mathjslab/src/ComplexDecimal.spec.ts

MathJSLab - An interpreter with language syntax like MATLAB®/Octave, ISBN 978-65-00-82338-7.

import path from 'node:path';
import { ComplexDecimal } from './ComplexDecimal';

const __filenameMatch = __filename.match(new RegExp(`.*\\${path.sep}([^\\${path.sep}]+)\\.spec\\.([cm]?[jt]s)\$`))!;
const unitName = __filenameMatch[1];
const testExtension = __filenameMatch[2];

describe(`${unitName} unit test (.${testExtension} test file).`, () => {
    jest.setTimeout(40000);

    it(`${unitName} should be defined.`, () => {
        expect(ComplexDecimal).toBeDefined();
    }, 20);

    it('sin(x)^2+cos(x)^2 should be equal 1 for any value of x (first cycle)', () => {
        let result: boolean = true;
        // One-by-one degree
        for (let i = 0; i <= 2 * Math.PI; i += Math.PI / 180) {
            const value = ComplexDecimal.add(
                ComplexDecimal.power(ComplexDecimal.sin(new ComplexDecimal(i)), ComplexDecimal.newThis(2)),
                ComplexDecimal.power(ComplexDecimal.cos(new ComplexDecimal(i)), ComplexDecimal.newThis(2)),
            );
            result &&= value.re.toNumber() === 1 && value.im.toNumber() === 0; // converting to native number type to comparison.
            result &&= Boolean(ComplexDecimal.eq(value, ComplexDecimal.one()).re.toNumber()); // using ComplexDecimal.eq to comparison.
        }

        expect(result).toBe(true);
    }, 10000);

    it('sin(x)^2+cos(x)^2 should be equal 1 for lower values of x', () => {
        let result: boolean = true;
        for (let i = 0; i <= 1e-300; i += 1e-302) {
            const value = ComplexDecimal.add(
                ComplexDecimal.power(ComplexDecimal.sin(new ComplexDecimal(i)), ComplexDecimal.newThis(2)),
                ComplexDecimal.power(ComplexDecimal.cos(new ComplexDecimal(i)), ComplexDecimal.newThis(2)),
            );
            result &&= value.re.toNumber() === 1 && value.im.toNumber() === 0; // converting to native number type to comparison.
            result &&= Boolean(ComplexDecimal.eq(value, ComplexDecimal.one()).re.toNumber()); // using ComplexDecimal.eq to comparison.
        }

        expect(result).toBe(true);
    }, 200);

    it('e^(i*pi) should be equal -1', () => {
        const value = ComplexDecimal.exp(ComplexDecimal.mul(ComplexDecimal.onei(), ComplexDecimal.pi()));
        const result = Boolean(ComplexDecimal.eq(value, ComplexDecimal.minusone()).re.toNumber()); // using ComplexDecimal.eq to comparison.
        expect(result).toBe(true);
    }, 100);

    it('abs(sin(n*pi+pi/2)) == 1 for integer n >= 0', () => {
        let result: boolean = true;
        for (let n = 0; n < 1000; n++) {
            const value = ComplexDecimal.abs(ComplexDecimal.sin(ComplexDecimal.add(ComplexDecimal.mul(new ComplexDecimal(n), ComplexDecimal.pi()), ComplexDecimal.pidiv2())));
            result &&= Boolean(ComplexDecimal.eq(value, ComplexDecimal.one()).re.toNumber()); // using ComplexDecimal.eq to comparison.
        }
        expect(result).toBe(true);
    }, 30000);
});