diff --git a/Doc/Sd1/languageFundamentals.xml b/Doc/Sd1/languageFundamentals.xml
index dd45e1dc2d7c2f9f0eda1d6c8ab4c22835ce6c81..8d9a4a24d73b37ac796829a1949393491ba515c5 100644
--- a/Doc/Sd1/languageFundamentals.xml
+++ b/Doc/Sd1/languageFundamentals.xml
@@ -301,7 +301,7 @@
<section xml:id="sw1IntegerLiterals">
<title>Integer value literals</title>
- <section xml:id="sd1BinaryIntLiteral">
+ <section xml:id="sd1SectBinaryIntLiteral">
<title>Binary literals</title>
<qandaset defaultlabel="qanda" xml:id="sd1QandaBinaryIntLiteral">
@@ -336,20 +336,20 @@
<answer>
<orderedlist>
<listitem>
- <programlisting language="java"> public static void main(String[] args) {
-
- System.out.println(0B1110100100);
- System.out.println( 512 +
- 256 +
- 128 +
- 32 +
- 4);
+ <programlisting language="java">public static void main(String[] args) {
+
+ System.out.println(" Binary:" + 0B11_10100100);
+ System.out.println("Decimal:" + (512 +
+ 256 +
+ 128 +
+ 32 +
+ 4));
}</programlisting>
<para>This yields:</para>
- <programlisting language="none">932
-932</programlisting>
+ <programlisting language="none"> Binary:932
+Decimal:932</programlisting>
</listitem>
<listitem>
@@ -375,6 +375,116 @@
</qandaset>
</section>
+ <section xml:id="sd1SectBracesInPrintln">
+ <title>Why using braces inside <code>System.out.println(...)</code>
+ ?</title>
+
+ <qandaset defaultlabel="qanda" xml:id="sd1QandaBracesInPrintln">
+ <qandadiv>
+ <qandaentry>
+ <question>
+ <para>Solution <xref linkend="sd1SectBinaryIntLiteral"/>
+ contains:</para>
+
+ <programlisting language="java">...
+ System.out.println("Decimal:" + (512 +
+ 256 +
+ 128 +
+ 32 +
+ 4)); ...</programlisting>
+
+ <para>Why are the <quote>inner</quote> braces immediately
+ preceding 512 and following 4 are being required?</para>
+
+ <tip>
+ <itemizedlist>
+ <listitem>
+ <para>Execute the above code omitting the
+ <quote>inner</quote> braces.</para>
+ </listitem>
+
+ <listitem>
+ <para>Read about the <quote>+</quote> operator's role e.g.
+ in <code>System.out.println("Some" + "
+ string").</code></para>
+ </listitem>
+ </itemizedlist>
+ </tip>
+ </question>
+
+ <answer>
+ <para>We start omitting the <quote>inner</quote> braces:</para>
+
+ <programlisting language="java">...
+ System.out.println("Decimal:" + 512 +
+ 256 +
+ 128 +
+ 32 +
+ 4); ...</programlisting>
+
+ <para>This results in the following output:</para>
+
+ <programlisting language="none">...
+Decimal:512256128324</programlisting>
+
+ <para>The numbers are being treated as strings rather than
+ integer values The above code is equivalent to:</para>
+
+ <programlisting language="java">...
+ System.out.println("Decimal:" + "512" +
+ "256" +
+ "128" +
+ "32" +
+ "4"); ...</programlisting>
+
+ <para>The <quote>+</quote> operator between two strings defines
+ their concatenation. So all six components get joined into a
+ single result string.</para>
+
+ <para>Supplying additional inner braces defines an expression
+ (512 + 256 + 128 + 32 + 4) solely involving integer values. In
+ this context each <quote>+</quote> operator effects the usual
+ integer arithmetic:</para>
+
+ <programlisting language="java">...
+ System.out.println("Decimal:" +<co linkends="sd1ListingPlusOpDuplicate-1"
+ xml:id="sd1ListingPlusOpDuplicate-1-co"/> (512 +<co
+ linkends="sd1ListingPlusOpDuplicate-2"
+ xml:id="sd1ListingPlusOpDuplicate-2-co"/>
+ 256 +<co
+ linkends="sd1ListingPlusOpDuplicate-2"
+ xml:id="sd1ListingPlusOpDuplicate-3-co"/>
+ 128 +<co
+ linkends="sd1ListingPlusOpDuplicate-2"
+ xml:id="sd1ListingPlusOpDuplicate-4-co"/>
+ 32 +<co
+ linkends="sd1ListingPlusOpDuplicate-2"
+ xml:id="sd1ListingPlusOpDuplicate-5-co"/>
+ 4)); ...</programlisting>
+
+ <calloutlist>
+ <callout arearefs="sd1ListingPlusOpDuplicate-1-co"
+ xml:id="sd1ListingPlusOpDuplicate-1">
+ <para><quote>+</quote> operator concatenating the two
+ strings <code>"Decimal:"</code> and <code>"932"</code>.
+ </para>
+ </callout>
+
+ <callout arearefs="sd1ListingPlusOpDuplicate-2-co sd1ListingPlusOpDuplicate-3-co sd1ListingPlusOpDuplicate-4-co sd1ListingPlusOpDuplicate-5-co"
+ xml:id="sd1ListingPlusOpDuplicate-2">
+ <para><quote>+</quote> operators computing the integer sum
+ of 512, 256, 128, 32 and 4 yielding a value of 932. This
+ value subsequently gets transformed into the String
+ <code>"932"</code> in order to be compatible with the
+ preceeding <code>"Decimal:"</code> string.</para>
+ </callout>
+ </calloutlist>
+ </answer>
+ </qandaentry>
+ </qandadiv>
+ </qandaset>
+ </section>
+
<section xml:id="sw1SectHexadecimalLiterals">
<title>Hexadecimal literals</title>
@@ -1076,6 +1186,85 @@ Seconds:31</programlisting>
</qandaset>
</section>
+ <section xml:id="sd1SectFloatPrecisionProblem">
+ <title>Representational float and double miracles</title>
+
+ <qandaset defaultlabel="qanda" xml:id="sd1QandaFloatPrecisionProblem">
+ <qandadiv>
+ <qandaentry>
+ <question>
+ <para>Consider and execute the following code snippet:</para>
+
+ <programlisting language="java">public static void main(String[] args) {
+ final double a = 0.7;
+ final double b = 0.9;
+ final double x = a + 0.1;
+ final double y = b - 0.1;
+ System.out.println(x == y);
+}</programlisting>
+
+ <para>Explain the result and supply a possible solution.</para>
+ </question>
+
+ <answer>
+ <para>The expression <code>x == y</code> evaluates to
+ <code>false</code>. This surprising result is due to limited
+ precision regarding both <code>float</code> and
+ <code>double</code> IEEE representations: A given value will be
+ approximated as close as possible.</para>
+
+ <para>Adding <code>System.out.println(x - y)</code> yields a
+ value of -1.1102230246251565E-16 denoting their representational
+ deviation.</para>
+
+ <para>So we may compare <code>float</code> and
+ <code>double</code> values by providing a representational error
+ limit:</para>
+
+ <programlisting language="java">final double a = 0.7;
+final double b = 0.9;
+final double x = a + 0.1;
+final double y = b - 0.1;
+System.out.println(<link
+ xlink:href="https://docs.oracle.com/javase/8/docs/api/java/lang/Math.html#abs-double-">Math.abs</link>(x - y) < 1.E-14);</programlisting>
+
+ <para>This implements the boolean expression <inlineequation>
+ <m:math display="inline">
+ <m:mrow>
+ <m:mrow>
+ <m:mo>|</m:mo>
+
+ <m:mrow>
+ <m:mi>x</m:mi>
+
+ <m:mo>-</m:mo>
+
+ <m:mi>y</m:mi>
+ </m:mrow>
+
+ <m:mo>|</m:mo>
+ </m:mrow>
+
+ <m:mo><</m:mo>
+
+ <m:msup>
+ <m:mi>10</m:mi>
+
+ <m:mrow>
+ <m:mo>-</m:mo>
+
+ <m:mi>14</m:mi>
+ </m:mrow>
+ </m:msup>
+ </m:mrow>
+ </m:math>
+ </inlineequation>.</para>
+ </answer>
+ </qandaentry>
+ </qandadiv>
+ </qandaset>
+ </section>
+
<section xml:id="sd1SectInterestSimple">
<title>Interest calculation</title>