sample-code: Add square root demo

sample-code/sqrt.cl

@@ -0,0 +1,59 @@
+#!/usr/bin/env conlang-run
+//! Square root approximation, and example applications
+
+/// A really small nonzero number
+const EPSILON: f64 // = 8.854... * 10^-12
+    = 88541878188 as f64
+    / 10000000000 as f64
+    / 1000000000000 as f64;
+
+/// Calcuates the absolute value of a number
+fn f64_abs(n: f64) -> f64 {
+    let n = n as f64
+    if n < (0 as f64) { -n } else { n }
+}
+
+/// Square root approximation using Newton's method
+fn sqrt(n: f64) -> f64 {
+    let n = n as f64
+    if n < 0 as f64 {
+        return 0 as f64 / 0 as f64 // TODO: NaN constant
+    }
+    if n == 0 as f64 {
+        return 0 as f64
+    }
+
+    let z = n
+    loop {
+        let adj = (z * z - n) / (2 as f64 * z)
+        z -= adj
+        if adj.f64_abs() < EPSILON {
+            break z;
+        }
+    }
+}
+
+/// Pythagorean theorem: a² + b² = c²
+fn pythag(a: f64, b: f64) -> f64 {
+    sqrt(a * a + b * b)
+}
+
+/// Quadratic formula: (-b ± √(b² - 4ac)) / 2a
+fn quadratic(a: f64, b: f64, c: f64) -> (f64, f64) {
+    let a = a as f64; let b = b as f64; let c = c as f64;
+    (
+        (-b + sqrt(b * b - 4 as f64 * a * c)) / 2 as f64 * a,
+        (-b - sqrt(b * b - 4 as f64 * a * c)) / 2 as f64 * a,
+    )
+}
+
+fn main() {
+    for i in 0..10 {
+        println("sqrt(",i,") ≅ ",sqrt(i))
+    }
+    println("\nPythagorean Theorem")
+    println("Hypotenuse of ⊿(5, 12): ", pythag(5, 12))
+
+    println("\nQuadratic formula")
+    println("Roots of 10x² + 4x - 1: ", quadratic(10, 44, -1))
+}