Merge pull request #14 from xenharmonic-devs/lens-add

Implement harmonic addition and subtraction

src/__tests__/fraction.spec.ts

@@ -371,4 +371,58 @@ describe('Fraction', () => {
     const fraction = new Fraction(3, 2);
     expect(fraction.geoRoundTo('10/9')!.equals('10000/6561')).toBe(true);
   });
+
+  it('has harmonic addition', () => {
+    const fraction = new Fraction('7/5');
+    expect(fraction.lensAdd('13/11').toFraction()).toBe('91/142');
+  });
+
+  it('has harmonic addition of zero (left)', () => {
+    const fraction = new Fraction(0);
+    expect(fraction.lensAdd('3/2').toFraction()).toBe('0');
+  });
+
+  it('has harmonic addition of zero (right)', () => {
+    const fraction = new Fraction('3/2');
+    expect(fraction.lensAdd(0).toFraction()).toBe('0');
+  });
+
+  it('has harmonic addition of zero (both)', () => {
+    const fraction = new Fraction(0);
+    expect(fraction.lensAdd(0).toFraction()).toBe('0');
+  });
+
+  it('has harmonic subtraction', () => {
+    const fraction = new Fraction('7/5');
+    expect(fraction.lensSub('13/11').toFraction()).toBe('-91/12');
+  });
+
+  it('has harmonic subtraction of zero (left)', () => {
+    const fraction = new Fraction(0);
+    expect(fraction.lensSub('3/2').toFraction()).toBe('0');
+  });
+
+  it('has harmonic subtraction of zero (right)', () => {
+    const fraction = new Fraction('3/2');
+    expect(fraction.lensSub(0).toFraction()).toBe('0');
+  });
+
+  it('has harmonic subtraction of zero (both)', () => {
+    const fraction = new Fraction(0);
+    expect(fraction.lensSub(0).toFraction()).toBe('0');
+  });
+
+  it('cancels harmonic addition with harmonic subtraction', () => {
+    const a = new Fraction(
+      Math.floor(Math.random() * 1000),
+      Math.floor(Math.random() * 1000) + 1
+    );
+    const b = new Fraction(
+      Math.floor(Math.random() * 1000),
+      Math.floor(Math.random() * 1000) + 1
+    );
+    const lensSum = a.lensAdd(b);
+    expect(lensSum.lensSub(b).equals(a)).toBe(true);
+    expect(lensSum.lensSub(a).equals(b)).toBe(true);
+  });
 });

src/fraction.ts

@@ -496,6 +496,34 @@ export class Fraction {
     return new Fraction(this.s * this.n * d - s * n * this.d, this.d * d);
   }
 
+  /**
+   * Perform harmonic addition of two rational numbers according to the thin lens equation f⁻¹ = u⁻¹ + v⁻¹
+   *
+   * Ex: new Fraction('5/3').lensAdd('3/2') => 15/19
+   */
+  lensAdd(other: FractionValue) {
+    const {s, n, d} = new Fraction(other);
+    if (!n) {
+      // Based on behavior in the limit where both terms become zero.
+      return new Fraction({s: 0, n: 0, d: 1});
+    }
+    return new Fraction(this.s * this.n * s * n, this.n * d + n * this.d);
+  }
+
+  /**
+   * Perform harmonic subtraction of two rational numbers u⁻¹ = f⁻¹ - v⁻¹ (rearranged thin lens equation)
+   *
+   * Ex: new Fraction('15/19').lensSub('3/2') => 5/3
+   */
+  lensSub(other: FractionValue) {
+    const {s, n, d} = new Fraction(other);
+    if (!n) {
+      // Based on behavior in the limit where both terms become zero.
+      return new Fraction({s: 0, n: 0, d: 1});
+    }
+    return new Fraction(this.s * this.n * s * n, n * this.d - this.n * d);
+  }
+
   /**
    * Multiplies two rational numbers
    *