From 5d7df1f8472acf4d945634491f0bd1aceece4049 Mon Sep 17 00:00:00 2001
From: Michael Johnson <michael.johnson.lucas@gmail.com>
Date: Sun, 15 Feb 2015 20:51:04 +0100
Subject: [PATCH 1/5] =?UTF-8?q?New=20Trigonometric=20and=20Hyperbolic=20fu?=
 =?UTF-8?q?nctions=20included.=20It=C2=B4s=20not=20totally=20polished.?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 classes/src/functions/acoth.php               | 27 +++++++++
 classes/src/functions/coth.php                | 26 +++++++++
 classes/src/functions/gudermannian.php        | 20 +++++++
 classes/src/functions/haversine.php           | 31 ++++++++++
 classes/src/functions/inversegudermannian.php | 21 +++++++
 classes/src/functions/inversehaversine.php    | 27 +++++++++
 classes/src/functions/tanh.php                | 21 +++++++
 examples/complexTest2.php                     | 17 ++++--
 examples/complexTest3.php                     | 56 +++++++++++++++++++
 9 files changed, 241 insertions(+), 5 deletions(-)
 create mode 100644 classes/src/functions/acoth.php
 create mode 100644 classes/src/functions/coth.php
 create mode 100644 classes/src/functions/gudermannian.php
 create mode 100644 classes/src/functions/haversine.php
 create mode 100644 classes/src/functions/inversegudermannian.php
 create mode 100644 classes/src/functions/inversehaversine.php
 create mode 100644 classes/src/functions/tanh.php
 create mode 100644 examples/complexTest3.php

diff --git a/classes/src/functions/acoth.php b/classes/src/functions/acoth.php
new file mode 100644
index 0000000..7c61bd9
--- /dev/null
+++ b/classes/src/functions/acoth.php
@@ -0,0 +1,27 @@
+<?php
+/**
+ * Created by PhpStorm.
+ * User: Michael
+ * Date: 12-Feb-15
+ * Time: 7:56 AM
+ */
+namespace Complex;
+
+function acoth( $complex )
+{
+    $complex = Complex::validateComplexArgument( $complex );
+
+    if ($complex->getImaginary() == 0.0) {
+        if ( ( $complex->getReal() == -1 ) || ( $complex->getReal() == 1 ) ) {
+            return INF;
+        } else {
+            $calc = clone $complex;
+            $complex = $complex->add( 1 );
+            $calc = $calc->subtract( 1 );
+            $complex = $complex->divideBy( $calc );
+            $complex = ln( $complex );
+            $complex = $complex->divideBy( 2 );
+            return $complex;
+        }
+    }
+}
\ No newline at end of file
diff --git a/classes/src/functions/coth.php b/classes/src/functions/coth.php
new file mode 100644
index 0000000..e25eea5
--- /dev/null
+++ b/classes/src/functions/coth.php
@@ -0,0 +1,26 @@
+<?php
+/**
+ * Created by PhpStorm.
+ * User: Michael
+ * Date: 12-Feb-15
+ * Time: 7:56 AM
+ */
+namespace Complex;
+
+function coth( $complex )
+{
+    $complex = Complex::validateComplexArgument( $complex );
+
+    if ($complex->getImaginary() == 0.0) {
+        $calc = clone $complex;
+        $complex = cosh( $complex );
+        $calc = sinh( $calc );
+
+        if ( $calc->getReal() != 0 ) {
+            $complex = $complex->divideBy( $calc );
+            return $complex;
+        } else {
+            return null;
+        }
+    }
+}
\ No newline at end of file
diff --git a/classes/src/functions/gudermannian.php b/classes/src/functions/gudermannian.php
new file mode 100644
index 0000000..9d40692
--- /dev/null
+++ b/classes/src/functions/gudermannian.php
@@ -0,0 +1,20 @@
+<?php
+/**
+ * Created by PhpStorm.
+ * User: Michael
+ * Date: 12-Feb-15
+ * Time: 7:56 AM
+ */
+namespace Complex;
+function gudermannian( $complex )
+{
+    $complex = Complex::validateComplexArgument( $complex );
+
+    if ($complex->getImaginary() == 0.0) {
+        $complex = exp( $complex );
+        $complex = atan( $complex );
+        $complex = $complex->multiply( 2 );
+        $complex = $complex->add( -( M_PI/2 ) );
+        return $complex;
+    }
+}
\ No newline at end of file
diff --git a/classes/src/functions/haversine.php b/classes/src/functions/haversine.php
new file mode 100644
index 0000000..be86d7f
--- /dev/null
+++ b/classes/src/functions/haversine.php
@@ -0,0 +1,31 @@
+<?php
+
+/**
+ *
+ * Function code for the complex haversine() function
+ *
+ * @copyright  Copyright (c) 2013-2015 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
+ * @author     Michael A. Johnosn
+ */
+namespace Complex;
+
+/**
+ * Returns the haversine of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The haversine of the complex argument.
+ * @throws    \Exception       If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function haversine( $complex )
+{
+    $complex = Complex::validateComplexArgument( $complex );
+
+    if ($complex->getImaginary() == 0.0) {
+        $complex = $complex->divideBy( 2 );
+        $complex = sin( $complex );
+        $complex = $complex->multiply( $complex );
+        return $complex;
+    }
+}
\ No newline at end of file
diff --git a/classes/src/functions/inversegudermannian.php b/classes/src/functions/inversegudermannian.php
new file mode 100644
index 0000000..7c5982d
--- /dev/null
+++ b/classes/src/functions/inversegudermannian.php
@@ -0,0 +1,21 @@
+<?php
+/**
+ * Created by PhpStorm.
+ * User: Michael
+ * Date: 12-Feb-15
+ * Time: 7:56 AM
+ */
+namespace Complex;
+
+function inversegudermannian( $complex )
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->getImaginary() == 0.0) {
+        $complex = $complex->divideBy( 2 );
+        $complex = $complex->add( M_PI/4 );
+        $complex = tan( $complex );
+        $complex = ln( $complex );
+        return $complex;
+    }
+}
\ No newline at end of file
diff --git a/classes/src/functions/inversehaversine.php b/classes/src/functions/inversehaversine.php
new file mode 100644
index 0000000..24afa56
--- /dev/null
+++ b/classes/src/functions/inversehaversine.php
@@ -0,0 +1,27 @@
+<?php
+/**
+ * Created by PhpStorm.
+ * User: Michael
+ * Date: 12-Feb-15
+ * Time: 7:55 AM
+ */
+namespace Complex;
+
+/**
+ * @param $complex
+ * @return Complex
+ * @throws \Exception
+ */
+function inversehaversine( $complex )
+{
+    $complex = Complex::validateComplexArgument( $complex );
+
+    if ( $complex->getImaginary() == 0.0 ) {
+        if (($complex->getReal() >= 0.0) && ($complex->getReal() <= 1.0)) {
+            $complex = sqrt( $complex );
+            $complex = asin( $complex );
+            $complex = $complex->multiply( 2 );
+            return $complex;
+        }
+    }
+}
\ No newline at end of file
diff --git a/classes/src/functions/tanh.php b/classes/src/functions/tanh.php
new file mode 100644
index 0000000..be92a71
--- /dev/null
+++ b/classes/src/functions/tanh.php
@@ -0,0 +1,21 @@
+<?php
+/**
+ * Created by PhpStorm.
+ * User: Michael
+ * Date: 12-Feb-15
+ * Time: 7:56 AM
+ */
+namespace Complex;
+
+function tanh( $complex )
+{
+    $complex = Complex::validateComplexArgument( $complex );
+
+    if ($complex->getImaginary() == 0.0) {
+        $calc = clone $complex;
+        $complex = sinh( $complex );
+        $calc = cosh( $calc );
+        $complex = $complex->divideBy( $calc );
+        return $complex;
+    }
+}
\ No newline at end of file
diff --git a/examples/complexTest2.php b/examples/complexTest2.php
index 91c827a..9bf4aa3 100644
--- a/examples/complexTest2.php
+++ b/examples/complexTest2.php
@@ -4,7 +4,7 @@
 
 include('../classes/Bootstrap.php');
 
-echo 'Function Examples', PHP_EOL;
+echo "<h3>Function Examples</h3><br/>", PHP_EOL;
 
 $functions = [
     'abs',
@@ -33,7 +33,14 @@
     'sin',
     'sinh',
     'sqrt',
-    'theta'
+    'theta',
+    'acoth',
+    'coth',
+    'gudermannian',
+    'haversine',
+    'inversegudermannian',
+    'inversehaversine',
+    'tanh'
 ];
 
 for($real = -3.5; $real <= 3.5; $real += 0.5) {
@@ -42,11 +49,11 @@
             $complexFunction = __NAMESPACE__ . '\\' . $function;
             $complex = new Complex($real, $imaginary);
             try {
-                echo $function, '(', $complex, ') = ', $complexFunction($complex), PHP_EOL;
+                echo $function, '(', $complex, ') = ', $complexFunction($complex), "<br/>",PHP_EOL;
             } catch(\Exception $e) {
-                echo $function, '(', $complex, ') ERROR: ', $e->getMessage(), PHP_EOL;
+                echo $function, '(', $complex, ') ERROR: ', $e->getMessage(), "<br/>", PHP_EOL;
             }
         }
-        echo PHP_EOL;
+        echo "<br/>",PHP_EOL;
     }
 }
diff --git a/examples/complexTest3.php b/examples/complexTest3.php
new file mode 100644
index 0000000..ae99c01
--- /dev/null
+++ b/examples/complexTest3.php
@@ -0,0 +1,56 @@
+<?php
+namespace Complex;
+include('../classes/Bootstrap.php');
+
+$complexFunction1 =  __NAMESPACE__ . '\\' . 'cos';
+$complexFunction2 =  __NAMESPACE__ . '\\' . 'haversine';
+$complexFunction3 =  __NAMESPACE__ . '\\' . 'inversehaversine';
+$complexFunction4 =  __NAMESPACE__ . '\\' . 'gudermannian';
+$complexFunction5 =  __NAMESPACE__ . '\\' . 'inversegudermannian';
+$complexFunction6 =  __NAMESPACE__ . '\\' . 'acoth';
+$complexFunction7 =  __NAMESPACE__ . '\\' . 'coth';
+$complexFunction8 =  __NAMESPACE__ . '\\' . 'tanh';
+
+
+echo $complexFunction1( 9 ) . '<br/>' . PHP_EOL;
+echo "<h3>Haversine</h3><br/>" . PHP_EOL;
+for ( $i = -10; $i <= 10; $i++ ) {
+    echo ( $i ) . ': ' . $complexFunction2( $i ) . '<br/>' . PHP_EOL;
+}
+unset($i);
+
+echo "<h3>Inverse haversine</h3><br/>" . PHP_EOL;
+for ( $i = -10; $i <= 10; $i++ ) {
+    echo ( $i ) . ': ' . $complexFunction3( $i ) . '<br/>' . PHP_EOL;
+}
+unset($i);
+
+echo "<h3>Gudermannian</h3><br/>" . PHP_EOL;
+for ( $i = -10; $i <= 10; $i++ ) {
+    echo ( $i ) . ': ' . $complexFunction4( $i ) . '<br/>' . PHP_EOL;
+}
+unset($i);
+
+echo "<h3>InverseGudermannian</h3><br/>" . PHP_EOL;
+for ( $i = -10; $i <= 10; $i++ ) {
+    echo ( $i ) . ': ' . $complexFunction5( $i ) . '<br/>' . PHP_EOL;
+}
+unset($i);
+
+echo "<h3>ArcCoth</h3><br/>" . PHP_EOL;
+for ( $i = -10; $i <= 10; $i++ ) {
+    echo ( $i ) . ': ' . $complexFunction6( $i ) . '<br/>' . PHP_EOL;
+}
+unset($i);
+
+echo "<h3>Coth</h3><br/>" . PHP_EOL;
+for ( $i = -10; $i <= 10; $i++ ) {
+    echo ( $i ) . ': ' . $complexFunction7( $i ) . '<br/>' . PHP_EOL;
+}
+unset($i);
+
+echo "<h3>Tanh</h3><br/>" . PHP_EOL;
+for ( $i = -10; $i <= 10; $i++ ) {
+    echo ( $i ) . ': ' . $complexFunction8( $i ) . '<br/>' . PHP_EOL;
+}
+unset($i);
\ No newline at end of file

From 1c280bf3949c8a3afbc32b12cb62c3ccaf164ba5 Mon Sep 17 00:00:00 2001
From: ephod <michael.johnson.lucas@gmail.com>
Date: Sun, 15 Feb 2015 21:01:05 +0100
Subject: [PATCH 2/5] Update README.md

---
 README.md | 12 +++++++++++-
 1 file changed, 11 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index ed65083..3939c33 100644
--- a/README.md
+++ b/README.md
@@ -58,4 +58,14 @@ Planned additional functionality, but still to implement
  * coth (hyperbolic cotangent)
  * acoth (inverse hyperbolic cotangent)
  * pow (power)
- 
\ No newline at end of file
+ 
+---
+Functions added
+- tanh (hyperbolic tangent)
+- coth (hyperbolic cotangent)
+- acoth (inverse hyperbolic cotangent)
+- gudermannian () Hyperbolic
+- inversegudermannian () Hyperbolic
+- haversine () Trigonometric
+- inversehaversine () Trigonometric
+ 

From 758a89e12036ceed76ee9f5a871550835dc20db5 Mon Sep 17 00:00:00 2001
From: Michael Johnson <michael.johnson.lucas@gmail.com>
Date: Sun, 15 Feb 2015 21:28:39 +0100
Subject: [PATCH 3/5] ArcTanh added.

---
 classes/src/functions/atanh.php | 46 +++++++++++++++++++++++++++++++++
 examples/complexTest2.php       |  3 ++-
 examples/complexTest3.php       | 13 ++++++++++
 3 files changed, 61 insertions(+), 1 deletion(-)
 create mode 100644 classes/src/functions/atanh.php

diff --git a/classes/src/functions/atanh.php b/classes/src/functions/atanh.php
new file mode 100644
index 0000000..31870d8
--- /dev/null
+++ b/classes/src/functions/atanh.php
@@ -0,0 +1,46 @@
+<?php
+
+/**
+ *
+ * Function code for the complex atan() function
+ *
+ * @copyright  Copyright (c) 2013-2015 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
+ */
+namespace Complex;
+
+//include_once 'Math/Complex.php';
+//include_once 'Math/ComplexOp.php';
+
+/**
+ * Returns the inverse tangent of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse tangent of the complex argument.
+ * @throws    \Exception       If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function atanh( $complex )
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->getImaginary() == 0.0) {
+        if ( ( $complex->getReal() == -1 )  || ( $complex->getReal() == 1 ) ){
+            return INF;
+        } else {
+            $calc = clone $complex;
+
+            $complex->add( 1 );
+            $complex = ln( $complex );
+
+            $calc = $calc->multiply( -1 );
+            $calc = $calc->add( 1 );
+            $calc = ln( $calc );
+
+            $complex = $complex->subtract( $calc );
+            $complex = $complex->divideBy( 2 );
+
+            return $complex;
+        }
+    }
+}
diff --git a/examples/complexTest2.php b/examples/complexTest2.php
index 9bf4aa3..b9a88c7 100644
--- a/examples/complexTest2.php
+++ b/examples/complexTest2.php
@@ -40,7 +40,8 @@
     'haversine',
     'inversegudermannian',
     'inversehaversine',
-    'tanh'
+    'tanh',
+    'atanh'
 ];
 
 for($real = -3.5; $real <= 3.5; $real += 0.5) {
diff --git a/examples/complexTest3.php b/examples/complexTest3.php
index ae99c01..7a0b711 100644
--- a/examples/complexTest3.php
+++ b/examples/complexTest3.php
@@ -10,6 +10,7 @@
 $complexFunction6 =  __NAMESPACE__ . '\\' . 'acoth';
 $complexFunction7 =  __NAMESPACE__ . '\\' . 'coth';
 $complexFunction8 =  __NAMESPACE__ . '\\' . 'tanh';
+$complexFunction9 =  __NAMESPACE__ . '\\' . 'atanh';
 
 
 echo $complexFunction1( 9 ) . '<br/>' . PHP_EOL;
@@ -53,4 +54,16 @@
 for ( $i = -10; $i <= 10; $i++ ) {
     echo ( $i ) . ': ' . $complexFunction8( $i ) . '<br/>' . PHP_EOL;
 }
+unset($i);
+
+echo "<h3>Tanh</h3><br/>" . PHP_EOL;
+for ( $i = -10; $i <= 10; $i++ ) {
+    echo ( $i ) . ': ' . $complexFunction8( $i ) . '<br/>' . PHP_EOL;
+}
+unset($i);
+
+echo "<h3>ArcTanh</h3><br/>" . PHP_EOL;
+for ( $i = -10; $i <= 10; $i++ ) {
+    echo ( $i ) . ': ' . $complexFunction9( $i ) . '<br/>' . PHP_EOL;
+}
 unset($i);
\ No newline at end of file

From c6755b2fe50770aa41060d8ad118500def1e47b5 Mon Sep 17 00:00:00 2001
From: ephod <michael.johnson.lucas@gmail.com>
Date: Sun, 15 Feb 2015 21:29:56 +0100
Subject: [PATCH 4/5] Update README.md

---
 README.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.md b/README.md
index 3939c33..741f5eb 100644
--- a/README.md
+++ b/README.md
@@ -62,6 +62,7 @@ Planned additional functionality, but still to implement
 ---
 Functions added
 - tanh (hyperbolic tangent)
+- atanh (inverse hyperbolic tangent)
 - coth (hyperbolic cotangent)
 - acoth (inverse hyperbolic cotangent)
 - gudermannian () Hyperbolic

From 9898045be68616786be6482a9997a5fe819b37f1 Mon Sep 17 00:00:00 2001
From: Michael Johnson <michael.johnson.lucas@gmail.com>
Date: Mon, 16 Feb 2015 08:57:48 +0100
Subject: [PATCH 5/5] PHP Docs modified.

---
 classes/src/functions/acoth.php               | 19 +++++++++++----
 classes/src/functions/atanh.php               | 24 ++++++++-----------
 classes/src/functions/coth.php                | 19 +++++++++++----
 classes/src/functions/gudermannian.php        | 20 ++++++++++++----
 classes/src/functions/haversine.php           | 18 +++++++-------
 classes/src/functions/inversegudermannian.php | 21 +++++++++++-----
 classes/src/functions/inversehaversine.php    | 20 +++++++++-------
 classes/src/functions/tanh.php                | 17 +++++++++----
 examples/complexTest3.php                     | 19 ++++++---------
 9 files changed, 107 insertions(+), 70 deletions(-)

diff --git a/classes/src/functions/acoth.php b/classes/src/functions/acoth.php
index 7c61bd9..ebd2f7e 100644
--- a/classes/src/functions/acoth.php
+++ b/classes/src/functions/acoth.php
@@ -1,17 +1,26 @@
 <?php
 /**
- * Created by PhpStorm.
- * User: Michael
- * Date: 12-Feb-15
- * Time: 7:56 AM
+ *
+ * Function code for the complex acoth() function
+ *
+ * @author Michael A. Johnson
+ * @License    http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
  */
 namespace Complex;
 
+/**
+ *
+ * Returns the inverse hyperbolic cotangent of a complex number.
+ *
+ * @param $complex Complex number or a numeric value.
+ * @return Complex|float The inverse hyperbolic cotangent of the complex argument.
+ * @throws \Exception f argument isn't a valid real or complex number.
+ */
 function acoth( $complex )
 {
     $complex = Complex::validateComplexArgument( $complex );
 
-    if ($complex->getImaginary() == 0.0) {
+    if ( $complex->getImaginary() == 0.0 ) {
         if ( ( $complex->getReal() == -1 ) || ( $complex->getReal() == 1 ) ) {
             return INF;
         } else {
diff --git a/classes/src/functions/atanh.php b/classes/src/functions/atanh.php
index 31870d8..b5e902a 100644
--- a/classes/src/functions/atanh.php
+++ b/classes/src/functions/atanh.php
@@ -1,30 +1,26 @@
 <?php
-
 /**
  *
- * Function code for the complex atan() function
+ * Function code for the complex atanh() function
  *
- * @copyright  Copyright (c) 2013-2015 Mark Baker (https://github.com/MarkBaker/PHPComplex)
- * @license    http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
+ * @author Michael A. Johnson
+ * @License    http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
  */
 namespace Complex;
 
-//include_once 'Math/Complex.php';
-//include_once 'Math/ComplexOp.php';
-
 /**
- * Returns the inverse tangent of a complex number.
  *
- * @param     Complex|mixed    $complex    Complex number or a numeric value.
- * @return    Complex          The inverse tangent of the complex argument.
- * @throws    \Exception       If argument isn't a valid real or complex number.
- * @throws    \InvalidArgumentException    If function would result in a division by zero
+ * Returns the inverse hyperbolic tangent of a complex number.
+ *
+ * @param $complex Complex number or a numeric value.
+ * @return Complex|float The inverse hyperbolic tangent of the complex argument.
+ * @throws \Exception f argument isn't a valid real or complex number.
  */
 function atanh( $complex )
 {
-    $complex = Complex::validateComplexArgument($complex);
+    $complex = Complex::validateComplexArgument( $complex );
 
-    if ($complex->getImaginary() == 0.0) {
+    if ( $complex->getImaginary() == 0.0 ) {
         if ( ( $complex->getReal() == -1 )  || ( $complex->getReal() == 1 ) ){
             return INF;
         } else {
diff --git a/classes/src/functions/coth.php b/classes/src/functions/coth.php
index e25eea5..0e19b78 100644
--- a/classes/src/functions/coth.php
+++ b/classes/src/functions/coth.php
@@ -1,17 +1,26 @@
 <?php
 /**
- * Created by PhpStorm.
- * User: Michael
- * Date: 12-Feb-15
- * Time: 7:56 AM
+ *
+ * Function code for the complex coth() function
+ *
+ * @author Michael A. Johnson
+ * @License    http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
  */
 namespace Complex;
 
+/**
+ *
+ * Returns the hyperbolic cotangent of a complex number.
+ *
+ * @param $complex Complex number or a numeric value.
+ * @return Complex|float|null The hyperbolic cotangent of the complex argument.
+ * @throws \Exception f argument isn't a valid real or complex number.
+ */
 function coth( $complex )
 {
     $complex = Complex::validateComplexArgument( $complex );
 
-    if ($complex->getImaginary() == 0.0) {
+    if ( $complex->getImaginary() == 0.0 ) {
         $calc = clone $complex;
         $complex = cosh( $complex );
         $calc = sinh( $calc );
diff --git a/classes/src/functions/gudermannian.php b/classes/src/functions/gudermannian.php
index 9d40692..415c27b 100644
--- a/classes/src/functions/gudermannian.php
+++ b/classes/src/functions/gudermannian.php
@@ -1,16 +1,26 @@
 <?php
 /**
- * Created by PhpStorm.
- * User: Michael
- * Date: 12-Feb-15
- * Time: 7:56 AM
+ *
+ * Function code for the complex gudermannian() function
+ *
+ * @author Michael A. Johnson
+ * @License    http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
  */
 namespace Complex;
+
+/**
+ *
+ * Returns the gudermannian of a complex number.
+ *
+ * @param $complex Complex number or a numeric value.
+ * @return Complex|float The gudermannian of the complex argument.
+ * @throws \Exception f argument isn't a valid real or complex number.
+ */
 function gudermannian( $complex )
 {
     $complex = Complex::validateComplexArgument( $complex );
 
-    if ($complex->getImaginary() == 0.0) {
+    if ( $complex->getImaginary() == 0.0 ) {
         $complex = exp( $complex );
         $complex = atan( $complex );
         $complex = $complex->multiply( 2 );
diff --git a/classes/src/functions/haversine.php b/classes/src/functions/haversine.php
index be86d7f..42eae81 100644
--- a/classes/src/functions/haversine.php
+++ b/classes/src/functions/haversine.php
@@ -1,28 +1,26 @@
 <?php
-
 /**
  *
  * Function code for the complex haversine() function
  *
- * @copyright  Copyright (c) 2013-2015 Mark Baker (https://github.com/MarkBaker/PHPComplex)
- * @license    http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
- * @author     Michael A. Johnosn
+ * @author Michael A. Johnson
+ * @License    http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
  */
 namespace Complex;
 
 /**
- * Returns the haversine of a complex number.
  *
- * @param     Complex|mixed    $complex    Complex number or a numeric value.
- * @return    Complex          The haversine of the complex argument.
- * @throws    \Exception       If argument isn't a valid real or complex number.
- * @throws    \InvalidArgumentException    If function would result in a division by zero
+ * Returns the haversine function of a complex number.
+ *
+ * @param $complex Complex number or a numeric value.
+ * @return Complex|float The haversine of the complex argument.
+ * @throws \Exception f argument isn't a valid real or complex number.
  */
 function haversine( $complex )
 {
     $complex = Complex::validateComplexArgument( $complex );
 
-    if ($complex->getImaginary() == 0.0) {
+    if ( $complex->getImaginary() == 0.0 ) {
         $complex = $complex->divideBy( 2 );
         $complex = sin( $complex );
         $complex = $complex->multiply( $complex );
diff --git a/classes/src/functions/inversegudermannian.php b/classes/src/functions/inversegudermannian.php
index 7c5982d..29da00b 100644
--- a/classes/src/functions/inversegudermannian.php
+++ b/classes/src/functions/inversegudermannian.php
@@ -1,17 +1,26 @@
 <?php
 /**
- * Created by PhpStorm.
- * User: Michael
- * Date: 12-Feb-15
- * Time: 7:56 AM
+ *
+ * Function code for the complex inversegudermannian() function
+ *
+ * @author Michael A. Johnson
+ * @License    http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
  */
 namespace Complex;
 
+/**
+ *
+ * Returns the inverse gudermannian of a complex number.
+ *
+ * @param $complex Complex number or a numeric value.
+ * @return Complex|float The inverse gudermannian of the complex argument.
+ * @throws \Exception f argument isn't a valid real or complex number.
+ */
 function inversegudermannian( $complex )
 {
-    $complex = Complex::validateComplexArgument($complex);
+    $complex = Complex::validateComplexArgument( $complex );
 
-    if ($complex->getImaginary() == 0.0) {
+    if ( $complex->getImaginary() == 0.0 ) {
         $complex = $complex->divideBy( 2 );
         $complex = $complex->add( M_PI/4 );
         $complex = tan( $complex );
diff --git a/classes/src/functions/inversehaversine.php b/classes/src/functions/inversehaversine.php
index 24afa56..c052479 100644
--- a/classes/src/functions/inversehaversine.php
+++ b/classes/src/functions/inversehaversine.php
@@ -1,23 +1,27 @@
 <?php
 /**
- * Created by PhpStorm.
- * User: Michael
- * Date: 12-Feb-15
- * Time: 7:55 AM
+ *
+ * Function code for the complex inversehaversine() function
+ *
+ * @author Michael A. Johnson
+ * @License    http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
  */
 namespace Complex;
 
 /**
- * @param $complex
- * @return Complex
- * @throws \Exception
+ *
+ * Returns the inverse haversine of a complex number.
+ *
+ * @param $complex Complex number or a numeric value.
+ * @return Complex|float The inverse haversine of the complex argument.
+ * @throws \Exception f argument isn't a valid real or complex number.
  */
 function inversehaversine( $complex )
 {
     $complex = Complex::validateComplexArgument( $complex );
 
     if ( $complex->getImaginary() == 0.0 ) {
-        if (($complex->getReal() >= 0.0) && ($complex->getReal() <= 1.0)) {
+        if ( ( $complex->getReal() >= 0.0 ) && ( $complex->getReal() <= 1.0 ) ) {
             $complex = sqrt( $complex );
             $complex = asin( $complex );
             $complex = $complex->multiply( 2 );
diff --git a/classes/src/functions/tanh.php b/classes/src/functions/tanh.php
index be92a71..efbd79c 100644
--- a/classes/src/functions/tanh.php
+++ b/classes/src/functions/tanh.php
@@ -1,17 +1,24 @@
 <?php
 /**
- * Created by PhpStorm.
- * User: Michael
- * Date: 12-Feb-15
- * Time: 7:56 AM
+ *
+ * Function code for the complex tanh() function
+ *
+ * @author Michael A. Johnson
+ * @License    http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
  */
 namespace Complex;
 
+/**
+ * Returns the hyperbolic tangent of a complex number.
+ *
+ * @param $complex Complex number or a numeric value.
+ * @return Complex|float The hyperbolic tangent of the complex argument.
+ */
 function tanh( $complex )
 {
     $complex = Complex::validateComplexArgument( $complex );
 
-    if ($complex->getImaginary() == 0.0) {
+    if ( $complex->getImaginary() == 0.0 ) {
         $calc = clone $complex;
         $complex = sinh( $complex );
         $calc = cosh( $calc );
diff --git a/examples/complexTest3.php b/examples/complexTest3.php
index 7a0b711..543c32f 100644
--- a/examples/complexTest3.php
+++ b/examples/complexTest3.php
@@ -7,13 +7,14 @@
 $complexFunction3 =  __NAMESPACE__ . '\\' . 'inversehaversine';
 $complexFunction4 =  __NAMESPACE__ . '\\' . 'gudermannian';
 $complexFunction5 =  __NAMESPACE__ . '\\' . 'inversegudermannian';
-$complexFunction6 =  __NAMESPACE__ . '\\' . 'acoth';
-$complexFunction7 =  __NAMESPACE__ . '\\' . 'coth';
+$complexFunction6 =  __NAMESPACE__ . '\\' . 'coth';
+$complexFunction7 =  __NAMESPACE__ . '\\' . 'acoth';
 $complexFunction8 =  __NAMESPACE__ . '\\' . 'tanh';
 $complexFunction9 =  __NAMESPACE__ . '\\' . 'atanh';
 
 
 echo $complexFunction1( 9 ) . '<br/>' . PHP_EOL;
+
 echo "<h3>Haversine</h3><br/>" . PHP_EOL;
 for ( $i = -10; $i <= 10; $i++ ) {
     echo ( $i ) . ': ' . $complexFunction2( $i ) . '<br/>' . PHP_EOL;
@@ -32,19 +33,19 @@
 }
 unset($i);
 
-echo "<h3>InverseGudermannian</h3><br/>" . PHP_EOL;
+echo "<h3>Inverse Gudermannian</h3><br/>" . PHP_EOL;
 for ( $i = -10; $i <= 10; $i++ ) {
     echo ( $i ) . ': ' . $complexFunction5( $i ) . '<br/>' . PHP_EOL;
 }
 unset($i);
 
-echo "<h3>ArcCoth</h3><br/>" . PHP_EOL;
+echo "<h3>Coth</h3><br/>" . PHP_EOL;
 for ( $i = -10; $i <= 10; $i++ ) {
     echo ( $i ) . ': ' . $complexFunction6( $i ) . '<br/>' . PHP_EOL;
 }
 unset($i);
 
-echo "<h3>Coth</h3><br/>" . PHP_EOL;
+echo "<h3>ArcCoth</h3><br/>" . PHP_EOL;
 for ( $i = -10; $i <= 10; $i++ ) {
     echo ( $i ) . ': ' . $complexFunction7( $i ) . '<br/>' . PHP_EOL;
 }
@@ -56,14 +57,8 @@
 }
 unset($i);
 
-echo "<h3>Tanh</h3><br/>" . PHP_EOL;
-for ( $i = -10; $i <= 10; $i++ ) {
-    echo ( $i ) . ': ' . $complexFunction8( $i ) . '<br/>' . PHP_EOL;
-}
-unset($i);
-
 echo "<h3>ArcTanh</h3><br/>" . PHP_EOL;
 for ( $i = -10; $i <= 10; $i++ ) {
     echo ( $i ) . ': ' . $complexFunction9( $i ) . '<br/>' . PHP_EOL;
 }
-unset($i);
\ No newline at end of file
+unset($i);