// 1-15-Kotlin.kt

import kotlin.math.abs
import kotlin.math.sin

// Kotlin has syntax that resembles languages such as
// Java and C++, but it also has some important
// differences. For example, the type follows the
// variable name:
//
//     x: Double
//
// Variables declared with 'var' may be modified,
// while variables declared with 'val' may not.

// mySin(x: Double): Double
//
// Approximate sin(x) using the Taylor series
//
//                 x^3   x^5   x^7
//     sin(x) = x - --- + --- - --- + ...
//                  3!    5!    7!
//
// Rather than calculating each power and factorial
// separately, calculate each term from the previous
// term:
//
//                    x^2
//     next = -term -----------,
//                  n(n + 1)
//
// where n takes the values 2, 4, 6, ...
fun mySin(x: Double): Double {
    if (!x.isFinite()) {
        return Double.NaN
    }

    var result = x
    var term = x
    var n = 2.0

    while (true) {
        term *= -(x/n)*(x/(n + 1.0))

        if (abs(term) < 1e-16) {
            break
        }

        result += term
        n += 2.0
    }

    return result
}

fun main() {
    val x = 3.2

    println("mySin(x): ${mySin(x)}")
    println("sin(x): ${sin(x)}")
    println("reference: ${-0.058374143427579909137}")

    println("mySin(Double.POSITIVE_INFINITY): " +
            "${mySin(Double.POSITIVE_INFINITY)}")
}