Monte Carlo estimation of Pi

MonteCarlo.kt

import kotlin.math.PI
import kotlin.math.abs
import kotlin.math.sqrt
import kotlin.random.Random
import kotlin.time.ExperimentalTime
import kotlin.time.measureTimedValue

object MonteCarlo {

    fun estimatePi(nrPicks: Int = 1_000_000_000) =
        generateSequence { pickRandomPoint() }
            .take(nrPicks)
            .filter { it.distanceFromCenter <= 1 }
            .count()
            .toDouble()
            .let { it / nrPicks * 4 }

    private fun pickRandomPoint() =
        UnitSquarePosition(
            Random.nextDouble(-1.0, 1.0),
            Random.nextDouble(-1.0, 1.0),
        )

    private data class UnitSquarePosition(private val x: Double, private val y: Double) {
        init {
            if (x !in -1.0..1.0) error("X coordinate outside the unit square: $x")
            if (y !in -1.0..1.0) error("Y coordinate outside the unit square: $y")
        }

        val distanceFromCenter = sqrt(x * x + y * y)
    }
}

/*
 * Sample output:
 *
 * Running the estimation with 500.000.000 picks...
 * Monte Carlo: 3,14144
 * Real value:  3,14159
 * The estimation took 14 seconds to complete
 * The estimation was 99,99504% close to Pi
 */
@OptIn(ExperimentalTime::class)
fun main() {
    val nrPicks = 500_000_000

    println("Running the estimation with ${"%,d".format(nrPicks)} picks...")

    val estimation = measureTimedValue { MonteCarlo.estimatePi(nrPicks) }
    val proximity = 100 * (1 - abs((PI - estimation.value) / PI))

    println("Monte Carlo: ${"%.5f".format(estimation.value)}")
    println("Real value:  ${"%.5f".format(PI)}")
    println("The estimation took ${estimation.duration.inWholeSeconds} seconds to complete")
    println("The estimation was ${"%.5f".format(proximity)}% close to Pi")
}