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Differences Between: [Versions 400 and 401] [Versions 400 and 402] [Versions 400 and 403]

   1  <?php
   2  
   3  namespace PhpOffice\PhpSpreadsheet\Calculation\Engineering;
   4  
   5  use PhpOffice\PhpSpreadsheet\Calculation\Exception;
   6  use PhpOffice\PhpSpreadsheet\Calculation\Functions;
   7  
   8  class BesselY
   9  {
  10      /**
  11       * BESSELY.
  12       *
  13       * Returns the Bessel function, which is also called the Weber function or the Neumann function.
  14       *
  15       *    Excel Function:
  16       *        BESSELY(x,ord)
  17       *
  18       * @param mixed $x A float value at which to evaluate the function.
  19       *                   If x is nonnumeric, BESSELY returns the #VALUE! error value.
  20       * @param mixed $ord The integer order of the Bessel function.
  21       *                       If ord is not an integer, it is truncated.
  22       *                       If $ord is nonnumeric, BESSELY returns the #VALUE! error value.
  23       *                       If $ord < 0, BESSELY returns the #NUM! error value.
  24       *
  25       * @return float|string Result, or a string containing an error
  26       */
  27      public static function BESSELY($x, $ord)
  28      {
  29          $x = Functions::flattenSingleValue($x);
  30          $ord = Functions::flattenSingleValue($ord);
  31  
  32          try {
  33              $x = EngineeringValidations::validateFloat($x);
  34              $ord = EngineeringValidations::validateInt($ord);
  35          } catch (Exception $e) {
  36              return $e->getMessage();
  37          }
  38  
  39          if (($ord < 0) || ($x <= 0.0)) {
  40              return Functions::NAN();
  41          }
  42  
  43          $fBy = self::calculate($x, $ord);
  44  
  45          return (is_nan($fBy)) ? Functions::NAN() : $fBy;
  46      }
  47  
  48      private static function calculate(float $x, int $ord): float
  49      {
  50          // special cases
  51          switch ($ord) {
  52              case 0:
  53                  return self::besselY0($x);
  54              case 1:
  55                  return self::besselY1($x);
  56          }
  57  
  58          return self::besselY2($x, $ord);
  59      }
  60  
  61      private static function besselY0(float $x): float
  62      {
  63          if ($x < 8.0) {
  64              $y = ($x * $x);
  65              $ans1 = -2957821389.0 + $y * (7062834065.0 + $y * (-512359803.6 + $y * (10879881.29 + $y *
  66                              (-86327.92757 + $y * 228.4622733))));
  67              $ans2 = 40076544269.0 + $y * (745249964.8 + $y * (7189466.438 + $y *
  68                          (47447.26470 + $y * (226.1030244 + $y))));
  69  
  70              return $ans1 / $ans2 + 0.636619772 * BesselJ::BESSELJ($x, 0) * log($x);
  71          }
  72  
  73          $z = 8.0 / $x;
  74          $y = ($z * $z);
  75          $xx = $x - 0.785398164;
  76          $ans1 = 1 + $y * (-0.1098628627e-2 + $y * (0.2734510407e-4 + $y * (-0.2073370639e-5 + $y * 0.2093887211e-6)));
  77          $ans2 = -0.1562499995e-1 + $y * (0.1430488765e-3 + $y * (-0.6911147651e-5 + $y * (0.7621095161e-6 + $y *
  78                          (-0.934945152e-7))));
  79  
  80          return sqrt(0.636619772 / $x) * (sin($xx) * $ans1 + $z * cos($xx) * $ans2);
  81      }
  82  
  83      private static function besselY1(float $x): float
  84      {
  85          if ($x < 8.0) {
  86              $y = ($x * $x);
  87              $ans1 = $x * (-0.4900604943e13 + $y * (0.1275274390e13 + $y * (-0.5153438139e11 + $y *
  88                              (0.7349264551e9 + $y * (-0.4237922726e7 + $y * 0.8511937935e4)))));
  89              $ans2 = 0.2499580570e14 + $y * (0.4244419664e12 + $y * (0.3733650367e10 + $y * (0.2245904002e8 + $y *
  90                              (0.1020426050e6 + $y * (0.3549632885e3 + $y)))));
  91  
  92              return ($ans1 / $ans2) + 0.636619772 * (BesselJ::BESSELJ($x, 1) * log($x) - 1 / $x);
  93          }
  94  
  95          $z = 8.0 / $x;
  96          $y = $z * $z;
  97          $xx = $x - 2.356194491;
  98          $ans1 = 1.0 + $y * (0.183105e-2 + $y * (-0.3516396496e-4 + $y * (0.2457520174e-5 + $y * (-0.240337019e-6))));
  99          $ans2 = 0.04687499995 + $y * (-0.2002690873e-3 + $y * (0.8449199096e-5 + $y *
 100                      (-0.88228987e-6 + $y * 0.105787412e-6)));
 101  
 102          return sqrt(0.636619772 / $x) * (sin($xx) * $ans1 + $z * cos($xx) * $ans2);
 103      }
 104  
 105      private static function besselY2(float $x, int $ord): float
 106      {
 107          $fTox = 2.0 / $x;
 108          $fBym = self::besselY0($x);
 109          $fBy = self::besselY1($x);
 110          for ($n = 1; $n < $ord; ++$n) {
 111              $fByp = $n * $fTox * $fBy - $fBym;
 112              $fBym = $fBy;
 113              $fBy = $fByp;
 114          }
 115  
 116          return $fBy;
 117      }
 118  }