Pre-reduce fraction multiplication and division to stay within safe l…

…imits

src/__tests__/fraction.spec.ts

@@ -440,4 +440,11 @@ describe('Fraction', () => {
       foo = foo.mul(foo);
     }
   });
+
+  it('multiplies large cancelling factors', () => {
+    const one = new Fraction('1234567890/987654321').mul(
+      '987654321/1234567890'
+    );
+    expect(one.equals(1)).toBe(true);
+  });
 });

src/__tests__/monzo.spec.ts

@@ -89,6 +89,12 @@ describe('Fraction to monzo converter', () => {
     ).toBeTruthy();
   });
 
+  it('converts a Pythagorean interval', () => {
+    const [monzo, residual] = toMonzoAndResidual('129140163/134217728', 6);
+    expect(monzo).toEqual([-27, 17, 0, 0, 0, 0]);
+    expect(residual.equals(1)).toBe(true);
+  });
+
   it('leaves residual 0 for zero (vector part)', () => {
     const [monzo, residual] = toMonzoAndResidual(0, 1);
     expect(residual.equals(0)).toBeTruthy();

src/fraction.ts

@@ -528,7 +528,13 @@ export class Fraction {
    **/
   mul(other: FractionValue) {
     const {s, n, d} = new Fraction(other);
-    return new Fraction(this.s * this.n * s * n, this.d * d);
+    // Must pre-reduce to avoid blowing the limits
+    const ndFactor = gcd(this.n, d);
+    const dnFactor = gcd(this.d, n);
+    return new Fraction(
+      this.s * (this.n / ndFactor) * s * (n / dnFactor),
+      (this.d / dnFactor) * (d / ndFactor)
+    );
   }
 
   /**
@@ -541,7 +547,13 @@ export class Fraction {
     if (n === 0) {
       throw new Error('Division by Zero');
     }
-    return new Fraction(this.s * this.n * s * d, this.d * n);
+    // Must pre-reduce to avoid blowing the limits
+    const nFactor = gcd(this.n, n);
+    const dFactor = gcd(this.d, d);
+    return new Fraction(
+      this.s * (this.n / nFactor) * s * (d / dFactor),
+      (this.d / dFactor) * (n / nFactor)
+    );
   }
 
   /**