beforeAll(() => {
resource = createResource(ref(100000));
});
describe("Without spending", () => {
test("Throws on formula with non-invertible integral", () => {
// eslint-disable-next-line @typescript-eslint/ban-ts-comment
/* @ts-ignore */
const maxAffordable = calculateMaxAffordable(Formula.neg(10), resource, false);
expect(() => maxAffordable.value).toThrow();
});
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(141);
expect(calculateCost(formula, maxAffordable.value, false)).compare_tolerance(
Decimal.pow(1.05, 141).times(100)
);
});
});
describe("With spending", () => {
test("Throws on non-invertible formula", () => {
const maxAffordable = calculateMaxAffordable(Formula.abs(10), resource);
expect(() => maxAffordable.value).toThrow();
});
test("Estimates max affordable and cost correctly with 0 purchases", () => {
const purchases = ref(0);
const variable = Formula.variable(purchases);
const formula = Formula.pow(1.05, variable).times(100);
const maxAffordable = calculateMaxAffordable(formula, resource, true, 0);
let actualAffordable = 0;
let summedCost = Decimal.dZero;
while (true) {
const nextCost = formula.evaluate(actualAffordable);
if (Decimal.add(summedCost, nextCost).lte(resource.value)) {
actualAffordable++;
summedCost = Decimal.add(summedCost, nextCost);
} else {
break;
}
}
expect(maxAffordable.value).compare_tolerance(actualAffordable);
const actualCost = new Array(actualAffordable)
.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);
});
test("Estimates max affordable and cost with 1 purchase", () => {
const purchases = ref(1);
const variable = Formula.variable(purchases);
const formula = Formula.pow(1.05, variable).times(100);
const maxAffordable = calculateMaxAffordable(formula, resource, true, 0);
let actualAffordable = 0;
let summedCost = Decimal.dZero;
while (true) {
const nextCost = formula.evaluate(Decimal.add(actualAffordable, 1));
if (Decimal.add(summedCost, nextCost).lte(resource.value)) {
actualAffordable++;
summedCost = Decimal.add(summedCost, nextCost);
} else {
break;
}
}
expect(maxAffordable.value).compare_tolerance(actualAffordable);
const actualCost = new Array(actualAffordable)
.fill(null)
.reduce((acc, _, i) => acc.add(formula.evaluate(i + 1)), 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);
});
test("Estimates max affordable and cost more accurately with summing last purchases", () => {
const purchases = ref(1);
const variable = Formula.variable(purchases);
const formula = Formula.pow(1.05, variable).times(100);
const maxAffordable = calculateMaxAffordable(formula, resource);
let actualAffordable = 0;
let summedCost = Decimal.dZero;
while (true) {
const nextCost = formula.evaluate(Decimal.add(actualAffordable, 1));
if (Decimal.add(summedCost, nextCost).lte(resource.value)) {
actualAffordable++;
summedCost = Decimal.add(summedCost, nextCost);
} else {
break;
}
}
expect(maxAffordable.value).compare_tolerance(actualAffordable);
const actualCost = new Array(actualAffordable)
.fill(null)
.reduce((acc, _, i) => acc.add(formula.evaluate(i + 1)), new Decimal(0));
const calculatedCost = calculateCost(formula, maxAffordable.value);
// Since we're summing the last few purchases, this has a tighter deviation allowed
expect(
Decimal.sub(actualCost, calculatedCost).abs().div(actualCost).toNumber()
).toBeLessThan(0.02);
});
test("Handles summing purchases when making few purchases", () => {
const purchases = ref(90);
const variable = Formula.variable(purchases);
const formula = Formula.pow(1.05, variable).times(100);
const maxAffordable = calculateMaxAffordable(formula, resource);
let actualAffordable = 0;
let summedCost = Decimal.dZero;
while (true) {
const nextCost = formula.evaluate(Decimal.add(actualAffordable, purchases.value));
if (Decimal.add(summedCost, nextCost).lte(resource.value)) {
actualAffordable++;
summedCost = Decimal.add(summedCost, nextCost);
} else {
break;
}
}
expect(maxAffordable.value).compare_tolerance(actualAffordable);
const actualCost = new Array(actualAffordable)
.fill(null)
.reduce(
(acc, _, i) => acc.add(formula.evaluate(i + purchases.value)),
new Decimal(0)
);
const calculatedCost = calculateCost(formula, maxAffordable.value);
// Since we're summing all the purchases this should be equivalent
expect(calculatedCost).compare_tolerance(actualCost);
});
test("Handles summing purchases when making very few purchases", () => {
const purchases = ref(0);
const variable = Formula.variable(purchases);
const formula = variable.add(1);
const resource = createResource(ref(3));
const maxAffordable = calculateMaxAffordable(formula, resource, true);
expect(maxAffordable.value).compare_tolerance(2);
const actualCost = new Array(2)
.fill(null)
.reduce(
(acc, _, i) => acc.add(formula.evaluate(i + purchases.value)),
new Decimal(0)
);
const calculatedCost = calculateCost(formula, maxAffordable.value, true);
// Since we're summing all the purchases this should be equivalent
expect(calculatedCost).compare_tolerance(actualCost);
});
test("Handles summing purchases when over e308 purchases", () => {
resource.value = "1ee308";
const purchases = ref(0);
const variable = Formula.variable(purchases);
const formula = variable;
const maxAffordable = calculateMaxAffordable(formula, resource);
const calculatedCost = calculateCost(formula, maxAffordable.value);
expect(Decimal.isNaN(calculatedCost)).toBe(false);
expect(Decimal.isFinite(calculatedCost)).toBe(true);
resource.value = 100000;
});
});
});
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