From 931d213d4395c6d0ef93f30fe606da8ee3baa6d2 Mon Sep 17 00:00:00 2001
From: Hong-Phuc Bui <hong-phuc.bui@htwsaar.de>
Date: Mon, 29 Apr 2024 02:14:56 +0200
Subject: [PATCH] update permutation
---
python-grundlage/sqrt-newton.py | 12 +++++++-----
1 files changed, 7 insertions(+), 5 deletions(-)
diff --git a/python-grundlage/sqrt-newton.py b/python-grundlage/sqrt-newton.py
old mode 100644
new mode 100755
index 00cfa07..3eb8e68
--- a/python-grundlage/sqrt-newton.py
+++ b/python-grundlage/sqrt-newton.py
@@ -1,10 +1,12 @@
+#! /usr/bin/env python
import sys
+from typing import Final
n = float(sys.argv[1])
-EPSILON = sys.float_info.epsilon
+EPSILON: Final[float] = sys.float_info.epsilon
-t = n
-while abs(t - n/t) > (EPSILON*t):
- t = (n / t + t) / 2
+x = n # !$x_0 = n$!
+while abs(x - (q := n / x)) > (EPSILON * x): # !$\left|\frac{x^2-n}{x^2}\right| > \varepsilon $!
+ x = (x + q) / 2.0 # !$x_{i+1} = \frac{1}{2}(x_i + \frac{n}{x_i})$!
-print(f"sqrt({n}) ~= {t}")
+print(f"sqrt({n}) ~ {x}")
--
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