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+ <style
+ ns1:version="14.10-05142318"
+ id="sozi-style">#sozi-toc text{fill:#eff;font-family:Verdana,sans-serif;font-size:12pt}#sozi-toc text:hover{fill:#0cf;cursor:pointer}#sozi-toc text.sozi-toc-current{fill:#fa4}#sozi-toc-background{stroke:#222;stroke-opacity:.1;stroke-width:10;fill:#222;fill-opacity:.9}.sozi-toc-arrow{fill:#eff;fill-opacity:.75;stroke:none}.sozi-toc-arrow:hover{fill:#0cf}#sozi-framenumber circle{stroke:#222;stroke-opacity:.1;stroke-width:4;fill:#222;fill-opacity:.9}#sozi-framenumber text{fill:#eff;font-family:Verdana,sans-serif;font-size:12pt}</style>
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+ ns1:show-in-frame-list="true"
+ ns1:clip="true"
+ ns1:hide="true"
+ ns1:sequence="1"
+ ns1:title="Gcd implementation"
+ ns1:refid="rect10351" />
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+ ns1:refid="rect10841"
+ ns1:title="Gcd maven packaging"
+ ns1:sequence="2"
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+ ns1:timeout-enable="false"
+ ns1:show-in-frame-list="true"
+ ns1:clip="true"
+ ns1:hide="true"
+ ns1:sequence="3"
+ ns1:title="Using Math.getGcd()"
+ ns1:refid="rect11089" />
+ <ns1:frame
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+ ns1:title="Fraction project"
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+ ns1:title="Maven dependency definition"
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diff --git a/Doc/Sd1/gettingStarted.xml b/Doc/Sd1/gettingStarted.xml
index eabc064c25280747e65bbf84512906e90ce6daa3..d98e2e2bc83a8636701c64cf8e76376da469291e 100644
--- a/Doc/Sd1/gettingStarted.xml
+++ b/Doc/Sd1/gettingStarted.xml
@@ -128,11 +128,11 @@
program's memory management:</para>
<para><link
- xlink:href="https://prog.mi.hdm-stuttgart.de/java_visualize">http://prog.mi.hdm-stuttgart.de/java_visualize</link></para>
+ xlink:href="https://prog.mi.hdm-stuttgart.de/java_visualize/visualize.html">http://prog.mi.hdm-stuttgart.de/java_visualize/visualize.html</link></para>
<para>Credits to <link
- xlink:href="https://github.com/daveagp/java_visualize/blob/master/README">David
- Pritchard</link>.</para>
+ xlink:href="https://github.com/pgbovine/OnlinePythonTutor/graphs/contributors">David
+ Pritchard et. alt</link>.</para>
</glossdef>
</glossentry>
diff --git a/Doc/Sd1/languageFundamentals.xml b/Doc/Sd1/languageFundamentals.xml
index 081363a136870043c3496701f2a18c4c0737100e..cb30af52efc160ee94f8f9f6065085f9522f124a 100644
--- a/Doc/Sd1/languageFundamentals.xml
+++ b/Doc/Sd1/languageFundamentals.xml
@@ -2,7 +2,9 @@
<chapter annotations="slide" version="5.0" xml:id="sw1LanguageFundamental"
xmlns="http://docbook.org/ns/docbook"
xmlns:xlink="http://www.w3.org/1999/xlink"
+ xmlns:xila="http://www.w3.org/2001/XInclude/local-attributes"
xmlns:xi="http://www.w3.org/2001/XInclude"
+ xmlns:trans="http://docbook.org/ns/transclusion"
xmlns:svg="http://www.w3.org/2000/svg"
xmlns:m="http://www.w3.org/1998/Math/MathML"
xmlns:html="http://www.w3.org/1999/xhtml"
@@ -242,6 +244,19 @@
<section xml:id="sd1_sect_variables">
<title>Variables</title>
+ <para>Variables are convenient handles for accessing memory. We don't need
+ to mess with memory addresses:</para>
+
+ <figure xml:id="sd1_fig_varMemoryHandle">
+ <title>Handle to memory</title>
+
+ <mediaobject>
+ <imageobject>
+ <imagedata fileref="Ref/LangFundament/variableToMemory.svg"/>
+ </imageobject>
+ </mediaobject>
+ </figure>
+
<para>Declaring a variable requires a type name like <code>double</code>
and an identifier:</para>
@@ -270,7 +285,7 @@ System.out.println(pi * 2.0. * 2.0);</programlisting>
<glosslist>
<glossentry>
- <glossterm>Separating declaration and initialization</glossterm>
+ <glossterm>Separate declaration and initialization</glossterm>
<glossdef>
<programlisting language="java">double pi; // Declaration of variable pi
@@ -280,7 +295,7 @@ pi = 3.1415926; // Value assignment</programlisting>
</glossentry>
<glossentry>
- <glossterm>Combining declaration and initialization</glossterm>
+ <glossterm>Combined declaration and initialization</glossterm>
<glossdef>
<programlisting language="java">double pi = 3.1415926;</programlisting>
@@ -289,6 +304,180 @@ pi = 3.1415926; // Value assignment</programlisting>
</glosslist>
</figure>
+ <figure xml:id="sd1_fig_varMultiple">
+ <title>Multiple variables of same type</title>
+
+ <programlisting language="java">int a;
+int b = 22;
+int c;</programlisting>
+
+ <para>is equivalent to either of:</para>
+
+ <informaltable border="1">
+ <tr>
+ <th>Compact</th>
+
+ <th>Multiple lines</th>
+ </tr>
+
+ <tr>
+ <td valign="top"><programlisting language="java">int a, b = 22, c; </programlisting></td>
+
+ <td valign="top"><programlisting language="java">int a,
+ b = 22,
+ c;</programlisting></td>
+ </tr>
+ </informaltable>
+ </figure>
+
+ <figure xml:id="sd1_fig_varNameConventions">
+ <title>Variable naming conventions</title>
+
+ <itemizedlist>
+ <listitem>
+ <para>Start with a small letter like <code>africa</code> rather than
+ <code>Africa</code>.</para>
+ </listitem>
+
+ <listitem>
+ <para>Use <quote>camel case</quote> e.g.
+ <code>myFirstCode</code>.</para>
+
+ <mediaobject>
+ <imageobject>
+ <imagedata fileref="Ref/LangFundament/camelCase.svg"/>
+ </imageobject>
+ </mediaobject>
+ </listitem>
+
+ <listitem>
+ <para>Do not start with <code>_</code> or <code>$</code>.</para>
+ </listitem>
+ </itemizedlist>
+ </figure>
+
+ <figure xml:id="sd1_fig_varFinal">
+ <title>Constants</title>
+
+ <programlisting language="java">final double pi = 3.1415926;
+...
+pi = 1.0; // Compile time error: Constant cannot be modified</programlisting>
+ </figure>
+
+ <figure xml:id="sd1_fig_legalVariableName">
+ <title>Variable names</title>
+
+ <para>A variable</para>
+
+ <informaltable border="1">
+ <tr>
+ <td><itemizedlist>
+ <listitem>
+ <para>Starts with a letter</para>
+ </listitem>
+
+ <listitem>
+ <para>May be followed by letters or digits</para>
+ </listitem>
+
+ <listitem>
+ <para>Must not match:</para>
+
+ <itemizedlist>
+ <listitem>
+ <para>a <xref linkend="glo_Java"/> keyword</para>
+ </listitem>
+
+ <listitem>
+ <para>a boolean literal</para>
+ </listitem>
+
+ <listitem>
+ <para>The <code>null</code> literal</para>
+ </listitem>
+ </itemizedlist>
+ </listitem>
+ </itemizedlist></td>
+
+ <td><glosslist>
+ <glossentry>
+ <glossterm>Legal</glossterm>
+
+ <glossdef>
+ <itemizedlist>
+ <listitem>
+ <para>$test</para>
+ </listitem>
+
+ <listitem>
+ <para>count</para>
+ </listitem>
+
+ <listitem>
+ <para>blue</para>
+ </listitem>
+ </itemizedlist>
+ </glossdef>
+ </glossentry>
+
+ <glossentry>
+ <glossterm>Illegal</glossterm>
+
+ <glossdef>
+ <itemizedlist>
+ <listitem>
+ <para>2sad</para>
+ </listitem>
+
+ <listitem>
+ <para>switch</para>
+ </listitem>
+
+ <listitem>
+ <para>true</para>
+ </listitem>
+ </itemizedlist>
+ </glossdef>
+ </glossentry>
+ </glosslist></td>
+ </tr>
+ </informaltable>
+ </figure>
+
+ <figure xml:id="sd1_fig_varCaseSensitive">
+ <title>Case sensitivity</title>
+
+ <para>Variable names are case sensitive:</para>
+
+ <programlisting language="java">int count = 32;
+int Count = 44;
+System.out.println(count + ":" + Count); // This yields "32:44"</programlisting>
+ </figure>
+
+ <figure xml:id="sd1_fig_varDeclareBeforeUse">
+ <title>Declare before use</title>
+
+ <glosslist>
+ <glossentry>
+ <glossterm>Correct:</glossterm>
+
+ <glossdef>
+ <programlisting language="java">double f;
+f = -4.55;</programlisting>
+ </glossdef>
+ </glossentry>
+
+ <glossentry>
+ <glossterm>Wrong</glossterm>
+
+ <glossdef>
+ <programlisting language="java">f = -4.55;
+double f;</programlisting>
+ </glossdef>
+ </glossentry>
+ </glosslist>
+ </figure>
+
<figure xml:id="sd1_fig_typeSafety">
<title>Type safety</title>
@@ -301,6 +490,207 @@ i = b; // Error: int and boolean are incompatible types
i = "Hello"; // Even worse: Assigning a String to an int</programlisting>
</figure>
+ <para><xref linkend="glo_Java"/> provides meta information on
+ types:</para>
+
+ <figure xml:id="sd1_fig_intTypeMaxMin">
+ <title>Maximum and minimum values</title>
+
+ <informaltable border="1">
+ <tr>
+ <th>Type</th>
+
+ <th>Bytes</th>
+
+ <th>Min value</th>
+
+ <th>Max value</th>
+ </tr>
+
+ <tr>
+ <td>byte</td>
+
+ <td><link
+ xlink:href="https://docs.oracle.com/javase/8/docs/api/java/lang/Byte.html#BYTES">1</link></td>
+
+ <td><link
+ xlink:href="https://docs.oracle.com/javase/8/docs/api/constant-values.html#java.lang.Byte.MIN_VALUE"><inlineequation>
+ <m:math display="inline">
+ <m:mrow>
+ <m:mo>-</m:mo>
+
+ <m:msup>
+ <m:mi>2</m:mi>
+
+ <m:mi>7</m:mi>
+ </m:msup>
+ </m:mrow>
+ </m:math>
+ </inlineequation></link></td>
+
+ <td><link
+ xlink:href="https://docs.oracle.com/javase/8/docs/api/constant-values.html#java.lang.Byte.MAX_VALUE"><inlineequation>
+ <m:math display="inline">
+ <m:mrow>
+ <m:msup>
+ <m:mi>2</m:mi>
+
+ <m:mi>7</m:mi>
+ </m:msup>
+
+ <m:mo>-</m:mo>
+
+ <m:mi>1</m:mi>
+ </m:mrow>
+ </m:math>
+ </inlineequation></link></td>
+ </tr>
+
+ <tr>
+ <td>char</td>
+
+ <td><link
+ xlink:href="https://docs.oracle.com/javase/8/docs/api/java/lang/Byte.html#BYTES">2</link></td>
+
+ <td>0</td>
+
+ <td><link
+ xlink:href="https://docs.oracle.com/javase/8/docs/api/constant-values.html#java.lang.Character.MAX_VALUE"><inlineequation>
+ <m:math display="inline">
+ <m:mrow>
+ <m:msup>
+ <m:mi>2</m:mi>
+
+ <m:mi>16</m:mi>
+ </m:msup>
+
+ <m:mo>-</m:mo>
+
+ <m:mi>1</m:mi>
+ </m:mrow>
+ </m:math>
+ </inlineequation></link></td>
+ </tr>
+
+ <tr>
+ <td>short</td>
+
+ <td><link
+ xlink:href="https://docs.oracle.com/javase/8/docs/api/constant-values.html#java.lang.Short.BYTES">2</link></td>
+
+ <td><link
+ xlink:href="https://docs.oracle.com/javase/8/docs/api/constant-values.html#java.lang.Short.MIN_VALUE"><inlineequation>
+ <m:math display="inline">
+ <m:mrow>
+ <m:mo>-</m:mo>
+
+ <m:msup>
+ <m:mi>2</m:mi>
+
+ <m:mi>15</m:mi>
+ </m:msup>
+ </m:mrow>
+ </m:math>
+ </inlineequation></link></td>
+
+ <td><link
+ xlink:href="https://docs.oracle.com/javase/8/docs/api/constant-values.html#java.lang.Short.MAX_VALUE"><inlineequation>
+ <m:math display="inline">
+ <m:mrow>
+ <m:msup>
+ <m:mi>2</m:mi>
+
+ <m:mi>15</m:mi>
+ </m:msup>
+
+ <m:mo>-</m:mo>
+
+ <m:mi>1</m:mi>
+ </m:mrow>
+ </m:math>
+ </inlineequation></link></td>
+ </tr>
+
+ <tr>
+ <td>int</td>
+
+ <td><link
+ xlink:href="https://docs.oracle.com/javase/8/docs/api/constant-values.html#java.lang.Integer.BYTES">4</link></td>
+
+ <td><link
+ xlink:href="https://docs.oracle.com/javase/8/docs/api/constant-values.html#java.lang.Integer.MIN_VALUE"><inlineequation>
+ <m:math display="inline">
+ <m:mrow>
+ <m:mo>-</m:mo>
+
+ <m:msup>
+ <m:mi>2</m:mi>
+
+ <m:mi>31</m:mi>
+ </m:msup>
+ </m:mrow>
+ </m:math>
+ </inlineequation></link></td>
+
+ <td><link
+ xlink:href="https://docs.oracle.com/javase/8/docs/api/constant-values.html#java.lang.Integer.MAX_VALUE"><inlineequation>
+ <m:math display="inline">
+ <m:mrow>
+ <m:msup>
+ <m:mi>2</m:mi>
+
+ <m:mi>31</m:mi>
+ </m:msup>
+
+ <m:mo>-</m:mo>
+
+ <m:mi>1</m:mi>
+ </m:mrow>
+ </m:math>
+ </inlineequation></link></td>
+ </tr>
+
+ <tr>
+ <td>long</td>
+
+ <td><link
+ xlink:href="https://docs.oracle.com/javase/8/docs/api/constant-values.html#java.lang.Long.BYTES">8</link></td>
+
+ <td><link
+ xlink:href="https://docs.oracle.com/javase/8/docs/api/constant-values.html#java.lang.Long.MIN_VALUE"><inlineequation>
+ <m:math display="inline">
+ <m:mrow>
+ <m:mo>-</m:mo>
+
+ <m:msup>
+ <m:mi>2</m:mi>
+
+ <m:mi>63</m:mi>
+ </m:msup>
+ </m:mrow>
+ </m:math>
+ </inlineequation></link></td>
+
+ <td><link
+ xlink:href="https://docs.oracle.com/javase/8/docs/api/constant-values.html#java.lang.Long.MAX_VALUE"><inlineequation>
+ <m:math display="inline">
+ <m:mrow>
+ <m:msup>
+ <m:mi>2</m:mi>
+
+ <m:mi>63</m:mi>
+ </m:msup>
+
+ <m:mo>-</m:mo>
+
+ <m:mi>1</m:mi>
+ </m:mrow>
+ </m:math>
+ </inlineequation></link></td>
+ </tr>
+ </informaltable>
+ </figure>
+
<figure xml:id="sd1_fig_variableCategories">
<title>Two categories of variables</title>
@@ -338,6 +728,71 @@ LocalDate birtday = LocalDate.of(1990, Month.JULY, 5);</programlisting>
</figure>
</section>
+ <section xml:id="sd1_sect_literals">
+ <title>Literals</title>
+
+ <para/>
+ </section>
+
+ <section xml:id="sd1_sect_arithmeticLimitations">
+ <title>Arithmetic limitations</title>
+
+ <para>Expect the unexpected:</para>
+
+ <figure xml:id="sd1_fig_byteLitteralAssign">
+ <title>Strange things</title>
+
+ <programlisting language="java">byte count = 91; // o.K.
+
+byte points = 130; // Compile error: Incompatible types
+ // Required: byte Found: int</programlisting>
+ </figure>
+
+ <figure xml:id="sd1_fig_byteOverflow">
+ <title>Funny things</title>
+
+ <programlisting language="java">int count = 2147483647;
+int points = 2147483647;
+
+int sum = count + points;
+System.out.println("Sum = " + sum);</programlisting>
+
+ <para>Result:</para>
+
+ <informaltable border="1">
+ <tr>
+ <td><programlisting language="none">Sum = -2</programlisting></td>
+
+ <td><programlisting language="none"> 01111111_11111111_11111111_11111111
++ 01111111_11111111_11111111_11111111
+_____________________________________
+ 11111111_11111111_11111111_11111110</programlisting></td>
+ </tr>
+ </informaltable>
+ </figure>
+
+ <para>Why not using float / double in favour of bounded <code>byte</code>,
+ <code>short</code>, <code>int</code>, <code>long</code> for
+ arithmetics?</para>
+
+ <figure xml:id="sd1_fig_floatPrecision">
+ <title>Limited precision</title>
+
+ <programlisting language="java">float float2Power31 = Integer.MAX_VALUE + 1f;
+
+float floatDoubleMAX_VALUE = 2 * float2Power31* float2Power31 - 1f; // 2^63 - 1
+
+System.out.format( " Float value: %f\n", floatDoubleMAX_VALUE);
+System.out.println("Expected value: " + Long.MAX_VALUE);</programlisting>
+
+ <para>Result:</para>
+
+ <programlisting language="none"> Float value: 9223372036854776000.000000
+Expected value: 9223372036854775807
+</programlisting>
+ </figure>
+ </section>
+
<section xml:id="sw1LegalVariableName">
<title>Legal variable names</title>
@@ -1694,13 +2149,14 @@ int i = d; // Error: Incompatible types</programlisting>
</question>
<answer>
- <para>When assigning <code>d = i</code> the <xref
- linkend="glo_Java"/> compiler will implicitly convert the
+ <para>The first snippet compiles by using the widening
+ conversion: When assigning <code>d = i</code> the <xref
+ linkend="glo_Java"/> compiler implicitly converts the
<code>int</code> into a <code>double</code> value.</para>
<para>Turning a double into an int is more cumbersome: The
- expression <code>i = 3.5</code> could be evaluated by applying
- agreeing on a specific rounding prescription. But what about i =
+ expression <code>i = 3.5</code> could be evaluated by agreeing
+ on a specific rounding prescription. But what about i =
3457357385783573478955345.45? A <xref linkend="glo_Java"/>
<code>int</code>'s maximum value is <inlineequation>
<m:math display="inline">
@@ -1738,23 +2194,43 @@ int i = (int) d; // Explicit cast double to int</programlisting>
<qandadiv>
<qandaentry>
<question>
- <para>A programmer named Joe intends to map <code>long</code>
- values to <code>int</code> values. This requires scaling the
- <code>long</code> data type's range <inlineequation>
+ <para>Joe programmer intends to map positive <code>long</code>
+ values to <code>int</code> values. This requires scaling down
+ <quote>half</quote> the <code>long</code> data type's range
+ <inlineequation>
<m:math display="inline">
<m:mrow>
<m:mo>[</m:mo>
<m:mrow>
- <m:mrow>
- <m:mo>-</m:mo>
+ <m:mn>0</m:mn>
+
+ <m:mo>,</m:mo>
+ <m:mrow>
<m:msup>
<m:mi>2</m:mi>
<m:mi>63</m:mi>
</m:msup>
+
+ <m:mo>-</m:mo>
+
+ <m:mi>1</m:mi>
</m:mrow>
+ </m:mrow>
+
+ <m:mo>]</m:mo>
+ </m:mrow>
+ </m:math>
+ </inlineequation> to the <code>int</code>'s range of
+ <inlineequation>
+ <m:math display="inline">
+ <m:mrow>
+ <m:mo>[</m:mo>
+
+ <m:mrow>
+ <m:mn>0</m:mn>
<m:mo>,</m:mo>
@@ -1762,7 +2238,7 @@ int i = (int) d; // Explicit cast double to int</programlisting>
<m:msup>
<m:mi>2</m:mi>
- <m:mi>63</m:mi>
+ <m:mi>31</m:mi>
</m:msup>
<m:mo>-</m:mo>
@@ -1774,25 +2250,157 @@ int i = (int) d; // Explicit cast double to int</programlisting>
<m:mo>]</m:mo>
</m:mrow>
</m:math>
- </inlineequation> down to an <code>int</code>'s range of
- <inlineequation>
- <m:math display="inline">
- <m:mrow>
- <m:mo>[</m:mo>
+ </inlineequation>:</para>
- <m:mrow>
+ <informaltable border="1">
+ <colgroup width="25%"/>
+
+ <colgroup width="30%"/>
+
+ <colgroup width="15%"/>
+
+ <colgroup width="30%"/>
+
+ <tr>
+ <th colspan="2">From</th>
+
+ <th colspan="2">To</th>
+ </tr>
+
+ <tr>
+ <th><code>long</code></th>
+
+ <th><code>remark</code></th>
+
+ <th><code>int</code></th>
+
+ <th>remark</th>
+ </tr>
+
+ <tr>
+ <td align="right">0</td>
+
+ <td align="right"/>
+
+ <td align="right">0</td>
+
+ <td align="right"/>
+ </tr>
+
+ <tr>
+ <td align="right">1</td>
+
+ <td align="right"/>
+
+ <td align="right">0</td>
+
+ <td align="right"/>
+ </tr>
+
+ <tr>
+ <td align="center" colspan="2">...</td>
+
+ <td align="right">0</td>
+
+ <td align="center">...</td>
+ </tr>
+
+ <tr>
+ <td align="right">4294967295</td>
+
+ <td align="right"><inlineequation>
+ <m:math display="inline">
<m:mrow>
+ <m:msup>
+ <m:mi>2</m:mi>
+
+ <m:mi>32</m:mi>
+ </m:msup>
+
<m:mo>-</m:mo>
+ <m:mi>1</m:mi>
+ </m:mrow>
+ </m:math>
+ </inlineequation></td>
+
+ <td align="right">0</td>
+
+ <td align="right"/>
+ </tr>
+
+ <tr>
+ <td align="right">4294967296</td>
+
+ <td align="right"><inlineequation>
+ <m:math display="inline">
+ <m:msup>
+ <m:mi>2</m:mi>
+
+ <m:mi>32</m:mi>
+ </m:msup>
+ </m:math>
+ </inlineequation></td>
+
+ <td align="right">1</td>
+
+ <td align="right"/>
+ </tr>
+
+ <tr>
+ <td align="right">4294967297</td>
+
+ <td align="right"><inlineequation>
+ <m:math display="inline">
+ <m:mrow>
<m:msup>
<m:mi>2</m:mi>
- <m:mi>31</m:mi>
+ <m:mi>32</m:mi>
</m:msup>
+
+ <m:mo>+</m:mo>
+
+ <m:mi>1</m:mi>
</m:mrow>
+ </m:math>
+ </inlineequation></td>
- <m:mo>,</m:mo>
+ <td align="right">1</td>
+
+ <td align="right"/>
+ </tr>
+
+ <tr>
+ <td align="center" colspan="4">...</td>
+ </tr>
+ <tr>
+ <td align="right">9223372036854775806</td>
+
+ <td align="right"><inlineequation>
+ <m:math display="inline">
+ <m:mrow>
+ <m:msup>
+ <m:mi>2</m:mi>
+
+ <m:mi>63</m:mi>
+ </m:msup>
+
+ <m:mo>-</m:mo>
+
+ <m:mi>2</m:mi>
+ </m:mrow>
+ </m:math>
+ </inlineequation> or <code
+ xlink:href="https://docs.oracle.com/javase/8/docs/api/constant-values.html#java.lang.Long.MAX_VALUE"><varname
+ xlink:href="https://docs.oracle.com/javase/8/docs/api/constant-values.html#java.lang.Long.MAX_VALUE">Long.MAX_VALUE</varname></code>
+ - 1</td>
+
+ <td align="right">2147483647</td>
+
+ <td align="right"><inlineequation>
+ <m:math display="inline">
<m:mrow>
<m:msup>
<m:mi>2</m:mi>
@@ -1804,14 +2412,54 @@ int i = (int) d; // Explicit cast double to int</programlisting>
<m:mi>1</m:mi>
</m:mrow>
- </m:mrow>
+ </m:math>
+ </inlineequation> or <varname
+ xlink:href="https://docs.oracle.com/javase/8/docs/api/constant-values.html#java.lang.Integer.MAX_VALUE">Integer.MAX_VALUE</varname></td>
+ </tr>
- <m:mo>]</m:mo>
- </m:mrow>
- </m:math>
- </inlineequation>.</para>
+ <tr>
+ <td align="right">9223372036854775807</td>
+
+ <td align="right"><inlineequation>
+ <m:math display="inline">
+ <m:mrow>
+ <m:msup>
+ <m:mi>2</m:mi>
+
+ <m:mi>63</m:mi>
+ </m:msup>
+
+ <m:mo>-</m:mo>
+
+ <m:mi>1</m:mi>
+ </m:mrow>
+ </m:math>
+ </inlineequation> or <varname
+ xlink:href="https://docs.oracle.com/javase/8/docs/api/constant-values.html#java.lang.Long.MAX_VALUE">Long.MAX_VALUE</varname></td>
+
+ <td align="right">2147483647</td>
- <para>Joe thinks of dividing long values by <inlineequation>
+ <td align="right"><inlineequation>
+ <m:math display="inline">
+ <m:mrow>
+ <m:msup>
+ <m:mi>2</m:mi>
+
+ <m:mi>31</m:mi>
+ </m:msup>
+
+ <m:mo>-</m:mo>
+
+ <m:mi>1</m:mi>
+ </m:mrow>
+ </m:math>
+ </inlineequation> or <varname
+ xlink:href="https://docs.oracle.com/javase/8/docs/api/constant-values.html#java.lang.Integer.MAX_VALUE">Integer.MAX_VALUE</varname></td>
+ </tr>
+ </informaltable>
+
+ <para>Joe's idea is dividing <code>long</code> values by
+ <inlineequation>
<m:math display="inline">
<m:msup>
<m:mi>2</m:mi>
@@ -1852,46 +2500,153 @@ int i = (int) d; // Explicit cast double to int</programlisting>
<m:mi>32</m:mi>
</m:msup>
</m:math>
- </inlineequation> seems to be equal to <code>2 *
- (Integer.MAX_VALUE + 1))</code> (why?) Joe's first attempt
- reads:</para>
+ </inlineequation> seems to be equal to <code>2 * (<link
+ xlink:href="https://docs.oracle.com/javase/8/docs/api/constant-values.html#java.lang.Integer.MAX_VALUE">Integer.MAX_VALUE</link>
+ + 1))</code> (why?) Joe's first attempt reads:</para>
+
+ <programlisting language="java" linenumbering="numbered"
+ startinglinenumber="26">final long longValue = 2147483648L;
+final int reducedValue = (int) (longValue / (2 * (Integer.MAX_VALUE + 1)));
+System.out.println(reducedValue);</programlisting>
+
+ <para>Unfortunately the results are not promising. This code
+ merely results in a runtime error:</para>
- <programlisting language="java">final long longValue = ...;
- ...
-final int reducedValue = (int) (longValue / (2 * (Integer.MAX_VALUE + 1)));</programlisting>
+ <programlisting language="none">/usr/lib/jvm/java-8-oracle/bin/java ...
+Exception in thread "main" java.lang.ArithmeticException: / by zero
+ at qq.App.main(App.java:27)
+
+Process finished with exit code 1</programlisting>
+
+ <para>Explain the underlying problem and correct Joe's
+ error.</para>
- <para>Unfortunately the results are not promising. May you help
- Joe correcting his error? Provide an example showing the
- problem.</para>
+ <tip>
+ <para>It may be helpful thinking of a smaller example before.
+ Consider hypothetic integer types <quote>TinyLong</quote> and
+ <quote>TinyInt</quote> requiring 4 and 2 bits respectively.
+ </para>
+ </tip>
</question>
<answer>
- <para>We consider:</para>
+ <para>As a prerequisite we represent the scaling of a hypothetic
+ integer type <quote>TinyLong</quote> to a smaller type
+ <quote>TinyInt</quote> of 4 and 2 bits respectively:</para>
- <programlisting language="java">final long longValue = Long.MAX_VALUE;
-
-final int reducedValue = (int) (longValue / (2 * (Integer.MAX_VALUE + 1)));
-System.out.println(reducedValue);</programlisting>
+ <informaltable border="1">
+ <colgroup width="20%"/>
+
+ <colgroup width="5%"/>
+
+ <colgroup width="5%"/>
+
+ <colgroup width="5%"/>
+
+ <colgroup width="5%"/>
- <para>The intended result should assign Integer.MAX_VALUE to the
- variable <code>reducedValue</code>. Actually Joe's attempt
- creates a runtime error:</para>
+ <colgroup width="5%"/>
- <programlisting language="none">Exception in thread "main" java.lang.ArithmeticException: / by zero</programlisting>
+ <colgroup width="5%"/>
+
+ <colgroup width="5%"/>
+
+ <colgroup width="5%"/>
+
+ <colgroup width="5%"/>
+
+ <colgroup width="5%"/>
+
+ <colgroup width="5%"/>
+
+ <colgroup width="5%"/>
+
+ <colgroup width="5%"/>
+
+ <colgroup width="5%"/>
+
+ <colgroup width="5%"/>
+
+ <colgroup width="5%"/>
+
+ <tr>
+ <td><quote>TinyLong</quote>, n = 4</td>
+
+ <td>-8</td>
+
+ <td>-7</td>
+
+ <td>-6</td>
+
+ <td>-5</td>
+
+ <td>-4</td>
+
+ <td>-3</td>
+
+ <td>-2</td>
+
+ <td>-1</td>
+
+ <td>0</td>
+
+ <td>1</td>
+
+ <td>2</td>
+
+ <td>3</td>
+
+ <td>4</td>
+
+ <td>5</td>
+
+ <td>6</td>
+
+ <td>7</td>
+ </tr>
+
+ <tr>
+ <td><quote>TinyInt</quote>, n = 2</td>
+
+ <td colspan="4">-2</td>
+
+ <td colspan="4">-1</td>
+
+ <td colspan="4">0</td>
+
+ <td colspan="4">1</td>
+ </tr>
+ </informaltable>
+
+ <para>Joe's assumption for these particular values implies
+ dividing <quote>TinyLong</quote> values by <inlineequation>
+ <m:math display="inline">
+ <m:msup>
+ <m:mi>2</m:mi>
+
+ <m:mi>2</m:mi>
+ </m:msup>
+ </m:math>
+ </inlineequation> (truncating). This indeed yields the desired
+ result for non-negative values. So why does Joe encounter a
+ division by zero runtime exception when executing
+ <code>longValue / (2 * (Integer.MAX_VALUE + 1))</code> ?</para>
- <para>Unfortunately Joe's assumption is seriously flawed:</para>
+ <para>Unfortunately Joe's implementation is seriously flawed for
+ even two reasons:</para>
<orderedlist>
<listitem>
<para>The constant <code>Integer.MAX_VALUE</code> already
suggests we will not be able to increase its value while
staying as an <code>int</code>. The expression
- <code>Integer.MAX_VALUE + 1</code> indeed returns
- <code>Integer.MIN_VALUE</code> due to an arithmetic
- overflow:</para>
+ <code>Integer.MAX_VALUE + 1</code> will be evaluated using
+ <code>int</code> rather than <code>long</code> arithmetic
+ thus returning <code>Integer.MIN_VALUE</code> (negative!)
+ due to an arithmetic overflow:</para>
<programlisting language="java"> 01111111_11111111_11111111_11111111
-+ 00000000_00000000_00000000_00000000
++ 00000000_00000000_00000000_00000001
_____________________________________
10000000_00000000_00000000_00000000</programlisting>
@@ -1906,7 +2661,8 @@ _____________________________________
</orderedlist>
<para>Both errors combined (surprisingly) result in a value of
- <code>0</code>. There are two possible solutions:</para>
+ <code>0</code> explaining the <quote>division by zero</quote>
+ error message. There are two possible solutions:</para>
<glosslist>
<glossentry>
@@ -1914,13 +2670,13 @@ _____________________________________
+ 1L)))</code></glossterm>
<glossdef>
- <para>Introducing <code>2L</code> and <code>1L</code> in
- favour of simply using 2 and 1 turns both addition and
- multiplication into operations involving one long
- argument. Thus for both operations the <xref
- linkend="glo_Java"/> runtime will use <code>long</code>
- arithmetic returning the desired <quote>reducing</quote>
- factor of <inlineequation>
+ <para>Introducing <code>2L</code> or <code>1L</code> (one
+ is sufficient) in favour of simply using 2 and 1 turns
+ both addition and multiplication into operations involving
+ at least one long argument. Thus for both operations the
+ <xref linkend="glo_Java"/> runtime will use
+ <code>long</code> arithmetic returning the desired
+ <quote>reducing</quote> factor of <inlineequation>
<m:math display="inline">
<m:msup>
<m:mi>2</m:mi>
@@ -1928,7 +2684,7 @@ _____________________________________
<m:mi>32</m:mi>
</m:msup>
</m:math>
- </inlineequation>.</para>
+ </inlineequation> of type <code>long</code>.</para>
</glossdef>
</glossentry>
@@ -1942,10 +2698,13 @@ _____________________________________
<note>
<para>This time the expression starts with
<code>longValue / 2 ...</code> Since the variable
- <code>longValue</code> already is of type
- <code>long</code> a division by <code>2</code> rather
- than <code>2L</code> is sufficient to enforce
- <code>long</code> arithmetic.</para>
+ <code>longValue</code> is of type <code>long</code> the
+ expression <code>longValue / 2</code> will be evaluated
+ by the <xref linkend="glo_Java"/> runtime using
+ <code>long</code> arithmetics. The result will
+ subsequently be multiplied with <code>Integer.MAX_VALUE
+ + 1L</code> again using <code>long</code>
+ arithmetic.</para>
</note>
</glossdef>
</glossentry>