In my previous article I derived the calculation for passive income from invested assets and demonstrated a small calculator. It struck me that there was a slight delay in the case of high annual numbers. The cause of the delay lies in my implementation of the formula $$ \sum_{k = 1}^{m-1} \frac {1} {\prod_ {t = 1} ^ {k} w_t}. $$ As described in more detail in the article mentioned above, $ w_t $ denotes the relative market value in the month $ t $ and $ m $ the total number of months. ...

How can you generate passive income from return on stock market investments or dividends*Dividends are of course also a kind of investment income. I just wanted to mention them again because they play a special role in this article. and when does that make sense? In addition to explanations and anecdotes, I also present mathematical formulas to answer this question🥳*That's a smiley celebrating the existence of math in this article.. ...

Some time ago I was able to listen to the episode We’re Teaching Functional Programming Wrong of the podcast Corecursive. Richard Feldman tells of a purely functional language with which you can actually create dynamic web pages. It is not even necessary to understand what a Monad is. Since I consider object-oriented programming to be overrated*The talk [Free your Functions](https://www.youtube.com/watch?v=WLDT1lDOsb4) by Klaus Iglberger highlights some practical aspects my point of view., I had a closer look at this approach. In this post I will report on my first steps, hurdles and progress in Elm and focus on aspects that were unfamiliar to me having an imperative background. ...

I’m just bringing my public diary back to life. I write in German and cooperate with machines to translate articles to English.

In the blog post from August 2014 we compared the modularization of image processing algorithms with template based policies against the dynamic polymophism based stragety pattern in terms of speed. We will compare the run-time of (almost) the same pixel-wise operations on images again. But this time, we consider different functional modularization techniques. More precisely, we will pass function pointers, lambdas, and derived functors to algorithms with corresponding argument types such as a templated one and std::function among others. ...

I was wondering for quite a while how much speed-up one can roughly expect by a policy*Modern C++ Design, A. Alexandrescu, 2001 based design of algorithms in C++ using templates compared to the strategy*Design Patterns, E. Gamma, R. Helm, R. Johnson, and J. Vlissides, 1995 pattern using polymorphism. Thereby, I am especially interested in algorithms for image processing. Strategy vs. Policy in C++ Both, policy and strategy, can be used to modularize algorithms. For more details I refer to the textbooks listed below. To compare both approaches exclusively in terms of speed, I created a simple example. I consider the binary operations addition and subtraction of two images pixel-wise and in place for all image pixels i. For the polymorphism based strategy pattern I use an abstract super class. ```cpp template struct BinaryOperator { virtual t_data sBinOperation(t_data a, t_data b) = 0; }; template struct Add : BinaryOperator { t_data sBinOperation(t_data a, t_data b) { return a+b; } }; template struct Subtract : BinaryOperator { t_data sBinOperation(t_data a, t_data b) { return a-b; } }; Further, I have a class that iterates over the image and applies the binary operation pixel-wise. The binary operation is contained as a polymorphic member. ```cpp template <class t_data> struct ImBinaryOperatorStrategy { BinaryOperator<t_data> *binOp; ImBinaryOperatorStrategy(BinaryOperator<t_data> *binOp):binOp(binOp){} void imBinOperation(t_data* im1, t_data* im2, int width, int height, int step1, int step2) { for (int y=0; y<height; y++) for (int x=0; x<width; x++) im1[x+y*step1] = binOp->sBinOperation(im1[x+y*step1],im2[x+y*step2]); } }; For the policy based design with templates, I use the classes Add and Subtract (but not their base class BinaryOperator) and the following class to operate on images. In contrast to the strategy pattern, the binary operation is not a member but passed as template parameter. ...