[TECH] Add the sec method

Add the sec method for the Decimal class and the tests
Add the sec method for the InfiniteDecimal class and the tests

Author: codisart

src/Decimal.php

@@ -759,6 +759,26 @@ function ($i) {
         );
     }
 
+    /**
+     * Calculates the secant of this with the highest possible accuracy
+     * Note that accuracy is limited by the accuracy of predefined PI;
+     *
+     * @param integer $scale
+     * @return Decimal
+     */
+    public function sec($scale = null)
+    {
+        $cos = $this->cos($scale + 2);
+        if ($cos->isZero()) {
+            throw new \DomainException(
+                "The secant of this 'angle' is undefined."
+            );
+        }
+
+        return Decimal::fromInteger(1)->div($cos)->round($scale);
+    }
+
+
     /**
      * Returns exp($this), said in other words: e^$this .
      *

src/InfiniteDecimal.php

@@ -339,6 +339,20 @@ public function cos($scale = null)
         );
     }
 
+    /**
+     * Throws exception because secant is undefined in the infinite.
+     *
+     * @param integer $scale
+     * @return null
+     */
+    public function sec($scale = null)
+    {
+        throw new \DomainException(($this === self::$pInf) ?
+            "Secant function hasn't limit in the positive infinite." :
+            "Secant function hasn't limit in the negative infinite."
+        );
+    }
+
     /**
      * Returns exp($this), said in other words: e^$this .
      *

tests/Decimal/DecimalSecTest.php

@@ -0,0 +1,32 @@
+<?php
+
+use Litipk\BigNumbers\Decimal as Decimal;
+
+/**
+ * @group sec
+ */
+class DecimalSecTest extends PHPUnit_Framework_TestCase
+{
+    public function SecProvider() {
+        // Some values provided by Mathematica
+        return [
+            ['5', '3.52532008581609', 14],
+            ['456.456', '-1.66172995090378344', 17],
+            ['28000000000', '-1.11551381955633891873', 20],
+        ];
+    }
+
+    /**
+     * @dataProvider secProvider
+     */
+    public function testSimple($nr, $answer, $digits)
+    {
+        $x = Decimal::fromString($nr);
+        $secX = $x->sec((int)$digits);
+
+        $this->assertTrue(
+            Decimal::fromString($answer)->equals($secX),
+            "The answer must be " . $answer . ", but was " . $secX
+        );
+    }
+}

tests/InfiniteDecimal/InfiniteDecimalCosecTest.php

@@ -3,7 +3,7 @@
 use Litipk\BigNumbers\InfiniteDecimal as InfiniteDecimal;
 
 /**
- * @group cos
+ * @group cosec
  */
 class InfiniteDecimalCosecTest extends PHPUnit_Framework_TestCase
 {

tests/InfiniteDecimal/InfiniteDecimalSecTest.php

@@ -0,0 +1,27 @@
+<?php
+
+use Litipk\BigNumbers\InfiniteDecimal as InfiniteDecimal;
+
+/**
+ * @group sec
+ */
+class InfiniteDecimalSecTest extends PHPUnit_Framework_TestCase
+{
+    /**
+     * @expectedException \DomainException
+     * @expectedExceptionMessage Secant function hasn't limit in the positive infinite.
+     */
+    public function testFinitePositiveInfiniteSec()
+    {
+        InfiniteDecimal::getPositiveInfinite()->sec();
+    }
+
+    /**
+     * @expectedException \DomainException
+     * @expectedExceptionMessage Secant function hasn't limit in the negative infinite.
+     */
+    public function testFiniteNegativeInfiniteSec()
+    {
+        InfiniteDecimal::getNegativeInfinite()->sec();
+    }
+}