\PHPExcel_Calculation_MathTrig

<?php
/**
 * PHPExcel
 *
 * Copyright (c) 2006 - 2014 PHPExcel
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
 *
 * @category	PHPExcel
 * @package		PHPExcel_Calculation
 * @copyright	Copyright (c) 2006 - 2014 PHPExcel (http://www.codeplex.com/PHPExcel)
 * @license		http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt	LGPL
 * @version		1.8.0, 2014-03-02
 */


/** PHPExcel root directory */
if (!defined('PHPEXCEL_ROOT')) {
	/**
	 * @ignore
	 */
	define('PHPEXCEL_ROOT', dirname(__FILE__) . '/../../');
	require(PHPEXCEL_ROOT . 'PHPExcel/Autoloader.php');
}


/**
 * PHPExcel_Calculation_MathTrig
 *
 * @category	PHPExcel
 * @package		PHPExcel_Calculation
 * @copyright	Copyright (c) 2006 - 2014 PHPExcel (http://www.codeplex.com/PHPExcel)
 */
class PHPExcel_Calculation_MathTrig {

	//
	//	Private method to return an array of the factors of the input value
	//
	private static function _factors($value) {
		$startVal = floor(sqrt($value));

		$factorArray = array();
		for ($i = $startVal; $i > 1; --$i) {
			if (($value % $i) == 0) {
				$factorArray = array_merge($factorArray,self::_factors($value / $i));
				$factorArray = array_merge($factorArray,self::_factors($i));
				if ($i <= sqrt($value)) {
					break;
				}
			}
		}
		if (!empty($factorArray)) {
			rsort($factorArray);
			return $factorArray;
		} else {
			return array((integer) $value);
		}
	}	//	function _factors()


	private static function _romanCut($num, $n) {
		return ($num - ($num % $n ) ) / $n;
	}	//	function _romanCut()


	/**
	 * ATAN2
	 *
	 * This function calculates the arc tangent of the two variables x and y. It is similar to
	 *		calculating the arc tangent of y ÷ x, except that the signs of both arguments are used
	 *		to determine the quadrant of the result.
	 * The arctangent is the angle from the x-axis to a line containing the origin (0, 0) and a
	 *		point with coordinates (xCoordinate, yCoordinate). The angle is given in radians between
	 *		-pi and pi, excluding -pi.
	 *
	 * Note that the Excel ATAN2() function accepts its arguments in the reverse order to the standard
	 *		PHP atan2() function, so we need to reverse them here before calling the PHP atan() function.
	 *
	 * Excel Function:
	 *		ATAN2(xCoordinate,yCoordinate)
	 *
	 * @access	public
	 * @category Mathematical and Trigonometric Functions
	 * @param	float	$xCoordinate		The x-coordinate of the point.
	 * @param	float	$yCoordinate		The y-coordinate of the point.
	 * @return	float	The inverse tangent of the specified x- and y-coordinates.
	 */
	public static function ATAN2($xCoordinate = NULL, $yCoordinate = NULL) {
		$xCoordinate	= PHPExcel_Calculation_Functions::flattenSingleValue($xCoordinate);
		$yCoordinate	= PHPExcel_Calculation_Functions::flattenSingleValue($yCoordinate);

		$xCoordinate	= ($xCoordinate !== NULL)	? $xCoordinate : 0.0;
		$yCoordinate	= ($yCoordinate !== NULL)	? $yCoordinate : 0.0;

		if (((is_numeric($xCoordinate)) || (is_bool($xCoordinate))) &&
			((is_numeric($yCoordinate)))  || (is_bool($yCoordinate))) {
			$xCoordinate	= (float) $xCoordinate;
			$yCoordinate	= (float) $yCoordinate;

			if (($xCoordinate == 0) && ($yCoordinate == 0)) {
				return PHPExcel_Calculation_Functions::DIV0();
			}

			return atan2($yCoordinate, $xCoordinate);
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function ATAN2()


	/**
	 * CEILING
	 *
	 * Returns number rounded up, away from zero, to the nearest multiple of significance.
	 *		For example, if you want to avoid using pennies in your prices and your product is
	 *		priced at $4.42, use the formula =CEILING(4.42,0.05) to round prices up to the
	 *		nearest nickel.
	 *
	 * Excel Function:
	 *		CEILING(number[,significance])
	 *
	 * @access	public
	 * @category Mathematical and Trigonometric Functions
	 * @param	float	$number			The number you want to round.
	 * @param	float	$significance	The multiple to which you want to round.
	 * @return	float	Rounded Number
	 */
	public static function CEILING($number, $significance = NULL) {
		$number			= PHPExcel_Calculation_Functions::flattenSingleValue($number);
		$significance	= PHPExcel_Calculation_Functions::flattenSingleValue($significance);

		if ((is_null($significance)) &&
			(PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC)) {
			$significance = $number/abs($number);
		}

		if ((is_numeric($number)) && (is_numeric($significance))) {
			if ($significance == 0.0) {
				return 0.0;
			} elseif (self::SIGN($number) == self::SIGN($significance)) {
				return ceil($number / $significance) * $significance;
			} else {
				return PHPExcel_Calculation_Functions::NaN();
			}
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function CEILING()


	/**
	 * COMBIN
	 *
	 * Returns the number of combinations for a given number of items. Use COMBIN to
	 *		determine the total possible number of groups for a given number of items.
	 *
	 * Excel Function:
	 *		COMBIN(numObjs,numInSet)
	 *
	 * @access	public
	 * @category Mathematical and Trigonometric Functions
	 * @param	int		$numObjs	Number of different objects
	 * @param	int		$numInSet	Number of objects in each combination
	 * @return	int		Number of combinations
	 */
	public static function COMBIN($numObjs, $numInSet) {
		$numObjs	= PHPExcel_Calculation_Functions::flattenSingleValue($numObjs);
		$numInSet	= PHPExcel_Calculation_Functions::flattenSingleValue($numInSet);

		if ((is_numeric($numObjs)) && (is_numeric($numInSet))) {
			if ($numObjs < $numInSet) {
				return PHPExcel_Calculation_Functions::NaN();
			} elseif ($numInSet < 0) {
				return PHPExcel_Calculation_Functions::NaN();
			}
			return round(self::FACT($numObjs) / self::FACT($numObjs - $numInSet)) / self::FACT($numInSet);
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function COMBIN()


	/**
	 * EVEN
	 *
	 * Returns number rounded up to the nearest even integer.
	 * You can use this function for processing items that come in twos. For example,
	 *		a packing crate accepts rows of one or two items. The crate is full when
	 *		the number of items, rounded up to the nearest two, matches the crate's
	 *		capacity.
	 *
	 * Excel Function:
	 *		EVEN(number)
	 *
	 * @access	public
	 * @category Mathematical and Trigonometric Functions
	 * @param	float	$number			Number to round
	 * @return	int		Rounded Number
	 */
	public static function EVEN($number) {
		$number	= PHPExcel_Calculation_Functions::flattenSingleValue($number);

		if (is_null($number)) {
			return 0;
		} elseif (is_bool($number)) {
			$number = (int) $number;
		}

		if (is_numeric($number)) {
			$significance = 2 * self::SIGN($number);
			return (int) self::CEILING($number,$significance);
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function EVEN()


	/**
	 * FACT
	 *
	 * Returns the factorial of a number.
	 * The factorial of a number is equal to 1*2*3*...* number.
	 *
	 * Excel Function:
	 *		FACT(factVal)
	 *
	 * @access	public
	 * @category Mathematical and Trigonometric Functions
	 * @param	float	$factVal	Factorial Value
	 * @return	int		Factorial
	 */
	public static function FACT($factVal) {
		$factVal	= PHPExcel_Calculation_Functions::flattenSingleValue($factVal);

		if (is_numeric($factVal)) {
			if ($factVal < 0) {
				return PHPExcel_Calculation_Functions::NaN();
			}
			$factLoop = floor($factVal);
			if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
				if ($factVal > $factLoop) {
					return PHPExcel_Calculation_Functions::NaN();
				}
			}

			$factorial = 1;
			while ($factLoop > 1) {
				$factorial *= $factLoop--;
			}
			return $factorial ;
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function FACT()


	/**
	 * FACTDOUBLE
	 *
	 * Returns the double factorial of a number.
	 *
	 * Excel Function:
	 *		FACTDOUBLE(factVal)
	 *
	 * @access	public
	 * @category Mathematical and Trigonometric Functions
	 * @param	float	$factVal	Factorial Value
	 * @return	int		Double Factorial
	 */
	public static function FACTDOUBLE($factVal) {
		$factLoop	= PHPExcel_Calculation_Functions::flattenSingleValue($factVal);

		if (is_numeric($factLoop)) {
			$factLoop	= floor($factLoop);
			if ($factVal < 0) {
				return PHPExcel_Calculation_Functions::NaN();
			}
			$factorial = 1;
			while ($factLoop > 1) {
				$factorial *= $factLoop--;
				--$factLoop;
			}
			return $factorial ;
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function FACTDOUBLE()


	/**
	 * FLOOR
	 *
	 * Rounds number down, toward zero, to the nearest multiple of significance.
	 *
	 * Excel Function:
	 *		FLOOR(number[,significance])
	 *
	 * @access	public
	 * @category Mathematical and Trigonometric Functions
	 * @param	float	$number			Number to round
	 * @param	float	$significance	Significance
	 * @return	float	Rounded Number
	 */
	public static function FLOOR($number, $significance = NULL) {
		$number			= PHPExcel_Calculation_Functions::flattenSingleValue($number);
		$significance	= PHPExcel_Calculation_Functions::flattenSingleValue($significance);

		if ((is_null($significance)) && (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC)) {
			$significance = $number/abs($number);
		}

		if ((is_numeric($number)) && (is_numeric($significance))) {
			if ((float) $significance == 0.0) {
				return PHPExcel_Calculation_Functions::DIV0();
			}
			if (self::SIGN($number) == self::SIGN($significance)) {
				return floor($number / $significance) * $significance;
			} else {
				return PHPExcel_Calculation_Functions::NaN();
			}
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function FLOOR()


	/**
	 * GCD
	 *
	 * Returns the greatest common divisor of a series of numbers.
	 * The greatest common divisor is the largest integer that divides both
	 *		number1 and number2 without a remainder.
	 *
	 * Excel Function:
	 *		GCD(number1[,number2[, ...]])
	 *
	 * @access	public
	 * @category Mathematical and Trigonometric Functions
	 * @param	mixed	$arg,...		Data values
	 * @return	integer					Greatest Common Divisor
	 */
	public static function GCD() {
		$returnValue = 1;
		$allValuesFactors = array();
		// Loop through arguments
		foreach(PHPExcel_Calculation_Functions::flattenArray(func_get_args()) as $value) {
			if (!is_numeric($value)) {
				return PHPExcel_Calculation_Functions::VALUE();
			} elseif ($value == 0) {
				continue;
			} elseif($value < 0) {
				return PHPExcel_Calculation_Functions::NaN();
			}
			$myFactors = self::_factors($value);
			$myCountedFactors = array_count_values($myFactors);
			$allValuesFactors[] = $myCountedFactors;
		}
		$allValuesCount = count($allValuesFactors);
		if ($allValuesCount == 0) {
			return 0;
		}

		$mergedArray = $allValuesFactors[0];
		for ($i=1;$i < $allValuesCount; ++$i) {
			$mergedArray = array_intersect_key($mergedArray,$allValuesFactors[$i]);
		}
		$mergedArrayValues = count($mergedArray);
		if ($mergedArrayValues == 0) {
			return $returnValue;
		} elseif ($mergedArrayValues > 1) {
			foreach($mergedArray as $mergedKey => $mergedValue) {
				foreach($allValuesFactors as $highestPowerTest) {
					foreach($highestPowerTest as $testKey => $testValue) {
						if (($testKey == $mergedKey) && ($testValue < $mergedValue)) {
							$mergedArray[$mergedKey] = $testValue;
							$mergedValue = $testValue;
						}
					}
				}
			}

			$returnValue = 1;
			foreach($mergedArray as $key => $value) {
				$returnValue *= pow($key,$value);
			}
			return $returnValue;
		} else {
			$keys = array_keys($mergedArray);
			$key = $keys[0];
			$value = $mergedArray[$key];
			foreach($allValuesFactors as $testValue) {
				foreach($testValue as $mergedKey => $mergedValue) {
					if (($mergedKey == $key) && ($mergedValue < $value)) {
						$value = $mergedValue;
					}
				}
			}
			return pow($key,$value);
		}
	}	//	function GCD()


	/**
	 * INT
	 *
	 * Casts a floating point value to an integer
	 *
	 * Excel Function:
	 *		INT(number)
	 *
	 * @access	public
	 * @category Mathematical and Trigonometric Functions
	 * @param	float	$number			Number to cast to an integer
	 * @return	integer	Integer value
	 */
	public static function INT($number) {
		$number	= PHPExcel_Calculation_Functions::flattenSingleValue($number);

		if (is_null($number)) {
			return 0;
		} elseif (is_bool($number)) {
			return (int) $number;
		}
		if (is_numeric($number)) {
			return (int) floor($number);
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function INT()


	/**
	 * LCM
	 *
	 * Returns the lowest common multiplier of a series of numbers
	 * The least common multiple is the smallest positive integer that is a multiple
	 * of all integer arguments number1, number2, and so on. Use LCM to add fractions
	 * with different denominators.
	 *
	 * Excel Function:
	 *		LCM(number1[,number2[, ...]])
	 *
	 * @access	public
	 * @category Mathematical and Trigonometric Functions
	 * @param	mixed	$arg,...		Data values
	 * @return	int		Lowest Common Multiplier
	 */
	public static function LCM() {
		$returnValue = 1;
		$allPoweredFactors = array();
		// Loop through arguments
		foreach(PHPExcel_Calculation_Functions::flattenArray(func_get_args()) as $value) {
			if (!is_numeric($value)) {
				return PHPExcel_Calculation_Functions::VALUE();
			}
			if ($value == 0) {
				return 0;
			} elseif ($value < 0) {
				return PHPExcel_Calculation_Functions::NaN();
			}
			$myFactors = self::_factors(floor($value));
			$myCountedFactors = array_count_values($myFactors);
			$myPoweredFactors = array();
			foreach($myCountedFactors as $myCountedFactor => $myCountedPower) {
				$myPoweredFactors[$myCountedFactor] = pow($myCountedFactor,$myCountedPower);
			}
			foreach($myPoweredFactors as $myPoweredValue => $myPoweredFactor) {
				if (array_key_exists($myPoweredValue,$allPoweredFactors)) {
					if ($allPoweredFactors[$myPoweredValue] < $myPoweredFactor) {
						$allPoweredFactors[$myPoweredValue] = $myPoweredFactor;
					}
				} else {
					$allPoweredFactors[$myPoweredValue] = $myPoweredFactor;
				}
			}
		}
		foreach($allPoweredFactors as $allPoweredFactor) {
			$returnValue *= (integer) $allPoweredFactor;
		}
		return $returnValue;
	}	//	function LCM()


	/**
	 * LOG_BASE
	 *
	 * Returns the logarithm of a number to a specified base. The default base is 10.
	 *
	 * Excel Function:
	 *		LOG(number[,base])
	 *
	 * @access	public
	 * @category Mathematical and Trigonometric Functions
	 * @param	float	$number		The positive real number for which you want the logarithm
	 * @param	float	$base		The base of the logarithm. If base is omitted, it is assumed to be 10.
	 * @return	float
	 */
	public static function LOG_BASE($number = NULL, $base = 10) {
		$number	= PHPExcel_Calculation_Functions::flattenSingleValue($number);
		$base	= (is_null($base)) ? 10 : (float) PHPExcel_Calculation_Functions::flattenSingleValue($base);

		if ((!is_numeric($base)) || (!is_numeric($number)))
			return PHPExcel_Calculation_Functions::VALUE();
		if (($base <= 0) || ($number <= 0))
			return PHPExcel_Calculation_Functions::NaN();
		return log($number, $base);
	}	//	function LOG_BASE()


	/**
	 * MDETERM
	 *
	 * Returns the matrix determinant of an array.
	 *
	 * Excel Function:
	 *		MDETERM(array)
	 *
	 * @access	public
	 * @category Mathematical and Trigonometric Functions
	 * @param	array	$matrixValues	A matrix of values
	 * @return	float
	 */
	public static function MDETERM($matrixValues) {
		$matrixData = array();
		if (!is_array($matrixValues)) { $matrixValues = array(array($matrixValues)); }

		$row = $maxColumn = 0;
		foreach($matrixValues as $matrixRow) {
			if (!is_array($matrixRow)) { $matrixRow = array($matrixRow); }
			$column = 0;
			foreach($matrixRow as $matrixCell) {
				if ((is_string($matrixCell)) || ($matrixCell === null)) {
					return PHPExcel_Calculation_Functions::VALUE();
				}
				$matrixData[$column][$row] = $matrixCell;
				++$column;
			}
			if ($column > $maxColumn) { $maxColumn = $column; }
			++$row;
		}
		if ($row != $maxColumn) { return PHPExcel_Calculation_Functions::VALUE(); }

		try {
			$matrix = new PHPExcel_Shared_JAMA_Matrix($matrixData);
			return $matrix->det();
		} catch (PHPExcel_Exception $ex) {
			return PHPExcel_Calculation_Functions::VALUE();
		}
	}	//	function MDETERM()


	/**
	 * MINVERSE
	 *
	 * Returns the inverse matrix for the matrix stored in an array.
	 *
	 * Excel Function:
	 *		MINVERSE(array)
	 *
	 * @access	public
	 * @category Mathematical and Trigonometric Functions
	 * @param	array	$matrixValues	A matrix of values
	 * @return	array
	 */
	public static function MINVERSE($matrixValues) {
		$matrixData = array();
		if (!is_array($matrixValues)) { $matrixValues = array(array($matrixValues)); }

		$row = $maxColumn = 0;
		foreach($matrixValues as $matrixRow) {
			if (!is_array($matrixRow)) { $matrixRow = array($matrixRow); }
			$column = 0;
			foreach($matrixRow as $matrixCell) {
				if ((is_string($matrixCell)) || ($matrixCell === null)) {
					return PHPExcel_Calculation_Functions::VALUE();
				}
				$matrixData[$column][$row] = $matrixCell;
				++$column;
			}
			if ($column > $maxColumn) { $maxColumn = $column; }
			++$row;
		}
		if ($row != $maxColumn) { return PHPExcel_Calculation_Functions::VALUE(); }

		try {
			$matrix = new PHPExcel_Shared_JAMA_Matrix($matrixData);
			return $matrix->inverse()->getArray();
		} catch (PHPExcel_Exception $ex) {
			return PHPExcel_Calculation_Functions::VALUE();
		}
	}	//	function MINVERSE()


	/**
	 * MMULT
	 *
	 * @param	array	$matrixData1	A matrix of values
	 * @param	array	$matrixData2	A matrix of values
	 * @return	array
	 */
	public static function MMULT($matrixData1,$matrixData2) {
		$matrixAData = $matrixBData = array();
		if (!is_array($matrixData1)) { $matrixData1 = array(array($matrixData1)); }
		if (!is_array($matrixData2)) { $matrixData2 = array(array($matrixData2)); }

		$rowA = 0;
		foreach($matrixData1 as $matrixRow) {
			if (!is_array($matrixRow)) { $matrixRow = array($matrixRow); }
			$columnA = 0;
			foreach($matrixRow as $matrixCell) {
				if ((is_string($matrixCell)) || ($matrixCell === null)) {
					return PHPExcel_Calculation_Functions::VALUE();
				}
				$matrixAData[$rowA][$columnA] = $matrixCell;
				++$columnA;
			}
			++$rowA;
		}
		try {
			$matrixA = new PHPExcel_Shared_JAMA_Matrix($matrixAData);
			$rowB = 0;
			foreach($matrixData2 as $matrixRow) {
				if (!is_array($matrixRow)) { $matrixRow = array($matrixRow); }
				$columnB = 0;
				foreach($matrixRow as $matrixCell) {
					if ((is_string($matrixCell)) || ($matrixCell === null)) {
						return PHPExcel_Calculation_Functions::VALUE();
					}
					$matrixBData[$rowB][$columnB] = $matrixCell;
					++$columnB;
				}
				++$rowB;
			}
			$matrixB = new PHPExcel_Shared_JAMA_Matrix($matrixBData);

			if (($rowA != $columnB) || ($rowB != $columnA)) {
				return PHPExcel_Calculation_Functions::VALUE();
			}

			return $matrixA->times($matrixB)->getArray();
		} catch (PHPExcel_Exception $ex) {
			return PHPExcel_Calculation_Functions::VALUE();
		}
	}	//	function MMULT()


	/**
	 * MOD
	 *
	 * @param	int		$a		Dividend
	 * @param	int		$b		Divisor
	 * @return	int		Remainder
	 */
	public static function MOD($a = 1, $b = 1) {
		$a		= PHPExcel_Calculation_Functions::flattenSingleValue($a);
		$b		= PHPExcel_Calculation_Functions::flattenSingleValue($b);

		if ($b == 0.0) {
			return PHPExcel_Calculation_Functions::DIV0();
		} elseif (($a < 0.0) && ($b > 0.0)) {
			return $b - fmod(abs($a),$b);
		} elseif (($a > 0.0) && ($b < 0.0)) {
			return $b + fmod($a,abs($b));
		}

		return fmod($a,$b);
	}	//	function MOD()


	/**
	 * MROUND
	 *
	 * Rounds a number to the nearest multiple of a specified value
	 *
	 * @param	float	$number			Number to round
	 * @param	int		$multiple		Multiple to which you want to round $number
	 * @return	float	Rounded Number
	 */
	public static function MROUND($number,$multiple) {
		$number		= PHPExcel_Calculation_Functions::flattenSingleValue($number);
		$multiple	= PHPExcel_Calculation_Functions::flattenSingleValue($multiple);

		if ((is_numeric($number)) && (is_numeric($multiple))) {
			if ($multiple == 0) {
				return 0;
			}
			if ((self::SIGN($number)) == (self::SIGN($multiple))) {
				$multiplier = 1 / $multiple;
				return round($number * $multiplier) / $multiplier;
			}
			return PHPExcel_Calculation_Functions::NaN();
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function MROUND()


	/**
	 * MULTINOMIAL
	 *
	 * Returns the ratio of the factorial of a sum of values to the product of factorials.
	 *
	 * @param	array of mixed		Data Series
	 * @return	float
	 */
	public static function MULTINOMIAL() {
		$summer = 0;
		$divisor = 1;
		// Loop through arguments
		foreach (PHPExcel_Calculation_Functions::flattenArray(func_get_args()) as $arg) {
			// Is it a numeric value?
			if (is_numeric($arg)) {
				if ($arg < 1) {
					return PHPExcel_Calculation_Functions::NaN();
				}
				$summer += floor($arg);
				$divisor *= self::FACT($arg);
			} else {
				return PHPExcel_Calculation_Functions::VALUE();
			}
		}

		// Return
		if ($summer > 0) {
			$summer = self::FACT($summer);
			return $summer / $divisor;
		}
		return 0;
	}	//	function MULTINOMIAL()


	/**
	 * ODD
	 *
	 * Returns number rounded up to the nearest odd integer.
	 *
	 * @param	float	$number			Number to round
	 * @return	int		Rounded Number
	 */
	public static function ODD($number) {
		$number	= PHPExcel_Calculation_Functions::flattenSingleValue($number);

		if (is_null($number)) {
			return 1;
		} elseif (is_bool($number)) {
			$number = (int) $number;
		}

		if (is_numeric($number)) {
			$significance = self::SIGN($number);
			if ($significance == 0) {
				return 1;
			}

			$result = self::CEILING($number,$significance);
			if ($result == self::EVEN($result)) {
				$result += $significance;
			}

			return (int) $result;
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function ODD()


	/**
	 * POWER
	 *
	 * Computes x raised to the power y.
	 *
	 * @param	float		$x
	 * @param	float		$y
	 * @return	float
	 */
	public static function POWER($x = 0, $y = 2) {
		$x	= PHPExcel_Calculation_Functions::flattenSingleValue($x);
		$y	= PHPExcel_Calculation_Functions::flattenSingleValue($y);

		// Validate parameters
		if ($x == 0.0 && $y == 0.0) {
			return PHPExcel_Calculation_Functions::NaN();
		} elseif ($x == 0.0 && $y < 0.0) {
			return PHPExcel_Calculation_Functions::DIV0();
		}

		// Return
		$result = pow($x, $y);
		return (!is_nan($result) && !is_infinite($result)) ? $result : PHPExcel_Calculation_Functions::NaN();
	}	//	function POWER()


	/**
	 * PRODUCT
	 *
	 * PRODUCT returns the product of all the values and cells referenced in the argument list.
	 *
	 * Excel Function:
	 *		PRODUCT(value1[,value2[, ...]])
	 *
	 * @access	public
	 * @category Mathematical and Trigonometric Functions
	 * @param	mixed		$arg,...		Data values
	 * @return	float
	 */
	public static function PRODUCT() {
		// Return value
		$returnValue = null;

		// Loop through arguments
		foreach (PHPExcel_Calculation_Functions::flattenArray(func_get_args()) as $arg) {
			// Is it a numeric value?
			if ((is_numeric($arg)) && (!is_string($arg))) {
				if (is_null($returnValue)) {
					$returnValue = $arg;
				} else {
					$returnValue *= $arg;
				}
			}
		}

		// Return
		if (is_null($returnValue)) {
			return 0;
		}
		return $returnValue;
	}	//	function PRODUCT()


	/**
	 * QUOTIENT
	 *
	 * QUOTIENT function returns the integer portion of a division. Numerator is the divided number
	 *		and denominator is the divisor.
	 *
	 * Excel Function:
	 *		QUOTIENT(value1[,value2[, ...]])
	 *
	 * @access	public
	 * @category Mathematical and Trigonometric Functions
	 * @param	mixed		$arg,...		Data values
	 * @return	float
	 */
	public static function QUOTIENT() {
		// Return value
		$returnValue = null;

		// Loop through arguments
		foreach (PHPExcel_Calculation_Functions::flattenArray(func_get_args()) as $arg) {
			// Is it a numeric value?
			if ((is_numeric($arg)) && (!is_string($arg))) {
				if (is_null($returnValue)) {
					$returnValue = ($arg == 0) ? 0 : $arg;
				} else {
					if (($returnValue == 0) || ($arg == 0)) {
						$returnValue = 0;
					} else {
						$returnValue /= $arg;
					}
				}
			}
		}

		// Return
		return intval($returnValue);
	}	//	function QUOTIENT()


	/**
	 * RAND
	 *
	 * @param	int		$min	Minimal value
	 * @param	int		$max	Maximal value
	 * @return	int		Random number
	 */
	public static function RAND($min = 0, $max = 0) {
		$min		= PHPExcel_Calculation_Functions::flattenSingleValue($min);
		$max		= PHPExcel_Calculation_Functions::flattenSingleValue($max);

		if ($min == 0 && $max == 0) {
			return (rand(0,10000000)) / 10000000;
		} else {
			return rand($min, $max);
		}
	}	//	function RAND()


	public static function ROMAN($aValue, $style=0) {
		$aValue	= PHPExcel_Calculation_Functions::flattenSingleValue($aValue);
		$style	= (is_null($style))	? 0 :	(integer) PHPExcel_Calculation_Functions::flattenSingleValue($style);
		if ((!is_numeric($aValue)) || ($aValue < 0) || ($aValue >= 4000)) {
			return PHPExcel_Calculation_Functions::VALUE();
		}
		$aValue = (integer) $aValue;
		if ($aValue == 0) {
			return '';
		}

		$mill = Array('', 'M', 'MM', 'MMM', 'MMMM', 'MMMMM');
		$cent = Array('', 'C', 'CC', 'CCC', 'CD', 'D', 'DC', 'DCC', 'DCCC', 'CM');
		$tens = Array('', 'X', 'XX', 'XXX', 'XL', 'L', 'LX', 'LXX', 'LXXX', 'XC');
		$ones = Array('', 'I', 'II', 'III', 'IV', 'V', 'VI', 'VII', 'VIII', 'IX');

		$roman = '';
		while ($aValue > 5999) {
			$roman .= 'M';
			$aValue -= 1000;
		}
		$m = self::_romanCut($aValue, 1000);	$aValue %= 1000;
		$c = self::_romanCut($aValue, 100);		$aValue %= 100;
		$t = self::_romanCut($aValue, 10);		$aValue %= 10;

		return $roman.$mill[$m].$cent[$c].$tens[$t].$ones[$aValue];
	}	//	function ROMAN()


	/**
	 * ROUNDUP
	 *
	 * Rounds a number up to a specified number of decimal places
	 *
	 * @param	float	$number			Number to round
	 * @param	int		$digits			Number of digits to which you want to round $number
	 * @return	float	Rounded Number
	 */
	public static function ROUNDUP($number,$digits) {
		$number	= PHPExcel_Calculation_Functions::flattenSingleValue($number);
		$digits	= PHPExcel_Calculation_Functions::flattenSingleValue($digits);

		if ((is_numeric($number)) && (is_numeric($digits))) {
			$significance = pow(10,(int) $digits);
			if ($number < 0.0) {
				return floor($number * $significance) / $significance;
			} else {
				return ceil($number * $significance) / $significance;
			}
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function ROUNDUP()


	/**
	 * ROUNDDOWN
	 *
	 * Rounds a number down to a specified number of decimal places
	 *
	 * @param	float	$number			Number to round
	 * @param	int		$digits			Number of digits to which you want to round $number
	 * @return	float	Rounded Number
	 */
	public static function ROUNDDOWN($number,$digits) {
		$number	= PHPExcel_Calculation_Functions::flattenSingleValue($number);
		$digits	= PHPExcel_Calculation_Functions::flattenSingleValue($digits);

		if ((is_numeric($number)) && (is_numeric($digits))) {
			$significance = pow(10,(int) $digits);
			if ($number < 0.0) {
				return ceil($number * $significance) / $significance;
			} else {
				return floor($number * $significance) / $significance;
			}
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function ROUNDDOWN()


	/**
	 * SERIESSUM
	 *
	 * Returns the sum of a power series
	 *
	 * @param	float			$x	Input value to the power series
	 * @param	float			$n	Initial power to which you want to raise $x
	 * @param	float			$m	Step by which to increase $n for each term in the series
	 * @param	array of mixed		Data Series
	 * @return	float
	 */
	public static function SERIESSUM() {
		// Return value
		$returnValue = 0;

		// Loop through arguments
		$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());

		$x = array_shift($aArgs);
		$n = array_shift($aArgs);
		$m = array_shift($aArgs);

		if ((is_numeric($x)) && (is_numeric($n)) && (is_numeric($m))) {
			// Calculate
			$i = 0;
			foreach($aArgs as $arg) {
				// Is it a numeric value?
				if ((is_numeric($arg)) && (!is_string($arg))) {
					$returnValue += $arg * pow($x,$n + ($m * $i++));
				} else {
					return PHPExcel_Calculation_Functions::VALUE();
				}
			}
			// Return
			return $returnValue;
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function SERIESSUM()


	/**
	 * SIGN
	 *
	 * Determines the sign of a number. Returns 1 if the number is positive, zero (0)
	 *		if the number is 0, and -1 if the number is negative.
	 *
	 * @param	float	$number			Number to round
	 * @return	int		sign value
	 */
	public static function SIGN($number) {
		$number	= PHPExcel_Calculation_Functions::flattenSingleValue($number);

		if (is_bool($number))
			return (int) $number;
		if (is_numeric($number)) {
			if ($number == 0.0) {
				return 0;
			}
			return $number / abs($number);
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function SIGN()


	/**
	 * SQRTPI
	 *
	 * Returns the square root of (number * pi).
	 *
	 * @param	float	$number		Number
	 * @return	float	Square Root of Number * Pi
	 */
	public static function SQRTPI($number) {
		$number	= PHPExcel_Calculation_Functions::flattenSingleValue($number);

		if (is_numeric($number)) {
			if ($number < 0) {
				return PHPExcel_Calculation_Functions::NaN();
			}
			return sqrt($number * M_PI) ;
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function SQRTPI()


	/**
	 * SUBTOTAL
	 *
	 * Returns a subtotal in a list or database.
	 *
	 * @param	int		the number 1 to 11 that specifies which function to
	 *					use in calculating subtotals within a list.
	 * @param	array of mixed		Data Series
	 * @return	float
	 */
	public static function SUBTOTAL() {
		$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());

		// Calculate
		$subtotal = array_shift($aArgs);

		if ((is_numeric($subtotal)) && (!is_string($subtotal))) {
			switch($subtotal) {
				case 1	:
					return PHPExcel_Calculation_Statistical::AVERAGE($aArgs);
					break;
				case 2	:
					return PHPExcel_Calculation_Statistical::COUNT($aArgs);
					break;
				case 3	:
					return PHPExcel_Calculation_Statistical::COUNTA($aArgs);
					break;
				case 4	:
					return PHPExcel_Calculation_Statistical::MAX($aArgs);
					break;
				case 5	:
					return PHPExcel_Calculation_Statistical::MIN($aArgs);
					break;
				case 6	:
					return self::PRODUCT($aArgs);
					break;
				case 7	:
					return PHPExcel_Calculation_Statistical::STDEV($aArgs);
					break;
				case 8	:
					return PHPExcel_Calculation_Statistical::STDEVP($aArgs);
					break;
				case 9	:
					return self::SUM($aArgs);
					break;
				case 10	:
					return PHPExcel_Calculation_Statistical::VARFunc($aArgs);
					break;
				case 11	:
					return PHPExcel_Calculation_Statistical::VARP($aArgs);
					break;
			}
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function SUBTOTAL()


	/**
	 * SUM
	 *
	 * SUM computes the sum of all the values and cells referenced in the argument list.
	 *
	 * Excel Function:
	 *		SUM(value1[,value2[, ...]])
	 *
	 * @access	public
	 * @category Mathematical and Trigonometric Functions
	 * @param	mixed		$arg,...		Data values
	 * @return	float
	 */
	public static function SUM() {
		// Return value
		$returnValue = 0;

		// Loop through the arguments
		foreach (PHPExcel_Calculation_Functions::flattenArray(func_get_args()) as $arg) {
			// Is it a numeric value?
			if ((is_numeric($arg)) && (!is_string($arg))) {
				$returnValue += $arg;
			}
		}

		// Return
		return $returnValue;
	}	//	function SUM()


	/**
	 * SUMIF
	 *
	 * Counts the number of cells that contain numbers within the list of arguments
	 *
	 * Excel Function:
	 *		SUMIF(value1[,value2[, ...]],condition)
	 *
	 * @access	public
	 * @category Mathematical and Trigonometric Functions
	 * @param	mixed		$arg,...		Data values
	 * @param	string		$condition		The criteria that defines which cells will be summed.
	 * @return	float
	 */
	public static function SUMIF($aArgs,$condition,$sumArgs = array()) {
		// Return value
		$returnValue = 0;

		$aArgs = PHPExcel_Calculation_Functions::flattenArray($aArgs);
		$sumArgs = PHPExcel_Calculation_Functions::flattenArray($sumArgs);
		if (empty($sumArgs)) {
			$sumArgs = $aArgs;
		}
		$condition = PHPExcel_Calculation_Functions::_ifCondition($condition);
		// Loop through arguments
		foreach ($aArgs as $key => $arg) {
			if (!is_numeric($arg)) {
				$arg = str_replace('"', '""', $arg);
				$arg = PHPExcel_Calculation::_wrapResult(strtoupper($arg));
			}

			$testCondition = '='.$arg.$condition;
			if (PHPExcel_Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
				// Is it a value within our criteria
				$returnValue += $sumArgs[$key];
			}
		}

		// Return
		return $returnValue;
	}	//	function SUMIF()


	/**
	 * SUMPRODUCT
	 *
	 * Excel Function:
	 *		SUMPRODUCT(value1[,value2[, ...]])
	 *
	 * @access	public
	 * @category Mathematical and Trigonometric Functions
	 * @param	mixed		$arg,...		Data values
	 * @return	float
	 */
	public static function SUMPRODUCT() {
		$arrayList = func_get_args();

		$wrkArray = PHPExcel_Calculation_Functions::flattenArray(array_shift($arrayList));
		$wrkCellCount = count($wrkArray);

		for ($i=0; $i< $wrkCellCount; ++$i) {
			if ((!is_numeric($wrkArray[$i])) || (is_string($wrkArray[$i]))) {
				$wrkArray[$i] = 0;
			}
		}

		foreach($arrayList as $matrixData) {
			$array2 = PHPExcel_Calculation_Functions::flattenArray($matrixData);
			$count = count($array2);
			if ($wrkCellCount != $count) {
				return PHPExcel_Calculation_Functions::VALUE();
			}

			foreach ($array2 as $i => $val) {
				if ((!is_numeric($val)) || (is_string($val))) {
					$val = 0;
				}
				$wrkArray[$i] *= $val;
			}
		}

		return array_sum($wrkArray);
	}	//	function SUMPRODUCT()


	/**
	 * SUMSQ
	 *
	 * SUMSQ returns the sum of the squares of the arguments
	 *
	 * Excel Function:
	 *		SUMSQ(value1[,value2[, ...]])
	 *
	 * @access	public
	 * @category Mathematical and Trigonometric Functions
	 * @param	mixed		$arg,...		Data values
	 * @return	float
	 */
	public static function SUMSQ() {
		// Return value
		$returnValue = 0;

		// Loop through arguments
		foreach (PHPExcel_Calculation_Functions::flattenArray(func_get_args()) as $arg) {
			// Is it a numeric value?
			if ((is_numeric($arg)) && (!is_string($arg))) {
				$returnValue += ($arg * $arg);
			}
		}

		// Return
		return $returnValue;
	}	//	function SUMSQ()


	/**
	 * SUMX2MY2
	 *
	 * @param	mixed[]	$matrixData1	Matrix #1
	 * @param	mixed[]	$matrixData2	Matrix #2
	 * @return	float
	 */
	public static function SUMX2MY2($matrixData1,$matrixData2) {
		$array1 = PHPExcel_Calculation_Functions::flattenArray($matrixData1);
		$array2 = PHPExcel_Calculation_Functions::flattenArray($matrixData2);
		$count1 = count($array1);
		$count2 = count($array2);
		if ($count1 < $count2) {
			$count = $count1;
		} else {
			$count = $count2;
		}

		$result = 0;
		for ($i = 0; $i < $count; ++$i) {
			if (((is_numeric($array1[$i])) && (!is_string($array1[$i]))) &&
				((is_numeric($array2[$i])) && (!is_string($array2[$i])))) {
				$result += ($array1[$i] * $array1[$i]) - ($array2[$i] * $array2[$i]);
			}
		}

		return $result;
	}	//	function SUMX2MY2()


	/**
	 * SUMX2PY2
	 *
	 * @param	mixed[]	$matrixData1	Matrix #1
	 * @param	mixed[]	$matrixData2	Matrix #2
	 * @return	float
	 */
	public static function SUMX2PY2($matrixData1,$matrixData2) {
		$array1 = PHPExcel_Calculation_Functions::flattenArray($matrixData1);
		$array2 = PHPExcel_Calculation_Functions::flattenArray($matrixData2);
		$count1 = count($array1);
		$count2 = count($array2);
		if ($count1 < $count2) {
			$count = $count1;
		} else {
			$count = $count2;
		}

		$result = 0;
		for ($i = 0; $i < $count; ++$i) {
			if (((is_numeric($array1[$i])) && (!is_string($array1[$i]))) &&
				((is_numeric($array2[$i])) && (!is_string($array2[$i])))) {
				$result += ($array1[$i] * $array1[$i]) + ($array2[$i] * $array2[$i]);
			}
		}

		return $result;
	}	//	function SUMX2PY2()


	/**
	 * SUMXMY2
	 *
	 * @param	mixed[]	$matrixData1	Matrix #1
	 * @param	mixed[]	$matrixData2	Matrix #2
	 * @return	float
	 */
	public static function SUMXMY2($matrixData1,$matrixData2) {
		$array1 = PHPExcel_Calculation_Functions::flattenArray($matrixData1);
		$array2 = PHPExcel_Calculation_Functions::flattenArray($matrixData2);
		$count1 = count($array1);
		$count2 = count($array2);
		if ($count1 < $count2) {
			$count = $count1;
		} else {
			$count = $count2;
		}

		$result = 0;
		for ($i = 0; $i < $count; ++$i) {
			if (((is_numeric($array1[$i])) && (!is_string($array1[$i]))) &&
				((is_numeric($array2[$i])) && (!is_string($array2[$i])))) {
				$result += ($array1[$i] - $array2[$i]) * ($array1[$i] - $array2[$i]);
			}
		}

		return $result;
	}	//	function SUMXMY2()


	/**
	 * TRUNC
	 *
	 * Truncates value to the number of fractional digits by number_digits.
	 *
	 * @param	float		$value
	 * @param	int			$digits
	 * @return	float		Truncated value
	 */
	public static function TRUNC($value = 0, $digits = 0) {
		$value	= PHPExcel_Calculation_Functions::flattenSingleValue($value);
		$digits	= PHPExcel_Calculation_Functions::flattenSingleValue($digits);

		// Validate parameters
		if ((!is_numeric($value)) || (!is_numeric($digits)))
			return PHPExcel_Calculation_Functions::VALUE();
		$digits	= floor($digits);

		// Truncate
		$adjust = pow(10, $digits);

		if (($digits > 0) && (rtrim(intval((abs($value) - abs(intval($value))) * $adjust),'0') < $adjust/10))
			return $value;

		return (intval($value * $adjust)) / $adjust;
	}	//	function TRUNC()

}	//	class PHPExcel_Calculation_MathTrig