New trigonometric and hyperbolic functions

README.md

@@ -58,4 +58,15 @@ Planned additional functionality, but still to implement
  * coth (hyperbolic cotangent)
  * acoth (inverse hyperbolic cotangent)
  * pow (power)
-
+
+---
+Functions added
+- tanh (hyperbolic tangent)
+- atanh (inverse hyperbolic tangent)
+- coth (hyperbolic cotangent)
+- acoth (inverse hyperbolic cotangent)
+- gudermannian () Hyperbolic
+- inversegudermannian () Hyperbolic
+- haversine () Trigonometric
+- inversehaversine () Trigonometric
+

classes/src/functions/acoth.php

@@ -0,0 +1,36 @@
+<?php
+/**
+ *
+ * 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->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;
+        }
+    }
+}

classes/src/functions/atanh.php

@@ -0,0 +1,42 @@
+<?php
+/**
+ *
+ * Function code for the complex atanh() function
+ *
+ * @author Michael A. Johnson
+ * @License    http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
+ */
+namespace Complex;
+
+/**
+ *
+ * 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 );
+
+    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;
+        }
+    }
+}

classes/src/functions/coth.php

@@ -0,0 +1,35 @@
+<?php
+/**
+ *
+ * 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 ) {
+        $calc = clone $complex;
+        $complex = cosh( $complex );
+        $calc = sinh( $calc );
+
+        if ( $calc->getReal() != 0 ) {
+            $complex = $complex->divideBy( $calc );
+            return $complex;
+        } else {
+            return null;
+        }
+    }
+}

classes/src/functions/gudermannian.php

@@ -0,0 +1,30 @@
+<?php
+/**
+ *
+ * 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 ) {
+        $complex = exp( $complex );
+        $complex = atan( $complex );
+        $complex = $complex->multiply( 2 );
+        $complex = $complex->add( -( M_PI/2 ) );
+        return $complex;
+    }
+}

classes/src/functions/haversine.php

@@ -0,0 +1,29 @@
+<?php
+/**
+ *
+ * Function code for the complex haversine() function
+ *
+ * @author Michael A. Johnson
+ * @License    http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
+ */
+namespace Complex;
+
+/**
+ *
+ * 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 ) {
+        $complex = $complex->divideBy( 2 );
+        $complex = sin( $complex );
+        $complex = $complex->multiply( $complex );
+        return $complex;
+    }
+}

classes/src/functions/inversegudermannian.php

@@ -0,0 +1,30 @@
+<?php
+/**
+ *
+ * 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 );
+
+    if ( $complex->getImaginary() == 0.0 ) {
+        $complex = $complex->divideBy( 2 );
+        $complex = $complex->add( M_PI/4 );
+        $complex = tan( $complex );
+        $complex = ln( $complex );
+        return $complex;
+    }
+}

classes/src/functions/inversehaversine.php

@@ -0,0 +1,31 @@
+<?php
+/**
+ *
+ * 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;
+
+/**
+ *
+ * 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 ) ) {
+            $complex = sqrt( $complex );
+            $complex = asin( $complex );
+            $complex = $complex->multiply( 2 );
+            return $complex;
+        }
+    }
+}

classes/src/functions/tanh.php

@@ -0,0 +1,28 @@
+<?php
+/**
+ *
+ * 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 ) {
+        $calc = clone $complex;
+        $complex = sinh( $complex );
+        $calc = cosh( $calc );
+        $complex = $complex->divideBy( $calc );
+        return $complex;
+    }
+}

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 +33,15 @@
     'sin',
     'sinh',
     'sqrt',
-    'theta'
+    'theta',
+    'acoth',
+    'coth',
+    'gudermannian',
+    'haversine',
+    'inversegudermannian',
+    'inversehaversine',
+    'tanh',
+    'atanh'
 ];
 
 for($real = -3.5; $real <= 3.5; $real += 0.5) {
@@ -42,11 +50,11 @@
             $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;
     }
 }

examples/complexTest3.php

@@ -0,0 +1,64 @@
+<?php
+namespace Complex;
+include('../classes/Bootstrap.php');
+
+$complexFunction1 =  __NAMESPACE__ . '\\' . 'cos';
+$complexFunction2 =  __NAMESPACE__ . '\\' . 'haversine';
+$complexFunction3 =  __NAMESPACE__ . '\\' . 'inversehaversine';
+$complexFunction4 =  __NAMESPACE__ . '\\' . 'gudermannian';
+$complexFunction5 =  __NAMESPACE__ . '\\' . 'inversegudermannian';
+$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( $i ) . '<br/>' . PHP_EOL;
+}
+unset($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>Inverse Gudermannian</h3><br/>" . PHP_EOL;
+for ( $i = -10; $i <= 10; $i++ ) {
+    echo ( $i ) . ': ' . $complexFunction5( $i ) . '<br/>' . PHP_EOL;
+}
+unset($i);
+
+echo "<h3>Coth</h3><br/>" . PHP_EOL;
+for ( $i = -10; $i <= 10; $i++ ) {
+    echo ( $i ) . ': ' . $complexFunction6( $i ) . '<br/>' . PHP_EOL;
+}
+unset($i);
+
+echo "<h3>ArcCoth</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);
+
+echo "<h3>ArcTanh</h3><br/>" . PHP_EOL;
+for ( $i = -10; $i <= 10; $i++ ) {
+    echo ( $i ) . ': ' . $complexFunction9( $i ) . '<br/>' . PHP_EOL;
+}
+unset($i);