WIP: Implement a method for accurately measuring the sizes of small c…

…ommas

src/__tests__/index.spec.ts

@@ -19,6 +19,7 @@ import {
   iteratedEuclid,
   norm,
   valueToCents,
+  monzoToCents,
 } from '../index';
 
 describe('Array equality tester', () => {
@@ -382,3 +383,23 @@ describe('Constant structure checker with a margin of equivalence', () => {
     expect(hasMarginConstantStructure([1199, 1200], 2)).toBe(false);
   });
 });
+
+describe('Monzo size measure', () => {
+  it('calculates the size of the perfect fourth accurately', () => {
+    expect(monzoToCents([2, -1])).toBeCloseTo(498.0449991346125, 12);
+  });
+
+  it('calculates the size of the neutrino accurately', () => {
+    expect(monzoToCents([1889, -2145, 138, 424])).toBeCloseTo(
+      1.6361187484440885e-10,
+      24
+    );
+  });
+
+  it('calculates the size of the demiquartervice comma accurately', () => {
+    expect(monzoToCents([-3, 2, -1, -1, 0, 0, -1, 0, 2])).toBeCloseTo(
+      0.3636664332386927,
+      14
+    );
+  });
+});

src/index.ts

@@ -1,4 +1,6 @@
 import {Fraction, mmod} from './fraction';
+import {Monzo, monzoToBigInt} from './monzo';
+import {PRIME_CENTS} from './primes';
 
 export * from './fraction';
 export * from './primes';
@@ -449,3 +451,28 @@ export function hasMarginConstantStructure(
   }
   return true;
 }
+
+const NATS_TO_CENTS = 1200 / Math.LN2;
+const IEEE_LIMIT = 2n ** 1024n;
+
+export function monzoToCents(monzo: Monzo) {
+  // TODO: dotPrecise
+  const result = dot(monzo, PRIME_CENTS);
+  if (Math.abs(result) > 10) {
+    return result;
+  }
+  for (const component of monzo) {
+    if (!Number.isInteger(component)) {
+      return result;
+    }
+  }
+  // TODO: monzoToBigNumeratorDenominator
+  const p = monzoToBigInt(monzo.map(c => Math.max(0, c)));
+  let q = monzoToBigInt(monzo.map(c => Math.max(0, -c)));
+  let n = p - q;
+  while (n > IEEE_LIMIT || q > IEEE_LIMIT) {
+    n >>= 1n;
+    q >>= 1n;
+  }
+  return Math.log1p(Number(n) / Number(q)) * NATS_TO_CENTS;
+}