/* @flow */

const SQRT_2PI = Math.sqrt(2 * Math.PI);

function cumulativeDistribution(z) {
    let sum = z,
        tmp = z;

    // 15 iterations are enough for 4-digit precision
    for (let i = 1; i < 15; i++) {
        tmp *= (z * z) / (2 * i + 1);
        sum += tmp;
    }
    return (
        Math.round((0.5 + (sum / SQRT_2PI) * Math.exp((-z * z) / 2)) * 1e4) /
        1e4
    );
}

/**
 * A standard normal table, also called the unit normal table or Z table,
 * is a mathematical table for the values of Φ (phi), which are the values of
 * the cumulative distribution function of the normal distribution.
 * It is used to find the probability that a statistic is observed below,
 * above, or between values on the standard normal distribution, and by
 * extension, any normal distribution.
 *
 * The probabilities are calculated using the
 * [Cumulative distribution function](https://en.wikipedia.org/wiki/Normal_distribution#Cumulative_distribution_function).
 * The table used is the cumulative, and not cumulative from 0 to mean
 * (even though the latter has 5 digits precision, instead of 4).
 */
const standardNormalTable /*: Array<number> */ = [];

for (let z = 0; z <= 3.09; z += 0.01) {
    standardNormalTable.push(cumulativeDistribution(z));
}

export default standardNormalTable;