From 83561bfec10a4121f57b9a4a57bc95bea994f883 Mon Sep 17 00:00:00 2001
From: Folkert Kevelam <contact@pyllr.nl>
Date: Sun, 30 Mar 2025 15:33:16 +0200
Subject: [PATCH] Add comprehensive testing functions

---
 SICP/exercise_1_7.janet | 78 ++++++++++++++++++++++++++++++++++-------
 SICP/exercise_1_7.py    | 55 +++++++++++++++++++++++++++++
 2 files changed, 120 insertions(+), 13 deletions(-)
 create mode 100644 SICP/exercise_1_7.py

diff --git a/SICP/exercise_1_7.janet b/SICP/exercise_1_7.janet
index efd0e64..2a3d77e 100644
--- a/SICP/exercise_1_7.janet
+++ b/SICP/exercise_1_7.janet
@@ -1,27 +1,79 @@
 (defn square [x] (* x x))
 
-(defn good-enough? [previous current]
+(defn good-enough2? [previous current acc]
   (>=
-    (* current 0.001)
+    (* current acc)
     (math/abs (- current previous))))
 
+(defn good-enough? [guess x acc]
+  (< (math/abs (- (square guess) x)) acc))
+
 (defn average [x y]
   (/ (+ x y) 2))
 
 (defn improve [guess x]
   (average guess (/ x guess)))
 
-(defn sqrt-iter [prev guess x]
-  (if (good-enough? prev guess)
+(defn sqrt-iter [guess x acc]
+  (if (good-enough? guess x acc)
           guess
-          (sqrt-iter guess (improve guess x) x)))
+          (sqrt-iter (improve guess x) x acc)))
 
-(defn sqrt [x]
-  (sqrt-iter 0.0 x x))
+(defn sqrt-iter2 [prev guess x acc]
+  (if (good-enough2? prev guess acc)
+          guess
+          (sqrt-iter2 guess (improve guess x) x acc)))
 
-(var i 0.0000001)
-(while (<= i 1000000000000.0)
-  (def meas (sqrt i))
-  (def rel (/ (- meas (math/sqrt i)) meas))
-  (print (string/format "Relative error %f=%f, %f" (math/sqrt i) meas rel))
-  (set i (* i 3.141519)))
+(defn sqrt-iter-max [guess x i acc]
+  (if (= i 0)
+    -1
+    (if (good-enough? guess x acc)
+          guess
+          (sqrt-iter-max (improve guess x) x (- i 1) acc))))
+
+(defn sqrt [x acc]
+  (sqrt-iter 1.0 x acc))
+
+(defn sqrt2 [x acc]
+  (sqrt-iter2 0.0 x x acc))
+
+(defn sqrt-max [x acc]
+  (sqrt-iter-max 1.0 x 500 acc))
+
+(defn relative-error [i f]
+  (def measurement (sqrt2 i 0.0001))
+  (def measurement2 (sqrt2 i 0.00001))
+  (def measurement3 (sqrt2 i 0.000001))
+  (def actual (math/sqrt i))
+  (def rel-error (/ (- measurement actual) measurement))
+  (def rel-error2 (/ (- measurement2 actual) measurement2))
+  (def rel-error3 (/ (- measurement3 actual) measurement3))
+  (file/write f (string/format "%e,%e,%e,%e\n" i rel-error rel-error2 rel-error3)))
+
+(defn find-breakpoint []
+  (var found? false)
+  (var base 1.0e12)
+  (var minimum 1.0e-3)
+  (var num 0.0)
+  (while (not found?)
+    (def test (+ num base))
+    (if (>= (sqrt-max test 0.001) 0)
+      (set num (+ num base))
+      (do
+        (set base (/ base 10.0))
+        (if (< base minimum)
+          (set found? true)))))
+  num)
+
+(print (find-breakpoint))
+
+(def f (file/open "exercise_1_7_data.csv" :w))
+(file/write f "i,0.001,0.0001,0.00001\n")
+(var total (* 2 50))
+(var num 1e25)
+(while (> total 0)
+  (relative-error num f)
+  (set num (/ num (math/sqrt 10.0)))
+  (set total (- total 1)))
+
+(file/close f)
diff --git a/SICP/exercise_1_7.py b/SICP/exercise_1_7.py
new file mode 100644
index 0000000..070ef1a
--- /dev/null
+++ b/SICP/exercise_1_7.py
@@ -0,0 +1,55 @@
+import matplotlib.pyplot as plt
+import numpy as np
+import csv
+import math
+
+def read_csv(filename):
+    data = list()
+    header = None
+    with open(filename, "r") as file:
+        reader = csv.reader(file)
+        header = next(reader, None)
+        print(header)
+        for row in reader:
+            data.append([float(d) for d in row])
+
+    return header, data
+
+def main(filename):
+    header, data = read_csv(filename)
+
+    x = [d[0] for d in data]
+    y = dict()
+    for h in range(1, len(header)):
+        y[header[h]] = list()
+
+    for d in data:
+        for idx in range(0, len(d)-1):
+            y[header[idx+1]].append(d[idx+1])
+
+    min_x = min(x)
+    max_x = max(x)
+
+    min_x_tick_power = math.floor(math.log10(min_x))
+    max_x_tick_power = math.ceil(math.log10(max_x))
+
+    xticks = [10**p for p in range(min_x_tick_power, max_x_tick_power)]
+
+    headers = list()
+    for key,value in y.items():
+        plt.plot(x, value)
+        headers.append(key)
+
+    plt.legend(["acc={}".format(h) for h in headers])
+
+    plt.xscale("log")
+    plt.grid(True)
+    plt.xlabel("Input to sqrt()")
+    plt.ylabel("Relative Error")
+    #plt.xticks(xticks)
+    plt.title("Relative error of sqrt()")
+    plt.show()
+
+
+if __name__ == "__main__":
+    main("exercise_1_7_data.csv")