vendor/phpoffice/phpexcel/Classes/PHPExcel/Writer/Excel5/Parser.php

   1 <?php
   2 /**
   3  * PHPExcel
   4  *
   5  * Copyright (c) 2006 - 2014 PHPExcel
   6  *
   7  * This library is free software; you can redistribute it and/or
   8  * modify it under the terms of the GNU Lesser General Public
   9  * License as published by the Free Software Foundation; either
  10  * version 2.1 of the License, or (at your option) any later version.
  11  *
  12  * This library is distributed in the hope that it will be useful,
  13  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  14  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  15  * Lesser General Public License for more details.
  16  *
  17  * You should have received a copy of the GNU Lesser General Public
  18  * License along with this library; if not, write to the Free Software
  19  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  20  *
  21  * @category   PHPExcel
  22  * @package    PHPExcel_Writer_Excel5
  23  * @copyright  Copyright (c) 2006 - 2014 PHPExcel (http://www.codeplex.com/PHPExcel)
  24  * @license    http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
  25  * @version    ##VERSION##, ##DATE##
  26  */
  27
  28 // Original file header of PEAR::Spreadsheet_Excel_Writer_Parser (used as the base for this class):
  29 // -----------------------------------------------------------------------------------------
  30 // *  Class for parsing Excel formulas
  31 // *
  32 // *  License Information:
  33 // *
  34 // *    Spreadsheet_Excel_Writer:  A library for generating Excel Spreadsheets
  35 // *    Copyright (c) 2002-2003 Xavier Noguer xnoguer@rezebra.com
  36 // *
  37 // *    This library is free software; you can redistribute it and/or
  38 // *    modify it under the terms of the GNU Lesser General Public
  39 // *    License as published by the Free Software Foundation; either
  40 // *    version 2.1 of the License, or (at your option) any later version.
  41 // *
  42 // *    This library is distributed in the hope that it will be useful,
  43 // *    but WITHOUT ANY WARRANTY; without even the implied warranty of
  44 // *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  45 // *    Lesser General Public License for more details.
  46 // *
  47 // *    You should have received a copy of the GNU Lesser General Public
  48 // *    License along with this library; if not, write to the Free Software
  49 // *    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  50 // */
  51
  52
  53 /**
  54  * PHPExcel_Writer_Excel5_Parser
  55  *
  56  * @category   PHPExcel
  57  * @package    PHPExcel_Writer_Excel5
  58  * @copyright  Copyright (c) 2006 - 2014 PHPExcel (http://www.codeplex.com/PHPExcel)
  59  */
  60 class PHPExcel_Writer_Excel5_Parser
  61 {
  62         /**     Constants                               */
  63         // Sheet title in unquoted form
  64         // Invalid sheet title characters cannot occur in the sheet title:
  65         //              *:/\?[]
  66         // Moreover, there are valid sheet title characters that cannot occur in unquoted form (there may be more?)
  67         // +-% '^&<>=,;#()"{}
  68         const REGEX_SHEET_TITLE_UNQUOTED = '[^\*\:\/\\\\\?\[\]\+\-\% \\\'\^\&\<\>\=\,\;\#\(\)\"\{\}]+';
  69
  70         // Sheet title in quoted form (without surrounding quotes)
  71         // Invalid sheet title characters cannot occur in the sheet title:
  72         // *:/\?[]                                      (usual invalid sheet title characters)
  73         // Single quote is represented as a pair ''
  74         const REGEX_SHEET_TITLE_QUOTED = '(([^\*\:\/\\\\\?\[\]\\\'])+|(\\\'\\\')+)+';
  75
  76         /**
  77          * The index of the character we are currently looking at
  78          * @var integer
  79          */
  80         public $_current_char;
  81
  82         /**
  83          * The token we are working on.
  84          * @var string
  85          */
  86         public $_current_token;
  87
  88         /**
  89          * The formula to parse
  90          * @var string
  91          */
  92         public $_formula;
  93
  94         /**
  95          * The character ahead of the current char
  96          * @var string
  97          */
  98         public $_lookahead;
  99
 100         /**
 101          * The parse tree to be generated
 102          * @var string
 103          */
 104         public $_parse_tree;
 105
 106         /**
 107          * Array of external sheets
 108          * @var array
 109          */
 110         public $_ext_sheets;
 111
 112         /**
 113          * Array of sheet references in the form of REF structures
 114          * @var array
 115          */
 116         public $_references;
 117
 118         /**
 119          * The class constructor
 120          *
 121          */
 122         public function __construct()
 123         {
 124                 $this->_current_char  = 0;
 125                 $this->_current_token = '';       // The token we are working on.
 126                 $this->_formula       = '';       // The formula to parse.
 127                 $this->_lookahead     = '';       // The character ahead of the current char.
 128                 $this->_parse_tree    = '';       // The parse tree to be generated.
 129                 $this->_initializeHashes();      // Initialize the hashes: ptg's and function's ptg's
 130                 $this->_ext_sheets = array();
 131                 $this->_references = array();
 132         }
 133
 134         /**
 135          * Initialize the ptg and function hashes.
 136          *
 137          * @access private
 138          */
 139         function _initializeHashes()
 140         {
 141                 // The Excel ptg indices
 142                 $this->ptg = array(
 143                         'ptgExp'       => 0x01,
 144                         'ptgTbl'       => 0x02,
 145                         'ptgAdd'       => 0x03,
 146                         'ptgSub'       => 0x04,
 147                         'ptgMul'       => 0x05,
 148                         'ptgDiv'       => 0x06,
 149                         'ptgPower'     => 0x07,
 150                         'ptgConcat'    => 0x08,
 151                         'ptgLT'        => 0x09,
 152                         'ptgLE'        => 0x0A,
 153                         'ptgEQ'        => 0x0B,
 154                         'ptgGE'        => 0x0C,
 155                         'ptgGT'        => 0x0D,
 156                         'ptgNE'        => 0x0E,
 157                         'ptgIsect'     => 0x0F,
 158                         'ptgUnion'     => 0x10,
 159                         'ptgRange'     => 0x11,
 160                         'ptgUplus'     => 0x12,
 161                         'ptgUminus'    => 0x13,
 162                         'ptgPercent'   => 0x14,
 163                         'ptgParen'     => 0x15,
 164                         'ptgMissArg'   => 0x16,
 165                         'ptgStr'       => 0x17,
 166                         'ptgAttr'      => 0x19,
 167                         'ptgSheet'     => 0x1A,
 168                         'ptgEndSheet'  => 0x1B,
 169                         'ptgErr'       => 0x1C,
 170                         'ptgBool'      => 0x1D,
 171                         'ptgInt'       => 0x1E,
 172                         'ptgNum'       => 0x1F,
 173                         'ptgArray'     => 0x20,
 174                         'ptgFunc'      => 0x21,
 175                         'ptgFuncVar'   => 0x22,
 176                         'ptgName'      => 0x23,
 177                         'ptgRef'       => 0x24,
 178                         'ptgArea'      => 0x25,
 179                         'ptgMemArea'   => 0x26,
 180                         'ptgMemErr'    => 0x27,
 181                         'ptgMemNoMem'  => 0x28,
 182                         'ptgMemFunc'   => 0x29,
 183                         'ptgRefErr'    => 0x2A,
 184                         'ptgAreaErr'   => 0x2B,
 185                         'ptgRefN'      => 0x2C,
 186                         'ptgAreaN'     => 0x2D,
 187                         'ptgMemAreaN'  => 0x2E,
 188                         'ptgMemNoMemN' => 0x2F,
 189                         'ptgNameX'     => 0x39,
 190                         'ptgRef3d'     => 0x3A,
 191                         'ptgArea3d'    => 0x3B,
 192                         'ptgRefErr3d'  => 0x3C,
 193                         'ptgAreaErr3d' => 0x3D,
 194                         'ptgArrayV'    => 0x40,
 195                         'ptgFuncV'     => 0x41,
 196                         'ptgFuncVarV'  => 0x42,
 197                         'ptgNameV'     => 0x43,
 198                         'ptgRefV'      => 0x44,
 199                         'ptgAreaV'     => 0x45,
 200                         'ptgMemAreaV'  => 0x46,
 201                         'ptgMemErrV'   => 0x47,
 202                         'ptgMemNoMemV' => 0x48,
 203                         'ptgMemFuncV'  => 0x49,
 204                         'ptgRefErrV'   => 0x4A,
 205                         'ptgAreaErrV'  => 0x4B,
 206                         'ptgRefNV'     => 0x4C,
 207                         'ptgAreaNV'    => 0x4D,
 208                         'ptgMemAreaNV' => 0x4E,
 209                         'ptgMemNoMemN' => 0x4F,
 210                         'ptgFuncCEV'   => 0x58,
 211                         'ptgNameXV'    => 0x59,
 212                         'ptgRef3dV'    => 0x5A,
 213                         'ptgArea3dV'   => 0x5B,
 214                         'ptgRefErr3dV' => 0x5C,
 215                         'ptgAreaErr3d' => 0x5D,
 216                         'ptgArrayA'    => 0x60,
 217                         'ptgFuncA'     => 0x61,
 218                         'ptgFuncVarA'  => 0x62,
 219                         'ptgNameA'     => 0x63,
 220                         'ptgRefA'      => 0x64,
 221                         'ptgAreaA'     => 0x65,
 222                         'ptgMemAreaA'  => 0x66,
 223                         'ptgMemErrA'   => 0x67,
 224                         'ptgMemNoMemA' => 0x68,
 225                         'ptgMemFuncA'  => 0x69,
 226                         'ptgRefErrA'   => 0x6A,
 227                         'ptgAreaErrA'  => 0x6B,
 228                         'ptgRefNA'     => 0x6C,
 229                         'ptgAreaNA'    => 0x6D,
 230                         'ptgMemAreaNA' => 0x6E,
 231                         'ptgMemNoMemN' => 0x6F,
 232                         'ptgFuncCEA'   => 0x78,
 233                         'ptgNameXA'    => 0x79,
 234                         'ptgRef3dA'    => 0x7A,
 235                         'ptgArea3dA'   => 0x7B,
 236                         'ptgRefErr3dA' => 0x7C,
 237                         'ptgAreaErr3d' => 0x7D
 238                         );
 239
 240                 // Thanks to Michael Meeks and Gnumeric for the initial arg values.
 241                 //
 242                 // The following hash was generated by "function_locale.pl" in the distro.
 243                 // Refer to function_locale.pl for non-English function names.
 244                 //
 245                 // The array elements are as follow:
 246                 // ptg:   The Excel function ptg code.
 247                 // args:  The number of arguments that the function takes:
 248                 //           >=0 is a fixed number of arguments.
 249                 //           -1  is a variable  number of arguments.
 250                 // class: The reference, value or array class of the function args.
 251                 // vol:   The function is volatile.
 252                 //
 253                 $this->_functions = array(
 254                           // function                  ptg  args  class  vol
 255                           'COUNT'           => array(   0,   -1,    0,    0 ),
 256                           'IF'              => array(   1,   -1,    1,    0 ),
 257                           'ISNA'            => array(   2,    1,    1,    0 ),
 258                           'ISERROR'         => array(   3,    1,    1,    0 ),
 259                           'SUM'             => array(   4,   -1,    0,    0 ),
 260                           'AVERAGE'         => array(   5,   -1,    0,    0 ),
 261                           'MIN'             => array(   6,   -1,    0,    0 ),
 262                           'MAX'             => array(   7,   -1,    0,    0 ),
 263                           'ROW'             => array(   8,   -1,    0,    0 ),
 264                           'COLUMN'          => array(   9,   -1,    0,    0 ),
 265                           'NA'              => array(  10,    0,    0,    0 ),
 266                           'NPV'             => array(  11,   -1,    1,    0 ),
 267                           'STDEV'           => array(  12,   -1,    0,    0 ),
 268                           'DOLLAR'          => array(  13,   -1,    1,    0 ),
 269                           'FIXED'           => array(  14,   -1,    1,    0 ),
 270                           'SIN'             => array(  15,    1,    1,    0 ),
 271                           'COS'             => array(  16,    1,    1,    0 ),
 272                           'TAN'             => array(  17,    1,    1,    0 ),
 273                           'ATAN'            => array(  18,    1,    1,    0 ),
 274                           'PI'              => array(  19,    0,    1,    0 ),
 275                           'SQRT'            => array(  20,    1,    1,    0 ),
 276                           'EXP'             => array(  21,    1,    1,    0 ),
 277                           'LN'              => array(  22,    1,    1,    0 ),
 278                           'LOG10'           => array(  23,    1,    1,    0 ),
 279                           'ABS'             => array(  24,    1,    1,    0 ),
 280                           'INT'             => array(  25,    1,    1,    0 ),
 281                           'SIGN'            => array(  26,    1,    1,    0 ),
 282                           'ROUND'           => array(  27,    2,    1,    0 ),
 283                           'LOOKUP'          => array(  28,   -1,    0,    0 ),
 284                           'INDEX'           => array(  29,   -1,    0,    1 ),
 285                           'REPT'            => array(  30,    2,    1,    0 ),
 286                           'MID'             => array(  31,    3,    1,    0 ),
 287                           'LEN'             => array(  32,    1,    1,    0 ),
 288                           'VALUE'           => array(  33,    1,    1,    0 ),
 289                           'TRUE'            => array(  34,    0,    1,    0 ),
 290                           'FALSE'           => array(  35,    0,    1,    0 ),
 291                           'AND'             => array(  36,   -1,    0,    0 ),
 292                           'OR'              => array(  37,   -1,    0,    0 ),
 293                           'NOT'             => array(  38,    1,    1,    0 ),
 294                           'MOD'             => array(  39,    2,    1,    0 ),
 295                           'DCOUNT'          => array(  40,    3,    0,    0 ),
 296                           'DSUM'            => array(  41,    3,    0,    0 ),
 297                           'DAVERAGE'        => array(  42,    3,    0,    0 ),
 298                           'DMIN'            => array(  43,    3,    0,    0 ),
 299                           'DMAX'            => array(  44,    3,    0,    0 ),
 300                           'DSTDEV'          => array(  45,    3,    0,    0 ),
 301                           'VAR'             => array(  46,   -1,    0,    0 ),
 302                           'DVAR'            => array(  47,    3,    0,    0 ),
 303                           'TEXT'            => array(  48,    2,    1,    0 ),
 304                           'LINEST'          => array(  49,   -1,    0,    0 ),
 305                           'TREND'           => array(  50,   -1,    0,    0 ),
 306                           'LOGEST'          => array(  51,   -1,    0,    0 ),
 307                           'GROWTH'          => array(  52,   -1,    0,    0 ),
 308                           'PV'              => array(  56,   -1,    1,    0 ),
 309                           'FV'              => array(  57,   -1,    1,    0 ),
 310                           'NPER'            => array(  58,   -1,    1,    0 ),
 311                           'PMT'             => array(  59,   -1,    1,    0 ),
 312                           'RATE'            => array(  60,   -1,    1,    0 ),
 313                           'MIRR'            => array(  61,    3,    0,    0 ),
 314                           'IRR'             => array(  62,   -1,    0,    0 ),
 315                           'RAND'            => array(  63,    0,    1,    1 ),
 316                           'MATCH'           => array(  64,   -1,    0,    0 ),
 317                           'DATE'            => array(  65,    3,    1,    0 ),
 318                           'TIME'            => array(  66,    3,    1,    0 ),
 319                           'DAY'             => array(  67,    1,    1,    0 ),
 320                           'MONTH'           => array(  68,    1,    1,    0 ),
 321                           'YEAR'            => array(  69,    1,    1,    0 ),
 322                           'WEEKDAY'         => array(  70,   -1,    1,    0 ),
 323                           'HOUR'            => array(  71,    1,    1,    0 ),
 324                           'MINUTE'          => array(  72,    1,    1,    0 ),
 325                           'SECOND'          => array(  73,    1,    1,    0 ),
 326                           'NOW'             => array(  74,    0,    1,    1 ),
 327                           'AREAS'           => array(  75,    1,    0,    1 ),
 328                           'ROWS'            => array(  76,    1,    0,    1 ),
 329                           'COLUMNS'         => array(  77,    1,    0,    1 ),
 330                           'OFFSET'          => array(  78,   -1,    0,    1 ),
 331                           'SEARCH'          => array(  82,   -1,    1,    0 ),
 332                           'TRANSPOSE'       => array(  83,    1,    1,    0 ),
 333                           'TYPE'            => array(  86,    1,    1,    0 ),
 334                           'ATAN2'           => array(  97,    2,    1,    0 ),
 335                           'ASIN'            => array(  98,    1,    1,    0 ),
 336                           'ACOS'            => array(  99,    1,    1,    0 ),
 337                           'CHOOSE'          => array( 100,   -1,    1,    0 ),
 338                           'HLOOKUP'         => array( 101,   -1,    0,    0 ),
 339                           'VLOOKUP'         => array( 102,   -1,    0,    0 ),
 340                           'ISREF'           => array( 105,    1,    0,    0 ),
 341                           'LOG'             => array( 109,   -1,    1,    0 ),
 342                           'CHAR'            => array( 111,    1,    1,    0 ),
 343                           'LOWER'           => array( 112,    1,    1,    0 ),
 344                           'UPPER'           => array( 113,    1,    1,    0 ),
 345                           'PROPER'          => array( 114,    1,    1,    0 ),
 346                           'LEFT'            => array( 115,   -1,    1,    0 ),
 347                           'RIGHT'           => array( 116,   -1,    1,    0 ),
 348                           'EXACT'           => array( 117,    2,    1,    0 ),
 349                           'TRIM'            => array( 118,    1,    1,    0 ),
 350                           'REPLACE'         => array( 119,    4,    1,    0 ),
 351                           'SUBSTITUTE'      => array( 120,   -1,    1,    0 ),
 352                           'CODE'            => array( 121,    1,    1,    0 ),
 353                           'FIND'            => array( 124,   -1,    1,    0 ),
 354                           'CELL'            => array( 125,   -1,    0,    1 ),
 355                           'ISERR'           => array( 126,    1,    1,    0 ),
 356                           'ISTEXT'          => array( 127,    1,    1,    0 ),
 357                           'ISNUMBER'        => array( 128,    1,    1,    0 ),
 358                           'ISBLANK'         => array( 129,    1,    1,    0 ),
 359                           'T'               => array( 130,    1,    0,    0 ),
 360                           'N'               => array( 131,    1,    0,    0 ),
 361                           'DATEVALUE'       => array( 140,    1,    1,    0 ),
 362                           'TIMEVALUE'       => array( 141,    1,    1,    0 ),
 363                           'SLN'             => array( 142,    3,    1,    0 ),
 364                           'SYD'             => array( 143,    4,    1,    0 ),
 365                           'DDB'             => array( 144,   -1,    1,    0 ),
 366                           'INDIRECT'        => array( 148,   -1,    1,    1 ),
 367                           'CALL'            => array( 150,   -1,    1,    0 ),
 368                           'CLEAN'           => array( 162,    1,    1,    0 ),
 369                           'MDETERM'         => array( 163,    1,    2,    0 ),
 370                           'MINVERSE'        => array( 164,    1,    2,    0 ),
 371                           'MMULT'           => array( 165,    2,    2,    0 ),
 372                           'IPMT'            => array( 167,   -1,    1,    0 ),
 373                           'PPMT'            => array( 168,   -1,    1,    0 ),
 374                           'COUNTA'          => array( 169,   -1,    0,    0 ),
 375                           'PRODUCT'         => array( 183,   -1,    0,    0 ),
 376                           'FACT'            => array( 184,    1,    1,    0 ),
 377                           'DPRODUCT'        => array( 189,    3,    0,    0 ),
 378                           'ISNONTEXT'       => array( 190,    1,    1,    0 ),
 379                           'STDEVP'          => array( 193,   -1,    0,    0 ),
 380                           'VARP'            => array( 194,   -1,    0,    0 ),
 381                           'DSTDEVP'         => array( 195,    3,    0,    0 ),
 382                           'DVARP'           => array( 196,    3,    0,    0 ),
 383                           'TRUNC'           => array( 197,   -1,    1,    0 ),
 384                           'ISLOGICAL'       => array( 198,    1,    1,    0 ),
 385                           'DCOUNTA'         => array( 199,    3,    0,    0 ),
 386                           'USDOLLAR'        => array( 204,   -1,    1,    0 ),
 387                           'FINDB'           => array( 205,   -1,    1,    0 ),
 388                           'SEARCHB'         => array( 206,   -1,    1,    0 ),
 389                           'REPLACEB'        => array( 207,    4,    1,    0 ),
 390                           'LEFTB'           => array( 208,   -1,    1,    0 ),
 391                           'RIGHTB'          => array( 209,   -1,    1,    0 ),
 392                           'MIDB'            => array( 210,    3,    1,    0 ),
 393                           'LENB'            => array( 211,    1,    1,    0 ),
 394                           'ROUNDUP'         => array( 212,    2,    1,    0 ),
 395                           'ROUNDDOWN'       => array( 213,    2,    1,    0 ),
 396                           'ASC'             => array( 214,    1,    1,    0 ),
 397                           'DBCS'            => array( 215,    1,    1,    0 ),
 398                           'RANK'            => array( 216,   -1,    0,    0 ),
 399                           'ADDRESS'         => array( 219,   -1,    1,    0 ),
 400                           'DAYS360'         => array( 220,   -1,    1,    0 ),
 401                           'TODAY'           => array( 221,    0,    1,    1 ),
 402                           'VDB'             => array( 222,   -1,    1,    0 ),
 403                           'MEDIAN'          => array( 227,   -1,    0,    0 ),
 404                           'SUMPRODUCT'      => array( 228,   -1,    2,    0 ),
 405                           'SINH'            => array( 229,    1,    1,    0 ),
 406                           'COSH'            => array( 230,    1,    1,    0 ),
 407                           'TANH'            => array( 231,    1,    1,    0 ),
 408                           'ASINH'           => array( 232,    1,    1,    0 ),
 409                           'ACOSH'           => array( 233,    1,    1,    0 ),
 410                           'ATANH'           => array( 234,    1,    1,    0 ),
 411                           'DGET'            => array( 235,    3,    0,    0 ),
 412                           'INFO'            => array( 244,    1,    1,    1 ),
 413                           'DB'              => array( 247,   -1,    1,    0 ),
 414                           'FREQUENCY'       => array( 252,    2,    0,    0 ),
 415                           'ERROR.TYPE'      => array( 261,    1,    1,    0 ),
 416                           'REGISTER.ID'     => array( 267,   -1,    1,    0 ),
 417                           'AVEDEV'          => array( 269,   -1,    0,    0 ),
 418                           'BETADIST'        => array( 270,   -1,    1,    0 ),
 419                           'GAMMALN'         => array( 271,    1,    1,    0 ),
 420                           'BETAINV'         => array( 272,   -1,    1,    0 ),
 421                           'BINOMDIST'       => array( 273,    4,    1,    0 ),
 422                           'CHIDIST'         => array( 274,    2,    1,    0 ),
 423                           'CHIINV'          => array( 275,    2,    1,    0 ),
 424                           'COMBIN'          => array( 276,    2,    1,    0 ),
 425                           'CONFIDENCE'      => array( 277,    3,    1,    0 ),
 426                           'CRITBINOM'       => array( 278,    3,    1,    0 ),
 427                           'EVEN'            => array( 279,    1,    1,    0 ),
 428                           'EXPONDIST'       => array( 280,    3,    1,    0 ),
 429                           'FDIST'           => array( 281,    3,    1,    0 ),
 430                           'FINV'            => array( 282,    3,    1,    0 ),
 431                           'FISHER'          => array( 283,    1,    1,    0 ),
 432                           'FISHERINV'       => array( 284,    1,    1,    0 ),
 433                           'FLOOR'           => array( 285,    2,    1,    0 ),
 434                           'GAMMADIST'       => array( 286,    4,    1,    0 ),
 435                           'GAMMAINV'        => array( 287,    3,    1,    0 ),
 436                           'CEILING'         => array( 288,    2,    1,    0 ),
 437                           'HYPGEOMDIST'     => array( 289,    4,    1,    0 ),
 438                           'LOGNORMDIST'     => array( 290,    3,    1,    0 ),
 439                           'LOGINV'          => array( 291,    3,    1,    0 ),
 440                           'NEGBINOMDIST'    => array( 292,    3,    1,    0 ),
 441                           'NORMDIST'        => array( 293,    4,    1,    0 ),
 442                           'NORMSDIST'       => array( 294,    1,    1,    0 ),
 443                           'NORMINV'         => array( 295,    3,    1,    0 ),
 444                           'NORMSINV'        => array( 296,    1,    1,    0 ),
 445                           'STANDARDIZE'     => array( 297,    3,    1,    0 ),
 446                           'ODD'             => array( 298,    1,    1,    0 ),
 447                           'PERMUT'          => array( 299,    2,    1,    0 ),
 448                           'POISSON'         => array( 300,    3,    1,    0 ),
 449                           'TDIST'           => array( 301,    3,    1,    0 ),
 450                           'WEIBULL'         => array( 302,    4,    1,    0 ),
 451                           'SUMXMY2'         => array( 303,    2,    2,    0 ),
 452                           'SUMX2MY2'        => array( 304,    2,    2,    0 ),
 453                           'SUMX2PY2'        => array( 305,    2,    2,    0 ),
 454                           'CHITEST'         => array( 306,    2,    2,    0 ),
 455                           'CORREL'          => array( 307,    2,    2,    0 ),
 456                           'COVAR'           => array( 308,    2,    2,    0 ),
 457                           'FORECAST'        => array( 309,    3,    2,    0 ),
 458                           'FTEST'           => array( 310,    2,    2,    0 ),
 459                           'INTERCEPT'       => array( 311,    2,    2,    0 ),
 460                           'PEARSON'         => array( 312,    2,    2,    0 ),
 461                           'RSQ'             => array( 313,    2,    2,    0 ),
 462                           'STEYX'           => array( 314,    2,    2,    0 ),
 463                           'SLOPE'           => array( 315,    2,    2,    0 ),
 464                           'TTEST'           => array( 316,    4,    2,    0 ),
 465                           'PROB'            => array( 317,   -1,    2,    0 ),
 466                           'DEVSQ'           => array( 318,   -1,    0,    0 ),
 467                           'GEOMEAN'         => array( 319,   -1,    0,    0 ),
 468                           'HARMEAN'         => array( 320,   -1,    0,    0 ),
 469                           'SUMSQ'           => array( 321,   -1,    0,    0 ),
 470                           'KURT'            => array( 322,   -1,    0,    0 ),
 471                           'SKEW'            => array( 323,   -1,    0,    0 ),
 472                           'ZTEST'           => array( 324,   -1,    0,    0 ),
 473                           'LARGE'           => array( 325,    2,    0,    0 ),
 474                           'SMALL'           => array( 326,    2,    0,    0 ),
 475                           'QUARTILE'        => array( 327,    2,    0,    0 ),
 476                           'PERCENTILE'      => array( 328,    2,    0,    0 ),
 477                           'PERCENTRANK'     => array( 329,   -1,    0,    0 ),
 478                           'MODE'            => array( 330,   -1,    2,    0 ),
 479                           'TRIMMEAN'        => array( 331,    2,    0,    0 ),
 480                           'TINV'            => array( 332,    2,    1,    0 ),
 481                           'CONCATENATE'     => array( 336,   -1,    1,    0 ),
 482                           'POWER'           => array( 337,    2,    1,    0 ),
 483                           'RADIANS'         => array( 342,    1,    1,    0 ),
 484                           'DEGREES'         => array( 343,    1,    1,    0 ),
 485                           'SUBTOTAL'        => array( 344,   -1,    0,    0 ),
 486                           'SUMIF'           => array( 345,   -1,    0,    0 ),
 487                           'COUNTIF'         => array( 346,    2,    0,    0 ),
 488                           'COUNTBLANK'      => array( 347,    1,    0,    0 ),
 489                           'ISPMT'           => array( 350,    4,    1,    0 ),
 490                           'DATEDIF'         => array( 351,    3,    1,    0 ),
 491                           'DATESTRING'      => array( 352,    1,    1,    0 ),
 492                           'NUMBERSTRING'    => array( 353,    2,    1,    0 ),
 493                           'ROMAN'           => array( 354,   -1,    1,    0 ),
 494                           'GETPIVOTDATA'    => array( 358,   -1,    0,    0 ),
 495                           'HYPERLINK'       => array( 359,   -1,    1,    0 ),
 496                           'PHONETIC'        => array( 360,    1,    0,    0 ),
 497                           'AVERAGEA'        => array( 361,   -1,    0,    0 ),
 498                           'MAXA'            => array( 362,   -1,    0,    0 ),
 499                           'MINA'            => array( 363,   -1,    0,    0 ),
 500                           'STDEVPA'         => array( 364,   -1,    0,    0 ),
 501                           'VARPA'           => array( 365,   -1,    0,    0 ),
 502                           'STDEVA'          => array( 366,   -1,    0,    0 ),
 503                           'VARA'            => array( 367,   -1,    0,    0 ),
 504                           'BAHTTEXT'        => array( 368,    1,    0,    0 ),
 505                           );
 506         }
 507
 508         /**
 509          * Convert a token to the proper ptg value.
 510          *
 511          * @access private
 512          * @param mixed $token The token to convert.
 513          * @return mixed the converted token on success
 514          */
 515         function _convert($token)
 516         {
 517                 if (preg_match("/\"([^\"]|\"\"){0,255}\"/", $token)) {
 518                         return $this->_convertString($token);
 519
 520                 } elseif (is_numeric($token)) {
 521                         return $this->_convertNumber($token);
 522
 523                 // match references like A1 or $A$1
 524                 } elseif (preg_match('/^\$?([A-Ia-i]?[A-Za-z])\$?(\d+)$/',$token)) {
 525                         return $this->_convertRef2d($token);
 526
 527                 // match external references like Sheet1!A1 or Sheet1:Sheet2!A1 or Sheet1!$A$1 or Sheet1:Sheet2!$A$1
 528                 } elseif (preg_match("/^" . self::REGEX_SHEET_TITLE_UNQUOTED . "(\:" . self::REGEX_SHEET_TITLE_UNQUOTED . ")?\!\\$?[A-Ia-i]?[A-Za-z]\\$?(\d+)$/u",$token)) {
 529                         return $this->_convertRef3d($token);
 530
 531                 // match external references like 'Sheet1'!A1 or 'Sheet1:Sheet2'!A1 or 'Sheet1'!$A$1 or 'Sheet1:Sheet2'!$A$1
 532                 } elseif (preg_match("/^'" . self::REGEX_SHEET_TITLE_QUOTED . "(\:" . self::REGEX_SHEET_TITLE_QUOTED . ")?'\!\\$?[A-Ia-i]?[A-Za-z]\\$?(\d+)$/u",$token)) {
 533                         return $this->_convertRef3d($token);
 534
 535                 // match ranges like A1:B2 or $A$1:$B$2
 536                 } elseif (preg_match('/^(\$)?[A-Ia-i]?[A-Za-z](\$)?(\d+)\:(\$)?[A-Ia-i]?[A-Za-z](\$)?(\d+)$/', $token)) {
 537                         return $this->_convertRange2d($token);
 538
 539                 // match external ranges like Sheet1!A1:B2 or Sheet1:Sheet2!A1:B2 or Sheet1!$A$1:$B$2 or Sheet1:Sheet2!$A$1:$B$2
 540                 } elseif (preg_match("/^" . self::REGEX_SHEET_TITLE_UNQUOTED . "(\:" . self::REGEX_SHEET_TITLE_UNQUOTED . ")?\!\\$?([A-Ia-i]?[A-Za-z])?\\$?(\d+)\:\\$?([A-Ia-i]?[A-Za-z])?\\$?(\d+)$/u",$token)) {
 541                         return $this->_convertRange3d($token);
 542
 543                 // match external ranges like 'Sheet1'!A1:B2 or 'Sheet1:Sheet2'!A1:B2 or 'Sheet1'!$A$1:$B$2 or 'Sheet1:Sheet2'!$A$1:$B$2
 544                 } elseif (preg_match("/^'" . self::REGEX_SHEET_TITLE_QUOTED . "(\:" . self::REGEX_SHEET_TITLE_QUOTED . ")?'\!\\$?([A-Ia-i]?[A-Za-z])?\\$?(\d+)\:\\$?([A-Ia-i]?[A-Za-z])?\\$?(\d+)$/u",$token)) {
 545                         return $this->_convertRange3d($token);
 546
 547                 // operators (including parentheses)
 548                 } elseif (isset($this->ptg[$token])) {
 549                         return pack("C", $this->ptg[$token]);
 550
 551         // match error codes
 552                 } elseif (preg_match("/^#[A-Z0\/]{3,5}[!?]{1}$/", $token) or $token == '#N/A') {
 553                     return $this->_convertError($token);
 554
 555                 // commented so argument number can be processed correctly. See toReversePolish().
 556                 /*elseif (preg_match("/[A-Z0-9\xc0-\xdc\.]+/",$token))
 557                 {
 558                         return($this->_convertFunction($token,$this->_func_args));
 559                 }*/
 560
 561                 // if it's an argument, ignore the token (the argument remains)
 562                 } elseif ($token == 'arg') {
 563                         return '';
 564                 }
 565
 566                 // TODO: use real error codes
 567                 throw new PHPExcel_Writer_Exception("Unknown token $token");
 568         }
 569
 570         /**
 571          * Convert a number token to ptgInt or ptgNum
 572          *
 573          * @access private
 574          * @param mixed $num an integer or double for conversion to its ptg value
 575          */
 576         function _convertNumber($num)
 577         {
 578                 // Integer in the range 0..2**16-1
 579                 if ((preg_match("/^\d+$/", $num)) and ($num <= 65535)) {
 580                         return pack("Cv", $this->ptg['ptgInt'], $num);
 581                 } else { // A float
 582                         if (PHPExcel_Writer_Excel5_BIFFwriter::getByteOrder()) { // if it's Big Endian
 583                                 $num = strrev($num);
 584                         }
 585                         return pack("Cd", $this->ptg['ptgNum'], $num);
 586                 }
 587         }
 588
 589         /**
 590          * Convert a string token to ptgStr
 591          *
 592          * @access private
 593          * @param string $string A string for conversion to its ptg value.
 594          * @return mixed the converted token on success
 595          */
 596         function _convertString($string)
 597         {
 598                 // chop away beggining and ending quotes
 599                 $string = substr($string, 1, strlen($string) - 2);
 600                 if (strlen($string) > 255) {
 601                         throw new PHPExcel_Writer_Exception("String is too long");
 602                 }
 603
 604                 return pack('C', $this->ptg['ptgStr']) . PHPExcel_Shared_String::UTF8toBIFF8UnicodeShort($string);
 605         }
 606
 607         /**
 608          * Convert a function to a ptgFunc or ptgFuncVarV depending on the number of
 609          * args that it takes.
 610          *
 611          * @access private
 612          * @param string  $token    The name of the function for convertion to ptg value.
 613          * @param integer $num_args The number of arguments the function receives.
 614          * @return string The packed ptg for the function
 615          */
 616         function _convertFunction($token, $num_args)
 617         {
 618                 $args     = $this->_functions[$token][1];
 619 //              $volatile = $this->_functions[$token][3];
 620
 621                 // Fixed number of args eg. TIME($i,$j,$k).
 622                 if ($args >= 0) {
 623                         return pack("Cv", $this->ptg['ptgFuncV'], $this->_functions[$token][0]);
 624                 }
 625                 // Variable number of args eg. SUM($i,$j,$k, ..).
 626                 if ($args == -1) {
 627                         return pack("CCv", $this->ptg['ptgFuncVarV'], $num_args, $this->_functions[$token][0]);
 628                 }
 629         }
 630
 631         /**
 632          * Convert an Excel range such as A1:D4 to a ptgRefV.
 633          *
 634          * @access private
 635          * @param string        $range  An Excel range in the A1:A2
 636          * @param int           $class
 637          */
 638         function _convertRange2d($range, $class=0)
 639         {
 640
 641                 // TODO: possible class value 0,1,2 check Formula.pm
 642                 // Split the range into 2 cell refs
 643                 if (preg_match('/^(\$)?([A-Ia-i]?[A-Za-z])(\$)?(\d+)\:(\$)?([A-Ia-i]?[A-Za-z])(\$)?(\d+)$/', $range)) {
 644                         list($cell1, $cell2) = explode(':', $range);
 645                 } else {
 646                         // TODO: use real error codes
 647                         throw new PHPExcel_Writer_Exception("Unknown range separator");
 648                 }
 649
 650                 // Convert the cell references
 651                 list($row1, $col1) = $this->_cellToPackedRowcol($cell1);
 652                 list($row2, $col2) = $this->_cellToPackedRowcol($cell2);
 653
 654                 // The ptg value depends on the class of the ptg.
 655                 if ($class == 0) {
 656                         $ptgArea = pack("C", $this->ptg['ptgArea']);
 657                 } elseif ($class == 1) {
 658                         $ptgArea = pack("C", $this->ptg['ptgAreaV']);
 659                 } elseif ($class == 2) {
 660                         $ptgArea = pack("C", $this->ptg['ptgAreaA']);
 661                 } else {
 662                         // TODO: use real error codes
 663                         throw new PHPExcel_Writer_Exception("Unknown class $class");
 664                 }
 665                 return $ptgArea . $row1 . $row2 . $col1. $col2;
 666         }
 667
 668         /**
 669          * Convert an Excel 3d range such as "Sheet1!A1:D4" or "Sheet1:Sheet2!A1:D4" to
 670          * a ptgArea3d.
 671          *
 672          * @access private
 673          * @param string $token An Excel range in the Sheet1!A1:A2 format.
 674          * @return mixed The packed ptgArea3d token on success.
 675          */
 676         function _convertRange3d($token)
 677         {
 678 //              $class = 0; // formulas like Sheet1!$A$1:$A$2 in list type data validation need this class (0x3B)
 679
 680                 // Split the ref at the ! symbol
 681                 list($ext_ref, $range) = explode('!', $token);
 682
 683                 // Convert the external reference part (different for BIFF8)
 684                 $ext_ref = $this->_getRefIndex($ext_ref);
 685
 686                 // Split the range into 2 cell refs
 687                 list($cell1, $cell2) = explode(':', $range);
 688
 689                 // Convert the cell references
 690                 if (preg_match("/^(\\$)?[A-Ia-i]?[A-Za-z](\\$)?(\d+)$/", $cell1)) {
 691                         list($row1, $col1) = $this->_cellToPackedRowcol($cell1);
 692                         list($row2, $col2) = $this->_cellToPackedRowcol($cell2);
 693                 } else { // It's a rows range (like 26:27)
 694                          list($row1, $col1, $row2, $col2) = $this->_rangeToPackedRange($cell1.':'.$cell2);
 695                 }
 696
 697                 // The ptg value depends on the class of the ptg.
 698 //              if ($class == 0) {
 699                         $ptgArea = pack("C", $this->ptg['ptgArea3d']);
 700 //              } elseif ($class == 1) {
 701 //                      $ptgArea = pack("C", $this->ptg['ptgArea3dV']);
 702 //              } elseif ($class == 2) {
 703 //                      $ptgArea = pack("C", $this->ptg['ptgArea3dA']);
 704 //              } else {
 705 //                      throw new PHPExcel_Writer_Exception("Unknown class $class");
 706 //              }
 707
 708                 return $ptgArea . $ext_ref . $row1 . $row2 . $col1. $col2;
 709         }
 710
 711         /**
 712          * Convert an Excel reference such as A1, $B2, C$3 or $D$4 to a ptgRefV.
 713          *
 714          * @access private
 715          * @param string $cell An Excel cell reference
 716          * @return string The cell in packed() format with the corresponding ptg
 717          */
 718         function _convertRef2d($cell)
 719         {
 720 //              $class = 2; // as far as I know, this is magick.
 721
 722                 // Convert the cell reference
 723                 $cell_array = $this->_cellToPackedRowcol($cell);
 724                 list($row, $col) = $cell_array;
 725
 726                 // The ptg value depends on the class of the ptg.
 727 //              if ($class == 0) {
 728 //                      $ptgRef = pack("C", $this->ptg['ptgRef']);
 729 //              } elseif ($class == 1) {
 730 //                      $ptgRef = pack("C", $this->ptg['ptgRefV']);
 731 //              } elseif ($class == 2) {
 732                         $ptgRef = pack("C", $this->ptg['ptgRefA']);
 733 //              } else {
 734 //                      // TODO: use real error codes
 735 //                      throw new PHPExcel_Writer_Exception("Unknown class $class");
 736 //              }
 737                 return $ptgRef.$row.$col;
 738         }
 739
 740         /**
 741          * Convert an Excel 3d reference such as "Sheet1!A1" or "Sheet1:Sheet2!A1" to a
 742          * ptgRef3d.
 743          *
 744          * @access private
 745          * @param string $cell An Excel cell reference
 746          * @return mixed The packed ptgRef3d token on success.
 747          */
 748         function _convertRef3d($cell)
 749         {
 750 //              $class = 2; // as far as I know, this is magick.
 751
 752                 // Split the ref at the ! symbol
 753                 list($ext_ref, $cell) = explode('!', $cell);
 754
 755                 // Convert the external reference part (different for BIFF8)
 756                 $ext_ref = $this->_getRefIndex($ext_ref);
 757
 758                 // Convert the cell reference part
 759                 list($row, $col) = $this->_cellToPackedRowcol($cell);
 760
 761                 // The ptg value depends on the class of the ptg.
 762 //              if ($class == 0) {
 763 //                      $ptgRef = pack("C", $this->ptg['ptgRef3d']);
 764 //              } elseif ($class == 1) {
 765 //                      $ptgRef = pack("C", $this->ptg['ptgRef3dV']);
 766 //              } elseif ($class == 2) {
 767                         $ptgRef = pack("C", $this->ptg['ptgRef3dA']);
 768 //              } else {
 769 //                      throw new PHPExcel_Writer_Exception("Unknown class $class");
 770 //              }
 771
 772                 return $ptgRef . $ext_ref. $row . $col;
 773         }
 774
 775     /**
 776      * Convert an error code to a ptgErr
 777      *
 778      * @access  private
 779          * @param       string  $errorCode      The error code for conversion to its ptg value
 780      * @return  string                          The error code ptgErr
 781      */
 782     function _convertError($errorCode)
 783     {
 784                 switch ($errorCode) {
 785                         case '#NULL!':  return pack("C", 0x00);
 786                         case '#DIV/0!': return pack("C", 0x07);
 787                         case '#VALUE!': return pack("C", 0x0F);
 788                         case '#REF!':   return pack("C", 0x17);
 789                         case '#NAME?':  return pack("C", 0x1D);
 790                         case '#NUM!':   return pack("C", 0x24);
 791                         case '#N/A':    return pack("C", 0x2A);
 792                 }
 793                 return pack("C", 0xFF);
 794     }
 795
 796         /**
 797          * Convert the sheet name part of an external reference, for example "Sheet1" or
 798          * "Sheet1:Sheet2", to a packed structure.
 799          *
 800          * @access      private
 801          * @param       string  $ext_ref        The name of the external reference
 802          * @return      string                          The reference index in packed() format
 803          */
 804         function _packExtRef($ext_ref)
 805         {
 806                 $ext_ref = preg_replace("/^'/", '', $ext_ref); // Remove leading  ' if any.
 807                 $ext_ref = preg_replace("/'$/", '', $ext_ref); // Remove trailing ' if any.
 808
 809                 // Check if there is a sheet range eg., Sheet1:Sheet2.
 810                 if (preg_match("/:/", $ext_ref)) {
 811                         list($sheet_name1, $sheet_name2) = explode(':', $ext_ref);
 812
 813                         $sheet1 = $this->_getSheetIndex($sheet_name1);
 814                         if ($sheet1 == -1) {
 815                                 throw new PHPExcel_Writer_Exception("Unknown sheet name $sheet_name1 in formula");
 816                         }
 817                         $sheet2 = $this->_getSheetIndex($sheet_name2);
 818                         if ($sheet2 == -1) {
 819                                 throw new PHPExcel_Writer_Exception("Unknown sheet name $sheet_name2 in formula");
 820                         }
 821
 822                         // Reverse max and min sheet numbers if necessary
 823                         if ($sheet1 > $sheet2) {
 824                                 list($sheet1, $sheet2) = array($sheet2, $sheet1);
 825                         }
 826                 } else { // Single sheet name only.
 827                         $sheet1 = $this->_getSheetIndex($ext_ref);
 828                         if ($sheet1 == -1) {
 829                                 throw new PHPExcel_Writer_Exception("Unknown sheet name $ext_ref in formula");
 830                         }
 831                         $sheet2 = $sheet1;
 832                 }
 833
 834                 // References are stored relative to 0xFFFF.
 835                 $offset = -1 - $sheet1;
 836
 837                 return pack('vdvv', $offset, 0x00, $sheet1, $sheet2);
 838         }
 839
 840         /**
 841          * Look up the REF index that corresponds to an external sheet name
 842          * (or range). If it doesn't exist yet add it to the workbook's references
 843          * array. It assumes all sheet names given must exist.
 844          *
 845          * @access private
 846          * @param string $ext_ref The name of the external reference
 847          * @return mixed The reference index in packed() format on success
 848          */
 849         function _getRefIndex($ext_ref)
 850         {
 851                 $ext_ref = preg_replace("/^'/", '', $ext_ref); // Remove leading  ' if any.
 852                 $ext_ref = preg_replace("/'$/", '', $ext_ref); // Remove trailing ' if any.
 853                 $ext_ref = str_replace('\'\'', '\'', $ext_ref); // Replace escaped '' with '
 854
 855                 // Check if there is a sheet range eg., Sheet1:Sheet2.
 856                 if (preg_match("/:/", $ext_ref)) {
 857                         list($sheet_name1, $sheet_name2) = explode(':', $ext_ref);
 858
 859                         $sheet1 = $this->_getSheetIndex($sheet_name1);
 860                         if ($sheet1 == -1) {
 861                                 throw new PHPExcel_Writer_Exception("Unknown sheet name $sheet_name1 in formula");
 862                         }
 863                         $sheet2 = $this->_getSheetIndex($sheet_name2);
 864                         if ($sheet2 == -1) {
 865                                 throw new PHPExcel_Writer_Exception("Unknown sheet name $sheet_name2 in formula");
 866                         }
 867
 868                         // Reverse max and min sheet numbers if necessary
 869                         if ($sheet1 > $sheet2) {
 870                                 list($sheet1, $sheet2) = array($sheet2, $sheet1);
 871                         }
 872                 } else { // Single sheet name only.
 873                         $sheet1 = $this->_getSheetIndex($ext_ref);
 874                         if ($sheet1 == -1) {
 875                                 throw new PHPExcel_Writer_Exception("Unknown sheet name $ext_ref in formula");
 876                         }
 877                         $sheet2 = $sheet1;
 878                 }
 879
 880                 // assume all references belong to this document
 881                 $supbook_index = 0x00;
 882                 $ref = pack('vvv', $supbook_index, $sheet1, $sheet2);
 883                 $total_references = count($this->_references);
 884                 $index = -1;
 885                 for ($i = 0; $i < $total_references; ++$i) {
 886                         if ($ref == $this->_references[$i]) {
 887                                 $index = $i;
 888                                 break;
 889                         }
 890                 }
 891                 // if REF was not found add it to references array
 892                 if ($index == -1) {
 893                         $this->_references[$total_references] = $ref;
 894                         $index = $total_references;
 895                 }
 896
 897                 return pack('v', $index);
 898         }
 899
 900         /**
 901          * Look up the index that corresponds to an external sheet name. The hash of
 902          * sheet names is updated by the addworksheet() method of the
 903          * PHPExcel_Writer_Excel5_Workbook class.
 904          *
 905          * @access      private
 906          * @param       string  $sheet_name             Sheet name
 907          * @return      integer                                 The sheet index, -1 if the sheet was not found
 908          */
 909         function _getSheetIndex($sheet_name)
 910         {
 911                 if (!isset($this->_ext_sheets[$sheet_name])) {
 912                         return -1;
 913                 } else {
 914                         return $this->_ext_sheets[$sheet_name];
 915                 }
 916         }
 917
 918         /**
 919          * This method is used to update the array of sheet names. It is
 920          * called by the addWorksheet() method of the
 921          * PHPExcel_Writer_Excel5_Workbook class.
 922          *
 923          * @access public
 924          * @see PHPExcel_Writer_Excel5_Workbook::addWorksheet()
 925          * @param string  $name  The name of the worksheet being added
 926          * @param integer $index The index of the worksheet being added
 927          */
 928         function setExtSheet($name, $index)
 929         {
 930                 $this->_ext_sheets[$name] = $index;
 931         }
 932
 933         /**
 934          * pack() row and column into the required 3 or 4 byte format.
 935          *
 936          * @access private
 937          * @param string $cell The Excel cell reference to be packed
 938          * @return array Array containing the row and column in packed() format
 939          */
 940         function _cellToPackedRowcol($cell)
 941         {
 942                 $cell = strtoupper($cell);
 943                 list($row, $col, $row_rel, $col_rel) = $this->_cellToRowcol($cell);
 944                 if ($col >= 256) {
 945                         throw new PHPExcel_Writer_Exception("Column in: $cell greater than 255");
 946                 }
 947                 if ($row >= 65536) {
 948                         throw new PHPExcel_Writer_Exception("Row in: $cell greater than 65536 ");
 949                 }
 950
 951                 // Set the high bits to indicate if row or col are relative.
 952                 $col |= $col_rel << 14;
 953                 $col |= $row_rel << 15;
 954                 $col = pack('v', $col);
 955
 956                 $row = pack('v', $row);
 957
 958                 return array($row, $col);
 959         }
 960
 961         /**
 962          * pack() row range into the required 3 or 4 byte format.
 963          * Just using maximum col/rows, which is probably not the correct solution
 964          *
 965          * @access private
 966          * @param string $range The Excel range to be packed
 967          * @return array Array containing (row1,col1,row2,col2) in packed() format
 968          */
 969         function _rangeToPackedRange($range)
 970         {
 971                 preg_match('/(\$)?(\d+)\:(\$)?(\d+)/', $range, $match);
 972                 // return absolute rows if there is a $ in the ref
 973                 $row1_rel = empty($match[1]) ? 1 : 0;
 974                 $row1     = $match[2];
 975                 $row2_rel = empty($match[3]) ? 1 : 0;
 976                 $row2     = $match[4];
 977                 // Convert 1-index to zero-index
 978                 --$row1;
 979                 --$row2;
 980                 // Trick poor inocent Excel
 981                 $col1 = 0;
 982                 $col2 = 65535; // FIXME: maximum possible value for Excel 5 (change this!!!)
 983
 984                 // FIXME: this changes for BIFF8
 985                 if (($row1 >= 65536) or ($row2 >= 65536)) {
 986                         throw new PHPExcel_Writer_Exception("Row in: $range greater than 65536 ");
 987                 }
 988
 989                 // Set the high bits to indicate if rows are relative.
 990                 $col1 |= $row1_rel << 15;
 991                 $col2 |= $row2_rel << 15;
 992                 $col1 = pack('v', $col1);
 993                 $col2 = pack('v', $col2);
 994
 995                 $row1 = pack('v', $row1);
 996                 $row2 = pack('v', $row2);
 997
 998                 return array($row1, $col1, $row2, $col2);
 999         }
1000
1001         /**
1002          * Convert an Excel cell reference such as A1 or $B2 or C$3 or $D$4 to a zero
1003          * indexed row and column number. Also returns two (0,1) values to indicate
1004          * whether the row or column are relative references.
1005          *
1006          * @access private
1007          * @param string $cell The Excel cell reference in A1 format.
1008          * @return array
1009          */
1010         function _cellToRowcol($cell)
1011         {
1012                 preg_match('/(\$)?([A-I]?[A-Z])(\$)?(\d+)/',$cell,$match);
1013                 // return absolute column if there is a $ in the ref
1014                 $col_rel = empty($match[1]) ? 1 : 0;
1015                 $col_ref = $match[2];
1016                 $row_rel = empty($match[3]) ? 1 : 0;
1017                 $row     = $match[4];
1018
1019                 // Convert base26 column string to a number.
1020                 $expn   = strlen($col_ref) - 1;
1021                 $col    = 0;
1022                 $col_ref_length = strlen($col_ref);
1023                 for ($i = 0; $i < $col_ref_length; ++$i) {
1024                         $col += (ord($col_ref{$i}) - 64) * pow(26, $expn);
1025                         --$expn;
1026                 }
1027
1028                 // Convert 1-index to zero-index
1029                 --$row;
1030                 --$col;
1031
1032                 return array($row, $col, $row_rel, $col_rel);
1033         }
1034
1035         /**
1036          * Advance to the next valid token.
1037          *
1038          * @access private
1039          */
1040         function _advance()
1041         {
1042                 $i = $this->_current_char;
1043                 $formula_length = strlen($this->_formula);
1044                 // eat up white spaces
1045                 if ($i < $formula_length) {
1046                         while ($this->_formula{$i} == " ") {
1047                                 ++$i;
1048                         }
1049
1050                         if ($i < ($formula_length - 1)) {
1051                                 $this->_lookahead = $this->_formula{$i+1};
1052                         }
1053                         $token = '';
1054                 }
1055
1056                 while ($i < $formula_length) {
1057                         $token .= $this->_formula{$i};
1058
1059                         if ($i < ($formula_length - 1)) {
1060                                 $this->_lookahead = $this->_formula{$i+1};
1061                         } else {
1062                                 $this->_lookahead = '';
1063                         }
1064
1065                         if ($this->_match($token) != '') {
1066                                 //if ($i < strlen($this->_formula) - 1) {
1067                                 //    $this->_lookahead = $this->_formula{$i+1};
1068                                 //}
1069                                 $this->_current_char = $i + 1;
1070                                 $this->_current_token = $token;
1071                                 return 1;
1072                         }
1073
1074                         if ($i < ($formula_length - 2)) {
1075                                 $this->_lookahead = $this->_formula{$i+2};
1076                         } else { // if we run out of characters _lookahead becomes empty
1077                                 $this->_lookahead = '';
1078                         }
1079                         ++$i;
1080                 }
1081                 //die("Lexical error ".$this->_current_char);
1082         }
1083
1084         /**
1085          * Checks if it's a valid token.
1086          *
1087          * @access private
1088          * @param mixed $token The token to check.
1089          * @return mixed       The checked token or false on failure
1090          */
1091         function _match($token)
1092         {
1093                 switch($token) {
1094                         case "+":
1095                         case "-":
1096                         case "*":
1097                         case "/":
1098                         case "(":
1099                         case ")":
1100                         case ",":
1101                         case ";":
1102                         case ">=":
1103                         case "<=":
1104                         case "=":
1105                         case "<>":
1106                         case "^":
1107                         case "&":
1108                         case "%":
1109                                 return $token;
1110                                 break;
1111                         case ">":
1112                                 if ($this->_lookahead == '=') { // it's a GE token
1113                                         break;
1114                                 }
1115                                 return $token;
1116                                 break;
1117                         case "<":
1118                                 // it's a LE or a NE token
1119                                 if (($this->_lookahead == '=') or ($this->_lookahead == '>')) {
1120                                         break;
1121                                 }
1122                                 return $token;
1123                                 break;
1124                         default:
1125                                 // if it's a reference A1 or $A$1 or $A1 or A$1
1126                                 if (preg_match('/^\$?[A-Ia-i]?[A-Za-z]\$?[0-9]+$/',$token) and
1127                                    !preg_match("/[0-9]/",$this->_lookahead) and
1128                                    ($this->_lookahead != ':') and ($this->_lookahead != '.') and
1129                                    ($this->_lookahead != '!'))
1130                                 {
1131                                         return $token;
1132                                 }
1133                                 // If it's an external reference (Sheet1!A1 or Sheet1:Sheet2!A1 or Sheet1!$A$1 or Sheet1:Sheet2!$A$1)
1134                                 elseif (preg_match("/^" . self::REGEX_SHEET_TITLE_UNQUOTED . "(\:" . self::REGEX_SHEET_TITLE_UNQUOTED . ")?\!\\$?[A-Ia-i]?[A-Za-z]\\$?[0-9]+$/u",$token) and
1135                                            !preg_match("/[0-9]/",$this->_lookahead) and
1136                                            ($this->_lookahead != ':') and ($this->_lookahead != '.'))
1137                                 {
1138                                         return $token;
1139                                 }
1140                                 // If it's an external reference ('Sheet1'!A1 or 'Sheet1:Sheet2'!A1 or 'Sheet1'!$A$1 or 'Sheet1:Sheet2'!$A$1)
1141                                 elseif (preg_match("/^'" . self::REGEX_SHEET_TITLE_QUOTED . "(\:" . self::REGEX_SHEET_TITLE_QUOTED . ")?'\!\\$?[A-Ia-i]?[A-Za-z]\\$?[0-9]+$/u",$token) and
1142                                            !preg_match("/[0-9]/",$this->_lookahead) and
1143                                            ($this->_lookahead != ':') and ($this->_lookahead != '.'))
1144                                 {
1145                                         return $token;
1146                                 }
1147                                 // if it's a range A1:A2 or $A$1:$A$2
1148                                 elseif (preg_match('/^(\$)?[A-Ia-i]?[A-Za-z](\$)?[0-9]+:(\$)?[A-Ia-i]?[A-Za-z](\$)?[0-9]+$/', $token) and
1149                                            !preg_match("/[0-9]/",$this->_lookahead))
1150                                 {
1151                                         return $token;
1152                                 }
1153                                 // If it's an external range like Sheet1!A1:B2 or Sheet1:Sheet2!A1:B2 or Sheet1!$A$1:$B$2 or Sheet1:Sheet2!$A$1:$B$2
1154                                 elseif (preg_match("/^" . self::REGEX_SHEET_TITLE_UNQUOTED . "(\:" . self::REGEX_SHEET_TITLE_UNQUOTED . ")?\!\\$?([A-Ia-i]?[A-Za-z])?\\$?[0-9]+:\\$?([A-Ia-i]?[A-Za-z])?\\$?[0-9]+$/u",$token) and
1155                                            !preg_match("/[0-9]/",$this->_lookahead))
1156                                 {
1157                                         return $token;
1158                                 }
1159                                 // If it's an external range like 'Sheet1'!A1:B2 or 'Sheet1:Sheet2'!A1:B2 or 'Sheet1'!$A$1:$B$2 or 'Sheet1:Sheet2'!$A$1:$B$2
1160                                 elseif (preg_match("/^'" . self::REGEX_SHEET_TITLE_QUOTED . "(\:" . self::REGEX_SHEET_TITLE_QUOTED . ")?'\!\\$?([A-Ia-i]?[A-Za-z])?\\$?[0-9]+:\\$?([A-Ia-i]?[A-Za-z])?\\$?[0-9]+$/u",$token) and
1161                                            !preg_match("/[0-9]/",$this->_lookahead))
1162                                 {
1163                                         return $token;
1164                                 }
1165                                 // If it's a number (check that it's not a sheet name or range)
1166                                 elseif (is_numeric($token) and
1167                                                 (!is_numeric($token.$this->_lookahead) or ($this->_lookahead == '')) and
1168                                                 ($this->_lookahead != '!') and ($this->_lookahead != ':'))
1169                                 {
1170                                         return $token;
1171                                 }
1172                                 // If it's a string (of maximum 255 characters)
1173                                 elseif (preg_match("/\"([^\"]|\"\"){0,255}\"/",$token) and $this->_lookahead != '"' and (substr_count($token, '"')%2 == 0))
1174                                 {
1175                                         return $token;
1176                                 }
1177                             // If it's an error code
1178                             elseif (preg_match("/^#[A-Z0\/]{3,5}[!?]{1}$/", $token) or $token == '#N/A')
1179                             {
1180                                 return $token;
1181                             }
1182                                 // if it's a function call
1183                                 elseif (preg_match("/^[A-Z0-9\xc0-\xdc\.]+$/i",$token) and ($this->_lookahead == "("))
1184                                 {
1185                                         return $token;
1186                                 }
1187                                 //      It's an argument of some description (e.g. a named range),
1188                                 //              precise nature yet to be determined
1189                                 elseif(substr($token,-1) == ')') {
1190                                         return $token;
1191                                 }
1192                                 return '';
1193                 }
1194         }
1195
1196         /**
1197          * The parsing method. It parses a formula.
1198          *
1199          * @access public
1200          * @param string $formula The formula to parse, without the initial equal
1201          *                        sign (=).
1202          * @return mixed true on success
1203          */
1204         function parse($formula)
1205         {
1206                 $this->_current_char = 0;
1207                 $this->_formula      = $formula;
1208                 $this->_lookahead    = isset($formula{1}) ? $formula{1} : '';
1209                 $this->_advance();
1210                 $this->_parse_tree   = $this->_condition();
1211                 return true;
1212         }
1213
1214         /**
1215          * It parses a condition. It assumes the following rule:
1216          * Cond -> Expr [(">" | "<") Expr]
1217          *
1218          * @access private
1219          * @return mixed The parsed ptg'd tree on success
1220          */
1221         function _condition()
1222         {
1223                 $result = $this->_expression();
1224                 if ($this->_current_token == "<") {
1225                         $this->_advance();
1226                         $result2 = $this->_expression();
1227                         $result = $this->_createTree('ptgLT', $result, $result2);
1228                 } elseif ($this->_current_token == ">") {
1229                         $this->_advance();
1230                         $result2 = $this->_expression();
1231                         $result = $this->_createTree('ptgGT', $result, $result2);
1232                 } elseif ($this->_current_token == "<=") {
1233                         $this->_advance();
1234                         $result2 = $this->_expression();
1235                         $result = $this->_createTree('ptgLE', $result, $result2);
1236                 } elseif ($this->_current_token == ">=") {
1237                         $this->_advance();
1238                         $result2 = $this->_expression();
1239                         $result = $this->_createTree('ptgGE', $result, $result2);
1240                 } elseif ($this->_current_token == "=") {
1241                         $this->_advance();
1242                         $result2 = $this->_expression();
1243                         $result = $this->_createTree('ptgEQ', $result, $result2);
1244                 } elseif ($this->_current_token == "<>") {
1245                         $this->_advance();
1246                         $result2 = $this->_expression();
1247                         $result = $this->_createTree('ptgNE', $result, $result2);
1248                 } elseif ($this->_current_token == "&") {
1249                     $this->_advance();
1250                     $result2 = $this->_expression();
1251                     $result = $this->_createTree('ptgConcat', $result, $result2);
1252                 }
1253                 return $result;
1254         }
1255
1256         /**
1257          * It parses a expression. It assumes the following rule:
1258          * Expr -> Term [("+" | "-") Term]
1259          *      -> "string"
1260          *      -> "-" Term : Negative value
1261          *      -> "+" Term : Positive value
1262          *      -> Error code
1263          *
1264          * @access private
1265          * @return mixed The parsed ptg'd tree on success
1266          */
1267         function _expression()
1268         {
1269                 // If it's a string return a string node
1270                 if (preg_match("/\"([^\"]|\"\"){0,255}\"/", $this->_current_token)) {
1271                         $tmp = str_replace('""', '"', $this->_current_token);
1272                         if (($tmp == '"') || ($tmp == '')) $tmp = '""'; //      Trap for "" that has been used for an empty string
1273                         $result = $this->_createTree($tmp, '', '');
1274                         $this->_advance();
1275                         return $result;
1276         // If it's an error code
1277         } elseif (preg_match("/^#[A-Z0\/]{3,5}[!?]{1}$/", $this->_current_token) or $this->_current_token == '#N/A'){
1278                     $result = $this->_createTree($this->_current_token, 'ptgErr', '');
1279                     $this->_advance();
1280                     return $result;
1281                 // If it's a negative value
1282         } elseif ($this->_current_token == "-") {
1283                         // catch "-" Term
1284                         $this->_advance();
1285                         $result2 = $this->_expression();
1286                         $result = $this->_createTree('ptgUminus', $result2, '');
1287                         return $result;
1288         // If it's a positive value
1289                 } elseif ($this->_current_token == "+") {
1290                         // catch "+" Term
1291                         $this->_advance();
1292                         $result2 = $this->_expression();
1293                         $result = $this->_createTree('ptgUplus', $result2, '');
1294                         return $result;
1295                 }
1296                 $result = $this->_term();
1297                 while (($this->_current_token == "+") or
1298                            ($this->_current_token == "-") or
1299                            ($this->_current_token == "^")) {
1300                 /**/
1301                         if ($this->_current_token == "+") {
1302                                 $this->_advance();
1303                                 $result2 = $this->_term();
1304                                 $result = $this->_createTree('ptgAdd', $result, $result2);
1305                         } elseif ($this->_current_token == "-") {
1306                                 $this->_advance();
1307                                 $result2 = $this->_term();
1308                                 $result = $this->_createTree('ptgSub', $result, $result2);
1309                         } else {
1310                                 $this->_advance();
1311                                 $result2 = $this->_term();
1312                                 $result = $this->_createTree('ptgPower', $result, $result2);
1313                         }
1314                 }
1315                 return $result;
1316         }
1317
1318         /**
1319          * This function just introduces a ptgParen element in the tree, so that Excel
1320          * doesn't get confused when working with a parenthesized formula afterwards.
1321          *
1322          * @access private
1323          * @see _fact()
1324          * @return array The parsed ptg'd tree
1325          */
1326         function _parenthesizedExpression()
1327         {
1328                 $result = $this->_createTree('ptgParen', $this->_expression(), '');
1329                 return $result;
1330         }
1331
1332         /**
1333          * It parses a term. It assumes the following rule:
1334          * Term -> Fact [("*" | "/") Fact]
1335          *
1336          * @access private
1337          * @return mixed The parsed ptg'd tree on success
1338          */
1339         function _term()
1340         {
1341                 $result = $this->_fact();
1342                 while (($this->_current_token == "*") or
1343                            ($this->_current_token == "/")) {
1344                 /**/
1345                         if ($this->_current_token == "*") {
1346                                 $this->_advance();
1347                                 $result2 = $this->_fact();
1348                                 $result = $this->_createTree('ptgMul', $result, $result2);
1349                         } else {
1350                                 $this->_advance();
1351                                 $result2 = $this->_fact();
1352                                 $result = $this->_createTree('ptgDiv', $result, $result2);
1353                         }
1354                 }
1355                 return $result;
1356         }
1357
1358         /**
1359          * It parses a factor. It assumes the following rule:
1360          * Fact -> ( Expr )
1361          *       | CellRef
1362          *       | CellRange
1363          *       | Number
1364          *       | Function
1365          *
1366          * @access private
1367          * @return mixed The parsed ptg'd tree on success
1368          */
1369         function _fact()
1370         {
1371                 if ($this->_current_token == "(") {
1372                         $this->_advance();         // eat the "("
1373                         $result = $this->_parenthesizedExpression();
1374                         if ($this->_current_token != ")") {
1375                                 throw new PHPExcel_Writer_Exception("')' token expected.");
1376                         }
1377                         $this->_advance();         // eat the ")"
1378                         return $result;
1379                 }
1380                 // if it's a reference
1381                 if (preg_match('/^\$?[A-Ia-i]?[A-Za-z]\$?[0-9]+$/',$this->_current_token))
1382                 {
1383                         $result = $this->_createTree($this->_current_token, '', '');
1384                         $this->_advance();
1385                         return $result;
1386                 }
1387                 // If it's an external reference (Sheet1!A1 or Sheet1:Sheet2!A1 or Sheet1!$A$1 or Sheet1:Sheet2!$A$1)
1388                 elseif (preg_match("/^" . self::REGEX_SHEET_TITLE_UNQUOTED . "(\:" . self::REGEX_SHEET_TITLE_UNQUOTED . ")?\!\\$?[A-Ia-i]?[A-Za-z]\\$?[0-9]+$/u",$this->_current_token))
1389                 {
1390                         $result = $this->_createTree($this->_current_token, '', '');
1391                         $this->_advance();
1392                         return $result;
1393                 }
1394                 // If it's an external reference ('Sheet1'!A1 or 'Sheet1:Sheet2'!A1 or 'Sheet1'!$A$1 or 'Sheet1:Sheet2'!$A$1)
1395                 elseif (preg_match("/^'" . self::REGEX_SHEET_TITLE_QUOTED . "(\:" . self::REGEX_SHEET_TITLE_QUOTED . ")?'\!\\$?[A-Ia-i]?[A-Za-z]\\$?[0-9]+$/u",$this->_current_token))
1396                 {
1397                         $result = $this->_createTree($this->_current_token, '', '');
1398                         $this->_advance();
1399                         return $result;
1400                 }
1401                 // if it's a range A1:B2 or $A$1:$B$2
1402                 elseif (preg_match('/^(\$)?[A-Ia-i]?[A-Za-z](\$)?[0-9]+:(\$)?[A-Ia-i]?[A-Za-z](\$)?[0-9]+$/',$this->_current_token) or
1403                                 preg_match('/^(\$)?[A-Ia-i]?[A-Za-z](\$)?[0-9]+\.\.(\$)?[A-Ia-i]?[A-Za-z](\$)?[0-9]+$/',$this->_current_token))
1404                 {
1405                         // must be an error?
1406                         $result = $this->_createTree($this->_current_token, '', '');
1407                         $this->_advance();
1408                         return $result;
1409                 }
1410                 // If it's an external range (Sheet1!A1:B2 or Sheet1:Sheet2!A1:B2 or Sheet1!$A$1:$B$2 or Sheet1:Sheet2!$A$1:$B$2)
1411                 elseif (preg_match("/^" . self::REGEX_SHEET_TITLE_UNQUOTED . "(\:" . self::REGEX_SHEET_TITLE_UNQUOTED . ")?\!\\$?([A-Ia-i]?[A-Za-z])?\\$?[0-9]+:\\$?([A-Ia-i]?[A-Za-z])?\\$?[0-9]+$/u",$this->_current_token))
1412                 {
1413                         // must be an error?
1414                         //$result = $this->_current_token;
1415                         $result = $this->_createTree($this->_current_token, '', '');
1416                         $this->_advance();
1417                         return $result;
1418                 }
1419                 // If it's an external range ('Sheet1'!A1:B2 or 'Sheet1'!A1:B2 or 'Sheet1'!$A$1:$B$2 or 'Sheet1'!$A$1:$B$2)
1420                 elseif (preg_match("/^'" . self::REGEX_SHEET_TITLE_QUOTED . "(\:" . self::REGEX_SHEET_TITLE_QUOTED . ")?'\!\\$?([A-Ia-i]?[A-Za-z])?\\$?[0-9]+:\\$?([A-Ia-i]?[A-Za-z])?\\$?[0-9]+$/u",$this->_current_token))
1421                 {
1422                         // must be an error?
1423                         //$result = $this->_current_token;
1424                         $result = $this->_createTree($this->_current_token, '', '');
1425                         $this->_advance();
1426                         return $result;
1427                 }
1428                 // If it's a number or a percent
1429                 elseif (is_numeric($this->_current_token))
1430                 {
1431                     if($this->_lookahead == '%'){
1432                         $result = $this->_createTree('ptgPercent', $this->_current_token, '');
1433                 $this->_advance();  // Skip the percentage operator once we've pre-built that tree
1434                     } else {
1435                         $result = $this->_createTree($this->_current_token, '', '');
1436                     }
1437                     $this->_advance();
1438                     return $result;
1439                 }
1440                 // if it's a function call
1441                 elseif (preg_match("/^[A-Z0-9\xc0-\xdc\.]+$/i",$this->_current_token))
1442                 {
1443                         $result = $this->_func();
1444                         return $result;
1445                 }
1446                 throw new PHPExcel_Writer_Exception("Syntax error: ".$this->_current_token.
1447                                                                  ", lookahead: ".$this->_lookahead.
1448                                                                  ", current char: ".$this->_current_char);
1449         }
1450
1451         /**
1452          * It parses a function call. It assumes the following rule:
1453          * Func -> ( Expr [,Expr]* )
1454          *
1455          * @access private
1456          * @return mixed The parsed ptg'd tree on success
1457          */
1458         function _func()
1459         {
1460                 $num_args = 0; // number of arguments received
1461                 $function = strtoupper($this->_current_token);
1462                 $result   = ''; // initialize result
1463                 $this->_advance();
1464                 $this->_advance();         // eat the "("
1465                 while ($this->_current_token != ')') {
1466                 /**/
1467                         if ($num_args > 0) {
1468                                 if ($this->_current_token == "," or
1469                                         $this->_current_token == ";")
1470                                 {
1471                                         $this->_advance();  // eat the "," or ";"
1472                                 } else {
1473                                         throw new PHPExcel_Writer_Exception("Syntax error: comma expected in ".
1474                                                                           "function $function, arg #{$num_args}");
1475                                 }
1476                                 $result2 = $this->_condition();
1477                                 $result = $this->_createTree('arg', $result, $result2);
1478                         } else { // first argument
1479                                 $result2 = $this->_condition();
1480                                 $result = $this->_createTree('arg', '', $result2);
1481                         }
1482                         ++$num_args;
1483                 }
1484                 if (!isset($this->_functions[$function])) {
1485                         throw new PHPExcel_Writer_Exception("Function $function() doesn't exist");
1486                 }
1487                 $args = $this->_functions[$function][1];
1488                 // If fixed number of args eg. TIME($i,$j,$k). Check that the number of args is valid.
1489                 if (($args >= 0) and ($args != $num_args)) {
1490                         throw new PHPExcel_Writer_Exception("Incorrect number of arguments in function $function() ");
1491                 }
1492
1493                 $result = $this->_createTree($function, $result, $num_args);
1494                 $this->_advance();         // eat the ")"
1495                 return $result;
1496         }
1497
1498         /**
1499          * Creates a tree. In fact an array which may have one or two arrays (sub-trees)
1500          * as elements.
1501          *
1502          * @access private
1503          * @param mixed $value The value of this node.
1504          * @param mixed $left  The left array (sub-tree) or a final node.
1505          * @param mixed $right The right array (sub-tree) or a final node.
1506          * @return array A tree
1507          */
1508         function _createTree($value, $left, $right)
1509         {
1510                 return array('value' => $value, 'left' => $left, 'right' => $right);
1511         }
1512
1513         /**
1514          * Builds a string containing the tree in reverse polish notation (What you
1515          * would use in a HP calculator stack).
1516          * The following tree:
1517          *
1518          *    +
1519          *   / \
1520          *  2   3
1521          *
1522          * produces: "23+"
1523          *
1524          * The following tree:
1525          *
1526          *    +
1527          *   / \
1528          *  3   *
1529          *     / \
1530          *    6   A1
1531          *
1532          * produces: "36A1*+"
1533          *
1534          * In fact all operands, functions, references, etc... are written as ptg's
1535          *
1536          * @access public
1537          * @param array $tree The optional tree to convert.
1538          * @return string The tree in reverse polish notation
1539          */
1540         function toReversePolish($tree = array())
1541         {
1542                 $polish = ""; // the string we are going to return
1543                 if (empty($tree)) { // If it's the first call use _parse_tree
1544                         $tree = $this->_parse_tree;
1545                 }
1546
1547                 if (is_array($tree['left'])) {
1548                         $converted_tree = $this->toReversePolish($tree['left']);
1549                         $polish .= $converted_tree;
1550                 } elseif ($tree['left'] != '') { // It's a final node
1551                         $converted_tree = $this->_convert($tree['left']);
1552                         $polish .= $converted_tree;
1553                 }
1554                 if (is_array($tree['right'])) {
1555                         $converted_tree = $this->toReversePolish($tree['right']);
1556                         $polish .= $converted_tree;
1557                 } elseif ($tree['right'] != '') { // It's a final node
1558                         $converted_tree = $this->_convert($tree['right']);
1559                         $polish .= $converted_tree;
1560                 }
1561                 // if it's a function convert it here (so we can set it's arguments)
1562                 if (preg_match("/^[A-Z0-9\xc0-\xdc\.]+$/",$tree['value']) and
1563                         !preg_match('/^([A-Ia-i]?[A-Za-z])(\d+)$/',$tree['value']) and
1564                         !preg_match("/^[A-Ia-i]?[A-Za-z](\d+)\.\.[A-Ia-i]?[A-Za-z](\d+)$/",$tree['value']) and
1565                         !is_numeric($tree['value']) and
1566                         !isset($this->ptg[$tree['value']]))
1567                 {
1568                         // left subtree for a function is always an array.
1569                         if ($tree['left'] != '') {
1570                                 $left_tree = $this->toReversePolish($tree['left']);
1571                         } else {
1572                                 $left_tree = '';
1573                         }
1574                         // add it's left subtree and return.
1575                         return $left_tree.$this->_convertFunction($tree['value'], $tree['right']);
1576                 } else {
1577                         $converted_tree = $this->_convert($tree['value']);
1578                 }
1579                 $polish .= $converted_tree;
1580                 return $polish;
1581         }
1582
1583 }