Initial commit

SICP/exercise_1_45.janet

@@ -0,0 +1,66 @@
+(def tolerance 0.00001)
+
+(defn fixed-point [f first-guess]
+  (defn close-enough? [v1 v2]
+    (< (math/abs (- v1 v2))
+       tolerance))
+  (defn try-it [guess]
+    (let [next (f guess)]
+      (if (close-enough? guess next)
+        next
+        (try-it next))))
+  (try-it first-guess))
+
+(defn compose [f g]
+  (fn [x] (f (g x))))
+
+(defn repeated [f n]
+  (defn iter [inner_f k]
+    (cond
+      (= k 1) inner_f
+      (iter (compose f inner_f) (- k 1))))
+  (iter f n))
+
+(defn average-damp [f]
+  (fn [x] (* 0.5 (+ x (f x)))))
+
+(defn nth-root [n x]
+  (fn [y]
+    (defn iter [k state]
+      (cond
+        (= k 2) (/ x state)
+        (iter (- k 1) (* state y))))
+    (iter n y)))
+
+(defn root [n x]
+  (def damping-count (math/floor (/ (math/log n) (math/log 2))))
+  ((repeated average-damp damping-count) (nth-root n x)))
+
+(defn pow [n x]
+  (defn iter [k state]
+    (cond
+      (= k 1) state
+      (iter (- k 1) (* state x))))
+  (iter n x))
+
+(var i 2)
+(while (< i 100)
+  (def result (fixed-point (root i 12312.0) 1.0))
+  (printf "%d,%f: 12312.0 = %f" i result (pow i result))
+  (set i (inc i)))
+
+# 2th-root, 1 damping
+# 3rd-root, 1 damping
+# 4th-root, 2 damping
+# 5th-root, 2 damping
+# 6th-root, 2 damping
+# 7th-root, 2 damping
+# 8th-root, 3 damping
+# 9th-root, 3 damping
+# 10th-root, 3 damping
+# 11th-root, 3 damping
+# 12th-root, 3 damping
+# 13th-root, 3 damping
+# 14th-root, 3 damping
+# 15th-root, 3 damping
+# 16th-root, 4 damping