Merge pull request #48 from codisart/add-arccot-method

[TECH] Add the arccot method and a new unit test. Thanx to @codisart .

Author: castarco

src/Decimal.php

@@ -873,7 +873,38 @@ public function arctan($scale = null)
         return self::simplePowerSerie(
             $this,
             DecimalConstants::zero(),
-            $scale
+            $scale + 2
+        )->round($scale);
+    }
+
+    /**
+     * Calculates the arccotangente of this with the highest possible accuracy
+     *
+     * @param integer $scale
+     * @return Decimal
+     */
+    public function arccot($scale = null) {
+        $scale = ($scale === null) ? 32 : $scale;
+
+        $piOverTwo = DecimalConstants::pi()->div(Decimal::fromInteger(2), $scale + 2);
+        if ($this->round($scale)->isZero()) {
+            return $piOverTwo->round($scale);
+        }
+
+        $piOverFour = DecimalConstants::pi()->div(Decimal::fromInteger(4), $scale + 2);
+        if ($this->round($scale)->equals(DecimalConstants::one())) {
+            return $piOverFour->round($scale);
+        }
+        if ($this->round($scale)->equals(DecimalConstants::negativeOne())) {
+            return DecimalConstants::negativeOne()->mul($piOverFour, $scale + 2)->round($scale);
+        }
+
+        return $piOverTwo->sub(
+            self::simplePowerSerie(
+                $this,
+                DecimalConstants::zero(),
+                $scale + 2
+            )
         )->round($scale);
     }
 

tests/Decimal/DecimalArccotTest.php

@@ -0,0 +1,33 @@
+<?php
+
+use Litipk\BigNumbers\Decimal as Decimal;
+
+/**
+ * @group arccot
+ */
+class DecimalArccotTest extends PHPUnit_Framework_TestCase
+{
+    public function arccotProvider() {
+        // Some values provided by wolframalpha
+        return [
+            ['0.154', '1.41799671285823', 14],
+            ['0', '1.57079632679489662', 17],
+            ['-1', '-0.78540', 5],
+        ];
+    }
+
+    /**
+     * @dataProvider arccotProvider
+     */
+    public function testSimple($nr, $answer, $digits)
+    {
+        $x = Decimal::fromString($nr);
+        $arccotX = $x->arccot($digits);
+
+        $this->assertTrue(
+            Decimal::fromString($answer)->equals($arccotX),
+            "The answer must be " . $answer . ", but was " . $arccotX
+        );
+    }
+
+}