De Morgan's laws

ChangeLog

@@ -1,5 +1,6 @@
 (This file is poorly maintained, since there is no reason to keep it at all...)
 
+   Nov-2019: Many blog posts from yurichev.com/blog has been copypasted into the book
    Jan-2019: There was a time when \IT macro was used for italic text and \ITA for Italian text.
              To be consistent, I'm using \emph for italic text now and \IT for Italian text.
              True for filename suffixes as well.
@@ -17,7 +18,7 @@
 20-Jul-2016: The book is now licensed under CC BY-SA 4.0 (like Wikipedia)
              instead of CC NC-ND 3.0.
 16-Jul-2016: Blog posts about C/C++ pointers has been copypasted into the book
-14-Jul-2016: No more LITE version, which was somewhat unpopular
+14-Jul-2016: No more LITE version, which was somewhat unwanted
 04-Nov-2015: All exercises has been moved to http://challenges.re
 21-Mar-2015: toupper() function example
 18-Mar-2015: Lite (introductory) version

other/DeMorgan_EN.tex

@@ -0,0 +1,109 @@
+\subsection{De Morgan's laws and decompilation}
+
+Sometimes a compiler's optimizer can use De Morgan's laws to make code shorter/faster.
+
+For example, this:
+
+\begin{lstlisting}[style=customc]
+void f(int a, int b, int c, int d)
+{
+	if (a>0 && b>0)
+		printf ("both a and b are positive\n");
+	else if (c>0 && d>0)
+		printf ("both c and d are positive\n");
+	else
+		printf ("something else\n");
+};
+\end{lstlisting}
+
+... looks pretty innocent, when compiled by optimizing GCC 5.4.0 x64:
+
+\begin{lstlisting}[style=customasmx86]
+; \verb|int __fastcall f(int a, int b, int c, int d)|
+                public f
+f               proc near
+                test    edi, edi
+                jle     short loc_8
+                test    esi, esi
+                jg      short loc_30
+
+loc_8:
+                test    edx, edx
+                jle     short loc_20
+                test    ecx, ecx
+                jle     short loc_20
+                mov     edi, offset s   ; "both c and d are positive"
+                jmp     puts
+
+loc_20:
+                mov     edi, offset aSomethingElse ; "something else"
+                jmp     puts
+
+loc_30:
+                mov     edi, offset aAAndBPositive ; "both a and b are positive"
+
+loc_35:
+                jmp     puts
+f               endp
+\end{lstlisting}
+
+... also looks innocent, but Hex-Rays 2.2.0 cannot clearly see that both AND operations were actually used in the source code:
+
+\begin{lstlisting}[style=customc]
+int __fastcall f(int a, int b, int c, int d)
+{
+  int result;
+
+  if ( a > 0 && b > 0 )
+  {
+    result = puts("both a and b are positive");
+  }
+  else if ( c <= 0 || d <= 0 )
+  {
+    result = puts("something else");
+  }
+  else
+  {
+    result = puts("both c and d are positive");
+  }
+  return result;
+}
+\end{lstlisting}
+
+The \verb|c <= 0 || d <= 0| expression is inversion of \verb|c>0 && d>0| since 
+$\overline{A \cup B} = \overline{A} \cap \overline{B}$ and
+$\overline{A \cap B} = \overline{A} \cup \overline{B}$,
+in other words,
+\verb~!(cond1 || cond2) == !cond1 && !cond2~ and \verb~!(cond1 && cond2) == !cond1 || !cond2~.
+
+These rules are worth to be kept in mind, since this compiler optimization is used heavily almost everywhere.
+
+Sometimes it's good idea to invert a condition, in order to understand a code better.
+This is a piece of a real code decompiled by Hex-Rays:
+
+\begin{lstlisting}[style=customc]
+	for (int i=0; i<12; i++)
+	{
+		if (v1[i-12] != 0.0 || v1[i] != 0.0)
+		{
+			v108=min(v108, (float)v0[i*24 -2]);
+			v113=max(v113, (float)v0[i*24]);
+		};
+	}
+\end{lstlisting}
+
+... it can be rewritten like:
+
+\begin{lstlisting}[style=customc]
+	for (int i=0; i<12; i++)
+	{
+		if (v1[i-12] == 0.0 && v1[i] == 0.0)
+			continue;
+
+		v108=min(v108, (float)v0[i*24 -2]);
+		v113=max(v113, (float)v0[i*24]);
+	}
+\end{lstlisting}
+
+Which is better? I don't know yet, but for better understanding, it's great to take a look on both.
+

other/hexrays_EN.tex

@@ -446,6 +446,8 @@ \subsection{Long and messed expressions}
 Mathematica has added two new variables: \TT{Compile`\$1} and \TT{Compile`\$2}, values of which are to be used several times in expression.
 So we can add two additional variables.
 
+\input{other/DeMorgan_EN}
+
 \subsection{My plan}
 
 \begin{itemize}

other/hexrays_FR.tex

@@ -461,6 +461,8 @@ \subsection{Expressions longues et confuses}
 qui vont être ré-utilisées plusieurs fois dans l'expression.
 Donc, nous pouvons ajouter deux variables supplémentaires.
 
+%\input{other/DeMorgan_FR}
+
 \subsection{Mon plan}
 
 \begin{itemize}

other/hexrays_RU.tex

@@ -447,6 +447,8 @@ \subsection{Длинные и запутанные выражения}
 в выражении несколько раз.
 Так что мы можем добавить две дополнительных переменных.
 
+%\input{other/DeMorgan_RU}
+
 \subsection{Мой план}
 
 \begin{itemize}