import { componentInterface, includeComponent } from '../../factory'

const getMathInfo = async (): Promise<componentInterface> => {
    return {
        acos: Math.acos(0.5),
        asin: integrate(Math.asin, -1, 1, 97),
        atan: integrate(Math.atan, -1, 1, 97),
        cos: integrate(Math.cos, 0, Math.PI, 97),
        cosh: Math.cosh(9/7),
        e: Math.E,
        largeCos: Math.cos(1e20),
        largeSin: Math.sin(1e20),
        largeTan: Math.tan(1e20),
        log: Math.log(1000),
        pi: Math.PI,
        sin: integrate(Math.sin, -Math.PI, Math.PI, 97),
        sinh: integrate(Math.sinh, -9/7, 7/9, 97),
        sqrt: Math.sqrt(2),
        tan: integrate(Math.tan, 0, 2 * Math.PI, 97),
        tanh: integrate(Math.tanh, -9/7, 7/9, 97),
    }
}

/** This might be a little excessive, but I wasn't sure what number to pick for some of the
 * trigonometric functions. Using an integral here, so a few numbers are calculated. However,
 * I do this mainly for those integrals that sum up to a small value, otherwise there's no point.
*/ 

const integrate = (f: (x: number) => number, a: number, b: number, n: number): number => {
    const h = (b - a) / n;
    let sum = 0;
    for (let i = 0; i < n; i++) {
        const x = a + (i + 0.5) * h;
        sum += f(x);
    }
    return sum * h;
};

includeComponent('math', getMathInfo);