diff --git a/src/__tests__/index.spec.ts b/src/__tests__/index.spec.ts index 07d3614..ac6e836 100644 --- a/src/__tests__/index.spec.ts +++ b/src/__tests__/index.spec.ts @@ -20,6 +20,8 @@ import { norm, valueToCents, monzoToCents, + tenneyHeight, + wilsonHeight, } from '../index'; describe('Array equality tester', () => { @@ -417,3 +419,203 @@ describe('Monzo size measure', () => { ); }); }); + +describe('Tenney complexity measure', () => { + it('calculates the complexity of 88', () => { + expect(tenneyHeight(88)).toBeCloseTo(4.477); + }); + + it('calculates the complexity of 11/8', () => { + expect(tenneyHeight('11/8')).toBeCloseTo(4.477); + }); + + it('calculates the complexity of -11/8', () => { + expect(tenneyHeight('-11/8')).toBeCloseTo(4.477); + }); + + it('calculates the complexity of 8/11', () => { + expect(tenneyHeight([3, 0, 0, 0, -1])).toBeCloseTo(4.477); + }); + + it('has a value for zero', () => { + expect(tenneyHeight(0)).toBe(Infinity); + }); + + it.skip('fuzzes the fraction property', () => { + for (let i = 0; i < 100000; ++i) { + const n = Math.floor(Math.random() * Number.MAX_SAFE_INTEGER); + const d = Math.floor(Math.random() * (Number.MAX_SAFE_INTEGER - 1)) + 1; + const f = new Fraction(n, d); + expect(tenneyHeight(f.n) + tenneyHeight(f.d)).toBeCloseTo( + tenneyHeight(f) + ); + } + }); + + it.skip('fuzzes the multiplicative property', () => { + for (let i = 0; i < 100000; ++i) { + const x = Math.floor(Math.random() * 94906265); + const y = Math.floor(Math.random() * 94906265); + expect(tenneyHeight(x) + tenneyHeight(y)).toBeCloseTo( + tenneyHeight(x * y) + ); + } + }); +}); + +describe('Wilson complexity measure', () => { + it('calculates the complexity of 88', () => { + expect(wilsonHeight(88)).toBe(17); + }); + + it('calculates the complexity of 11/8', () => { + expect(wilsonHeight('11/8')).toBe(17); + }); + + it('calculates the complexity of -11/8', () => { + expect(wilsonHeight('-11/8')).toBe(17); + }); + + it('calculates the complexity of 8/11', () => { + expect(wilsonHeight([3, 0, 0, 0, -1])).toBe(17); + }); + + it('calculates the complexity of -8/11', () => { + expect( + wilsonHeight( + new Map([ + [-1, 1], + [2, 3], + [11, -1], + ]) + ) + ).toBe(17); + }); + + it('has a value for zero', () => { + expect(wilsonHeight(0)).toBe(Infinity); + }); + + it.each([ + ['2/1', 2], + ['3/2', 5], + ['4/3', 7], + ['5/4', 9], + ['6/5', 10], + ['7/6', 12], + ['9/8', 12], + ['8/7', 13], + ['10/9', 13], + ['16/15', 16], + ['15/14', 17], + ['11/10', 18], + ['12/11', 18], + ['21/20', 19], + ['25/24', 19], + ['13/12', 20], + ['28/27', 20], + ['14/13', 22], + ['36/35', 22], + ['22/21', 23], + ['27/26', 24], + ['33/32', 24], + ['17/16', 25], + ['18/17', 25], + ['26/25', 25], + ['49/48', 25], + ['64/63', 25], + ['81/80', 25], + ['45/44', 26], + ['50/49', 26], + ['19/18', 27], + ['40/39', 27], + ['55/54', 27], + ['20/19', 28], + ['56/55', 29], + ['65/64', 30], + ['35/34', 31], + ['100/99', 31], + ['24/23', 32], + ['51/50', 32], + ['34/33', 33], + ['91/90', 33], + ['99/98', 33], + ['66/65', 34], + ['57/56', 35], + ['23/22', 36], + ['46/45', 36], + ['76/75', 36], + ['78/77', 36], + ['85/84', 36], + ['39/38', 37], + ['52/51', 37], + ['96/95', 37], + ['30/29', 39], + ['29/28', 40], + ['70/69', 40], + ['31/30', 41], + ['32/31', 41], + ['77/76', 41], + ['63/62', 46], + ['37/36', 47], + ['69/68', 47], + ['92/91', 47], + ['88/87', 49], + ['41/40', 52], + ['75/74', 52], + ['42/41', 53], + ['58/57', 53], + ['43/42', 55], + ['82/81', 55], + ['38/37', 58], + ['44/43', 58], + ['48/47', 58], + ['93/92', 61], + ['54/53', 64], + ['86/85', 67], + ['53/52', 70], + ['60/59', 71], + ['47/46', 72], + ['61/60', 73], + ['95/94', 73], + ['87/86', 77], + ['67/66', 83], + ['72/71', 83], + ['94/93', 83], + ['71/70', 85], + ['73/72', 85], + ['68/67', 88], + ['59/58', 90], + ['80/79', 92], + ['62/61', 94], + ['79/78', 97], + ['84/83', 97], + ['90/89', 102], + ['89/88', 106], + ['97/96', 110], + ['74/73', 112], + ['98/97', 113], + ['83/82', 126], + ])('Agrees with XenWiki on %s ~ %s', (fraction, height) => { + expect(wilsonHeight(fraction)).toBe(height); + }); + + it.skip('fuzzes the fraction property', () => { + for (let i = 0; i < 100; ++i) { + const n = Math.floor(Math.random() * 1073741823); + const d = Math.floor(Math.random() * 1073741822) + 1; + const f = new Fraction(n, d); + expect(wilsonHeight(f.n) + wilsonHeight(f.d)).toBe(wilsonHeight(f)); + } + }); + + it.skip('fuzzes the multiplicative property', () => { + for (let i = 0; i < 10000; ++i) { + const x = Math.floor(Math.random() * 32768); + const y = Math.floor(Math.random() * 32768); + expect(wilsonHeight(x) + wilsonHeight(y), `Failed on ${x} * ${y}`).toBe( + wilsonHeight(x * y) + ); + } + }); +}); diff --git a/src/__tests__/monzo.spec.ts b/src/__tests__/monzo.spec.ts index 40534d4..8bbf796 100644 --- a/src/__tests__/monzo.spec.ts +++ b/src/__tests__/monzo.spec.ts @@ -423,9 +423,25 @@ describe('Sparse monzos', () => { }); it.each([ - 49305423, 4104956, 8375509, 27826943, 44852222, 22932439, 46933379, - 59598447, 9693451, 54191546, 61834729, 26866018, 46410510, 47335837, + 49305423, + 4104956, + 8375509, + 27826943, + 44852222, + 22932439, + 46933379, + 59598447, + 9693451, + 54191546, + 61834729, + 26866018, + 46410510, + 47335837, 43839566, + 27470 * 5043, + 17719 * 21909, + 15812 * 27083, + 21097 * 29468, ])('works on a tough case %s found during fuzzing', n => { const exponentByPrime = primeFactorize(n); let m = 1; diff --git a/src/index.ts b/src/index.ts index 5d22e48..a633706 100644 --- a/src/index.ts +++ b/src/index.ts @@ -1,6 +1,6 @@ -import {Fraction, mmod} from './fraction'; -import {Monzo, monzoToBigNumeratorDenominator} from './monzo'; -import {PRIME_CENTS} from './primes'; +import {Fraction, FractionValue, mmod} from './fraction'; +import {Monzo, monzoToBigNumeratorDenominator, primeFactorize} from './monzo'; +import {LOG_PRIMES, PRIMES, PRIME_CENTS} from './primes'; import {sum} from './polyfills/sum-precise'; export * from './fraction'; @@ -500,3 +500,50 @@ export function monzoToCents(monzo: Monzo) { } return Math.log1p(Number(delta) / Number(denominator)) * NATS_TO_CENTS; } + +/** + * Given fraction p/q calculate log(abs(p*q)). + * @param value Rational number or an array of its prime exponents. + * @returns The Tenney-height of the number. + */ +export function tenneyHeight(value: Monzo | FractionValue) { + if (Array.isArray(value)) { + return dotPrecise( + value.map(x => Math.abs(x)), + LOG_PRIMES + ); + } + const {s, n, d} = new Fraction(value); + if (!s) { + return Infinity; + } + return Math.log(n) + Math.log(d); +} + +/** + * Given fraction p/q calculate sopfr(p) + sopfr(q), ignoring sign. + * @param value Rational number, an array of its prime exponents or a `Map` of its prime exponents. + * @returns Sum of prime factors with repetition of p*q. + */ +export function wilsonHeight( + value: Monzo | FractionValue | Map +) { + if (Array.isArray(value)) { + return dot( + value.map(x => Math.abs(x)), + PRIMES + ); + } + if (!(value instanceof Map)) { + value = primeFactorize(value); + } + if (value.has(0)) { + return Infinity; + } + value.delete(-1); + let result = 0; + for (const [prime, exponent] of value) { + result += Math.abs(exponent) * prime; + } + return result; +} diff --git a/src/monzo.ts b/src/monzo.ts index 93a8196..5279c3a 100644 --- a/src/monzo.ts +++ b/src/monzo.ts @@ -718,6 +718,18 @@ export function primeFactorize(value: FractionValue): Map { } else if (subFactor === 1241) { result.set(17, (result.get(17) ?? 0) + 1); result.set(73, (result.get(73) ?? 0) + 1); + } else if (subFactor === 1681) { + result.set(41, (result.get(41) ?? 0) + 2); + } else if (subFactor === 3149) { + result.set(47, (result.get(47) ?? 0) + 1); + result.set(67, (result.get(67) ?? 0) + 1); + } else if (subFactor === 3869) { + result.set(53, (result.get(53) ?? 0) + 1); + result.set(73, (result.get(73) ?? 0) + 1); + } else if (subFactor === 65773) { + result.set(17, (result.get(17) ?? 0) + 1); + result.set(53, (result.get(53) ?? 0) + 1); + result.set(73, (result.get(73) ?? 0) + 1); } else { result.set(subFactor, (result.get(subFactor) ?? 0) + 1); }