<?php

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

/**
 * FINANCIAL_MAX_ITERATIONS
 */
define ( 'FINANCIAL_MAX_ITERATIONS', 128 );

/**
 * FINANCIAL_PRECISION
 */
define ( 'FINANCIAL_PRECISION', 1.0e-08 );

/**
 * PHPExcel_Calculation_Financial
 *
 * Copyright (c) 2006 - 2015 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 - 2015 PHPExcel (http://www.codeplex.com/PHPExcel)
 * @license http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt LGPL
 * @version ##VERSION##, ##DATE##
 */
class PHPExcel_Calculation_Financial
{
  /**
   * isLastDayOfMonth
   *
   * Returns a boolean TRUE/FALSE indicating if this date is the last date of the month
   *
   * @param DateTime $testDate
   *          The date for testing
   * @return boolean
   */
  private static function isLastDayOfMonth($testDate)
  {
    return ($testDate->format ( 'd' ) == $testDate->format ( 't' ));
  }
  
  /**
   * isFirstDayOfMonth
   *
   * Returns a boolean TRUE/FALSE indicating if this date is the first date of the month
   *
   * @param DateTime $testDate
   *          The date for testing
   * @return boolean
   */
  private static function isFirstDayOfMonth($testDate)
  {
    return ($testDate->format ( 'd' ) == 1);
  }
  private static function couponFirstPeriodDate($settlement, $maturity, $frequency, $next)
  {
    $months = 12 / $frequency;
    
    $result = PHPExcel_Shared_Date::ExcelToPHPObject ( $maturity );
    $eom = self::isLastDayOfMonth ( $result );
    
    while ( $settlement < PHPExcel_Shared_Date::PHPToExcel ( $result ) )
    {
      $result->modify ( '-' . $months . ' months' );
    }
    if ($next)
    {
      $result->modify ( '+' . $months . ' months' );
    }
    
    if ($eom)
    {
      $result->modify ( '-1 day' );
    }
    
    return PHPExcel_Shared_Date::PHPToExcel ( $result );
  }
  private static function isValidFrequency($frequency)
  {
    if (($frequency == 1) || ($frequency == 2) || ($frequency == 4))
    {
      return true;
    }
    if ((PHPExcel_Calculation_Functions::getCompatibilityMode () == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) && (($frequency == 6) || ($frequency == 12)))
    {
      return true;
    }
    return false;
  }
  
  /**
   * daysPerYear
   *
   * Returns the number of days in a specified year, as defined by the "basis" value
   *
   * @param integer $year
   *          The year against which we're testing
   * @param integer $basis
   *          The type of day count:
   *          0 or omitted US (NASD) 360
   *          1 Actual (365 or 366 in a leap year)
   *          2 360
   *          3 365
   *          4 European 360
   * @return integer
   */
  private static function daysPerYear($year, $basis = 0)
  {
    switch ($basis)
    {
      case 0 :
      case 2 :
      case 4 :
        $daysPerYear = 360;
        break;
      case 3 :
        $daysPerYear = 365;
        break;
      case 1 :
        $daysPerYear = (PHPExcel_Calculation_DateTime::isLeapYear ( $year )) ? 366 : 365;
        break;
      default :
        return PHPExcel_Calculation_Functions::NaN ();
    }
    return $daysPerYear;
  }
  private static function interestAndPrincipal($rate = 0, $per = 0, $nper = 0, $pv = 0, $fv = 0, $type = 0)
  {
    $pmt = self::PMT ( $rate, $nper, $pv, $fv, $type );
    $capital = $pv;
    for($i = 1; $i <= $per; ++ $i)
    {
      $interest = ($type && $i == 1) ? 0 : - $capital * $rate;
      $principal = $pmt - $interest;
      $capital += $principal;
    }
    return array (
        $interest,
        $principal 
    );
  }
  
  /**
   * ACCRINT
   *
   * Returns the accrued interest for a security that pays periodic interest.
   *
   * Excel Function:
   * ACCRINT(issue,firstinterest,settlement,rate,par,frequency[,basis])
   *
   * @access public
   * @category Financial Functions
   * @param mixed $issue
   *          The security's issue date.
   * @param mixed $firstinterest
   *          The security's first interest date.
   * @param mixed $settlement
   *          The security's settlement date.
   *          The security settlement date is the date after the issue date
   *          when the security is traded to the buyer.
   * @param float $rate
   *          The security's annual coupon rate.
   * @param float $par
   *          The security's par value.
   *          If you omit par, ACCRINT uses $1,000.
   * @param integer $frequency
   *          the number of coupon payments per year.
   *          Valid frequency values are:
   *          1 Annual
   *          2 Semi-Annual
   *          4 Quarterly
   *          If working in Gnumeric Mode, the following frequency options are
   *          also available
   *          6 Bimonthly
   *          12 Monthly
   * @param integer $basis
   *          The type of day count to use.
   *          0 or omitted US (NASD) 30/360
   *          1 Actual/actual
   *          2 Actual/360
   *          3 Actual/365
   *          4 European 30/360
   * @return float
   */
  public static function ACCRINT($issue, $firstinterest, $settlement, $rate, $par = 1000, $frequency = 1, $basis = 0)
  {
    $issue = PHPExcel_Calculation_Functions::flattenSingleValue ( $issue );
    $firstinterest = PHPExcel_Calculation_Functions::flattenSingleValue ( $firstinterest );
    $settlement = PHPExcel_Calculation_Functions::flattenSingleValue ( $settlement );
    $rate = PHPExcel_Calculation_Functions::flattenSingleValue ( $rate );
    $par = (is_null ( $par )) ? 1000 : PHPExcel_Calculation_Functions::flattenSingleValue ( $par );
    $frequency = (is_null ( $frequency )) ? 1 : PHPExcel_Calculation_Functions::flattenSingleValue ( $frequency );
    $basis = (is_null ( $basis )) ? 0 : PHPExcel_Calculation_Functions::flattenSingleValue ( $basis );
    
    // Validate
    if ((is_numeric ( $rate )) && (is_numeric ( $par )))
    {
      $rate = ( float ) $rate;
      $par = ( float ) $par;
      if (($rate <= 0) || ($par <= 0))
      {
        return PHPExcel_Calculation_Functions::NaN ();
      }
      $daysBetweenIssueAndSettlement = PHPExcel_Calculation_DateTime::YEARFRAC ( $issue, $settlement, $basis );
      if (! is_numeric ( $daysBetweenIssueAndSettlement ))
      {
        // return date error
        return $daysBetweenIssueAndSettlement;
      }
      
      return $par * $rate * $daysBetweenIssueAndSettlement;
    }
    return PHPExcel_Calculation_Functions::VALUE ();
  }
  
  /**
   * ACCRINTM
   *
   * Returns the accrued interest for a security that pays interest at maturity.
   *
   * Excel Function:
   * ACCRINTM(issue,settlement,rate[,par[,basis]])
   *
   * @access public
   * @category Financial Functions
   * @param
   *          mixed issue The security's issue date.
   * @param
   *          mixed settlement The security's settlement (or maturity) date.
   * @param
   *          float rate The security's annual coupon rate.
   * @param
   *          float par The security's par value.
   *          If you omit par, ACCRINT uses $1,000.
   * @param
   *          integer basis The type of day count to use.
   *          0 or omitted US (NASD) 30/360
   *          1 Actual/actual
   *          2 Actual/360
   *          3 Actual/365
   *          4 European 30/360
   * @return float
   */
  public static function ACCRINTM($issue, $settlement, $rate, $par = 1000, $basis = 0)
  {
    $issue = PHPExcel_Calculation_Functions::flattenSingleValue ( $issue );
    $settlement = PHPExcel_Calculation_Functions::flattenSingleValue ( $settlement );
    $rate = PHPExcel_Calculation_Functions::flattenSingleValue ( $rate );
    $par = (is_null ( $par )) ? 1000 : PHPExcel_Calculation_Functions::flattenSingleValue ( $par );
    $basis = (is_null ( $basis )) ? 0 : PHPExcel_Calculation_Functions::flattenSingleValue ( $basis );
    
    // Validate
    if ((is_numeric ( $rate )) && (is_numeric ( $par )))
    {
      $rate = ( float ) $rate;
      $par = ( float ) $par;
      if (($rate <= 0) || ($par <= 0))
      {
        return PHPExcel_Calculation_Functions::NaN ();
      }
      $daysBetweenIssueAndSettlement = PHPExcel_Calculation_DateTime::YEARFRAC ( $issue, $settlement, $basis );
      if (! is_numeric ( $daysBetweenIssueAndSettlement ))
      {
        // return date error
        return $daysBetweenIssueAndSettlement;
      }
      return $par * $rate * $daysBetweenIssueAndSettlement;
    }
    return PHPExcel_Calculation_Functions::VALUE ();
  }
  
  /**
   * AMORDEGRC
   *
   * Returns the depreciation for each accounting period.
   * This function is provided for the French accounting system. If an asset is purchased in
   * the middle of the accounting period, the prorated depreciation is taken into account.
   * The function is similar to AMORLINC, except that a depreciation coefficient is applied in
   * the calculation depending on the life of the assets.
   * This function will return the depreciation until the last period of the life of the assets
   * or until the cumulated value of depreciation is greater than the cost of the assets minus
   * the salvage value.
   *
   * Excel Function:
   * AMORDEGRC(cost,purchased,firstPeriod,salvage,period,rate[,basis])
   *
   * @access public
   * @category Financial Functions
   * @param
   *          float cost The cost of the asset.
   * @param
   *          mixed purchased Date of the purchase of the asset.
   * @param
   *          mixed firstPeriod Date of the end of the first period.
   * @param
   *          mixed salvage The salvage value at the end of the life of the asset.
   * @param
   *          float period The period.
   * @param
   *          float rate Rate of depreciation.
   * @param
   *          integer basis The type of day count to use.
   *          0 or omitted US (NASD) 30/360
   *          1 Actual/actual
   *          2 Actual/360
   *          3 Actual/365
   *          4 European 30/360
   * @return float
   */
  public static function AMORDEGRC($cost, $purchased, $firstPeriod, $salvage, $period, $rate, $basis = 0)
  {
    $cost = PHPExcel_Calculation_Functions::flattenSingleValue ( $cost );
    $purchased = PHPExcel_Calculation_Functions::flattenSingleValue ( $purchased );
    $firstPeriod = PHPExcel_Calculation_Functions::flattenSingleValue ( $firstPeriod );
    $salvage = PHPExcel_Calculation_Functions::flattenSingleValue ( $salvage );
    $period = floor ( PHPExcel_Calculation_Functions::flattenSingleValue ( $period ) );
    $rate = PHPExcel_Calculation_Functions::flattenSingleValue ( $rate );
    $basis = (is_null ( $basis )) ? 0 : ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $basis );
    
    // The depreciation coefficients are:
    // Life of assets (1/rate) Depreciation coefficient
    // Less than 3 years 1
    // Between 3 and 4 years 1.5
    // Between 5 and 6 years 2
    // More than 6 years 2.5
    $fUsePer = 1.0 / $rate;
    if ($fUsePer < 3.0)
    {
      $amortiseCoeff = 1.0;
    }
    elseif ($fUsePer < 5.0)
    {
      $amortiseCoeff = 1.5;
    }
    elseif ($fUsePer <= 6.0)
    {
      $amortiseCoeff = 2.0;
    }
    else
    {
      $amortiseCoeff = 2.5;
    }
    
    $rate *= $amortiseCoeff;
    $fNRate = round ( PHPExcel_Calculation_DateTime::YEARFRAC ( $purchased, $firstPeriod, $basis ) * $rate * $cost, 0 );
    $cost -= $fNRate;
    $fRest = $cost - $salvage;
    
    for($n = 0; $n < $period; ++ $n)
    {
      $fNRate = round ( $rate * $cost, 0 );
      $fRest -= $fNRate;
      
      if ($fRest < 0.0)
      {
        switch ($period - $n)
        {
          case 0 :
          case 1 :
            return round ( $cost * 0.5, 0 );
          default :
            return 0.0;
        }
      }
      $cost -= $fNRate;
    }
    return $fNRate;
  }
  
  /**
   * AMORLINC
   *
   * Returns the depreciation for each accounting period.
   * This function is provided for the French accounting system. If an asset is purchased in
   * the middle of the accounting period, the prorated depreciation is taken into account.
   *
   * Excel Function:
   * AMORLINC(cost,purchased,firstPeriod,salvage,period,rate[,basis])
   *
   * @access public
   * @category Financial Functions
   * @param
   *          float cost The cost of the asset.
   * @param
   *          mixed purchased Date of the purchase of the asset.
   * @param
   *          mixed firstPeriod Date of the end of the first period.
   * @param
   *          mixed salvage The salvage value at the end of the life of the asset.
   * @param
   *          float period The period.
   * @param
   *          float rate Rate of depreciation.
   * @param
   *          integer basis The type of day count to use.
   *          0 or omitted US (NASD) 30/360
   *          1 Actual/actual
   *          2 Actual/360
   *          3 Actual/365
   *          4 European 30/360
   * @return float
   */
  public static function AMORLINC($cost, $purchased, $firstPeriod, $salvage, $period, $rate, $basis = 0)
  {
    $cost = PHPExcel_Calculation_Functions::flattenSingleValue ( $cost );
    $purchased = PHPExcel_Calculation_Functions::flattenSingleValue ( $purchased );
    $firstPeriod = PHPExcel_Calculation_Functions::flattenSingleValue ( $firstPeriod );
    $salvage = PHPExcel_Calculation_Functions::flattenSingleValue ( $salvage );
    $period = PHPExcel_Calculation_Functions::flattenSingleValue ( $period );
    $rate = PHPExcel_Calculation_Functions::flattenSingleValue ( $rate );
    $basis = (is_null ( $basis )) ? 0 : ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $basis );
    
    $fOneRate = $cost * $rate;
    $fCostDelta = $cost - $salvage;
    // Note, quirky variation for leap years on the YEARFRAC for this function
    $purchasedYear = PHPExcel_Calculation_DateTime::YEAR ( $purchased );
    $yearFrac = PHPExcel_Calculation_DateTime::YEARFRAC ( $purchased, $firstPeriod, $basis );
    
    if (($basis == 1) && ($yearFrac < 1) && (PHPExcel_Calculation_DateTime::isLeapYear ( $purchasedYear )))
    {
      $yearFrac *= 365 / 366;
    }
    
    $f0Rate = $yearFrac * $rate * $cost;
    $nNumOfFullPeriods = intval ( ($cost - $salvage - $f0Rate) / $fOneRate );
    
    if ($period == 0)
    {
      return $f0Rate;
    }
    elseif ($period <= $nNumOfFullPeriods)
    {
      return $fOneRate;
    }
    elseif ($period == ($nNumOfFullPeriods + 1))
    {
      return ($fCostDelta - $fOneRate * $nNumOfFullPeriods - $f0Rate);
    }
    else
    {
      return 0.0;
    }
  }
  
  /**
   * COUPDAYBS
   *
   * Returns the number of days from the beginning of the coupon period to the settlement date.
   *
   * Excel Function:
   * COUPDAYBS(settlement,maturity,frequency[,basis])
   *
   * @access public
   * @category Financial Functions
   * @param
   *          mixed settlement The security's settlement date.
   *          The security settlement date is the date after the issue
   *          date when the security is traded to the buyer.
   * @param
   *          mixed maturity The security's maturity date.
   *          The maturity date is the date when the security expires.
   * @param
   *          mixed frequency the number of coupon payments per year.
   *          Valid frequency values are:
   *          1 Annual
   *          2 Semi-Annual
   *          4 Quarterly
   *          If working in Gnumeric Mode, the following frequency options are
   *          also available
   *          6 Bimonthly
   *          12 Monthly
   * @param
   *          integer basis The type of day count to use.
   *          0 or omitted US (NASD) 30/360
   *          1 Actual/actual
   *          2 Actual/360
   *          3 Actual/365
   *          4 European 30/360
   * @return float
   */
  public static function COUPDAYBS($settlement, $maturity, $frequency, $basis = 0)
  {
    $settlement = PHPExcel_Calculation_Functions::flattenSingleValue ( $settlement );
    $maturity = PHPExcel_Calculation_Functions::flattenSingleValue ( $maturity );
    $frequency = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $frequency );
    $basis = (is_null ( $basis )) ? 0 : ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $basis );
    
    if (is_string ( $settlement = PHPExcel_Calculation_DateTime::getDateValue ( $settlement ) ))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    if (is_string ( $maturity = PHPExcel_Calculation_DateTime::getDateValue ( $maturity ) ))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    
    if (($settlement > $maturity) || (! self::isValidFrequency ( $frequency )) || (($basis < 0) || ($basis > 4)))
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    
    $daysPerYear = self::daysPerYear ( PHPExcel_Calculation_DateTime::YEAR ( $settlement ), $basis );
    $prev = self::couponFirstPeriodDate ( $settlement, $maturity, $frequency, false );
    
    return PHPExcel_Calculation_DateTime::YEARFRAC ( $prev, $settlement, $basis ) * $daysPerYear;
  }
  
  /**
   * COUPDAYS
   *
   * Returns the number of days in the coupon period that contains the settlement date.
   *
   * Excel Function:
   * COUPDAYS(settlement,maturity,frequency[,basis])
   *
   * @access public
   * @category Financial Functions
   * @param
   *          mixed settlement The security's settlement date.
   *          The security settlement date is the date after the issue
   *          date when the security is traded to the buyer.
   * @param
   *          mixed maturity The security's maturity date.
   *          The maturity date is the date when the security expires.
   * @param
   *          mixed frequency the number of coupon payments per year.
   *          Valid frequency values are:
   *          1 Annual
   *          2 Semi-Annual
   *          4 Quarterly
   *          If working in Gnumeric Mode, the following frequency options are
   *          also available
   *          6 Bimonthly
   *          12 Monthly
   * @param
   *          integer basis The type of day count to use.
   *          0 or omitted US (NASD) 30/360
   *          1 Actual/actual
   *          2 Actual/360
   *          3 Actual/365
   *          4 European 30/360
   * @return float
   */
  public static function COUPDAYS($settlement, $maturity, $frequency, $basis = 0)
  {
    $settlement = PHPExcel_Calculation_Functions::flattenSingleValue ( $settlement );
    $maturity = PHPExcel_Calculation_Functions::flattenSingleValue ( $maturity );
    $frequency = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $frequency );
    $basis = (is_null ( $basis )) ? 0 : ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $basis );
    
    if (is_string ( $settlement = PHPExcel_Calculation_DateTime::getDateValue ( $settlement ) ))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    if (is_string ( $maturity = PHPExcel_Calculation_DateTime::getDateValue ( $maturity ) ))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    
    if (($settlement > $maturity) || (! self::isValidFrequency ( $frequency )) || (($basis < 0) || ($basis > 4)))
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    
    switch ($basis)
    {
      case 3 :
        // Actual/365
        return 365 / $frequency;
      case 1 :
        // Actual/actual
        if ($frequency == 1)
        {
          $daysPerYear = self::daysPerYear ( PHPExcel_Calculation_DateTime::YEAR ( $maturity ), $basis );
          return ($daysPerYear / $frequency);
        }
        $prev = self::couponFirstPeriodDate ( $settlement, $maturity, $frequency, false );
        $next = self::couponFirstPeriodDate ( $settlement, $maturity, $frequency, true );
        return ($next - $prev);
      default :
        // US (NASD) 30/360, Actual/360 or European 30/360
        return 360 / $frequency;
    }
    return PHPExcel_Calculation_Functions::VALUE ();
  }
  
  /**
   * COUPDAYSNC
   *
   * Returns the number of days from the settlement date to the next coupon date.
   *
   * Excel Function:
   * COUPDAYSNC(settlement,maturity,frequency[,basis])
   *
   * @access public
   * @category Financial Functions
   * @param
   *          mixed settlement The security's settlement date.
   *          The security settlement date is the date after the issue
   *          date when the security is traded to the buyer.
   * @param
   *          mixed maturity The security's maturity date.
   *          The maturity date is the date when the security expires.
   * @param
   *          mixed frequency the number of coupon payments per year.
   *          Valid frequency values are:
   *          1 Annual
   *          2 Semi-Annual
   *          4 Quarterly
   *          If working in Gnumeric Mode, the following frequency options are
   *          also available
   *          6 Bimonthly
   *          12 Monthly
   * @param
   *          integer basis The type of day count to use.
   *          0 or omitted US (NASD) 30/360
   *          1 Actual/actual
   *          2 Actual/360
   *          3 Actual/365
   *          4 European 30/360
   * @return float
   */
  public static function COUPDAYSNC($settlement, $maturity, $frequency, $basis = 0)
  {
    $settlement = PHPExcel_Calculation_Functions::flattenSingleValue ( $settlement );
    $maturity = PHPExcel_Calculation_Functions::flattenSingleValue ( $maturity );
    $frequency = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $frequency );
    $basis = (is_null ( $basis )) ? 0 : ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $basis );
    
    if (is_string ( $settlement = PHPExcel_Calculation_DateTime::getDateValue ( $settlement ) ))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    if (is_string ( $maturity = PHPExcel_Calculation_DateTime::getDateValue ( $maturity ) ))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    
    if (($settlement > $maturity) || (! self::isValidFrequency ( $frequency )) || (($basis < 0) || ($basis > 4)))
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    
    $daysPerYear = self::daysPerYear ( PHPExcel_Calculation_DateTime::YEAR ( $settlement ), $basis );
    $next = self::couponFirstPeriodDate ( $settlement, $maturity, $frequency, true );
    
    return PHPExcel_Calculation_DateTime::YEARFRAC ( $settlement, $next, $basis ) * $daysPerYear;
  }
  
  /**
   * COUPNCD
   *
   * Returns the next coupon date after the settlement date.
   *
   * Excel Function:
   * COUPNCD(settlement,maturity,frequency[,basis])
   *
   * @access public
   * @category Financial Functions
   * @param
   *          mixed settlement The security's settlement date.
   *          The security settlement date is the date after the issue
   *          date when the security is traded to the buyer.
   * @param
   *          mixed maturity The security's maturity date.
   *          The maturity date is the date when the security expires.
   * @param
   *          mixed frequency the number of coupon payments per year.
   *          Valid frequency values are:
   *          1 Annual
   *          2 Semi-Annual
   *          4 Quarterly
   *          If working in Gnumeric Mode, the following frequency options are
   *          also available
   *          6 Bimonthly
   *          12 Monthly
   * @param
   *          integer basis The type of day count to use.
   *          0 or omitted US (NASD) 30/360
   *          1 Actual/actual
   *          2 Actual/360
   *          3 Actual/365
   *          4 European 30/360
   * @return mixed Excel date/time serial value, PHP date/time serial value or PHP date/time object,
   *         depending on the value of the ReturnDateType flag
   */
  public static function COUPNCD($settlement, $maturity, $frequency, $basis = 0)
  {
    $settlement = PHPExcel_Calculation_Functions::flattenSingleValue ( $settlement );
    $maturity = PHPExcel_Calculation_Functions::flattenSingleValue ( $maturity );
    $frequency = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $frequency );
    $basis = (is_null ( $basis )) ? 0 : ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $basis );
    
    if (is_string ( $settlement = PHPExcel_Calculation_DateTime::getDateValue ( $settlement ) ))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    if (is_string ( $maturity = PHPExcel_Calculation_DateTime::getDateValue ( $maturity ) ))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    
    if (($settlement > $maturity) || (! self::isValidFrequency ( $frequency )) || (($basis < 0) || ($basis > 4)))
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    
    return self::couponFirstPeriodDate ( $settlement, $maturity, $frequency, true );
  }
  
  /**
   * COUPNUM
   *
   * Returns the number of coupons payable between the settlement date and maturity date,
   * rounded up to the nearest whole coupon.
   *
   * Excel Function:
   * COUPNUM(settlement,maturity,frequency[,basis])
   *
   * @access public
   * @category Financial Functions
   * @param
   *          mixed settlement The security's settlement date.
   *          The security settlement date is the date after the issue
   *          date when the security is traded to the buyer.
   * @param
   *          mixed maturity The security's maturity date.
   *          The maturity date is the date when the security expires.
   * @param
   *          mixed frequency the number of coupon payments per year.
   *          Valid frequency values are:
   *          1 Annual
   *          2 Semi-Annual
   *          4 Quarterly
   *          If working in Gnumeric Mode, the following frequency options are
   *          also available
   *          6 Bimonthly
   *          12 Monthly
   * @param
   *          integer basis The type of day count to use.
   *          0 or omitted US (NASD) 30/360
   *          1 Actual/actual
   *          2 Actual/360
   *          3 Actual/365
   *          4 European 30/360
   * @return integer
   */
  public static function COUPNUM($settlement, $maturity, $frequency, $basis = 0)
  {
    $settlement = PHPExcel_Calculation_Functions::flattenSingleValue ( $settlement );
    $maturity = PHPExcel_Calculation_Functions::flattenSingleValue ( $maturity );
    $frequency = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $frequency );
    $basis = (is_null ( $basis )) ? 0 : ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $basis );
    
    if (is_string ( $settlement = PHPExcel_Calculation_DateTime::getDateValue ( $settlement ) ))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    if (is_string ( $maturity = PHPExcel_Calculation_DateTime::getDateValue ( $maturity ) ))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    
    if (($settlement > $maturity) || (! self::isValidFrequency ( $frequency )) || (($basis < 0) || ($basis > 4)))
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    
    $settlement = self::couponFirstPeriodDate ( $settlement, $maturity, $frequency, true );
    $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC ( $settlement, $maturity, $basis ) * 365;
    
    switch ($frequency)
    {
      case 1 : // annual payments
        return ceil ( $daysBetweenSettlementAndMaturity / 360 );
      case 2 : // half-yearly
        return ceil ( $daysBetweenSettlementAndMaturity / 180 );
      case 4 : // quarterly
        return ceil ( $daysBetweenSettlementAndMaturity / 90 );
      case 6 : // bimonthly
        return ceil ( $daysBetweenSettlementAndMaturity / 60 );
      case 12 : // monthly
        return ceil ( $daysBetweenSettlementAndMaturity / 30 );
    }
    return PHPExcel_Calculation_Functions::VALUE ();
  }
  
  /**
   * COUPPCD
   *
   * Returns the previous coupon date before the settlement date.
   *
   * Excel Function:
   * COUPPCD(settlement,maturity,frequency[,basis])
   *
   * @access public
   * @category Financial Functions
   * @param
   *          mixed settlement The security's settlement date.
   *          The security settlement date is the date after the issue
   *          date when the security is traded to the buyer.
   * @param
   *          mixed maturity The security's maturity date.
   *          The maturity date is the date when the security expires.
   * @param
   *          mixed frequency the number of coupon payments per year.
   *          Valid frequency values are:
   *          1 Annual
   *          2 Semi-Annual
   *          4 Quarterly
   *          If working in Gnumeric Mode, the following frequency options are
   *          also available
   *          6 Bimonthly
   *          12 Monthly
   * @param
   *          integer basis The type of day count to use.
   *          0 or omitted US (NASD) 30/360
   *          1 Actual/actual
   *          2 Actual/360
   *          3 Actual/365
   *          4 European 30/360
   * @return mixed Excel date/time serial value, PHP date/time serial value or PHP date/time object,
   *         depending on the value of the ReturnDateType flag
   */
  public static function COUPPCD($settlement, $maturity, $frequency, $basis = 0)
  {
    $settlement = PHPExcel_Calculation_Functions::flattenSingleValue ( $settlement );
    $maturity = PHPExcel_Calculation_Functions::flattenSingleValue ( $maturity );
    $frequency = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $frequency );
    $basis = (is_null ( $basis )) ? 0 : ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $basis );
    
    if (is_string ( $settlement = PHPExcel_Calculation_DateTime::getDateValue ( $settlement ) ))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    if (is_string ( $maturity = PHPExcel_Calculation_DateTime::getDateValue ( $maturity ) ))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    
    if (($settlement > $maturity) || (! self::isValidFrequency ( $frequency )) || (($basis < 0) || ($basis > 4)))
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    
    return self::couponFirstPeriodDate ( $settlement, $maturity, $frequency, false );
  }
  
  /**
   * CUMIPMT
   *
   * Returns the cumulative interest paid on a loan between the start and end periods.
   *
   * Excel Function:
   * CUMIPMT(rate,nper,pv,start,end[,type])
   *
   * @access public
   * @category Financial Functions
   * @param float $rate
   *          The Interest rate
   * @param integer $nper
   *          The total number of payment periods
   * @param float $pv
   *          Present Value
   * @param integer $start
   *          The first period in the calculation.
   *          Payment periods are numbered beginning with 1.
   * @param integer $end
   *          The last period in the calculation.
   * @param integer $type
   *          A number 0 or 1 and indicates when payments are due:
   *          0 or omitted At the end of the period.
   *          1 At the beginning of the period.
   * @return float
   */
  public static function CUMIPMT($rate, $nper, $pv, $start, $end, $type = 0)
  {
    $rate = PHPExcel_Calculation_Functions::flattenSingleValue ( $rate );
    $nper = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $nper );
    $pv = PHPExcel_Calculation_Functions::flattenSingleValue ( $pv );
    $start = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $start );
    $end = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $end );
    $type = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $type );
    
    // Validate parameters
    if ($type != 0 && $type != 1)
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    if ($start < 1 || $start > $end)
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    
    // Calculate
    $interest = 0;
    for($per = $start; $per <= $end; ++ $per)
    {
      $interest += self::IPMT ( $rate, $per, $nper, $pv, 0, $type );
    }
    
    return $interest;
  }
  
  /**
   * CUMPRINC
   *
   * Returns the cumulative principal paid on a loan between the start and end periods.
   *
   * Excel Function:
   * CUMPRINC(rate,nper,pv,start,end[,type])
   *
   * @access public
   * @category Financial Functions
   * @param float $rate
   *          The Interest rate
   * @param integer $nper
   *          The total number of payment periods
   * @param float $pv
   *          Present Value
   * @param integer $start
   *          The first period in the calculation.
   *          Payment periods are numbered beginning with 1.
   * @param integer $end
   *          The last period in the calculation.
   * @param integer $type
   *          A number 0 or 1 and indicates when payments are due:
   *          0 or omitted At the end of the period.
   *          1 At the beginning of the period.
   * @return float
   */
  public static function CUMPRINC($rate, $nper, $pv, $start, $end, $type = 0)
  {
    $rate = PHPExcel_Calculation_Functions::flattenSingleValue ( $rate );
    $nper = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $nper );
    $pv = PHPExcel_Calculation_Functions::flattenSingleValue ( $pv );
    $start = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $start );
    $end = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $end );
    $type = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $type );
    
    // Validate parameters
    if ($type != 0 && $type != 1)
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    if ($start < 1 || $start > $end)
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    
    // Calculate
    $principal = 0;
    for($per = $start; $per <= $end; ++ $per)
    {
      $principal += self::PPMT ( $rate, $per, $nper, $pv, 0, $type );
    }
    
    return $principal;
  }
  
  /**
   * DB
   *
   * Returns the depreciation of an asset for a specified period using the
   * fixed-declining balance method.
   * This form of depreciation is used if you want to get a higher depreciation value
   * at the beginning of the depreciation (as opposed to linear depreciation). The
   * depreciation value is reduced with every depreciation period by the depreciation
   * already deducted from the initial cost.
   *
   * Excel Function:
   * DB(cost,salvage,life,period[,month])
   *
   * @access public
   * @category Financial Functions
   * @param
   *          float cost Initial cost of the asset.
   * @param
   *          float salvage Value at the end of the depreciation.
   *          (Sometimes called the salvage value of the asset)
   * @param
   *          integer life Number of periods over which the asset is depreciated.
   *          (Sometimes called the useful life of the asset)
   * @param
   *          integer period The period for which you want to calculate the
   *          depreciation. Period must use the same units as life.
   * @param
   *          integer month Number of months in the first year. If month is omitted,
   *          it defaults to 12.
   * @return float
   */
  public static function DB($cost, $salvage, $life, $period, $month = 12)
  {
    $cost = PHPExcel_Calculation_Functions::flattenSingleValue ( $cost );
    $salvage = PHPExcel_Calculation_Functions::flattenSingleValue ( $salvage );
    $life = PHPExcel_Calculation_Functions::flattenSingleValue ( $life );
    $period = PHPExcel_Calculation_Functions::flattenSingleValue ( $period );
    $month = PHPExcel_Calculation_Functions::flattenSingleValue ( $month );
    
    // Validate
    if ((is_numeric ( $cost )) && (is_numeric ( $salvage )) && (is_numeric ( $life )) && (is_numeric ( $period )) && (is_numeric ( $month )))
    {
      $cost = ( float ) $cost;
      $salvage = ( float ) $salvage;
      $life = ( int ) $life;
      $period = ( int ) $period;
      $month = ( int ) $month;
      if ($cost == 0)
      {
        return 0.0;
      }
      elseif (($cost < 0) || (($salvage / $cost) < 0) || ($life <= 0) || ($period < 1) || ($month < 1))
      {
        return PHPExcel_Calculation_Functions::NaN ();
      }
      // Set Fixed Depreciation Rate
      $fixedDepreciationRate = 1 - pow ( ($salvage / $cost), (1 / $life) );
      $fixedDepreciationRate = round ( $fixedDepreciationRate, 3 );
      
      // Loop through each period calculating the depreciation
      $previousDepreciation = 0;
      for($per = 1; $per <= $period; ++ $per)
      {
        if ($per == 1)
        {
          $depreciation = $cost * $fixedDepreciationRate * $month / 12;
        }
        elseif ($per == ($life + 1))
        {
          $depreciation = ($cost - $previousDepreciation) * $fixedDepreciationRate * (12 - $month) / 12;
        }
        else
        {
          $depreciation = ($cost - $previousDepreciation) * $fixedDepreciationRate;
        }
        $previousDepreciation += $depreciation;
      }
      if (PHPExcel_Calculation_Functions::getCompatibilityMode () == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC)
      {
        $depreciation = round ( $depreciation, 2 );
      }
      return $depreciation;
    }
    return PHPExcel_Calculation_Functions::VALUE ();
  }
  
  /**
   * DDB
   *
   * Returns the depreciation of an asset for a specified period using the
   * double-declining balance method or some other method you specify.
   *
   * Excel Function:
   * DDB(cost,salvage,life,period[,factor])
   *
   * @access public
   * @category Financial Functions
   * @param
   *          float cost Initial cost of the asset.
   * @param
   *          float salvage Value at the end of the depreciation.
   *          (Sometimes called the salvage value of the asset)
   * @param
   *          integer life Number of periods over which the asset is depreciated.
   *          (Sometimes called the useful life of the asset)
   * @param
   *          integer period The period for which you want to calculate the
   *          depreciation. Period must use the same units as life.
   * @param
   *          float factor The rate at which the balance declines.
   *          If factor is omitted, it is assumed to be 2 (the
   *          double-declining balance method).
   * @return float
   */
  public static function DDB($cost, $salvage, $life, $period, $factor = 2.0)
  {
    $cost = PHPExcel_Calculation_Functions::flattenSingleValue ( $cost );
    $salvage = PHPExcel_Calculation_Functions::flattenSingleValue ( $salvage );
    $life = PHPExcel_Calculation_Functions::flattenSingleValue ( $life );
    $period = PHPExcel_Calculation_Functions::flattenSingleValue ( $period );
    $factor = PHPExcel_Calculation_Functions::flattenSingleValue ( $factor );
    
    // Validate
    if ((is_numeric ( $cost )) && (is_numeric ( $salvage )) && (is_numeric ( $life )) && (is_numeric ( $period )) && (is_numeric ( $factor )))
    {
      $cost = ( float ) $cost;
      $salvage = ( float ) $salvage;
      $life = ( int ) $life;
      $period = ( int ) $period;
      $factor = ( float ) $factor;
      if (($cost <= 0) || (($salvage / $cost) < 0) || ($life <= 0) || ($period < 1) || ($factor <= 0.0) || ($period > $life))
      {
        return PHPExcel_Calculation_Functions::NaN ();
      }
      // Set Fixed Depreciation Rate
      $fixedDepreciationRate = 1 - pow ( ($salvage / $cost), (1 / $life) );
      $fixedDepreciationRate = round ( $fixedDepreciationRate, 3 );
      
      // Loop through each period calculating the depreciation
      $previousDepreciation = 0;
      for($per = 1; $per <= $period; ++ $per)
      {
        $depreciation = min ( ($cost - $previousDepreciation) * ($factor / $life), ($cost - $salvage - $previousDepreciation) );
        $previousDepreciation += $depreciation;
      }
      if (PHPExcel_Calculation_Functions::getCompatibilityMode () == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC)
      {
        $depreciation = round ( $depreciation, 2 );
      }
      return $depreciation;
    }
    return PHPExcel_Calculation_Functions::VALUE ();
  }
  
  /**
   * DISC
   *
   * Returns the discount rate for a security.
   *
   * Excel Function:
   * DISC(settlement,maturity,price,redemption[,basis])
   *
   * @access public
   * @category Financial Functions
   * @param
   *          mixed settlement The security's settlement date.
   *          The security settlement date is the date after the issue
   *          date when the security is traded to the buyer.
   * @param
   *          mixed maturity The security's maturity date.
   *          The maturity date is the date when the security expires.
   * @param
   *          integer price The security's price per $100 face value.
   * @param
   *          integer redemption The security's redemption value per $100 face value.
   * @param
   *          integer basis The type of day count to use.
   *          0 or omitted US (NASD) 30/360
   *          1 Actual/actual
   *          2 Actual/360
   *          3 Actual/365
   *          4 European 30/360
   * @return float
   */
  public static function DISC($settlement, $maturity, $price, $redemption, $basis = 0)
  {
    $settlement = PHPExcel_Calculation_Functions::flattenSingleValue ( $settlement );
    $maturity = PHPExcel_Calculation_Functions::flattenSingleValue ( $maturity );
    $price = PHPExcel_Calculation_Functions::flattenSingleValue ( $price );
    $redemption = PHPExcel_Calculation_Functions::flattenSingleValue ( $redemption );
    $basis = PHPExcel_Calculation_Functions::flattenSingleValue ( $basis );
    
    // Validate
    if ((is_numeric ( $price )) && (is_numeric ( $redemption )) && (is_numeric ( $basis )))
    {
      $price = ( float ) $price;
      $redemption = ( float ) $redemption;
      $basis = ( int ) $basis;
      if (($price <= 0) || ($redemption <= 0))
      {
        return PHPExcel_Calculation_Functions::NaN ();
      }
      $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC ( $settlement, $maturity, $basis );
      if (! is_numeric ( $daysBetweenSettlementAndMaturity ))
      {
        // return date error
        return $daysBetweenSettlementAndMaturity;
      }
      
      return ((1 - $price / $redemption) / $daysBetweenSettlementAndMaturity);
    }
    return PHPExcel_Calculation_Functions::VALUE ();
  }
  
  /**
   * DOLLARDE
   *
   * Converts a dollar price expressed as an integer part and a fraction
   * part into a dollar price expressed as a decimal number.
   * Fractional dollar numbers are sometimes used for security prices.
   *
   * Excel Function:
   * DOLLARDE(fractional_dollar,fraction)
   *
   * @access public
   * @category Financial Functions
   * @param float $fractional_dollar
   *          Fractional Dollar
   * @param integer $fraction
   *          Fraction
   * @return float
   */
  public static function DOLLARDE($fractional_dollar = null, $fraction = 0)
  {
    $fractional_dollar = PHPExcel_Calculation_Functions::flattenSingleValue ( $fractional_dollar );
    $fraction = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $fraction );
    
    // Validate parameters
    if (is_null ( $fractional_dollar ) || $fraction < 0)
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    if ($fraction == 0)
    {
      return PHPExcel_Calculation_Functions::DIV0 ();
    }
    
    $dollars = floor ( $fractional_dollar );
    $cents = fmod ( $fractional_dollar, 1 );
    $cents /= $fraction;
    $cents *= pow ( 10, ceil ( log10 ( $fraction ) ) );
    return $dollars + $cents;
  }
  
  /**
   * DOLLARFR
   *
   * Converts a dollar price expressed as a decimal number into a dollar price
   * expressed as a fraction.
   * Fractional dollar numbers are sometimes used for security prices.
   *
   * Excel Function:
   * DOLLARFR(decimal_dollar,fraction)
   *
   * @access public
   * @category Financial Functions
   * @param float $decimal_dollar
   *          Decimal Dollar
   * @param integer $fraction
   *          Fraction
   * @return float
   */
  public static function DOLLARFR($decimal_dollar = null, $fraction = 0)
  {
    $decimal_dollar = PHPExcel_Calculation_Functions::flattenSingleValue ( $decimal_dollar );
    $fraction = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $fraction );
    
    // Validate parameters
    if (is_null ( $decimal_dollar ) || $fraction < 0)
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    if ($fraction == 0)
    {
      return PHPExcel_Calculation_Functions::DIV0 ();
    }
    
    $dollars = floor ( $decimal_dollar );
    $cents = fmod ( $decimal_dollar, 1 );
    $cents *= $fraction;
    $cents *= pow ( 10, - ceil ( log10 ( $fraction ) ) );
    return $dollars + $cents;
  }
  
  /**
   * EFFECT
   *
   * Returns the effective interest rate given the nominal rate and the number of
   * compounding payments per year.
   *
   * Excel Function:
   * EFFECT(nominal_rate,npery)
   *
   * @access public
   * @category Financial Functions
   * @param float $nominal_rate
   *          Nominal interest rate
   * @param integer $npery
   *          Number of compounding payments per year
   * @return float
   */
  public static function EFFECT($nominal_rate = 0, $npery = 0)
  {
    $nominal_rate = PHPExcel_Calculation_Functions::flattenSingleValue ( $nominal_rate );
    $npery = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $npery );
    
    // Validate parameters
    if ($nominal_rate <= 0 || $npery < 1)
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    
    return pow ( (1 + $nominal_rate / $npery), $npery ) - 1;
  }
  
  /**
   * FV
   *
   * Returns the Future Value of a cash flow with constant payments and interest rate (annuities).
   *
   * Excel Function:
   * FV(rate,nper,pmt[,pv[,type]])
   *
   * @access public
   * @category Financial Functions
   * @param float $rate
   *          The interest rate per period
   * @param int $nper
   *          Total number of payment periods in an annuity
   * @param float $pmt
   *          The payment made each period: it cannot change over the
   *          life of the annuity. Typically, pmt contains principal
   *          and interest but no other fees or taxes.
   * @param float $pv
   *          Present Value, or the lump-sum amount that a series of
   *          future payments is worth right now.
   * @param integer $type
   *          A number 0 or 1 and indicates when payments are due:
   *          0 or omitted At the end of the period.
   *          1 At the beginning of the period.
   * @return float
   */
  public static function FV($rate = 0, $nper = 0, $pmt = 0, $pv = 0, $type = 0)
  {
    $rate = PHPExcel_Calculation_Functions::flattenSingleValue ( $rate );
    $nper = PHPExcel_Calculation_Functions::flattenSingleValue ( $nper );
    $pmt = PHPExcel_Calculation_Functions::flattenSingleValue ( $pmt );
    $pv = PHPExcel_Calculation_Functions::flattenSingleValue ( $pv );
    $type = PHPExcel_Calculation_Functions::flattenSingleValue ( $type );
    
    // Validate parameters
    if ($type != 0 && $type != 1)
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    
    // Calculate
    if (! is_null ( $rate ) && $rate != 0)
    {
      return - $pv * pow ( 1 + $rate, $nper ) - $pmt * (1 + $rate * $type) * (pow ( 1 + $rate, $nper ) - 1) / $rate;
    }
    return - $pv - $pmt * $nper;
  }
  
  /**
   * FVSCHEDULE
   *
   * Returns the future value of an initial principal after applying a series of compound interest rates.
   * Use FVSCHEDULE to calculate the future value of an investment with a variable or adjustable rate.
   *
   * Excel Function:
   * FVSCHEDULE(principal,schedule)
   *
   * @param float $principal
   *          The present value.
   * @param float[] $schedule
   *          An array of interest rates to apply.
   * @return float
   */
  public static function FVSCHEDULE($principal, $schedule)
  {
    $principal = PHPExcel_Calculation_Functions::flattenSingleValue ( $principal );
    $schedule = PHPExcel_Calculation_Functions::flattenArray ( $schedule );
    
    foreach ( $schedule as $rate )
    {
      $principal *= 1 + $rate;
    }
    
    return $principal;
  }
  
  /**
   * INTRATE
   *
   * Returns the interest rate for a fully invested security.
   *
   * Excel Function:
   * INTRATE(settlement,maturity,investment,redemption[,basis])
   *
   * @param mixed $settlement
   *          The security's settlement date.
   *          The security settlement date is the date after the issue date when the security is traded to the buyer.
   * @param mixed $maturity
   *          The security's maturity date.
   *          The maturity date is the date when the security expires.
   * @param integer $investment
   *          The amount invested in the security.
   * @param integer $redemption
   *          The amount to be received at maturity.
   * @param integer $basis
   *          The type of day count to use.
   *          0 or omitted US (NASD) 30/360
   *          1 Actual/actual
   *          2 Actual/360
   *          3 Actual/365
   *          4 European 30/360
   * @return float
   */
  public static function INTRATE($settlement, $maturity, $investment, $redemption, $basis = 0)
  {
    $settlement = PHPExcel_Calculation_Functions::flattenSingleValue ( $settlement );
    $maturity = PHPExcel_Calculation_Functions::flattenSingleValue ( $maturity );
    $investment = PHPExcel_Calculation_Functions::flattenSingleValue ( $investment );
    $redemption = PHPExcel_Calculation_Functions::flattenSingleValue ( $redemption );
    $basis = PHPExcel_Calculation_Functions::flattenSingleValue ( $basis );
    
    // Validate
    if ((is_numeric ( $investment )) && (is_numeric ( $redemption )) && (is_numeric ( $basis )))
    {
      $investment = ( float ) $investment;
      $redemption = ( float ) $redemption;
      $basis = ( int ) $basis;
      if (($investment <= 0) || ($redemption <= 0))
      {
        return PHPExcel_Calculation_Functions::NaN ();
      }
      $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC ( $settlement, $maturity, $basis );
      if (! is_numeric ( $daysBetweenSettlementAndMaturity ))
      {
        // return date error
        return $daysBetweenSettlementAndMaturity;
      }
      
      return (($redemption / $investment) - 1) / ($daysBetweenSettlementAndMaturity);
    }
    return PHPExcel_Calculation_Functions::VALUE ();
  }
  
  /**
   * IPMT
   *
   * Returns the interest payment for a given period for an investment based on periodic, constant payments and a constant interest rate.
   *
   * Excel Function:
   * IPMT(rate,per,nper,pv[,fv][,type])
   *
   * @param float $rate
   *          Interest rate per period
   * @param int $per
   *          Period for which we want to find the interest
   * @param int $nper
   *          Number of periods
   * @param float $pv
   *          Present Value
   * @param float $fv
   *          Future Value
   * @param int $type
   *          Payment type: 0 = at the end of each period, 1 = at the beginning of each period
   * @return float
   */
  public static function IPMT($rate, $per, $nper, $pv, $fv = 0, $type = 0)
  {
    $rate = PHPExcel_Calculation_Functions::flattenSingleValue ( $rate );
    $per = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $per );
    $nper = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $nper );
    $pv = PHPExcel_Calculation_Functions::flattenSingleValue ( $pv );
    $fv = PHPExcel_Calculation_Functions::flattenSingleValue ( $fv );
    $type = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $type );
    
    // Validate parameters
    if ($type != 0 && $type != 1)
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    if ($per <= 0 || $per > $nper)
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    
    // Calculate
    $interestAndPrincipal = self::interestAndPrincipal ( $rate, $per, $nper, $pv, $fv, $type );
    return $interestAndPrincipal [0];
  }
  
  /**
   * IRR
   *
   * Returns the internal rate of return for a series of cash flows represented by the numbers in values.
   * These cash flows do not have to be even, as they would be for an annuity. However, the cash flows must occur
   * at regular intervals, such as monthly or annually. The internal rate of return is the interest rate received
   * for an investment consisting of payments (negative values) and income (positive values) that occur at regular
   * periods.
   *
   * Excel Function:
   * IRR(values[,guess])
   *
   * @param float[] $values
   *          An array or a reference to cells that contain numbers for which you want
   *          to calculate the internal rate of return.
   *          Values must contain at least one positive value and one negative value to
   *          calculate the internal rate of return.
   * @param float $guess
   *          A number that you guess is close to the result of IRR
   * @return float
   */
  public static function IRR($values, $guess = 0.1)
  {
    if (! is_array ( $values ))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    $values = PHPExcel_Calculation_Functions::flattenArray ( $values );
    $guess = PHPExcel_Calculation_Functions::flattenSingleValue ( $guess );
    
    // create an initial range, with a root somewhere between 0 and guess
    $x1 = 0.0;
    $x2 = $guess;
    $f1 = self::NPV ( $x1, $values );
    $f2 = self::NPV ( $x2, $values );
    for($i = 0; $i < FINANCIAL_MAX_ITERATIONS; ++ $i)
    {
      if (($f1 * $f2) < 0.0)
      {
        break;
      }
      if (abs ( $f1 ) < abs ( $f2 ))
      {
        $f1 = self::NPV ( $x1 += 1.6 * ($x1 - $x2), $values );
      }
      else
      {
        $f2 = self::NPV ( $x2 += 1.6 * ($x2 - $x1), $values );
      }
    }
    if (($f1 * $f2) > 0.0)
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    
    $f = self::NPV ( $x1, $values );
    if ($f < 0.0)
    {
      $rtb = $x1;
      $dx = $x2 - $x1;
    }
    else
    {
      $rtb = $x2;
      $dx = $x1 - $x2;
    }
    
    for($i = 0; $i < FINANCIAL_MAX_ITERATIONS; ++ $i)
    {
      $dx *= 0.5;
      $x_mid = $rtb + $dx;
      $f_mid = self::NPV ( $x_mid, $values );
      if ($f_mid <= 0.0)
      {
        $rtb = $x_mid;
      }
      if ((abs ( $f_mid ) < FINANCIAL_PRECISION) || (abs ( $dx ) < FINANCIAL_PRECISION))
      {
        return $x_mid;
      }
    }
    return PHPExcel_Calculation_Functions::VALUE ();
  }
  
  /**
   * ISPMT
   *
   * Returns the interest payment for an investment based on an interest rate and a constant payment schedule.
   *
   * Excel Function:
   * =ISPMT(interest_rate, period, number_payments, PV)
   *
   * interest_rate is the interest rate for the investment
   *
   * period is the period to calculate the interest rate. It must be betweeen 1 and number_payments.
   *
   * number_payments is the number of payments for the annuity
   *
   * PV is the loan amount or present value of the payments
   */
  public static function ISPMT()
  {
    // Return value
    $returnValue = 0;
    
    // Get the parameters
    $aArgs = PHPExcel_Calculation_Functions::flattenArray ( func_get_args () );
    $interestRate = array_shift ( $aArgs );
    $period = array_shift ( $aArgs );
    $numberPeriods = array_shift ( $aArgs );
    $principleRemaining = array_shift ( $aArgs );
    
    // Calculate
    $principlePayment = ($principleRemaining * 1.0) / ($numberPeriods * 1.0);
    for($i = 0; $i <= $period; ++ $i)
    {
      $returnValue = $interestRate * $principleRemaining * - 1;
      $principleRemaining -= $principlePayment;
      // principle needs to be 0 after the last payment, don't let floating point screw it up
      if ($i == $numberPeriods)
      {
        $returnValue = 0;
      }
    }
    return ($returnValue);
  }
  
  /**
   * MIRR
   *
   * Returns the modified internal rate of return for a series of periodic cash flows. MIRR considers both
   * the cost of the investment and the interest received on reinvestment of cash.
   *
   * Excel Function:
   * MIRR(values,finance_rate, reinvestment_rate)
   *
   * @param float[] $values
   *          An array or a reference to cells that contain a series of payments and
   *          income occurring at regular intervals.
   *          Payments are negative value, income is positive values.
   * @param float $finance_rate
   *          The interest rate you pay on the money used in the cash flows
   * @param float $reinvestment_rate
   *          The interest rate you receive on the cash flows as you reinvest them
   * @return float
   */
  public static function MIRR($values, $finance_rate, $reinvestment_rate)
  {
    if (! is_array ( $values ))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    $values = PHPExcel_Calculation_Functions::flattenArray ( $values );
    $finance_rate = PHPExcel_Calculation_Functions::flattenSingleValue ( $finance_rate );
    $reinvestment_rate = PHPExcel_Calculation_Functions::flattenSingleValue ( $reinvestment_rate );
    $n = count ( $values );
    
    $rr = 1.0 + $reinvestment_rate;
    $fr = 1.0 + $finance_rate;
    
    $npv_pos = $npv_neg = 0.0;
    foreach ( $values as $i => $v )
    {
      if ($v >= 0)
      {
        $npv_pos += $v / pow ( $rr, $i );
      }
      else
      {
        $npv_neg += $v / pow ( $fr, $i );
      }
    }
    
    if (($npv_neg == 0) || ($npv_pos == 0) || ($reinvestment_rate <= - 1))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    
    $mirr = pow ( (- $npv_pos * pow ( $rr, $n )) / ($npv_neg * ($rr)), (1.0 / ($n - 1)) ) - 1.0;
    
    return (is_finite ( $mirr ) ? $mirr : PHPExcel_Calculation_Functions::VALUE ());
  }
  
  /**
   * NOMINAL
   *
   * Returns the nominal interest rate given the effective rate and the number of compounding payments per year.
   *
   * @param float $effect_rate
   *          Effective interest rate
   * @param int $npery
   *          Number of compounding payments per year
   * @return float
   */
  public static function NOMINAL($effect_rate = 0, $npery = 0)
  {
    $effect_rate = PHPExcel_Calculation_Functions::flattenSingleValue ( $effect_rate );
    $npery = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $npery );
    
    // Validate parameters
    if ($effect_rate <= 0 || $npery < 1)
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    
    // Calculate
    return $npery * (pow ( $effect_rate + 1, 1 / $npery ) - 1);
  }
  
  /**
   * NPER
   *
   * Returns the number of periods for a cash flow with constant periodic payments (annuities), and interest rate.
   *
   * @param float $rate
   *          Interest rate per period
   * @param int $pmt
   *          Periodic payment (annuity)
   * @param float $pv
   *          Present Value
   * @param float $fv
   *          Future Value
   * @param int $type
   *          Payment type: 0 = at the end of each period, 1 = at the beginning of each period
   * @return float
   */
  public static function NPER($rate = 0, $pmt = 0, $pv = 0, $fv = 0, $type = 0)
  {
    $rate = PHPExcel_Calculation_Functions::flattenSingleValue ( $rate );
    $pmt = PHPExcel_Calculation_Functions::flattenSingleValue ( $pmt );
    $pv = PHPExcel_Calculation_Functions::flattenSingleValue ( $pv );
    $fv = PHPExcel_Calculation_Functions::flattenSingleValue ( $fv );
    $type = PHPExcel_Calculation_Functions::flattenSingleValue ( $type );
    
    // Validate parameters
    if ($type != 0 && $type != 1)
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    
    // Calculate
    if (! is_null ( $rate ) && $rate != 0)
    {
      if ($pmt == 0 && $pv == 0)
      {
        return PHPExcel_Calculation_Functions::NaN ();
      }
      return log ( ($pmt * (1 + $rate * $type) / $rate - $fv) / ($pv + $pmt * (1 + $rate * $type) / $rate) ) / log ( 1 + $rate );
    }
    if ($pmt == 0)
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    return (- $pv - $fv) / $pmt;
  }
  
  /**
   * NPV
   *
   * Returns the Net Present Value of a cash flow series given a discount rate.
   *
   * @return float
   */
  public static function NPV()
  {
    // Return value
    $returnValue = 0;
    
    // Loop through arguments
    $aArgs = PHPExcel_Calculation_Functions::flattenArray ( func_get_args () );
    
    // Calculate
    $rate = array_shift ( $aArgs );
    for($i = 1; $i <= count ( $aArgs ); ++ $i)
    {
      // Is it a numeric value?
      if (is_numeric ( $aArgs [$i - 1] ))
      {
        $returnValue += $aArgs [$i - 1] / pow ( 1 + $rate, $i );
      }
    }
    
    // Return
    return $returnValue;
  }
  
  /**
   * PMT
   *
   * Returns the constant payment (annuity) for a cash flow with a constant interest rate.
   *
   * @param float $rate
   *          Interest rate per period
   * @param int $nper
   *          Number of periods
   * @param float $pv
   *          Present Value
   * @param float $fv
   *          Future Value
   * @param int $type
   *          Payment type: 0 = at the end of each period, 1 = at the beginning of each period
   * @return float
   */
  public static function PMT($rate = 0, $nper = 0, $pv = 0, $fv = 0, $type = 0)
  {
    $rate = PHPExcel_Calculation_Functions::flattenSingleValue ( $rate );
    $nper = PHPExcel_Calculation_Functions::flattenSingleValue ( $nper );
    $pv = PHPExcel_Calculation_Functions::flattenSingleValue ( $pv );
    $fv = PHPExcel_Calculation_Functions::flattenSingleValue ( $fv );
    $type = PHPExcel_Calculation_Functions::flattenSingleValue ( $type );
    
    // Validate parameters
    if ($type != 0 && $type != 1)
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    
    // Calculate
    if (! is_null ( $rate ) && $rate != 0)
    {
      return (- $fv - $pv * pow ( 1 + $rate, $nper )) / (1 + $rate * $type) / ((pow ( 1 + $rate, $nper ) - 1) / $rate);
    }
    return (- $pv - $fv) / $nper;
  }
  
  /**
   * PPMT
   *
   * Returns the interest payment for a given period for an investment based on periodic, constant payments and a constant interest rate.
   *
   * @param float $rate
   *          Interest rate per period
   * @param int $per
   *          Period for which we want to find the interest
   * @param int $nper
   *          Number of periods
   * @param float $pv
   *          Present Value
   * @param float $fv
   *          Future Value
   * @param int $type
   *          Payment type: 0 = at the end of each period, 1 = at the beginning of each period
   * @return float
   */
  public static function PPMT($rate, $per, $nper, $pv, $fv = 0, $type = 0)
  {
    $rate = PHPExcel_Calculation_Functions::flattenSingleValue ( $rate );
    $per = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $per );
    $nper = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $nper );
    $pv = PHPExcel_Calculation_Functions::flattenSingleValue ( $pv );
    $fv = PHPExcel_Calculation_Functions::flattenSingleValue ( $fv );
    $type = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $type );
    
    // Validate parameters
    if ($type != 0 && $type != 1)
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    if ($per <= 0 || $per > $nper)
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    
    // Calculate
    $interestAndPrincipal = self::interestAndPrincipal ( $rate, $per, $nper, $pv, $fv, $type );
    return $interestAndPrincipal [1];
  }
  public static function PRICE($settlement, $maturity, $rate, $yield, $redemption, $frequency, $basis = 0)
  {
    $settlement = PHPExcel_Calculation_Functions::flattenSingleValue ( $settlement );
    $maturity = PHPExcel_Calculation_Functions::flattenSingleValue ( $maturity );
    $rate = ( float ) PHPExcel_Calculation_Functions::flattenSingleValue ( $rate );
    $yield = ( float ) PHPExcel_Calculation_Functions::flattenSingleValue ( $yield );
    $redemption = ( float ) PHPExcel_Calculation_Functions::flattenSingleValue ( $redemption );
    $frequency = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $frequency );
    $basis = (is_null ( $basis )) ? 0 : ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $basis );
    
    if (is_string ( $settlement = PHPExcel_Calculation_DateTime::getDateValue ( $settlement ) ))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    if (is_string ( $maturity = PHPExcel_Calculation_DateTime::getDateValue ( $maturity ) ))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    
    if (($settlement > $maturity) || (! self::isValidFrequency ( $frequency )) || (($basis < 0) || ($basis > 4)))
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    
    $dsc = self::COUPDAYSNC ( $settlement, $maturity, $frequency, $basis );
    $e = self::COUPDAYS ( $settlement, $maturity, $frequency, $basis );
    $n = self::COUPNUM ( $settlement, $maturity, $frequency, $basis );
    $a = self::COUPDAYBS ( $settlement, $maturity, $frequency, $basis );
    
    $baseYF = 1.0 + ($yield / $frequency);
    $rfp = 100 * ($rate / $frequency);
    $de = $dsc / $e;
    
    $result = $redemption / pow ( $baseYF, (-- $n + $de) );
    for($k = 0; $k <= $n; ++ $k)
    {
      $result += $rfp / (pow ( $baseYF, ($k + $de) ));
    }
    $result -= $rfp * ($a / $e);
    
    return $result;
  }
  
  /**
   * PRICEDISC
   *
   * Returns the price per $100 face value of a discounted security.
   *
   * @param
   *          mixed settlement The security's settlement date.
   *          The security settlement date is the date after the issue date when the security is traded to the buyer.
   * @param
   *          mixed maturity The security's maturity date.
   *          The maturity date is the date when the security expires.
   * @param
   *          int discount The security's discount rate.
   * @param
   *          int redemption The security's redemption value per $100 face value.
   * @param
   *          int basis The type of day count to use.
   *          0 or omitted US (NASD) 30/360
   *          1 Actual/actual
   *          2 Actual/360
   *          3 Actual/365
   *          4 European 30/360
   * @return float
   */
  public static function PRICEDISC($settlement, $maturity, $discount, $redemption, $basis = 0)
  {
    $settlement = PHPExcel_Calculation_Functions::flattenSingleValue ( $settlement );
    $maturity = PHPExcel_Calculation_Functions::flattenSingleValue ( $maturity );
    $discount = ( float ) PHPExcel_Calculation_Functions::flattenSingleValue ( $discount );
    $redemption = ( float ) PHPExcel_Calculation_Functions::flattenSingleValue ( $redemption );
    $basis = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $basis );
    
    // Validate
    if ((is_numeric ( $discount )) && (is_numeric ( $redemption )) && (is_numeric ( $basis )))
    {
      if (($discount <= 0) || ($redemption <= 0))
      {
        return PHPExcel_Calculation_Functions::NaN ();
      }
      $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC ( $settlement, $maturity, $basis );
      if (! is_numeric ( $daysBetweenSettlementAndMaturity ))
      {
        // return date error
        return $daysBetweenSettlementAndMaturity;
      }
      
      return $redemption * (1 - $discount * $daysBetweenSettlementAndMaturity);
    }
    return PHPExcel_Calculation_Functions::VALUE ();
  }
  
  /**
   * PRICEMAT
   *
   * Returns the price per $100 face value of a security that pays interest at maturity.
   *
   * @param
   *          mixed settlement The security's settlement date.
   *          The security's settlement date is the date after the issue date when the security is traded to the buyer.
   * @param
   *          mixed maturity The security's maturity date.
   *          The maturity date is the date when the security expires.
   * @param
   *          mixed issue The security's issue date.
   * @param
   *          int rate The security's interest rate at date of issue.
   * @param
   *          int yield The security's annual yield.
   * @param
   *          int basis The type of day count to use.
   *          0 or omitted US (NASD) 30/360
   *          1 Actual/actual
   *          2 Actual/360
   *          3 Actual/365
   *          4 European 30/360
   * @return float
   */
  public static function PRICEMAT($settlement, $maturity, $issue, $rate, $yield, $basis = 0)
  {
    $settlement = PHPExcel_Calculation_Functions::flattenSingleValue ( $settlement );
    $maturity = PHPExcel_Calculation_Functions::flattenSingleValue ( $maturity );
    $issue = PHPExcel_Calculation_Functions::flattenSingleValue ( $issue );
    $rate = PHPExcel_Calculation_Functions::flattenSingleValue ( $rate );
    $yield = PHPExcel_Calculation_Functions::flattenSingleValue ( $yield );
    $basis = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $basis );
    
    // Validate
    if (is_numeric ( $rate ) && is_numeric ( $yield ))
    {
      if (($rate <= 0) || ($yield <= 0))
      {
        return PHPExcel_Calculation_Functions::NaN ();
      }
      $daysPerYear = self::daysPerYear ( PHPExcel_Calculation_DateTime::YEAR ( $settlement ), $basis );
      if (! is_numeric ( $daysPerYear ))
      {
        return $daysPerYear;
      }
      $daysBetweenIssueAndSettlement = PHPExcel_Calculation_DateTime::YEARFRAC ( $issue, $settlement, $basis );
      if (! is_numeric ( $daysBetweenIssueAndSettlement ))
      {
        // return date error
        return $daysBetweenIssueAndSettlement;
      }
      $daysBetweenIssueAndSettlement *= $daysPerYear;
      $daysBetweenIssueAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC ( $issue, $maturity, $basis );
      if (! is_numeric ( $daysBetweenIssueAndMaturity ))
      {
        // return date error
        return $daysBetweenIssueAndMaturity;
      }
      $daysBetweenIssueAndMaturity *= $daysPerYear;
      $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC ( $settlement, $maturity, $basis );
      if (! is_numeric ( $daysBetweenSettlementAndMaturity ))
      {
        // return date error
        return $daysBetweenSettlementAndMaturity;
      }
      $daysBetweenSettlementAndMaturity *= $daysPerYear;
      
      return ((100 + (($daysBetweenIssueAndMaturity / $daysPerYear) * $rate * 100)) / (1 + (($daysBetweenSettlementAndMaturity / $daysPerYear) * $yield)) - (($daysBetweenIssueAndSettlement / $daysPerYear) * $rate * 100));
    }
    return PHPExcel_Calculation_Functions::VALUE ();
  }
  
  /**
   * PV
   *
   * Returns the Present Value of a cash flow with constant payments and interest rate (annuities).
   *
   * @param float $rate
   *          Interest rate per period
   * @param int $nper
   *          Number of periods
   * @param float $pmt
   *          Periodic payment (annuity)
   * @param float $fv
   *          Future Value
   * @param int $type
   *          Payment type: 0 = at the end of each period, 1 = at the beginning of each period
   * @return float
   */
  public static function PV($rate = 0, $nper = 0, $pmt = 0, $fv = 0, $type = 0)
  {
    $rate = PHPExcel_Calculation_Functions::flattenSingleValue ( $rate );
    $nper = PHPExcel_Calculation_Functions::flattenSingleValue ( $nper );
    $pmt = PHPExcel_Calculation_Functions::flattenSingleValue ( $pmt );
    $fv = PHPExcel_Calculation_Functions::flattenSingleValue ( $fv );
    $type = PHPExcel_Calculation_Functions::flattenSingleValue ( $type );
    
    // Validate parameters
    if ($type != 0 && $type != 1)
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    
    // Calculate
    if (! is_null ( $rate ) && $rate != 0)
    {
      return (- $pmt * (1 + $rate * $type) * ((pow ( 1 + $rate, $nper ) - 1) / $rate) - $fv) / pow ( 1 + $rate, $nper );
    }
    return - $fv - $pmt * $nper;
  }
  
  /**
   * RATE
   *
   * Returns the interest rate per period of an annuity.
   * RATE is calculated by iteration and can have zero or more solutions.
   * If the successive results of RATE do not converge to within 0.0000001 after 20 iterations,
   * RATE returns the #NUM! error value.
   *
   * Excel Function:
   * RATE(nper,pmt,pv[,fv[,type[,guess]]])
   *
   * @access public
   * @category Financial Functions
   * @param
   *          float nper The total number of payment periods in an annuity.
   * @param
   *          float pmt The payment made each period and cannot change over the life
   *          of the annuity.
   *          Typically, pmt includes principal and interest but no other
   *          fees or taxes.
   * @param
   *          float pv The present value - the total amount that a series of future
   *          payments is worth now.
   * @param
   *          float fv The future value, or a cash balance you want to attain after
   *          the last payment is made. If fv is omitted, it is assumed
   *          to be 0 (the future value of a loan, for example, is 0).
   * @param
   *          integer type A number 0 or 1 and indicates when payments are due:
   *          0 or omitted At the end of the period.
   *          1 At the beginning of the period.
   * @param
   *          float guess Your guess for what the rate will be.
   *          If you omit guess, it is assumed to be 10 percent.
   * @return float
   *
   */
  public static function RATE($nper, $pmt, $pv, $fv = 0.0, $type = 0, $guess = 0.1)
  {
    $nper = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $nper );
    $pmt = PHPExcel_Calculation_Functions::flattenSingleValue ( $pmt );
    $pv = PHPExcel_Calculation_Functions::flattenSingleValue ( $pv );
    $fv = (is_null ( $fv )) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue ( $fv );
    $type = (is_null ( $type )) ? 0 : ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $type );
    $guess = (is_null ( $guess )) ? 0.1 : PHPExcel_Calculation_Functions::flattenSingleValue ( $guess );
    
    $rate = $guess;
    if (abs ( $rate ) < FINANCIAL_PRECISION)
    {
      $y = $pv * (1 + $nper * $rate) + $pmt * (1 + $rate * $type) * $nper + $fv;
    }
    else
    {
      $f = exp ( $nper * log ( 1 + $rate ) );
      $y = $pv * $f + $pmt * (1 / $rate + $type) * ($f - 1) + $fv;
    }
    $y0 = $pv + $pmt * $nper + $fv;
    $y1 = $pv * $f + $pmt * (1 / $rate + $type) * ($f - 1) + $fv;
    
    // find root by secant method
    $i = $x0 = 0.0;
    $x1 = $rate;
    while ( (abs ( $y0 - $y1 ) > FINANCIAL_PRECISION) && ($i < FINANCIAL_MAX_ITERATIONS) )
    {
      $rate = ($y1 * $x0 - $y0 * $x1) / ($y1 - $y0);
      $x0 = $x1;
      $x1 = $rate;
      if (($nper * abs ( $pmt )) > ($pv - $fv))
      {
        $x1 = abs ( $x1 );
      }
      if (abs ( $rate ) < FINANCIAL_PRECISION)
      {
        $y = $pv * (1 + $nper * $rate) + $pmt * (1 + $rate * $type) * $nper + $fv;
      }
      else
      {
        $f = exp ( $nper * log ( 1 + $rate ) );
        $y = $pv * $f + $pmt * (1 / $rate + $type) * ($f - 1) + $fv;
      }
      
      $y0 = $y1;
      $y1 = $y;
      ++ $i;
    }
    return $rate;
  }
  
  /**
   * RECEIVED
   *
   * Returns the price per $100 face value of a discounted security.
   *
   * @param
   *          mixed settlement The security's settlement date.
   *          The security settlement date is the date after the issue date when the security is traded to the buyer.
   * @param
   *          mixed maturity The security's maturity date.
   *          The maturity date is the date when the security expires.
   * @param
   *          int investment The amount invested in the security.
   * @param
   *          int discount The security's discount rate.
   * @param
   *          int basis The type of day count to use.
   *          0 or omitted US (NASD) 30/360
   *          1 Actual/actual
   *          2 Actual/360
   *          3 Actual/365
   *          4 European 30/360
   * @return float
   */
  public static function RECEIVED($settlement, $maturity, $investment, $discount, $basis = 0)
  {
    $settlement = PHPExcel_Calculation_Functions::flattenSingleValue ( $settlement );
    $maturity = PHPExcel_Calculation_Functions::flattenSingleValue ( $maturity );
    $investment = ( float ) PHPExcel_Calculation_Functions::flattenSingleValue ( $investment );
    $discount = ( float ) PHPExcel_Calculation_Functions::flattenSingleValue ( $discount );
    $basis = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $basis );
    
    // Validate
    if ((is_numeric ( $investment )) && (is_numeric ( $discount )) && (is_numeric ( $basis )))
    {
      if (($investment <= 0) || ($discount <= 0))
      {
        return PHPExcel_Calculation_Functions::NaN ();
      }
      $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC ( $settlement, $maturity, $basis );
      if (! is_numeric ( $daysBetweenSettlementAndMaturity ))
      {
        // return date error
        return $daysBetweenSettlementAndMaturity;
      }
      
      return $investment / (1 - ($discount * $daysBetweenSettlementAndMaturity));
    }
    return PHPExcel_Calculation_Functions::VALUE ();
  }
  
  /**
   * SLN
   *
   * Returns the straight-line depreciation of an asset for one period
   *
   * @param
   *          cost Initial cost of the asset
   * @param
   *          salvage Value at the end of the depreciation
   * @param
   *          life Number of periods over which the asset is depreciated
   * @return float
   */
  public static function SLN($cost, $salvage, $life)
  {
    $cost = PHPExcel_Calculation_Functions::flattenSingleValue ( $cost );
    $salvage = PHPExcel_Calculation_Functions::flattenSingleValue ( $salvage );
    $life = PHPExcel_Calculation_Functions::flattenSingleValue ( $life );
    
    // Calculate
    if ((is_numeric ( $cost )) && (is_numeric ( $salvage )) && (is_numeric ( $life )))
    {
      if ($life < 0)
      {
        return PHPExcel_Calculation_Functions::NaN ();
      }
      return ($cost - $salvage) / $life;
    }
    return PHPExcel_Calculation_Functions::VALUE ();
  }
  
  /**
   * SYD
   *
   * Returns the sum-of-years' digits depreciation of an asset for a specified period.
   *
   * @param
   *          cost Initial cost of the asset
   * @param
   *          salvage Value at the end of the depreciation
   * @param
   *          life Number of periods over which the asset is depreciated
   * @param
   *          period Period
   * @return float
   */
  public static function SYD($cost, $salvage, $life, $period)
  {
    $cost = PHPExcel_Calculation_Functions::flattenSingleValue ( $cost );
    $salvage = PHPExcel_Calculation_Functions::flattenSingleValue ( $salvage );
    $life = PHPExcel_Calculation_Functions::flattenSingleValue ( $life );
    $period = PHPExcel_Calculation_Functions::flattenSingleValue ( $period );
    
    // Calculate
    if ((is_numeric ( $cost )) && (is_numeric ( $salvage )) && (is_numeric ( $life )) && (is_numeric ( $period )))
    {
      if (($life < 1) || ($period > $life))
      {
        return PHPExcel_Calculation_Functions::NaN ();
      }
      return (($cost - $salvage) * ($life - $period + 1) * 2) / ($life * ($life + 1));
    }
    return PHPExcel_Calculation_Functions::VALUE ();
  }
  
  /**
   * TBILLEQ
   *
   * Returns the bond-equivalent yield for a Treasury bill.
   *
   * @param
   *          mixed settlement The Treasury bill's settlement date.
   *          The Treasury bill's settlement date is the date after the issue date when the Treasury bill is traded to the buyer.
   * @param
   *          mixed maturity The Treasury bill's maturity date.
   *          The maturity date is the date when the Treasury bill expires.
   * @param
   *          int discount The Treasury bill's discount rate.
   * @return float
   */
  public static function TBILLEQ($settlement, $maturity, $discount)
  {
    $settlement = PHPExcel_Calculation_Functions::flattenSingleValue ( $settlement );
    $maturity = PHPExcel_Calculation_Functions::flattenSingleValue ( $maturity );
    $discount = PHPExcel_Calculation_Functions::flattenSingleValue ( $discount );
    
    // Use TBILLPRICE for validation
    $testValue = self::TBILLPRICE ( $settlement, $maturity, $discount );
    if (is_string ( $testValue ))
    {
      return $testValue;
    }
    
    if (is_string ( $maturity = PHPExcel_Calculation_DateTime::getDateValue ( $maturity ) ))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    
    if (PHPExcel_Calculation_Functions::getCompatibilityMode () == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE)
    {
      ++ $maturity;
      $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC ( $settlement, $maturity ) * 360;
    }
    else
    {
      $daysBetweenSettlementAndMaturity = (PHPExcel_Calculation_DateTime::getDateValue ( $maturity ) - PHPExcel_Calculation_DateTime::getDateValue ( $settlement ));
    }
    
    return (365 * $discount) / (360 - $discount * $daysBetweenSettlementAndMaturity);
  }
  
  /**
   * TBILLPRICE
   *
   * Returns the yield for a Treasury bill.
   *
   * @param
   *          mixed settlement The Treasury bill's settlement date.
   *          The Treasury bill's settlement date is the date after the issue date when the Treasury bill is traded to the buyer.
   * @param
   *          mixed maturity The Treasury bill's maturity date.
   *          The maturity date is the date when the Treasury bill expires.
   * @param
   *          int discount The Treasury bill's discount rate.
   * @return float
   */
  public static function TBILLPRICE($settlement, $maturity, $discount)
  {
    $settlement = PHPExcel_Calculation_Functions::flattenSingleValue ( $settlement );
    $maturity = PHPExcel_Calculation_Functions::flattenSingleValue ( $maturity );
    $discount = PHPExcel_Calculation_Functions::flattenSingleValue ( $discount );
    
    if (is_string ( $maturity = PHPExcel_Calculation_DateTime::getDateValue ( $maturity ) ))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    
    // Validate
    if (is_numeric ( $discount ))
    {
      if ($discount <= 0)
      {
        return PHPExcel_Calculation_Functions::NaN ();
      }
      
      if (PHPExcel_Calculation_Functions::getCompatibilityMode () == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE)
      {
        ++ $maturity;
        $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC ( $settlement, $maturity ) * 360;
        if (! is_numeric ( $daysBetweenSettlementAndMaturity ))
        {
          // return date error
          return $daysBetweenSettlementAndMaturity;
        }
      }
      else
      {
        $daysBetweenSettlementAndMaturity = (PHPExcel_Calculation_DateTime::getDateValue ( $maturity ) - PHPExcel_Calculation_DateTime::getDateValue ( $settlement ));
      }
      
      if ($daysBetweenSettlementAndMaturity > 360)
      {
        return PHPExcel_Calculation_Functions::NaN ();
      }
      
      $price = 100 * (1 - (($discount * $daysBetweenSettlementAndMaturity) / 360));
      if ($price <= 0)
      {
        return PHPExcel_Calculation_Functions::NaN ();
      }
      return $price;
    }
    return PHPExcel_Calculation_Functions::VALUE ();
  }
  
  /**
   * TBILLYIELD
   *
   * Returns the yield for a Treasury bill.
   *
   * @param
   *          mixed settlement The Treasury bill's settlement date.
   *          The Treasury bill's settlement date is the date after the issue date when the Treasury bill is traded to the buyer.
   * @param
   *          mixed maturity The Treasury bill's maturity date.
   *          The maturity date is the date when the Treasury bill expires.
   * @param
   *          int price The Treasury bill's price per $100 face value.
   * @return float
   */
  public static function TBILLYIELD($settlement, $maturity, $price)
  {
    $settlement = PHPExcel_Calculation_Functions::flattenSingleValue ( $settlement );
    $maturity = PHPExcel_Calculation_Functions::flattenSingleValue ( $maturity );
    $price = PHPExcel_Calculation_Functions::flattenSingleValue ( $price );
    
    // Validate
    if (is_numeric ( $price ))
    {
      if ($price <= 0)
      {
        return PHPExcel_Calculation_Functions::NaN ();
      }
      
      if (PHPExcel_Calculation_Functions::getCompatibilityMode () == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE)
      {
        ++ $maturity;
        $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC ( $settlement, $maturity ) * 360;
        if (! is_numeric ( $daysBetweenSettlementAndMaturity ))
        {
          // return date error
          return $daysBetweenSettlementAndMaturity;
        }
      }
      else
      {
        $daysBetweenSettlementAndMaturity = (PHPExcel_Calculation_DateTime::getDateValue ( $maturity ) - PHPExcel_Calculation_DateTime::getDateValue ( $settlement ));
      }
      
      if ($daysBetweenSettlementAndMaturity > 360)
      {
        return PHPExcel_Calculation_Functions::NaN ();
      }
      
      return ((100 - $price) / $price) * (360 / $daysBetweenSettlementAndMaturity);
    }
    return PHPExcel_Calculation_Functions::VALUE ();
  }
  public static function XIRR($values, $dates, $guess = 0.1)
  {
    if ((! is_array ( $values )) && (! is_array ( $dates )))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    $values = PHPExcel_Calculation_Functions::flattenArray ( $values );
    $dates = PHPExcel_Calculation_Functions::flattenArray ( $dates );
    $guess = PHPExcel_Calculation_Functions::flattenSingleValue ( $guess );
    if (count ( $values ) != count ( $dates ))
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    
    // create an initial range, with a root somewhere between 0 and guess
    $x1 = 0.0;
    $x2 = $guess;
    $f1 = self::XNPV ( $x1, $values, $dates );
    $f2 = self::XNPV ( $x2, $values, $dates );
    for($i = 0; $i < FINANCIAL_MAX_ITERATIONS; ++ $i)
    {
      if (($f1 * $f2) < 0.0)
      {
        break;
      }
      elseif (abs ( $f1 ) < abs ( $f2 ))
      {
        $f1 = self::XNPV ( $x1 += 1.6 * ($x1 - $x2), $values, $dates );
      }
      else
      {
        $f2 = self::XNPV ( $x2 += 1.6 * ($x2 - $x1), $values, $dates );
      }
    }
    if (($f1 * $f2) > 0.0)
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    
    $f = self::XNPV ( $x1, $values, $dates );
    if ($f < 0.0)
    {
      $rtb = $x1;
      $dx = $x2 - $x1;
    }
    else
    {
      $rtb = $x2;
      $dx = $x1 - $x2;
    }
    
    for($i = 0; $i < FINANCIAL_MAX_ITERATIONS; ++ $i)
    {
      $dx *= 0.5;
      $x_mid = $rtb + $dx;
      $f_mid = self::XNPV ( $x_mid, $values, $dates );
      if ($f_mid <= 0.0)
      {
        $rtb = $x_mid;
      }
      if ((abs ( $f_mid ) < FINANCIAL_PRECISION) || (abs ( $dx ) < FINANCIAL_PRECISION))
      {
        return $x_mid;
      }
    }
    return PHPExcel_Calculation_Functions::VALUE ();
  }
  
  /**
   * XNPV
   *
   * Returns the net present value for a schedule of cash flows that is not necessarily periodic.
   * To calculate the net present value for a series of cash flows that is periodic, use the NPV function.
   *
   * Excel Function:
   * =XNPV(rate,values,dates)
   *
   * @param float $rate
   *          The discount rate to apply to the cash flows.
   * @param
   *          array of float $values A series of cash flows that corresponds to a schedule of payments in dates.
   *          The first payment is optional and corresponds to a cost or payment that occurs at the beginning of the investment.
   *          If the first value is a cost or payment, it must be a negative value. All succeeding payments are discounted based on a 365-day year.
   *          The series of values must contain at least one positive value and one negative value.
   * @param
   *          array of mixed $dates A schedule of payment dates that corresponds to the cash flow payments.
   *          The first payment date indicates the beginning of the schedule of payments.
   *          All other dates must be later than this date, but they may occur in any order.
   * @return float
   */
  public static function XNPV($rate, $values, $dates)
  {
    $rate = PHPExcel_Calculation_Functions::flattenSingleValue ( $rate );
    if (! is_numeric ( $rate ))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    if ((! is_array ( $values )) || (! is_array ( $dates )))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    $values = PHPExcel_Calculation_Functions::flattenArray ( $values );
    $dates = PHPExcel_Calculation_Functions::flattenArray ( $dates );
    $valCount = count ( $values );
    if ($valCount != count ( $dates ))
    {
      return PHPExcel_Calculation_Functions::NaN ();
    }
    if ((min ( $values ) > 0) || (max ( $values ) < 0))
    {
      return PHPExcel_Calculation_Functions::VALUE ();
    }
    
    $xnpv = 0.0;
    for($i = 0; $i < $valCount; ++ $i)
    {
      if (! is_numeric ( $values [$i] ))
      {
        return PHPExcel_Calculation_Functions::VALUE ();
      }
      $xnpv += $values [$i] / pow ( 1 + $rate, PHPExcel_Calculation_DateTime::DATEDIF ( $dates [0], $dates [$i], 'd' ) / 365 );
    }
    return (is_finite ( $xnpv )) ? $xnpv : PHPExcel_Calculation_Functions::VALUE ();
  }
  
  /**
   * YIELDDISC
   *
   * Returns the annual yield of a security that pays interest at maturity.
   *
   * @param
   *          mixed settlement The security's settlement date.
   *          The security's settlement date is the date after the issue date when the security is traded to the buyer.
   * @param
   *          mixed maturity The security's maturity date.
   *          The maturity date is the date when the security expires.
   * @param
   *          int price The security's price per $100 face value.
   * @param
   *          int redemption The security's redemption value per $100 face value.
   * @param
   *          int basis The type of day count to use.
   *          0 or omitted US (NASD) 30/360
   *          1 Actual/actual
   *          2 Actual/360
   *          3 Actual/365
   *          4 European 30/360
   * @return float
   */
  public static function YIELDDISC($settlement, $maturity, $price, $redemption, $basis = 0)
  {
    $settlement = PHPExcel_Calculation_Functions::flattenSingleValue ( $settlement );
    $maturity = PHPExcel_Calculation_Functions::flattenSingleValue ( $maturity );
    $price = PHPExcel_Calculation_Functions::flattenSingleValue ( $price );
    $redemption = PHPExcel_Calculation_Functions::flattenSingleValue ( $redemption );
    $basis = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $basis );
    
    // Validate
    if (is_numeric ( $price ) && is_numeric ( $redemption ))
    {
      if (($price <= 0) || ($redemption <= 0))
      {
        return PHPExcel_Calculation_Functions::NaN ();
      }
      $daysPerYear = self::daysPerYear ( PHPExcel_Calculation_DateTime::YEAR ( $settlement ), $basis );
      if (! is_numeric ( $daysPerYear ))
      {
        return $daysPerYear;
      }
      $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC ( $settlement, $maturity, $basis );
      if (! is_numeric ( $daysBetweenSettlementAndMaturity ))
      {
        // return date error
        return $daysBetweenSettlementAndMaturity;
      }
      $daysBetweenSettlementAndMaturity *= $daysPerYear;
      
      return (($redemption - $price) / $price) * ($daysPerYear / $daysBetweenSettlementAndMaturity);
    }
    return PHPExcel_Calculation_Functions::VALUE ();
  }
  
  /**
   * YIELDMAT
   *
   * Returns the annual yield of a security that pays interest at maturity.
   *
   * @param
   *          mixed settlement The security's settlement date.
   *          The security's settlement date is the date after the issue date when the security is traded to the buyer.
   * @param
   *          mixed maturity The security's maturity date.
   *          The maturity date is the date when the security expires.
   * @param
   *          mixed issue The security's issue date.
   * @param
   *          int rate The security's interest rate at date of issue.
   * @param
   *          int price The security's price per $100 face value.
   * @param
   *          int basis The type of day count to use.
   *          0 or omitted US (NASD) 30/360
   *          1 Actual/actual
   *          2 Actual/360
   *          3 Actual/365
   *          4 European 30/360
   * @return float
   */
  public static function YIELDMAT($settlement, $maturity, $issue, $rate, $price, $basis = 0)
  {
    $settlement = PHPExcel_Calculation_Functions::flattenSingleValue ( $settlement );
    $maturity = PHPExcel_Calculation_Functions::flattenSingleValue ( $maturity );
    $issue = PHPExcel_Calculation_Functions::flattenSingleValue ( $issue );
    $rate = PHPExcel_Calculation_Functions::flattenSingleValue ( $rate );
    $price = PHPExcel_Calculation_Functions::flattenSingleValue ( $price );
    $basis = ( int ) PHPExcel_Calculation_Functions::flattenSingleValue ( $basis );
    
    // Validate
    if (is_numeric ( $rate ) && is_numeric ( $price ))
    {
      if (($rate <= 0) || ($price <= 0))
      {
        return PHPExcel_Calculation_Functions::NaN ();
      }
      $daysPerYear = self::daysPerYear ( PHPExcel_Calculation_DateTime::YEAR ( $settlement ), $basis );
      if (! is_numeric ( $daysPerYear ))
      {
        return $daysPerYear;
      }
      $daysBetweenIssueAndSettlement = PHPExcel_Calculation_DateTime::YEARFRAC ( $issue, $settlement, $basis );
      if (! is_numeric ( $daysBetweenIssueAndSettlement ))
      {
        // return date error
        return $daysBetweenIssueAndSettlement;
      }
      $daysBetweenIssueAndSettlement *= $daysPerYear;
      $daysBetweenIssueAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC ( $issue, $maturity, $basis );
      if (! is_numeric ( $daysBetweenIssueAndMaturity ))
      {
        // return date error
        return $daysBetweenIssueAndMaturity;
      }
      $daysBetweenIssueAndMaturity *= $daysPerYear;
      $daysBetweenSettlementAndMaturity = PHPExcel_Calculation_DateTime::YEARFRAC ( $settlement, $maturity, $basis );
      if (! is_numeric ( $daysBetweenSettlementAndMaturity ))
      {
        // return date error
        return $daysBetweenSettlementAndMaturity;
      }
      $daysBetweenSettlementAndMaturity *= $daysPerYear;
      
      return ((1 + (($daysBetweenIssueAndMaturity / $daysPerYear) * $rate) - (($price / 100) + (($daysBetweenIssueAndSettlement / $daysPerYear) * $rate))) / (($price / 100) + (($daysBetweenIssueAndSettlement / $daysPerYear) * $rate))) * ($daysPerYear / $daysBetweenSettlementAndMaturity);
    }
    return PHPExcel_Calculation_Functions::VALUE ();
  }
}
