Calculate empirical formulas of chemical compounds given their stoichiometric mass composition data (assuming a ~1% error rate)

empirical.js

// Calculate empirical formulas of chemical compounds given their stochiometric 
// composition data

// USAGE:
// `node index.js {percentage}%{symbol} ...`

// Imports
const MolarMass = require('molarmass.js')
const molar = new MolarMass()

const lcm = require('lcm')


// Argument parsing
const args = process.argv.slice(2)
switch ( args.length ) {
    case 0: throw new Error('No arguments given')
    case 1: console.log(args[0].split('%')[1] + '1'); process.exit(0)
}


// Embedded utils
let simplify = (continued) => {
    // Simplify a continued fraction 
    // into a fraction with numerator `p` 
    // and denominator `q`:
    // return [p, q]

    let p = continued[continued.length - 1]
    let q = 1

    for ( let i = continued.length - 2; i >= 0; i-- ) {
        
        // Cache `p` and `q`
        let p_cache = p
        let q_cache = q

        
        // Update `p` and `q`
        
        // Reciprocal
        p = q_cache
        q = p_cache

        // Add
        p += continued[i] * q

    }

    return [p, q]

}

let rational = (decimal, error=0.01) => {
    // Express `decimal` as a continued fraction,
    // then simplify the result and 
    // return the numerator (p) and denominator (q)
    // in an array: [p, q]
    // while guaranteeing that |p/(q*d) - 1| <= e
    // where e is the error and d is `decimal`

    // Express as continued fraction
    let expansion = []
    let latest = decimal
    let p = Math.floor(decimal); let q = 1;

    while ( Math.abs(p / (q * decimal) - 1) > error ) {

        // Append to expansion
        expansion.push(
            Math.floor(latest)
        )

        // Update latest
        latest = 1 / (latest - Math.floor(latest))

        // Update p and q
        fraction = simplify(expansion)
        p = fraction[0]; q = fraction[1]

    }

    return [p, q]

}


// Main
let map = {}

// Parse arguments as raw percentages (masses) into `map`
for ( let arg of args ) {

    let [percentage, symbol] = arg.split('%')
    map[symbol] = parseFloat(percentage)

}

// Convert masses to moles
for ( let [symbol, mass] of Object.entries(map) ) {
    map[symbol] = mass / molar.getMolarMass(symbol)
}

// Convert moles to ratios (in terms of first element)
const first = map[Object.keys(map)[0]]
for ( let [symbol, moles] of Object.entries(map) ) {
    map[symbol] = moles / first 
}

// Convert ratios to rational approximations ([p, q])
for ( let [symbol, ratio] of Object.entries(map) ) {
    map[symbol] = rational(ratio)
}

// Get rid of all the denominators (`q`)
let denominators = Object.values(map).map(fraction => fraction[1])
let k = 1

for ( let denominator of denominators ) k = lcm(k, denominator)
for ( let [symbol, [p, q]] of Object.entries(map) ) {
    map[symbol] = Math.floor(k * p / q)
}


// Print
let str = ''
for ( let [symbol, subscript] of Object.entries(map) ) {
    str += symbol + subscript
}

console.log(str)