/protected/extensions/phpexcel/Classes/PHPExcel/Calculation/Statistical.php

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<?php
/**
 * PHPExcel
 *
 * Copyright (c) 2006 - 2012 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 - 2012 PHPExcel (http://www.codeplex.com/PHPExcel)
 * @license		http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt	LGPL
 * @version		1.7.8, 2012-10-12
 */


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


require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/trend/trendClass.php';


/** LOG_GAMMA_X_MAX_VALUE */
define('LOG_GAMMA_X_MAX_VALUE', 2.55e305);

/** XMININ */
define('XMININ', 2.23e-308);

/** EPS */
define('EPS', 2.22e-16);

/** SQRT2PI */
define('SQRT2PI', 2.5066282746310005024157652848110452530069867406099);


/**
 * PHPExcel_Calculation_Statistical
 *
 * @category	PHPExcel
 * @package		PHPExcel_Calculation
 * @copyright	Copyright (c) 2006 - 2012 PHPExcel (http://www.codeplex.com/PHPExcel)
 */
class PHPExcel_Calculation_Statistical {


	private static function _checkTrendArrays(&$array1,&$array2) {
		if (!is_array($array1)) { $array1 = array($array1); }
		if (!is_array($array2)) { $array2 = array($array2); }

		$array1 = PHPExcel_Calculation_Functions::flattenArray($array1);
		$array2 = PHPExcel_Calculation_Functions::flattenArray($array2);
		foreach($array1 as $key => $value) {
			if ((is_bool($value)) || (is_string($value)) || (is_null($value))) {
				unset($array1[$key]);
				unset($array2[$key]);
			}
		}
		foreach($array2 as $key => $value) {
			if ((is_bool($value)) || (is_string($value)) || (is_null($value))) {
				unset($array1[$key]);
				unset($array2[$key]);
			}
		}
		$array1 = array_merge($array1);
		$array2 = array_merge($array2);

		return True;
	}	//	function _checkTrendArrays()


	/**
	 * Beta function.
	 *
	 * @author Jaco van Kooten
	 *
	 * @param p require p>0
	 * @param q require q>0
	 * @return 0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow
	 */
	private static function _beta($p, $q) {
		if ($p <= 0.0 || $q <= 0.0 || ($p + $q) > LOG_GAMMA_X_MAX_VALUE) {
			return 0.0;
		} else {
			return exp(self::_logBeta($p, $q));
		}
	}	//	function _beta()


	/**
	 * Incomplete beta function
	 *
	 * @author Jaco van Kooten
	 * @author Paul Meagher
	 *
	 * The computation is based on formulas from Numerical Recipes, Chapter 6.4 (W.H. Press et al, 1992).
	 * @param x require 0<=x<=1
	 * @param p require p>0
	 * @param q require q>0
	 * @return 0 if x<0, p<=0, q<=0 or p+q>2.55E305 and 1 if x>1 to avoid errors and over/underflow
	 */
	private static function _incompleteBeta($x, $p, $q) {
		if ($x <= 0.0) {
			return 0.0;
		} elseif ($x >= 1.0) {
			return 1.0;
		} elseif (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > LOG_GAMMA_X_MAX_VALUE)) {
			return 0.0;
		}
		$beta_gam = exp((0 - self::_logBeta($p, $q)) + $p * log($x) + $q * log(1.0 - $x));
		if ($x < ($p + 1.0) / ($p + $q + 2.0)) {
			return $beta_gam * self::_betaFraction($x, $p, $q) / $p;
		} else {
			return 1.0 - ($beta_gam * self::_betaFraction(1 - $x, $q, $p) / $q);
		}
	}	//	function _incompleteBeta()


	// Function cache for _logBeta function
	private static $_logBetaCache_p			= 0.0;
	private static $_logBetaCache_q			= 0.0;
	private static $_logBetaCache_result	= 0.0;

	/**
	 * The natural logarithm of the beta function.
	 *
	 * @param p require p>0
	 * @param q require q>0
	 * @return 0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow
	 * @author Jaco van Kooten
	 */
	private static function _logBeta($p, $q) {
		if ($p != self::$_logBetaCache_p || $q != self::$_logBetaCache_q) {
			self::$_logBetaCache_p = $p;
			self::$_logBetaCache_q = $q;
			if (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > LOG_GAMMA_X_MAX_VALUE)) {
				self::$_logBetaCache_result = 0.0;
			} else {
				self::$_logBetaCache_result = self::_logGamma($p) + self::_logGamma($q) - self::_logGamma($p + $q);
			}
		}
		return self::$_logBetaCache_result;
	}	//	function _logBeta()


	/**
	 * Evaluates of continued fraction part of incomplete beta function.
	 * Based on an idea from Numerical Recipes (W.H. Press et al, 1992).
	 * @author Jaco van Kooten
	 */
	private static function _betaFraction($x, $p, $q) {
		$c = 1.0;
		$sum_pq = $p + $q;
		$p_plus = $p + 1.0;
		$p_minus = $p - 1.0;
		$h = 1.0 - $sum_pq * $x / $p_plus;
		if (abs($h) < XMININ) {
			$h = XMININ;
		}
		$h = 1.0 / $h;
		$frac = $h;
		$m	 = 1;
		$delta = 0.0;
		while ($m <= MAX_ITERATIONS && abs($delta-1.0) > PRECISION ) {
			$m2 = 2 * $m;
			// even index for d
			$d = $m * ($q - $m) * $x / ( ($p_minus + $m2) * ($p + $m2));
			$h = 1.0 + $d * $h;
			if (abs($h) < XMININ) {
				$h = XMININ;
			}
			$h = 1.0 / $h;
			$c = 1.0 + $d / $c;
			if (abs($c) < XMININ) {
				$c = XMININ;
			}
			$frac *= $h * $c;
			// odd index for d
			$d = -($p + $m) * ($sum_pq + $m) * $x / (($p + $m2) * ($p_plus + $m2));
			$h = 1.0 + $d * $h;
			if (abs($h) < XMININ) {
				$h = XMININ;
			}
			$h = 1.0 / $h;
			$c = 1.0 + $d / $c;
			if (abs($c) < XMININ) {
				$c = XMININ;
			}
			$delta = $h * $c;
			$frac *= $delta;
			++$m;
		}
		return $frac;
	}	//	function _betaFraction()


	/**
	 * logGamma function
	 *
	 * @version 1.1
	 * @author Jaco van Kooten
	 *
	 * Original author was Jaco van Kooten. Ported to PHP by Paul Meagher.
	 *
	 * The natural logarithm of the gamma function. <br />
	 * Based on public domain NETLIB (Fortran) code by W. J. Cody and L. Stoltz <br />
	 * Applied Mathematics Division <br />
	 * Argonne National Laboratory <br />
	 * Argonne, IL 60439 <br />
	 * <p>
	 * References:
	 * <ol>
	 * <li>W. J. Cody and K. E. Hillstrom, 'Chebyshev Approximations for the Natural
	 *	 Logarithm of the Gamma Function,' Math. Comp. 21, 1967, pp. 198-203.</li>
	 * <li>K. E. Hillstrom, ANL/AMD Program ANLC366S, DGAMMA/DLGAMA, May, 1969.</li>
	 * <li>Hart, Et. Al., Computer Approximations, Wiley and sons, New York, 1968.</li>
	 * </ol>
	 * </p>
	 * <p>
	 * From the original documentation:
	 * </p>
	 * <p>
	 * This routine calculates the LOG(GAMMA) function for a positive real argument X.
	 * Computation is based on an algorithm outlined in references 1 and 2.
	 * The program uses rational functions that theoretically approximate LOG(GAMMA)
	 * to at least 18 significant decimal digits. The approximation for X > 12 is from
	 * reference 3, while approximations for X < 12.0 are similar to those in reference
	 * 1, but are unpublished. The accuracy achieved depends on the arithmetic system,
	 * the compiler, the intrinsic functions, and proper selection of the
	 * machine-dependent constants.
	 * </p>
	 * <p>
	 * Error returns: <br />
	 * The program returns the value XINF for X .LE. 0.0 or when overflow would occur.
	 * The computation is believed to be free of underflow and overflow.
	 * </p>
	 * @return MAX_VALUE for x < 0.0 or when overflow would occur, i.e. x > 2.55E305
	 */

	// Function cache for logGamma
	private static $_logGammaCache_result	= 0.0;
	private static $_logGammaCache_x		= 0.0;

	private static function _logGamma($x) {
		// Log Gamma related constants
		static $lg_d1 = -0.5772156649015328605195174;
		static $lg_d2 = 0.4227843350984671393993777;
		static $lg_d4 = 1.791759469228055000094023;

		static $lg_p1 = array(	4.945235359296727046734888,
								201.8112620856775083915565,
								2290.838373831346393026739,
								11319.67205903380828685045,
								28557.24635671635335736389,
								38484.96228443793359990269,
								26377.48787624195437963534,
								7225.813979700288197698961 );
		static $lg_p2 = array(	4.974607845568932035012064,
								542.4138599891070494101986,
								15506.93864978364947665077,
								184793.2904445632425417223,
								1088204.76946882876749847,
								3338152.967987029735917223,
								5106661.678927352456275255,
								3074109.054850539556250927 );
		static $lg_p4 = array(	14745.02166059939948905062,
								2426813.369486704502836312,
								121475557.4045093227939592,
								2663432449.630976949898078,
								29403789566.34553899906876,
								170266573776.5398868392998,
								492612579337.743088758812,
								560625185622.3951465078242 );

		static $lg_q1 = array(	67.48212550303777196073036,
								1113.332393857199323513008,
								7738.757056935398733233834,
								27639.87074403340708898585,
								54993.10206226157329794414,
								61611.22180066002127833352,
								36351.27591501940507276287,
								8785.536302431013170870835 );
		static $lg_q2 = array(	183.0328399370592604055942,
								7765.049321445005871323047,
								133190.3827966074194402448,
								1136705.821321969608938755,
								5267964.117437946917577538,
								13467014.54311101692290052,
								17827365.30353274213975932,
								9533095.591844353613395747 );
		static $lg_q4 = array(	2690.530175870899333379843,
								639388.5654300092398984238,
								41355999.30241388052042842,
								1120872109.61614794137657,
								14886137286.78813811542398,
								101680358627.2438228077304,
								341747634550.7377132798597,
								446315818741.9713286462081 );

		static $lg_c  = array(	-0.001910444077728,
								8.4171387781295e-4,
								-5.952379913043012e-4,
								7.93650793500350248e-4,
								-0.002777777777777681622553,
								0.08333333333333333331554247,
								0.0057083835261 );

	// Rough estimate of the fourth root of logGamma_xBig
	static $lg_frtbig = 2.25e76;
	static $pnt68	 = 0.6796875;


	if ($x == self::$_logGammaCache_x) {
		return self::$_logGammaCache_result;
	}
	$y = $x;
	if ($y > 0.0 && $y <= LOG_GAMMA_X_MAX_VALUE) {
		if ($y <= EPS) {
			$res = -log(y);
		} elseif ($y <= 1.5) {
			// ---------------------
			//	EPS .LT. X .LE. 1.5
			// ---------------------
			if ($y < $pnt68) {
				$corr = -log($y);
				$xm1 = $y;
			} else {
				$corr = 0.0;
				$xm1 = $y - 1.0;
			}
			if ($y <= 0.5 || $y >= $pnt68) {
				$xden = 1.0;
				$xnum = 0.0;
				for ($i = 0; $i < 8; ++$i) {
					$xnum = $xnum * $xm1 + $lg_p1[$i];
					$xden = $xden * $xm1 + $lg_q1[$i];
				}
				$res = $corr + $xm1 * ($lg_d1 + $xm1 * ($xnum / $xden));
			} else {
				$xm2 = $y - 1.0;
				$xden = 1.0;
				$xnum = 0.0;
				for ($i = 0; $i < 8; ++$i) {
					$xnum = $xnum * $xm2 + $lg_p2[$i];
					$xden = $xden * $xm2 + $lg_q2[$i];
				}
				$res = $corr + $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden));
			}
		} elseif ($y <= 4.0) {
			// ---------------------
			//	1.5 .LT. X .LE. 4.0
			// ---------------------
			$xm2 = $y - 2.0;
			$xden = 1.0;
			$xnum = 0.0;
			for ($i = 0; $i < 8; ++$i) {
				$xnum = $xnum * $xm2 + $lg_p2[$i];
				$xden = $xden * $xm2 + $lg_q2[$i];
			}
			$res = $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden));
		} elseif ($y <= 12.0) {
			// ----------------------
			//	4.0 .LT. X .LE. 12.0
			// ----------------------
			$xm4 = $y - 4.0;
			$xden = -1.0;
			$xnum = 0.0;
			for ($i = 0; $i < 8; ++$i) {
				$xnum = $xnum * $xm4 + $lg_p4[$i];
				$xden = $xden * $xm4 + $lg_q4[$i];
			}
			$res = $lg_d4 + $xm4 * ($xnum / $xden);
		} else {
			// ---------------------------------
			//	Evaluate for argument .GE. 12.0
			// ---------------------------------
			$res = 0.0;
			if ($y <= $lg_frtbig) {
				$res = $lg_c[6];
				$ysq = $y * $y;
				for ($i = 0; $i < 6; ++$i)
					$res = $res / $ysq + $lg_c[$i];
				}
				$res /= $y;
				$corr = log($y);
				$res = $res + log(SQRT2PI) - 0.5 * $corr;
				$res += $y * ($corr - 1.0);
			}
		} else {
			// --------------------------
			//	Return for bad arguments
			// --------------------------
			$res = MAX_VALUE;
		}
		// ------------------------------
		//	Final adjustments and return
		// ------------------------------
		self::$_logGammaCache_x = $x;
		self::$_logGammaCache_result = $res;
		return $res;
	}	//	function _logGamma()


	//
	//	Private implementation of the incomplete Gamma function
	//
	private static function _incompleteGamma($a,$x) {
		static $max = 32;
		$summer = 0;
		for ($n=0; $n<=$max; ++$n) {
			$divisor = $a;
			for ($i=1; $i<=$n; ++$i) {
				$divisor *= ($a + $i);
			}
			$summer += (pow($x,$n) / $divisor);
		}
		return pow($x,$a) * exp(0-$x) * $summer;
	}	//	function _incompleteGamma()


	//
	//	Private implementation of the Gamma function
	//
	private static function _gamma($data) {
		if ($data == 0.0) return 0;

		static $p0 = 1.000000000190015;
		static $p = array ( 1 => 76.18009172947146,
							2 => -86.50532032941677,
							3 => 24.01409824083091,
							4 => -1.231739572450155,
							5 => 1.208650973866179e-3,
							6 => -5.395239384953e-6
						  );

		$y = $x = $data;
		$tmp = $x + 5.5;
		$tmp -= ($x + 0.5) * log($tmp);

		$summer = $p0;
		for ($j=1;$j<=6;++$j) {
			$summer += ($p[$j] / ++$y);
		}
		return exp(0 - $tmp + log(SQRT2PI * $summer / $x));
	}	//	function _gamma()


	/***************************************************************************
	 *								inverse_ncdf.php
	 *							-------------------
	 *	begin				: Friday, January 16, 2004
	 *	copyright			: (C) 2004 Michael Nickerson
	 *	email				: nickersonm@yahoo.com
	 *
	 ***************************************************************************/
	private static function _inverse_ncdf($p) {
		//	Inverse ncdf approximation by Peter J. Acklam, implementation adapted to
		//	PHP by Michael Nickerson, using Dr. Thomas Ziegler's C implementation as
		//	a guide. http://home.online.no/~pjacklam/notes/invnorm/index.html
		//	I have not checked the accuracy of this implementation. Be aware that PHP
		//	will truncate the coeficcients to 14 digits.

		//	You have permission to use and distribute this function freely for
		//	whatever purpose you want, but please show common courtesy and give credit
		//	where credit is due.

		//	Input paramater is $p - probability - where 0 < p < 1.

		//	Coefficients in rational approximations
		static $a = array(	1 => -3.969683028665376e+01,
							2 => 2.209460984245205e+02,
							3 => -2.759285104469687e+02,
							4 => 1.383577518672690e+02,
							5 => -3.066479806614716e+01,
							6 => 2.506628277459239e+00
						 );

		static $b = array(	1 => -5.447609879822406e+01,
							2 => 1.615858368580409e+02,
							3 => -1.556989798598866e+02,
							4 => 6.680131188771972e+01,
							5 => -1.328068155288572e+01
						 );

		static $c = array(	1 => -7.784894002430293e-03,
							2 => -3.223964580411365e-01,
							3 => -2.400758277161838e+00,
							4 => -2.549732539343734e+00,
							5 => 4.374664141464968e+00,
							6 => 2.938163982698783e+00
						 );

		static $d = array(	1 => 7.784695709041462e-03,
							2 => 3.224671290700398e-01,
							3 => 2.445134137142996e+00,
							4 => 3.754408661907416e+00
						 );

		//	Define lower and upper region break-points.
		$p_low = 0.02425;			//Use lower region approx. below this
		$p_high = 1 - $p_low;		//Use upper region approx. above this

		if (0 < $p && $p < $p_low) {
			//	Rational approximation for lower region.
			$q = sqrt(-2 * log($p));
			return ((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) /
					(((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
		} elseif ($p_low <= $p && $p <= $p_high) {
			//	Rational approximation for central region.
			$q = $p - 0.5;
			$r = $q * $q;
			return ((((($a[1] * $r + $a[2]) * $r + $a[3]) * $r + $a[4]) * $r + $a[5]) * $r + $a[6]) * $q /
				   ((((($b[1] * $r + $b[2]) * $r + $b[3]) * $r + $b[4]) * $r + $b[5]) * $r + 1);
		} elseif ($p_high < $p && $p < 1) {
			//	Rational approximation for upper region.
			$q = sqrt(-2 * log(1 - $p));
			return -((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) /
					 (((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
		}
		//	If 0 < p < 1, return a null value
		return PHPExcel_Calculation_Functions::NULL();
	}	//	function _inverse_ncdf()


	private static function _inverse_ncdf2($prob) {
		//	Approximation of inverse standard normal CDF developed by
		//	B. Moro, "The Full Monte," Risk 8(2), Feb 1995, 57-58.

		$a1 = 2.50662823884;
		$a2 = -18.61500062529;
		$a3 = 41.39119773534;
		$a4 = -25.44106049637;

		$b1 = -8.4735109309;
		$b2 = 23.08336743743;
		$b3 = -21.06224101826;
		$b4 = 3.13082909833;

		$c1 = 0.337475482272615;
		$c2 = 0.976169019091719;
		$c3 = 0.160797971491821;
		$c4 = 2.76438810333863E-02;
		$c5 = 3.8405729373609E-03;
		$c6 = 3.951896511919E-04;
		$c7 = 3.21767881768E-05;
		$c8 = 2.888167364E-07;
		$c9 = 3.960315187E-07;

		$y = $prob - 0.5;
		if (abs($y) < 0.42) {
			$z = ($y * $y);
			$z = $y * ((($a4 * $z + $a3) * $z + $a2) * $z + $a1) / (((($b4 * $z + $b3) * $z + $b2) * $z + $b1) * $z + 1);
		} else {
			if ($y > 0) {
				$z = log(-log(1 - $prob));
			} else {
				$z = log(-log($prob));
			}
			$z = $c1 + $z * ($c2 + $z * ($c3 + $z * ($c4 + $z * ($c5 + $z * ($c6 + $z * ($c7 + $z * ($c8 + $z * $c9)))))));
			if ($y < 0) {
				$z = -$z;
			}
		}
		return $z;
	}	//	function _inverse_ncdf2()


	private static function _inverse_ncdf3($p) {
		//	ALGORITHM AS241 APPL. STATIST. (1988) VOL. 37, NO. 3.
		//	Produces the normal deviate Z corresponding to a given lower
		//	tail area of P; Z is accurate to about 1 part in 10**16.
		//
		//	This is a PHP version of the original FORTRAN code that can
		//	be found at http://lib.stat.cmu.edu/apstat/
		$split1 = 0.425;
		$split2 = 5;
		$const1 = 0.180625;
		$const2 = 1.6;

		//	coefficients for p close to 0.5
		$a0 = 3.3871328727963666080;
		$a1 = 1.3314166789178437745E+2;
		$a2 = 1.9715909503065514427E+3;
		$a3 = 1.3731693765509461125E+4;
		$a4 = 4.5921953931549871457E+4;
		$a5 = 6.7265770927008700853E+4;
		$a6 = 3.3430575583588128105E+4;
		$a7 = 2.5090809287301226727E+3;

		$b1 = 4.2313330701600911252E+1;
		$b2 = 6.8718700749205790830E+2;
		$b3 = 5.3941960214247511077E+3;
		$b4 = 2.1213794301586595867E+4;
		$b5 = 3.9307895800092710610E+4;
		$b6 = 2.8729085735721942674E+4;
		$b7 = 5.2264952788528545610E+3;

		//	coefficients for p not close to 0, 0.5 or 1.
		$c0 = 1.42343711074968357734;
		$c1 = 4.63033784615654529590;
		$c2 = 5.76949722146069140550;
		$c3 = 3.64784832476320460504;
		$c4 = 1.27045825245236838258;
		$c5 = 2.41780725177450611770E-1;
		$c6 = 2.27238449892691845833E-2;
		$c7 = 7.74545014278341407640E-4;

		$d1 = 2.05319162663775882187;
		$d2 = 1.67638483018380384940;
		$d3 = 6.89767334985100004550E-1;
		$d4 = 1.48103976427480074590E-1;
		$d5 = 1.51986665636164571966E-2;
		$d6 = 5.47593808499534494600E-4;
		$d7 = 1.05075007164441684324E-9;

		//	coefficients for p near 0 or 1.
		$e0 = 6.65790464350110377720;
		$e1 = 5.46378491116411436990;
		$e2 = 1.78482653991729133580;
		$e3 = 2.96560571828504891230E-1;
		$e4 = 2.65321895265761230930E-2;
		$e5 = 1.24266094738807843860E-3;
		$e6 = 2.71155556874348757815E-5;
		$e7 = 2.01033439929228813265E-7;

		$f1 = 5.99832206555887937690E-1;
		$f2 = 1.36929880922735805310E-1;
		$f3 = 1.48753612908506148525E-2;
		$f4 = 7.86869131145613259100E-4;
		$f5 = 1.84631831751005468180E-5;
		$f6 = 1.42151175831644588870E-7;
		$f7 = 2.04426310338993978564E-15;

		$q = $p - 0.5;

		//	computation for p close to 0.5
		if (abs($q) <= split1) {
			$R = $const1 - $q * $q;
			$z = $q * ((((((($a7 * $R + $a6) * $R + $a5) * $R + $a4) * $R + $a3) * $R + $a2) * $R + $a1) * $R + $a0) /
					  ((((((($b7 * $R + $b6) * $R + $b5) * $R + $b4) * $R + $b3) * $R + $b2) * $R + $b1) * $R + 1);
		} else {
			if ($q < 0) {
				$R = $p;
			} else {
				$R = 1 - $p;
			}
			$R = pow(-log($R),2);

			//	computation for p not close to 0, 0.5 or 1.
			If ($R <= $split2) {
				$R = $R - $const2;
				$z = ((((((($c7 * $R + $c6) * $R + $c5) * $R + $c4) * $R + $c3) * $R + $c2) * $R + $c1) * $R + $c0) /
					 ((((((($d7 * $R + $d6) * $R + $d5) * $R + $d4) * $R + $d3) * $R + $d2) * $R + $d1) * $R + 1);
			} else {
			//	computation for p near 0 or 1.
				$R = $R - $split2;
				$z = ((((((($e7 * $R + $e6) * $R + $e5) * $R + $e4) * $R + $e3) * $R + $e2) * $R + $e1) * $R + $e0) /
					 ((((((($f7 * $R + $f6) * $R + $f5) * $R + $f4) * $R + $f3) * $R + $f2) * $R + $f1) * $R + 1);
			}
			if ($q < 0) {
				$z = -$z;
			}
		}
		return $z;
	}	//	function _inverse_ncdf3()


	/**
	 * AVEDEV
	 *
	 * Returns the average of the absolute deviations of data points from their mean.
	 * AVEDEV is a measure of the variability in a data set.
	 *
	 * Excel Function:
	 *		AVEDEV(value1[,value2[, ...]])
	 *
	 * @access	public
	 * @category Statistical Functions
	 * @param	mixed		$arg,...		Data values
	 * @return	float
	 */
	public static function AVEDEV() {
		$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());

		// Return value
		$returnValue = null;

		$aMean = self::AVERAGE($aArgs);
		if ($aMean != PHPExcel_Calculation_Functions::DIV0()) {
			$aCount = 0;
			foreach ($aArgs as $k => $arg) {
				if ((is_bool($arg)) &&
					((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
					$arg = (integer) $arg;
				}
				// Is it a numeric value?
				if ((is_numeric($arg)) && (!is_string($arg))) {
					if (is_null($returnValue)) {
						$returnValue = abs($arg - $aMean);
					} else {
						$returnValue += abs($arg - $aMean);
					}
					++$aCount;
				}
			}

			// Return
			if ($aCount == 0) {
				return PHPExcel_Calculation_Functions::DIV0();
			}
			return $returnValue / $aCount;
		}
		return PHPExcel_Calculation_Functions::NaN();
	}	//	function AVEDEV()


	/**
	 * AVERAGE
	 *
	 * Returns the average (arithmetic mean) of the arguments
	 *
	 * Excel Function:
	 *		AVERAGE(value1[,value2[, ...]])
	 *
	 * @access	public
	 * @category Statistical Functions
	 * @param	mixed		$arg,...		Data values
	 * @return	float
	 */
	public static function AVERAGE() {
		$returnValue = $aCount = 0;

		// Loop through arguments
		foreach (PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args()) as $k => $arg) {
			if ((is_bool($arg)) &&
				((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
				$arg = (integer) $arg;
			}
			// Is it a numeric value?
			if ((is_numeric($arg)) && (!is_string($arg))) {
				if (is_null($returnValue)) {
					$returnValue = $arg;
				} else {
					$returnValue += $arg;
				}
				++$aCount;
			}
		}

		// Return
		if ($aCount > 0) {
			return $returnValue / $aCount;
		} else {
			return PHPExcel_Calculation_Functions::DIV0();
		}
	}	//	function AVERAGE()


	/**
	 * AVERAGEA
	 *
	 * Returns the average of its arguments, including numbers, text, and logical values
	 *
	 * Excel Function:
	 *		AVERAGEA(value1[,value2[, ...]])
	 *
	 * @access	public
	 * @category Statistical Functions
	 * @param	mixed		$arg,...		Data values
	 * @return	float
	 */
	public static function AVERAGEA() {
		// Return value
		$returnValue = null;

		$aCount = 0;
		// Loop through arguments
		foreach (PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args()) as $k => $arg) {
			if ((is_bool($arg)) &&
				(!PHPExcel_Calculation_Functions::isMatrixValue($k))) {
			} else {
				if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) {
					if (is_bool($arg)) {
						$arg = (integer) $arg;
					} elseif (is_string($arg)) {
						$arg = 0;
					}
					if (is_null($returnValue)) {
						$returnValue = $arg;
					} else {
						$returnValue += $arg;
					}
					++$aCount;
				}
			}
		}

		// Return
		if ($aCount > 0) {
			return $returnValue / $aCount;
		} else {
			return PHPExcel_Calculation_Functions::DIV0();
		}
	}	//	function AVERAGEA()


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

		$aArgs = PHPExcel_Calculation_Functions::flattenArray($aArgs);
		$averageArgs = PHPExcel_Calculation_Functions::flattenArray($averageArgs);
		if (empty($averageArgs)) {
			$averageArgs = $aArgs;
		}
		$condition = PHPExcel_Calculation_Functions::_ifCondition($condition);
		// Loop through arguments
		$aCount = 0;
		foreach ($aArgs as $key => $arg) {
			if (!is_numeric($arg)) { $arg = PHPExcel_Calculation::_wrapResult(strtoupper($arg)); }
			$testCondition = '='.$arg.$condition;
			if (PHPExcel_Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
				if ((is_null($returnValue)) || ($arg > $returnValue)) {
					$returnValue += $arg;
					++$aCount;
				}
			}
		}

		// Return
		if ($aCount > 0) {
			return $returnValue / $aCount;
		} else {
			return PHPExcel_Calculation_Functions::DIV0();
		}
	}	//	function AVERAGEIF()


	/**
	 * BETADIST
	 *
	 * Returns the beta distribution.
	 *
	 * @param	float		$value			Value at which you want to evaluate the distribution
	 * @param	float		$alpha			Parameter to the distribution
	 * @param	float		$beta			Parameter to the distribution
	 * @param	boolean		$cumulative
	 * @return	float
	 *
	 */
	public static function BETADIST($value,$alpha,$beta,$rMin=0,$rMax=1) {
		$value	= PHPExcel_Calculation_Functions::flattenSingleValue($value);
		$alpha	= PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
		$beta	= PHPExcel_Calculation_Functions::flattenSingleValue($beta);
		$rMin	= PHPExcel_Calculation_Functions::flattenSingleValue($rMin);
		$rMax	= PHPExcel_Calculation_Functions::flattenSingleValue($rMax);

		if ((is_numeric($value)) && (is_numeric($alpha)) && (is_numeric($beta)) && (is_numeric($rMin)) && (is_numeric($rMax))) {
			if (($value < $rMin) || ($value > $rMax) || ($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax)) {
				return PHPExcel_Calculation_Functions::NaN();
			}
			if ($rMin > $rMax) {
				$tmp = $rMin;
				$rMin = $rMax;
				$rMax = $tmp;
			}
			$value -= $rMin;
			$value /= ($rMax - $rMin);
			return self::_incompleteBeta($value,$alpha,$beta);
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function BETADIST()


	/**
	 * BETAINV
	 *
	 * Returns the inverse of the beta distribution.
	 *
	 * @param	float		$probability	Probability at which you want to evaluate the distribution
	 * @param	float		$alpha			Parameter to the distribution
	 * @param	float		$beta			Parameter to the distribution
	 * @param	boolean		$cumulative
	 * @return	float
	 *
	 */
	public static function BETAINV($probability,$alpha,$beta,$rMin=0,$rMax=1) {
		$probability	= PHPExcel_Calculation_Functions::flattenSingleValue($probability);
		$alpha			= PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
		$beta			= PHPExcel_Calculation_Functions::flattenSingleValue($beta);
		$rMin			= PHPExcel_Calculation_Functions::flattenSingleValue($rMin);
		$rMax			= PHPExcel_Calculation_Functions::flattenSingleValue($rMax);

		if ((is_numeric($probability)) && (is_numeric($alpha)) && (is_numeric($beta)) && (is_numeric($rMin)) && (is_numeric($rMax))) {
			if (($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax) || ($probability <= 0) || ($probability > 1)) {
				return PHPExcel_Calculation_Functions::NaN();
			}
			if ($rMin > $rMax) {
				$tmp = $rMin;
				$rMin = $rMax;
				$rMax = $tmp;
			}
			$a = 0;
			$b = 2;

			$i = 0;
			while ((($b - $a) > PRECISION) && ($i++ < MAX_ITERATIONS)) {
				$guess = ($a + $b) / 2;
				$result = self::BETADIST($guess, $alpha, $beta);
				if (($result == $probability) || ($result == 0)) {
					$b = $a;
				} elseif ($result > $probability) {
					$b = $guess;
				} else {
					$a = $guess;
				}
			}
			if ($i == MAX_ITERATIONS) {
				return PHPExcel_Calculation_Functions::NA();
			}
			return round($rMin + $guess * ($rMax - $rMin),12);
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function BETAINV()


	/**
	 * BINOMDIST
	 *
	 * Returns the individual term binomial distribution probability. Use BINOMDIST in problems with
	 *		a fixed number of tests or trials, when the outcomes of any trial are only success or failure,
	 *		when trials are independent, and when the probability of success is constant throughout the
	 *		experiment. For example, BINOMDIST can calculate the probability that two of the next three
	 *		babies born are male.
	 *
	 * @param	float		$value			Number of successes in trials
	 * @param	float		$trials			Number of trials
	 * @param	float		$probability	Probability of success on each trial
	 * @param	boolean		$cumulative
	 * @return	float
	 *
	 * @todo	Cumulative distribution function
	 *
	 */
	public static function BINOMDIST($value, $trials, $probability, $cumulative) {
		$value			= floor(PHPExcel_Calculation_Functions::flattenSingleValue($value));
		$trials			= floor(PHPExcel_Calculation_Functions::flattenSingleValue($trials));
		$probability	= PHPExcel_Calculation_Functions::flattenSingleValue($probability);

		if ((is_numeric($value)) && (is_numeric($trials)) && (is_numeric($probability))) {
			if (($value < 0) || ($value > $trials)) {
				return PHPExcel_Calculation_Functions::NaN();
			}
			if (($probability < 0) || ($probability > 1)) {
				return PHPExcel_Calculation_Functions::NaN();
			}
			if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
				if ($cumulative) {
					$summer = 0;
					for ($i = 0; $i <= $value; ++$i) {
						$summer += PHPExcel_Calculation_MathTrig::COMBIN($trials,$i) * pow($probability,$i) * pow(1 - $probability,$trials - $i);
					}
					return $summer;
				} else {
					return PHPExcel_Calculation_MathTrig::COMBIN($trials,$value) * pow($probability,$value) * pow(1 - $probability,$trials - $value) ;
				}
			}
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function BINOMDIST()


	/**
	 * CHIDIST
	 *
	 * Returns the one-tailed probability of the chi-squared distribution.
	 *
	 * @param	float		$value			Value for the function
	 * @param	float		$degrees		degrees of freedom
	 * @return	float
	 */
	public static function CHIDIST($value, $degrees) {
		$value		= PHPExcel_Calculation_Functions::flattenSingleValue($value);
		$degrees	= floor(PHPExcel_Calculation_Functions::flattenSingleValue($degrees));

		if ((is_numeric($value)) && (is_numeric($degrees))) {
			if ($degrees < 1) {
				return PHPExcel_Calculation_Functions::NaN();
			}
			if ($value < 0) {
				if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
					return 1;
				}
				return PHPExcel_Calculation_Functions::NaN();
			}
			return 1 - (self::_incompleteGamma($degrees/2,$value/2) / self::_gamma($degrees/2));
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function CHIDIST()


	/**
	 * CHIINV
	 *
	 * Returns the one-tailed probability of the chi-squared distribution.
	 *
	 * @param	float		$probability	Probability for the function
	 * @param	float		$degrees		degrees of freedom
	 * @return	float
	 */
	public static function CHIINV($probability, $degrees) {
		$probability	= PHPExcel_Calculation_Functions::flattenSingleValue($probability);
		$degrees		= floor(PHPExcel_Calculation_Functions::flattenSingleValue($degrees));

		if ((is_numeric($probability)) && (is_numeric($degrees))) {

			$xLo = 100;
			$xHi = 0;

			$x = $xNew = 1;
			$dx	= 1;
			$i = 0;

			while ((abs($dx) > PRECISION) && ($i++ < MAX_ITERATIONS)) {
				// Apply Newton-Raphson step
				$result = self::CHIDIST($x, $degrees);
				$error = $result - $probability;
				if ($error == 0.0) {
					$dx = 0;
				} elseif ($error < 0.0) {
					$xLo = $x;
				} else {
					$xHi = $x;
				}
				// Avoid division by zero
				if ($result != 0.0) {
					$dx = $error / $result;
					$xNew = $x - $dx;
				}
				// If the NR fails to converge (which for example may be the
				// case if the initial guess is too rough) we apply a bisection
				// step to determine a more narrow interval around the root.
				if (($xNew < $xLo) || ($xNew > $xHi) || ($result == 0.0)) {
					$xNew = ($xLo + $xHi) / 2;
					$dx = $xNew - $x;
				}
				$x = $xNew;
			}
			if ($i == MAX_ITERATIONS) {
				return PHPExcel_Calculation_Functions::NA();
			}
			return round($x,12);
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function CHIINV()


	/**
	 * CONFIDENCE
	 *
	 * Returns the confidence interval for a population mean
	 *
	 * @param	float		$alpha
	 * @param	float		$stdDev		Standard Deviation
	 * @param	float		$size
	 * @return	float
	 *
	 */
	public static function CONFIDENCE($alpha,$stdDev,$size) {
		$alpha	= PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
		$stdDev	= PHPExcel_Calculation_Functions::flattenSingleValue($stdDev);
		$size	= floor(PHPExcel_Calculation_Functions::flattenSingleValue($size));

		if ((is_numeric($alpha)) && (is_numeric($stdDev)) && (is_numeric($size))) {
			if (($alpha <= 0) || ($alpha >= 1)) {
				return PHPExcel_Calculation_Functions::NaN();
			}
			if (($stdDev <= 0) || ($size < 1)) {
				return PHPExcel_Calculation_Functions::NaN();
			}
			return self::NORMSINV(1 - $alpha / 2) * $stdDev / sqrt($size);
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function CONFIDENCE()


	/**
	 * CORREL
	 *
	 * Returns covariance, the average of the products of deviations for each data point pair.
	 *
	 * @param	array of mixed		Data Series Y
	 * @param	array of mixed		Data Series X
	 * @return	float
	 */
	public static function CORREL($yValues,$xValues=null) {
		if ((is_null($xValues)) || (!is_array($yValues)) || (!is_array($xValues))) {
			return PHPExcel_Calculation_Functions::VALUE();
		}
		if (!self::_checkTrendArrays($yValues,$xValues)) {
			return PHPExcel_Calculation_Functions::VALUE();
		}
		$yValueCount = count($yValues);
		$xValueCount = count($xValues);

		if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
			return PHPExcel_Calculation_Functions::NA();
		} elseif ($yValueCount == 1) {
			return PHPExcel_Calculation_Functions::DIV0();
		}

		$bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
		return $bestFitLinear->getCorrelation();
	}	//	function CORREL()


	/**
	 * COUNT
	 *
	 * Counts the number of cells that contain numbers within the list of arguments
	 *
	 * Excel Function:
	 *		COUNT(value1[,value2[, ...]])
	 *
	 * @access	public
	 * @category Statistical Functions
	 * @param	mixed		$arg,...		Data values
	 * @return	int
	 */
	public static function COUNT() {
		// Return value
		$returnValue = 0;

		// Loop through arguments
		$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());
		foreach ($aArgs as $k => $arg) {
			if ((is_bool($arg)) &&
				((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
				$arg = (integer) $arg;
			}
			// Is it a numeric value?
			if ((is_numeric($arg)) && (!is_string($arg))) {
				++$returnValue;
			}
		}

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


	/**
	 * COUNTA
	 *
	 * Counts the number of cells that are not empty within the list of arguments
	 *
	 * Excel Function:
	 *		COUNTA(value1[,value2[, ...]])
	 *
	 * @access	public
	 * @category Statistical Functions
	 * @param	mixed		$arg,...		Data values
	 * @return	int
	 */
	public static function COUNTA() {
		// Return value
		$returnValue = 0;

		// Loop through arguments
		$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
		foreach ($aArgs as $arg) {
			// Is it a numeric, boolean or string value?
			if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) {
				++$returnValue;
			}
		}

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


	/**
	 * COUNTBLANK
	 *
	 * Counts the number of empty cells within the list of arguments
	 *
	 * Excel Function:
	 *		COUNTBLANK(value1[,value2[, ...]])
	 *
	 * @access	public
	 * @category Statistical Functions
	 * @param	mixed		$arg,...		Data values
	 * @return	int
	 */
	public static function COUNTBLANK() {
		// Return value
		$returnValue = 0;

		// Loop through arguments
		$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
		foreach ($aArgs as $arg) {
			// Is it a blank cell?
			if ((is_null($arg)) || ((is_string($arg)) && ($arg == ''))) {
				++$returnValue;
			}
		}

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


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

		$aArgs = PHPExcel_Calculation_Functions::flattenArray($aArgs);
		$condition = PHPExcel_Calculation_Functions::_ifCondition($condition);
		// Loop through arguments
		foreach ($aArgs as $arg) {
			if (!is_numeric($arg)) { $arg = PHPExcel_Calculation::_wrapResult(strtoupper($arg)); }
			$testCondition = '='.$arg.$condition;
			if (PHPExcel_Calculation::getInstance()->_calculateFormulaValue($testCondition)) {
				// Is it a value within our criteria
				++$returnValue;
			}
		}

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


	/**
	 * COVAR
	 *
	 * Returns covariance, the average of the products of deviations for each data point pair.
	 *
	 * @param	array of mixed		Data Series Y
	 * @param	array of mixed		Data Series X
	 * @return	float
	 */
	public static function COVAR($yValues,$xValues) {
		if (!self::_checkTrendArrays($yValues,$xValues)) {
			return PHPExcel_Calculation_Functions::VALUE();
		}
		$yValueCount = count($yValues);
		$xValueCount = count($xValues);

		if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
			return PHPExcel_Calculation_Functions::NA();
		} elseif ($yValueCount == 1) {
			return PHPExcel_Calculation_Functions::DIV0();
		}

		$bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
		return $bestFitLinear->getCovariance();
	}	//	function COVAR()


	/**
	 * CRITBINOM
	 *
	 * Returns the smallest value for which the cumulative binomial distribution is greater
	 *		than or equal to a criterion value
	 *
	 * See http://support.microsoft.com/kb/828117/ for details of the algorithm used
	 *
	 * @param	float		$trials			number of Bernoulli trials
	 * @param	float		$probability	probability of a success on each trial
	 * @param	float		$alpha			criterion value
	 * @return	int
	 *
	 * @todo	Warning. This implementation differs from the algorithm detailed on the MS
	 *			web site in that $CumPGuessMinus1 = $CumPGuess - 1 rather than $CumPGuess - $PGuess
	 *			This eliminates a potential endless loop error, but may have an adverse affect on the
	 *			accuracy of the function (although all my tests have so far returned correct results).
	 *
	 */
	public static function CRITBINOM($trials, $probability, $alpha) {
		$trials			= floor(PHPExcel_Calculation_Functions::flattenSingleValue($trials));
		$probability	= PHPExcel_Calculation_Functions::flattenSingleValue($probability);
		$alpha			= PHPExcel_Calculation_Functions::flattenSingleValue($alpha);

		if ((is_numeric($trials)) && (is_numeric($probability)) && (is_numeric($alpha))) {
			if ($trials < 0) {
				return PHPExcel_Calculation_Functions::NaN();
			}
			if (($probability < 0) || ($probability > 1)) {
				return PHPExcel_Calculation_Functions::NaN();
			}
			if (($alpha < 0) || ($alpha > 1)) {
				return PHPExcel_Calculation_Functions::NaN();
			}
			if ($alpha <= 0.5) {
				$t = sqrt(log(1 / ($alpha * $alpha)));
				$trialsApprox = 0 - ($t + (2.515517 + 0.802853 * $t + 0.010328 * $t * $t) / (1 + 1.432788 * $t + 0.189269 * $t * $t + 0.001308 * $t * $t * $t));
			} else {
				$t = sqrt(log(1 / pow(1 - $alpha,2)));
				$trialsApprox = $t - (2.515517 + 0.802853 * $t + 0.010328 * $t * $t) / (1 + 1.432788 * $t + 0.189269 * $t * $t + 0.001308 * $t * $t * $t);
			}
			$Guess = floor($trials * $probability + $trialsApprox * sqrt($trials * $probability * (1 - $probability)));
			if ($Guess < 0) {
				$Guess = 0;
			} elseif ($Guess > $trials) {
				$Guess = $trials;
			}

			$TotalUnscaledProbability = $UnscaledPGuess = $UnscaledCumPGuess = 0.0;
			$EssentiallyZero = 10e-12;

			$m = floor($trials * $probability);
			++$TotalUnscaledProbability;
			if ($m == $Guess) { ++$UnscaledPGuess; }
			if ($m <= $Guess) { ++$UnscaledCumPGuess; }

			$PreviousValue = 1;
			$Done = False;
			$k = $m + 1;
			while ((!$Done) && ($k <= $trials)) {
				$CurrentValue = $PreviousValue * ($trials - $k + 1) * $probability / ($k * (1 - $probability));
				$TotalUnscaledProbability += $CurrentValue;
				if ($k == $Guess) { $UnscaledPGuess += $CurrentValue; }
				if ($k <= $Guess) { $UnscaledCumPGuess += $CurrentValue; }
				if ($CurrentValue <= $EssentiallyZero) { $Done = True; }
				$PreviousValue = $CurrentValue;
				++$k;
			}

			$PreviousValue = 1;
			$Done = False;
			$k = $m - 1;
			while ((!$Done) && ($k >= 0)) {
				$CurrentValue = $PreviousValue * $k + 1 * (1 - $probability) / (($trials - $k) * $probability);
				$TotalUnscaledProbability += $CurrentValue;
				if ($k == $Guess) { $UnscaledPGuess += $CurrentValue; }
				if ($k <= $Guess) { $UnscaledCumPGuess += $CurrentValue; }
				if ($CurrentValue <= $EssentiallyZero) { $Done = True; }
				$PreviousValue = $CurrentValue;
				--$k;
			}

			$PGuess = $UnscaledPGuess / $TotalUnscaledProbability;
			$CumPGuess = $UnscaledCumPGuess / $TotalUnscaledProbability;

//			$CumPGuessMinus1 = $CumPGuess - $PGuess;
			$CumPGuessMinus1 = $CumPGuess - 1;

			while (True) {
				if (($CumPGuessMinus1 < $alpha) && ($CumPGuess >= $alpha)) {
					return $Guess;
				} elseif (($CumPGuessMinus1 < $alpha) && ($CumPGuess < $alpha)) {
					$PGuessPlus1 = $PGuess * ($trials - $Guess) * $probability / $Guess / (1 - $probability);
					$CumPGuessMinus1 = $CumPGuess;
					$CumPGuess = $CumPGuess + $PGuessPlus1;
					$PGuess = $PGuessPlus1;
					++$Guess;
				} elseif (($CumPGuessMinus1 >= $alpha) && ($CumPGuess >= $alpha)) {
					$PGuessMinus1 = $PGuess * $Guess * (1 - $probability) / ($trials - $Guess + 1) / $probability;
					$CumPGuess = $CumPGuessMinus1;
					$CumPGuessMinus1 = $CumPGuessMinus1 - $PGuess;
					$PGuess = $PGuessMinus1;
					--$Guess;
				}
			}
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function CRITBINOM()


	/**
	 * DEVSQ
	 *
	 * Returns the sum of squares of deviations of data points from their sample mean.
	 *
	 * Excel Function:
	 *		DEVSQ(value1[,value2[, ...]])
	 *
	 * @access	public
	 * @category Statistical Functions
	 * @param	mixed		$arg,...		Data values
	 * @return	float
	 */
	public static function DEVSQ() {
		$aArgs = PHPExcel_Calculation_Functions::flattenArrayIndexed(func_get_args());

		// Return value
		$returnValue = null;

		$aMean = self::AVERAGE($aArgs);
		if ($aMean != PHPExcel_Calculation_Functions::DIV0()) {
			$aCount = -1;
			foreach ($aArgs as $k => $arg) {
				// Is it a numeric value?
				if ((is_bool($arg)) &&
					((!PHPExcel_Calculation_Functions::isCellValue($k)) || (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE))) {
					$arg = (integer) $arg;
				}
				if ((is_numeric($arg)) && (!is_string($arg))) {
					if (is_null($returnValue)) {
						$returnValue = pow(($arg - $aMean),2);
					} else {
						$returnValue += pow(($arg - $aMean),2);
					}
					++$aCount;
				}
			}

			// Return
			if (is_null($returnValue)) {
				return PHPExcel_Calculation_Functions::NaN();
			} else {
				return $returnValue;
			}
		}
		return self::NA();
	}	//	function DEVSQ()


	/**
	 * EXPONDIST
	 *
	 *	Returns the exponential distribution. Use EXPONDIST to model the time between events,
	 *		such as how long an automated bank teller takes to deliver cash. For example, you can
	 *		use EXPONDIST to determine the probability that the process takes at most 1 minute.
	 *
	 * @param	float		$value			Value of the function
	 * @param	float		$lambda			The parameter value
	 * @param	boolean		$cumulative
	 * @return	float
	 */
	public static function EXPONDIST($value, $lambda, $cumulative) {
		$value	= PHPExcel_Calculation_Functions::flattenSingleValue($value);
		$lambda	= PHPExcel_Calculation_Functions::flattenSingleValue($lambda);
		$cumulative	= PHPExcel_Calculation_Functions::flattenSingleValue($cumulative);

		if ((is_numeric($value)) && (is_numeric($lambda))) {
			if (($value < 0) || ($lambda < 0)) {
				return PHPExcel_Calculation_Functions::NaN();
			}
			if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
				if ($cumulative) {
					return 1 - exp(0-$value*$lambda);
				} else {
					return $lambda * exp(0-$value*$lambda);
				}
			}
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function EXPONDIST()


	/**
	 * FISHER
	 *
	 * Returns the Fisher transformation at x. This transformation produces a function that
	 *		is normally distributed rather than skewed. Use this function to perform hypothesis
	 *		testing on the correlation coefficient.
	 *
	 * @param	float		$value
	 * @return	float
	 */
	public static function FISHER($value) {
		$value	= PHPExcel_Calculation_Functions::flattenSingleValue($value);

		if (is_numeric($value)) {
			if (($value <= -1) || ($value >= 1)) {
				return PHPExcel_Calculation_Functions::NaN();
			}
			return 0.5 * log((1+$value)/(1-$value));
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function FISHER()


	/**
	 * FISHERINV
	 *
	 * Returns the inverse of the Fisher transformation. Use this transformation when
	 *		analyzing correlations between ranges or arrays of data. If y = FISHER(x), then
	 *		FISHERINV(y) = x.
	 *
	 * @param	float		$value
	 * @return	float
	 */
	public static function FISHERINV($value) {
		$value	= PHPExcel_Calculation_Functions::flattenSingleValue($value);

		if (is_numeric($value)) {
			return (exp(2 * $value) - 1) / (exp(2 * $value) + 1);
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function FISHERINV()


	/**
	 * FORECAST
	 *
	 * Calculates, or predicts, a future value by using existing values. The predicted value is a y-value for a given x-value.
	 *
	 * @param	float				Value of X for which we want to find Y
	 * @param	array of mixed		Data Series Y
	 * @param	array of mixed		Data Series X
	 * @return	float
	 */
	public static function FORECAST($xValue,$yValues,$xValues) {
		$xValue	= PHPExcel_Calculation_Functions::flattenSingleValue($xValue);
		if (!is_numeric($xValue)) {
			return PHPExcel_Calculation_Functions::VALUE();
		}

		if (!self::_checkTrendArrays($yValues,$xValues)) {
			return PHPExcel_Calculation_Functions::VALUE();
		}
		$yValueCount = count($yValues);
		$xValueCount = count($xValues);

		if (($yValueCount == 0) || ($yValueCount != $xValueCount)) {
			return PHPExcel_Calculation_Functions::NA();
		} elseif ($yValueCount == 1) {
			return PHPExcel_Calculation_Functions::DIV0();
		}

		$bestFitLinear = trendClass::calculate(trendClass::TREND_LINEAR,$yValues,$xValues);
		return $bestFitLinear->getValueOfYForX($xValue);
	}	//	function FORECAST()


	/**
	 * GAMMADIST
	 *
	 * Returns the gamma distribution.
	 *
	 * @param	float		$value			Value at which you want to evaluate the distribution
	 * @param	float		$a				Parameter to the distribution
	 * @param	float		$b				Parameter to the distribution
	 * @param	boolean		$cumulative
	 * @return	float
	 *
	 */
	public static function GAMMADIST($value,$a,$b,$cumulative) {
		$value	= PHPExcel_Calculation_Functions::flattenSingleValue($value);
		$a		= PHPExcel_Calculation_Functions::flattenSingleValue($a);
		$b		= PHPExcel_Calculation_Functions::flattenSingleValue($b);

		if ((is_numeric($value)) && (is_numeric($a)) && (is_numeric($b))) {
			if (($value < 0) || ($a <= 0) || ($b <= 0)) {
				return PHPExcel_Calculation_Functions::NaN();
			}
			if ((is_numeric($cumulative)) || (is_bool($cumulative))) {
				if ($cumulative) {
					return self::_incompleteGamma($a,$value / $b) / self::_gamma($a);
				} else {
					return (1 / (pow($b,$a) * self::_gamma($a))) * pow($value,$a-1) * exp(0-($value / $b));
				}
			}
		}
		return PHPExcel_Calculation_Functions::VALUE();
	}	//	function GAMMADIST()


	/**
	 * GAMMAINV
	 *
	 * Returns the inverse of the beta distribution.
	 *
	 * @param	float		$probability	Probability at which you want to evaluate the distribution
	 * @param	float		$alpha			Parameter to the distribution
	 * @param	float		$beta			Parameter to the distribution
	 * @return	float
	 *
	 */
	public static function GAMMAINV($probability,$alpha,$beta) {
		$probability	= PHPExcel_Calculation_Functions::flattenSingleValue($probability);
		$alpha			= PHPExcel_Calculation_Functions::flattenSingleValue($alpha);
		$beta			= PHPExcel_Calculation_Functions::flattenSingleValue($beta);

		if ((is_numeric($probability)) && (is_numeric($alpha)) && (is_numeric($beta))) {
			if (($alpha <= 0) || ($beta <= 0) || ($probability < 0) || ($probability > 1)) {
				return PHPExcel_Calculation_Functions::NaN();
			}

			$xLo = 0;
	…