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Lots of formula changes

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Many tests fail and inverting integrals is basically non-functional because it just chains stuff
Will need to implement integration by parts and/or integration by substitution for that
This commit is contained in:
thepaperpilot 2023-02-04 17:56:05 -06:00
parent 5293a2ba92
commit aebf318f83
3 changed files with 1475 additions and 291 deletions
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2
package.json
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@ -48,7 +48,7 @@
"jsdom": "^20.0.0", "jsdom": "^20.0.0",
"prettier": "^2.5.1", "prettier": "^2.5.1",
"typescript": "^4.7.4", "typescript": "^4.7.4",
"vitest": "^0.26.3", "vitest": "^0.27.3",
"vue-tsc": "^0.38.1" "vue-tsc": "^0.38.1"
}, },
"engines": { "engines": {

1081
src/game/formulas.ts
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File diff suppressed because it is too large Load diff

681
tests/game/formulas.test.ts
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@ -1,7 +1,13 @@
import Formula, { GenericFormula, InvertibleFormula, unrefFormulaSource } from "game/formulas"; import { createResource, Resource } from "features/resources/resource";
import Formula, {
calculateMaxAffordable,
GenericFormula,
InvertibleFormula,
unrefFormulaSource
} from "game/formulas";
import Decimal, { DecimalSource, format } from "util/bignum"; import Decimal, { DecimalSource, format } from "util/bignum";
import { beforeAll, describe, expect, test } from "vitest"; import { beforeAll, describe, expect, test } from "vitest";
import { Ref, ref } from "vue"; import { ref } from "vue";
type FormulaFunctions = keyof GenericFormula & keyof typeof Formula & keyof typeof Decimal; type FormulaFunctions = keyof GenericFormula & keyof typeof Formula & keyof typeof Decimal;
@ -43,98 +49,6 @@ declare global {
} }
} }
function testConstant(
desc: string,
formulaFunc: () => InvertibleFormula,
expectedValue: DecimalSource = 10
) {
describe(desc, () => {
let formula: GenericFormula;
beforeAll(() => {
formula = formulaFunc();
});
test("Evaluates correctly", () =>
expect(formula.evaluate()).compare_tolerance(expectedValue));
test("Invert is pass-through", () => expect(formula.invert(25)).compare_tolerance(25));
test("Is not marked as having a variable", () => expect(formula.hasVariable()).toBe(false));
});
}
function testFormula<T extends FormulaFunctions>(
functionName: T,
args: Readonly<Parameters<typeof Formula[T]>>,
invertible = true
) {
let formula: GenericFormula;
beforeAll(() => {
// eslint-disable-next-line @typescript-eslint/ban-ts-comment
// @ts-ignore
formula = Formula[functionName](...args);
});
test("Formula is not marked as having a variable", () =>
expect(formula.hasVariable()).toBe(false));
test(`Formula is${invertible ? "" : " not"} invertible`, () =>
expect(formula.isInvertible()).toBe(invertible));
if (invertible) {
test(`Formula throws if inverting without any variables`, () =>
expect(() => formula.invert(10)).toThrow());
}
}
// 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]>>
) {
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
}
});
}
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));
});
});
}
const testValues = ["-1e400", 0, 0.25] as const; const testValues = ["-1e400", 0, 0.25] as const;
const invertibleZeroParamFunctionNames = [ const invertibleZeroParamFunctionNames = [
@ -164,7 +78,6 @@ const invertibleZeroParamFunctionNames = [
"acosh", "acosh",
"atanh" "atanh"
] as const; ] as const;
const nonInvertibleZeroParamFunctionNames = [ const nonInvertibleZeroParamFunctionNames = [
"abs", "abs",
"sign", "sign",
@ -178,6 +91,64 @@ const nonInvertibleZeroParamFunctionNames = [
"gamma", "gamma",
"lngamma" "lngamma"
] as const; ] 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"
] as const;
const nonInvertibleIntegralZeroPramFunctionNames = [
...nonIntegrableZeroParamFunctionNames,
"neg",
"exp",
"sin",
"cos",
"tan",
"asin",
"acos",
"atan",
"sinh",
"cosh",
"tanh",
"asinh",
"acosh",
"atanh"
] as const;
const invertibleOneParamFunctionNames = [ const invertibleOneParamFunctionNames = [
"add", "add",
@ -189,7 +160,6 @@ const invertibleOneParamFunctionNames = [
"root", "root",
"slog" "slog"
] as const; ] as const;
const nonInvertibleOneParamFunctionNames = [ const nonInvertibleOneParamFunctionNames = [
"max", "max",
"min", "min",
@ -199,10 +169,18 @@ const nonInvertibleOneParamFunctionNames = [
"clampMax", "clampMax",
"layeradd10" "layeradd10"
] as const; ] 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 invertibleTwoParamFunctionNames = ["tetrate", "layeradd", "iteratedexp"] as const; const invertibleTwoParamFunctionNames = ["tetrate", "layeradd", "iteratedexp"] as const;
const nonInvertibleTwoParamFunctionNames = ["clamp", "iteratedlog", "pentate"] as const; const nonInvertibleTwoParamFunctionNames = ["clamp", "iteratedlog", "pentate"] as const;
const nonIntegrableTwoParamFunctionNames = [
...invertibleTwoParamFunctionNames,
...nonInvertibleZeroParamFunctionNames
];
const nonInvertibleIntegralTwoParamFunctionNames = nonIntegrableTwoParamFunctionNames;
describe("Formula Equality Checking", () => { describe("Formula Equality Checking", () => {
describe("Equality Checks", () => { describe("Equality Checks", () => {
@ -214,6 +192,25 @@ describe("Formula Equality Checking", () => {
}); });
describe("Formula aliases", () => { 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(["neg", "negate", "negated"], [1]);
testAliases(["recip", "reciprocal", "reciprocate"], [1]); testAliases(["recip", "reciprocal", "reciprocate"], [1]);
testAliases(["sign", "sgn"], [1]); testAliases(["sign", "sgn"], [1]);
@ -263,6 +260,30 @@ describe("Formula Equality Checking", () => {
describe("Creating Formulas", () => { describe("Creating Formulas", () => {
describe("Constants", () => { 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));
test("Invert throws", () => expect(() => formula.invert(25)).toThrow());
test("Integrate throws", () => expect(() => formula.evaluateIntegral()).toThrow());
test("Invert integral throws", () =>
expect(() => formula.invertIntegral(25)).toThrow());
});
}
testConstant("number", () => Formula.constant(10)); testConstant("number", () => Formula.constant(10));
testConstant("string", () => Formula.constant("10")); testConstant("string", () => Formula.constant("10"));
testConstant("formula", () => Formula.constant(Formula.constant(10))); testConstant("formula", () => Formula.constant(Formula.constant(10)));
@ -270,10 +291,64 @@ describe("Creating Formulas", () => {
testConstant("ref", () => Formula.constant(ref(10))); 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`, () =>
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]>>
) {
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("Invertible 0-param", () => { describe("Invertible 0-param", () => {
invertibleZeroParamFunctionNames.forEach(names => invertibleZeroParamFunctionNames.forEach(names =>
describe(names, () => { describe(names, () => {
testFormula(names, [0] as const); checkFormula(names, [0] as const);
testValues.forEach(i => testFormulaCall(names, [i] as const)); testValues.forEach(i => testFormulaCall(names, [i] as const));
}) })
); );
@ -281,7 +356,7 @@ describe("Creating Formulas", () => {
describe("Non-Invertible 0-param", () => { describe("Non-Invertible 0-param", () => {
nonInvertibleZeroParamFunctionNames.forEach(names => nonInvertibleZeroParamFunctionNames.forEach(names =>
describe(names, () => { describe(names, () => {
testFormula(names, [0] as const, false); checkFormula(names, [0] as const);
testValues.forEach(i => testFormulaCall(names, [i] as const)); testValues.forEach(i => testFormulaCall(names, [i] as const));
}) })
); );
@ -289,7 +364,7 @@ describe("Creating Formulas", () => {
describe("Invertible 1-param", () => { describe("Invertible 1-param", () => {
invertibleOneParamFunctionNames.forEach(names => invertibleOneParamFunctionNames.forEach(names =>
describe(names, () => { describe(names, () => {
testFormula(names, [0, 0] as const); checkFormula(names, [0, 0] as const);
testValues.forEach(i => testValues.forEach(i =>
testValues.forEach(j => testFormulaCall(names, [i, j] as const)) testValues.forEach(j => testFormulaCall(names, [i, j] as const))
); );
@ -299,7 +374,7 @@ describe("Creating Formulas", () => {
describe("Non-Invertible 1-param", () => { describe("Non-Invertible 1-param", () => {
nonInvertibleOneParamFunctionNames.forEach(names => nonInvertibleOneParamFunctionNames.forEach(names =>
describe(names, () => { describe(names, () => {
testFormula(names, [0, 0] as const, false); checkFormula(names, [0, 0] as const);
testValues.forEach(i => testValues.forEach(i =>
testValues.forEach(j => testFormulaCall(names, [i, j] as const)) testValues.forEach(j => testFormulaCall(names, [i, j] as const))
); );
@ -309,7 +384,7 @@ describe("Creating Formulas", () => {
describe("Invertible 2-param", () => { describe("Invertible 2-param", () => {
invertibleTwoParamFunctionNames.forEach(names => invertibleTwoParamFunctionNames.forEach(names =>
describe(names, () => { describe(names, () => {
testFormula(names, [0, 0, 0] as const); checkFormula(names, [0, 0, 0] as const);
testValues.forEach(i => testValues.forEach(i =>
testValues.forEach(j => testValues.forEach(j =>
testValues.forEach(k => testFormulaCall(names, [i, j, k] as const)) testValues.forEach(k => testFormulaCall(names, [i, j, k] as const))
@ -321,7 +396,7 @@ describe("Creating Formulas", () => {
describe("Non-Invertible 2-param", () => { describe("Non-Invertible 2-param", () => {
nonInvertibleTwoParamFunctionNames.forEach(names => nonInvertibleTwoParamFunctionNames.forEach(names =>
describe(names, () => { describe(names, () => {
testFormula(names, [0, 0, 0] as const, false); checkFormula(names, [0, 0, 0] as const);
testValues.forEach(i => testValues.forEach(i =>
testValues.forEach(j => testValues.forEach(j =>
testValues.forEach(k => testFormulaCall(names, [i, j, k] as const)) testValues.forEach(k => testFormulaCall(names, [i, j, k] as const))
@ -342,14 +417,27 @@ describe("Variables", () => {
test("Created variable is marked as a variable", () => test("Created variable is marked as a variable", () =>
expect(variable.hasVariable()).toBe(true)); expect(variable.hasVariable()).toBe(true));
test("Evaluate() returns variable's value", () => test("evaluate() returns variable's value", () =>
expect(variable.evaluate()).compare_tolerance(10)); expect(variable.evaluate()).compare_tolerance(10));
test("Invert() is pass-through", () => expect(variable.invert(100)).compare_tolerance(100)); test("evaluate(variable) overrides variable value", () =>
expect(variable.add(10).evaluate(20)).compare_tolerance(30));
test("Nested variable is marked as having a variable", () => test("Nested variable is marked as having a variable", () =>
expect(variable.add(10).div(3).pow(2).hasVariable()).toBe(true)); expect(variable.add(10).div(3).pow(2).hasVariable()).toBe(true));
test("Nested non-variable is marked as not having a variable", () => test("Nested non-variable is marked as not having a variable", () =>
expect(constant.add(10).div(3).pow(2).hasVariable()).toBe(false)); expect(constant.add(10).div(3).pow(2).hasVariable()).toBe(false));
});
describe("Inverting", () => {
let variable: GenericFormula;
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", () => { describe("Invertible Formulas correctly calculate when they contain a variable", () => {
function checkFormula(formula: GenericFormula, expectedBool = true) { function checkFormula(formula: GenericFormula, expectedBool = true) {
@ -392,42 +480,43 @@ describe("Variables", () => {
}); });
}); });
describe("Non-Invertible Formulas never marked as having a variable", () => { describe("Non-invertible formulas marked as such", () => {
function checkFormula(formula: GenericFormula) { function checkFormula(formula: GenericFormula) {
expect(formula.isInvertible()).toBe(false); expect(formula.isInvertible()).toBe(false);
expect(formula.hasVariable()).toBe(false); expect(formula.isIntegrable()).toBe(false);
expect(formula.isIntegralInvertible()).toBe(false);
} }
nonInvertibleZeroParamFunctionNames.forEach(name => { nonInvertibleZeroParamFunctionNames.forEach(name => {
describe(name, () => { describe(name, () => {
test(`${name}(var) is marked as not invertible and not having a variable`, () => test(`${name}(var) is marked as not invertible`, () =>
checkFormula(Formula[name](variable))); checkFormula(Formula[name](variable)));
}); });
}); });
nonInvertibleOneParamFunctionNames.forEach(name => { nonInvertibleOneParamFunctionNames.forEach(name => {
describe(name, () => { describe(name, () => {
test(`${name}(var, const) is marked as not invertible and not having a variable`, () => test(`${name}(var, const) is marked as not invertible`, () =>
checkFormula(Formula[name](variable, constant))); checkFormula(Formula[name](variable, constant)));
test(`${name}(const, var) is marked as not invertible and not having a variable`, () => test(`${name}(const, var) is marked as not invertible`, () =>
checkFormula(Formula[name](constant, variable))); checkFormula(Formula[name](constant, variable)));
test(`${name}(var, var) is marked as not invertible and not having a variable`, () => test(`${name}(var, var) is marked as not invertible`, () =>
checkFormula(Formula[name](variable, variable))); checkFormula(Formula[name](variable, variable)));
}); });
}); });
nonInvertibleTwoParamFunctionNames.forEach(name => { nonInvertibleTwoParamFunctionNames.forEach(name => {
describe(name, () => { describe(name, () => {
test(`${name}(var, const, const) is marked as not invertible and not having a variable`, () => test(`${name}(var, const, const) is marked as not invertible`, () =>
checkFormula(Formula[name](variable, constant, constant))); checkFormula(Formula[name](variable, constant, constant)));
test(`${name}(const, var, const) is marked as not invertible and not having a variable`, () => test(`${name}(const, var, const) is marked as not invertible`, () =>
checkFormula(Formula[name](constant, variable, constant))); checkFormula(Formula[name](constant, variable, constant)));
test(`${name}(const, const, var) is marked as not invertible and not having a variable`, () => test(`${name}(const, const, var) is marked as not invertible`, () =>
checkFormula(Formula[name](constant, constant, variable))); checkFormula(Formula[name](constant, constant, variable)));
test(`${name}(var, var, const) is marked as not invertible and not having a variable`, () => test(`${name}(var, var, const) is marked as not invertible`, () =>
checkFormula(Formula[name](variable, variable, constant))); checkFormula(Formula[name](variable, variable, constant)));
test(`${name}(var, const, var) is marked as not invertible and not having a variable`, () => test(`${name}(var, const, var) is marked as not invertible`, () =>
checkFormula(Formula[name](variable, constant, variable))); checkFormula(Formula[name](variable, constant, variable)));
test(`${name}(const, var, var) is marked as not invertible and not having a variable`, () => test(`${name}(const, var, var) is marked as not invertible`, () =>
checkFormula(Formula[name](constant, variable, variable))); checkFormula(Formula[name](constant, variable, variable)));
test(`${name}(var, var, var) is marked as not invertible and not having a variable`, () => test(`${name}(var, var, var) is marked as not invertible`, () =>
checkFormula(Formula[name](variable, variable, variable))); checkFormula(Formula[name](variable, variable, variable)));
}); });
}); });
@ -476,6 +565,164 @@ describe("Variables", () => {
}); });
}); });
describe("Integrating", () => {
let variable: GenericFormula;
let constant: GenericFormula;
beforeAll(() => {
variable = Formula.variable(10);
constant = Formula.constant(10);
});
test("evaluateIntegral() returns variable's value", () =>
expect(variable.evaluate()).compare_tolerance(10));
test("evaluateIntegral(variable) overrides variable value", () =>
expect(variable.add(10).evaluateIntegral(20)).compare_tolerance(400));
describe("Integrable functions marked as such", () => {
function checkFormula(formula: GenericFormula) {
expect(formula.isIntegrable()).toBe(true);
expect(() => formula.evaluateIntegral()).to.not.throw();
}
integrableZeroParamFunctionNames.forEach(name => {
describe(name, () => {
test(`${name}(var) is marked as integrable`, () =>
checkFormula(Formula[name](variable)));
});
});
integrableOneParamFunctionNames.forEach(name => {
describe(name, () => {
test(`${name}(var, const) is marked as integrable`, () =>
checkFormula(Formula[name](variable, constant)));
test(`${name}(const, var) is marked as integrable`, () =>
checkFormula(Formula[name](constant, variable)));
test(`${name}(var, var) is marked as integrable`, () =>
checkFormula(Formula[name](variable, variable)));
});
});
});
describe("Non-Integrable functions marked as such", () => {
function checkFormula(formula: GenericFormula) {
expect(formula.isIntegrable()).toBe(false);
}
nonIntegrableZeroParamFunctionNames.forEach(name => {
describe(name, () => {
test(`${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");
});
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)));
test(`${name}(const, var) is marked as having an invertible integral`, () =>
checkFormula(Formula[name](constant, variable)));
test(`${name}(var, var) is marked as having an invertible integral`, () =>
checkFormula(Formula[name](variable, variable)));
});
});
});
describe("Non-Invertible integral functions marked as such", () => {
function checkFormula(formula: GenericFormula) {
expect(formula.isIntegralInvertible()).toBe(false);
}
nonInvertibleIntegralZeroPramFunctionNames.forEach(name => {
describe(name, () => {
test(`${name}(var) is marked as not integrable`, () =>
checkFormula(Formula[name](variable)));
});
});
nonInvertibleIntegralOneParamFunctionNames.forEach(name => {
describe(name, () => {
test(`${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)));
});
});
nonInvertibleIntegralTwoParamFunctionNames.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("Invertible Integral formulas invert correctly");
});
describe("Step-wise", () => { describe("Step-wise", () => {
let variable: GenericFormula; let variable: GenericFormula;
let constant: GenericFormula; let constant: GenericFormula;
@ -485,7 +732,7 @@ describe("Step-wise", () => {
}); });
test("Formula without variable is marked as such", () => { test("Formula without variable is marked as such", () => {
expect(Formula.step(constant, 10, value => Formula.sqrt(value)).isInvertible()).toBe(true); expect(Formula.step(constant, 10, value => Formula.sqrt(value)).isInvertible()).toBe(false);
expect(Formula.step(constant, 10, value => Formula.sqrt(value)).hasVariable()).toBe(false); expect(Formula.step(constant, 10, value => Formula.sqrt(value)).hasVariable()).toBe(false);
}); });
@ -499,6 +746,24 @@ describe("Step-wise", () => {
expect(Formula.step(constant, 10, value => Formula.abs(value)).hasVariable()).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", () => { test("Formula modifiers with variables mark formula as non-invertible", () => {
expect( expect(
Formula.step(constant, 10, value => Formula.add(value, variable)).isInvertible() Formula.step(constant, 10, value => Formula.add(value, variable)).isInvertible()
@ -540,7 +805,7 @@ describe("Conditionals", () => {
}); });
test("Formula without variable is marked as such", () => { test("Formula without variable is marked as such", () => {
expect(Formula.if(constant, true, value => Formula.sqrt(value)).isInvertible()).toBe(true); expect(Formula.if(constant, true, value => Formula.sqrt(value)).isInvertible()).toBe(false);
expect(Formula.if(constant, true, value => Formula.sqrt(value)).hasVariable()).toBe(false); expect(Formula.if(constant, true, value => Formula.sqrt(value)).hasVariable()).toBe(false);
}); });
@ -554,6 +819,24 @@ describe("Conditionals", () => {
expect(Formula.if(constant, true, value => Formula.abs(value)).hasVariable()).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", () => { test("Formula modifiers with variables mark formula as non-invertible", () => {
expect( expect(
Formula.if(constant, true, value => Formula.add(value, variable)).isInvertible() Formula.if(constant, true, value => Formula.add(value, variable)).isInvertible()
@ -587,53 +870,143 @@ describe("Conditionals", () => {
}); });
describe("Custom Formulas", () => { describe("Custom Formulas", () => {
describe("Formula with just one input", () => {
let formula: GenericFormula;
beforeAll(() => {
formula = new Formula([10]);
});
test("Is not invertible", () => expect(formula.isInvertible()).toBe(false));
test("Is not marked as having a variable", () => expect(formula.hasVariable()).toBe(false));
test("Evaluates correctly", () => expect(formula.evaluate()).compare_tolerance(10));
test("Invert is pass-through", () => expect(formula.invert(20)).compare_tolerance(20));
});
describe("Formula with non-one inputs without required other params", () => {
test("Zero inputs throws", () => expect(() => new Formula([])).toThrow());
test("Two inputs throws", () => expect(() => new Formula([1, 2])).toThrow());
test("Zero inputs and invert throws", () =>
expect(() => new Formula([], undefined, value => value)).toThrow());
test("Two inputs and invert throws", () =>
expect(() => new Formula([1, 2], undefined, value => value)).toThrow());
test("Zero inputs and evaluate and hasVariable throws", () =>
expect(() => new Formula([], () => 10, undefined, true)).toThrow());
test("Two inputs and evaluate and hasVariable throws", () =>
expect(() => new Formula([1, 2], () => 10, undefined, true)).toThrow());
});
describe("Formula with evaluate", () => { describe("Formula with evaluate", () => {
test("Zero input evaluates correctly", () => test("Zero input evaluates correctly", () =>
expect(new Formula([], () => 10).evaluate()).compare_tolerance(10)); expect(new Formula({ inputs: [], evaluate: () => 10 }).evaluate()).compare_tolerance(
10
));
test("One input evaluates correctly", () => test("One input evaluates correctly", () =>
expect(new Formula([1], value => value).evaluate()).compare_tolerance(1)); expect(
new Formula({ inputs: [1], evaluate: value => value }).evaluate()
).compare_tolerance(1));
test("Two inputs evaluates correctly", () => test("Two inputs evaluates correctly", () =>
expect(new Formula([1, 2], (v1, v2) => v1).evaluate()).compare_tolerance(1)); expect(
new Formula({ inputs: [1, 2], evaluate: (v1, v2) => v1 }).evaluate()
).compare_tolerance(1));
}); });
describe("Formula with invert", () => { describe("Formula with invert", () => {
test("Zero input inverts correctly", () => test("Zero input inverts correctly", () =>
expect(new Formula([], undefined, value => value).invert(10)).compare_tolerance(10)); expect(
new Formula({ inputs: [], evaluate: () => 6, invert: value => value }).invert(10)
).compare_tolerance(10));
test("One input inverts correctly", () => test("One input inverts correctly", () =>
expect(new Formula([1], undefined, (value, v1) => v1).invert(10)).compare_tolerance(1)); expect(
new Formula({ inputs: [1], evaluate: () => 10, invert: (value, v1) => v1 }).invert(
10
)
).compare_tolerance(1));
test("Two inputs inverts correctly", () => test("Two inputs inverts correctly", () =>
expect( expect(
new Formula([1, 2], undefined, (value, v1, v2) => v2).invert(10) new Formula({
inputs: [1, 2],
evaluate: () => 10,
invert: (value, v1, v2) => v2
}).invert(10)
).compare_tolerance(2)); ).compare_tolerance(2));
}); });
test("Formula with hasVariable", () => { describe("Formula with integrate", () => {
const formula = new Formula([], undefined, value => value, true); test("Zero input integrates correctly", () =>
expect(formula.isInvertible()).toBe(true); expect(
expect(formula.hasVariable()).toBe(true); new Formula({
inputs: [],
evaluate: () => 10,
integrate: () => 20
}).evaluateIntegral()
).compare_tolerance(20));
test("One input integrates correctly", () =>
expect(
new Formula({
inputs: [1],
evaluate: () => 10,
integrate: val => val ?? 20
}).evaluateIntegral()
).compare_tolerance(20));
test("Two inputs integrates correctly", () =>
expect(
new Formula({
inputs: [1, 2],
evaluate: (v1, v2) => 10,
integrate: (v1, v2) => 3
}).evaluateIntegral()
).compare_tolerance(3));
});
describe("Formula with invertIntegral", () => {
test("Zero input inverts integral correctly", () =>
expect(
new Formula({
inputs: [],
evaluate: () => 10,
invertIntegral: () => 1
}).invertIntegral(8)
).compare_tolerance(1));
test("One input inverts integral correctly", () =>
expect(
new Formula({
inputs: [1],
evaluate: () => 10,
invertIntegral: val => 1
}).invertIntegral(8)
).compare_tolerance(1));
test("Two inputs inverts integral correctly", () =>
expect(
new Formula({
inputs: [1, 2],
evaluate: (v1, v2) => 10,
invertIntegral: (v1, v2) => 1
}).invertIntegral(8)
).compare_tolerance(1));
});
});
describe("Buy Max", () => {
let resource: Resource;
beforeAll(() => {
resource = createResource(10);
});
describe("With spending", () => {
test("Throws on formula with non-invertible integral", () => {
const { maxAffordable, cost } = calculateMaxAffordable(
Formula.neg(10),
resource,
false
);
expect(() => maxAffordable.value).toThrow();
expect(() => cost.value).toThrow();
});
// https://www.desmos.com/calculator/5vgletdc1p
test("Calculates max affordable and cost correctly", () => {
const variable = Formula.variable(10);
const { maxAffordable, cost } = calculateMaxAffordable(
Formula.pow(1.05, variable),
resource,
false
);
expect(maxAffordable.value).compare_tolerance(47);
expect(cost.value).compare_tolerance(Decimal.pow(1.05, 47));
});
});
describe("Without spending", () => {
test("Throws on non-invertible formula", () => {
const { maxAffordable, cost } = calculateMaxAffordable(
Formula.abs(10),
resource,
false
);
expect(() => maxAffordable.value).toThrow();
expect(() => cost.value).toThrow();
});
// https://www.desmos.com/calculator/5vgletdc1p
test("Calculates max affordable and cost correctly", () => {
const variable = Formula.variable(10);
const { maxAffordable, cost } = calculateMaxAffordable(
Formula.pow(1.05, variable),
resource
);
expect(maxAffordable.value).compare_tolerance(7);
expect(cost.value).compare_tolerance(7.35);
});
}); });
}); });