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/lib/PHPExcel/Calculation/Engineering.php

https://github.com/yuweijun/blog
PHP | 2650 lines | 1653 code | 205 blank | 792 comment | 317 complexity | a4b06723b736f16bec005211e6aa5fed MD5 | raw file
    

  1. <?php
    2. 

  2. 

  3. /** PHPExcel root directory */
    4. 

  4. if (!defined('PHPEXCEL_ROOT')) {
    5. 

  5.     /**
    6. 

  6.      * @ignore
    7. 

  7.      */
    8. 

  8.     define('PHPEXCEL_ROOT', dirname(__FILE__) . '/../../');
    9. 

  9.     require(PHPEXCEL_ROOT . 'PHPExcel/Autoloader.php');
    10. 

  10. }
    11. 

  11. 

  12. /** EULER */
    13. 

  13. define('EULER', 2.71828182845904523536);
    14. 

  14. 

  15. /**
    16. 

  16.  * PHPExcel_Calculation_Engineering
    17. 

  17.  *
    18. 

  18.  * Copyright (c) 2006 - 2015 PHPExcel
    19. 

  19.  *
    20. 

  20.  * This library is free software; you can redistribute it and/or
    21. 

  21.  * modify it under the terms of the GNU Lesser General Public
    22. 

  22.  * License as published by the Free Software Foundation; either
    23. 

  23.  * version 2.1 of the License, or (at your option) any later version.
    24. 

  24.  *
    25. 

  25.  * This library is distributed in the hope that it will be useful,
    26. 

  26.  * but WITHOUT ANY WARRANTY; without even the implied warranty of
    27. 

  27.  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
    28. 

  28.  * Lesser General Public License for more details.
    29. 

  29.  *
    30. 

  30.  * You should have received a copy of the GNU Lesser General Public
    31. 

  31.  * License along with this library; if not, write to the Free Software
    32. 

  32.  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
    33. 

  33.  *
    34. 

  34.  * @category    PHPExcel
    35. 

  35.  * @package        PHPExcel_Calculation
    36. 

  36.  * @copyright    Copyright (c) 2006 - 2015 PHPExcel (http://www.codeplex.com/PHPExcel)
    37. 

  37.  * @license        http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
    38. 

  38.  * @version        ##VERSION##, ##DATE##
    39. 

  39.  */
    40. 

  40. class PHPExcel_Calculation_Engineering
    41. 

  41. {
    42. 

  42.     /**
    43. 

  43.      * Details of the Units of measure that can be used in CONVERTUOM()
    44. 

  44.      *
    45. 

  45.      * @var mixed[]
    46. 

  46.      */
    47. 

  47.     private static $conversionUnits = array(
    48. 

  48.         'g'     => array('Group' => 'Mass',        'Unit Name' => 'Gram',                     'AllowPrefix' => true),
    49. 

  49.         'sg'    => array('Group' => 'Mass',        'Unit Name' => 'Slug',                     'AllowPrefix' => false),
    50. 

  50.         'lbm'   => array('Group' => 'Mass',        'Unit Name' => 'Pound mass (avoirdupois)', 'AllowPrefix' => false),
    51. 

  51.         'u'     => array('Group' => 'Mass',        'Unit Name' => 'U (atomic mass unit)',     'AllowPrefix' => true),
    52. 

  52.         'ozm'   => array('Group' => 'Mass',        'Unit Name' => 'Ounce mass (avoirdupois)', 'AllowPrefix' => false),
    53. 

  53.         'm'     => array('Group' => 'Distance',    'Unit Name' => 'Meter',                    'AllowPrefix' => true),
    54. 

  54.         'mi'    => array('Group' => 'Distance',    'Unit Name' => 'Statute mile',             'AllowPrefix' => false),
    55. 

  55.         'Nmi'   => array('Group' => 'Distance',    'Unit Name' => 'Nautical mile',            'AllowPrefix' => false),
    56. 

  56.         'in'    => array('Group' => 'Distance',    'Unit Name' => 'Inch',                     'AllowPrefix' => false),
    57. 

  57.         'ft'    => array('Group' => 'Distance',    'Unit Name' => 'Foot',                     'AllowPrefix' => false),
    58. 

  58.         'yd'    => array('Group' => 'Distance',    'Unit Name' => 'Yard',                     'AllowPrefix' => false),
    59. 

  59.         'ang'   => array('Group' => 'Distance',    'Unit Name' => 'Angstrom',                 'AllowPrefix' => true),
    60. 

  60.         'Pica'  => array('Group' => 'Distance',    'Unit Name' => 'Pica (1/72 in)',           'AllowPrefix' => false),
    61. 

  61.         'yr'    => array('Group' => 'Time',        'Unit Name' => 'Year',                     'AllowPrefix' => false),
    62. 

  62.         'day'   => array('Group' => 'Time',        'Unit Name' => 'Day',                      'AllowPrefix' => false),
    63. 

  63.         'hr'    => array('Group' => 'Time',        'Unit Name' => 'Hour',                     'AllowPrefix' => false),
    64. 

  64.         'mn'    => array('Group' => 'Time',        'Unit Name' => 'Minute',                   'AllowPrefix' => false),
    65. 

  65.         'sec'   => array('Group' => 'Time',        'Unit Name' => 'Second',                   'AllowPrefix' => true),
    66. 

  66.         'Pa'    => array('Group' => 'Pressure',    'Unit Name' => 'Pascal',                   'AllowPrefix' => true),
    67. 

  67.         'p'     => array('Group' => 'Pressure',    'Unit Name' => 'Pascal',                   'AllowPrefix' => true),
    68. 

  68.         'atm'   => array('Group' => 'Pressure',    'Unit Name' => 'Atmosphere',               'AllowPrefix' => true),
    69. 

  69.         'at'    => array('Group' => 'Pressure',    'Unit Name' => 'Atmosphere',               'AllowPrefix' => true),
    70. 

  70.         'mmHg'  => array('Group' => 'Pressure',    'Unit Name' => 'mm of Mercury',            'AllowPrefix' => true),
    71. 

  71.         'N'     => array('Group' => 'Force',       'Unit Name' => 'Newton',                   'AllowPrefix' => true),
    72. 

  72.         'dyn'   => array('Group' => 'Force',       'Unit Name' => 'Dyne',                     'AllowPrefix' => true),
    73. 

  73.         'dy'    => array('Group' => 'Force',       'Unit Name' => 'Dyne',                     'AllowPrefix' => true),
    74. 

  74.         'lbf'   => array('Group' => 'Force',       'Unit Name' => 'Pound force',              'AllowPrefix' => false),
    75. 

  75.         'J'     => array('Group' => 'Energy',      'Unit Name' => 'Joule',                    'AllowPrefix' => true),
    76. 

  76.         'e'     => array('Group' => 'Energy',      'Unit Name' => 'Erg',                      'AllowPrefix' => true),
    77. 

  77.         'c'     => array('Group' => 'Energy',      'Unit Name' => 'Thermodynamic calorie',    'AllowPrefix' => true),
    78. 

  78.         'cal'   => array('Group' => 'Energy',      'Unit Name' => 'IT calorie',               'AllowPrefix' => true),
    79. 

  79.         'eV'    => array('Group' => 'Energy',      'Unit Name' => 'Electron volt',            'AllowPrefix' => true),
    80. 

  80.         'ev'    => array('Group' => 'Energy',      'Unit Name' => 'Electron volt',            'AllowPrefix' => true),
    81. 

  81.         'HPh'   => array('Group' => 'Energy',      'Unit Name' => 'Horsepower-hour',          'AllowPrefix' => false),
    82. 

  82.         'hh'    => array('Group' => 'Energy',      'Unit Name' => 'Horsepower-hour',          'AllowPrefix' => false),
    83. 

  83.         'Wh'    => array('Group' => 'Energy',      'Unit Name' => 'Watt-hour',                'AllowPrefix' => true),
    84. 

  84.         'wh'    => array('Group' => 'Energy',      'Unit Name' => 'Watt-hour',                'AllowPrefix' => true),
    85. 

  85.         'flb'   => array('Group' => 'Energy',      'Unit Name' => 'Foot-pound',               'AllowPrefix' => false),
    86. 

  86.         'BTU'   => array('Group' => 'Energy',      'Unit Name' => 'BTU',                      'AllowPrefix' => false),
    87. 

  87.         'btu'   => array('Group' => 'Energy',      'Unit Name' => 'BTU',                      'AllowPrefix' => false),
    88. 

  88.         'HP'    => array('Group' => 'Power',       'Unit Name' => 'Horsepower',               'AllowPrefix' => false),
    89. 

  89.         'h'     => array('Group' => 'Power',       'Unit Name' => 'Horsepower',               'AllowPrefix' => false),
    90. 

  90.         'W'     => array('Group' => 'Power',       'Unit Name' => 'Watt',                     'AllowPrefix' => true),
    91. 

  91.         'w'     => array('Group' => 'Power',       'Unit Name' => 'Watt',                     'AllowPrefix' => true),
    92. 

  92.         'T'     => array('Group' => 'Magnetism',   'Unit Name' => 'Tesla',                    'AllowPrefix' => true),
    93. 

  93.         'ga'    => array('Group' => 'Magnetism',   'Unit Name' => 'Gauss',                    'AllowPrefix' => true),
    94. 

  94.         'C'     => array('Group' => 'Temperature', 'Unit Name' => 'Celsius',                  'AllowPrefix' => false),
    95. 

  95.         'cel'   => array('Group' => 'Temperature', 'Unit Name' => 'Celsius',                  'AllowPrefix' => false),
    96. 

  96.         'F'     => array('Group' => 'Temperature', 'Unit Name' => 'Fahrenheit',               'AllowPrefix' => false),
    97. 

  97.         'fah'   => array('Group' => 'Temperature', 'Unit Name' => 'Fahrenheit',               'AllowPrefix' => false),
    98. 

  98.         'K'     => array('Group' => 'Temperature', 'Unit Name' => 'Kelvin',                   'AllowPrefix' => false),
    99. 

  99.         'kel'   => array('Group' => 'Temperature', 'Unit Name' => 'Kelvin',                   'AllowPrefix' => false),
    100. 

  100.         'tsp'   => array('Group' => 'Liquid',      'Unit Name' => 'Teaspoon',                 'AllowPrefix' => false),
    101. 

  101.         'tbs'   => array('Group' => 'Liquid',      'Unit Name' => 'Tablespoon',               'AllowPrefix' => false),
    102. 

  102.         'oz'    => array('Group' => 'Liquid',      'Unit Name' => 'Fluid Ounce',              'AllowPrefix' => false),
    103. 

  103.         'cup'   => array('Group' => 'Liquid',      'Unit Name' => 'Cup',                      'AllowPrefix' => false),
    104. 

  104.         'pt'    => array('Group' => 'Liquid',      'Unit Name' => 'U.S. Pint',                'AllowPrefix' => false),
    105. 

  105.         'us_pt' => array('Group' => 'Liquid',      'Unit Name' => 'U.S. Pint',                'AllowPrefix' => false),
    106. 

  106.         'uk_pt' => array('Group' => 'Liquid',      'Unit Name' => 'U.K. Pint',                'AllowPrefix' => false),
    107. 

  107.         'qt'    => array('Group' => 'Liquid',      'Unit Name' => 'Quart',                    'AllowPrefix' => false),
    108. 

  108.         'gal'   => array('Group' => 'Liquid',      'Unit Name' => 'Gallon',                   'AllowPrefix' => false),
    109. 

  109.         'l'     => array('Group' => 'Liquid',      'Unit Name' => 'Litre',                    'AllowPrefix' => true),
    110. 

  110.         'lt'    => array('Group' => 'Liquid',      'Unit Name' => 'Litre',                    'AllowPrefix' => true),
    111. 

  111.     );
    112. 

  112. 

  113.     /**
    114. 

  114.      * Details of the Multiplier prefixes that can be used with Units of Measure in CONVERTUOM()
    115. 

  115.      *
    116. 

  116.      * @var mixed[]
    117. 

  117.      */
    118. 

  118.     private static $conversionMultipliers = array(
    119. 

  119.         'Y' => array('multiplier' => 1E24,  'name' => 'yotta'),
    120. 

  120.         'Z' => array('multiplier' => 1E21,  'name' => 'zetta'),
    121. 

  121.         'E' => array('multiplier' => 1E18,  'name' => 'exa'),
    122. 

  122.         'P' => array('multiplier' => 1E15,  'name' => 'peta'),
    123. 

  123.         'T' => array('multiplier' => 1E12,  'name' => 'tera'),
    124. 

  124.         'G' => array('multiplier' => 1E9,   'name' => 'giga'),
    125. 

  125.         'M' => array('multiplier' => 1E6,   'name' => 'mega'),
    126. 

  126.         'k' => array('multiplier' => 1E3,   'name' => 'kilo'),
    127. 

  127.         'h' => array('multiplier' => 1E2,   'name' => 'hecto'),
    128. 

  128.         'e' => array('multiplier' => 1E1,   'name' => 'deka'),
    129. 

  129.         'd' => array('multiplier' => 1E-1,  'name' => 'deci'),
    130. 

  130.         'c' => array('multiplier' => 1E-2,  'name' => 'centi'),
    131. 

  131.         'm' => array('multiplier' => 1E-3,  'name' => 'milli'),
    132. 

  132.         'u' => array('multiplier' => 1E-6,  'name' => 'micro'),
    133. 

  133.         'n' => array('multiplier' => 1E-9,  'name' => 'nano'),
    134. 

  134.         'p' => array('multiplier' => 1E-12, 'name' => 'pico'),
    135. 

  135.         'f' => array('multiplier' => 1E-15, 'name' => 'femto'),
    136. 

  136.         'a' => array('multiplier' => 1E-18, 'name' => 'atto'),
    137. 

  137.         'z' => array('multiplier' => 1E-21, 'name' => 'zepto'),
    138. 

  138.         'y' => array('multiplier' => 1E-24, 'name' => 'yocto'),
    139. 

  139.     );
    140. 

  140. 

  141.     /**
    142. 

  142.      * Details of the Units of measure conversion factors, organised by group
    143. 

  143.      *
    144. 

  144.      * @var mixed[]
    145. 

  145.      */
    146. 

  146.     private static $unitConversions = array(
    147. 

  147.         'Mass' => array(
    148. 

  148.             'g' => array(
    149. 

  149.                 'g'   => 1.0,
    150. 

  150.                 'sg'  => 6.85220500053478E-05,
    151. 

  151.                 'lbm' => 2.20462291469134E-03,
    152. 

  152.                 'u'   => 6.02217000000000E+23,
    153. 

  153.                 'ozm' => 3.52739718003627E-02,
    154. 

  154.             ),
    155. 

  155.             'sg' => array(
    156. 

  156.                 'g'   => 1.45938424189287E+04,
    157. 

  157.                 'sg'  => 1.0,
    158. 

  158.                 'lbm' => 3.21739194101647E+01,
    159. 

  159.                 'u'   => 8.78866000000000E+27,
    160. 

  160.                 'ozm' => 5.14782785944229E+02,
    161. 

  161.             ),
    162. 

  162.             'lbm' => array(
    163. 

  163.                 'g'   => 4.5359230974881148E+02,
    164. 

  164.                 'sg'  => 3.10810749306493E-02,
    165. 

  165.                 'lbm' => 1.0,
    166. 

  166.                 'u'   => 2.73161000000000E+26,
    167. 

  167.                 'ozm' => 1.60000023429410E+01,
    168. 

  168.             ),
    169. 

  169.             'u' => array(
    170. 

  170.                 'g'   => 1.66053100460465E-24,
    171. 

  171.                 'sg'  => 1.13782988532950E-28,
    172. 

  172.                 'lbm' => 3.66084470330684E-27,
    173. 

  173.                 'u'   => 1.0,
    174. 

  174.                 'ozm' => 5.85735238300524E-26,
    175. 

  175.             ),
    176. 

  176.             'ozm' => array(
    177. 

  177.                 'g'   => 2.83495152079732E+01,
    178. 

  178.                 'sg'  => 1.94256689870811E-03,
    179. 

  179.                 'lbm' => 6.24999908478882E-02,
    180. 

  180.                 'u'   => 1.70725600000000E+25,
    181. 

  181.                 'ozm' => 1.0,
    182. 

  182.             ),
    183. 

  183.         ),
    184. 

  184.         'Distance' => array(
    185. 

  185.             'm' => array(
    186. 

  186.                 'm'    => 1.0,
    187. 

  187.                 'mi'   => 6.21371192237334E-04,
    188. 

  188.                 'Nmi'  => 5.39956803455724E-04,
    189. 

  189.                 'in'   => 3.93700787401575E+01,
    190. 

  190.                 'ft'   => 3.28083989501312E+00,
    191. 

  191.                 'yd'   => 1.09361329797891E+00,
    192. 

  192.                 'ang'  => 1.00000000000000E+10,
    193. 

  193.                 'Pica' => 2.83464566929116E+03,
    194. 

  194.             ),
    195. 

  195.             'mi' => array(
    196. 

  196.                 'm'    => 1.60934400000000E+03,
    197. 

  197.                 'mi'   => 1.0,
    198. 

  198.                 'Nmi'  => 8.68976241900648E-01,
    199. 

  199.                 'in'   => 6.33600000000000E+04,
    200. 

  200.                 'ft'   => 5.28000000000000E+03,
    201. 

  201.                 'yd'   => 1.76000000000000E+03,
    202. 

  202.                 'ang'  => 1.60934400000000E+13,
    203. 

  203.                 'Pica' => 4.56191999999971E+06,
    204. 

  204.             ),
    205. 

  205.             'Nmi' => array(
    206. 

  206.                 'm'    => 1.85200000000000E+03,
    207. 

  207.                 'mi'   => 1.15077944802354E+00,
    208. 

  208.                 'Nmi'  => 1.0,
    209. 

  209.                 'in'   => 7.29133858267717E+04,
    210. 

  210.                 'ft'   => 6.07611548556430E+03,
    211. 

  211.                 'yd'   => 2.02537182785694E+03,
    212. 

  212.                 'ang'  => 1.85200000000000E+13,
    213. 

  213.                 'Pica' => 5.24976377952723E+06,
    214. 

  214.             ),
    215. 

  215.             'in' => array(
    216. 

  216.                 'm'    => 2.54000000000000E-02,
    217. 

  217.                 'mi'   => 1.57828282828283E-05,
    218. 

  218.                 'Nmi'  => 1.37149028077754E-05,
    219. 

  219.                 'in'   => 1.0,
    220. 

  220.                 'ft'   => 8.33333333333333E-02,
    221. 

  221.                 'yd'   => 2.77777777686643E-02,
    222. 

  222.                 'ang'  => 2.54000000000000E+08,
    223. 

  223.                 'Pica' => 7.19999999999955E+01,
    224. 

  224.             ),
    225. 

  225.             'ft' => array(
    226. 

  226.                 'm'    => 3.04800000000000E-01,
    227. 

  227.                 'mi'   => 1.89393939393939E-04,
    228. 

  228.                 'Nmi'  => 1.64578833693305E-04,
    229. 

  229.                 'in'   => 1.20000000000000E+01,
    230. 

  230.                 'ft'   => 1.0,
    231. 

  231.                 'yd'   => 3.33333333223972E-01,
    232. 

  232.                 'ang'  => 3.04800000000000E+09,
    233. 

  233.                 'Pica' => 8.63999999999946E+02,
    234. 

  234.             ),
    235. 

  235.             'yd' => array(
    236. 

  236.                 'm'    => 9.14400000300000E-01,
    237. 

  237.                 'mi'   => 5.68181818368230E-04,
    238. 

  238.                 'Nmi'  => 4.93736501241901E-04,
    239. 

  239.                 'in'   => 3.60000000118110E+01,
    240. 

  240.                 'ft'   => 3.00000000000000E+00,
    241. 

  241.                 'yd'   => 1.0,
    242. 

  242.                 'ang'  => 9.14400000300000E+09,
    243. 

  243.                 'Pica' => 2.59200000085023E+03,
    244. 

  244.             ),
    245. 

  245.             'ang' => array(
    246. 

  246.                 'm'    => 1.00000000000000E-10,
    247. 

  247.                 'mi'   => 6.21371192237334E-14,
    248. 

  248.                 'Nmi'  => 5.39956803455724E-14,
    249. 

  249.                 'in'   => 3.93700787401575E-09,
    250. 

  250.                 'ft'   => 3.28083989501312E-10,
    251. 

  251.                 'yd'   => 1.09361329797891E-10,
    252. 

  252.                 'ang'  => 1.0,
    253. 

  253.                 'Pica' => 2.83464566929116E-07,
    254. 

  254.             ),
    255. 

  255.             'Pica' => array(
    256. 

  256.                 'm'    => 3.52777777777800E-04,
    257. 

  257.                 'mi'   => 2.19205948372629E-07,
    258. 

  258.                 'Nmi'  => 1.90484761219114E-07,
    259. 

  259.                 'in'   => 1.38888888888898E-02,
    260. 

  260.                 'ft'   => 1.15740740740748E-03,
    261. 

  261.                 'yd'   => 3.85802469009251E-04,
    262. 

  262.                 'ang'  => 3.52777777777800E+06,
    263. 

  263.                 'Pica' => 1.0,
    264. 

  264.             ),
    265. 

  265.         ),
    266. 

  266.         'Time' => array(
    267. 

  267.             'yr' => array(
    268. 

  268.                 'yr'  => 1.0,
    269. 

  269.                 'day' => 365.25,
    270. 

  270.                 'hr'  => 8766.0,
    271. 

  271.                 'mn'  => 525960.0,
    272. 

  272.                 'sec' => 31557600.0,
    273. 

  273.             ),
    274. 

  274.             'day' => array(
    275. 

  275.                 'yr'  => 2.73785078713210E-03,
    276. 

  276.                 'day' => 1.0,
    277. 

  277.                 'hr'  => 24.0,
    278. 

  278.                 'mn'  => 1440.0,
    279. 

  279.                 'sec' => 86400.0,
    280. 

  280.             ),
    281. 

  281.             'hr' => array(
    282. 

  282.                 'yr'  => 1.14077116130504E-04,
    283. 

  283.                 'day' => 4.16666666666667E-02,
    284. 

  284.                 'hr'  => 1.0,
    285. 

  285.                 'mn'  => 60.0,
    286. 

  286.                 'sec' => 3600.0,
    287. 

  287.             ),
    288. 

  288.             'mn' => array(
    289. 

  289.                 'yr'  => 1.90128526884174E-06,
    290. 

  290.                 'day' => 6.94444444444444E-04,
    291. 

  291.                 'hr'  => 1.66666666666667E-02,
    292. 

  292.                 'mn'  => 1.0,
    293. 

  293.                 'sec' => 60.0,
    294. 

  294.             ),
    295. 

  295.             'sec' => array(
    296. 

  296.                 'yr'  => 3.16880878140289E-08,
    297. 

  297.                 'day' => 1.15740740740741E-05,
    298. 

  298.                 'hr'  => 2.77777777777778E-04,
    299. 

  299.                 'mn'  => 1.66666666666667E-02,
    300. 

  300.                 'sec' => 1.0,
    301. 

  301.             ),
    302. 

  302.         ),
    303. 

  303.         'Pressure' => array(
    304. 

  304.             'Pa' => array(
    305. 

  305.                 'Pa'   => 1.0,
    306. 

  306.                 'p'    => 1.0,
    307. 

  307.                 'atm'  => 9.86923299998193E-06,
    308. 

  308.                 'at'   => 9.86923299998193E-06,
    309. 

  309.                 'mmHg' => 7.50061707998627E-03,
    310. 

  310.             ),
    311. 

  311.             'p' => array(
    312. 

  312.                 'Pa'   => 1.0,
    313. 

  313.                 'p'    => 1.0,
    314. 

  314.                 'atm'  => 9.86923299998193E-06,
    315. 

  315.                 'at'   => 9.86923299998193E-06,
    316. 

  316.                 'mmHg' => 7.50061707998627E-03,
    317. 

  317.             ),
    318. 

  318.             'atm' => array(
    319. 

  319.                 'Pa'   => 1.01324996583000E+05,
    320. 

  320.                 'p'    => 1.01324996583000E+05,
    321. 

  321.                 'atm'  => 1.0,
    322. 

  322.                 'at'   => 1.0,
    323. 

  323.                 'mmHg' => 760.0,
    324. 

  324.             ),
    325. 

  325.             'at' => array(
    326. 

  326.                 'Pa'   => 1.01324996583000E+05,
    327. 

  327.                 'p'    => 1.01324996583000E+05,
    328. 

  328.                 'atm'  => 1.0,
    329. 

  329.                 'at'   => 1.0,
    330. 

  330.                 'mmHg' => 760.0,
    331. 

  331.             ),
    332. 

  332.             'mmHg' => array(
    333. 

  333.                 'Pa'   => 1.33322363925000E+02,
    334. 

  334.                 'p'    => 1.33322363925000E+02,
    335. 

  335.                 'atm'  => 1.31578947368421E-03,
    336. 

  336.                 'at'   => 1.31578947368421E-03,
    337. 

  337.                 'mmHg' => 1.0,
    338. 

  338.             ),
    339. 

  339.         ),
    340. 

  340.         'Force' => array(
    341. 

  341.             'N' => array(
    342. 

  342.                 'N'   => 1.0,
    343. 

  343.                 'dyn' => 1.0E+5,
    344. 

  344.                 'dy'  => 1.0E+5,
    345. 

  345.                 'lbf' => 2.24808923655339E-01,
    346. 

  346.             ),
    347. 

  347.             'dyn' => array(
    348. 

  348.                 'N'   => 1.0E-5,
    349. 

  349.                 'dyn' => 1.0,
    350. 

  350.                 'dy'  => 1.0,
    351. 

  351.                 'lbf' => 2.24808923655339E-06,
    352. 

  352.             ),
    353. 

  353.             'dy' => array(
    354. 

  354.                 'N'   => 1.0E-5,
    355. 

  355.                 'dyn' => 1.0,
    356. 

  356.                 'dy'  => 1.0,
    357. 

  357.                 'lbf' => 2.24808923655339E-06,
    358. 

  358.             ),
    359. 

  359.             'lbf' => array(
    360. 

  360.                 'N'   => 4.448222,
    361. 

  361.                 'dyn' => 4.448222E+5,
    362. 

  362.                 'dy'  => 4.448222E+5,
    363. 

  363.                 'lbf' => 1.0,
    364. 

  364.             ),
    365. 

  365.         ),
    366. 

  366.         'Energy' => array(
    367. 

  367.             'J' => array(
    368. 

  368.                 'J'   => 1.0,
    369. 

  369.                 'e'   => 9.99999519343231E+06,
    370. 

  370.                 'c'   => 2.39006249473467E-01,
    371. 

  371.                 'cal' => 2.38846190642017E-01,
    372. 

  372.                 'eV'  => 6.24145700000000E+18,
    373. 

  373.                 'ev'  => 6.24145700000000E+18,
    374. 

  374.                 'HPh' => 3.72506430801000E-07,
    375. 

  375.                 'hh'  => 3.72506430801000E-07,
    376. 

  376.                 'Wh'  => 2.77777916238711E-04,
    377. 

  377.                 'wh'  => 2.77777916238711E-04,
    378. 

  378.                 'flb' => 2.37304222192651E+01,
    379. 

  379.                 'BTU' => 9.47815067349015E-04,
    380. 

  380.                 'btu' => 9.47815067349015E-04,
    381. 

  381.             ),
    382. 

  382.             'e' => array(
    383. 

  383.                 'J'   => 1.00000048065700E-07,
    384. 

  384.                 'e'   => 1.0,
    385. 

  385.                 'c'   => 2.39006364353494E-08,
    386. 

  386.                 'cal' => 2.38846305445111E-08,
    387. 

  387.                 'eV'  => 6.24146000000000E+11,
    388. 

  388.                 'ev'  => 6.24146000000000E+11,
    389. 

  389.                 'HPh' => 3.72506609848824E-14,
    390. 

  390.                 'hh'  => 3.72506609848824E-14,
    391. 

  391.                 'Wh'  => 2.77778049754611E-11,
    392. 

  392.                 'wh'  => 2.77778049754611E-11,
    393. 

  393.                 'flb' => 2.37304336254586E-06,
    394. 

  394.                 'BTU' => 9.47815522922962E-11,
    395. 

  395.                 'btu' => 9.47815522922962E-11,
    396. 

  396.             ),
    397. 

  397.             'c' => array(
    398. 

  398.                 'J'   => 4.18399101363672E+00,
    399. 

  399.                 'e'   => 4.18398900257312E+07,
    400. 

  400.                 'c'   => 1.0,
    401. 

  401.                 'cal' => 9.99330315287563E-01,
    402. 

  402.                 'eV'  => 2.61142000000000E+19,
    403. 

  403.                 'ev'  => 2.61142000000000E+19,
    404. 

  404.                 'HPh' => 1.55856355899327E-06,
    405. 

  405.                 'hh'  => 1.55856355899327E-06,
    406. 

  406.                 'Wh'  => 1.16222030532950E-03,
    407. 

  407.                 'wh'  => 1.16222030532950E-03,
    408. 

  408.                 'flb' => 9.92878733152102E+01,
    409. 

  409.                 'BTU' => 3.96564972437776E-03,
    410. 

  410.                 'btu' => 3.96564972437776E-03,
    411. 

  411.             ),
    412. 

  412.             'cal' => array(
    413. 

  413.                 'J'   => 4.18679484613929E+00,
    414. 

  414.                 'e'   => 4.18679283372801E+07,
    415. 

  415.                 'c'   => 1.00067013349059E+00,
    416. 

  416.                 'cal' => 1.0,
    417. 

  417.                 'eV'  => 2.61317000000000E+19,
    418. 

  418.                 'ev'  => 2.61317000000000E+19,
    419. 

  419.                 'HPh' => 1.55960800463137E-06,
    420. 

  420.                 'hh'  => 1.55960800463137E-06,
    421. 

  421.                 'Wh'  => 1.16299914807955E-03,
    422. 

  422.                 'wh'  => 1.16299914807955E-03,
    423. 

  423.                 'flb' => 9.93544094443283E+01,
    424. 

  424.                 'BTU' => 3.96830723907002E-03,
    425. 

  425.                 'btu' => 3.96830723907002E-03,
    426. 

  426.             ),
    427. 

  427.             'eV' => array(
    428. 

  428.                 'J'   => 1.60219000146921E-19,
    429. 

  429.                 'e'   => 1.60218923136574E-12,
    430. 

  430.                 'c'   => 3.82933423195043E-20,
    431. 

  431.                 'cal' => 3.82676978535648E-20,
    432. 

  432.                 'eV'  => 1.0,
    433. 

  433.                 'ev'  => 1.0,
    434. 

  434.                 'HPh' => 5.96826078912344E-26,
    435. 

  435.                 'hh'  => 5.96826078912344E-26,
    436. 

  436.                 'Wh'  => 4.45053000026614E-23,
    437. 

  437.                 'wh'  => 4.45053000026614E-23,
    438. 

  438.                 'flb' => 3.80206452103492E-18,
    439. 

  439.                 'BTU' => 1.51857982414846E-22,
    440. 

  440.                 'btu' => 1.51857982414846E-22,
    441. 

  441.             ),
    442. 

  442.             'ev' => array(
    443. 

  443.                 'J'   => 1.60219000146921E-19,
    444. 

  444.                 'e'   => 1.60218923136574E-12,
    445. 

  445.                 'c'   => 3.82933423195043E-20,
    446. 

  446.                 'cal' => 3.82676978535648E-20,
    447. 

  447.                 'eV'  => 1.0,
    448. 

  448.                 'ev'  => 1.0,
    449. 

  449.                 'HPh' => 5.96826078912344E-26,
    450. 

  450.                 'hh'  => 5.96826078912344E-26,
    451. 

  451.                 'Wh'  => 4.45053000026614E-23,
    452. 

  452.                 'wh'  => 4.45053000026614E-23,
    453. 

  453.                 'flb' => 3.80206452103492E-18,
    454. 

  454.                 'BTU' => 1.51857982414846E-22,
    455. 

  455.                 'btu' => 1.51857982414846E-22,
    456. 

  456.             ),
    457. 

  457.             'HPh' => array(
    458. 

  458.                 'J'   => 2.68451741316170E+06,
    459. 

  459.                 'e'   => 2.68451612283024E+13,
    460. 

  460.                 'c'   => 6.41616438565991E+05,
    461. 

  461.                 'cal' => 6.41186757845835E+05,
    462. 

  462.                 'eV'  => 1.67553000000000E+25,
    463. 

  463.                 'ev'  => 1.67553000000000E+25,
    464. 

  464.                 'HPh' => 1.0,
    465. 

  465.                 'hh'  => 1.0,
    466. 

  466.                 'Wh'  => 7.45699653134593E+02,
    467. 

  467.                 'wh'  => 7.45699653134593E+02,
    468. 

  468.                 'flb' => 6.37047316692964E+07,
    469. 

  469.                 'BTU' => 2.54442605275546E+03,
    470. 

  470.                 'btu' => 2.54442605275546E+03,
    471. 

  471.             ),
    472. 

  472.             'hh' => array(
    473. 

  473.                 'J'   => 2.68451741316170E+06,
    474. 

  474.                 'e'   => 2.68451612283024E+13,
    475. 

  475.                 'c'   => 6.41616438565991E+05,
    476. 

  476.                 'cal' => 6.41186757845835E+05,
    477. 

  477.                 'eV'  => 1.67553000000000E+25,
    478. 

  478.                 'ev'  => 1.67553000000000E+25,
    479. 

  479.                 'HPh' => 1.0,
    480. 

  480.                 'hh'  => 1.0,
    481. 

  481.                 'Wh'  => 7.45699653134593E+02,
    482. 

  482.                 'wh'  => 7.45699653134593E+02,
    483. 

  483.                 'flb' => 6.37047316692964E+07,
    484. 

  484.                 'BTU' => 2.54442605275546E+03,
    485. 

  485.                 'btu' => 2.54442605275546E+03,
    486. 

  486.             ),
    487. 

  487.             'Wh' => array(
    488. 

  488.                 'J'   => 3.59999820554720E+03,
    489. 

  489.                 'e'   => 3.59999647518369E+10,
    490. 

  490.                 'c'   => 8.60422069219046E+02,
    491. 

  491.                 'cal' => 8.59845857713046E+02,
    492. 

  492.                 'eV'  => 2.24692340000000E+22,
    493. 

  493.                 'ev'  => 2.24692340000000E+22,
    494. 

  494.                 'HPh' => 1.34102248243839E-03,
    495. 

  495.                 'hh'  => 1.34102248243839E-03,
    496. 

  496.                 'Wh'  => 1.0,
    497. 

  497.                 'wh'  => 1.0,
    498. 

  498.                 'flb' => 8.54294774062316E+04,
    499. 

  499.                 'BTU' => 3.41213254164705E+00,
    500. 

  500.                 'btu' => 3.41213254164705E+00,
    501. 

  501.             ),
    502. 

  502.             'wh' => array(
    503. 

  503.                 'J'   => 3.59999820554720E+03,
    504. 

  504.                 'e'   => 3.59999647518369E+10,
    505. 

  505.                 'c'   => 8.60422069219046E+02,
    506. 

  506.                 'cal' => 8.59845857713046E+02,
    507. 

  507.                 'eV'  => 2.24692340000000E+22,
    508. 

  508.                 'ev'  => 2.24692340000000E+22,
    509. 

  509.                 'HPh' => 1.34102248243839E-03,
    510. 

  510.                 'hh'  => 1.34102248243839E-03,
    511. 

  511.                 'Wh'  => 1.0,
    512. 

  512.                 'wh'  => 1.0,
    513. 

  513.                 'flb' => 8.54294774062316E+04,
    514. 

  514.                 'BTU' => 3.41213254164705E+00,
    515. 

  515.                 'btu' => 3.41213254164705E+00,
    516. 

  516.             ),
    517. 

  517.             'flb' => array(
    518. 

  518.                 'J'   => 4.21400003236424E-02,
    519. 

  519.                 'e'   => 4.21399800687660E+05,
    520. 

  520.                 'c'   => 1.00717234301644E-02,
    521. 

  521.                 'cal' => 1.00649785509554E-02,
    522. 

  522.                 'eV'  => 2.63015000000000E+17,
    523. 

  523.                 'ev'  => 2.63015000000000E+17,
    524. 

  524.                 'HPh' => 1.56974211145130E-08,
    525. 

  525.                 'hh'  => 1.56974211145130E-08,
    526. 

  526.                 'Wh'  => 1.17055614802000E-05,
    527. 

  527.                 'wh'  => 1.17055614802000E-05,
    528. 

  528.                 'flb' => 1.0,
    529. 

  529.                 'BTU' => 3.99409272448406E-05,
    530. 

  530.                 'btu' => 3.99409272448406E-05,
    531. 

  531.             ),
    532. 

  532.             'BTU' => array(
    533. 

  533.                 'J'   => 1.05505813786749E+03,
    534. 

  534.                 'e'   => 1.05505763074665E+10,
    535. 

  535.                 'c'   => 2.52165488508168E+02,
    536. 

  536.                 'cal' => 2.51996617135510E+02,
    537. 

  537.                 'eV'  => 6.58510000000000E+21,
    538. 

  538.                 'ev'  => 6.58510000000000E+21,
    539. 

  539.                 'HPh' => 3.93015941224568E-04,
    540. 

  540.                 'hh'  => 3.93015941224568E-04,
    541. 

  541.                 'Wh'  => 2.93071851047526E-01,
    542. 

  542.                 'wh'  => 2.93071851047526E-01,
    543. 

  543.                 'flb' => 2.50369750774671E+04,
    544. 

  544.                 'BTU' => 1.0,
    545. 

  545.                 'btu' => 1.0,
    546. 

  546.             ),
    547. 

  547.             'btu' => array(
    548. 

  548.                 'J'   => 1.05505813786749E+03,
    549. 

  549.                 'e'   => 1.05505763074665E+10,
    550. 

  550.                 'c'   => 2.52165488508168E+02,
    551. 

  551.                 'cal' => 2.51996617135510E+02,
    552. 

  552.                 'eV'  => 6.58510000000000E+21,
    553. 

  553.                 'ev'  => 6.58510000000000E+21,
    554. 

  554.                 'HPh' => 3.93015941224568E-04,
    555. 

  555.                 'hh'  => 3.93015941224568E-04,
    556. 

  556.                 'Wh'  => 2.93071851047526E-01,
    557. 

  557.                 'wh'  => 2.93071851047526E-01,
    558. 

  558.                 'flb' => 2.50369750774671E+04,
    559. 

  559.                 'BTU' => 1.0,
    560. 

  560.                 'btu' => 1.0,
    561. 

  561.             ),
    562. 

  562.         ),
    563. 

  563.         'Power' => array(
    564. 

  564.             'HP' => array(
    565. 

  565.                 'HP' => 1.0,
    566. 

  566.                 'h'  => 1.0,
    567. 

  567.                 'W'  => 7.45701000000000E+02,
    568. 

  568.                 'w'  => 7.45701000000000E+02,
    569. 

  569.             ),
    570. 

  570.             'h' => array(
    571. 

  571.                 'HP' => 1.0,
    572. 

  572.                 'h'  => 1.0,
    573. 

  573.                 'W'  => 7.45701000000000E+02,
    574. 

  574.                 'w'  => 7.45701000000000E+02,
    575. 

  575.             ),
    576. 

  576.             'W' => array(
    577. 

  577.                 'HP' => 1.34102006031908E-03,
    578. 

  578.                 'h'  => 1.34102006031908E-03,
    579. 

  579.                 'W'  => 1.0,
    580. 

  580.                 'w'  => 1.0,
    581. 

  581.             ),
    582. 

  582.             'w' => array(
    583. 

  583.                 'HP' => 1.34102006031908E-03,
    584. 

  584.                 'h'  => 1.34102006031908E-03,
    585. 

  585.                 'W'  => 1.0,
    586. 

  586.                 'w'  => 1.0,
    587. 

  587.             ),
    588. 

  588.         ),
    589. 

  589.         'Magnetism' => array(
    590. 

  590.             'T' => array(
    591. 

  591.                 'T'  => 1.0,
    592. 

  592.                 'ga' => 10000.0,
    593. 

  593.             ),
    594. 

  594.             'ga' => array(
    595. 

  595.                 'T'  => 0.0001,
    596. 

  596.                 'ga' => 1.0,
    597. 

  597.             ),
    598. 

  598.         ),
    599. 

  599.         'Liquid' => array(
    600. 

  600.             'tsp' => array(
    601. 

  601.                 'tsp'   => 1.0,
    602. 

  602.                 'tbs'   => 3.33333333333333E-01,
    603. 

  603.                 'oz'    => 1.66666666666667E-01,
    604. 

  604.                 'cup'   => 2.08333333333333E-02,
    605. 

  605.                 'pt'    => 1.04166666666667E-02,
    606. 

  606.                 'us_pt' => 1.04166666666667E-02,
    607. 

  607.                 'uk_pt' => 8.67558516821960E-03,
    608. 

  608.                 'qt'    => 5.20833333333333E-03,
    609. 

  609.                 'gal'   => 1.30208333333333E-03,
    610. 

  610.                 'l'     => 4.92999408400710E-03,
    611. 

  611.                 'lt'    => 4.92999408400710E-03,
    612. 

  612.             ),
    613. 

  613.             'tbs' => array(
    614. 

  614.                 'tsp'   => 3.00000000000000E+00,
    615. 

  615.                 'tbs'   => 1.0,
    616. 

  616.                 'oz'    => 5.00000000000000E-01,
    617. 

  617.                 'cup'   => 6.25000000000000E-02,
    618. 

  618.                 'pt'    => 3.12500000000000E-02,
    619. 

  619.                 'us_pt' => 3.12500000000000E-02,
    620. 

  620.                 'uk_pt' => 2.60267555046588E-02,
    621. 

  621.                 'qt'    => 1.56250000000000E-02,
    622. 

  622.                 'gal'   => 3.90625000000000E-03,
    623. 

  623.                 'l'     => 1.47899822520213E-02,
    624. 

  624.                 'lt'    => 1.47899822520213E-02,
    625. 

  625.             ),
    626. 

  626.             'oz' => array(
    627. 

  627.                 'tsp'   => 6.00000000000000E+00,
    628. 

  628.                 'tbs'   => 2.00000000000000E+00,
    629. 

  629.                 'oz'    => 1.0,
    630. 

  630.                 'cup'   => 1.25000000000000E-01,
    631. 

  631.                 'pt'    => 6.25000000000000E-02,
    632. 

  632.                 'us_pt' => 6.25000000000000E-02,
    633. 

  633.                 'uk_pt' => 5.20535110093176E-02,
    634. 

  634.                 'qt'    => 3.12500000000000E-02,
    635. 

  635.                 'gal'   => 7.81250000000000E-03,
    636. 

  636.                 'l'     => 2.95799645040426E-02,
    637. 

  637.                 'lt'    => 2.95799645040426E-02,
    638. 

  638.             ),
    639. 

  639.             'cup' => array(
    640. 

  640.                 'tsp'   => 4.80000000000000E+01,
    641. 

  641.                 'tbs'   => 1.60000000000000E+01,
    642. 

  642.                 'oz'    => 8.00000000000000E+00,
    643. 

  643.                 'cup'   => 1.0,
    644. 

  644.                 'pt'    => 5.00000000000000E-01,
    645. 

  645.                 'us_pt' => 5.00000000000000E-01,
    646. 

  646.                 'uk_pt' => 4.16428088074541E-01,
    647. 

  647.                 'qt'    => 2.50000000000000E-01,
    648. 

  648.                 'gal'   => 6.25000000000000E-02,
    649. 

  649.                 'l'     => 2.36639716032341E-01,
    650. 

  650.                 'lt'    => 2.36639716032341E-01,
    651. 

  651.             ),
    652. 

  652.             'pt' => array(
    653. 

  653.                 'tsp'   => 9.60000000000000E+01,
    654. 

  654.                 'tbs'   => 3.20000000000000E+01,
    655. 

  655.                 'oz'    => 1.60000000000000E+01,
    656. 

  656.                 'cup'   => 2.00000000000000E+00,
    657. 

  657.                 'pt'    => 1.0,
    658. 

  658.                 'us_pt' => 1.0,
    659. 

  659.                 'uk_pt' => 8.32856176149081E-01,
    660. 

  660.                 'qt'    => 5.00000000000000E-01,
    661. 

  661.                 'gal'   => 1.25000000000000E-01,
    662. 

  662.                 'l'     => 4.73279432064682E-01,
    663. 

  663.                 'lt'    => 4.73279432064682E-01,
    664. 

  664.             ),
    665. 

  665.             'us_pt' => array(
    666. 

  666.                 'tsp'   => 9.60000000000000E+01,
    667. 

  667.                 'tbs'   => 3.20000000000000E+01,
    668. 

  668.                 'oz'    => 1.60000000000000E+01,
    669. 

  669.                 'cup'   => 2.00000000000000E+00,
    670. 

  670.                 'pt'    => 1.0,
    671. 

  671.                 'us_pt' => 1.0,
    672. 

  672.                 'uk_pt' => 8.32856176149081E-01,
    673. 

  673.                 'qt'    => 5.00000000000000E-01,
    674. 

  674.                 'gal'   => 1.25000000000000E-01,
    675. 

  675.                 'l'     => 4.73279432064682E-01,
    676. 

  676.                 'lt'    => 4.73279432064682E-01,
    677. 

  677.             ),
    678. 

  678.             'uk_pt' => array(
    679. 

  679.                 'tsp'   => 1.15266000000000E+02,
    680. 

  680.                 'tbs'   => 3.84220000000000E+01,
    681. 

  681.                 'oz'    => 1.92110000000000E+01,
    682. 

  682.                 'cup'   => 2.40137500000000E+00,
    683. 

  683.                 'pt'    => 1.20068750000000E+00,
    684. 

  684.                 'us_pt' => 1.20068750000000E+00,
    685. 

  685.                 'uk_pt' => 1.0,
    686. 

  686.                 'qt'    => 6.00343750000000E-01,
    687. 

  687.                 'gal'   => 1.50085937500000E-01,
    688. 

  688.                 'l'     => 5.68260698087162E-01,
    689. 

  689.                 'lt'    => 5.68260698087162E-01,
    690. 

  690.             ),
    691. 

  691.             'qt' => array(
    692. 

  692.                 'tsp'   => 1.92000000000000E+02,
    693. 

  693.                 'tbs'   => 6.40000000000000E+01,
    694. 

  694.                 'oz'    => 3.20000000000000E+01,
    695. 

  695.                 'cup'   => 4.00000000000000E+00,
    696. 

  696.                 'pt'    => 2.00000000000000E+00,
    697. 

  697.                 'us_pt' => 2.00000000000000E+00,
    698. 

  698.                 'uk_pt' => 1.66571235229816E+00,
    699. 

  699.                 'qt'    => 1.0,
    700. 

  700.                 'gal'   => 2.50000000000000E-01,
    701. 

  701.                 'l'     => 9.46558864129363E-01,
    702. 

  702.                 'lt'    => 9.46558864129363E-01,
    703. 

  703.             ),
    704. 

  704.             'gal' => array(
    705. 

  705.                 'tsp'   => 7.68000000000000E+02,
    706. 

  706.                 'tbs'   => 2.56000000000000E+02,
    707. 

  707.                 'oz'    => 1.28000000000000E+02,
    708. 

  708.                 'cup'   => 1.60000000000000E+01,
    709. 

  709.                 'pt'    => 8.00000000000000E+00,
    710. 

  710.                 'us_pt' => 8.00000000000000E+00,
    711. 

  711.                 'uk_pt' => 6.66284940919265E+00,
    712. 

  712.                 'qt'    => 4.00000000000000E+00,
    713. 

  713.                 'gal'   => 1.0,
    714. 

  714.                 'l'     => 3.78623545651745E+00,
    715. 

  715.                 'lt'    => 3.78623545651745E+00,
    716. 

  716.             ),
    717. 

  717.             'l' => array(
    718. 

  718.                 'tsp'   => 2.02840000000000E+02,
    719. 

  719.                 'tbs'   => 6.76133333333333E+01,
    720. 

  720.                 'oz'    => 3.38066666666667E+01,
    721. 

  721.                 'cup'   => 4.22583333333333E+00,
    722. 

  722.                 'pt'    => 2.11291666666667E+00,
    723. 

  723.                 'us_pt' => 2.11291666666667E+00,
    724. 

  724.                 'uk_pt' => 1.75975569552166E+00,
    725. 

  725.                 'qt'    => 1.05645833333333E+00,
    726. 

  726.                 'gal'   => 2.64114583333333E-01,
    727. 

  727.                 'l'     => 1.0,
    728. 

  728.                 'lt'    => 1.0,
    729. 

  729.             ),
    730. 

  730.             'lt' => array(
    731. 

  731.                 'tsp'   => 2.02840000000000E+02,
    732. 

  732.                 'tbs'   => 6.76133333333333E+01,
    733. 

  733.                 'oz'    => 3.38066666666667E+01,
    734. 

  734.                 'cup'   => 4.22583333333333E+00,
    735. 

  735.                 'pt'    => 2.11291666666667E+00,
    736. 

  736.                 'us_pt' => 2.11291666666667E+00,
    737. 

  737.                 'uk_pt' => 1.75975569552166E+00,
    738. 

  738.                 'qt'    => 1.05645833333333E+00,
    739. 

  739.                 'gal'   => 2.64114583333333E-01,
    740. 

  740.                 'l'     => 1.0,
    741. 

  741.                 'lt'    => 1.0,
    742. 

  742.             ),
    743. 

  743.         ),
    744. 

  744.     );
    745. 

  745. 

  746. 

  747.     /**
    748. 

  748.      * parseComplex
    749. 

  749.      *
    750. 

  750.      * Parses a complex number into its real and imaginary parts, and an I or J suffix
    751. 

  751.      *
    752. 

  752.      * @param    string        $complexNumber    The complex number
    753. 

  753.      * @return    string[]    Indexed on "real", "imaginary" and "suffix"
    754. 

  754.      */
    755. 

  755.     public static function parseComplex($complexNumber)
    756. 

  756.     {
    757. 

  757.         $workString = (string) $complexNumber;
    758. 

  758. 

  759.         $realNumber = $imaginary = 0;
    760. 

  760.         //    Extract the suffix, if there is one
    761. 

  761.         $suffix = substr($workString, -1);
    762. 

  762.         if (!is_numeric($suffix)) {
    763. 

  763.             $workString = substr($workString, 0, -1);
    764. 

  764.         } else {
    765. 

  765.             $suffix = '';
    766. 

  766.         }
    767. 

  767. 

  768.         //    Split the input into its Real and Imaginary components
    769. 

  769.         $leadingSign = 0;
    770. 

  770.         if (strlen($workString) > 0) {
    771. 

  771.             $leadingSign = (($workString{0} == '+') || ($workString{0} == '-')) ? 1 : 0;
    772. 

  772.         }
    773. 

  773.         $power = '';
    774. 

  774.         $realNumber = strtok($workString, '+-');
    775. 

  775.         if (strtoupper(substr($realNumber, -1)) == 'E') {
    776. 

  776.             $power = strtok('+-');
    777. 

  777.             ++$leadingSign;
    778. 

  778.         }
    779. 

  779. 

  780.         $realNumber = substr($workString, 0, strlen($realNumber)+strlen($power)+$leadingSign);
    781. 

  781. 

  782.         if ($suffix != '') {
    783. 

  783.             $imaginary = substr($workString, strlen($realNumber));
    784. 

  784. 

  785.             if (($imaginary == '') && (($realNumber == '') || ($realNumber == '+') || ($realNumber == '-'))) {
    786. 

  786.                 $imaginary = $realNumber.'1';
    787. 

  787.                 $realNumber = '0';
    788. 

  788.             } elseif ($imaginary == '') {
    789. 

  789.                 $imaginary = $realNumber;
    790. 

  790.                 $realNumber = '0';
    791. 

  791.             } elseif (($imaginary == '+') || ($imaginary == '-')) {
    792. 

  792.                 $imaginary .= '1';
    793. 

  793.             }
    794. 

  794.         }
    795. 

  795. 

  796.         return array(
    797. 

  797.             'real'   => $realNumber,
    798. 

  798.             'imaginary' => $imaginary,
    799. 

  799.             'suffix' => $suffix
    800. 

  800.         );
    801. 

  801.     }
    802. 

  802. 

  803. 

  804.     /**
    805. 

  805.      * Cleans the leading characters in a complex number string
    806. 

  806.      *
    807. 

  807.      * @param    string        $complexNumber    The complex number to clean
    808. 

  808.      * @return    string        The "cleaned" complex number
    809. 

  809.      */
    810. 

  810.     private static function cleanComplex($complexNumber)
    811. 

  811.     {
    812. 

  812.         if ($complexNumber{0} == '+') {
    813. 

  813.             $complexNumber = substr($complexNumber, 1);
    814. 

  814.         }
    815. 

  815.         if ($complexNumber{0} == '0') {
    816. 

  816.             $complexNumber = substr($complexNumber, 1);
    817. 

  817.         }
    818. 

  818.         if ($complexNumber{0} == '.') {
    819. 

  819.             $complexNumber = '0'.$complexNumber;
    820. 

  820.         }
    821. 

  821.         if ($complexNumber{0} == '+') {
    822. 

  822.             $complexNumber = substr($complexNumber, 1);
    823. 

  823.         }
    824. 

  824.         return $complexNumber;
    825. 

  825.     }
    826. 

  826. 

  827.     /**
    828. 

  828.      * Formats a number base string value with leading zeroes
    829. 

  829.      *
    830. 

  830.      * @param    string        $xVal        The "number" to pad
    831. 

  831.      * @param    integer        $places        The length that we want to pad this value
    832. 

  832.      * @return    string        The padded "number"
    833. 

  833.      */
    834. 

  834.     private static function nbrConversionFormat($xVal, $places)
    835. 

  835.     {
    836. 

  836.         if (!is_null($places)) {
    837. 

  837.             if (strlen($xVal) <= $places) {
    838. 

  838.                 return substr(str_pad($xVal, $places, '0', STR_PAD_LEFT), -10);
    839. 

  839.             } else {
    840. 

  840.                 return PHPExcel_Calculation_Functions::NaN();
    841. 

  841.             }
    842. 

  842.         }
    843. 

  843. 

  844.         return substr($xVal, -10);
    845. 

  845.     }
    846. 

  846. 

  847.     /**
    848. 

  848.      *    BESSELI
    849. 

  849.      *
    850. 

  850.      *    Returns the modified Bessel function In(x), which is equivalent to the Bessel function evaluated
    851. 

  851.      *        for purely imaginary arguments
    852. 

  852.      *
    853. 

  853.      *    Excel Function:
    854. 

  854.      *        BESSELI(x,ord)
    855. 

  855.      *
    856. 

  856.      *    @access    public
    857. 

  857.      *    @category Engineering Functions
    858. 

  858.      *    @param    float        $x        The value at which to evaluate the function.
    859. 

  859.      *                                If x is nonnumeric, BESSELI returns the #VALUE! error value.
    860. 

  860.      *    @param    integer        $ord    The order of the Bessel function.
    861. 

  861.      *                                If ord is not an integer, it is truncated.
    862. 

  862.      *                                If $ord is nonnumeric, BESSELI returns the #VALUE! error value.
    863. 

  863.      *                                If $ord < 0, BESSELI returns the #NUM! error value.
    864. 

  864.      *    @return    float
    865. 

  865.      *
    866. 

  866.      */
    867. 

  867.     public static function BESSELI($x, $ord)
    868. 

  868.     {
    869. 

  869.         $x    = (is_null($x))    ? 0.0 :    PHPExcel_Calculation_Functions::flattenSingleValue($x);
    870. 

  870.         $ord    = (is_null($ord))    ? 0.0 :    PHPExcel_Calculation_Functions::flattenSingleValue($ord);
    871. 

  871. 

  872.         if ((is_numeric($x)) && (is_numeric($ord))) {
    873. 

  873.             $ord    = floor($ord);
    874. 

  874.             if ($ord < 0) {
    875. 

  875.                 return PHPExcel_Calculation_Functions::NaN();
    876. 

  876.             }
    877. 

  877. 

  878.             if (abs($x) <= 30) {
    879. 

  879.                 $fResult = $fTerm = pow($x / 2, $ord) / PHPExcel_Calculation_MathTrig::FACT($ord);
    880. 

  880.                 $ordK = 1;
    881. 

  881.                 $fSqrX = ($x * $x) / 4;
    882. 

  882.                 do {
    883. 

  883.                     $fTerm *= $fSqrX;
    884. 

  884.                     $fTerm /= ($ordK * ($ordK + $ord));
    885. 

  885.                     $fResult += $fTerm;
    886. 

  886.                 } while ((abs($fTerm) > 1e-12) && (++$ordK < 100));
    887. 

  887.             } else {
    888. 

  888.                 $f_2_PI = 2 * M_PI;
    889. 

  889. 

  890.                 $fXAbs = abs($x);
    891. 

  891.                 $fResult = exp($fXAbs) / sqrt($f_2_PI * $fXAbs);
    892. 

  892.                 if (($ord & 1) && ($x < 0)) {
    893. 

  893.                     $fResult = -$fResult;
    894. 

  894.                 }
    895. 

  895.             }
    896. 

  896.             return (is_nan($fResult)) ? PHPExcel_Calculation_Functions::NaN() : $fResult;
    897. 

  897.         }
    898. 

  898.         return PHPExcel_Calculation_Functions::VALUE();
    899. 

  899.     }
    900. 

  900. 

  901. 

  902.     /**
    903. 

  903.      *    BESSELJ
    904. 

  904.      *
    905. 

  905.      *    Returns the Bessel function
    906. 

  906.      *
    907. 

  907.      *    Excel Function:
    908. 

  908.      *        BESSELJ(x,ord)
    909. 

  909.      *
    910. 

  910.      *    @access    public
    911. 

  911.      *    @category Engineering Functions
    912. 

  912.      *    @param    float        $x        The value at which to evaluate the function.
    913. 

  913.      *                                If x is nonnumeric, BESSELJ returns the #VALUE! error value.
    914. 

  914.      *    @param    integer        $ord    The order of the Bessel function. If n is not an integer, it is truncated.
    915. 

  915.      *                                If $ord is nonnumeric, BESSELJ returns the #VALUE! error value.
    916. 

  916.      *                                If $ord < 0, BESSELJ returns the #NUM! error value.
    917. 

  917.      *    @return    float
    918. 

  918.      *
    919. 

  919.      */
    920. 

  920.     public static function BESSELJ($x, $ord)
    921. 

  921.     {
    922. 

  922.         $x    = (is_null($x))    ? 0.0 :    PHPExcel_Calculation_Functions::flattenSingleValue($x);
    923. 

  923.         $ord    = (is_null($ord))    ? 0.0 :    PHPExcel_Calculation_Functions::flattenSingleValue($ord);
    924. 

  924. 

  925.         if ((is_numeric($x)) && (is_numeric($ord))) {
    926. 

  926.             $ord    = floor($ord);
    927. 

  927.             if ($ord < 0) {
    928. 

  928.                 return PHPExcel_Calculation_Functions::NaN();
    929. 

  929.             }
    930. 

  930. 

  931.             $fResult = 0;
    932. 

  932.             if (abs($x) <= 30) {
    933. 

  933.                 $fResult = $fTerm = pow($x / 2, $ord) / PHPExcel_Calculation_MathTrig::FACT($ord);
    934. 

  934.                 $ordK = 1;
    935. 

  935.                 $fSqrX = ($x * $x) / -4;
    936. 

  936.                 do {
    937. 

  937.                     $fTerm *= $fSqrX;
    938. 

  938.                     $fTerm /= ($ordK * ($ordK + $ord));
    939. 

  939.                     $fResult += $fTerm;
    940. 

  940.                 } while ((abs($fTerm) > 1e-12) && (++$ordK < 100));
    941. 

  941.             } else {
    942. 

  942.                 $f_PI_DIV_2 = M_PI / 2;
    943. 

  943.                 $f_PI_DIV_4 = M_PI / 4;
    944. 

  944. 

  945.                 $fXAbs = abs($x);
    946. 

  946.                 $fResult = sqrt(M_2DIVPI / $fXAbs) * cos($fXAbs - $ord * $f_PI_DIV_2 - $f_PI_DIV_4);
    947. 

  947.                 if (($ord & 1) && ($x < 0)) {
    948. 

  948.                     $fResult = -$fResult;
    949. 

  949.                 }
    950. 

  950.             }
    951. 

  951.             return (is_nan($fResult)) ? PHPExcel_Calculation_Functions::NaN() : $fResult;
    952. 

  952.         }
    953. 

  953.         return PHPExcel_Calculation_Functions::VALUE();
    954. 

  954.     }
    955. 

  955. 

  956. 

  957.     private static function besselK0($fNum)
    958. 

  958.     {
    959. 

  959.         if ($fNum <= 2) {
    960. 

  960.             $fNum2 = $fNum * 0.5;
    961. 

  961.             $y = ($fNum2 * $fNum2);
    962. 

  962.             $fRet = -log($fNum2) * self::BESSELI($fNum, 0) +
    963. 

  963.                 (-0.57721566 + $y * (0.42278420 + $y * (0.23069756 + $y * (0.3488590e-1 + $y * (0.262698e-2 + $y *
    964. 

  964.                 (0.10750e-3 + $y * 0.74e-5))))));
    965. 

  965.         } else {
    966. 

  966.             $y = 2 / $fNum;
    967. 

  967.             $fRet = exp(-$fNum) / sqrt($fNum) *
    968. 

  968.                 (1.25331414 + $y * (-0.7832358e-1 + $y * (0.2189568e-1 + $y * (-0.1062446e-1 + $y *
    969. 

  969.                 (0.587872e-2 + $y * (-0.251540e-2 + $y * 0.53208e-3))))));
    970. 

  970.         }
    971. 

  971.         return $fRet;
    972. 

  972.     }
    973. 

  973. 

  974. 

  975.     private static function besselK1($fNum)
    976. 

  976.     {
    977. 

  977.         if ($fNum <= 2) {
    978. 

  978.             $fNum2 = $fNum * 0.5;
    979. 

  979.             $y = ($fNum2 * $fNum2);
    980. 

  980.             $fRet = log($fNum2) * self::BESSELI($fNum, 1) +
    981. 

  981.                 (1 + $y * (0.15443144 + $y * (-0.67278579 + $y * (-0.18156897 + $y * (-0.1919402e-1 + $y *
    982. 

  982.                 (-0.110404e-2 + $y * (-0.4686e-4))))))) / $fNum;
    983. 

  983.         } else {
    984. 

  984.             $y = 2 / $fNum;
    985. 

  985.             $fRet = exp(-$fNum) / sqrt($fNum) *
    986. 

  986.                 (1.25331414 + $y * (0.23498619 + $y * (-0.3655620e-1 + $y * (0.1504268e-1 + $y * (-0.780353e-2 + $y *
    987. 

  987.                 (0.325614e-2 + $y * (-0.68245e-3)))))));
    988. 

  988.         }
    989. 

  989.         return $fRet;
    990. 

  990.     }
    991. 

  991. 

  992. 

  993.     /**
    994. 

  994.      *    BESSELK
    995. 

  995.      *
    996. 

  996.      *    Returns the modified Bessel function Kn(x), which is equivalent to the Bessel functions evaluated
    997. 

  997.      *        for purely imaginary arguments.
    998. 

  998.      *
    999. 

  999.      *    Excel Function:
    1000. 

  1000.      *        BESSELK(x,ord)
    1001. 

  1001.      *
    1002. 

  1002.      *    @access    public
    1003. 

  1003.      *    @category Engineering Functions
    1004. 

  1004.      *    @param    float        $x        The value at which to evaluate the function.
    1005. 

  1005.      *                                If x is nonnumeric, BESSELK returns the #VALUE! error value.
    1006. 

  1006.      *    @param    integer        $ord    The order of the Bessel function. If n is not an integer, it is truncated.
    1007. 

  1007.      *                                If $ord is nonnumeric, BESSELK returns the #VALUE! error value.
    1008. 

  1008.      *                                If $ord < 0, BESSELK returns the #NUM! error value.
    1009. 

  1009.      *    @return    float
    1010. 

  1010.      *
    1011. 

  1011.      */
    1012. 

  1012.     public static function BESSELK($x, $ord)
    1013. 

  1013.     {
    1014. 

  1014.         $x        = (is_null($x))        ? 0.0 :    PHPExcel_Calculation_Functions::flattenSingleValue($x);
    1015. 

  1015.         $ord    = (is_null($ord))    ? 0.0 :    PHPExcel_Calculation_Functions::flattenSingleValue($ord);
    1016. 

  1016. 

  1017.         if ((is_numeric($x)) && (is_numeric($ord))) {
    1018. 

  1018.             if (($ord < 0) || ($x == 0.0)) {
    1019. 

  1019.                 return PHPExcel_Calculation_Functions::NaN();
    1020. 

  1020.             }
    1021. 

  1021. 

  1022.             switch (floor($ord)) {
    1023. 

  1023.                 case 0:
    1024. 

  1024.                     return self::besselK0($x);
    1025. 

  1025.                 case 1:
    1026. 

  1026.                     return self::besselK1($x);
    1027. 

  1027.                 default:
    1028. 

  1028.                     $fTox    = 2 / $x;
    1029. 

  1029.                     $fBkm    = self::besselK0($x);
    1030. 

  1030.                     $fBk    = self::besselK1($x);
    1031. 

  1031.                     for ($n = 1; $n < $ord; ++$n) {
    1032. 

  1032.                         $fBkp    = $fBkm + $n * $fTox * $fBk;
    1033. 

  1033.                         $fBkm    = $fBk;
    1034. 

  1034.                         $fBk    = $fBkp;
    1035. 

  1035.                     }
    1036. 

  1036.             }
    1037. 

  1037.             return (is_nan($fBk)) ? PHPExcel_Calculation_Functions::NaN() : $fBk;
    1038. 

  1038.         }
    1039. 

  1039.         return PHPExcel_Calculation_Functions::VALUE();
    1040. 

  1040.     }
    1041. 

  1041. 

  1042. 

  1043.     private static function besselY0($fNum)
    1044. 

  1044.     {
    1045. 

  1045.         if ($fNum < 8.0) {
    1046. 

  1046.             $y = ($fNum * $fNum);
    1047. 

  1047.             $f1 = -2957821389.0 + $y * (7062834065.0 + $y * (-512359803.6 + $y * (10879881.29 + $y * (-86327.92757 + $y * 228.4622733))));
    1048. 

  1048.             $f2 = 40076544269.0 + $y * (745249964.8 + $y * (7189466.438 + $y * (47447.26470 + $y * (226.1030244 + $y))));
    1049. 

  1049.             $fRet = $f1 / $f2 + 0.636619772 * self::BESSELJ($fNum, 0) * log($fNum);
    1050. 

  1050.         } else {
    1051. 

  1051.             $z = 8.0 / $fNum;
    1052. 

  1052.             $y = ($z * $z);
    1053. 

  1053.             $xx = $fNum - 0.785398164;
    1054. 

  1054.             $f1 = 1 + $y * (-0.1098628627e-2 + $y * (0.2734510407e-4 + $y * (-0.2073370639e-5 + $y * 0.2093887211e-6)));
    1055. 

  1055.             $f2 = -0.1562499995e-1 + $y * (0.1430488765e-3 + $y * (-0.6911147651e-5 + $y * (0.7621095161e-6 + $y * (-0.934945152e-7))));
    1056. 

  1056.             $fRet = sqrt(0.636619772 / $fNum) * (sin($xx) * $f1 + $z * cos($xx) * $f2);
    1057. 

  1057.         }
    1058. 

  1058.         return $fRet;
    1059. 

  1059.     }
    1060. 

  1060. 

  1061. 

  1062.     private static function besselY1($fNum)
    1063. 

  1063.     {
    1064. 

  1064.         if ($fNum < 8.0) {
    1065. 

  1065.             $y = ($fNum * $fNum);
    1066. 

  1066.             $f1 = $fNum * (-0.4900604943e13 + $y * (0.1275274390e13 + $y * (-0.5153438139e11 + $y * (0.7349264551e9 + $y *
    1067. 

  1067.                 (-0.4237922726e7 + $y * 0.8511937935e4)))));
    1068. 

  1068.             $f2 = 0.2499580570e14 + $y * (0.4244419664e12 + $y * (0.3733650367e10 + $y * (0.2245904002e8 + $y *
    1069. 

  1069.                 (0.1020426050e6 + $y * (0.3549632885e3 + $y)))));
    1070. 

  1070.             $fRet = $f1 / $f2 + 0.636619772 * ( self::BESSELJ($fNum, 1) * log($fNum) - 1 / $fNum);
    1071. 

  1071.         } else {
    1072. 

  1072.             $fRet = sqrt(0.636619772 / $fNum) * sin($fNum - 2.356194491);
    1073. 

  1073.         }
    1074. 

  1074.         return $fRet;
    1075. 

  1075.     }
    1076. 

  1076. 

  1077. 

  1078.     /**
    1079. 

  1079.      *    BESSELY
    1080. 

  1080.      *
    1081. 

  1081.      *    Returns the Bessel function, which is also called the Weber function or the Neumann function.
    1082. 

  1082.      *
    1083. 

  1083.      *    Excel Function:
    1084. 

  1084.      *        BESSELY(x,ord)
    1085. 

  1085.      *
    1086. 

  1086.      *    @access    public
    1087. 

  1087.      *    @category Engineering Functions
    1088. 

  1088.      *    @param    float        $x        The value at which to evaluate the function.
    1089. 

  1089.      *                                If x is nonnumeric, BESSELK returns the #VALUE! error value.
    1090. 

  1090.      *    @param    integer        $ord    The order of the Bessel function. If n is not an integer, it is truncated.
    1091. 

  1091.      *                                If $ord is nonnumeric, BESSELK returns the #VALUE! error value.
    1092. 

  1092.      *                                If $ord < 0, BESSELK returns the #NUM! error value.
    1093. 

  1093.      *
    1094. 

  1094.      *    @return    float
    1095. 

  1095.      */
    1096. 

  1096.     public static function BESSELY($x, $ord)
    1097. 

  1097.     {
    1098. 

  1098.         $x        = (is_null($x))        ? 0.0 :    PHPExcel_Calculation_Functions::flattenSingleValue($x);
    1099. 

  1099.         $ord    = (is_null($ord))    ? 0.0 :    PHPExcel_Calculation_Functions::flattenSingleValue($ord);
    1100. 

  1100. 

  1101.         if ((is_numeric($x)) && (is_numeric($ord))) {
    1102. 

  1102.             if (($ord < 0) || ($x == 0.0)) {
    1103. 

  1103.                 return PHPExcel_Calculation_Functions::NaN();
    1104. 

  1104.             }
    1105. 

  1105. 

  1106.             switch (floor($ord)) {
    1107. 

  1107.                 case 0:
    1108. 

  1108.                     return self::besselY0($x);
    1109. 

  1109.                 case 1:
    1110. 

  1110.                     return self::besselY1($x);
    1111. 

  1111.                 default:
    1112. 

  1112.                     $fTox    = 2 / $x;
    1113. 

  1113.                     $fBym    = self::besselY0($x);
    1114. 

  1114.                     $fBy    = self::besselY1($x);
    1115. 

  1115.                     for ($n = 1; $n < $ord; ++$n) {
    1116. 

  1116.                         $fByp    = $n * $fTox * $fBy - $fBym;
    1117. 

  1117.                         $fBym    = $fBy;
    1118. 

  1118.                         $fBy    = $fByp;
    1119. 

  1119.                     }
    1120. 

  1120.             }
    1121. 

  1121.             return (is_nan($fBy)) ? PHPExcel_Calculation_Functions::NaN() : $fBy;
    1122. 

  1122.         }
    1123. 

  1123.         return PHPExcel_Calculation_Functions::VALUE();
    1124. 

  1124.     }
    1125. 

  1125. 

  1126. 

  1127.     /**
    1128. 

  1128.      * BINTODEC
    1129. 

  1129.      *
    1130. 

  1130.      * Return a binary value as decimal.
    1131. 

  1131.      *
    1132. 

  1132.      * Excel Function:
    1133. 

  1133.      *        BIN2DEC(x)
    1134. 

  1134.      *
    1135. 

  1135.      * @access    public
    1136. 

  1136.      * @category Engineering Functions
    1137. 

  1137.      * @param    string        $x        The binary number (as a string) that you want to convert. The number
    1138. 

  1138.      *                                cannot contain more than 10 characters (10 bits). The most significant
    1139. 

  1139.      *                                bit of number is the sign bit. The remaining 9 bits are magnitude bits.
    1140. 

  1140.      *                                Negative numbers are represented using two's-complement notation.
    1141. 

  1141.      *                                If number is not a valid binary number, or if number contains more than
    1142. 

  1142.      *                                10 characters (10 bits), BIN2DEC returns the #NUM! error value.
    1143. 

  1143.      * @return    string
    1144. 

  1144.      */
    1145. 

  1145.     public static function BINTODEC($x)
    1146. 

  1146.     {
    1147. 

  1147.         $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);
    1148. 

  1148. 

  1149.         if (is_bool($x)) {
    1150. 

  1150.             if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
    1151. 

  1151.                 $x = (int) $x;
    1152. 

  1152.             } else {
    1153. 

  1153.                 return PHPExcel_Calculation_Functions::VALUE();
    1154. 

  1154.             }
    1155. 

  1155.         }
    1156. 

  1156.         if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
    1157. 

  1157.             $x = floor($x);
    1158. 

  1158.         }
    1159. 

  1159.         $x = (string) $x;
    1160. 

  1160.         if (strlen($x) > preg_match_all('/[01]/', $x, $out)) {
    1161. 

  1161.             return PHPExcel_Calculation_Functions::NaN();
    1162. 

  1162.         }
    1163. 

  1163.         if (strlen($x) > 10) {
    1164. 

  1164.             return PHPExcel_Calculation_Functions::NaN();
    1165. 

  1165.         } elseif (strlen($x) == 10) {
    1166. 

  1166.             //    Two's Complement
    1167. 

  1167.             $x = substr($x, -9);
    1168. 

  1168.             return '-'.(512-bindec($x));
    1169. 

  1169.         }
    1170. 

  1170.         return bindec($x);
    1171. 

  1171.     }
    1172. 

  1172. 

  1173. 

  1174.     /**
    1175. 

  1175.      * BINTOHEX
    1176. 

  1176.      *
    1177. 

  1177.      * Return a binary value as hex.
    1178. 

  1178.      *
    1179. 

  1179.      * Excel Function:
    1180. 

  1180.      *        BIN2HEX(x[,places])
    1181. 

  1181.      *
    1182. 

  1182.      * @access    public
    1183. 

  1183.      * @category Engineering Functions
    1184. 

  1184.      * @param    string        $x        The binary number (as a string) that you want to convert. The number
    1185. 

  1185.      *                                cannot contain more than 10 characters (10 bits). The most significant
    1186. 

  1186.      *                                bit of number is the sign bit. The remaining 9 bits are magnitude bits.
    1187. 

  1187.      *                                Negative numbers are represented using two's-complement notation.
    1188. 

  1188.      *                                If number is not a valid binary number, or if number contains more than
    1189. 

  1189.      *                                10 characters (10 bits), BIN2HEX returns the #NUM! error value.
    1190. 

  1190.      * @param    integer        $places    The number of characters to use. If places is omitted, BIN2HEX uses the
    1191. 

  1191.      *                                minimum number of characters necessary. Places is useful for padding the
    1192. 

  1192.      *                                return value with leading 0s (zeros).
    1193. 

  1193.      *                                If places is not an integer, it is truncated.
    1194. 

  1194.      *                                If places is nonnumeric, BIN2HEX returns the #VALUE! error value.
    1195. 

  1195.      *                                If places is negative, BIN2HEX returns the #NUM! error value.
    1196. 

  1196.      * @return    string
    1197. 

  1197.      */
    1198. 

  1198.     public static function BINTOHEX($x, $places = null)
    1199. 

  1199.     {
    1200. 

  1200.         $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);
    1201. 

  1201.         $places    = PHPExcel_Calculation_Functions::flattenSingleValue($places);
    1202. 

  1202. 

  1203.         if (is_bool($x)) {
    1204. 

  1204.             if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
    1205. 

  1205.                 $x = (int) $x;
    1206. 

  1206.             } else {
    1207. 

  1207.                 return PHPExcel_Calculation_Functions::VALUE();
    1208. 

  1208.             }
    1209. 

  1209.         }
    1210. 

  1210.         if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
    1211. 

  1211.             $x = floor($x);
    1212. 

  1212.         }
    1213. 

  1213.         $x = (string) $x;
    1214. 

  1214.         if (strlen($x) > preg_match_all('/[01]/', $x, $out)) {
    1215. 

  1215.             return PHPExcel_Calculation_Functions::NaN();
    1216. 

  1216.         }
    1217. 

  1217.         if (strlen($x) > 10) {
    1218. 

  1218.             return PHPExcel_Calculation_Functions::NaN();
    1219. 

  1219.         } elseif (strlen($x) == 10) {
    1220. 

  1220.             //    Two's Complement
    1221. 

  1221.             return str_repeat('F', 8).substr(strtoupper(dechex(bindec(substr($x, -9)))), -2);
    1222. 

  1222.         }
    1223. 

  1223.         $hexVal = (string) strtoupper(dechex(bindec($x)));
    1224. 

  1224. 

  1225.         return self::nbrConversionFormat($hexVal, $places);
    1226. 

  1226.     }
    1227. 

  1227. 

  1228. 

  1229.     /**
    1230. 

  1230.      * BINTOOCT
    1231. 

  1231.      *
    1232. 

  1232.      * Return a binary value as octal.
    1233. 

  1233.      *
    1234. 

  1234.      * Excel Function:
    1235. 

  1235.      *        BIN2OCT(x[,places])
    1236. 

  1236.      *
    1237. 

  1237.      * @access    public
    1238. 

  1238.      * @category Engineering Functions
    1239. 

  1239.      * @param    string        $x        The binary number (as a string) that you want to convert. The number
    1240. 

  1240.      *                                cannot contain more than 10 characters (10 bits). The most significant
    1241. 

  1241.      *                                bit of number is the sign bit. The remaining 9 bits are magnitude bits.
    1242. 

  1242.      *                                Negative numbers are represented using two's-complement notation.
    1243. 

  1243.      *                                If number is not a valid binary number, or if number contains more than
    1244. 

  1244.      *                                10 characters (10 bits), BIN2OCT returns the #NUM! error value.
    1245. 

  1245.      * @param    integer        $places    The number of characters to use. If places is omitted, BIN2OCT uses the
    1246. 

  1246.      *                                minimum number of characters necessary. Places is useful for padding the
    1247. 

  1247.      *                                return value with leading 0s (zeros).
    1248. 

  1248.      *                                If places is not an integer, it is truncated.
    1249. 

  1249.      *                                If places is nonnumeric, BIN2OCT returns the #VALUE! error value.
    1250. 

  1250.      *                                If places is negative, BIN2OCT returns the #NUM! error value.
    1251. 

  1251.      * @return    string
    1252. 

  1252.      */
    1253. 

  1253.     public static function BINTOOCT($x, $places = null)
    1254. 

  1254.     {
    1255. 

  1255.         $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);
    1256. 

  1256.         $places    = PHPExcel_Calculation_Functions::flattenSingleValue($places);
    1257. 

  1257. 

  1258.         if (is_bool($x)) {
    1259. 

  1259.             if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
    1260. 

  1260.                 $x = (int) $x;
    1261. 

  1261.             } else {
    1262. 

  1262.                 return PHPExcel_Calculation_Functions::VALUE();
    1263. 

  1263.             }
    1264. 

  1264.         }
    1265. 

  1265.         if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
    1266. 

  1266.             $x = floor($x);
    1267. 

  1267.         }
    1268. 

  1268.         $x = (string) $x;
    1269. 

  1269.         if (strlen($x) > preg_match_all('/[01]/', $x, $out)) {
    1270. 

  1270.             return PHPExcel_Calculation_Functions::NaN();
    1271. 

  1271.         }
    1272. 

  1272.         if (strlen($x) > 10) {
    1273. 

  1273.             return PHPExcel_Calculation_Functions::NaN();
    1274. 

  1274.         } elseif (strlen($x) == 10) {
    1275. 

  1275.             //    Two's Complement
    1276. 

  1276.             return str_repeat('7', 7).substr(strtoupper(decoct(bindec(substr($x, -9)))), -3);
    1277. 

  1277.         }
    1278. 

  1278.         $octVal = (string) decoct(bindec($x));
    1279. 

  1279. 

  1280.         return self::nbrConversionFormat($octVal, $places);
    1281. 

  1281.     }
    1282. 

  1282. 

  1283. 

  1284.     /**
    1285. 

  1285.      * DECTOBIN
    1286. 

  1286.      *
    1287. 

  1287.      * Return a decimal value as binary.
    1288. 

  1288.      *
    1289. 

  1289.      * Excel Function:
    1290. 

  1290.      *        DEC2BIN(x[,places])
    1291. 

  1291.      *
    1292. 

  1292.      * @access    public
    1293. 

  1293.      * @category Engineering Functions
    1294. 

  1294.      * @param    string        $x        The decimal integer you want to convert. If number is negative,
    1295. 

  1295.      *                                valid place values are ignored and DEC2BIN returns a 10-character
    1296. 

  1296.      *                                (10-bit) binary number in which the most significant bit is the sign
    1297. 

  1297.      *                                bit. The remaining 9 bits are magnitude bits. Negative numbers are
    1298. 

  1298.      *                                represented using two's-complement notation.
    1299. 

  1299.      *                                If number < -512 or if number > 511, DEC2BIN returns the #NUM! error
    1300. 

  1300.      *                                value.
    1301. 

  1301.      *                                If number is nonnumeric, DEC2BIN returns the #VALUE! error value.
    1302. 

  1302.      *                                If DEC2BIN requires more than places characters, it returns the #NUM!
    1303. 

  1303.      *                                error value.
    1304. 

  1304.      * @param    integer        $places    The number of characters to use. If places is omitted, DEC2BIN uses
    1305. 

  1305.      *                                the minimum number of characters necessary. Places is useful for
    1306. 

  1306.      *                                padding the return value with leading 0s (zeros).
    1307. 

  1307.      *                                If places is not an integer, it is truncated.
    1308. 

  1308.      *                                If places is nonnumeric, DEC2BIN returns the #VALUE! error value.
    1309. 

  1309.      *                                If places is zero or negative, DEC2BIN returns the #NUM! error value.
    1310. 

  1310.      * @return    string
    1311. 

  1311.      */
    1312. 

  1312.     public static function DECTOBIN($x, $places = null)
    1313. 

  1313.     {
    1314. 

  1314.         $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);
    1315. 

  1315.         $places    = PHPExcel_Calculation_Functions::flattenSingleValue($places);
    1316. 

  1316. 

  1317.         if (is_bool($x)) {
    1318. 

  1318.             if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
    1319. 

  1319.                 $x = (int) $x;
    1320. 

  1320.             } else {
    1321. 

  1321.                 return PHPExcel_Calculation_Functions::VALUE();
    1322. 

  1322.             }
    1323. 

  1323.         }
    1324. 

  1324.         $x = (string) $x;
    1325. 

  1325.         if (strlen($x) > preg_match_all('/[-0123456789.]/', $x, $out)) {
    1326. 

  1326.             return PHPExcel_Calculation_Functions::VALUE();
    1327. 

  1327.         }
    1328. 

  1328.         $x = (string) floor($x);
    1329. 

  1329.         $r = decbin($x);
    1330. 

  1330.         if (strlen($r) == 32) {
    1331. 

  1331.             //    Two's Complement
    1332. 

  1332.             $r = substr($r, -10);
    1333. 

  1333.         } elseif (strlen($r) > 11) {
    1334. 

  1334.             return PHPExcel_Calculation_Functions::NaN();
    1335. 

  1335.         }
    1336. 

  1336. 

  1337.         return self::nbrConversionFormat($r, $places);
    1338. 

  1338.     }
    1339. 

  1339. 

  1340. 

  1341.     /**
    1342. 

  1342.      * DECTOHEX
    1343. 

  1343.      *
    1344. 

  1344.      * Return a decimal value as hex.
    1345. 

  1345.      *
    1346. 

  1346.      * Excel Function:
    1347. 

  1347.      *        DEC2HEX(x[,places])
    1348. 

  1348.      *
    1349. 

  1349.      * @access    public
    1350. 

  1350.      * @category Engineering Functions
    1351. 

  1351.      * @param    string        $x        The decimal integer you want to convert. If number is negative,
    1352. 

  1352.      *                                places is ignored and DEC2HEX returns a 10-character (40-bit)
    1353. 

  1353.      *                                hexadecimal number in which the most significant bit is the sign
    1354. 

  1354.      *                                bit. The remaining 39 bits are magnitude bits. Negative numbers
    1355. 

  1355.      *                                are represented using two's-complement notation.
    1356. 

  1356.      *                                If number < -549,755,813,888 or if number > 549,755,813,887,
    1357. 

  1357.      *                                DEC2HEX returns the #NUM! error value.
    1358. 

  1358.      *                                If number is nonnumeric, DEC2HEX returns the #VALUE! error value.
    1359. 

  1359.      *                                If DEC2HEX requires more than places characters, it returns the
    1360. 

  1360.      *                                #NUM! error value.
    1361. 

  1361.      * @param    integer        $places    The number of characters to use. If places is omitted, DEC2HEX uses
    1362. 

  1362.      *                                the minimum number of characters necessary. Places is useful for
    1363. 

  1363.      *                                padding the return value with leading 0s (zeros).
    1364. 

  1364.      *                                If places is not an integer, it is truncated.
    1365. 

  1365.      *                                If places is nonnumeric, DEC2HEX returns the #VALUE! error value.
    1366. 

  1366.      *                                If places is zero or negative, DEC2HEX returns the #NUM! error value.
    1367. 

  1367.      * @return    string
    1368. 

  1368.      */
    1369. 

  1369.     public static function DECTOHEX($x, $places = null)
    1370. 

  1370.     {
    1371. 

  1371.         $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);
    1372. 

  1372.         $places    = PHPExcel_Calculation_Functions::flattenSingleValue($places);
    1373. 

  1373. 

  1374.         if (is_bool($x)) {
    1375. 

  1375.             if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
    1376. 

  1376.                 $x = (int) $x;
    1377. 

  1377.             } else {
    1378. 

  1378.                 return PHPExcel_Calculation_Functions::VALUE();
    1379. 

  1379.             }
    1380. 

  1380.         }
    1381. 

  1381.         $x = (string) $x;
    1382. 

  1382.         if (strlen($x) > preg_match_all('/[-0123456789.]/', $x, $out)) {
    1383. 

  1383.             return PHPExcel_Calculation_Functions::VALUE();
    1384. 

  1384.         }
    1385. 

  1385.         $x = (string) floor($x);
    1386. 

  1386.         $r = strtoupper(dechex($x));
    1387. 

  1387.         if (strlen($r) == 8) {
    1388. 

  1388.             //    Two's Complement
    1389. 

  1389.             $r = 'FF'.$r;
    1390. 

  1390.         }
    1391. 

  1391. 

  1392.         return self::nbrConversionFormat($r, $places);
    1393. 

  1393.     }
    1394. 

  1394. 

  1395. 

  1396.     /**
    1397. 

  1397.      * DECTOOCT
    1398. 

  1398.      *
    1399. 

  1399.      * Return an decimal value as octal.
    1400. 

  1400.      *
    1401. 

  1401.      * Excel Function:
    1402. 

  1402.      *        DEC2OCT(x[,places])
    1403. 

  1403.      *
    1404. 

  1404.      * @access    public
    1405. 

  1405.      * @category Engineering Functions
    1406. 

  1406.      * @param    string        $x        The decimal integer you want to convert. If number is negative,
    1407. 

  1407.      *                                places is ignored and DEC2OCT returns a 10-character (30-bit)
    1408. 

  1408.      *                                octal number in which the most significant bit is the sign bit.
    1409. 

  1409.      *                                The remaining 29 bits are magnitude bits. Negative numbers are
    1410. 

  1410.      *                                represented using two's-complement notation.
    1411. 

  1411.      *                                If number < -536,870,912 or if number > 536,870,911, DEC2OCT
    1412. 

  1412.      *                                returns the #NUM! error value.
    1413. 

  1413.      *                                If number is nonnumeric, DEC2OCT returns the #VALUE! error value.
    1414. 

  1414.      *                                If DEC2OCT requires more than places characters, it returns the
    1415. 

  1415.      *                                #NUM! error value.
    1416. 

  1416.      * @param    integer        $places    The number of characters to use. If places is omitted, DEC2OCT uses
    1417. 

  1417.      *                                the minimum number of characters necessary. Places is useful for
    1418. 

  1418.      *                                padding the return value with leading 0s (zeros).
    1419. 

  1419.      *                                If places is not an integer, it is truncated.
    1420. 

  1420.      *                                If places is nonnumeric, DEC2OCT returns the #VALUE! error value.
    1421. 

  1421.      *                                If places is zero or negative, DEC2OCT returns the #NUM! error value.
    1422. 

  1422.      * @return    string
    1423. 

  1423.      */
    1424. 

  1424.     public static function DECTOOCT($x, $places = null)
    1425. 

  1425.     {
    1426. 

  1426.         $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);
    1427. 

  1427.         $places    = PHPExcel_Calculation_Functions::flattenSingleValue($places);
    1428. 

  1428. 

  1429.         if (is_bool($x)) {
    1430. 

  1430.             if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
    1431. 

  1431.                 $x = (int) $x;
    1432. 

  1432.             } else {
    1433. 

  1433.                 return PHPExcel_Calculation_Functions::VALUE();
    1434. 

  1434.             }
    1435. 

  1435.         }
    1436. 

  1436.         $x = (string) $x;
    1437. 

  1437.         if (strlen($x) > preg_match_all('/[-0123456789.]/', $x, $out)) {
    1438. 

  1438.             return PHPExcel_Calculation_Functions::VALUE();
    1439. 

  1439.         }
    1440. 

  1440.         $x = (string) floor($x);
    1441. 

  1441.         $r = decoct($x);
    1442. 

  1442.         if (strlen($r) == 11) {
    1443. 

  1443.             //    Two's Complement
    1444. 

  1444.             $r = substr($r, -10);
    1445. 

  1445.         }
    1446. 

  1446. 

  1447.         return self::nbrConversionFormat($r, $places);
    1448. 

  1448.     }
    1449. 

  1449. 

  1450. 

  1451.     /**
    1452. 

  1452.      * HEXTOBIN
    1453. 

  1453.      *
    1454. 

  1454.      * Return a hex value as binary.
    1455. 

  1455.      *
    1456. 

  1456.      * Excel Function:
    1457. 

  1457.      *        HEX2BIN(x[,places])
    1458. 

  1458.      *
    1459. 

  1459.      * @access    public
    1460. 

  1460.      * @category Engineering Functions
    1461. 

  1461.      * @param    string        $x            the hexadecimal number you want to convert. Number cannot
    1462. 

  1462.      *                                    contain more than 10 characters. The most significant bit of
    1463. 

  1463.      *                                    number is the sign bit (40th bit from the right). The remaining
    1464. 

  1464.      *                                    9 bits are magnitude bits. Negative numbers are represented
    1465. 

  1465.      *                                    using two's-complement notation.
    1466. 

  1466.      *                                    If number is negative, HEX2BIN ignores places and returns a
    1467. 

  1467.      *                                    10-character binary number.
    1468. 

  1468.      *                                    If number is negative, it cannot be less than FFFFFFFE00, and
    1469. 

  1469.      *                                    if number is positive, it cannot be greater than 1FF.
    1470. 

  1470.      *                                    If number is not a valid hexadecimal number, HEX2BIN returns
    1471. 

  1471.      *                                    the #NUM! error value.
    1472. 

  1472.      *                                    If HEX2BIN requires more than places characters, it returns
    1473. 

  1473.      *                                    the #NUM! error value.
    1474. 

  1474.      * @param    integer        $places        The number of characters to use. If places is omitted,
    1475. 

  1475.      *                                    HEX2BIN uses the minimum number of characters necessary. Places
    1476. 

  1476.      *                                    is useful for padding the return value with leading 0s (zeros).
    1477. 

  1477.      *                                    If places is not an integer, it is truncated.
    1478. 

  1478.      *                                    If places is nonnumeric, HEX2BIN returns the #VALUE! error value.
    1479. 

  1479.      *                                    If places is negative, HEX2BIN returns the #NUM! error value.
    1480. 

  1480.      * @return    string
    1481. 

  1481.      */
    1482. 

  1482.     public static function HEXTOBIN($x, $places = null)
    1483. 

  1483.     {
    1484. 

  1484.         $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);
    1485. 

  1485.         $places    = PHPExcel_Calculation_Functions::flattenSingleValue($places);
    1486. 

  1486. 

  1487.         if (is_bool($x)) {
    1488. 

  1488.             return PHPExcel_Calculation_Functions::VALUE();
    1489. 

  1489.         }
    1490. 

  1490.         $x = (string) $x;
    1491. 

  1491.         if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/', strtoupper($x), $out)) {
    1492. 

  1492.             return PHPExcel_Calculation_Functions::NaN();
    1493. 

  1493.         }
    1494. 

  1494.         $binVal = decbin(hexdec($x));
    1495. 

  1495. 

  1496.         return substr(self::nbrConversionFormat($binVal, $places), -10);
    1497. 

  1497.     }
    1498. 

  1498. 

  1499. 

  1500.     /**
    1501. 

  1501.      * HEXTODEC
    1502. 

  1502.      *
    1503. 

  1503.      * Return a hex value as decimal.
    1504. 

  1504.      *
    1505. 

  1505.      * Excel Function:
    1506. 

  1506.      *        HEX2DEC(x)
    1507. 

  1507.      *
    1508. 

  1508.      * @access    public
    1509. 

  1509.      * @category Engineering Functions
    1510. 

  1510.      * @param    string        $x        The hexadecimal number you want to convert. This number cannot
    1511. 

  1511.      *                                contain more than 10 characters (40 bits). The most significant
    1512. 

  1512.      *                                bit of number is the sign bit. The remaining 39 bits are magnitude
    1513. 

  1513.      *                                bits. Negative numbers are represented using two's-complement
    1514. 

  1514.      *                                notation.
    1515. 

  1515.      *                                If number is not a valid hexadecimal number, HEX2DEC returns the
    1516. 

  1516.      *                                #NUM! error value.
    1517. 

  1517.      * @return    string
    1518. 

  1518.      */
    1519. 

  1519.     public static function HEXTODEC($x)
    1520. 

  1520.     {
    1521. 

  1521.         $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);
    1522. 

  1522. 

  1523.         if (is_bool($x)) {
    1524. 

  1524.             return PHPExcel_Calculation_Functions::VALUE();
    1525. 

  1525.         }
    1526. 

  1526.         $x = (string) $x;
    1527. 

  1527.         if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/', strtoupper($x), $out)) {
    1528. 

  1528.             return PHPExcel_Calculation_Functions::NaN();
    1529. 

  1529.         }
    1530. 

  1530.         return hexdec($x);
    1531. 

  1531.     }
    1532. 

  1532. 

  1533. 

  1534.     /**
    1535. 

  1535.      * HEXTOOCT
    1536. 

  1536.      *
    1537. 

  1537.      * Return a hex value as octal.
    1538. 

  1538.      *
    1539. 

  1539.      * Excel Function:
    1540. 

  1540.      *        HEX2OCT(x[,places])
    1541. 

  1541.      *
    1542. 

  1542.      * @access    public
    1543. 

  1543.      * @category Engineering Functions
    1544. 

  1544.      * @param    string        $x            The hexadecimal number you want to convert. Number cannot
    1545. 

  1545.      *                                    contain more than 10 characters. The most significant bit of
    1546. 

  1546.      *                                    number is the sign bit. The remaining 39 bits are magnitude
    1547. 

  1547.      *                                    bits. Negative numbers are represented using two's-complement
    1548. 

  1548.      *                                    notation.
    1549. 

  1549.      *                                    If number is negative, HEX2OCT ignores places and returns a
    1550. 

  1550.      *                                    10-character octal number.
    1551. 

  1551.      *                                    If number is negative, it cannot be less than FFE0000000, and
    1552. 

  1552.      *                                    if number is positive, it cannot be greater than 1FFFFFFF.
    1553. 

  1553.      *                                    If number is not a valid hexadecimal number, HEX2OCT returns
    1554. 

  1554.      *                                    the #NUM! error value.
    1555. 

  1555.      *                                    If HEX2OCT requires more than places characters, it returns
    1556. 

  1556.      *                                    the #NUM! error value.
    1557. 

  1557.      * @param    integer        $places        The number of characters to use. If places is omitted, HEX2OCT
    1558. 

  1558.      *                                    uses the minimum number of characters necessary. Places is
    1559. 

  1559.      *                                    useful for padding the return value with leading 0s (zeros).
    1560. 

  1560.      *                                    If places is not an integer, it is truncated.
    1561. 

  1561.      *                                    If places is nonnumeric, HEX2OCT returns the #VALUE! error
    1562. 

  1562.      *                                    value.
    1563. 

  1563.      *                                    If places is negative, HEX2OCT returns the #NUM! error value.
    1564. 

  1564.      * @return    string
    1565. 

  1565.      */
    1566. 

  1566.     public static function HEXTOOCT($x, $places = null)
    1567. 

  1567.     {
    1568. 

  1568.         $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);
    1569. 

  1569.         $places    = PHPExcel_Calculation_Functions::flattenSingleValue($places);
    1570. 

  1570. 

  1571.         if (is_bool($x)) {
    1572. 

  1572.             return PHPExcel_Calculation_Functions::VALUE();
    1573. 

  1573.         }
    1574. 

  1574.         $x = (string) $x;
    1575. 

  1575.         if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/', strtoupper($x), $out)) {
    1576. 

  1576.             return PHPExcel_Calculation_Functions::NaN();
    1577. 

  1577.         }
    1578. 

  1578.         $octVal = decoct(hexdec($x));
    1579. 

  1579. 

  1580.         return self::nbrConversionFormat($octVal, $places);
    1581. 

  1581.     }    //    function HEXTOOCT()
    1582. 

  1582. 

  1583. 

  1584.     /**
    1585. 

  1585.      * OCTTOBIN
    1586. 

  1586.      *
    1587. 

  1587.      * Return an octal value as binary.
    1588. 

  1588.      *
    1589. 

  1589.      * Excel Function:
    1590. 

  1590.      *        OCT2BIN(x[,places])
    1591. 

  1591.      *
    1592. 

  1592.      * @access    public
    1593. 

  1593.      * @category Engineering Functions
    1594. 

  1594.      * @param    string        $x            The octal number you want to convert. Number may not
    1595. 

  1595.      *                                    contain more than 10 characters. The most significant
    1596. 

  1596.      *                                    bit of number is the sign bit. The remaining 29 bits
    1597. 

  1597.      *                                    are magnitude bits. Negative numbers are represented
    1598. 

  1598.      *                                    using two's-complement notation.
    1599. 

  1599.      *                                    If number is negative, OCT2BIN ignores places and returns
    1600. 

  1600.      *                                    a 10-character binary number.
    1601. 

  1601.      *                                    If number is negative, it cannot be less than 7777777000,
    1602. 

  1602.      *                                    and if number is positive, it cannot be greater than 777.
    1603. 

  1603.      *                                    If number is not a valid octal number, OCT2BIN returns
    1604. 

  1604.      *                                    the #NUM! error value.
    1605. 

  1605.      *                                    If OCT2BIN requires more than places characters, it
    1606. 

  1606.      *                                    returns the #NUM! error value.
    1607. 

  1607.      * @param    integer        $places        The number of characters to use. If places is omitted,
    1608. 

  1608.      *                                    OCT2BIN uses the minimum number of characters necessary.
    1609. 

  1609.      *                                    Places is useful for padding the return value with
    1610. 

  1610.      *                                    leading 0s (zeros).
    1611. 

  1611.      *                                    If places is not an integer, it is truncated.
    1612. 

  1612.      *                                    If places is nonnumeric, OCT2BIN returns the #VALUE!
    1613. 

  1613.      *                                    error value.
    1614. 

  1614.      *                                    If places is negative, OCT2BIN returns the #NUM! error
    1615. 

  1615.      *                                    value.
    1616. 

  1616.      * @return    string
    1617. 

  1617.      */
    1618. 

  1618.     public static function OCTTOBIN($x, $places = null)
    1619. 

  1619.     {
    1620. 

  1620.         $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);
    1621. 

  1621.         $places    = PHPExcel_Calculation_Functions::flattenSingleValue($places);
    1622. 

  1622. 

  1623.         if (is_bool($x)) {
    1624. 

  1624.             return PHPExcel_Calculation_Functions::VALUE();
    1625. 

  1625.         }
    1626. 

  1626.         $x = (string) $x;
    1627. 

  1627.         if (preg_match_all('/[01234567]/', $x, $out) != strlen($x)) {
    1628. 

  1628.             return PHPExcel_Calculation_Functions::NaN();
    1629. 

  1629.         }
    1630. 

  1630.         $r = decbin(octdec($x));
    1631. 

  1631. 

  1632.         return self::nbrConversionFormat($r, $places);
    1633. 

  1633.     }
    1634. 

  1634. 

  1635. 

  1636.     /**
    1637. 

  1637.      * OCTTODEC
    1638. 

  1638.      *
    1639. 

  1639.      * Return an octal value as decimal.
    1640. 

  1640.      *
    1641. 

  1641.      * Excel Function:
    1642. 

  1642.      *        OCT2DEC(x)
    1643. 

  1643.      *
    1644. 

  1644.      * @access    public
    1645. 

  1645.      * @category Engineering Functions
    1646. 

  1646.      * @param    string        $x        The octal number you want to convert. Number may not contain
    1647. 

  1647.      *                                more than 10 octal characters (30 bits). The most significant
    1648. 

  1648.      *                                bit of number is the sign bit. The remaining 29 bits are
    1649. 

  1649.      *                                magnitude bits. Negative numbers are represented using
    1650. 

  1650.      *                                two's-complement notation.
    1651. 

  1651.      *                                If number is not a valid octal number, OCT2DEC returns the
    1652. 

  1652.      *                                #NUM! error value.
    1653. 

  1653.      * @return    string
    1654. 

  1654.      */
    1655. 

  1655.     public static function OCTTODEC($x)
    1656. 

  1656.     {
    1657. 

  1657.         $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);
    1658. 

  1658. 

  1659.         if (is_bool($x)) {
    1660. 

  1660.             return PHPExcel_Calculation_Functions::VALUE();
    1661. 

  1661.         }
    1662. 

  1662.         $x = (string) $x;
    1663. 

  1663.         if (preg_match_all('/[01234567]/', $x, $out) != strlen($x)) {
    1664. 

  1664.             return PHPExcel_Calculation_Functions::NaN();
    1665. 

  1665.         }
    1666. 

  1666.         return octdec($x);
    1667. 

  1667.     }
    1668. 

  1668. 

  1669. 

  1670.     /**
    1671. 

  1671.      * OCTTOHEX
    1672. 

  1672.      *
    1673. 

  1673.      * Return an octal value as hex.
    1674. 

  1674.      *
    1675. 

  1675.      * Excel Function:
    1676. 

  1676.      *        OCT2HEX(x[,places])
    1677. 

  1677.      *
    1678. 

  1678.      * @access    public
    1679. 

  1679.      * @category Engineering Functions
    1680. 

  1680.      * @param    string        $x            The octal number you want to convert. Number may not contain
    1681. 

  1681.      *                                    more than 10 octal characters (30 bits). The most significant
    1682. 

  1682.      *                                    bit of number is the sign bit. The remaining 29 bits are
    1683. 

  1683.      *                                    magnitude bits. Negative numbers are represented using
    1684. 

  1684.      *                                    two's-complement notation.
    1685. 

  1685.      *                                    If number is negative, OCT2HEX ignores places and returns a
    1686. 

  1686.      *                                    10-character hexadecimal number.
    1687. 

  1687.      *                                    If number is not a valid octal number, OCT2HEX returns the
    1688. 

  1688.      *                                    #NUM! error value.
    1689. 

  1689.      *                                    If OCT2HEX requires more than places characters, it returns
    1690. 

  1690.      *                                    the #NUM! error value.
    1691. 

  1691.      * @param    integer        $places        The number of characters to use. If places is omitted, OCT2HEX
    1692. 

  1692.      *                                    uses the minimum number of characters necessary. Places is useful
    1693. 

  1693.      *                                    for padding the return value with leading 0s (zeros).
    1694. 

  1694.      *                                    If places is not an integer, it is truncated.
    1695. 

  1695.      *                                    If places is nonnumeric, OCT2HEX returns the #VALUE! error value.
    1696. 

  1696.      *                                    If places is negative, OCT2HEX returns the #NUM! error value.
    1697. 

  1697.      * @return    string
    1698. 

  1698.      */
    1699. 

  1699.     public static function OCTTOHEX($x, $places = null)
    1700. 

  1700.     {
    1701. 

  1701.         $x    = PHPExcel_Calculation_Functions::flattenSingleValue($x);
    1702. 

  1702.         $places    = PHPExcel_Calculation_Functions::flattenSingleValue($places);
    1703. 

  1703. 

  1704.         if (is_bool($x)) {
    1705. 

  1705.             return PHPExcel_Calculation_Functions::VALUE();
    1706. 

  1706.         }
    1707. 

  1707.         $x = (string) $x;
    1708. 

  1708.         if (preg_match_all('/[01234567]/', $x, $out) != strlen($x)) {
    1709. 

  1709.             return PHPExcel_Calculation_Functions::NaN();
    1710. 

  1710.         }
    1711. 

  1711.         $hexVal = strtoupper(dechex(octdec($x)));
    1712. 

  1712. 

  1713.         return self::nbrConversionFormat($hexVal, $places);
    1714. 

  1714.     }
    1715. 

  1715. 

  1716. 

  1717.     /**
    1718. 

  1718.      * COMPLEX
    1719. 

  1719.      *
    1720. 

  1720.      * Converts real and imaginary coefficients into a complex number of the form x + yi or x + yj.
    1721. 

  1721.      *
    1722. 

  1722.      * Excel Function:
    1723. 

  1723.      *        COMPLEX(realNumber,imaginary[,places])
    1724. 

  1724.      *
    1725. 

  1725.      * @access    public
    1726. 

  1726.      * @category Engineering Functions
    1727. 

  1727.      * @param    float        $realNumber        The real coefficient of the complex number.
    1728. 

  1728.      * @param    float        $imaginary        The imaginary coefficient of the complex number.
    1729. 

  1729.      * @param    string        $suffix            The suffix for the imaginary component of the complex number.
    1730. 

  1730.      *                                        If omitted, the suffix is assumed to be "i".
    1731. 

  1731.      * @return    string
    1732. 

  1732.      */
    1733. 

  1733.     public static function COMPLEX($realNumber = 0.0, $imaginary = 0.0, $suffix = 'i')
    1734. 

  1734.     {
    1735. 

  1735.         $realNumber = (is_null($realNumber)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($realNumber);
    1736. 

  1736.         $imaginary  = (is_null($imaginary))  ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($imaginary);
    1737. 

  1737.         $suffix     = (is_null($suffix))     ? 'i' : PHPExcel_Calculation_Functions::flattenSingleValue($suffix);
    1738. 

  1738. 

  1739.         if (((is_numeric($realNumber)) && (is_numeric($imaginary))) &&
    1740. 

  1740.             (($suffix == 'i') || ($suffix == 'j') || ($suffix == ''))) {
    1741. 

  1741.             $realNumber    = (float) $realNumber;
    1742. 

  1742.             $imaginary    = (float) $imaginary;
    1743. 

  1743. 

  1744.             if ($suffix == '') {
    1745. 

  1745.                 $suffix = 'i';
    1746. 

  1746.             }
    1747. 

  1747.             if ($realNumber == 0.0) {
    1748. 

  1748.                 if ($imaginary == 0.0) {
    1749. 

  1749.                     return (string) '0';
    1750. 

  1750.                 } elseif ($imaginary == 1.0) {
    1751. 

  1751.                     return (string) $suffix;
    1752. 

  1752.                 } elseif ($imaginary == -1.0) {
    1753. 

  1753.                     return (string) '-'.$suffix;
    1754. 

  1754.                 }
    1755. 

  1755.                 return (string) $imaginary.$suffix;
    1756. 

  1756.             } elseif ($imaginary == 0.0) {
    1757. 

  1757.                 return (string) $realNumber;
    1758. 

  1758.             } elseif ($imaginary == 1.0) {
    1759. 

  1759.                 return (string) $realNumber.'+'.$suffix;
    1760. 

  1760.             } elseif ($imaginary == -1.0) {
    1761. 

  1761.                 return (string) $realNumber.'-'.$suffix;
    1762. 

  1762.             }
    1763. 

  1763.             if ($imaginary > 0) {
    1764. 

  1764.                 $imaginary = (string) '+'.$imaginary;
    1765. 

  1765.             }
    1766. 

  1766.             return (string) $realNumber.$imaginary.$suffix;
    1767. 

  1767.         }
    1768. 

  1768. 

  1769.         return PHPExcel_Calculation_Functions::VALUE();
    1770. 

  1770.     }
    1771. 

  1771. 

  1772. 

  1773.     /**
    1774. 

  1774.      * IMAGINARY
    1775. 

  1775.      *
    1776. 

  1776.      * Returns the imaginary coefficient of a complex number in x + yi or x + yj text format.
    1777. 

  1777.      *
    1778. 

  1778.      * Excel Function:
    1779. 

  1779.      *        IMAGINARY(complexNumber)
    1780. 

  1780.      *
    1781. 

  1781.      * @access    public
    1782. 

  1782.      * @category Engineering Functions
    1783. 

  1783.      * @param    string        $complexNumber    The complex number for which you want the imaginary
    1784. 

  1784.      *                                         coefficient.
    1785. 

  1785.      * @return    float
    1786. 

  1786.      */
    1787. 

  1787.     public static function IMAGINARY($complexNumber)
    1788. 

  1788.     {
    1789. 

  1789.         $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
    1790. 

  1790. 

  1791.         $parsedComplex = self::parseComplex($complexNumber);
    1792. 

  1792.         return $parsedComplex['imaginary'];
    1793. 

  1793.     }
    1794. 

  1794. 

  1795. 

  1796.     /**
    1797. 

  1797.      * IMREAL
    1798. 

  1798.      *
    1799. 

  1799.      * Returns the real coefficient of a complex number in x + yi or x + yj text format.
    1800. 

  1800.      *
    1801. 

  1801.      * Excel Function:
    1802. 

  1802.      *        IMREAL(complexNumber)
    1803. 

  1803.      *
    1804. 

  1804.      * @access    public
    1805. 

  1805.      * @category Engineering Functions
    1806. 

  1806.      * @param    string        $complexNumber    The complex number for which you want the real coefficient.
    1807. 

  1807.      * @return    float
    1808. 

  1808.      */
    1809. 

  1809.     public static function IMREAL($complexNumber)
    1810. 

  1810.     {
    1811. 

  1811.         $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
    1812. 

  1812. 

  1813.         $parsedComplex = self::parseComplex($complexNumber);
    1814. 

  1814.         return $parsedComplex['real'];
    1815. 

  1815.     }
    1816. 

  1816. 

  1817. 

  1818.     /**
    1819. 

  1819.      * IMABS
    1820. 

  1820.      *
    1821. 

  1821.      * Returns the absolute value (modulus) of a complex number in x + yi or x + yj text format.
    1822. 

  1822.      *
    1823. 

  1823.      * Excel Function:
    1824. 

  1824.      *        IMABS(complexNumber)
    1825. 

  1825.      *
    1826. 

  1826.      * @param    string        $complexNumber    The complex number for which you want the absolute value.
    1827. 

  1827.      * @return    float
    1828. 

  1828.      */
    1829. 

  1829.     public static function IMABS($complexNumber)
    1830. 

  1830.     {
    1831. 

  1831.         $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
    1832. 

  1832. 

  1833.         $parsedComplex = self::parseComplex($complexNumber);
    1834. 

  1834. 

  1835.         return sqrt(
    1836. 

  1836.             ($parsedComplex['real'] * $parsedComplex['real']) +
    1837. 

  1837.             ($parsedComplex['imaginary'] * $parsedComplex['imaginary'])
    1838. 

  1838.         );
    1839. 

  1839.     }
    1840. 

  1840. 

  1841. 

  1842.     /**
    1843. 

  1843.      * IMARGUMENT
    1844. 

  1844.      *
    1845. 

  1845.      * Returns the argument theta of a complex number, i.e. the angle in radians from the real
    1846. 

  1846.      * axis to the representation of the number in polar coordinates.
    1847. 

  1847.      *
    1848. 

  1848.      * Excel Function:
    1849. 

  1849.      *        IMARGUMENT(complexNumber)
    1850. 

  1850.      *
    1851. 

  1851.      * @param    string        $complexNumber    The complex number for which you want the argument theta.
    1852. 

  1852.      * @return    float
    1853. 

  1853.      */
    1854. 

  1854.     public static function IMARGUMENT($complexNumber)
    1855. 

  1855.     {
    1856. 

  1856.         $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
    1857. 

  1857. 

  1858.         $parsedComplex = self::parseComplex($complexNumber);
    1859. 

  1859. 

  1860.         if ($parsedComplex['real'] == 0.0) {
    1861. 

  1861.             if ($parsedComplex['imaginary'] == 0.0) {
    1862. 

  1862.                 return 0.0;
    1863. 

  1863.             } elseif ($parsedComplex['imaginary'] < 0.0) {
    1864. 

  1864.                 return M_PI / -2;
    1865. 

  1865.             } else {
    1866. 

  1866.                 return M_PI / 2;
    1867. 

  1867.             }
    1868. 

  1868.         } elseif ($parsedComplex['real'] > 0.0) {
    1869. 

  1869.             return atan($parsedComplex['imaginary'] / $parsedComplex['real']);
    1870. 

  1870.         } elseif ($parsedComplex['imaginary'] < 0.0) {
    1871. 

  1871.             return 0 - (M_PI - atan(abs($parsedComplex['imaginary']) / abs($parsedComplex['real'])));
    1872. 

  1872.         } else {
    1873. 

  1873.             return M_PI - atan($parsedComplex['imaginary'] / abs($parsedComplex['real']));
    1874. 

  1874.         }
    1875. 

  1875.     }
    1876. 

  1876. 

  1877. 

  1878.     /**
    1879. 

  1879.      * IMCONJUGATE
    1880. 

  1880.      *
    1881. 

  1881.      * Returns the complex conjugate of a complex number in x + yi or x + yj text format.
    1882. 

  1882.      *
    1883. 

  1883.      * Excel Function:
    1884. 

  1884.      *        IMCONJUGATE(complexNumber)
    1885. 

  1885.      *
    1886. 

  1886.      * @param    string        $complexNumber    The complex number for which you want the conjugate.
    1887. 

  1887.      * @return    string
    1888. 

  1888.      */
    1889. 

  1889.     public static function IMCONJUGATE($complexNumber)
    1890. 

  1890.     {
    1891. 

  1891.         $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
    1892. 

  1892. 

  1893.         $parsedComplex = self::parseComplex($complexNumber);
    1894. 

  1894. 

  1895.         if ($parsedComplex['imaginary'] == 0.0) {
    1896. 

  1896.             return $parsedComplex['real'];
    1897. 

  1897.         } else {
    1898. 

  1898.             return self::cleanComplex(
    1899. 

  1899.                 self::COMPLEX(
    1900. 

  1900.                     $parsedComplex['real'],
    1901. 

  1901.                     0 - $parsedComplex['imaginary'],
    1902. 

  1902.                     $parsedComplex['suffix']
    1903. 

  1903.                 )
    1904. 

  1904.             );
    1905. 

  1905.         }
    1906. 

  1906.     }
    1907. 

  1907. 

  1908. 

  1909.     /**
    1910. 

  1910.      * IMCOS
    1911. 

  1911.      *
    1912. 

  1912.      * Returns the cosine of a complex number in x + yi or x + yj text format.
    1913. 

  1913.      *
    1914. 

  1914.      * Excel Function:
    1915. 

  1915.      *        IMCOS(complexNumber)
    1916. 

  1916.      *
    1917. 

  1917.      * @param    string        $complexNumber    The complex number for which you want the cosine.
    1918. 

  1918.      * @return    string|float
    1919. 

  1919.      */
    1920. 

  1920.     public static function IMCOS($complexNumber)
    1921. 

  1921.     {
    1922. 

  1922.         $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
    1923. 

  1923. 

  1924.         $parsedComplex = self::parseComplex($complexNumber);
    1925. 

  1925. 

  1926.         if ($parsedComplex['imaginary'] == 0.0) {
    1927. 

  1927.             return cos($parsedComplex['real']);
    1928. 

  1928.         } else {
    1929. 

  1929.             return self::IMCONJUGATE(
    1930. 

  1930.                 self::COMPLEX(
    1931. 

  1931.                     cos($parsedComplex['real']) * cosh($parsedComplex['imaginary']),
    1932. 

  1932.                     sin($parsedComplex['real']) * sinh($parsedComplex['imaginary']),
    1933. 

  1933.                     $parsedComplex['suffix']
    1934. 

  1934.                 )
    1935. 

  1935.             );
    1936. 

  1936.         }
    1937. 

  1937.     }
    1938. 

  1938. 

  1939. 

  1940.     /**
    1941. 

  1941.      * IMSIN
    1942. 

  1942.      *
    1943. 

  1943.      * Returns the sine of a complex number in x + yi or x + yj text format.
    1944. 

  1944.      *
    1945. 

  1945.      * Excel Function:
    1946. 

  1946.      *        IMSIN(complexNumber)
    1947. 

  1947.      *
    1948. 

  1948.      * @param    string        $complexNumber    The complex number for which you want the sine.
    1949. 

  1949.      * @return    string|float
    1950. 

  1950.      */
    1951. 

  1951.     public static function IMSIN($complexNumber)
    1952. 

  1952.     {
    1953. 

  1953.         $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
    1954. 

  1954. 

  1955.         $parsedComplex = self::parseComplex($complexNumber);
    1956. 

  1956. 

  1957.         if ($parsedComplex['imaginary'] == 0.0) {
    1958. 

  1958.             return sin($parsedComplex['real']);
    1959. 

  1959.         } else {
    1960. 

  1960.             return self::COMPLEX(
    1961. 

  1961.                 sin($parsedComplex['real']) * cosh($parsedComplex['imaginary']),
    1962. 

  1962.                 cos($parsedComplex['real']) * sinh($parsedComplex['imaginary']),
    1963. 

  1963.                 $parsedComplex['suffix']
    1964. 

  1964.             );
    1965. 

  1965.         }
    1966. 

  1966.     }
    1967. 

  1967. 

  1968. 

  1969.     /**
    1970. 

  1970.      * IMSQRT
    1971. 

  1971.      *
    1972. 

  1972.      * Returns the square root of a complex number in x + yi or x + yj text format.
    1973. 

  1973.      *
    1974. 

  1974.      * Excel Function:
    1975. 

  1975.      *        IMSQRT(complexNumber)
    1976. 

  1976.      *
    1977. 

  1977.      * @param    string        $complexNumber    The complex number for which you want the square root.
    1978. 

  1978.      * @return    string
    1979. 

  1979.      */
    1980. 

  1980.     public static function IMSQRT($complexNumber)
    1981. 

  1981.     {
    1982. 

  1982.         $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
    1983. 

  1983. 

  1984.         $parsedComplex = self::parseComplex($complexNumber);
    1985. 

  1985. 

  1986.         $theta = self::IMARGUMENT($complexNumber);
    1987. 

  1987.         $d1 = cos($theta / 2);
    1988. 

  1988.         $d2 = sin($theta / 2);
    1989. 

  1989.         $r = sqrt(sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary'])));
    1990. 

  1990. 

  1991.         if ($parsedComplex['suffix'] == '') {
    1992. 

  1992.             return self::COMPLEX($d1 * $r, $d2 * $r);
    1993. 

  1993.         } else {
    1994. 

  1994.             return self::COMPLEX($d1 * $r, $d2 * $r, $parsedComplex['suffix']);
    1995. 

  1995.         }
    1996. 

  1996.     }
    1997. 

  1997. 

  1998. 

  1999.     /**
    2000. 

  2000.      * IMLN
    2001. 

  2001.      *
    2002. 

  2002.      * Returns the natural logarithm of a complex number in x + yi or x + yj text format.
    2003. 

  2003.      *
    2004. 

  2004.      * Excel Function:
    2005. 

  2005.      *        IMLN(complexNumber)
    2006. 

  2006.      *
    2007. 

  2007.      * @param    string        $complexNumber    The complex number for which you want the natural logarithm.
    2008. 

  2008.      * @return    string
    2009. 

  2009.      */
    2010. 

  2010.     public static function IMLN($complexNumber)
    2011. 

  2011.     {
    2012. 

  2012.         $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
    2013. 

  2013. 

  2014.         $parsedComplex = self::parseComplex($complexNumber);
    2015. 

  2015. 

  2016.         if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
    2017. 

  2017.             return PHPExcel_Calculation_Functions::NaN();
    2018. 

  2018.         }
    2019. 

  2019. 

  2020.         $logR = log(sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary'])));
    2021. 

  2021.         $t = self::IMARGUMENT($complexNumber);
    2022. 

  2022. 

  2023.         if ($parsedComplex['suffix'] == '') {
    2024. 

  2024.             return self::COMPLEX($logR, $t);
    2025. 

  2025.         } else {
    2026. 

  2026.             return self::COMPLEX($logR, $t, $parsedComplex['suffix']);
    2027. 

  2027.         }
    2028. 

  2028.     }
    2029. 

  2029. 

  2030. 

  2031.     /**
    2032. 

  2032.      * IMLOG10
    2033. 

  2033.      *
    2034. 

  2034.      * Returns the common logarithm (base 10) of a complex number in x + yi or x + yj text format.
    2035. 

  2035.      *
    2036. 

  2036.      * Excel Function:
    2037. 

  2037.      *        IMLOG10(complexNumber)
    2038. 

  2038.      *
    2039. 

  2039.      * @param    string        $complexNumber    The complex number for which you want the common logarithm.
    2040. 

  2040.      * @return    string
    2041. 

  2041.      */
    2042. 

  2042.     public static function IMLOG10($complexNumber)
    2043. 

  2043.     {
    2044. 

  2044.         $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
    2045. 

  2045. 

  2046.         $parsedComplex = self::parseComplex($complexNumber);
    2047. 

  2047. 

  2048.         if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
    2049. 

  2049.             return PHPExcel_Calculation_Functions::NaN();
    2050. 

  2050.         } elseif (($parsedComplex['real'] > 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
    2051. 

  2051.             return log10($parsedComplex['real']);
    2052. 

  2052.         }
    2053. 

  2053. 

  2054.         return self::IMPRODUCT(log10(EULER), self::IMLN($complexNumber));
    2055. 

  2055.     }
    2056. 

  2056. 

  2057. 

  2058.     /**
    2059. 

  2059.      * IMLOG2
    2060. 

  2060.      *
    2061. 

  2061.      * Returns the base-2 logarithm of a complex number in x + yi or x + yj text format.
    2062. 

  2062.      *
    2063. 

  2063.      * Excel Function:
    2064. 

  2064.      *        IMLOG2(complexNumber)
    2065. 

  2065.      *
    2066. 

  2066.      * @param    string        $complexNumber    The complex number for which you want the base-2 logarithm.
    2067. 

  2067.      * @return    string
    2068. 

  2068.      */
    2069. 

  2069.     public static function IMLOG2($complexNumber)
    2070. 

  2070.     {
    2071. 

  2071.         $complexNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
    2072. 

  2072. 

  2073.         $parsedComplex = self::parseComplex($complexNumber);
    2074. 

  2074. 

  2075.         if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
    2076. 

  2076.             return PHPExcel_Calculation_Functions::NaN();
    2077. 

  2077.         } elseif (($parsedComplex['real'] > 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
    2078. 

  2078.             return log($parsedComplex['real'], 2);
    2079. 

  2079.         }
    2080. 

  2080. 

  2081.         return self::IMPRODUCT(log(EULER, 2), self::IMLN($complexNumber));
    2082. 

  2082.     }
    2083. 

  2083. 

  2084. 

  2085.     /**
    2086. 

  2086.      * IMEXP
    2087. 

  2087.      *
    2088. 

  2088.      * Returns the exponential of a complex number in x + yi or x + yj text format.
    2089. 

  2089.      *
    2090. 

  2090.      * Excel Function:
    2091. 

  2091.      *        IMEXP(complexNumber)
    2092. 

  2092.      *
    2093. 

  2093.      * @param    string        $complexNumber    The complex number for which you want the exponential.
    2094. 

  2094.      * @return    string
    2095. 

  2095.      */
    2096. 

  2096.     public static function IMEXP($complexNumber)
    2097. 

  2097.     {
    2098. 

  2098.         $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
    2099. 

  2099. 

  2100.         $parsedComplex = self::parseComplex($complexNumber);
    2101. 

  2101. 

  2102.         if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
    2103. 

  2103.             return '1';
    2104. 

  2104.         }
    2105. 

  2105. 

  2106.         $e = exp($parsedComplex['real']);
    2107. 

  2107.         $eX = $e * cos($parsedComplex['imaginary']);
    2108. 

  2108.         $eY = $e * sin($parsedComplex['imaginary']);
    2109. 

  2109. 

  2110.         if ($parsedComplex['suffix'] == '') {
    2111. 

  2111.             return self::COMPLEX($eX, $eY);
    2112. 

  2112.         } else {
    2113. 

  2113.             return self::COMPLEX($eX, $eY, $parsedComplex['suffix']);
    2114. 

  2114.         }
    2115. 

  2115.     }
    2116. 

  2116. 

  2117. 

  2118.     /**
    2119. 

  2119.      * IMPOWER
    2120. 

  2120.      *
    2121. 

  2121.      * Returns a complex number in x + yi or x + yj text format raised to a power.
    2122. 

  2122.      *
    2123. 

  2123.      * Excel Function:
    2124. 

  2124.      *        IMPOWER(complexNumber,realNumber)
    2125. 

  2125.      *
    2126. 

  2126.      * @param    string        $complexNumber    The complex number you want to raise to a power.
    2127. 

  2127.      * @param    float        $realNumber        The power to which you want to raise the complex number.
    2128. 

  2128.      * @return    string
    2129. 

  2129.      */
    2130. 

  2130.     public static function IMPOWER($complexNumber, $realNumber)
    2131. 

  2131.     {
    2132. 

  2132.         $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
    2133. 

  2133.         $realNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($realNumber);
    2134. 

  2134. 

  2135.         if (!is_numeric($realNumber)) {
    2136. 

  2136.             return PHPExcel_Calculation_Functions::VALUE();
    2137. 

  2137.         }
    2138. 

  2138. 

  2139.         $parsedComplex = self::parseComplex($complexNumber);
    2140. 

  2140. 

  2141.         $r = sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary']));
    2142. 

  2142.         $rPower = pow($r, $realNumber);
    2143. 

  2143.         $theta = self::IMARGUMENT($complexNumber) * $realNumber;
    2144. 

  2144.         if ($theta == 0) {
    2145. 

  2145.             return 1;
    2146. 

  2146.         } elseif ($parsedComplex['imaginary'] == 0.0) {
    2147. 

  2147.             return self::COMPLEX($rPower * cos($theta), $rPower * sin($theta), $parsedComplex['suffix']);
    2148. 

  2148.         } else {
    2149. 

  2149.             return self::COMPLEX($rPower * cos($theta), $rPower * sin($theta), $parsedComplex['suffix']);
    2150. 

  2150.         }
    2151. 

  2151.     }
    2152. 

  2152. 

  2153. 

  2154.     /**
    2155. 

  2155.      * IMDIV
    2156. 

  2156.      *
    2157. 

  2157.      * Returns the quotient of two complex numbers in x + yi or x + yj text format.
    2158. 

  2158.      *
    2159. 

  2159.      * Excel Function:
    2160. 

  2160.      *        IMDIV(complexDividend,complexDivisor)
    2161. 

  2161.      *
    2162. 

  2162.      * @param    string        $complexDividend    The complex numerator or dividend.
    2163. 

  2163.      * @param    string        $complexDivisor        The complex denominator or divisor.
    2164. 

  2164.      * @return    string
    2165. 

  2165.      */
    2166. 

  2166.     public static function IMDIV($complexDividend, $complexDivisor)
    2167. 

  2167.     {
    2168. 

  2168.         $complexDividend    = PHPExcel_Calculation_Functions::flattenSingleValue($complexDividend);
    2169. 

  2169.         $complexDivisor    = PHPExcel_Calculation_Functions::flattenSingleValue($complexDivisor);
    2170. 

  2170. 

  2171.         $parsedComplexDividend = self::parseComplex($complexDividend);
    2172. 

  2172.         $parsedComplexDivisor = self::parseComplex($complexDivisor);
    2173. 

  2173. 

  2174.         if (($parsedComplexDividend['suffix'] != '') && ($parsedComplexDivisor['suffix'] != '') &&
    2175. 

  2175.             ($parsedComplexDividend['suffix'] != $parsedComplexDivisor['suffix'])) {
    2176. 

  2176.             return PHPExcel_Calculation_Functions::NaN();
    2177. 

  2177.         }
    2178. 

  2178.         if (($parsedComplexDividend['suffix'] != '') && ($parsedComplexDivisor['suffix'] == '')) {
    2179. 

  2179.             $parsedComplexDivisor['suffix'] = $parsedComplexDividend['suffix'];
    2180. 

  2180.         }
    2181. 

  2181. 

  2182.         $d1 = ($parsedComplexDividend['real'] * $parsedComplexDivisor['real']) + ($parsedComplexDividend['imaginary'] * $parsedComplexDivisor['imaginary']);
    2183. 

  2183.         $d2 = ($parsedComplexDividend['imaginary'] * $parsedComplexDivisor['real']) - ($parsedComplexDividend['real'] * $parsedComplexDivisor['imaginary']);
    2184. 

  2184.         $d3 = ($parsedComplexDivisor['real'] * $parsedComplexDivisor['real']) + ($parsedComplexDivisor['imaginary'] * $parsedComplexDivisor['imaginary']);
    2185. 

  2185. 

  2186.         $r = $d1 / $d3;
    2187. 

  2187.         $i = $d2 / $d3;
    2188. 

  2188. 

  2189.         if ($i > 0.0) {
    2190. 

  2190.             return self::cleanComplex($r.'+'.$i.$parsedComplexDivisor['suffix']);
    2191. 

  2191.         } elseif ($i < 0.0) {
    2192. 

  2192.             return self::cleanComplex($r.$i.$parsedComplexDivisor['suffix']);
    2193. 

  2193.         } else {
    2194. 

  2194.             return $r;
    2195. 

  2195.         }
    2196. 

  2196.     }
    2197. 

  2197. 

  2198. 

  2199.     /**
    2200. 

  2200.      * IMSUB
    2201. 

  2201.      *
    2202. 

  2202.      * Returns the difference of two complex numbers in x + yi or x + yj text format.
    2203. 

  2203.      *
    2204. 

  2204.      * Excel Function:
    2205. 

  2205.      *        IMSUB(complexNumber1,complexNumber2)
    2206. 

  2206.      *
    2207. 

  2207.      * @param    string        $complexNumber1        The complex number from which to subtract complexNumber2.
    2208. 

  2208.      * @param    string        $complexNumber2        The complex number to subtract from complexNumber1.
    2209. 

  2209.      * @return    string
    2210. 

  2210.      */
    2211. 

  2211.     public static function IMSUB($complexNumber1, $complexNumber2)
    2212. 

  2212.     {
    2213. 

  2213.         $complexNumber1    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber1);
    2214. 

  2214.         $complexNumber2    = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber2);
    2215. 

  2215. 

  2216.         $parsedComplex1 = self::parseComplex($complexNumber1);
    2217. 

  2217.         $parsedComplex2 = self::parseComplex($complexNumber2);
    2218. 

  2218. 

  2219.         if ((($parsedComplex1['suffix'] != '') && ($parsedComplex2['suffix'] != '')) &&
    2220. 

  2220.             ($parsedComplex1['suffix'] != $parsedComplex2['suffix'])) {
    2221. 

  2221.             return PHPExcel_Calculation_Functions::NaN();
    2222. 

  2222.         } elseif (($parsedComplex1['suffix'] == '') && ($parsedComplex2['suffix'] != '')) {
    2223. 

  2223.             $parsedComplex1['suffix'] = $parsedComplex2['suffix'];
    2224. 

  2224.         }
    2225. 

  2225. 

  2226.         $d1 = $parsedComplex1['real'] - $parsedComplex2['real'];
    2227. 

  2227.         $d2 = $parsedComplex1['imaginary'] - $parsedComplex2['imaginary'];
    2228. 

  2228. 

  2229.         return self::COMPLEX($d1, $d2, $parsedComplex1['suffix']);
    2230. 

  2230.     }
    2231. 

  2231. 

  2232. 

  2233.     /**
    2234. 

  2234.      * IMSUM
    2235. 

  2235.      *
    2236. 

  2236.      * Returns the sum of two or more complex numbers in x + yi or x + yj text format.
    2237. 

  2237.      *
    2238. 

  2238.      * Excel Function:
    2239. 

  2239.      *        IMSUM(complexNumber[,complexNumber[,...]])
    2240. 

  2240.      *
    2241. 

  2241.      * @param    string        $complexNumber,...    Series of complex numbers to add
    2242. 

  2242.      * @return    string
    2243. 

  2243.      */
    2244. 

  2244.     public static function IMSUM()
    2245. 

  2245.     {
    2246. 

  2246.         // Return value
    2247. 

  2247.         $returnValue = self::parseComplex('0');
    2248. 

  2248.         $activeSuffix = '';
    2249. 

  2249. 

  2250.         // Loop through the arguments
    2251. 

  2251.         $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
    2252. 

  2252.         foreach ($aArgs as $arg) {
    2253. 

  2253.             $parsedComplex = self::parseComplex($arg);
    2254. 

  2254. 

  2255.             if ($activeSuffix == '') {
    2256. 

  2256.                 $activeSuffix = $parsedComplex['suffix'];
    2257. 

  2257.             } elseif (($parsedComplex['suffix'] != '') && ($activeSuffix != $parsedComplex['suffix'])) {
    2258. 

  2258.                 return PHPExcel_Calculation_Functions::VALUE();
    2259. 

  2259.             }
    2260. 

  2260. 

  2261.             $returnValue['real'] += $parsedComplex['real'];
    2262. 

  2262.             $returnValue['imaginary'] += $parsedComplex['imaginary'];
    2263. 

  2263.         }
    2264. 

  2264. 

  2265.         if ($returnValue['imaginary'] == 0.0) {
    2266. 

  2266.             $activeSuffix = '';
    2267. 

  2267.         }
    2268. 

  2268.         return self::COMPLEX($returnValue['real'], $returnValue['imaginary'], $activeSuffix);
    2269. 

  2269.     }
    2270. 

  2270. 

  2271. 

  2272.     /**
    2273. 

  2273.      * IMPRODUCT
    2274. 

  2274.      *
    2275. 

  2275.      * Returns the product of two or more complex numbers in x + yi or x + yj text format.
    2276. 

  2276.      *
    2277. 

  2277.      * Excel Function:
    2278. 

  2278.      *        IMPRODUCT(complexNumber[,complexNumber[,...]])
    2279. 

  2279.      *
    2280. 

  2280.      * @param    string        $complexNumber,...    Series of complex numbers to multiply
    2281. 

  2281.      * @return    string
    2282. 

  2282.      */
    2283. 

  2283.     public static function IMPRODUCT()
    2284. 

  2284.     {
    2285. 

  2285.         // Return value
    2286. 

  2286.         $returnValue = self::parseComplex('1');
    2287. 

  2287.         $activeSuffix = '';
    2288. 

  2288. 

  2289.         // Loop through the arguments
    2290. 

  2290.         $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
    2291. 

  2291.         foreach ($aArgs as $arg) {
    2292. 

  2292.             $parsedComplex = self::parseComplex($arg);
    2293. 

  2293. 

  2294.             $workValue = $returnValue;
    2295. 

  2295.             if (($parsedComplex['suffix'] != '') && ($activeSuffix == '')) {
    2296. 

  2296.                 $activeSuffix = $parsedComplex['suffix'];
    2297. 

  2297.             } elseif (($parsedComplex['suffix'] != '') && ($activeSuffix != $parsedComplex['suffix'])) {
    2298. 

  2298.                 return PHPExcel_Calculation_Functions::NaN();
    2299. 

  2299.             }
    2300. 

  2300.             $returnValue['real'] = ($workValue['real'] * $parsedComplex['real']) - ($workValue['imaginary'] * $parsedComplex['imaginary']);
    2301. 

  2301.             $returnValue['imaginary'] = ($workValue['real'] * $parsedComplex['imaginary']) + ($workValue['imaginary'] * $parsedComplex['real']);
    2302. 

  2302.         }
    2303. 

  2303. 

  2304.         if ($returnValue['imaginary'] == 0.0) {
    2305. 

  2305.             $activeSuffix = '';
    2306. 

  2306.         }
    2307. 

  2307.         return self::COMPLEX($returnValue['real'], $returnValue['imaginary'], $activeSuffix);
    2308. 

  2308.     }
    2309. 

  2309. 

  2310. 

  2311.     /**
    2312. 

  2312.      *    DELTA
    2313. 

  2313.      *
    2314. 

  2314.      *    Tests whether two values are equal. Returns 1 if number1 = number2; returns 0 otherwise.
    2315. 

  2315.      *    Use this function to filter a set of values. For example, by summing several DELTA
    2316. 

  2316.      *    functions you calculate the count of equal pairs. This function is also known as the
    2317. 

  2317.      *    Kronecker Delta function.
    2318. 

  2318.      *
    2319. 

  2319.      *    Excel Function:
    2320. 

  2320.      *        DELTA(a[,b])
    2321. 

  2321.      *
    2322. 

  2322.      *    @param    float        $a    The first number.
    2323. 

  2323.      *    @param    float        $b    The second number. If omitted, b is assumed to be zero.
    2324. 

  2324.      *    @return    int
    2325. 

  2325.      */
    2326. 

  2326.     public static function DELTA($a, $b = 0)
    2327. 

  2327.     {
    2328. 

  2328.         $a = PHPExcel_Calculation_Functions::flattenSingleValue($a);
    2329. 

  2329.         $b = PHPExcel_Calculation_Functions::flattenSingleValue($b);
    2330. 

  2330. 

  2331.         return (int) ($a == $b);
    2332. 

  2332.     }
    2333. 

  2333. 

  2334. 

  2335.     /**
    2336. 

  2336.      *    GESTEP
    2337. 

  2337.      *
    2338. 

  2338.      *    Excel Function:
    2339. 

  2339.      *        GESTEP(number[,step])
    2340. 

  2340.      *
    2341. 

  2341.      *    Returns 1 if number >= step; returns 0 (zero) otherwise
    2342. 

  2342.      *    Use this function to filter a set of values. For example, by summing several GESTEP
    2343. 

  2343.      *    functions you calculate the count of values that exceed a threshold.
    2344. 

  2344.      *
    2345. 

  2345.      *    @param    float        $number        The value to test against step.
    2346. 

  2346.      *    @param    float        $step        The threshold value.
    2347. 

  2347.      *                                    If you omit a value for step, GESTEP uses zero.
    2348. 

  2348.      *    @return    int
    2349. 

  2349.      */
    2350. 

  2350.     public static function GESTEP($number, $step = 0)
    2351. 

  2351.     {
    2352. 

  2352.         $number    = PHPExcel_Calculation_Functions::flattenSingleValue($number);
    2353. 

  2353.         $step    = PHPExcel_Calculation_Functions::flattenSingleValue($step);
    2354. 

  2354. 

  2355.         return (int) ($number >= $step);
    2356. 

  2356.     }
    2357. 

  2357. 

  2358. 

  2359.     //
    2360. 

  2360.     //    Private method to calculate the erf value
    2361. 

  2361.     //
    2362. 

  2362.     private static $twoSqrtPi = 1.128379167095512574;
    2363. 

  2363. 

  2364.     public static function erfVal($x)
    2365. 

  2365.     {
    2366. 

  2366.         if (abs($x) > 2.2) {
    2367. 

  2367.             return 1 - self::erfcVal($x);
    2368. 

  2368.         }
    2369. 

  2369.         $sum = $term = $x;
    2370. 

  2370.         $xsqr = ($x * $x);
    2371. 

  2371.         $j = 1;
    2372. 

  2372.         do {
    2373. 

  2373.             $term *= $xsqr / $j;
    2374. 

  2374.             $sum -= $term / (2 * $j + 1);
    2375. 

  2375.             ++$j;
    2376. 

  2376.             $term *= $xsqr / $j;
    2377. 

  2377.             $sum += $term / (2 * $j + 1);
    2378. 

  2378.             ++$j;
    2379. 

  2379.             if ($sum == 0.0) {
    2380. 

  2380.                 break;
    2381. 

  2381.             }
    2382. 

  2382.         } while (abs($term / $sum) > PRECISION);
    2383. 

  2383.         return self::$twoSqrtPi * $sum;
    2384. 

  2384.     }
    2385. 

  2385. 

  2386. 

  2387.     /**
    2388. 

  2388.      *    ERF
    2389. 

  2389.      *
    2390. 

  2390.      *    Returns the error function integrated between the lower and upper bound arguments.
    2391. 

  2391.      *
    2392. 

  2392.      *    Note: In Excel 2007 or earlier, if you input a negative value for the upper or lower bound arguments,
    2393. 

  2393.      *            the function would return a #NUM! error. However, in Excel 2010, the function algorithm was
    2394. 

  2394.      *            improved, so that it can now calculate the function for both positive and negative ranges.
    2395. 

  2395.      *            PHPExcel follows Excel 2010 behaviour, and accepts nagative arguments.
    2396. 

  2396.      *
    2397. 

  2397.      *    Excel Function:
    2398. 

  2398.      *        ERF(lower[,upper])
    2399. 

  2399.      *
    2400. 

  2400.      *    @param    float        $lower    lower bound for integrating ERF
    2401. 

  2401.      *    @param    float        $upper    upper bound for integrating ERF.
    2402. 

  2402.      *                                If omitted, ERF integrates between zero and lower_limit
    2403. 

  2403.      *    @return    float
    2404. 

  2404.      */
    2405. 

  2405.     public static function ERF($lower, $upper = null)
    2406. 

  2406.     {
    2407. 

  2407.         $lower    = PHPExcel_Calculation_Functions::flattenSingleValue($lower);
    2408. 

  2408.         $upper    = PHPExcel_Calculation_Functions::flattenSingleValue($upper);
    2409. 

  2409. 

  2410.         if (is_numeric($lower)) {
    2411. 

  2411.             if (is_null($upper)) {
    2412. 

  2412.                 return self::erfVal($lower);
    2413. 

  2413.             }
    2414. 

  2414.             if (is_numeric($upper)) {
    2415. 

  2415.                 return self::erfVal($upper) - self::erfVal($lower);
    2416. 

  2416.             }
    2417. 

  2417.         }
    2418. 

  2418.         return PHPExcel_Calculation_Functions::VALUE();
    2419. 

  2419.     }
    2420. 

  2420. 

  2421. 

  2422.     //
    2423. 

  2423.     //    Private method to calculate the erfc value
    2424. 

  2424.     //
    2425. 

  2425.     private static $oneSqrtPi = 0.564189583547756287;
    2426. 

  2426. 

  2427.     private static function erfcVal($x)
    2428. 

  2428.     {
    2429. 

  2429.         if (abs($x) < 2.2) {
    2430. 

  2430.             return 1 - self::erfVal($x);
    2431. 

  2431.         }
    2432. 

  2432.         if ($x < 0) {
    2433. 

  2433.             return 2 - self::ERFC(-$x);
    2434. 

  2434.         }
    2435. 

  2435.         $a = $n = 1;
    2436. 

  2436.         $b = $c = $x;
    2437. 

  2437.         $d = ($x * $x) + 0.5;
    2438. 

  2438.         $q1 = $q2 = $b / $d;
    2439. 

  2439.         $t = 0;
    2440. 

  2440.         do {
    2441. 

  2441.             $t = $a * $n + $b * $x;
    2442. 

  2442.             $a = $b;
    2443. 

  2443.             $b = $t;
    2444. 

  2444.             $t = $c * $n + $d * $x;
    2445. 

  2445.             $c = $d;
    2446. 

  2446.             $d = $t;
    2447. 

  2447.             $n += 0.5;
    2448. 

  2448.             $q1 = $q2;
    2449. 

  2449.             $q2 = $b / $d;
    2450. 

  2450.         } while ((abs($q1 - $q2) / $q2) > PRECISION);
    2451. 

  2451.         return self::$oneSqrtPi * exp(-$x * $x) * $q2;
    2452. 

  2452.     }
    2453. 

  2453. 

  2454. 

  2455.     /**
    2456. 

  2456.      *    ERFC
    2457. 

  2457.      *
    2458. 

  2458.      *    Returns the complementary ERF function integrated between x and infinity
    2459. 

  2459.      *
    2460. 

  2460.      *    Note: In Excel 2007 or earlier, if you input a negative value for the lower bound argument,
    2461. 

  2461.      *        the function would return a #NUM! error. However, in Excel 2010, the function algorithm was
    2462. 

  2462.      *        improved, so that it can now calculate the function for both positive and negative x values.
    2463. 

  2463.      *            PHPExcel follows Excel 2010 behaviour, and accepts nagative arguments.
    2464. 

  2464.      *
    2465. 

  2465.      *    Excel Function:
    2466. 

  2466.      *        ERFC(x)
    2467. 

  2467.      *
    2468. 

  2468.      *    @param    float    $x    The lower bound for integrating ERFC
    2469. 

  2469.      *    @return    float
    2470. 

  2470.      */
    2471. 

  2471.     public static function ERFC($x)
    2472. 

  2472.     {
    2473. 

  2473.         $x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
    2474. 

  2474. 

  2475.         if (is_numeric($x)) {
    2476. 

  2476.             return self::erfcVal($x);
    2477. 

  2477.         }
    2478. 

  2478.         return PHPExcel_Calculation_Functions::VALUE();
    2479. 

  2479.     }
    2480. 

  2480. 

  2481. 

  2482.     /**
    2483. 

  2483.      *    getConversionGroups
    2484. 

  2484.      *    Returns a list of the different conversion groups for UOM conversions
    2485. 

  2485.      *
    2486. 

  2486.      *    @return    array
    2487. 

  2487.      */
    2488. 

  2488.     public static function getConversionGroups()
    2489. 

  2489.     {
    2490. 

  2490.         $conversionGroups = array();
    2491. 

  2491.         foreach (self::$conversionUnits as $conversionUnit) {
    2492. 

  2492.             $conversionGroups[] = $conversionUnit['Group'];
    2493. 

  2493.         }
    2494. 

  2494.         return array_merge(array_unique($conversionGroups));
    2495. 

  2495.     }
    2496. 

  2496. 

  2497. 

  2498.     /**
    2499. 

  2499.      *    getConversionGroupUnits
    2500. 

  2500.      *    Returns an array of units of measure, for a specified conversion group, or for all groups
    2501. 

  2501.      *
    2502. 

  2502.      *    @param    string    $group    The group whose units of measure you want to retrieve
    2503. 

  2503.      *    @return    array
    2504. 

  2504.      */
    2505. 

  2505.     public static function getConversionGroupUnits($group = null)
    2506. 

  2506.     {
    2507. 

  2507.         $conversionGroups = array();
    2508. 

  2508.         foreach (self::$conversionUnits as $conversionUnit => $conversionGroup) {
    2509. 

  2509.             if ((is_null($group)) || ($conversionGroup['Group'] == $group)) {
    2510. 

  2510.                 $conversionGroups[$conversionGroup['Group']][] = $conversionUnit;
    2511. 

  2511.             }
    2512. 

  2512.         }
    2513. 

  2513.         return $conversionGroups;
    2514. 

  2514.     }
    2515. 

  2515. 

  2516. 

  2517.     /**
    2518. 

  2518.      *    getConversionGroupUnitDetails
    2519. 

  2519.      *
    2520. 

  2520.      *    @param    string    $group    The group whose units of measure you want to retrieve
    2521. 

  2521.      *    @return    array
    2522. 

  2522.      */
    2523. 

  2523.     public static function getConversionGroupUnitDetails($group = null)
    2524. 

  2524.     {
    2525. 

  2525.         $conversionGroups = array();
    2526. 

  2526.         foreach (self::$conversionUnits as $conversionUnit => $conversionGroup) {
    2527. 

  2527.             if ((is_null($group)) || ($conversionGroup['Group'] == $group)) {
    2528. 

  2528.                 $conversionGroups[$conversionGroup['Group']][] = array(
    2529. 

  2529.                     'unit'        => $conversionUnit,
    2530. 

  2530.                     'description' => $conversionGroup['Unit Name']
    2531. 

  2531.                 );
    2532. 

  2532.             }
    2533. 

  2533.         }
    2534. 

  2534.         return $conversionGroups;
    2535. 

  2535.     }
    2536. 

  2536. 

  2537. 

  2538.     /**
    2539. 

  2539.      *    getConversionMultipliers
    2540. 

  2540.      *    Returns an array of the Multiplier prefixes that can be used with Units of Measure in CONVERTUOM()
    2541. 

  2541.      *
    2542. 

  2542.      *    @return    array of mixed
    2543. 

  2543.      */
    2544. 

  2544.     public static function getConversionMultipliers()
    2545. 

  2545.     {
    2546. 

  2546.         return self::$conversionMultipliers;
    2547. 

  2547.     }
    2548. 

  2548. 

  2549. 

  2550.     /**
    2551. 

  2551.      *    CONVERTUOM
    2552. 

  2552.      *
    2553. 

  2553.      *    Converts a number from one measurement system to another.
    2554. 

  2554.      *    For example, CONVERT can translate a table of distances in miles to a table of distances
    2555. 

  2555.      *    in kilometers.
    2556. 

  2556.      *
    2557. 

  2557.      *    Excel Function:
    2558. 

  2558.      *        CONVERT(value,fromUOM,toUOM)
    2559. 

  2559.      *
    2560. 

  2560.      *    @param    float        $value        The value in fromUOM to convert.
    2561. 

  2561.      *    @param    string        $fromUOM    The units for value.
    2562. 

  2562.      *    @param    string        $toUOM        The units for the result.
    2563. 

  2563.      *
    2564. 

  2564.      *    @return    float
    2565. 

  2565.      */
    2566. 

  2566.     public static function CONVERTUOM($value, $fromUOM, $toUOM)
    2567. 

  2567.     {
    2568. 

  2568.         $value   = PHPExcel_Calculation_Functions::flattenSingleValue($value);
    2569. 

  2569.         $fromUOM = PHPExcel_Calculation_Functions::flattenSingleValue($fromUOM);
    2570. 

  2570.         $toUOM   = PHPExcel_Calculation_Functions::flattenSingleValue($toUOM);
    2571. 

  2571. 

  2572.         if (!is_numeric($value)) {
    2573. 

  2573.             return PHPExcel_Calculation_Functions::VALUE();
    2574. 

  2574.         }
    2575. 

  2575.         $fromMultiplier = 1.0;
    2576. 

  2576.         if (isset(self::$conversionUnits[$fromUOM])) {
    2577. 

  2577.             $unitGroup1 = self::$conversionUnits[$fromUOM]['Group'];
    2578. 

  2578.         } else {
    2579. 

  2579.             $fromMultiplier = substr($fromUOM, 0, 1);
    2580. 

  2580.             $fromUOM = substr($fromUOM, 1);
    2581. 

  2581.             if (isset(self::$conversionMultipliers[$fromMultiplier])) {
    2582. 

  2582.                 $fromMultiplier = self::$conversionMultipliers[$fromMultiplier]['multiplier'];
    2583. 

  2583.             } else {
    2584. 

  2584.                 return PHPExcel_Calculation_Functions::NA();
    2585. 

  2585.             }
    2586. 

  2586.             if ((isset(self::$conversionUnits[$fromUOM])) && (self::$conversionUnits[$fromUOM]['AllowPrefix'])) {
    2587. 

  2587.                 $unitGroup1 = self::$conversionUnits[$fromUOM]['Group'];
    2588. 

  2588.             } else {
    2589. 

  2589.                 return PHPExcel_Calculation_Functions::NA();
    2590. 

  2590.             }
    2591. 

  2591.         }
    2592. 

  2592.         $value *= $fromMultiplier;
    2593. 

  2593. 

  2594.         $toMultiplier = 1.0;
    2595. 

  2595.         if (isset(self::$conversionUnits[$toUOM])) {
    2596. 

  2596.             $unitGroup2 = self::$conversionUnits[$toUOM]['Group'];
    2597. 

  2597.         } else {
    2598. 

  2598.             $toMultiplier = substr($toUOM, 0, 1);
    2599. 

  2599.             $toUOM = substr($toUOM, 1);
    2600. 

  2600.             if (isset(self::$conversionMultipliers[$toMultiplier])) {
    2601. 

  2601.                 $toMultiplier = self::$conversionMultipliers[$toMultiplier]['multiplier'];
    2602. 

  2602.             } else {
    2603. 

  2603.                 return PHPExcel_Calculation_Functions::NA();
    2604. 

  2604.             }
    2605. 

  2605.             if ((isset(self::$conversionUnits[$toUOM])) && (self::$conversionUnits[$toUOM]['AllowPrefix'])) {
    2606. 

  2606.                 $unitGroup2 = self::$conversionUnits[$toUOM]['Group'];
    2607. 

  2607.             } else {
    2608. 

  2608.                 return PHPExcel_Calculation_Functions::NA();
    2609. 

  2609.             }
    2610. 

  2610.         }
    2611. 

  2611.         if ($unitGroup1 != $unitGroup2) {
    2612. 

  2612.             return PHPExcel_Calculation_Functions::NA();
    2613. 

  2613.         }
    2614. 

  2614. 

  2615.         if (($fromUOM == $toUOM) && ($fromMultiplier == $toMultiplier)) {
    2616. 

  2616.             //    We've already factored $fromMultiplier into the value, so we need
    2617. 

  2617.             //        to reverse it again
    2618. 

  2618.             return $value / $fromMultiplier;
    2619. 

  2619.         } elseif ($unitGroup1 == 'Temperature') {
    2620. 

  2620.             if (($fromUOM == 'F') || ($fromUOM == 'fah')) {
    2621. 

  2621.                 if (($toUOM == 'F') || ($toUOM == 'fah')) {
    2622. 

  2622.                     return $value;
    2623. 

  2623.                 } else {
    2624. 

  2624.                     $value = (($value - 32) / 1.8);
    2625. 

  2625.                     if (($toUOM == 'K') || ($toUOM == 'kel')) {
    2626. 

  2626.                         $value += 273.15;
    2627. 

  2627.                     }
    2628. 

  2628.                     return $value;
    2629. 

  2629.                 }
    2630. 

  2630.             } elseif ((($fromUOM == 'K') || ($fromUOM == 'kel')) &&
    2631. 

  2631.                       (($toUOM == 'K') || ($toUOM == 'kel'))) {
    2632. 

  2632.                         return $value;
    2633. 

  2633.             } elseif ((($fromUOM == 'C') || ($fromUOM == 'cel')) &&
    2634. 

  2634.                       (($toUOM == 'C') || ($toUOM == 'cel'))) {
    2635. 

  2635.                     return $value;
    2636. 

  2636.             }
    2637. 

  2637.             if (($toUOM == 'F') || ($toUOM == 'fah')) {
    2638. 

  2638.                 if (($fromUOM == 'K') || ($fromUOM == 'kel')) {
    2639. 

  2639.                     $value -= 273.15;
    2640. 

  2640.                 }
    2641. 

  2641.                 return ($value * 1.8) + 32;
    2642. 

  2642.             }
    2643. 

  2643.             if (($toUOM == 'C') || ($toUOM == 'cel')) {
    2644. 

  2644.                 return $value - 273.15;
    2645. 

  2645.             }
    2646. 

  2646.             return $value + 273.15;
    2647. 

  2647.         }
    2648. 

  2648.         return ($value * self::$unitConversions[$unitGroup1][$fromUOM][$toUOM]) / $toMultiplier;
    2649. 

  2649.     }
    2650. 

  2650. }
    2651. 

  2651.