Monte Carlo Pi algorithm

add Monte Carlo Pi algorithm

Author: 0xbrayo

other/monte_carlo_pi/monte_carlo_pi.go

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+// Monte Carlo Pi
+// [Monte Carlo method](https://en.wikipedia.org/wiki/Monte_Carlo_method) to calculate Pi
+//
+// The basic idea of Monte Carlo is:
+//  1. Define a domain of possible inputs
+//  2. Generate inputs randomly from a probability distribution over the domain
+//  3. Perform a deterministic computation on the inputs
+//  4. Aggregate the results
+//
+// Thus the algorithm to calculate Pi is:
+//
+// 1. Given a circle inscribed in a square with side length 1.
+// 2. randomly draw n points (x, y) | x,y in [0.0,1.0)
+// 3. Count the amount of points inside the circle
+// 4. pi = 4 * (points inside the circle) / n
+//
+// A point (x, y) is inside the circle if:
+//
+// x*x + y*y <= 1
+//
+
+package main
+
+import (
+	"math"
+	"math/rand"
+)
+
+// MonteCarloPi calculates Pi using the Monte Carlo method
+func MonteCarloPi(iterations uint) float64 {
+	var inside, total uint
+
+	for total = uint(0); total < iterations; total++ {
+		if in := math.Hypot(rand.Float64(), rand.Float64()) <= 1; in {
+			inside++
+		}
+	}
+
+	return float64(4) * (float64(inside) / float64(total))
+}

other/monte_carlo_pi/monte_carlo_pi_test.go

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+package main
+
+import (
+	"math"
+	"testing"
+)
+
+func TestMonteCarloPi(t *testing.T) {
+	delta := 0.0001
+
+	pi := MonteCarloPi(100000000)
+
+	if math.Abs(pi-math.Pi) > delta {
+		t.Errorf("Given: %.4f, expected: %.4f", pi, math.Pi)
+	}
+}