Implement step-wise functions

src/game/formulas.ts

@@ -432,6 +432,46 @@ export default class Formula<T extends [FormulaSource] | FormulaSource[]> {
         );
     }
 
+    /**
+     * Creates a step-wise formula. After {@ref start} the formula will have an additional modifier.
+     * This function assumes the incoming {@ref value} will be continuous and monotonically increasing.
+     * @param value The value before applying the step
+     * @param start The value at which to start applying the step
+     * @param formulaModifier How this step should modify the formula. The incoming value will be the unmodified formula value _minus the start value_. So for example if an incoming formula evaluates to 200 and has a step that starts at 150, the formulaModifier would be given 50 as the parameter
+     */
+    public static step<T extends FormulaSource>(
+        value: T,
+        start: ProcessedComputable<DecimalSource>,
+        formulaModifier: (value: Ref<DecimalSource>) => GenericFormula
+    ) {
+        const lhsRef = ref<DecimalSource>(0);
+        const formula = formulaModifier(lhsRef);
+        function evalStep(lhs: DecimalSource) {
+            if (Decimal.lt(lhs, unref(start))) {
+                return lhs;
+            }
+            lhsRef.value = Decimal.sub(lhs, unref(start));
+            return Decimal.add(formula.evaluate(), unref(start));
+        }
+        function invertStep(value: DecimalSource, lhs: FormulaSource) {
+            if (hasVariable(lhs)) {
+                if (Decimal.gt(value, unref(start))) {
+                    value = Decimal.add(
+                        formula.invert(Decimal.sub(value, unref(start))),
+                        unref(start)
+                    );
+                }
+                return lhs.invert(value);
+            }
+            throw "Could not invert due to no input being a variable";
+        }
+        return new Formula(
+            [value],
+            evalStep,
+            formula.isInvertible() && !formula.hasVariable() ? invertStep : undefined
+        );
+    }
+
     public static constant(value: InvertibleFormulaSource): InvertibleFormula {
         return new Formula([value]) as InvertibleFormula;
     }

tests/game/formulas.test.ts

@@ -1,7 +1,7 @@
 import Formula, { GenericFormula, InvertibleFormula, unrefFormulaSource } from "game/formulas";
 import Decimal, { DecimalSource, format } from "util/bignum";
 import { beforeAll, describe, expect, test } from "vitest";
-import { ref } from "vue";
+import { Ref, ref } from "vue";
 
 type FormulaFunctions = keyof GenericFormula & keyof typeof Formula & keyof typeof Decimal;
 
@@ -53,10 +53,10 @@ function testConstant(
         beforeAll(() => {
             formula = formulaFunc();
         });
-        test("evaluates correctly", () =>
+        test("Evaluates correctly", () =>
             expect(formula.evaluate()).compare_tolerance(expectedValue));
-        test("invert is pass-through", () => expect(formula.invert(25)).compare_tolerance(25));
+        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));
+        test("Is not marked as having a variable", () => expect(formula.hasVariable()).toBe(false));
     });
 }
 
@@ -475,3 +475,58 @@ describe("Variables", () => {
         );
     });
 });
+
+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(true);
+        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 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("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));
+    });
+});