Kotlin Calculating with BigDecimal vs Double

Question

I have 2 Functions. One uses BigInteger and BigDecimal. I want to calculate sin(z) using the Taylor series:

Here is my code:

fun sinus(z: BigDecimal, upperBound: Int = 100): BigDecimal = calcSin(z, upperBound)

fun cosinus(z: BigDecimal, upperBound: Int = 100): BigDecimal = calcSin(z, upperBound, false)

fun calcSin(z: BigDecimal, upperBound: Int = 100, isSin: Boolean = true): BigDecimal {
    var erg: BigDecimal = BigDecimal.ZERO
    for (n in 0..upperBound) {
//        val zaehler = (-1.0).pow(n).toBigDecimal() * z.pow(2 * n + (if (isSin) 1 else 0))
//        val nenner = fac(2 * n + (if (isSin) 1 else 0)).toBigDecimal()
        val zaehler = (-1.0).pow(n).toBigDecimal() * z.pow(2 * n + 1)
        val nenner = fac(2 * n + 1).toBigDecimal()
        erg += (zaehler / nenner)
    }
    return erg
}

fun calcSin(z: Double, upperBound: Int = 100): Double {
    var res = 0.0
    for (n in 0..upperBound) {
        val zaehler = (-1.0).pow(n) * z.pow(2 * n + 1)
        val nenner = fac(2 * n + 1, true)
        res += (zaehler / nenner)
    }
    return res
}

fun fac(n: Int): BigInteger = if (n == 0 || n == 1) BigInteger.ONE else n.toBigInteger() * fac(n - 1)

fun fac(n: Int, dummy: Boolean): Double = if (n == 0 || n == 1) 1.0 else n.toDouble() * fac(n - 1, dummy)

According to Google, Sin(1) is

0.8414709848

The Output of the following is however:

println("Sinus 1: ${sinus(1.0.toBigDecimal())}")
println("Sinus 1: ${sinus(1.0.toBigDecimal()).toDouble()}")
println("Sinus 1: ${sinus(1.0.toBigDecimal(), 1000)}")
println("Sinus 1: ${calcSin(1.0)}")

Output:

Sinus 1: 0.8414373208078281027995610599000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Sinus 1: 0.8414373208078281
Sinus 1: 0.8414373208078281027995610599000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Sinus 1: 0.8414709848078965

Wha am I missing? Why does the Double-Variant gives the correct value, while The BigDecimal doesn't? Even with 1000 Iterations. The commented out code was meant for calculation Cos as well, but wanted to figure out that Problem first, so i made both Functions look the same

Answer 1

In the BigDecimal variant, try replacing erg += (zaehler / nenner) with erg += (zaehler.divide(nenner, 20, RoundingMode.HALF_EVEN))

I suspect that the defaults for scaling the division results (as described here https://docs.oracle.com/en/java/javase/11/docs/api/java.base/java/math/BigDecimal.html) are not what you want.

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BTW - I assume that performance is not part of the exercise, otherwise your implementation of factorial is a low hanging fruit.