From 0d504952f4cab1b8ffd50a9330a1d55c52f4b038 Mon Sep 17 00:00:00 2001
From: "Dr. Martin Goik" <goik@hdm-stuttgart.de>
Date: Thu, 9 May 2019 22:46:17 +0200
Subject: [PATCH] Supplementary slide explaining test principle
---
.../Tests/unitTest.multi.svg | 1522 +++++++++++++++++
Doc/Sd1/objectsClasses.xml | 545 +++---
2 files changed, 1802 insertions(+), 265 deletions(-)
create mode 100644 Doc/Sd1/Ref/ObjectsAndClasses/Tests/unitTest.multi.svg
diff --git a/Doc/Sd1/Ref/ObjectsAndClasses/Tests/unitTest.multi.svg b/Doc/Sd1/Ref/ObjectsAndClasses/Tests/unitTest.multi.svg
new file mode 100644
index 000000000..021e001f3
--- /dev/null
+++ b/Doc/Sd1/Ref/ObjectsAndClasses/Tests/unitTest.multi.svg
@@ -0,0 +1,1522 @@
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+ style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:4.23333311px;line-height:1.25;font-family:'DejaVu Sans';-inkscape-font-specification:'DejaVu Sans Bold';letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.26458332"
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diff --git a/Doc/Sd1/objectsClasses.xml b/Doc/Sd1/objectsClasses.xml
index 3d64a2620..064ea8e2b 100644
--- a/Doc/Sd1/objectsClasses.xml
+++ b/Doc/Sd1/objectsClasses.xml
@@ -4276,7 +4276,7 @@ System.out.println("Club's headcount:" + <emphasis role="red">john.</emphasis>ge
<para>This is actually a regression with respect to the <code
language="java">static</code> class method variant since the
number of club members in fact does not depend on any
- individual member instance. </para>
+ individual member instance.</para>
<para>We may reveal this changes futility by:</para>
@@ -10531,12 +10531,8 @@ public class Prime {
</calloutlist>
</figure>
- <para>The <code language="java">static</code> method
- <methodname>getFirstNegative(...)</methodname> may be executed from an
- arbitrary context:</para>
-
<figure xml:id="sd1_fig_firstNegMethodExecFrmMain">
- <title>Obviously execution yet flawed</title>
+ <title>Execution yet being flawed</title>
<programlisting language="java">for (int i = 1; i < 20;i++) {
System.out.println(i + " is " + (Prime.isPrime(i) ? " a " : " not a ")
@@ -10551,6 +10547,16 @@ public class Prime {
...</screen>
</figure>
+ <figure xml:id="sd1_fig_unitTestPrinciple">
+ <title>Unit test principle</title>
+
+ <mediaobject>
+ <imageobject>
+ <imagedata fileref="Ref/ObjectsAndClasses/Tests/unitTest.multi.svg"/>
+ </imageobject>
+ </mediaobject>
+ </figure>
+
<figure xml:id="sd1_fig_SpecificationExamples">
<title>Sample test data</title>
@@ -10668,7 +10674,7 @@ public class Prime {
<para>Any methods not being annotated by <classname
xlink:href="https://junit.org/junit4/javadoc/latest/org/junit/Test.html">@Test</classname>
will not be called by the <xref linkend="glo_Junit"/> framework.
- They may however be called by e.g.
+ They may however be called indirectly by test methods e.g.
<methodname>test_1_isNotPrime()</methodname> thus acting as helper
methods.</para>
</callout>
@@ -10677,7 +10683,7 @@ public class Prime {
<figure xml:id="sd1_fig_testSkeletonImplementationIde">
<title><xref linkend="glo_Junit"/> skeleton test result (<xref
- linkend="glo_Maven"/> CLI)</title>
+ linkend="glo_Maven"/> <abbrev>CLI</abbrev>)</title>
<screen>goik@goiki Prime_v01> mvn test
...
@@ -10803,10 +10809,13 @@ Results :
<emphasis role="red">Tests run: 5, Failures: 0, Errors: 0</emphasis>, Skipped: 0</screen>
</figure>
- <figure xml:id="sd1_fig_primeV1Observe">
- <title>Implementation observation</title>
+ <section xml:id="sd1_sect_junitPrimBetterImpl">
+ <title>Improving the algorithm</title>
+
+ <figure xml:id="sd1_fig_primeV1Observe">
+ <title>Implementation observation</title>
- <screen><emphasis role="red">101 / 2 = 50.5
+ <screen><emphasis role="red">101 / 2 = 50.5
101 / 3 = 33.6...
101 / 4 = 25.25
101 / 5 = 20.20
@@ -10819,12 +10828,12 @@ Results :
101 / 12 = 8.4...
101 / 13 = 7.7...
...</screen>
- </figure>
+ </figure>
- <figure xml:id="sd1_fig_primeV2Implemet">
- <title>Changing the implementation</title>
+ <figure xml:id="sd1_fig_primeV2Implemet">
+ <title>Changing the implementation</title>
- <programlisting language="none">public static boolean isPrime(int value) {
+ <programlisting language="none">public static boolean isPrime(int value) {
for (int i = 2; <emphasis role="red">i * i < value</emphasis>; i++) {
if (0 == value % i) {
return false;
@@ -10832,23 +10841,23 @@ Results :
}
return value != 1;
}</programlisting>
- </figure>
+ </figure>
- <figure xml:id="sd1_fig_primeRegressionTest">
- <title>Regression test</title>
+ <figure xml:id="sd1_fig_primeRegressionTest">
+ <title>Regression test</title>
- <mediaobject>
- <imageobject>
- <imagedata fileref="Ref/ObjectsAndClasses/Tests/ideaTestV2Error.svg"/>
- </imageobject>
- </mediaobject>
- </figure>
+ <mediaobject>
+ <imageobject>
+ <imagedata fileref="Ref/ObjectsAndClasses/Tests/ideaTestV2Error.svg"/>
+ </imageobject>
+ </mediaobject>
+ </figure>
- <figure xml:id="sd1_fig_primeV2ImplementCorrect">
- <title>Correcting the implementation</title>
+ <figure xml:id="sd1_fig_primeV2ImplementCorrect">
+ <title>Correcting the implementation</title>
- <programlisting language="none">public static boolean <link
- xlink:href="https://gitlab.mi.hdm-stuttgart.de/goik/GoikLectures/blob/master/Doc/Sd1/Ref/ObjectsAndClasses/Tests/Prime_v02/src/main/java/de/hdm_stuttgart/mi/sd1/Prime.java">isPrime</link>(int value) {
+ <programlisting language="none">public static boolean <link
+ xlink:href="https://gitlab.mi.hdm-stuttgart.de/goik/GoikLectures/blob/master/Doc/Sd1/Ref/ObjectsAndClasses/Tests/Prime_v02/src/main/java/de/hdm_stuttgart/mi/sd1/Prime.java">isPrime</link>(int value) {
for (int i = 2; i * i <emphasis role="red"><=</emphasis> value; i++) {
if (0 == value % i) {
return false;
@@ -10856,96 +10865,100 @@ Results :
}
return value != 1;
}</programlisting>
- </figure>
+ </figure>
- <figure xml:id="sd1_fig_primeRegressionTestFinal">
- <title>Repeating regression test</title>
+ <figure xml:id="sd1_fig_primeRegressionTestFinal">
+ <title>Repeating regression test</title>
- <mediaobject>
- <imageobject>
- <imagedata fileref="Ref/ObjectsAndClasses/Tests/ideaTestV2Corrected.svg"/>
- </imageobject>
- </mediaobject>
- </figure>
+ <mediaobject>
+ <imageobject>
+ <imagedata fileref="Ref/ObjectsAndClasses/Tests/ideaTestV2Corrected.svg"/>
+ </imageobject>
+ </mediaobject>
+ </figure>
+ </section>
- <figure xml:id="sd1_fig_availableResultMethods">
- <title>Available comparison methods</title>
+ <section xml:id="sd1_sect_junitDetails">
+ <title><xref linkend="glo_Junit"/>, important details</title>
- <itemizedlist>
- <listitem>
- <para><methodname
- xlink:href="http://junit.org/junit4/javadoc/latest/org/junit/Assert.html">assertEquals([String
- message],...)</methodname></para>
- </listitem>
+ <figure xml:id="sd1_fig_availableResultMethods">
+ <title>Available comparison methods</title>
- <listitem>
- <para><methodname
- xlink:href="http://junit.org/junit4/javadoc/latest/org/junit/Assert.html">assertArrayEquals([String
- message],...)</methodname></para>
- </listitem>
+ <itemizedlist>
+ <listitem>
+ <para><methodname
+ xlink:href="http://junit.org/junit4/javadoc/latest/org/junit/Assert.html">assertEquals([String
+ message],...)</methodname></para>
+ </listitem>
- <listitem>
- <para><methodname
- xlink:href="http://junit.org/junit4/javadoc/latest/org/junit/Assert.html">assertFalse([String
- message],...)</methodname></para>
- </listitem>
+ <listitem>
+ <para><methodname
+ xlink:href="http://junit.org/junit4/javadoc/latest/org/junit/Assert.html">assertArrayEquals([String
+ message],...)</methodname></para>
+ </listitem>
- <listitem>
- <para><methodname
- xlink:href="http://junit.org/junit4/javadoc/latest/org/junit/Assert.html">assertNotEquals([String
- message],...)</methodname></para>
- </listitem>
+ <listitem>
+ <para><methodname
+ xlink:href="http://junit.org/junit4/javadoc/latest/org/junit/Assert.html">assertFalse([String
+ message],...)</methodname></para>
+ </listitem>
- <listitem>
- <para><methodname
- xlink:href="http://junit.org/junit4/javadoc/latest/org/junit/Assert.html">assertNull([String
- message],...)</methodname></para>
- </listitem>
+ <listitem>
+ <para><methodname
+ xlink:href="http://junit.org/junit4/javadoc/latest/org/junit/Assert.html">assertNotEquals([String
+ message],...)</methodname></para>
+ </listitem>
- <listitem>
- <para><methodname
- xlink:href="http://junit.org/junit4/javadoc/latest/org/junit/Assert.html">fail([String
- message],...)</methodname></para>
- </listitem>
- </itemizedlist>
- </figure>
+ <listitem>
+ <para><methodname
+ xlink:href="http://junit.org/junit4/javadoc/latest/org/junit/Assert.html">assertNull([String
+ message],...)</methodname></para>
+ </listitem>
+
+ <listitem>
+ <para><methodname
+ xlink:href="http://junit.org/junit4/javadoc/latest/org/junit/Assert.html">fail([String
+ message],...)</methodname></para>
+ </listitem>
+ </itemizedlist>
+ </figure>
- <figure xml:id="sd1_fig_equalsDoubleCaveat">
- <title>Caution comparing <code language="java">float</code> / <code
- language="java">double</code> !!</title>
+ <figure xml:id="sd1_fig_equalsDoubleCaveat">
+ <title>Caution comparing <code language="java">float</code> / <code
+ language="java">double</code> !!</title>
- <mediaobject>
- <imageobject>
- <imagedata fileref="Ref/ObjectsAndClasses/Tests/cautionEqualsDouble.png"/>
- </imageobject>
- </mediaobject>
- </figure>
+ <mediaobject>
+ <imageobject>
+ <imagedata fileref="Ref/ObjectsAndClasses/Tests/cautionEqualsDouble.png"/>
+ </imageobject>
+ </mediaobject>
+ </figure>
- <figure xml:id="sd1_fig_equalsDoubleCaveatResult">
- <title>Weird arithmetics?</title>
+ <figure xml:id="sd1_fig_equalsDoubleCaveatResult">
+ <title>Weird arithmetics?</title>
- <screen>java.lang.AssertionError: <emphasis role="red">Use assertEquals(expected, actual, delta)</emphasis>
+ <screen>java.lang.AssertionError: <emphasis role="red">Use assertEquals(expected, actual, delta)</emphasis>
to compare floating-point numbers
at org.junit.Assert.assertEquals(Assert.java:656)
at qq.doubleCompareTest.test1_3(<emphasis role="red">doubleCompareTest.java:15</emphasis>)
...</screen>
- </figure>
+ </figure>
- <figure xml:id="sd1_fig_equalsDoubleCaveatUnderlyingProblem">
- <title>Limited representation precision</title>
+ <figure xml:id="sd1_fig_equalsDoubleCaveatUnderlyingProblem">
+ <title>Limited representation precision</title>
- <programlisting language="java">System.out.println("3.6 - 3 * 1.2 == " + (3.6 - 3 * 1.2));</programlisting>
+ <programlisting language="java">System.out.println("3.6 - 3 * 1.2 == " + (3.6 - 3 * 1.2));</programlisting>
- <para>Result:</para>
+ <para>Result:</para>
- <screen>3.6 - 3 * 1.2 == 4.440892098500626E-16</screen>
- </figure>
+ <screen>3.6 - 3 * 1.2 == 4.440892098500626E-16</screen>
+ </figure>
- <figure xml:id="sd1_fig_equalsDoubleSolve">
- <title>Solving the issue</title>
+ <figure xml:id="sd1_fig_equalsDoubleSolve">
+ <title>Solving the issue</title>
- <programlisting language="java">public class doubleCompareTest {
+ <programlisting language="java">public class doubleCompareTest {
static final double delta = 1E-15;
/**
* Comparing 3.6 and 3 * 1.2 within delta's limit
@@ -10955,22 +10968,22 @@ at qq.doubleCompareTest.test1_3(<emphasis role="red">doubleCompareTest.java:15</
Assert.assertEquals(3.6, 3 * 1.2 , delta);
}
}</programlisting>
- </figure>
+ </figure>
- <qandaset defaultlabel="qanda" xml:id="sd1QandaSumInteger">
- <title>Summing up integers to a given limit</title>
+ <qandaset defaultlabel="qanda" xml:id="sd1QandaSumInteger">
+ <title>Summing up integers to a given limit</title>
- <qandadiv>
- <qandaentry>
- <question>
- <para>Suppose an arbitrary number n is given e.g n=5. We want to
- compute the sum of all integers ranging from 1 to 5:</para>
+ <qandadiv>
+ <qandaentry>
+ <question>
+ <para>Suppose an arbitrary number n is given e.g n=5. We want to
+ compute the sum of all integers ranging from 1 to 5:</para>
- <para>1 + 2 + 3 + 4 + 5 = 15</para>
+ <para>1 + 2 + 3 + 4 + 5 = 15</para>
- <para>Implement the following method by using a loop:</para>
+ <para>Implement the following method by using a loop:</para>
- <programlisting language="java">/**
+ <programlisting language="java">/**
* Summing up all integers starting from 0 up to and including a given limit
* Example: Let the limit be 5, then the result is 1 + 2 + 3 + 4 + 5
*
@@ -10981,25 +10994,25 @@ public static long getSum (int limit) {
...
}</programlisting>
- <para>For the sake of getting used to it write some unit tests
- beforehand.</para>
+ <para>For the sake of getting used to it write some unit tests
+ beforehand.</para>
- <para>BTW: Is it possible to avoid the loop completely achieving
- the same result?</para>
- </question>
+ <para>BTW: Is it possible to avoid the loop completely achieving
+ the same result?</para>
+ </question>
- <answer>
- <para>The solution's class
- <classname>de.hdm_stuttgart.de.sd1.sum.Summing</classname> is
- being contained within:</para>
+ <answer>
+ <para>The solution's class
+ <classname>de.hdm_stuttgart.de.sd1.sum.Summing</classname> is
+ being contained within:</para>
- <annotation role="make">
- <para role="eclipse">Sd1/summing/V1</para>
- </annotation>
+ <annotation role="make">
+ <para role="eclipse">Sd1/summing/V1</para>
+ </annotation>
- <para>We start by defining unit tests beforehand:</para>
+ <para>We start by defining unit tests beforehand:</para>
- <programlisting language="java">/**
+ <programlisting language="java">/**
* Testing negative values and zero.
*/
@Test
@@ -11019,92 +11032,93 @@ public static long getSum (int limit) {
assertEquals(2147450880, Summing.getSum(65535));// Highest Integer.MAX_VALUE compatible value
}</programlisting>
- <para>The crucial part here is determining 1 + 2 + ... + 65535
- being equal to 2147450880. Legend has it the young <personname
- xlink:href="https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss">Carl
- Friedrich Gauss</personname> at school was asked summing up 1 + 2
- + ... + 99 + 100. His teacher was keen for some peaceful time but
- the young pupil decided otherwise:</para>
+ <para>The crucial part here is determining 1 + 2 + ... + 65535
+ being equal to 2147450880. Legend has it the young <personname
+ xlink:href="https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss">Carl
+ Friedrich Gauss</personname> at school was asked summing up 1 +
+ 2 + ... + 99 + 100. His teacher was keen for some peaceful time
+ but the young pupil decided otherwise:</para>
- <informalequation>
- <mathphrase>$\underbrace{1 + \underbrace{2 + \underbrace{3 +
- \dots + 98}_{101} + 99}_{101} + 100}_{101}$</mathphrase>
- </informalequation>
+ <informalequation>
+ <mathphrase>$\underbrace{1 + \underbrace{2 + \underbrace{3 +
+ \dots + 98}_{101} + 99}_{101} + 100}_{101}$</mathphrase>
+ </informalequation>
- <para>Since there are 50 such terms the result is <inlineequation>
- <m:math display="inline">
- <m:mrow>
+ <para>Since there are 50 such terms the result is
+ <inlineequation>
+ <m:math display="inline">
<m:mrow>
- <m:mi>50</m:mi>
+ <m:mrow>
+ <m:mi>50</m:mi>
- <m:mo>×</m:mo>
+ <m:mo>×</m:mo>
- <m:mi>101</m:mi>
- </m:mrow>
+ <m:mi>101</m:mi>
+ </m:mrow>
- <m:mo>=</m:mo>
+ <m:mo>=</m:mo>
- <m:mi>5050</m:mi>
- </m:mrow>
- </m:math>
- </inlineequation>. Generalizing this example we have:</para>
+ <m:mi>5050</m:mi>
+ </m:mrow>
+ </m:math>
+ </inlineequation>. Generalizing this example we have:</para>
- <informalequation>
- <m:math display="block">
- <m:mrow>
+ <informalequation>
+ <m:math display="block">
<m:mrow>
- <m:munderover>
- <m:mo>∑</m:mo>
-
- <m:mrow>
- <m:mi>i</m:mi>
-
- <m:mo>=</m:mo>
+ <m:mrow>
+ <m:munderover>
+ <m:mo>∑</m:mo>
- <m:mi>1</m:mi>
- </m:mrow>
+ <m:mrow>
+ <m:mi>i</m:mi>
- <m:mi>n</m:mi>
- </m:munderover>
+ <m:mo>=</m:mo>
- <m:mi>i</m:mi>
- </m:mrow>
+ <m:mi>1</m:mi>
+ </m:mrow>
- <m:mo>=</m:mo>
+ <m:mi>n</m:mi>
+ </m:munderover>
- <m:mfrac>
- <m:mrow>
- <m:mi>n</m:mi>
+ <m:mi>i</m:mi>
+ </m:mrow>
- <m:mo>â¢</m:mo>
+ <m:mo>=</m:mo>
+ <m:mfrac>
<m:mrow>
- <m:mo>(</m:mo>
+ <m:mi>n</m:mi>
+
+ <m:mo>â¢</m:mo>
<m:mrow>
- <m:mi>n</m:mi>
+ <m:mo>(</m:mo>
- <m:mo>+</m:mo>
+ <m:mrow>
+ <m:mi>n</m:mi>
- <m:mi>1</m:mi>
- </m:mrow>
+ <m:mo>+</m:mo>
- <m:mo>)</m:mo>
+ <m:mi>1</m:mi>
+ </m:mrow>
+
+ <m:mo>)</m:mo>
+ </m:mrow>
</m:mrow>
- </m:mrow>
- <m:mi>2</m:mi>
- </m:mfrac>
- </m:mrow>
- </m:math>
- </informalequation>
+ <m:mi>2</m:mi>
+ </m:mfrac>
+ </m:mrow>
+ </m:math>
+ </informalequation>
- <para>For the current exercise we do not make use of this. Instead
- we implement <link
- xlink:href="P/Sd1/summing/target/site/apidocs/de/hdm_stuttgart/sd1/sum/Summing.html#getSum-int-">Summing.getSum(...)</link>
- by coding a loop:</para>
+ <para>For the current exercise we do not make use of this.
+ Instead we implement <link
+ xlink:href="P/Sd1/summing/target/site/apidocs/de/hdm_stuttgart/sd1/sum/Summing.html#getSum-int-">Summing.getSum(...)</link>
+ by coding a loop:</para>
- <programlisting language="java">/**
+ <programlisting language="java">/**
* Summing up all integers starting from 0 up to and including a given limit
* Example: Let the limit be 5, then the result is 1 + 2 + 3 + 4 + 5
*
@@ -11120,82 +11134,82 @@ public static long getSum (int limit) {
}
}</programlisting>
- <para>This passes all tests.</para>
- </answer>
- </qandaentry>
- </qandadiv>
- </qandaset>
+ <para>This passes all tests.</para>
+ </answer>
+ </qandaentry>
+ </qandadiv>
+ </qandaset>
- <qandaset defaultlabel="qanda" xml:id="sd1QandaSumIntegerGauss">
- <title>Summing up, the better way</title>
+ <qandaset defaultlabel="qanda" xml:id="sd1QandaSumIntegerGauss">
+ <title>Summing up, the better way</title>
- <qandadiv>
- <qandaentry>
- <question>
- <para>The previous solution of <xref
- linkend="sd1QandaSumInteger"/> suffers from a performance issue.
- When dealing with large values like 65535 looping will take some
- time:</para>
+ <qandadiv>
+ <qandaentry>
+ <question>
+ <para>The previous solution of <xref
+ linkend="sd1QandaSumInteger"/> suffers from a performance issue.
+ When dealing with large values like 65535 looping will take some
+ time:</para>
- <programlisting language="java">long start = System.nanoTime();
+ <programlisting language="java">long start = System.nanoTime();
System.out.println("1 + 2 + ... + 65535" + "=" + getSum(65535));
long end = System.nanoTime();
System.out.println("Elapsed time: " + (end - start) + " nanoseconds");</programlisting>
- <screen>1 + 2 + ... + 65535=2147450880
+ <screen>1 + 2 + ... + 65535=2147450880
Elapsed time: 1169805 nanoseconds</screen>
- <para>Barely more than one millisecond seems to be acceptable. But
- using the method for calculations inside some tight loop this
- might have a serious negative performance impact.</para>
+ <para>Barely more than one millisecond seems to be acceptable.
+ But using the method for calculations inside some tight loop
+ this might have a serious negative performance impact.</para>
- <para>Thus implement a better (quicker) solution avoiding the loop
- by using the explicit form. When you are finished re-estimate
- execution time and compare the result to the previous
- solution.</para>
+ <para>Thus implement a better (quicker) solution avoiding the
+ loop by using the explicit form. When you are finished
+ re-estimate execution time and compare the result to the
+ previous solution.</para>
- <para>Provide unit tests and take care of larger values. What is
- the largest possible value? Test it as well!</para>
+ <para>Provide unit tests and take care of larger values. What is
+ the largest possible value? Test it as well!</para>
- <tip>
- <para>Read <quote
- xlink:href="https://betterexplained.com/articles/techniques-for-adding-the-numbers-1-to-100">Techniques
- for Adding the Numbers 1 to 100</quote>.</para>
- </tip>
- </question>
+ <tip>
+ <para>Read <quote
+ xlink:href="https://betterexplained.com/articles/techniques-for-adding-the-numbers-1-to-100">Techniques
+ for Adding the Numbers 1 to 100</quote>.</para>
+ </tip>
+ </question>
- <answer>
- <para>The solution's class
- <classname>de.hdm_stuttgart.de.sd1.sum.Summing</classname> is
- being contained within:</para>
+ <answer>
+ <para>The solution's class
+ <classname>de.hdm_stuttgart.de.sd1.sum.Summing</classname> is
+ being contained within:</para>
- <annotation role="make">
- <para role="eclipse">Sd1/summing/V2</para>
- </annotation>
+ <annotation role="make">
+ <para role="eclipse">Sd1/summing/V2</para>
+ </annotation>
- <para>Since only our implementation changes we reuse our existing
- unit tests. Our first straightforward implementation attempt
- reads:</para>
+ <para>Since only our implementation changes we reuse our
+ existing unit tests. Our first straightforward implementation
+ attempt reads:</para>
- <programlisting language="java" linenumbering="unnumbered">public static long getSum (int limit) {
+ <programlisting language="java" linenumbering="unnumbered">public static long getSum (int limit) {
return limit * (limit + 1) / 2;
}</programlisting>
- <para>This fails both unit tests. The first error happens
- at:</para>
+ <para>This fails both unit tests. The first error happens
+ at:</para>
- <programlisting language="java" linenumbering="unnumbered">assertEquals(0, Summing.getSum(-5));</programlisting>
+ <programlisting language="java" linenumbering="unnumbered">assertEquals(0, Summing.getSum(-5));</programlisting>
- <screen>java.lang.AssertionError:
+ <screen>java.lang.AssertionError:
Expected :0
Actual :10</screen>
- <para>We forgot to deal with negative <code
- language="java">limit</code> values. Our sum is supposed to start
- with 0 so negative <code language="java">limit</code> values
- should yield 0 like in our loop based solution:</para>
+ <para>We forgot to deal with negative <code
+ language="java">limit</code> values. Our sum is supposed to
+ start with 0 so negative <code language="java">limit</code>
+ values should yield 0 like in our loop based solution:</para>
- <programlisting language="java">public static long getSum(int limit) {
+ <programlisting language="java">public static long getSum(int limit) {
if (limit < 0) {
return 0;
} else {
@@ -11203,29 +11217,29 @@ Actual :10</screen>
}
}</programlisting>
- <para>This helps but one test still fails:</para>
+ <para>This helps but one test still fails:</para>
- <programlisting language="java">assertEquals(2147450880, Summing.getSumUsingGauss(65535));</programlisting>
+ <programlisting language="java">assertEquals(2147450880, Summing.getSumUsingGauss(65535));</programlisting>
- <screen>java.lang.AssertionError:
+ <screen>java.lang.AssertionError:
Expected :2147450880
Actual :-32768</screen>
- <para>This actually is a showstopper for large <code
- language="java">limit</code> values: The algebraic value of <code
- language="java">limit * (limit + 1) / 2</code> might still fit
- into an <code language="java">int</code>. But <code
- language="java">limit * (limit + 1)</code> itself not yet divided
- by 2 may exceed <code language="java"
- xlink:href="https://docs.oracle.com/javase/10/docs/api/java/lang/Integer.html#MAX_VALUE">Integer.MAX_VALUE</code>.
- Since the multiplication happens prior to dividing by 2 we see
- this overflow error happen.</para>
-
- <para>Solving this issue requires changing the order of operations
- avoiding arithmetic overflow. Unfortunately the following simple
- solution does not work either:</para>
-
- <programlisting language="java">public static long getSum(int limit) {
+ <para>This actually is a showstopper for large <code
+ language="java">limit</code> values: The algebraic value of
+ <code language="java">limit * (limit + 1) / 2</code> might still
+ fit into an <code language="java">int</code>. But <code
+ language="java">limit * (limit + 1)</code> itself not yet
+ divided by 2 may exceed <code language="java"
+ xlink:href="https://docs.oracle.com/javase/10/docs/api/java/lang/Integer.html#MAX_VALUE">Integer.MAX_VALUE</code>.
+ Since the multiplication happens prior to dividing by 2 we see
+ this overflow error happen.</para>
+
+ <para>Solving this issue requires changing the order of
+ operations avoiding arithmetic overflow. Unfortunately the
+ following simple solution does not work either:</para>
+
+ <programlisting language="java">public static long getSum(int limit) {
if (limit < 0) {
return 0;
} else {
@@ -11233,15 +11247,15 @@ Actual :-32768</screen>
}
}</programlisting>
- <para>This is only correct if <code language="java">limit</code>
- is even. Otherwise division by 2 leaves us with a remainder of
- 1.</para>
+ <para>This is only correct if <code language="java">limit</code>
+ is even. Otherwise division by 2 leaves us with a remainder of
+ 1.</para>
- <para>However if <code language="java">limit</code> is uneven the
- second factor <code language="java">limit + 1</code> will be even.
- This observation leads us to the final solution:</para>
+ <para>However if <code language="java">limit</code> is uneven
+ the second factor <code language="java">limit + 1</code> will be
+ even. This observation leads us to the final solution:</para>
- <programlisting language="java">public static long getSum(int limit) {
+ <programlisting language="java">public static long getSum(int limit) {
if (limit < 0) {
return 0;
} else if (0 == limit % 2){ // even limit, divide by 2
@@ -11251,18 +11265,19 @@ Actual :-32768</screen>
}
}</programlisting>
- <para>This passes all tests. We finally reconsider execution
- time:</para>
+ <para>This passes all tests. We finally reconsider execution
+ time:</para>
- <screen>1 + 2 + ... + 65535=2147450880
+ <screen>1 + 2 + ... + 65535=2147450880
Elapsed time: 25422 nanoseconds</screen>
- <para>Thus execution is roughly 46 times faster compared to the
- loop based approach. This is not surprising since loop execution
- is expensive in terms of performance.</para>
- </answer>
- </qandaentry>
- </qandadiv>
- </qandaset>
+ <para>Thus execution is roughly 46 times faster compared to the
+ loop based approach. This is not surprising since loop execution
+ is expensive in terms of performance.</para>
+ </answer>
+ </qandaentry>
+ </qandadiv>
+ </qandaset>
+ </section>
</section>
</chapter>
--
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