Skip to content

Commit

Permalink
Move approximation methods to a separate file
Browse files Browse the repository at this point in the history
  • Loading branch information
@frostburn
frostburn committed Dec 25, 2023
1 parent 163299d commit 598a58d
Show file tree
Hide file tree
Showing 4 changed files with 389 additions and 383 deletions.
116 changes: 116 additions & 0 deletions src/__tests__/approximation.spec.ts
View file
Original file line number Diff line number Diff line change
@@ -0,0 +1,116 @@
import {describe, it, expect} from 'vitest';
import {
approximateOddLimit,
approximatePrimeLimit,
approximatePrimeLimitWithErrors,
getConvergents,
} from '../approximation';
import {valueToCents} from '../conversion';
import {PRIMES} from '../primes';

describe('Odd limit approximator', () => {
it('can approximate tau in the 15-odd-limit', () => {
const approximation = approximateOddLimit(valueToCents(2 * Math.PI), 15)[0];
expect(approximation.equals('44/7')).toBeTruthy();
expect(approximation.valueOf()).toBeCloseTo(2 * Math.PI);
});

it('can approximate e in the 21-odd-limit', () => {
const approximations = approximateOddLimit(valueToCents(Math.E), 21);
expect(approximations[0].equals('19/7')).toBeTruthy();
expect(approximations[0].valueOf()).toBeCloseTo(Math.E);
expect(approximations[7].equals('21/8')).toBeTruthy();
expect(approximations[7].valueOf()).toBeCloseTo(Math.E, 0);
});
});

describe('Prime limit approximator', () => {
it('can approximate pi in the 11-limit', () => {
const approximation = approximatePrimeLimit(
valueToCents(Math.PI),
PRIMES.indexOf(11),
3
)[0];
expect(approximation.equals('12544/3993')).toBeTruthy();
expect(approximation.valueOf()).toBeCloseTo(Math.PI);
});

it('can approximate pi in the 13-limit with a small sized result', () => {
const approximations = approximatePrimeLimit(
valueToCents(Math.PI),
PRIMES.indexOf(13),
3,
15,
4
);
expect(approximations).toHaveLength(4);
});

it('can approximate the square root of two in the 7-limit within maximum error', () => {
const approximationsAndErrors = approximatePrimeLimitWithErrors(
600,
PRIMES.indexOf(7),
5,
10
);
expect(approximationsAndErrors).toHaveLength(28);
approximationsAndErrors.forEach(([approximation, error]) => {
const cents = valueToCents(approximation.valueOf());
const calculatedError = Math.abs(cents - 600);
expect(error).toBeCloseTo(calculatedError);
expect(calculatedError).toBeLessThanOrEqual(10);
});
});
});

describe('Convergent calculator', () => {
it('calculates the convergents of pi', () => {
const convergents = getConvergents(Math.PI, undefined, 10);
expect(convergents).toHaveLength(10);
expect(convergents[0].equals(3)).toBeTruthy();
expect(convergents[1].equals('22/7')).toBeTruthy();
expect(convergents[2].equals('333/106')).toBeTruthy();
expect(convergents[3].equals('355/113')).toBeTruthy();
expect(convergents[4].equals('103993/33102')).toBeTruthy();
expect(convergents[5].equals('104348/33215')).toBeTruthy();
expect(convergents[6].equals('208341/66317')).toBeTruthy();
expect(convergents[7].equals('312689/99532')).toBeTruthy();
expect(convergents[8].equals('833719/265381')).toBeTruthy();
expect(convergents[9].equals('1146408/364913')).toBeTruthy();
});

it('calculates the semiconvergents of pi', () => {
const semiconvergents = getConvergents(Math.PI, undefined, 13, true);
expect(semiconvergents).toHaveLength(13);
expect(semiconvergents[0].equals(3)).toBeTruthy();
expect(semiconvergents[1].equals('13/4')).toBeTruthy();
expect(semiconvergents[2].equals('16/5')).toBeTruthy();
expect(semiconvergents[3].equals('19/6')).toBeTruthy();
expect(semiconvergents[4].equals('22/7')).toBeTruthy();
expect(semiconvergents[5].equals('179/57')).toBeTruthy();
expect(semiconvergents[6].equals('201/64')).toBeTruthy();
expect(semiconvergents[7].equals('223/71')).toBeTruthy();
expect(semiconvergents[8].equals('245/78')).toBeTruthy();
expect(semiconvergents[9].equals('267/85')).toBeTruthy();
expect(semiconvergents[10].equals('289/92')).toBeTruthy();
expect(semiconvergents[11].equals('311/99')).toBeTruthy();
expect(semiconvergents[12].equals('333/106')).toBeTruthy();

let error = Infinity;
semiconvergents.forEach(semiconvergent => {
const newError = Math.abs(Math.PI - semiconvergent.valueOf());
expect(newError).toBeLessThan(error);
error = newError;
});
});

it('calculates the non-monotonic semiconvergents of pi', () => {
const semiconvergents = getConvergents(Math.PI, undefined, 5, true, true);
expect(semiconvergents).toHaveLength(5);
expect(semiconvergents[0].equals(3)).toBeTruthy();
expect(semiconvergents[1].equals(4)).toBeTruthy();
expect(semiconvergents[2].equals('7/2')).toBeTruthy();
expect(semiconvergents[3].equals('10/3')).toBeTruthy();
expect(semiconvergents[4].equals('13/4')).toBeTruthy();
});
});
112 changes: 0 additions & 112 deletions src/__tests__/index.spec.ts
View file
Original file line number Diff line number Diff line change
@@ -1,8 +1,5 @@
import {describe, it, expect} from 'vitest';
import {
approximateOddLimit,
approximatePrimeLimit,
approximatePrimeLimitWithErrors,
arraysEqual,
binomial,
circleDifference,
Expand All @@ -12,10 +9,8 @@ import {
dot,
extendedEuclid,
gcd,
getConvergents,
iteratedEuclid,
norm,
PRIMES,
valueToCents,
} from '../index';

Expand Down Expand Up @@ -78,113 +73,6 @@ describe('binomial coefficient', () => {
});
});

describe('Odd limit approximator', () => {
it('can approximate tau in the 15-odd-limit', () => {
const approximation = approximateOddLimit(valueToCents(2 * Math.PI), 15)[0];
expect(approximation.equals('44/7')).toBeTruthy();
expect(approximation.valueOf()).toBeCloseTo(2 * Math.PI);
});

it('can approximate e in the 21-odd-limit', () => {
const approximations = approximateOddLimit(valueToCents(Math.E), 21);
expect(approximations[0].equals('19/7')).toBeTruthy();
expect(approximations[0].valueOf()).toBeCloseTo(Math.E);
expect(approximations[7].equals('21/8')).toBeTruthy();
expect(approximations[7].valueOf()).toBeCloseTo(Math.E, 0);
});
});

describe('Prime limit approximator', () => {
it('can approximate pi in the 11-limit', () => {
const approximation = approximatePrimeLimit(
valueToCents(Math.PI),
PRIMES.indexOf(11),
3
)[0];
expect(approximation.equals('12544/3993')).toBeTruthy();
expect(approximation.valueOf()).toBeCloseTo(Math.PI);
});

it('can approximate pi in the 13-limit with a small sized result', () => {
const approximations = approximatePrimeLimit(
valueToCents(Math.PI),
PRIMES.indexOf(13),
3,
15,
4
);
expect(approximations).toHaveLength(4);
});

it('can approximate the square root of two in the 7-limit within maximum error', () => {
const approximationsAndErrors = approximatePrimeLimitWithErrors(
600,
PRIMES.indexOf(7),
5,
10
);
expect(approximationsAndErrors).toHaveLength(28);
approximationsAndErrors.forEach(([approximation, error]) => {
const cents = valueToCents(approximation.valueOf());
const calculatedError = Math.abs(cents - 600);
expect(error).toBeCloseTo(calculatedError);
expect(calculatedError).toBeLessThanOrEqual(10);
});
});
});

describe('Convergent calculator', () => {
it('calculates the convergents of pi', () => {
const convergents = getConvergents(Math.PI, undefined, 10);
expect(convergents).toHaveLength(10);
expect(convergents[0].equals(3)).toBeTruthy();
expect(convergents[1].equals('22/7')).toBeTruthy();
expect(convergents[2].equals('333/106')).toBeTruthy();
expect(convergents[3].equals('355/113')).toBeTruthy();
expect(convergents[4].equals('103993/33102')).toBeTruthy();
expect(convergents[5].equals('104348/33215')).toBeTruthy();
expect(convergents[6].equals('208341/66317')).toBeTruthy();
expect(convergents[7].equals('312689/99532')).toBeTruthy();
expect(convergents[8].equals('833719/265381')).toBeTruthy();
expect(convergents[9].equals('1146408/364913')).toBeTruthy();
});

it('calculates the semiconvergents of pi', () => {
const semiconvergents = getConvergents(Math.PI, undefined, 13, true);
expect(semiconvergents).toHaveLength(13);
expect(semiconvergents[0].equals(3)).toBeTruthy();
expect(semiconvergents[1].equals('13/4')).toBeTruthy();
expect(semiconvergents[2].equals('16/5')).toBeTruthy();
expect(semiconvergents[3].equals('19/6')).toBeTruthy();
expect(semiconvergents[4].equals('22/7')).toBeTruthy();
expect(semiconvergents[5].equals('179/57')).toBeTruthy();
expect(semiconvergents[6].equals('201/64')).toBeTruthy();
expect(semiconvergents[7].equals('223/71')).toBeTruthy();
expect(semiconvergents[8].equals('245/78')).toBeTruthy();
expect(semiconvergents[9].equals('267/85')).toBeTruthy();
expect(semiconvergents[10].equals('289/92')).toBeTruthy();
expect(semiconvergents[11].equals('311/99')).toBeTruthy();
expect(semiconvergents[12].equals('333/106')).toBeTruthy();

let error = Infinity;
semiconvergents.forEach(semiconvergent => {
const newError = Math.abs(Math.PI - semiconvergent.valueOf());
expect(newError).toBeLessThan(error);
error = newError;
});
});

it('calculates the non-monotonic semiconvergents of pi', () => {
const semiconvergents = getConvergents(Math.PI, undefined, 5, true, true);
expect(semiconvergents).toHaveLength(5);
expect(semiconvergents[0].equals(3)).toBeTruthy();
expect(semiconvergents[1].equals(4)).toBeTruthy();
expect(semiconvergents[2].equals('7/2')).toBeTruthy();
expect(semiconvergents[3].equals('10/3')).toBeTruthy();
expect(semiconvergents[4].equals('13/4')).toBeTruthy();
});
});

describe('Dot product', () => {
it('can be used with all number arrays', () => {
const a = new Float32Array([1, 2, 3, 4]);
Expand Down
Loading

0 comments on commit 598a58d

Please sign in to comment.