feat(lib): support rationalizing decimal arguments to Rational

src/math/rational.ts

@@ -54,10 +54,20 @@ export class Rational
   #d: number;
 
   constructor(numerator: number, denominator: number = 1) {
-    assertInteger(numerator, denominator);
+    if (denominator === 0) {
+      throw new RangeError("Cannot divide by zero");
+    }
 
-    this.#n = numerator;
-    this.#d = denominator;
+    if (!Number.isInteger(numerator) || !Number.isInteger(denominator)) {
+      const n = new Rational(...Rational.#rationalize(numerator));
+      const self = n.div(...Rational.#rationalize(denominator));
+
+      this.#n = self.numerator;
+      this.#d = self.denominator;
+    } else {
+      this.#n = numerator;
+      this.#d = denominator;
+    }
 
     this.#simplify();
   }
@@ -77,9 +87,7 @@ export class Rational
       ? base
       : typeof base === "string"
       ? Rational.parse(base)
-      : typeof opt === "number"
-      ? (assertInteger(base, opt), new Rational(base, opt))
-      : (assertInteger(base), new Rational(base, opt));
+      : new Rational(base, opt);
   }
 
   static parse(fraction: string): Rational {
@@ -89,18 +97,53 @@ export class Rational
     if (second !== undefined) {
       const denominator = Number(dString);
       const numerator = Number(first) * denominator + Number(second);
-
-      assertInteger(numerator, denominator);
       return new Rational(numerator, denominator);
     } else {
       const denominator = Number(dString);
       const numerator = Number(first);
-
-      assertInteger(numerator, denominator);
       return new Rational(numerator, denominator);
     }
   }
 
+  static #rationalize(
+    n: number,
+    precision: number = 0.0000001
+  ): [number, number] {
+    // TODO: implement with Stern-Brocot tree?
+    // https://en.wikipedia.org/wiki/Stern%E2%80%93Brocot_tree
+
+    // Continued fraction method
+    // https://en.wikipedia.org/wiki/Continued_fraction
+    if (Number.isInteger(n)) return [n, 1];
+
+    function integerDecimal(n: number): [number, number] {
+      return [Math.trunc(n), n % 1];
+    }
+
+    const components = [];
+    let x = n;
+    while (true) {
+      const [integer, decimal] = integerDecimal(x);
+      components.unshift(integer);
+
+      if (decimal < precision) {
+        break;
+      }
+
+      if (decimal !== 0) {
+        x = 1 / decimal;
+      }
+    }
+
+    const base = components.pop()!;
+    let r = new Rational(0);
+    for (const c of components) {
+      r = new Rational(c).add(r).recip();
+    }
+    r = r.add(base);
+    return [r.numerator, r.denominator];
+  }
+
   #simplify() {
     const factor = gcf(this.numerator, this.denominator);
     if (factor !== 1) {
@@ -143,10 +186,7 @@ export class Rational
   add(...addend: RationalLike): Rational {
     const other = Rational.from(...addend);
     if (other.denominator === this.denominator) {
-      return new Rational(
-        this.numerator + other.numerator,
-        this.denominator
-      );
+      return new Rational(this.numerator + other.numerator, this.denominator);
     }
 
     const { denominator, numerator, otherNumerator } = this.#factor(other);
@@ -156,10 +196,7 @@ export class Rational
   sub(...subtrahend: RationalLike): Rational {
     const other = Rational.from(...subtrahend);
     if (other.denominator === this.denominator) {
-      return new Rational(
-        this.numerator - other.numerator,
-        this.denominator
-      );
+      return new Rational(this.numerator - other.numerator, this.denominator);
     }
 
     const { denominator, numerator, otherNumerator } = this.#factor(other);
@@ -200,10 +237,7 @@ export class Rational
   }
 
   abs(): Rational {
-    return new Rational(
-      Math.abs(this.numerator),
-      Math.abs(this.denominator)
-    );
+    return new Rational(Math.abs(this.numerator), Math.abs(this.denominator));
   }
 
   eq(...other: RationalLike): boolean {

test/math/rational.test.ts

@@ -3,12 +3,6 @@ import { Rational, FRACTION_SLASH } from "../../src/math";
 
 describe("Rational", () => {
   describe("constructor", () => {
-    it("throws with non-integral arguments", () => {
-      expect(() => new Rational(2, 3.5)).toThrowError(
-        "Arguments must be integers"
-      );
-    });
-
     it("constructs a rational", () => {
       const r = new Rational(2, 9);
       expect(r.numerator).toBe(2);
@@ -19,6 +13,14 @@ describe("Rational", () => {
       const r = new Rational(8, -24);
       expect([r.numerator, r.denominator]).toStrictEqual([-1, 3]);
     });
+
+    it("constructs from decimals", () => {
+      const r = new Rational(4.462365591397849);
+      expect([r.numerator, r.denominator]).toStrictEqual([415, 93]);
+
+      const s = new Rational(5 / 6548646);
+      expect([s.numerator, s.denominator]).toStrictEqual([5, 6548646]);
+    });
   });
 
   describe("parse", () => {
@@ -50,10 +52,9 @@ describe("Rational", () => {
       expect(fiveAndOneSeventh.denominator).toBe(7);
     });
 
-    it("throws with decimals", () => {
-      expect(() => Rational.parse("9.3 / 5")).toThrowError(
-        "Arguments must be integers"
-      );
+    it("parses decimals", () => {
+      const r = Rational.parse("9.3 / 5");
+      expect([r.numerator, r.denominator]).toStrictEqual([93, 50]);
     });
   });
 
@@ -76,10 +77,9 @@ describe("Rational", () => {
       expect(r.denominator).toBe(11);
     });
 
-    it("throws with decimals", () => {
-      expect(() => Rational.from("1 / 4.7")).toThrowError(
-        "Arguments must be integers"
-      );
+    it("parses decimals", () => {
+      const r = Rational.from("1 / 4.7");
+      expect([r.numerator, r.denominator]).toStrictEqual([10, 47]);
     });
   });
 
@@ -102,30 +102,22 @@ describe("Rational", () => {
     });
 
     it("adds similar fractions", () => {
-      const fourths = Rational.from("1 / 4").add(
-        Rational.from("2 / 4")
-      );
+      const fourths = Rational.from("1 / 4").add(Rational.from("2 / 4"));
       expect([fourths.numerator, fourths.denominator]).toStrictEqual([3, 4]);
 
-      const thirteenths = new Rational(5, 13).add(
-        new Rational(1, 13)
-      );
+      const thirteenths = new Rational(5, 13).add(new Rational(1, 13));
       expect([thirteenths.numerator, thirteenths.denominator]).toStrictEqual([
         6, 13,
       ]);
     });
 
     it("adds dissimilar fractions", () => {
-      const thirtyFifths = new Rational(6, 7).add(
-        new Rational(1, 5)
-      );
+      const thirtyFifths = new Rational(6, 7).add(new Rational(1, 5));
       expect([thirtyFifths.numerator, thirtyFifths.denominator]).toStrictEqual([
         37, 35,
       ]);
 
-      const twentyEigths = new Rational(2, 7).add(
-        new Rational(1, 4)
-      );
+      const twentyEigths = new Rational(2, 7).add(new Rational(1, 4));
       expect([twentyEigths.numerator, twentyEigths.denominator]).toStrictEqual([
         15, 28,
       ]);
@@ -139,30 +131,22 @@ describe("Rational", () => {
     });
 
     it("subtracts similar fractions", () => {
-      const fourths = Rational.from("1 / 4").sub(
-        Rational.from("2 / 4")
-      );
+      const fourths = Rational.from("1 / 4").sub(Rational.from("2 / 4"));
       expect([fourths.numerator, fourths.denominator]).toStrictEqual([-1, 4]);
 
-      const thirteenths = new Rational(5, 13).sub(
-        new Rational(1, 13)
-      );
+      const thirteenths = new Rational(5, 13).sub(new Rational(1, 13));
       expect([thirteenths.numerator, thirteenths.denominator]).toStrictEqual([
         4, 13,
       ]);
     });
 
     it("subtracts dissimilar fractions", () => {
-      const thirtyFifths = new Rational(6, 7).sub(
-        new Rational(1, 5)
-      );
+      const thirtyFifths = new Rational(6, 7).sub(new Rational(1, 5));
       expect([thirtyFifths.numerator, thirtyFifths.denominator]).toStrictEqual([
         23, 35,
       ]);
 
-      const twentyEigths = new Rational(2, 7).sub(
-        new Rational(1, 4)
-      );
+      const twentyEigths = new Rational(2, 7).sub(new Rational(1, 4));
       expect([twentyEigths.numerator, twentyEigths.denominator]).toStrictEqual([
         1, 28,
       ]);