1<?php
2/**
3 * PHPExcel
4 *
5 * Copyright (c) 2006 - 2014 PHPExcel
6 *
7 * This library is free software; you can redistribute it and/or
8 * modify it under the terms of the GNU Lesser General Public
9 * License as published by the Free Software Foundation; either
10 * version 2.1 of the License, or (at your option) any later version.
11 *
12 * This library is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
15 * Lesser General Public License for more details.
16 *
17 * You should have received a copy of the GNU Lesser General Public
18 * License along with this library; if not, write to the Free Software
19 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
20 *
21 * @category	PHPExcel
22 * @package		PHPExcel_Calculation
23 * @copyright	Copyright (c) 2006 - 2014 PHPExcel (http://www.codeplex.com/PHPExcel)
24 * @license		http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt	LGPL
25 * @version		##VERSION##, ##DATE##
26 */
27
28
29/** PHPExcel root directory */
30if (!defined('PHPEXCEL_ROOT')) {
31	/**
32	 * @ignore
33	 */
34	define('PHPEXCEL_ROOT', dirname(__FILE__) . '/../../');
35	require(PHPEXCEL_ROOT . 'PHPExcel/Autoloader.php');
36}
37
38
39/** EULER */
40define('EULER', 2.71828182845904523536);
41
42
43/**
44 * PHPExcel_Calculation_Engineering
45 *
46 * @category	PHPExcel
47 * @package		PHPExcel_Calculation
48 * @copyright	Copyright (c) 2006 - 2014 PHPExcel (http://www.codeplex.com/PHPExcel)
49 */
50class PHPExcel_Calculation_Engineering {
51
52	/**
53	 * Details of the Units of measure that can be used in CONVERTUOM()
54	 *
55	 * @var mixed[]
56	 */
57	private static $_conversionUnits = array( 'g'		=> array(	'Group'	=> 'Mass',			'Unit Name'	=> 'Gram',						'AllowPrefix'	=> True		),
58											  'sg'		=> array(	'Group'	=> 'Mass',			'Unit Name'	=> 'Slug',						'AllowPrefix'	=> False	),
59											  'lbm'		=> array(	'Group'	=> 'Mass',			'Unit Name'	=> 'Pound mass (avoirdupois)',	'AllowPrefix'	=> False	),
60											  'u'		=> array(	'Group'	=> 'Mass',			'Unit Name'	=> 'U (atomic mass unit)',		'AllowPrefix'	=> True		),
61											  'ozm'		=> array(	'Group'	=> 'Mass',			'Unit Name'	=> 'Ounce mass (avoirdupois)',	'AllowPrefix'	=> False	),
62											  'm'		=> array(	'Group'	=> 'Distance',		'Unit Name'	=> 'Meter',						'AllowPrefix'	=> True		),
63											  'mi'		=> array(	'Group'	=> 'Distance',		'Unit Name'	=> 'Statute mile',				'AllowPrefix'	=> False	),
64											  'Nmi'		=> array(	'Group'	=> 'Distance',		'Unit Name'	=> 'Nautical mile',				'AllowPrefix'	=> False	),
65											  'in'		=> array(	'Group'	=> 'Distance',		'Unit Name'	=> 'Inch',						'AllowPrefix'	=> False	),
66											  'ft'		=> array(	'Group'	=> 'Distance',		'Unit Name'	=> 'Foot',						'AllowPrefix'	=> False	),
67											  'yd'		=> array(	'Group'	=> 'Distance',		'Unit Name'	=> 'Yard',						'AllowPrefix'	=> False	),
68											  'ang'		=> array(	'Group'	=> 'Distance',		'Unit Name'	=> 'Angstrom',					'AllowPrefix'	=> True		),
69											  'Pica'	=> array(	'Group'	=> 'Distance',		'Unit Name'	=> 'Pica (1/72 in)',			'AllowPrefix'	=> False	),
70											  'yr'		=> array(	'Group'	=> 'Time',			'Unit Name'	=> 'Year',						'AllowPrefix'	=> False	),
71											  'day'		=> array(	'Group'	=> 'Time',			'Unit Name'	=> 'Day',						'AllowPrefix'	=> False	),
72											  'hr'		=> array(	'Group'	=> 'Time',			'Unit Name'	=> 'Hour',						'AllowPrefix'	=> False	),
73											  'mn'		=> array(	'Group'	=> 'Time',			'Unit Name'	=> 'Minute',					'AllowPrefix'	=> False	),
74											  'sec'		=> array(	'Group'	=> 'Time',			'Unit Name'	=> 'Second',					'AllowPrefix'	=> True		),
75											  'Pa'		=> array(	'Group'	=> 'Pressure',		'Unit Name'	=> 'Pascal',					'AllowPrefix'	=> True		),
76											  'p'		=> array(	'Group'	=> 'Pressure',		'Unit Name'	=> 'Pascal',					'AllowPrefix'	=> True		),
77											  'atm'		=> array(	'Group'	=> 'Pressure',		'Unit Name'	=> 'Atmosphere',				'AllowPrefix'	=> True		),
78											  'at'		=> array(	'Group'	=> 'Pressure',		'Unit Name'	=> 'Atmosphere',				'AllowPrefix'	=> True		),
79											  'mmHg'	=> array(	'Group'	=> 'Pressure',		'Unit Name'	=> 'mm of Mercury',				'AllowPrefix'	=> True		),
80											  'N'		=> array(	'Group'	=> 'Force',			'Unit Name'	=> 'Newton',					'AllowPrefix'	=> True		),
81											  'dyn'		=> array(	'Group'	=> 'Force',			'Unit Name'	=> 'Dyne',						'AllowPrefix'	=> True		),
82											  'dy'		=> array(	'Group'	=> 'Force',			'Unit Name'	=> 'Dyne',						'AllowPrefix'	=> True		),
83											  'lbf'		=> array(	'Group'	=> 'Force',			'Unit Name'	=> 'Pound force',				'AllowPrefix'	=> False	),
84											  'J'		=> array(	'Group'	=> 'Energy',		'Unit Name'	=> 'Joule',						'AllowPrefix'	=> True		),
85											  'e'		=> array(	'Group'	=> 'Energy',		'Unit Name'	=> 'Erg',						'AllowPrefix'	=> True		),
86											  'c'		=> array(	'Group'	=> 'Energy',		'Unit Name'	=> 'Thermodynamic calorie',		'AllowPrefix'	=> True		),
87											  'cal'		=> array(	'Group'	=> 'Energy',		'Unit Name'	=> 'IT calorie',				'AllowPrefix'	=> True		),
88											  'eV'		=> array(	'Group'	=> 'Energy',		'Unit Name'	=> 'Electron volt',				'AllowPrefix'	=> True		),
89											  'ev'		=> array(	'Group'	=> 'Energy',		'Unit Name'	=> 'Electron volt',				'AllowPrefix'	=> True		),
90											  'HPh'		=> array(	'Group'	=> 'Energy',		'Unit Name'	=> 'Horsepower-hour',			'AllowPrefix'	=> False	),
91											  'hh'		=> array(	'Group'	=> 'Energy',		'Unit Name'	=> 'Horsepower-hour',			'AllowPrefix'	=> False	),
92											  'Wh'		=> array(	'Group'	=> 'Energy',		'Unit Name'	=> 'Watt-hour',					'AllowPrefix'	=> True		),
93											  'wh'		=> array(	'Group'	=> 'Energy',		'Unit Name'	=> 'Watt-hour',					'AllowPrefix'	=> True		),
94											  'flb'		=> array(	'Group'	=> 'Energy',		'Unit Name'	=> 'Foot-pound',				'AllowPrefix'	=> False	),
95											  'BTU'		=> array(	'Group'	=> 'Energy',		'Unit Name'	=> 'BTU',						'AllowPrefix'	=> False	),
96											  'btu'		=> array(	'Group'	=> 'Energy',		'Unit Name'	=> 'BTU',						'AllowPrefix'	=> False	),
97											  'HP'		=> array(	'Group'	=> 'Power',			'Unit Name'	=> 'Horsepower',				'AllowPrefix'	=> False	),
98											  'h'		=> array(	'Group'	=> 'Power',			'Unit Name'	=> 'Horsepower',				'AllowPrefix'	=> False	),
99											  'W'		=> array(	'Group'	=> 'Power',			'Unit Name'	=> 'Watt',						'AllowPrefix'	=> True		),
100											  'w'		=> array(	'Group'	=> 'Power',			'Unit Name'	=> 'Watt',						'AllowPrefix'	=> True		),
101											  'T'		=> array(	'Group'	=> 'Magnetism',		'Unit Name'	=> 'Tesla',						'AllowPrefix'	=> True		),
102											  'ga'		=> array(	'Group'	=> 'Magnetism',		'Unit Name'	=> 'Gauss',						'AllowPrefix'	=> True		),
103											  'C'		=> array(	'Group'	=> 'Temperature',	'Unit Name'	=> 'Celsius',					'AllowPrefix'	=> False	),
104											  'cel'		=> array(	'Group'	=> 'Temperature',	'Unit Name'	=> 'Celsius',					'AllowPrefix'	=> False	),
105											  'F'		=> array(	'Group'	=> 'Temperature',	'Unit Name'	=> 'Fahrenheit',				'AllowPrefix'	=> False	),
106											  'fah'		=> array(	'Group'	=> 'Temperature',	'Unit Name'	=> 'Fahrenheit',				'AllowPrefix'	=> False	),
107											  'K'		=> array(	'Group'	=> 'Temperature',	'Unit Name'	=> 'Kelvin',					'AllowPrefix'	=> False	),
108											  'kel'		=> array(	'Group'	=> 'Temperature',	'Unit Name'	=> 'Kelvin',					'AllowPrefix'	=> False	),
109											  'tsp'		=> array(	'Group'	=> 'Liquid',		'Unit Name'	=> 'Teaspoon',					'AllowPrefix'	=> False	),
110											  'tbs'		=> array(	'Group'	=> 'Liquid',		'Unit Name'	=> 'Tablespoon',				'AllowPrefix'	=> False	),
111											  'oz'		=> array(	'Group'	=> 'Liquid',		'Unit Name'	=> 'Fluid Ounce',				'AllowPrefix'	=> False	),
112											  'cup'		=> array(	'Group'	=> 'Liquid',		'Unit Name'	=> 'Cup',						'AllowPrefix'	=> False	),
113											  'pt'		=> array(	'Group'	=> 'Liquid',		'Unit Name'	=> 'U.S. Pint',					'AllowPrefix'	=> False	),
114											  'us_pt'	=> array(	'Group'	=> 'Liquid',		'Unit Name'	=> 'U.S. Pint',					'AllowPrefix'	=> False	),
115											  'uk_pt'	=> array(	'Group'	=> 'Liquid',		'Unit Name'	=> 'U.K. Pint',					'AllowPrefix'	=> False	),
116											  'qt'		=> array(	'Group'	=> 'Liquid',		'Unit Name'	=> 'Quart',						'AllowPrefix'	=> False	),
117											  'gal'		=> array(	'Group'	=> 'Liquid',		'Unit Name'	=> 'Gallon',					'AllowPrefix'	=> False	),
118											  'l'		=> array(	'Group'	=> 'Liquid',		'Unit Name'	=> 'Litre',						'AllowPrefix'	=> True		),
119											  'lt'		=> array(	'Group'	=> 'Liquid',		'Unit Name'	=> 'Litre',						'AllowPrefix'	=> True		)
120											);
121
122	/**
123	 * Details of the Multiplier prefixes that can be used with Units of Measure in CONVERTUOM()
124	 *
125	 * @var mixed[]
126	 */
127	private static $_conversionMultipliers = array(	'Y'	=> array(	'multiplier'	=> 1E24,	'name'	=> 'yotta'	),
128													'Z'	=> array(	'multiplier'	=> 1E21,	'name'	=> 'zetta'	),
129													'E'	=> array(	'multiplier'	=> 1E18,	'name'	=> 'exa'	),
130													'P'	=> array(	'multiplier'	=> 1E15,	'name'	=> 'peta'	),
131													'T'	=> array(	'multiplier'	=> 1E12,	'name'	=> 'tera'	),
132													'G'	=> array(	'multiplier'	=> 1E9,		'name'	=> 'giga'	),
133													'M'	=> array(	'multiplier'	=> 1E6,		'name'	=> 'mega'	),
134													'k'	=> array(	'multiplier'	=> 1E3,		'name'	=> 'kilo'	),
135													'h'	=> array(	'multiplier'	=> 1E2,		'name'	=> 'hecto'	),
136													'e'	=> array(	'multiplier'	=> 1E1,		'name'	=> 'deka'	),
137													'd'	=> array(	'multiplier'	=> 1E-1,	'name'	=> 'deci'	),
138													'c'	=> array(	'multiplier'	=> 1E-2,	'name'	=> 'centi'	),
139													'm'	=> array(	'multiplier'	=> 1E-3,	'name'	=> 'milli'	),
140													'u'	=> array(	'multiplier'	=> 1E-6,	'name'	=> 'micro'	),
141													'n'	=> array(	'multiplier'	=> 1E-9,	'name'	=> 'nano'	),
142													'p'	=> array(	'multiplier'	=> 1E-12,	'name'	=> 'pico'	),
143													'f'	=> array(	'multiplier'	=> 1E-15,	'name'	=> 'femto'	),
144													'a'	=> array(	'multiplier'	=> 1E-18,	'name'	=> 'atto'	),
145													'z'	=> array(	'multiplier'	=> 1E-21,	'name'	=> 'zepto'	),
146													'y'	=> array(	'multiplier'	=> 1E-24,	'name'	=> 'yocto'	)
147												 );
148
149	/**
150	 * Details of the Units of measure conversion factors, organised by group
151	 *
152	 * @var mixed[]
153	 */
154	private static $_unitConversions = array(	'Mass'		=> array(	'g'		=> array(	'g'		=> 1.0,
155																							'sg'	=> 6.85220500053478E-05,
156																							'lbm'	=> 2.20462291469134E-03,
157																							'u'		=> 6.02217000000000E+23,
158																							'ozm'	=> 3.52739718003627E-02
159																						),
160																		'sg'	=> array(	'g'		=> 1.45938424189287E+04,
161																							'sg'	=> 1.0,
162																							'lbm'	=> 3.21739194101647E+01,
163																							'u'		=> 8.78866000000000E+27,
164																							'ozm'	=> 5.14782785944229E+02
165																						),
166																		'lbm'	=> array(	'g'		=> 4.5359230974881148E+02,
167																							'sg'	=> 3.10810749306493E-02,
168																							'lbm'	=> 1.0,
169																							'u'		=> 2.73161000000000E+26,
170																							'ozm'	=> 1.60000023429410E+01
171																						),
172																		'u'		=> array(	'g'		=> 1.66053100460465E-24,
173																							'sg'	=> 1.13782988532950E-28,
174																							'lbm'	=> 3.66084470330684E-27,
175																							'u'		=> 1.0,
176																							'ozm'	=> 5.85735238300524E-26
177																						),
178																		'ozm'	=> array(	'g'		=> 2.83495152079732E+01,
179																							'sg'	=> 1.94256689870811E-03,
180																							'lbm'	=> 6.24999908478882E-02,
181																							'u'		=> 1.70725600000000E+25,
182																							'ozm'	=> 1.0
183																						)
184																	),
185												'Distance'	=> array(	'm'		=> array(	'm'		=> 1.0,
186																							'mi'	=> 6.21371192237334E-04,
187																							'Nmi'	=> 5.39956803455724E-04,
188																							'in'	=> 3.93700787401575E+01,
189																							'ft'	=> 3.28083989501312E+00,
190																							'yd'	=> 1.09361329797891E+00,
191																							'ang'	=> 1.00000000000000E+10,
192																							'Pica'	=> 2.83464566929116E+03
193																						),
194																		'mi'	=> array(	'm'		=> 1.60934400000000E+03,
195																							'mi'	=> 1.0,
196																							'Nmi'	=> 8.68976241900648E-01,
197																							'in'	=> 6.33600000000000E+04,
198																							'ft'	=> 5.28000000000000E+03,
199																							'yd'	=> 1.76000000000000E+03,
200																							'ang'	=> 1.60934400000000E+13,
201																							'Pica'	=> 4.56191999999971E+06
202																						),
203																		'Nmi'	=> array(	'm'		=> 1.85200000000000E+03,
204																							'mi'	=> 1.15077944802354E+00,
205																							'Nmi'	=> 1.0,
206																							'in'	=> 7.29133858267717E+04,
207																							'ft'	=> 6.07611548556430E+03,
208																							'yd'	=> 2.02537182785694E+03,
209																							'ang'	=> 1.85200000000000E+13,
210																							'Pica'	=> 5.24976377952723E+06
211																						),
212																		'in'	=> array(	'm'		=> 2.54000000000000E-02,
213																							'mi'	=> 1.57828282828283E-05,
214																							'Nmi'	=> 1.37149028077754E-05,
215																							'in'	=> 1.0,
216																							'ft'	=> 8.33333333333333E-02,
217																							'yd'	=> 2.77777777686643E-02,
218																							'ang'	=> 2.54000000000000E+08,
219																							'Pica'	=> 7.19999999999955E+01
220																						),
221																		'ft'	=> array(	'm'		=> 3.04800000000000E-01,
222																							'mi'	=> 1.89393939393939E-04,
223																							'Nmi'	=> 1.64578833693305E-04,
224																							'in'	=> 1.20000000000000E+01,
225																							'ft'	=> 1.0,
226																							'yd'	=> 3.33333333223972E-01,
227																							'ang'	=> 3.04800000000000E+09,
228																							'Pica'	=> 8.63999999999946E+02
229																						),
230																		'yd'	=> array(	'm'		=> 9.14400000300000E-01,
231																							'mi'	=> 5.68181818368230E-04,
232																							'Nmi'	=> 4.93736501241901E-04,
233																							'in'	=> 3.60000000118110E+01,
234																							'ft'	=> 3.00000000000000E+00,
235																							'yd'	=> 1.0,
236																							'ang'	=> 9.14400000300000E+09,
237																							'Pica'	=> 2.59200000085023E+03
238																						),
239																		'ang'	=> array(	'm'		=> 1.00000000000000E-10,
240																							'mi'	=> 6.21371192237334E-14,
241																							'Nmi'	=> 5.39956803455724E-14,
242																							'in'	=> 3.93700787401575E-09,
243																							'ft'	=> 3.28083989501312E-10,
244																							'yd'	=> 1.09361329797891E-10,
245																							'ang'	=> 1.0,
246																							'Pica'	=> 2.83464566929116E-07
247																						),
248																		'Pica'	=> array(	'm'		=> 3.52777777777800E-04,
249																							'mi'	=> 2.19205948372629E-07,
250																							'Nmi'	=> 1.90484761219114E-07,
251																							'in'	=> 1.38888888888898E-02,
252																							'ft'	=> 1.15740740740748E-03,
253																							'yd'	=> 3.85802469009251E-04,
254																							'ang'	=> 3.52777777777800E+06,
255																							'Pica'	=> 1.0
256																						)
257																	),
258												'Time'		=> array(	'yr'	=> array(	'yr'		=> 1.0,
259																							'day'		=> 365.25,
260																							'hr'		=> 8766.0,
261																							'mn'		=> 525960.0,
262																							'sec'		=> 31557600.0
263																						),
264																		'day'	=> array(	'yr'		=> 2.73785078713210E-03,
265																							'day'		=> 1.0,
266																							'hr'		=> 24.0,
267																							'mn'		=> 1440.0,
268																							'sec'		=> 86400.0
269																						),
270																		'hr'	=> array(	'yr'		=> 1.14077116130504E-04,
271																							'day'		=> 4.16666666666667E-02,
272																							'hr'		=> 1.0,
273																							'mn'		=> 60.0,
274																							'sec'		=> 3600.0
275																						),
276																		'mn'	=> array(	'yr'		=> 1.90128526884174E-06,
277																							'day'		=> 6.94444444444444E-04,
278																							'hr'		=> 1.66666666666667E-02,
279																							'mn'		=> 1.0,
280																							'sec'		=> 60.0
281																						),
282																		'sec'	=> array(	'yr'		=> 3.16880878140289E-08,
283																							'day'		=> 1.15740740740741E-05,
284																							'hr'		=> 2.77777777777778E-04,
285																							'mn'		=> 1.66666666666667E-02,
286																							'sec'		=> 1.0
287																						)
288																	),
289												'Pressure'	=> array(	'Pa'	=> array(	'Pa'		=> 1.0,
290																							'p'			=> 1.0,
291																							'atm'		=> 9.86923299998193E-06,
292																							'at'		=> 9.86923299998193E-06,
293																							'mmHg'		=> 7.50061707998627E-03
294																						),
295																		'p'		=> array(	'Pa'		=> 1.0,
296																							'p'			=> 1.0,
297																							'atm'		=> 9.86923299998193E-06,
298																							'at'		=> 9.86923299998193E-06,
299																							'mmHg'		=> 7.50061707998627E-03
300																						),
301																		'atm'	=> array(	'Pa'		=> 1.01324996583000E+05,
302																							'p'			=> 1.01324996583000E+05,
303																							'atm'		=> 1.0,
304																							'at'		=> 1.0,
305																							'mmHg'		=> 760.0
306																						),
307																		'at'	=> array(	'Pa'		=> 1.01324996583000E+05,
308																							'p'			=> 1.01324996583000E+05,
309																							'atm'		=> 1.0,
310																							'at'		=> 1.0,
311																							'mmHg'		=> 760.0
312																						),
313																		'mmHg'	=> array(	'Pa'		=> 1.33322363925000E+02,
314																							'p'			=> 1.33322363925000E+02,
315																							'atm'		=> 1.31578947368421E-03,
316																							'at'		=> 1.31578947368421E-03,
317																							'mmHg'		=> 1.0
318																						)
319																	),
320												'Force'		=> array(	'N'		=> array(	'N'			=> 1.0,
321																							'dyn'		=> 1.0E+5,
322																							'dy'		=> 1.0E+5,
323																							'lbf'		=> 2.24808923655339E-01
324																						),
325																		'dyn'	=> array(	'N'			=> 1.0E-5,
326																							'dyn'		=> 1.0,
327																							'dy'		=> 1.0,
328																							'lbf'		=> 2.24808923655339E-06
329																						),
330																		'dy'	=> array(	'N'			=> 1.0E-5,
331																							'dyn'		=> 1.0,
332																							'dy'		=> 1.0,
333																							'lbf'		=> 2.24808923655339E-06
334																						),
335																		'lbf'	=> array(	'N'			=> 4.448222,
336																							'dyn'		=> 4.448222E+5,
337																							'dy'		=> 4.448222E+5,
338																							'lbf'		=> 1.0
339																						)
340																	),
341												'Energy'	=> array(	'J'		=> array(	'J'			=> 1.0,
342																							'e'			=> 9.99999519343231E+06,
343																							'c'			=> 2.39006249473467E-01,
344																							'cal'		=> 2.38846190642017E-01,
345																							'eV'		=> 6.24145700000000E+18,
346																							'ev'		=> 6.24145700000000E+18,
347																							'HPh'		=> 3.72506430801000E-07,
348																							'hh'		=> 3.72506430801000E-07,
349																							'Wh'		=> 2.77777916238711E-04,
350																							'wh'		=> 2.77777916238711E-04,
351																							'flb'		=> 2.37304222192651E+01,
352																							'BTU'		=> 9.47815067349015E-04,
353																							'btu'		=> 9.47815067349015E-04
354																						),
355																		'e'		=> array(	'J'			=> 1.00000048065700E-07,
356																							'e'			=> 1.0,
357																							'c'			=> 2.39006364353494E-08,
358																							'cal'		=> 2.38846305445111E-08,
359																							'eV'		=> 6.24146000000000E+11,
360																							'ev'		=> 6.24146000000000E+11,
361																							'HPh'		=> 3.72506609848824E-14,
362																							'hh'		=> 3.72506609848824E-14,
363																							'Wh'		=> 2.77778049754611E-11,
364																							'wh'		=> 2.77778049754611E-11,
365																							'flb'		=> 2.37304336254586E-06,
366																							'BTU'		=> 9.47815522922962E-11,
367																							'btu'		=> 9.47815522922962E-11
368																						),
369																		'c'		=> array(	'J'			=> 4.18399101363672E+00,
370																							'e'			=> 4.18398900257312E+07,
371																							'c'			=> 1.0,
372																							'cal'		=> 9.99330315287563E-01,
373																							'eV'		=> 2.61142000000000E+19,
374																							'ev'		=> 2.61142000000000E+19,
375																							'HPh'		=> 1.55856355899327E-06,
376																							'hh'		=> 1.55856355899327E-06,
377																							'Wh'		=> 1.16222030532950E-03,
378																							'wh'		=> 1.16222030532950E-03,
379																							'flb'		=> 9.92878733152102E+01,
380																							'BTU'		=> 3.96564972437776E-03,
381																							'btu'		=> 3.96564972437776E-03
382																						),
383																		'cal'	=> array(	'J'			=> 4.18679484613929E+00,
384																							'e'			=> 4.18679283372801E+07,
385																							'c'			=> 1.00067013349059E+00,
386																							'cal'		=> 1.0,
387																							'eV'		=> 2.61317000000000E+19,
388																							'ev'		=> 2.61317000000000E+19,
389																							'HPh'		=> 1.55960800463137E-06,
390																							'hh'		=> 1.55960800463137E-06,
391																							'Wh'		=> 1.16299914807955E-03,
392																							'wh'		=> 1.16299914807955E-03,
393																							'flb'		=> 9.93544094443283E+01,
394																							'BTU'		=> 3.96830723907002E-03,
395																							'btu'		=> 3.96830723907002E-03
396																						),
397																		'eV'	=> array(	'J'			=> 1.60219000146921E-19,
398																							'e'			=> 1.60218923136574E-12,
399																							'c'			=> 3.82933423195043E-20,
400																							'cal'		=> 3.82676978535648E-20,
401																							'eV'		=> 1.0,
402																							'ev'		=> 1.0,
403																							'HPh'		=> 5.96826078912344E-26,
404																							'hh'		=> 5.96826078912344E-26,
405																							'Wh'		=> 4.45053000026614E-23,
406																							'wh'		=> 4.45053000026614E-23,
407																							'flb'		=> 3.80206452103492E-18,
408																							'BTU'		=> 1.51857982414846E-22,
409																							'btu'		=> 1.51857982414846E-22
410																						),
411																		'ev'	=> array(	'J'			=> 1.60219000146921E-19,
412																							'e'			=> 1.60218923136574E-12,
413																							'c'			=> 3.82933423195043E-20,
414																							'cal'		=> 3.82676978535648E-20,
415																							'eV'		=> 1.0,
416																							'ev'		=> 1.0,
417																							'HPh'		=> 5.96826078912344E-26,
418																							'hh'		=> 5.96826078912344E-26,
419																							'Wh'		=> 4.45053000026614E-23,
420																							'wh'		=> 4.45053000026614E-23,
421																							'flb'		=> 3.80206452103492E-18,
422																							'BTU'		=> 1.51857982414846E-22,
423																							'btu'		=> 1.51857982414846E-22
424																						),
425																		'HPh'	=> array(	'J'			=> 2.68451741316170E+06,
426																							'e'			=> 2.68451612283024E+13,
427																							'c'			=> 6.41616438565991E+05,
428																							'cal'		=> 6.41186757845835E+05,
429																							'eV'		=> 1.67553000000000E+25,
430																							'ev'		=> 1.67553000000000E+25,
431																							'HPh'		=> 1.0,
432																							'hh'		=> 1.0,
433																							'Wh'		=> 7.45699653134593E+02,
434																							'wh'		=> 7.45699653134593E+02,
435																							'flb'		=> 6.37047316692964E+07,
436																							'BTU'		=> 2.54442605275546E+03,
437																							'btu'		=> 2.54442605275546E+03
438																						),
439																		'hh'	=> array(	'J'			=> 2.68451741316170E+06,
440																							'e'			=> 2.68451612283024E+13,
441																							'c'			=> 6.41616438565991E+05,
442																							'cal'		=> 6.41186757845835E+05,
443																							'eV'		=> 1.67553000000000E+25,
444																							'ev'		=> 1.67553000000000E+25,
445																							'HPh'		=> 1.0,
446																							'hh'		=> 1.0,
447																							'Wh'		=> 7.45699653134593E+02,
448																							'wh'		=> 7.45699653134593E+02,
449																							'flb'		=> 6.37047316692964E+07,
450																							'BTU'		=> 2.54442605275546E+03,
451																							'btu'		=> 2.54442605275546E+03
452																						),
453																		'Wh'	=> array(	'J'			=> 3.59999820554720E+03,
454																							'e'			=> 3.59999647518369E+10,
455																							'c'			=> 8.60422069219046E+02,
456																							'cal'		=> 8.59845857713046E+02,
457																							'eV'		=> 2.24692340000000E+22,
458																							'ev'		=> 2.24692340000000E+22,
459																							'HPh'		=> 1.34102248243839E-03,
460																							'hh'		=> 1.34102248243839E-03,
461																							'Wh'		=> 1.0,
462																							'wh'		=> 1.0,
463																							'flb'		=> 8.54294774062316E+04,
464																							'BTU'		=> 3.41213254164705E+00,
465																							'btu'		=> 3.41213254164705E+00
466																						),
467																		'wh'	=> array(	'J'			=> 3.59999820554720E+03,
468																							'e'			=> 3.59999647518369E+10,
469																							'c'			=> 8.60422069219046E+02,
470																							'cal'		=> 8.59845857713046E+02,
471																							'eV'		=> 2.24692340000000E+22,
472																							'ev'		=> 2.24692340000000E+22,
473																							'HPh'		=> 1.34102248243839E-03,
474																							'hh'		=> 1.34102248243839E-03,
475																							'Wh'		=> 1.0,
476																							'wh'		=> 1.0,
477																							'flb'		=> 8.54294774062316E+04,
478																							'BTU'		=> 3.41213254164705E+00,
479																							'btu'		=> 3.41213254164705E+00
480																						),
481																		'flb'	=> array(	'J'			=> 4.21400003236424E-02,
482																							'e'			=> 4.21399800687660E+05,
483																							'c'			=> 1.00717234301644E-02,
484																							'cal'		=> 1.00649785509554E-02,
485																							'eV'		=> 2.63015000000000E+17,
486																							'ev'		=> 2.63015000000000E+17,
487																							'HPh'		=> 1.56974211145130E-08,
488																							'hh'		=> 1.56974211145130E-08,
489																							'Wh'		=> 1.17055614802000E-05,
490																							'wh'		=> 1.17055614802000E-05,
491																							'flb'		=> 1.0,
492																							'BTU'		=> 3.99409272448406E-05,
493																							'btu'		=> 3.99409272448406E-05
494																						),
495																		'BTU'	=> array(	'J'			=> 1.05505813786749E+03,
496																							'e'			=> 1.05505763074665E+10,
497																							'c'			=> 2.52165488508168E+02,
498																							'cal'		=> 2.51996617135510E+02,
499																							'eV'		=> 6.58510000000000E+21,
500																							'ev'		=> 6.58510000000000E+21,
501																							'HPh'		=> 3.93015941224568E-04,
502																							'hh'		=> 3.93015941224568E-04,
503																							'Wh'		=> 2.93071851047526E-01,
504																							'wh'		=> 2.93071851047526E-01,
505																							'flb'		=> 2.50369750774671E+04,
506																							'BTU'		=> 1.0,
507																							'btu'		=> 1.0,
508																						),
509																		'btu'	=> array(	'J'			=> 1.05505813786749E+03,
510																							'e'			=> 1.05505763074665E+10,
511																							'c'			=> 2.52165488508168E+02,
512																							'cal'		=> 2.51996617135510E+02,
513																							'eV'		=> 6.58510000000000E+21,
514																							'ev'		=> 6.58510000000000E+21,
515																							'HPh'		=> 3.93015941224568E-04,
516																							'hh'		=> 3.93015941224568E-04,
517																							'Wh'		=> 2.93071851047526E-01,
518																							'wh'		=> 2.93071851047526E-01,
519																							'flb'		=> 2.50369750774671E+04,
520																							'BTU'		=> 1.0,
521																							'btu'		=> 1.0,
522																						)
523																	),
524												'Power'		=> array(	'HP'	=> array(	'HP'		=> 1.0,
525																							'h'			=> 1.0,
526																							'W'			=> 7.45701000000000E+02,
527																							'w'			=> 7.45701000000000E+02
528																						),
529																		'h'		=> array(	'HP'		=> 1.0,
530																							'h'			=> 1.0,
531																							'W'			=> 7.45701000000000E+02,
532																							'w'			=> 7.45701000000000E+02
533																						),
534																		'W'		=> array(	'HP'		=> 1.34102006031908E-03,
535																							'h'			=> 1.34102006031908E-03,
536																							'W'			=> 1.0,
537																							'w'			=> 1.0
538																						),
539																		'w'		=> array(	'HP'		=> 1.34102006031908E-03,
540																							'h'			=> 1.34102006031908E-03,
541																							'W'			=> 1.0,
542																							'w'			=> 1.0
543																						)
544																	),
545												'Magnetism'	=> array(	'T'		=> array(	'T'			=> 1.0,
546																							'ga'		=> 10000.0
547																						),
548																		'ga'	=> array(	'T'			=> 0.0001,
549																							'ga'		=> 1.0
550																						)
551																	),
552												'Liquid'	=> array(	'tsp'	=> array(	'tsp'		=> 1.0,
553																							'tbs'		=> 3.33333333333333E-01,
554																							'oz'		=> 1.66666666666667E-01,
555																							'cup'		=> 2.08333333333333E-02,
556																							'pt'		=> 1.04166666666667E-02,
557																							'us_pt'		=> 1.04166666666667E-02,
558																							'uk_pt'		=> 8.67558516821960E-03,
559																							'qt'		=> 5.20833333333333E-03,
560																							'gal'		=> 1.30208333333333E-03,
561																							'l'			=> 4.92999408400710E-03,
562																							'lt'		=> 4.92999408400710E-03
563																						),
564																		'tbs'	=> array(	'tsp'		=> 3.00000000000000E+00,
565																							'tbs'		=> 1.0,
566																							'oz'		=> 5.00000000000000E-01,
567																							'cup'		=> 6.25000000000000E-02,
568																							'pt'		=> 3.12500000000000E-02,
569																							'us_pt'		=> 3.12500000000000E-02,
570																							'uk_pt'		=> 2.60267555046588E-02,
571																							'qt'		=> 1.56250000000000E-02,
572																							'gal'		=> 3.90625000000000E-03,
573																							'l'			=> 1.47899822520213E-02,
574																							'lt'		=> 1.47899822520213E-02
575																						),
576																		'oz'	=> array(	'tsp'		=> 6.00000000000000E+00,
577																							'tbs'		=> 2.00000000000000E+00,
578																							'oz'		=> 1.0,
579																							'cup'		=> 1.25000000000000E-01,
580																							'pt'		=> 6.25000000000000E-02,
581																							'us_pt'		=> 6.25000000000000E-02,
582																							'uk_pt'		=> 5.20535110093176E-02,
583																							'qt'		=> 3.12500000000000E-02,
584																							'gal'		=> 7.81250000000000E-03,
585																							'l'			=> 2.95799645040426E-02,
586																							'lt'		=> 2.95799645040426E-02
587																						),
588																		'cup'	=> array(	'tsp'		=> 4.80000000000000E+01,
589																							'tbs'		=> 1.60000000000000E+01,
590																							'oz'		=> 8.00000000000000E+00,
591																							'cup'		=> 1.0,
592																							'pt'		=> 5.00000000000000E-01,
593																							'us_pt'		=> 5.00000000000000E-01,
594																							'uk_pt'		=> 4.16428088074541E-01,
595																							'qt'		=> 2.50000000000000E-01,
596																							'gal'		=> 6.25000000000000E-02,
597																							'l'			=> 2.36639716032341E-01,
598																							'lt'		=> 2.36639716032341E-01
599																						),
600																		'pt'	=> array(	'tsp'		=> 9.60000000000000E+01,
601																							'tbs'		=> 3.20000000000000E+01,
602																							'oz'		=> 1.60000000000000E+01,
603																							'cup'		=> 2.00000000000000E+00,
604																							'pt'		=> 1.0,
605																							'us_pt'		=> 1.0,
606																							'uk_pt'		=> 8.32856176149081E-01,
607																							'qt'		=> 5.00000000000000E-01,
608																							'gal'		=> 1.25000000000000E-01,
609																							'l'			=> 4.73279432064682E-01,
610																							'lt'		=> 4.73279432064682E-01
611																						),
612																		'us_pt'	=> array(	'tsp'		=> 9.60000000000000E+01,
613																							'tbs'		=> 3.20000000000000E+01,
614																							'oz'		=> 1.60000000000000E+01,
615																							'cup'		=> 2.00000000000000E+00,
616																							'pt'		=> 1.0,
617																							'us_pt'		=> 1.0,
618																							'uk_pt'		=> 8.32856176149081E-01,
619																							'qt'		=> 5.00000000000000E-01,
620																							'gal'		=> 1.25000000000000E-01,
621																							'l'			=> 4.73279432064682E-01,
622																							'lt'		=> 4.73279432064682E-01
623																						),
624																		'uk_pt'	=> array(	'tsp'		=> 1.15266000000000E+02,
625																							'tbs'		=> 3.84220000000000E+01,
626																							'oz'		=> 1.92110000000000E+01,
627																							'cup'		=> 2.40137500000000E+00,
628																							'pt'		=> 1.20068750000000E+00,
629																							'us_pt'		=> 1.20068750000000E+00,
630																							'uk_pt'		=> 1.0,
631																							'qt'		=> 6.00343750000000E-01,
632																							'gal'		=> 1.50085937500000E-01,
633																							'l'			=> 5.68260698087162E-01,
634																							'lt'		=> 5.68260698087162E-01
635																						),
636																		'qt'	=> array(	'tsp'		=> 1.92000000000000E+02,
637																							'tbs'		=> 6.40000000000000E+01,
638																							'oz'		=> 3.20000000000000E+01,
639																							'cup'		=> 4.00000000000000E+00,
640																							'pt'		=> 2.00000000000000E+00,
641																							'us_pt'		=> 2.00000000000000E+00,
642																							'uk_pt'		=> 1.66571235229816E+00,
643																							'qt'		=> 1.0,
644																							'gal'		=> 2.50000000000000E-01,
645																							'l'			=> 9.46558864129363E-01,
646																							'lt'		=> 9.46558864129363E-01
647																						),
648																		'gal'	=> array(	'tsp'		=> 7.68000000000000E+02,
649																							'tbs'		=> 2.56000000000000E+02,
650																							'oz'		=> 1.28000000000000E+02,
651																							'cup'		=> 1.60000000000000E+01,
652																							'pt'		=> 8.00000000000000E+00,
653																							'us_pt'		=> 8.00000000000000E+00,
654																							'uk_pt'		=> 6.66284940919265E+00,
655																							'qt'		=> 4.00000000000000E+00,
656																							'gal'		=> 1.0,
657																							'l'			=> 3.78623545651745E+00,
658																							'lt'		=> 3.78623545651745E+00
659																						),
660																		'l'		=> array(	'tsp'		=> 2.02840000000000E+02,
661																							'tbs'		=> 6.76133333333333E+01,
662																							'oz'		=> 3.38066666666667E+01,
663																							'cup'		=> 4.22583333333333E+00,
664																							'pt'		=> 2.11291666666667E+00,
665																							'us_pt'		=> 2.11291666666667E+00,
666																							'uk_pt'		=> 1.75975569552166E+00,
667																							'qt'		=> 1.05645833333333E+00,
668																							'gal'		=> 2.64114583333333E-01,
669																							'l'			=> 1.0,
670																							'lt'		=> 1.0
671																						),
672																		'lt'	=> array(	'tsp'		=> 2.02840000000000E+02,
673																							'tbs'		=> 6.76133333333333E+01,
674																							'oz'		=> 3.38066666666667E+01,
675																							'cup'		=> 4.22583333333333E+00,
676																							'pt'		=> 2.11291666666667E+00,
677																							'us_pt'		=> 2.11291666666667E+00,
678																							'uk_pt'		=> 1.75975569552166E+00,
679																							'qt'		=> 1.05645833333333E+00,
680																							'gal'		=> 2.64114583333333E-01,
681																							'l'			=> 1.0,
682																							'lt'		=> 1.0
683																						)
684																	)
685											);
686
687
688	/**
689	 * _parseComplex
690	 *
691	 * Parses a complex number into its real and imaginary parts, and an I or J suffix
692	 *
693	 * @param	string		$complexNumber	The complex number
694	 * @return	string[]	Indexed on "real", "imaginary" and "suffix"
695	 */
696	public static function _parseComplex($complexNumber) {
697		$workString = (string) $complexNumber;
698
699		$realNumber = $imaginary = 0;
700		//	Extract the suffix, if there is one
701		$suffix = substr($workString,-1);
702		if (!is_numeric($suffix)) {
703			$workString = substr($workString,0,-1);
704		} else {
705			$suffix = '';
706		}
707
708		//	Split the input into its Real and Imaginary components
709		$leadingSign = 0;
710		if (strlen($workString) > 0) {
711			$leadingSign = (($workString{0} == '+') || ($workString{0} == '-')) ? 1 : 0;
712		}
713		$power = '';
714		$realNumber = strtok($workString, '+-');
715		if (strtoupper(substr($realNumber,-1)) == 'E') {
716			$power = strtok('+-');
717			++$leadingSign;
718		}
719
720		$realNumber = substr($workString,0,strlen($realNumber)+strlen($power)+$leadingSign);
721
722		if ($suffix != '') {
723			$imaginary = substr($workString,strlen($realNumber));
724
725			if (($imaginary == '') && (($realNumber == '') || ($realNumber == '+') || ($realNumber == '-'))) {
726				$imaginary = $realNumber.'1';
727				$realNumber = '0';
728			} else if ($imaginary == '') {
729				$imaginary = $realNumber;
730				$realNumber = '0';
731			} elseif (($imaginary == '+') || ($imaginary == '-')) {
732				$imaginary .= '1';
733			}
734		}
735
736		return array( 'real'		=> $realNumber,
737					  'imaginary'	=> $imaginary,
738					  'suffix'		=> $suffix
739					);
740	}	//	function _parseComplex()
741
742
743	/**
744	 * Cleans the leading characters in a complex number string
745	 *
746	 * @param	string		$complexNumber	The complex number to clean
747	 * @return	string		The "cleaned" complex number
748	 */
749	private static function _cleanComplex($complexNumber) {
750		if ($complexNumber{0} == '+') $complexNumber = substr($complexNumber,1);
751		if ($complexNumber{0} == '0') $complexNumber = substr($complexNumber,1);
752		if ($complexNumber{0} == '.') $complexNumber = '0'.$complexNumber;
753		if ($complexNumber{0} == '+') $complexNumber = substr($complexNumber,1);
754		return $complexNumber;
755	}
756
757	/**
758	 * Formats a number base string value with leading zeroes
759	 *
760	 * @param	string		$xVal		The "number" to pad
761	 * @param	integer		$places		The length that we want to pad this value
762	 * @return	string		The padded "number"
763	 */
764	private static function _nbrConversionFormat($xVal, $places) {
765		if (!is_null($places)) {
766			if (strlen($xVal) <= $places) {
767				return substr(str_pad($xVal, $places, '0', STR_PAD_LEFT), -10);
768			} else {
769				return PHPExcel_Calculation_Functions::NaN();
770			}
771		}
772
773		return substr($xVal, -10);
774	}	//	function _nbrConversionFormat()
775
776	/**
777	 *	BESSELI
778	 *
779	 *	Returns the modified Bessel function In(x), which is equivalent to the Bessel function evaluated
780	 *		for purely imaginary arguments
781	 *
782	 *	Excel Function:
783	 *		BESSELI(x,ord)
784	 *
785	 *	@access	public
786	 *	@category Engineering Functions
787	 *	@param	float		$x		The value at which to evaluate the function.
788	 *								If x is nonnumeric, BESSELI returns the #VALUE! error value.
789	 *	@param	integer		$ord	The order of the Bessel function.
790	 *								If ord is not an integer, it is truncated.
791	 *								If $ord is nonnumeric, BESSELI returns the #VALUE! error value.
792	 *								If $ord < 0, BESSELI returns the #NUM! error value.
793	 *	@return	float
794	 *
795	 */
796	public static function BESSELI($x, $ord) {
797		$x	= (is_null($x))	? 0.0 :	PHPExcel_Calculation_Functions::flattenSingleValue($x);
798		$ord	= (is_null($ord))	? 0.0 :	PHPExcel_Calculation_Functions::flattenSingleValue($ord);
799
800		if ((is_numeric($x)) && (is_numeric($ord))) {
801			$ord	= floor($ord);
802			if ($ord < 0) {
803				return PHPExcel_Calculation_Functions::NaN();
804			}
805
806			if (abs($x) <= 30) {
807				$fResult = $fTerm = pow($x / 2, $ord) / PHPExcel_Calculation_MathTrig::FACT($ord);
808				$ordK = 1;
809				$fSqrX = ($x * $x) / 4;
810				do {
811					$fTerm *= $fSqrX;
812					$fTerm /= ($ordK * ($ordK + $ord));
813					$fResult += $fTerm;
814				} while ((abs($fTerm) > 1e-12) && (++$ordK < 100));
815			} else {
816				$f_2_PI = 2 * M_PI;
817
818				$fXAbs = abs($x);
819				$fResult = exp($fXAbs) / sqrt($f_2_PI * $fXAbs);
820				if (($ord & 1) && ($x < 0)) {
821					$fResult = -$fResult;
822				}
823			}
824			return (is_nan($fResult)) ? PHPExcel_Calculation_Functions::NaN() : $fResult;
825		}
826		return PHPExcel_Calculation_Functions::VALUE();
827	}	//	function BESSELI()
828
829
830	/**
831	 *	BESSELJ
832	 *
833	 *	Returns the Bessel function
834	 *
835	 *	Excel Function:
836	 *		BESSELJ(x,ord)
837	 *
838	 *	@access	public
839	 *	@category Engineering Functions
840	 *	@param	float		$x		The value at which to evaluate the function.
841	 *								If x is nonnumeric, BESSELJ returns the #VALUE! error value.
842	 *	@param	integer		$ord	The order of the Bessel function. If n is not an integer, it is truncated.
843	 *								If $ord is nonnumeric, BESSELJ returns the #VALUE! error value.
844	 *								If $ord < 0, BESSELJ returns the #NUM! error value.
845	 *	@return	float
846	 *
847	 */
848	public static function BESSELJ($x, $ord) {
849		$x	= (is_null($x))	? 0.0 :	PHPExcel_Calculation_Functions::flattenSingleValue($x);
850		$ord	= (is_null($ord))	? 0.0 :	PHPExcel_Calculation_Functions::flattenSingleValue($ord);
851
852		if ((is_numeric($x)) && (is_numeric($ord))) {
853			$ord	= floor($ord);
854			if ($ord < 0) {
855				return PHPExcel_Calculation_Functions::NaN();
856			}
857
858			$fResult = 0;
859			if (abs($x) <= 30) {
860				$fResult = $fTerm = pow($x / 2, $ord) / PHPExcel_Calculation_MathTrig::FACT($ord);
861				$ordK = 1;
862				$fSqrX = ($x * $x) / -4;
863				do {
864					$fTerm *= $fSqrX;
865					$fTerm /= ($ordK * ($ordK + $ord));
866					$fResult += $fTerm;
867				} while ((abs($fTerm) > 1e-12) && (++$ordK < 100));
868			} else {
869				$f_PI_DIV_2 = M_PI / 2;
870				$f_PI_DIV_4 = M_PI / 4;
871
872				$fXAbs = abs($x);
873				$fResult = sqrt(M_2DIVPI / $fXAbs) * cos($fXAbs - $ord * $f_PI_DIV_2 - $f_PI_DIV_4);
874				if (($ord & 1) && ($x < 0)) {
875					$fResult = -$fResult;
876				}
877			}
878			return (is_nan($fResult)) ? PHPExcel_Calculation_Functions::NaN() : $fResult;
879		}
880		return PHPExcel_Calculation_Functions::VALUE();
881	}	//	function BESSELJ()
882
883
884	private static function _Besselk0($fNum) {
885		if ($fNum <= 2) {
886			$fNum2 = $fNum * 0.5;
887			$y = ($fNum2 * $fNum2);
888			$fRet = -log($fNum2) * self::BESSELI($fNum, 0) +
889					(-0.57721566 + $y * (0.42278420 + $y * (0.23069756 + $y * (0.3488590e-1 + $y * (0.262698e-2 + $y *
890					(0.10750e-3 + $y * 0.74e-5))))));
891		} else {
892			$y = 2 / $fNum;
893			$fRet = exp(-$fNum) / sqrt($fNum) *
894					(1.25331414 + $y * (-0.7832358e-1 + $y * (0.2189568e-1 + $y * (-0.1062446e-1 + $y *
895					(0.587872e-2 + $y * (-0.251540e-2 + $y * 0.53208e-3))))));
896		}
897		return $fRet;
898	}	//	function _Besselk0()
899
900
901	private static function _Besselk1($fNum) {
902		if ($fNum <= 2) {
903			$fNum2 = $fNum * 0.5;
904			$y = ($fNum2 * $fNum2);
905			$fRet = log($fNum2) * self::BESSELI($fNum, 1) +
906					(1 + $y * (0.15443144 + $y * (-0.67278579 + $y * (-0.18156897 + $y * (-0.1919402e-1 + $y *
907					(-0.110404e-2 + $y * (-0.4686e-4))))))) / $fNum;
908		} else {
909			$y = 2 / $fNum;
910			$fRet = exp(-$fNum) / sqrt($fNum) *
911					(1.25331414 + $y * (0.23498619 + $y * (-0.3655620e-1 + $y * (0.1504268e-1 + $y * (-0.780353e-2 + $y *
912					(0.325614e-2 + $y * (-0.68245e-3)))))));
913		}
914		return $fRet;
915	}	//	function _Besselk1()
916
917
918	/**
919	 *	BESSELK
920	 *
921	 *	Returns the modified Bessel function Kn(x), which is equivalent to the Bessel functions evaluated
922	 *		for purely imaginary arguments.
923	 *
924	 *	Excel Function:
925	 *		BESSELK(x,ord)
926	 *
927	 *	@access	public
928	 *	@category Engineering Functions
929	 *	@param	float		$x		The value at which to evaluate the function.
930	 *								If x is nonnumeric, BESSELK returns the #VALUE! error value.
931	 *	@param	integer		$ord	The order of the Bessel function. If n is not an integer, it is truncated.
932	 *								If $ord is nonnumeric, BESSELK returns the #VALUE! error value.
933	 *								If $ord < 0, BESSELK returns the #NUM! error value.
934	 *	@return	float
935	 *
936	 */
937	public static function BESSELK($x, $ord) {
938		$x		= (is_null($x))		? 0.0 :	PHPExcel_Calculation_Functions::flattenSingleValue($x);
939		$ord	= (is_null($ord))	? 0.0 :	PHPExcel_Calculation_Functions::flattenSingleValue($ord);
940
941		if ((is_numeric($x)) && (is_numeric($ord))) {
942			if (($ord < 0) || ($x == 0.0)) {
943				return PHPExcel_Calculation_Functions::NaN();
944			}
945
946			switch(floor($ord)) {
947				case 0 :	return self::_Besselk0($x);
948							break;
949				case 1 :	return self::_Besselk1($x);
950							break;
951				default :	$fTox	= 2 / $x;
952							$fBkm	= self::_Besselk0($x);
953							$fBk	= self::_Besselk1($x);
954							for ($n = 1; $n < $ord; ++$n) {
955								$fBkp	= $fBkm + $n * $fTox * $fBk;
956								$fBkm	= $fBk;
957								$fBk	= $fBkp;
958							}
959			}
960			return (is_nan($fBk)) ? PHPExcel_Calculation_Functions::NaN() : $fBk;
961		}
962		return PHPExcel_Calculation_Functions::VALUE();
963	}	//	function BESSELK()
964
965
966	private static function _Bessely0($fNum) {
967		if ($fNum < 8.0) {
968			$y = ($fNum * $fNum);
969			$f1 = -2957821389.0 + $y * (7062834065.0 + $y * (-512359803.6 + $y * (10879881.29 + $y * (-86327.92757 + $y * 228.4622733))));
970			$f2 = 40076544269.0 + $y * (745249964.8 + $y * (7189466.438 + $y * (47447.26470 + $y * (226.1030244 + $y))));
971			$fRet = $f1 / $f2 + 0.636619772 * self::BESSELJ($fNum, 0) * log($fNum);
972		} else {
973			$z = 8.0 / $fNum;
974			$y = ($z * $z);
975			$xx = $fNum - 0.785398164;
976			$f1 = 1 + $y * (-0.1098628627e-2 + $y * (0.2734510407e-4 + $y * (-0.2073370639e-5 + $y * 0.2093887211e-6)));
977			$f2 = -0.1562499995e-1 + $y * (0.1430488765e-3 + $y * (-0.6911147651e-5 + $y * (0.7621095161e-6 + $y * (-0.934945152e-7))));
978			$fRet = sqrt(0.636619772 / $fNum) * (sin($xx) * $f1 + $z * cos($xx) * $f2);
979		}
980		return $fRet;
981	}	//	function _Bessely0()
982
983
984	private static function _Bessely1($fNum) {
985		if ($fNum < 8.0) {
986			$y = ($fNum * $fNum);
987			$f1 = $fNum * (-0.4900604943e13 + $y * (0.1275274390e13 + $y * (-0.5153438139e11 + $y * (0.7349264551e9 + $y *
988				(-0.4237922726e7 + $y * 0.8511937935e4)))));
989			$f2 = 0.2499580570e14 + $y * (0.4244419664e12 + $y * (0.3733650367e10 + $y * (0.2245904002e8 + $y *
990				(0.1020426050e6 + $y * (0.3549632885e3 + $y)))));
991			$fRet = $f1 / $f2 + 0.636619772 * ( self::BESSELJ($fNum, 1) * log($fNum) - 1 / $fNum);
992		} else {
993			$fRet = sqrt(0.636619772 / $fNum) * sin($fNum - 2.356194491);
994		}
995		return $fRet;
996	}	//	function _Bessely1()
997
998
999	/**
1000	 *	BESSELY
1001	 *
1002	 *	Returns the Bessel function, which is also called the Weber function or the Neumann function.
1003	 *
1004	 *	Excel Function:
1005	 *		BESSELY(x,ord)
1006	 *
1007	 *	@access	public
1008	 *	@category Engineering Functions
1009	 *	@param	float		$x		The value at which to evaluate the function.
1010	 *								If x is nonnumeric, BESSELK returns the #VALUE! error value.
1011	 *	@param	integer		$ord	The order of the Bessel function. If n is not an integer, it is truncated.
1012	 *								If $ord is nonnumeric, BESSELK returns the #VALUE! error value.
1013	 *								If $ord < 0, BESSELK returns the #NUM! error value.
1014	 *
1015	 *	@return	float
1016	 */
1017	public static function BESSELY($x, $ord) {
1018		$x		= (is_null($x))		? 0.0 :	PHPExcel_Calculation_Functions::flattenSingleValue($x);
1019		$ord	= (is_null($ord))	? 0.0 :	PHPExcel_Calculation_Functions::flattenSingleValue($ord);
1020
1021		if ((is_numeric($x)) && (is_numeric($ord))) {
1022			if (($ord < 0) || ($x == 0.0)) {
1023				return PHPExcel_Calculation_Functions::NaN();
1024			}
1025
1026			switch(floor($ord)) {
1027				case 0 :	return self::_Bessely0($x);
1028							break;
1029				case 1 :	return self::_Bessely1($x);
1030							break;
1031				default:	$fTox	= 2 / $x;
1032							$fBym	= self::_Bessely0($x);
1033							$fBy	= self::_Bessely1($x);
1034							for ($n = 1; $n < $ord; ++$n) {
1035								$fByp	= $n * $fTox * $fBy - $fBym;
1036								$fBym	= $fBy;
1037								$fBy	= $fByp;
1038							}
1039			}
1040			return (is_nan($fBy)) ? PHPExcel_Calculation_Functions::NaN() : $fBy;
1041		}
1042		return PHPExcel_Calculation_Functions::VALUE();
1043	}	//	function BESSELY()
1044
1045
1046	/**
1047	 * BINTODEC
1048	 *
1049	 * Return a binary value as decimal.
1050	 *
1051	 * Excel Function:
1052	 *		BIN2DEC(x)
1053	 *
1054	 * @access	public
1055	 * @category Engineering Functions
1056	 * @param	string		$x		The binary number (as a string) that you want to convert. The number
1057	 *								cannot contain more than 10 characters (10 bits). The most significant
1058	 *								bit of number is the sign bit. The remaining 9 bits are magnitude bits.
1059	 *								Negative numbers are represented using two's-complement notation.
1060	 *								If number is not a valid binary number, or if number contains more than
1061	 *								10 characters (10 bits), BIN2DEC returns the #NUM! error value.
1062	 * @return	string
1063	 */
1064	public static function BINTODEC($x) {
1065		$x	= PHPExcel_Calculation_Functions::flattenSingleValue($x);
1066
1067		if (is_bool($x)) {
1068			if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
1069				$x = (int) $x;
1070			} else {
1071				return PHPExcel_Calculation_Functions::VALUE();
1072			}
1073		}
1074		if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
1075			$x = floor($x);
1076		}
1077		$x = (string) $x;
1078		if (strlen($x) > preg_match_all('/[01]/',$x,$out)) {
1079			return PHPExcel_Calculation_Functions::NaN();
1080		}
1081		if (strlen($x) > 10) {
1082			return PHPExcel_Calculation_Functions::NaN();
1083		} elseif (strlen($x) == 10) {
1084			//	Two's Complement
1085			$x = substr($x,-9);
1086			return '-'.(512-bindec($x));
1087		}
1088		return bindec($x);
1089	}	//	function BINTODEC()
1090
1091
1092	/**
1093	 * BINTOHEX
1094	 *
1095	 * Return a binary value as hex.
1096	 *
1097	 * Excel Function:
1098	 *		BIN2HEX(x[,places])
1099	 *
1100	 * @access	public
1101	 * @category Engineering Functions
1102	 * @param	string		$x		The binary number (as a string) that you want to convert. The number
1103	 *								cannot contain more than 10 characters (10 bits). The most significant
1104	 *								bit of number is the sign bit. The remaining 9 bits are magnitude bits.
1105	 *								Negative numbers are represented using two's-complement notation.
1106	 *								If number is not a valid binary number, or if number contains more than
1107	 *								10 characters (10 bits), BIN2HEX returns the #NUM! error value.
1108	 * @param	integer		$places	The number of characters to use. If places is omitted, BIN2HEX uses the
1109	 *								minimum number of characters necessary. Places is useful for padding the
1110	 *								return value with leading 0s (zeros).
1111	 *								If places is not an integer, it is truncated.
1112	 *								If places is nonnumeric, BIN2HEX returns the #VALUE! error value.
1113	 *								If places is negative, BIN2HEX returns the #NUM! error value.
1114	 * @return	string
1115	 */
1116	public static function BINTOHEX($x, $places=NULL) {
1117		$x	= PHPExcel_Calculation_Functions::flattenSingleValue($x);
1118		$places	= PHPExcel_Calculation_Functions::flattenSingleValue($places);
1119
1120		if (is_bool($x)) {
1121			if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
1122				$x = (int) $x;
1123			} else {
1124				return PHPExcel_Calculation_Functions::VALUE();
1125			}
1126		}
1127		if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
1128			$x = floor($x);
1129		}
1130		$x = (string) $x;
1131		if (strlen($x) > preg_match_all('/[01]/',$x,$out)) {
1132			return PHPExcel_Calculation_Functions::NaN();
1133		}
1134		if (strlen($x) > 10) {
1135			return PHPExcel_Calculation_Functions::NaN();
1136		} elseif (strlen($x) == 10) {
1137			//	Two's Complement
1138			return str_repeat('F',8).substr(strtoupper(dechex(bindec(substr($x,-9)))),-2);
1139		}
1140		$hexVal = (string) strtoupper(dechex(bindec($x)));
1141
1142		return self::_nbrConversionFormat($hexVal,$places);
1143	}	//	function BINTOHEX()
1144
1145
1146	/**
1147	 * BINTOOCT
1148	 *
1149	 * Return a binary value as octal.
1150	 *
1151	 * Excel Function:
1152	 *		BIN2OCT(x[,places])
1153	 *
1154	 * @access	public
1155	 * @category Engineering Functions
1156	 * @param	string		$x		The binary number (as a string) that you want to convert. The number
1157	 *								cannot contain more than 10 characters (10 bits). The most significant
1158	 *								bit of number is the sign bit. The remaining 9 bits are magnitude bits.
1159	 *								Negative numbers are represented using two's-complement notation.
1160	 *								If number is not a valid binary number, or if number contains more than
1161	 *								10 characters (10 bits), BIN2OCT returns the #NUM! error value.
1162	 * @param	integer		$places	The number of characters to use. If places is omitted, BIN2OCT uses the
1163	 *								minimum number of characters necessary. Places is useful for padding the
1164	 *								return value with leading 0s (zeros).
1165	 *								If places is not an integer, it is truncated.
1166	 *								If places is nonnumeric, BIN2OCT returns the #VALUE! error value.
1167	 *								If places is negative, BIN2OCT returns the #NUM! error value.
1168	 * @return	string
1169	 */
1170	public static function BINTOOCT($x, $places=NULL) {
1171		$x	= PHPExcel_Calculation_Functions::flattenSingleValue($x);
1172		$places	= PHPExcel_Calculation_Functions::flattenSingleValue($places);
1173
1174		if (is_bool($x)) {
1175			if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
1176				$x = (int) $x;
1177			} else {
1178				return PHPExcel_Calculation_Functions::VALUE();
1179			}
1180		}
1181		if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
1182			$x = floor($x);
1183		}
1184		$x = (string) $x;
1185		if (strlen($x) > preg_match_all('/[01]/',$x,$out)) {
1186			return PHPExcel_Calculation_Functions::NaN();
1187		}
1188		if (strlen($x) > 10) {
1189			return PHPExcel_Calculation_Functions::NaN();
1190		} elseif (strlen($x) == 10) {
1191			//	Two's Complement
1192			return str_repeat('7',7).substr(strtoupper(decoct(bindec(substr($x,-9)))),-3);
1193		}
1194		$octVal = (string) decoct(bindec($x));
1195
1196		return self::_nbrConversionFormat($octVal,$places);
1197	}	//	function BINTOOCT()
1198
1199
1200	/**
1201	 * DECTOBIN
1202	 *
1203	 * Return a decimal value as binary.
1204	 *
1205	 * Excel Function:
1206	 *		DEC2BIN(x[,places])
1207	 *
1208	 * @access	public
1209	 * @category Engineering Functions
1210	 * @param	string		$x		The decimal integer you want to convert. If number is negative,
1211	 *								valid place values are ignored and DEC2BIN returns a 10-character
1212	 *								(10-bit) binary number in which the most significant bit is the sign
1213	 *								bit. The remaining 9 bits are magnitude bits. Negative numbers are
1214	 *								represented using two's-complement notation.
1215	 *								If number < -512 or if number > 511, DEC2BIN returns the #NUM! error
1216	 *								value.
1217	 *								If number is nonnumeric, DEC2BIN returns the #VALUE! error value.
1218	 *								If DEC2BIN requires more than places characters, it returns the #NUM!
1219	 *								error value.
1220	 * @param	integer		$places	The number of characters to use. If places is omitted, DEC2BIN uses
1221	 *								the minimum number of characters necessary. Places is useful for
1222	 *								padding the return value with leading 0s (zeros).
1223	 *								If places is not an integer, it is truncated.
1224	 *								If places is nonnumeric, DEC2BIN returns the #VALUE! error value.
1225	 *								If places is zero or negative, DEC2BIN returns the #NUM! error value.
1226	 * @return	string
1227	 */
1228	public static function DECTOBIN($x, $places=NULL) {
1229		$x	= PHPExcel_Calculation_Functions::flattenSingleValue($x);
1230		$places	= PHPExcel_Calculation_Functions::flattenSingleValue($places);
1231
1232		if (is_bool($x)) {
1233			if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
1234				$x = (int) $x;
1235			} else {
1236				return PHPExcel_Calculation_Functions::VALUE();
1237			}
1238		}
1239		$x = (string) $x;
1240		if (strlen($x) > preg_match_all('/[-0123456789.]/',$x,$out)) {
1241			return PHPExcel_Calculation_Functions::VALUE();
1242		}
1243		$x = (string) floor($x);
1244		$r = decbin($x);
1245		if (strlen($r) == 32) {
1246			//	Two's Complement
1247			$r = substr($r,-10);
1248		} elseif (strlen($r) > 11) {
1249			return PHPExcel_Calculation_Functions::NaN();
1250		}
1251
1252		return self::_nbrConversionFormat($r,$places);
1253	}	//	function DECTOBIN()
1254
1255
1256	/**
1257	 * DECTOHEX
1258	 *
1259	 * Return a decimal value as hex.
1260	 *
1261	 * Excel Function:
1262	 *		DEC2HEX(x[,places])
1263	 *
1264	 * @access	public
1265	 * @category Engineering Functions
1266	 * @param	string		$x		The decimal integer you want to convert. If number is negative,
1267	 *								places is ignored and DEC2HEX returns a 10-character (40-bit)
1268	 *								hexadecimal number in which the most significant bit is the sign
1269	 *								bit. The remaining 39 bits are magnitude bits. Negative numbers
1270	 *								are represented using two's-complement notation.
1271	 *								If number < -549,755,813,888 or if number > 549,755,813,887,
1272	 *								DEC2HEX returns the #NUM! error value.
1273	 *								If number is nonnumeric, DEC2HEX returns the #VALUE! error value.
1274	 *								If DEC2HEX requires more than places characters, it returns the
1275	 *								#NUM! error value.
1276	 * @param	integer		$places	The number of characters to use. If places is omitted, DEC2HEX uses
1277	 *								the minimum number of characters necessary. Places is useful for
1278	 *								padding the return value with leading 0s (zeros).
1279	 *								If places is not an integer, it is truncated.
1280	 *								If places is nonnumeric, DEC2HEX returns the #VALUE! error value.
1281	 *								If places is zero or negative, DEC2HEX returns the #NUM! error value.
1282	 * @return	string
1283	 */
1284	public static function DECTOHEX($x, $places=null) {
1285		$x	= PHPExcel_Calculation_Functions::flattenSingleValue($x);
1286		$places	= PHPExcel_Calculation_Functions::flattenSingleValue($places);
1287
1288		if (is_bool($x)) {
1289			if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
1290				$x = (int) $x;
1291			} else {
1292				return PHPExcel_Calculation_Functions::VALUE();
1293			}
1294		}
1295		$x = (string) $x;
1296		if (strlen($x) > preg_match_all('/[-0123456789.]/',$x,$out)) {
1297			return PHPExcel_Calculation_Functions::VALUE();
1298		}
1299		$x = (string) floor($x);
1300		$r = strtoupper(dechex($x));
1301		if (strlen($r) == 8) {
1302			//	Two's Complement
1303			$r = 'FF'.$r;
1304		}
1305
1306		return self::_nbrConversionFormat($r,$places);
1307	}	//	function DECTOHEX()
1308
1309
1310	/**
1311	 * DECTOOCT
1312	 *
1313	 * Return an decimal value as octal.
1314	 *
1315	 * Excel Function:
1316	 *		DEC2OCT(x[,places])
1317	 *
1318	 * @access	public
1319	 * @category Engineering Functions
1320	 * @param	string		$x		The decimal integer you want to convert. If number is negative,
1321	 *								places is ignored and DEC2OCT returns a 10-character (30-bit)
1322	 *								octal number in which the most significant bit is the sign bit.
1323	 *								The remaining 29 bits are magnitude bits. Negative numbers are
1324	 *								represented using two's-complement notation.
1325	 *								If number < -536,870,912 or if number > 536,870,911, DEC2OCT
1326	 *								returns the #NUM! error value.
1327	 *								If number is nonnumeric, DEC2OCT returns the #VALUE! error value.
1328	 *								If DEC2OCT requires more than places characters, it returns the
1329	 *								#NUM! error value.
1330	 * @param	integer		$places	The number of characters to use. If places is omitted, DEC2OCT uses
1331	 *								the minimum number of characters necessary. Places is useful for
1332	 *								padding the return value with leading 0s (zeros).
1333	 *								If places is not an integer, it is truncated.
1334	 *								If places is nonnumeric, DEC2OCT returns the #VALUE! error value.
1335	 *								If places is zero or negative, DEC2OCT returns the #NUM! error value.
1336	 * @return	string
1337	 */
1338	public static function DECTOOCT($x, $places=null) {
1339		$x	= PHPExcel_Calculation_Functions::flattenSingleValue($x);
1340		$places	= PHPExcel_Calculation_Functions::flattenSingleValue($places);
1341
1342		if (is_bool($x)) {
1343			if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
1344				$x = (int) $x;
1345			} else {
1346				return PHPExcel_Calculation_Functions::VALUE();
1347			}
1348		}
1349		$x = (string) $x;
1350		if (strlen($x) > preg_match_all('/[-0123456789.]/',$x,$out)) {
1351			return PHPExcel_Calculation_Functions::VALUE();
1352		}
1353		$x = (string) floor($x);
1354		$r = decoct($x);
1355		if (strlen($r) == 11) {
1356			//	Two's Complement
1357			$r = substr($r,-10);
1358		}
1359
1360		return self::_nbrConversionFormat($r,$places);
1361	}	//	function DECTOOCT()
1362
1363
1364	/**
1365	 * HEXTOBIN
1366	 *
1367	 * Return a hex value as binary.
1368	 *
1369	 * Excel Function:
1370	 *		HEX2BIN(x[,places])
1371	 *
1372	 * @access	public
1373	 * @category Engineering Functions
1374	 * @param	string		$x			the hexadecimal number you want to convert. Number cannot
1375	 *									contain more than 10 characters. The most significant bit of
1376	 *									number is the sign bit (40th bit from the right). The remaining
1377	 *									9 bits are magnitude bits. Negative numbers are represented
1378	 *									using two's-complement notation.
1379	 *									If number is negative, HEX2BIN ignores places and returns a
1380	 *									10-character binary number.
1381	 *									If number is negative, it cannot be less than FFFFFFFE00, and
1382	 *									if number is positive, it cannot be greater than 1FF.
1383	 *									If number is not a valid hexadecimal number, HEX2BIN returns
1384	 *									the #NUM! error value.
1385	 *									If HEX2BIN requires more than places characters, it returns
1386	 *									the #NUM! error value.
1387	 * @param	integer		$places		The number of characters to use. If places is omitted,
1388	 *									HEX2BIN uses the minimum number of characters necessary. Places
1389	 *									is useful for padding the return value with leading 0s (zeros).
1390	 *									If places is not an integer, it is truncated.
1391	 *									If places is nonnumeric, HEX2BIN returns the #VALUE! error value.
1392	 *									If places is negative, HEX2BIN returns the #NUM! error value.
1393	 * @return	string
1394	 */
1395	public static function HEXTOBIN($x, $places=null) {
1396		$x	= PHPExcel_Calculation_Functions::flattenSingleValue($x);
1397		$places	= PHPExcel_Calculation_Functions::flattenSingleValue($places);
1398
1399		if (is_bool($x)) {
1400			return PHPExcel_Calculation_Functions::VALUE();
1401		}
1402		$x = (string) $x;
1403		if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/',strtoupper($x),$out)) {
1404			return PHPExcel_Calculation_Functions::NaN();
1405		}
1406		$binVal = decbin(hexdec($x));
1407
1408		return substr(self::_nbrConversionFormat($binVal,$places),-10);
1409	}	//	function HEXTOBIN()
1410
1411
1412	/**
1413	 * HEXTODEC
1414	 *
1415	 * Return a hex value as decimal.
1416	 *
1417	 * Excel Function:
1418	 *		HEX2DEC(x)
1419	 *
1420	 * @access	public
1421	 * @category Engineering Functions
1422	 * @param	string		$x		The hexadecimal number you want to convert. This number cannot
1423	 *								contain more than 10 characters (40 bits). The most significant
1424	 *								bit of number is the sign bit. The remaining 39 bits are magnitude
1425	 *								bits. Negative numbers are represented using two's-complement
1426	 *								notation.
1427	 *								If number is not a valid hexadecimal number, HEX2DEC returns the
1428	 *								#NUM! error value.
1429	 * @return	string
1430	 */
1431	public static function HEXTODEC($x) {
1432		$x	= PHPExcel_Calculation_Functions::flattenSingleValue($x);
1433
1434		if (is_bool($x)) {
1435			return PHPExcel_Calculation_Functions::VALUE();
1436		}
1437		$x = (string) $x;
1438		if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/',strtoupper($x),$out)) {
1439			return PHPExcel_Calculation_Functions::NaN();
1440		}
1441		return hexdec($x);
1442	}	//	function HEXTODEC()
1443
1444
1445	/**
1446	 * HEXTOOCT
1447	 *
1448	 * Return a hex value as octal.
1449	 *
1450	 * Excel Function:
1451	 *		HEX2OCT(x[,places])
1452	 *
1453	 * @access	public
1454	 * @category Engineering Functions
1455	 * @param	string		$x			The hexadecimal number you want to convert. Number cannot
1456	 *									contain more than 10 characters. The most significant bit of
1457	 *									number is the sign bit. The remaining 39 bits are magnitude
1458	 *									bits. Negative numbers are represented using two's-complement
1459	 *									notation.
1460	 *									If number is negative, HEX2OCT ignores places and returns a
1461	 *									10-character octal number.
1462	 *									If number is negative, it cannot be less than FFE0000000, and
1463	 *									if number is positive, it cannot be greater than 1FFFFFFF.
1464	 *									If number is not a valid hexadecimal number, HEX2OCT returns
1465	 *									the #NUM! error value.
1466	 *									If HEX2OCT requires more than places characters, it returns
1467	 *									the #NUM! error value.
1468	 * @param	integer		$places		The number of characters to use. If places is omitted, HEX2OCT
1469	 *									uses the minimum number of characters necessary. Places is
1470	 *									useful for padding the return value with leading 0s (zeros).
1471	 *									If places is not an integer, it is truncated.
1472	 *									If places is nonnumeric, HEX2OCT returns the #VALUE! error
1473	 *									value.
1474	 *									If places is negative, HEX2OCT returns the #NUM! error value.
1475	 * @return	string
1476	 */
1477	public static function HEXTOOCT($x, $places=null) {
1478		$x	= PHPExcel_Calculation_Functions::flattenSingleValue($x);
1479		$places	= PHPExcel_Calculation_Functions::flattenSingleValue($places);
1480
1481		if (is_bool($x)) {
1482			return PHPExcel_Calculation_Functions::VALUE();
1483		}
1484		$x = (string) $x;
1485		if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/',strtoupper($x),$out)) {
1486			return PHPExcel_Calculation_Functions::NaN();
1487		}
1488		$octVal = decoct(hexdec($x));
1489
1490		return self::_nbrConversionFormat($octVal,$places);
1491	}	//	function HEXTOOCT()
1492
1493
1494	/**
1495	 * OCTTOBIN
1496	 *
1497	 * Return an octal value as binary.
1498	 *
1499	 * Excel Function:
1500	 *		OCT2BIN(x[,places])
1501	 *
1502	 * @access	public
1503	 * @category Engineering Functions
1504	 * @param	string		$x			The octal number you want to convert. Number may not
1505	 *									contain more than 10 characters. The most significant
1506	 *									bit of number is the sign bit. The remaining 29 bits
1507	 *									are magnitude bits. Negative numbers are represented
1508	 *									using two's-complement notation.
1509	 *									If number is negative, OCT2BIN ignores places and returns
1510	 *									a 10-character binary number.
1511	 *									If number is negative, it cannot be less than 7777777000,
1512	 *									and if number is positive, it cannot be greater than 777.
1513	 *									If number is not a valid octal number, OCT2BIN returns
1514	 *									the #NUM! error value.
1515	 *									If OCT2BIN requires more than places characters, it
1516	 *									returns the #NUM! error value.
1517	 * @param	integer		$places		The number of characters to use. If places is omitted,
1518	 *									OCT2BIN uses the minimum number of characters necessary.
1519	 *									Places is useful for padding the return value with
1520	 *									leading 0s (zeros).
1521	 *									If places is not an integer, it is truncated.
1522	 *									If places is nonnumeric, OCT2BIN returns the #VALUE!
1523	 *									error value.
1524	 *									If places is negative, OCT2BIN returns the #NUM! error
1525	 *									value.
1526	 * @return	string
1527	 */
1528	public static function OCTTOBIN($x, $places=null) {
1529		$x	= PHPExcel_Calculation_Functions::flattenSingleValue($x);
1530		$places	= PHPExcel_Calculation_Functions::flattenSingleValue($places);
1531
1532		if (is_bool($x)) {
1533			return PHPExcel_Calculation_Functions::VALUE();
1534		}
1535		$x = (string) $x;
1536		if (preg_match_all('/[01234567]/',$x,$out) != strlen($x)) {
1537			return PHPExcel_Calculation_Functions::NaN();
1538		}
1539		$r = decbin(octdec($x));
1540
1541		return self::_nbrConversionFormat($r,$places);
1542	}	//	function OCTTOBIN()
1543
1544
1545	/**
1546	 * OCTTODEC
1547	 *
1548	 * Return an octal value as decimal.
1549	 *
1550	 * Excel Function:
1551	 *		OCT2DEC(x)
1552	 *
1553	 * @access	public
1554	 * @category Engineering Functions
1555	 * @param	string		$x		The octal number you want to convert. Number may not contain
1556	 *								more than 10 octal characters (30 bits). The most significant
1557	 *								bit of number is the sign bit. The remaining 29 bits are
1558	 *								magnitude bits. Negative numbers are represented using
1559	 *								two's-complement notation.
1560	 *								If number is not a valid octal number, OCT2DEC returns the
1561	 *								#NUM! error value.
1562	 * @return	string
1563	 */
1564	public static function OCTTODEC($x) {
1565		$x	= PHPExcel_Calculation_Functions::flattenSingleValue($x);
1566
1567		if (is_bool($x)) {
1568			return PHPExcel_Calculation_Functions::VALUE();
1569		}
1570		$x = (string) $x;
1571		if (preg_match_all('/[01234567]/',$x,$out) != strlen($x)) {
1572			return PHPExcel_Calculation_Functions::NaN();
1573		}
1574		return octdec($x);
1575	}	//	function OCTTODEC()
1576
1577
1578	/**
1579	 * OCTTOHEX
1580	 *
1581	 * Return an octal value as hex.
1582	 *
1583	 * Excel Function:
1584	 *		OCT2HEX(x[,places])
1585	 *
1586	 * @access	public
1587	 * @category Engineering Functions
1588	 * @param	string		$x			The octal number you want to convert. Number may not contain
1589	 *									more than 10 octal characters (30 bits). The most significant
1590	 *									bit of number is the sign bit. The remaining 29 bits are
1591	 *									magnitude bits. Negative numbers are represented using
1592	 *									two's-complement notation.
1593	 *									If number is negative, OCT2HEX ignores places and returns a
1594	 *									10-character hexadecimal number.
1595	 *									If number is not a valid octal number, OCT2HEX returns the
1596	 *									#NUM! error value.
1597	 *									If OCT2HEX requires more than places characters, it returns
1598	 *									the #NUM! error value.
1599	 * @param	integer		$places		The number of characters to use. If places is omitted, OCT2HEX
1600	 *									uses the minimum number of characters necessary. Places is useful
1601	 *									for padding the return value with leading 0s (zeros).
1602	 *									If places is not an integer, it is truncated.
1603	 *									If places is nonnumeric, OCT2HEX returns the #VALUE! error value.
1604	 *									If places is negative, OCT2HEX returns the #NUM! error value.
1605	 * @return	string
1606	 */
1607	public static function OCTTOHEX($x, $places=null) {
1608		$x	= PHPExcel_Calculation_Functions::flattenSingleValue($x);
1609		$places	= PHPExcel_Calculation_Functions::flattenSingleValue($places);
1610
1611		if (is_bool($x)) {
1612			return PHPExcel_Calculation_Functions::VALUE();
1613		}
1614		$x = (string) $x;
1615		if (preg_match_all('/[01234567]/',$x,$out) != strlen($x)) {
1616			return PHPExcel_Calculation_Functions::NaN();
1617		}
1618		$hexVal = strtoupper(dechex(octdec($x)));
1619
1620		return self::_nbrConversionFormat($hexVal,$places);
1621	}	//	function OCTTOHEX()
1622
1623
1624	/**
1625	 * COMPLEX
1626	 *
1627	 * Converts real and imaginary coefficients into a complex number of the form x + yi or x + yj.
1628	 *
1629	 * Excel Function:
1630	 *		COMPLEX(realNumber,imaginary[,places])
1631	 *
1632	 * @access	public
1633	 * @category Engineering Functions
1634	 * @param	float		$realNumber		The real coefficient of the complex number.
1635	 * @param	float		$imaginary		The imaginary coefficient of the complex number.
1636	 * @param	string		$suffix			The suffix for the imaginary component of the complex number.
1637	 *										If omitted, the suffix is assumed to be "i".
1638	 * @return	string
1639	 */
1640	public static function COMPLEX($realNumber=0.0, $imaginary=0.0, $suffix='i') {
1641		$realNumber	= (is_null($realNumber))	? 0.0 :	PHPExcel_Calculation_Functions::flattenSingleValue($realNumber);
1642		$imaginary	= (is_null($imaginary))		? 0.0 :	PHPExcel_Calculation_Functions::flattenSingleValue($imaginary);
1643		$suffix		= (is_null($suffix))		? 'i' :	PHPExcel_Calculation_Functions::flattenSingleValue($suffix);
1644
1645		if (((is_numeric($realNumber)) && (is_numeric($imaginary))) &&
1646			(($suffix == 'i') || ($suffix == 'j') || ($suffix == ''))) {
1647			$realNumber	= (float) $realNumber;
1648			$imaginary	= (float) $imaginary;
1649
1650			if ($suffix == '') $suffix = 'i';
1651			if ($realNumber == 0.0) {
1652				if ($imaginary == 0.0) {
1653					return (string) '0';
1654				} elseif ($imaginary == 1.0) {
1655					return (string) $suffix;
1656				} elseif ($imaginary == -1.0) {
1657					return (string) '-'.$suffix;
1658				}
1659				return (string) $imaginary.$suffix;
1660			} elseif ($imaginary == 0.0) {
1661				return (string) $realNumber;
1662			} elseif ($imaginary == 1.0) {
1663				return (string) $realNumber.'+'.$suffix;
1664			} elseif ($imaginary == -1.0) {
1665				return (string) $realNumber.'-'.$suffix;
1666			}
1667			if ($imaginary > 0) { $imaginary = (string) '+'.$imaginary; }
1668			return (string) $realNumber.$imaginary.$suffix;
1669		}
1670
1671		return PHPExcel_Calculation_Functions::VALUE();
1672	}	//	function COMPLEX()
1673
1674
1675	/**
1676	 * IMAGINARY
1677	 *
1678	 * Returns the imaginary coefficient of a complex number in x + yi or x + yj text format.
1679	 *
1680	 * Excel Function:
1681	 *		IMAGINARY(complexNumber)
1682	 *
1683	 * @access	public
1684	 * @category Engineering Functions
1685	 * @param	string		$complexNumber	The complex number for which you want the imaginary
1686	 * 										coefficient.
1687	 * @return	float
1688	 */
1689	public static function IMAGINARY($complexNumber) {
1690		$complexNumber	= PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1691
1692		$parsedComplex = self::_parseComplex($complexNumber);
1693		return $parsedComplex['imaginary'];
1694	}	//	function IMAGINARY()
1695
1696
1697	/**
1698	 * IMREAL
1699	 *
1700	 * Returns the real coefficient of a complex number in x + yi or x + yj text format.
1701	 *
1702	 * Excel Function:
1703	 *		IMREAL(complexNumber)
1704	 *
1705	 * @access	public
1706	 * @category Engineering Functions
1707	 * @param	string		$complexNumber	The complex number for which you want the real coefficient.
1708	 * @return	float
1709	 */
1710	public static function IMREAL($complexNumber) {
1711		$complexNumber	= PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1712
1713		$parsedComplex = self::_parseComplex($complexNumber);
1714		return $parsedComplex['real'];
1715	}	//	function IMREAL()
1716
1717
1718	/**
1719	 * IMABS
1720	 *
1721	 * Returns the absolute value (modulus) of a complex number in x + yi or x + yj text format.
1722	 *
1723	 * Excel Function:
1724	 *		IMABS(complexNumber)
1725	 *
1726	 * @param	string		$complexNumber	The complex number for which you want the absolute value.
1727	 * @return	float
1728	 */
1729	public static function IMABS($complexNumber) {
1730		$complexNumber	= PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1731
1732		$parsedComplex = self::_parseComplex($complexNumber);
1733
1734		return sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary']));
1735	}	//	function IMABS()
1736
1737
1738	/**
1739	 * IMARGUMENT
1740	 *
1741	 * Returns the argument theta of a complex number, i.e. the angle in radians from the real
1742	 * axis to the representation of the number in polar coordinates.
1743	 *
1744	 * Excel Function:
1745	 *		IMARGUMENT(complexNumber)
1746	 *
1747	 * @param	string		$complexNumber	The complex number for which you want the argument theta.
1748	 * @return	float
1749	 */
1750	public static function IMARGUMENT($complexNumber) {
1751		$complexNumber	= PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1752
1753		$parsedComplex = self::_parseComplex($complexNumber);
1754
1755		if ($parsedComplex['real'] == 0.0) {
1756			if ($parsedComplex['imaginary'] == 0.0) {
1757				return 0.0;
1758			} elseif($parsedComplex['imaginary'] < 0.0) {
1759				return M_PI / -2;
1760			} else {
1761				return M_PI / 2;
1762			}
1763		} elseif ($parsedComplex['real'] > 0.0) {
1764			return atan($parsedComplex['imaginary'] / $parsedComplex['real']);
1765		} elseif ($parsedComplex['imaginary'] < 0.0) {
1766			return 0 - (M_PI - atan(abs($parsedComplex['imaginary']) / abs($parsedComplex['real'])));
1767		} else {
1768			return M_PI - atan($parsedComplex['imaginary'] / abs($parsedComplex['real']));
1769		}
1770	}	//	function IMARGUMENT()
1771
1772
1773	/**
1774	 * IMCONJUGATE
1775	 *
1776	 * Returns the complex conjugate of a complex number in x + yi or x + yj text format.
1777	 *
1778	 * Excel Function:
1779	 *		IMCONJUGATE(complexNumber)
1780	 *
1781	 * @param	string		$complexNumber	The complex number for which you want the conjugate.
1782	 * @return	string
1783	 */
1784	public static function IMCONJUGATE($complexNumber) {
1785		$complexNumber	= PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1786
1787		$parsedComplex = self::_parseComplex($complexNumber);
1788
1789		if ($parsedComplex['imaginary'] == 0.0) {
1790			return $parsedComplex['real'];
1791		} else {
1792			return self::_cleanComplex( self::COMPLEX( $parsedComplex['real'],
1793													   0 - $parsedComplex['imaginary'],
1794													   $parsedComplex['suffix']
1795													 )
1796									  );
1797		}
1798	}	//	function IMCONJUGATE()
1799
1800
1801	/**
1802	 * IMCOS
1803	 *
1804	 * Returns the cosine of a complex number in x + yi or x + yj text format.
1805	 *
1806	 * Excel Function:
1807	 *		IMCOS(complexNumber)
1808	 *
1809	 * @param	string		$complexNumber	The complex number for which you want the cosine.
1810	 * @return	string|float
1811	 */
1812	public static function IMCOS($complexNumber) {
1813		$complexNumber	= PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1814
1815		$parsedComplex = self::_parseComplex($complexNumber);
1816
1817		if ($parsedComplex['imaginary'] == 0.0) {
1818			return cos($parsedComplex['real']);
1819		} else {
1820			return self::IMCONJUGATE(self::COMPLEX(cos($parsedComplex['real']) * cosh($parsedComplex['imaginary']),sin($parsedComplex['real']) * sinh($parsedComplex['imaginary']),$parsedComplex['suffix']));
1821		}
1822	}	//	function IMCOS()
1823
1824
1825	/**
1826	 * IMSIN
1827	 *
1828	 * Returns the sine of a complex number in x + yi or x + yj text format.
1829	 *
1830	 * Excel Function:
1831	 *		IMSIN(complexNumber)
1832	 *
1833	 * @param	string		$complexNumber	The complex number for which you want the sine.
1834	 * @return	string|float
1835	 */
1836	public static function IMSIN($complexNumber) {
1837		$complexNumber	= PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1838
1839		$parsedComplex = self::_parseComplex($complexNumber);
1840
1841		if ($parsedComplex['imaginary'] == 0.0) {
1842			return sin($parsedComplex['real']);
1843		} else {
1844			return self::COMPLEX(sin($parsedComplex['real']) * cosh($parsedComplex['imaginary']),cos($parsedComplex['real']) * sinh($parsedComplex['imaginary']),$parsedComplex['suffix']);
1845		}
1846	}	//	function IMSIN()
1847
1848
1849	/**
1850	 * IMSQRT
1851	 *
1852	 * Returns the square root of a complex number in x + yi or x + yj text format.
1853	 *
1854	 * Excel Function:
1855	 *		IMSQRT(complexNumber)
1856	 *
1857	 * @param	string		$complexNumber	The complex number for which you want the square root.
1858	 * @return	string
1859	 */
1860	public static function IMSQRT($complexNumber) {
1861		$complexNumber	= PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1862
1863		$parsedComplex = self::_parseComplex($complexNumber);
1864
1865		$theta = self::IMARGUMENT($complexNumber);
1866		$d1 = cos($theta / 2);
1867		$d2 = sin($theta / 2);
1868		$r = sqrt(sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary'])));
1869
1870		if ($parsedComplex['suffix'] == '') {
1871			return self::COMPLEX($d1 * $r,$d2 * $r);
1872		} else {
1873			return self::COMPLEX($d1 * $r,$d2 * $r,$parsedComplex['suffix']);
1874		}
1875	}	//	function IMSQRT()
1876
1877
1878	/**
1879	 * IMLN
1880	 *
1881	 * Returns the natural logarithm of a complex number in x + yi or x + yj text format.
1882	 *
1883	 * Excel Function:
1884	 *		IMLN(complexNumber)
1885	 *
1886	 * @param	string		$complexNumber	The complex number for which you want the natural logarithm.
1887	 * @return	string
1888	 */
1889	public static function IMLN($complexNumber) {
1890		$complexNumber	= PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1891
1892		$parsedComplex = self::_parseComplex($complexNumber);
1893
1894		if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
1895			return PHPExcel_Calculation_Functions::NaN();
1896		}
1897
1898		$logR = log(sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary'])));
1899		$t = self::IMARGUMENT($complexNumber);
1900
1901		if ($parsedComplex['suffix'] == '') {
1902			return self::COMPLEX($logR,$t);
1903		} else {
1904			return self::COMPLEX($logR,$t,$parsedComplex['suffix']);
1905		}
1906	}	//	function IMLN()
1907
1908
1909	/**
1910	 * IMLOG10
1911	 *
1912	 * Returns the common logarithm (base 10) of a complex number in x + yi or x + yj text format.
1913	 *
1914	 * Excel Function:
1915	 *		IMLOG10(complexNumber)
1916	 *
1917	 * @param	string		$complexNumber	The complex number for which you want the common logarithm.
1918	 * @return	string
1919	 */
1920	public static function IMLOG10($complexNumber) {
1921		$complexNumber	= PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1922
1923		$parsedComplex = self::_parseComplex($complexNumber);
1924
1925		if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
1926			return PHPExcel_Calculation_Functions::NaN();
1927		} elseif (($parsedComplex['real'] > 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
1928			return log10($parsedComplex['real']);
1929		}
1930
1931		return self::IMPRODUCT(log10(EULER),self::IMLN($complexNumber));
1932	}	//	function IMLOG10()
1933
1934
1935	/**
1936	 * IMLOG2
1937	 *
1938	 * Returns the base-2 logarithm of a complex number in x + yi or x + yj text format.
1939	 *
1940	 * Excel Function:
1941	 *		IMLOG2(complexNumber)
1942	 *
1943	 * @param	string		$complexNumber	The complex number for which you want the base-2 logarithm.
1944	 * @return	string
1945	 */
1946	public static function IMLOG2($complexNumber) {
1947		$complexNumber	= PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1948
1949		$parsedComplex = self::_parseComplex($complexNumber);
1950
1951		if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
1952			return PHPExcel_Calculation_Functions::NaN();
1953		} elseif (($parsedComplex['real'] > 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
1954			return log($parsedComplex['real'],2);
1955		}
1956
1957		return self::IMPRODUCT(log(EULER,2),self::IMLN($complexNumber));
1958	}	//	function IMLOG2()
1959
1960
1961	/**
1962	 * IMEXP
1963	 *
1964	 * Returns the exponential of a complex number in x + yi or x + yj text format.
1965	 *
1966	 * Excel Function:
1967	 *		IMEXP(complexNumber)
1968	 *
1969	 * @param	string		$complexNumber	The complex number for which you want the exponential.
1970	 * @return	string
1971	 */
1972	public static function IMEXP($complexNumber) {
1973		$complexNumber	= PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1974
1975		$parsedComplex = self::_parseComplex($complexNumber);
1976
1977		if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
1978			return '1';
1979		}
1980
1981		$e = exp($parsedComplex['real']);
1982		$eX = $e * cos($parsedComplex['imaginary']);
1983		$eY = $e * sin($parsedComplex['imaginary']);
1984
1985		if ($parsedComplex['suffix'] == '') {
1986			return self::COMPLEX($eX,$eY);
1987		} else {
1988			return self::COMPLEX($eX,$eY,$parsedComplex['suffix']);
1989		}
1990	}	//	function IMEXP()
1991
1992
1993	/**
1994	 * IMPOWER
1995	 *
1996	 * Returns a complex number in x + yi or x + yj text format raised to a power.
1997	 *
1998	 * Excel Function:
1999	 *		IMPOWER(complexNumber,realNumber)
2000	 *
2001	 * @param	string		$complexNumber	The complex number you want to raise to a power.
2002	 * @param	float		$realNumber		The power to which you want to raise the complex number.
2003	 * @return	string
2004	 */
2005	public static function IMPOWER($complexNumber,$realNumber) {
2006		$complexNumber	= PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
2007		$realNumber		= PHPExcel_Calculation_Functions::flattenSingleValue($realNumber);
2008
2009		if (!is_numeric($realNumber)) {
2010			return PHPExcel_Calculation_Functions::VALUE();
2011		}
2012
2013		$parsedComplex = self::_parseComplex($complexNumber);
2014
2015		$r = sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary']));
2016		$rPower = pow($r,$realNumber);
2017		$theta = self::IMARGUMENT($complexNumber) * $realNumber;
2018		if ($theta == 0) {
2019			return 1;
2020		} elseif ($parsedComplex['imaginary'] == 0.0) {
2021			return self::COMPLEX($rPower * cos($theta),$rPower * sin($theta),$parsedComplex['suffix']);
2022		} else {
2023			return self::COMPLEX($rPower * cos($theta),$rPower * sin($theta),$parsedComplex['suffix']);
2024		}
2025	}	//	function IMPOWER()
2026
2027
2028	/**
2029	 * IMDIV
2030	 *
2031	 * Returns the quotient of two complex numbers in x + yi or x + yj text format.
2032	 *
2033	 * Excel Function:
2034	 *		IMDIV(complexDividend,complexDivisor)
2035	 *
2036	 * @param	string		$complexDividend	The complex numerator or dividend.
2037	 * @param	string		$complexDivisor		The complex denominator or divisor.
2038	 * @return	string
2039	 */
2040	public static function IMDIV($complexDividend,$complexDivisor) {
2041		$complexDividend	= PHPExcel_Calculation_Functions::flattenSingleValue($complexDividend);
2042		$complexDivisor	= PHPExcel_Calculation_Functions::flattenSingleValue($complexDivisor);
2043
2044		$parsedComplexDividend = self::_parseComplex($complexDividend);
2045		$parsedComplexDivisor = self::_parseComplex($complexDivisor);
2046
2047		if (($parsedComplexDividend['suffix'] != '') && ($parsedComplexDivisor['suffix'] != '') &&
2048			($parsedComplexDividend['suffix'] != $parsedComplexDivisor['suffix'])) {
2049			return PHPExcel_Calculation_Functions::NaN();
2050		}
2051		if (($parsedComplexDividend['suffix'] != '') && ($parsedComplexDivisor['suffix'] == '')) {
2052			$parsedComplexDivisor['suffix'] = $parsedComplexDividend['suffix'];
2053		}
2054
2055		$d1 = ($parsedComplexDividend['real'] * $parsedComplexDivisor['real']) + ($parsedComplexDividend['imaginary'] * $parsedComplexDivisor['imaginary']);
2056		$d2 = ($parsedComplexDividend['imaginary'] * $parsedComplexDivisor['real']) - ($parsedComplexDividend['real'] * $parsedComplexDivisor['imaginary']);
2057		$d3 = ($parsedComplexDivisor['real'] * $parsedComplexDivisor['real']) + ($parsedComplexDivisor['imaginary'] * $parsedComplexDivisor['imaginary']);
2058
2059		$r = $d1/$d3;
2060		$i = $d2/$d3;
2061
2062		if ($i > 0.0) {
2063			return self::_cleanComplex($r.'+'.$i.$parsedComplexDivisor['suffix']);
2064		} elseif ($i < 0.0) {
2065			return self::_cleanComplex($r.$i.$parsedComplexDivisor['suffix']);
2066		} else {
2067			return $r;
2068		}
2069	}	//	function IMDIV()
2070
2071
2072	/**
2073	 * IMSUB
2074	 *
2075	 * Returns the difference of two complex numbers in x + yi or x + yj text format.
2076	 *
2077	 * Excel Function:
2078	 *		IMSUB(complexNumber1,complexNumber2)
2079	 *
2080	 * @param	string		$complexNumber1		The complex number from which to subtract complexNumber2.
2081	 * @param	string		$complexNumber2		The complex number to subtract from complexNumber1.
2082	 * @return	string
2083	 */
2084	public static function IMSUB($complexNumber1,$complexNumber2) {
2085		$complexNumber1	= PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber1);
2086		$complexNumber2	= PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber2);
2087
2088		$parsedComplex1 = self::_parseComplex($complexNumber1);
2089		$parsedComplex2 = self::_parseComplex($complexNumber2);
2090
2091		if ((($parsedComplex1['suffix'] != '') && ($parsedComplex2['suffix'] != '')) &&
2092			($parsedComplex1['suffix'] != $parsedComplex2['suffix'])) {
2093			return PHPExcel_Calculation_Functions::NaN();
2094		} elseif (($parsedComplex1['suffix'] == '') && ($parsedComplex2['suffix'] != '')) {
2095			$parsedComplex1['suffix'] = $parsedComplex2['suffix'];
2096		}
2097
2098		$d1 = $parsedComplex1['real'] - $parsedComplex2['real'];
2099		$d2 = $parsedComplex1['imaginary'] - $parsedComplex2['imaginary'];
2100
2101		return self::COMPLEX($d1,$d2,$parsedComplex1['suffix']);
2102	}	//	function IMSUB()
2103
2104
2105	/**
2106	 * IMSUM
2107	 *
2108	 * Returns the sum of two or more complex numbers in x + yi or x + yj text format.
2109	 *
2110	 * Excel Function:
2111	 *		IMSUM(complexNumber[,complexNumber[,...]])
2112	 *
2113	 * @param	string		$complexNumber,...	Series of complex numbers to add
2114	 * @return	string
2115	 */
2116	public static function IMSUM() {
2117		// Return value
2118		$returnValue = self::_parseComplex('0');
2119		$activeSuffix = '';
2120
2121		// Loop through the arguments
2122		$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
2123		foreach ($aArgs as $arg) {
2124			$parsedComplex = self::_parseComplex($arg);
2125
2126			if ($activeSuffix == '') {
2127				$activeSuffix = $parsedComplex['suffix'];
2128			} elseif (($parsedComplex['suffix'] != '') && ($activeSuffix != $parsedComplex['suffix'])) {
2129				return PHPExcel_Calculation_Functions::VALUE();
2130			}
2131
2132			$returnValue['real'] += $parsedComplex['real'];
2133			$returnValue['imaginary'] += $parsedComplex['imaginary'];
2134		}
2135
2136		if ($returnValue['imaginary'] == 0.0) { $activeSuffix = ''; }
2137		return self::COMPLEX($returnValue['real'],$returnValue['imaginary'],$activeSuffix);
2138	}	//	function IMSUM()
2139
2140
2141	/**
2142	 * IMPRODUCT
2143	 *
2144	 * Returns the product of two or more complex numbers in x + yi or x + yj text format.
2145	 *
2146	 * Excel Function:
2147	 *		IMPRODUCT(complexNumber[,complexNumber[,...]])
2148	 *
2149	 * @param	string		$complexNumber,...	Series of complex numbers to multiply
2150	 * @return	string
2151	 */
2152	public static function IMPRODUCT() {
2153		// Return value
2154		$returnValue = self::_parseComplex('1');
2155		$activeSuffix = '';
2156
2157		// Loop through the arguments
2158		$aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
2159		foreach ($aArgs as $arg) {
2160			$parsedComplex = self::_parseComplex($arg);
2161
2162			$workValue = $returnValue;
2163			if (($parsedComplex['suffix'] != '') && ($activeSuffix == '')) {
2164				$activeSuffix = $parsedComplex['suffix'];
2165			} elseif (($parsedComplex['suffix'] != '') && ($activeSuffix != $parsedComplex['suffix'])) {
2166				return PHPExcel_Calculation_Functions::NaN();
2167			}
2168			$returnValue['real'] = ($workValue['real'] * $parsedComplex['real']) - ($workValue['imaginary'] * $parsedComplex['imaginary']);
2169			$returnValue['imaginary'] = ($workValue['real'] * $parsedComplex['imaginary']) + ($workValue['imaginary'] * $parsedComplex['real']);
2170		}
2171
2172		if ($returnValue['imaginary'] == 0.0) { $activeSuffix = ''; }
2173		return self::COMPLEX($returnValue['real'],$returnValue['imaginary'],$activeSuffix);
2174	}	//	function IMPRODUCT()
2175
2176
2177	/**
2178	 *	DELTA
2179	 *
2180	 *	Tests whether two values are equal. Returns 1 if number1 = number2; returns 0 otherwise.
2181	 *	Use this function to filter a set of values. For example, by summing several DELTA
2182	 *	functions you calculate the count of equal pairs. This function is also known as the
2183	 *	Kronecker Delta function.
2184	 *
2185	 *	Excel Function:
2186	 *		DELTA(a[,b])
2187	 *
2188	 *	@param	float		$a	The first number.
2189	 *	@param	float		$b	The second number. If omitted, b is assumed to be zero.
2190	 *	@return	int
2191	 */
2192	public static function DELTA($a, $b=0) {
2193		$a	= PHPExcel_Calculation_Functions::flattenSingleValue($a);
2194		$b	= PHPExcel_Calculation_Functions::flattenSingleValue($b);
2195
2196		return (int) ($a == $b);
2197	}	//	function DELTA()
2198
2199
2200	/**
2201	 *	GESTEP
2202	 *
2203	 *	Excel Function:
2204	 *		GESTEP(number[,step])
2205	 *
2206	 *	Returns 1 if number >= step; returns 0 (zero) otherwise
2207	 *	Use this function to filter a set of values. For example, by summing several GESTEP
2208	 *	functions you calculate the count of values that exceed a threshold.
2209	 *
2210	 *	@param	float		$number		The value to test against step.
2211	 *	@param	float		$step		The threshold value.
2212	 *									If you omit a value for step, GESTEP uses zero.
2213	 *	@return	int
2214	 */
2215	public static function GESTEP($number, $step=0) {
2216		$number	= PHPExcel_Calculation_Functions::flattenSingleValue($number);
2217		$step	= PHPExcel_Calculation_Functions::flattenSingleValue($step);
2218
2219		return (int) ($number >= $step);
2220	}	//	function GESTEP()
2221
2222
2223	//
2224	//	Private method to calculate the erf value
2225	//
2226	private static $_two_sqrtpi = 1.128379167095512574;
2227
2228	public static function _erfVal($x) {
2229		if (abs($x) > 2.2) {
2230			return 1 - self::_erfcVal($x);
2231		}
2232		$sum = $term = $x;
2233		$xsqr = ($x * $x);
2234		$j = 1;
2235		do {
2236			$term *= $xsqr / $j;
2237			$sum -= $term / (2 * $j + 1);
2238			++$j;
2239			$term *= $xsqr / $j;
2240			$sum += $term / (2 * $j + 1);
2241			++$j;
2242			if ($sum == 0.0) {
2243				break;
2244			}
2245		} while (abs($term / $sum) > PRECISION);
2246		return self::$_two_sqrtpi * $sum;
2247	}	//	function _erfVal()
2248
2249
2250	/**
2251	 *	ERF
2252	 *
2253	 *	Returns the error function integrated between the lower and upper bound arguments.
2254	 *
2255	 *	Note: In Excel 2007 or earlier, if you input a negative value for the upper or lower bound arguments,
2256	 *			the function would return a #NUM! error. However, in Excel 2010, the function algorithm was
2257	 *			improved, so that it can now calculate the function for both positive and negative ranges.
2258	 *			PHPExcel follows Excel 2010 behaviour, and accepts nagative arguments.
2259	 *
2260	 *	Excel Function:
2261	 *		ERF(lower[,upper])
2262	 *
2263	 *	@param	float		$lower	lower bound for integrating ERF
2264	 *	@param	float		$upper	upper bound for integrating ERF.
2265	 *								If omitted, ERF integrates between zero and lower_limit
2266	 *	@return	float
2267	 */
2268	public static function ERF($lower, $upper = NULL) {
2269		$lower	= PHPExcel_Calculation_Functions::flattenSingleValue($lower);
2270		$upper	= PHPExcel_Calculation_Functions::flattenSingleValue($upper);
2271
2272		if (is_numeric($lower)) {
2273			if (is_null($upper)) {
2274				return self::_erfVal($lower);
2275			}
2276			if (is_numeric($upper)) {
2277				return self::_erfVal($upper) - self::_erfVal($lower);
2278			}
2279		}
2280		return PHPExcel_Calculation_Functions::VALUE();
2281	}	//	function ERF()
2282
2283
2284	//
2285	//	Private method to calculate the erfc value
2286	//
2287	private static $_one_sqrtpi = 0.564189583547756287;
2288
2289	private static function _erfcVal($x) {
2290		if (abs($x) < 2.2) {
2291			return 1 - self::_erfVal($x);
2292		}
2293		if ($x < 0) {
2294			return 2 - self::ERFC(-$x);
2295		}
2296		$a = $n = 1;
2297		$b = $c = $x;
2298		$d = ($x * $x) + 0.5;
2299		$q1 = $q2 = $b / $d;
2300		$t = 0;
2301		do {
2302			$t = $a * $n + $b * $x;
2303			$a = $b;
2304			$b = $t;
2305			$t = $c * $n + $d * $x;
2306			$c = $d;
2307			$d = $t;
2308			$n += 0.5;
2309			$q1 = $q2;
2310			$q2 = $b / $d;
2311		} while ((abs($q1 - $q2) / $q2) > PRECISION);
2312		return self::$_one_sqrtpi * exp(-$x * $x) * $q2;
2313	}	//	function _erfcVal()
2314
2315
2316	/**
2317	 *	ERFC
2318	 *
2319	 *	Returns the complementary ERF function integrated between x and infinity
2320	 *
2321	 *	Note: In Excel 2007 or earlier, if you input a negative value for the lower bound argument,
2322	 *		the function would return a #NUM! error. However, in Excel 2010, the function algorithm was
2323	 *		improved, so that it can now calculate the function for both positive and negative x values.
2324	 *			PHPExcel follows Excel 2010 behaviour, and accepts nagative arguments.
2325	 *
2326	 *	Excel Function:
2327	 *		ERFC(x)
2328	 *
2329	 *	@param	float	$x	The lower bound for integrating ERFC
2330	 *	@return	float
2331	 */
2332	public static function ERFC($x) {
2333		$x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
2334
2335		if (is_numeric($x)) {
2336			return self::_erfcVal($x);
2337		}
2338		return PHPExcel_Calculation_Functions::VALUE();
2339	}	//	function ERFC()
2340
2341
2342	/**
2343	 *	getConversionGroups
2344	 *	Returns a list of the different conversion groups for UOM conversions
2345	 *
2346	 *	@return	array
2347	 */
2348	public static function getConversionGroups() {
2349		$conversionGroups = array();
2350		foreach(self::$_conversionUnits as $conversionUnit) {
2351			$conversionGroups[] = $conversionUnit['Group'];
2352		}
2353		return array_merge(array_unique($conversionGroups));
2354	}	//	function getConversionGroups()
2355
2356
2357	/**
2358	 *	getConversionGroupUnits
2359	 *	Returns an array of units of measure, for a specified conversion group, or for all groups
2360	 *
2361	 *	@param	string	$group	The group whose units of measure you want to retrieve
2362	 *	@return	array
2363	 */
2364	public static function getConversionGroupUnits($group = NULL) {
2365		$conversionGroups = array();
2366		foreach(self::$_conversionUnits as $conversionUnit => $conversionGroup) {
2367			if ((is_null($group)) || ($conversionGroup['Group'] == $group)) {
2368				$conversionGroups[$conversionGroup['Group']][] = $conversionUnit;
2369			}
2370		}
2371		return $conversionGroups;
2372	}	//	function getConversionGroupUnits()
2373
2374
2375	/**
2376	 *	getConversionGroupUnitDetails
2377	 *
2378	 *	@param	string	$group	The group whose units of measure you want to retrieve
2379	 *	@return	array
2380	 */
2381	public static function getConversionGroupUnitDetails($group = NULL) {
2382		$conversionGroups = array();
2383		foreach(self::$_conversionUnits as $conversionUnit => $conversionGroup) {
2384			if ((is_null($group)) || ($conversionGroup['Group'] == $group)) {
2385				$conversionGroups[$conversionGroup['Group']][] = array(	'unit'			=> $conversionUnit,
2386																		'description'	=> $conversionGroup['Unit Name']
2387																	  );
2388			}
2389		}
2390		return $conversionGroups;
2391	}	//	function getConversionGroupUnitDetails()
2392
2393
2394	/**
2395	 *	getConversionMultipliers
2396	 *	Returns an array of the Multiplier prefixes that can be used with Units of Measure in CONVERTUOM()
2397	 *
2398	 *	@return	array of mixed
2399	 */
2400	public static function getConversionMultipliers() {
2401		return self::$_conversionMultipliers;
2402	}	//	function getConversionGroups()
2403
2404
2405	/**
2406	 *	CONVERTUOM
2407	 *
2408	 *	Converts a number from one measurement system to another.
2409	 *	For example, CONVERT can translate a table of distances in miles to a table of distances
2410	 *	in kilometers.
2411	 *
2412	 *	Excel Function:
2413	 *		CONVERT(value,fromUOM,toUOM)
2414	 *
2415	 *	@param	float		$value		The value in fromUOM to convert.
2416	 *	@param	string		$fromUOM	The units for value.
2417	 *	@param	string		$toUOM		The units for the result.
2418	 *
2419	 *	@return	float
2420	 */
2421	public static function CONVERTUOM($value, $fromUOM, $toUOM) {
2422		$value		= PHPExcel_Calculation_Functions::flattenSingleValue($value);
2423		$fromUOM	= PHPExcel_Calculation_Functions::flattenSingleValue($fromUOM);
2424		$toUOM		= PHPExcel_Calculation_Functions::flattenSingleValue($toUOM);
2425
2426		if (!is_numeric($value)) {
2427			return PHPExcel_Calculation_Functions::VALUE();
2428		}
2429		$fromMultiplier = 1.0;
2430		if (isset(self::$_conversionUnits[$fromUOM])) {
2431			$unitGroup1 = self::$_conversionUnits[$fromUOM]['Group'];
2432		} else {
2433			$fromMultiplier = substr($fromUOM,0,1);
2434			$fromUOM = substr($fromUOM,1);
2435			if (isset(self::$_conversionMultipliers[$fromMultiplier])) {
2436				$fromMultiplier = self::$_conversionMultipliers[$fromMultiplier]['multiplier'];
2437			} else {
2438				return PHPExcel_Calculation_Functions::NA();
2439			}
2440			if ((isset(self::$_conversionUnits[$fromUOM])) && (self::$_conversionUnits[$fromUOM]['AllowPrefix'])) {
2441				$unitGroup1 = self::$_conversionUnits[$fromUOM]['Group'];
2442			} else {
2443				return PHPExcel_Calculation_Functions::NA();
2444			}
2445		}
2446		$value *= $fromMultiplier;
2447
2448		$toMultiplier = 1.0;
2449		if (isset(self::$_conversionUnits[$toUOM])) {
2450			$unitGroup2 = self::$_conversionUnits[$toUOM]['Group'];
2451		} else {
2452			$toMultiplier = substr($toUOM,0,1);
2453			$toUOM = substr($toUOM,1);
2454			if (isset(self::$_conversionMultipliers[$toMultiplier])) {
2455				$toMultiplier = self::$_conversionMultipliers[$toMultiplier]['multiplier'];
2456			} else {
2457				return PHPExcel_Calculation_Functions::NA();
2458			}
2459			if ((isset(self::$_conversionUnits[$toUOM])) && (self::$_conversionUnits[$toUOM]['AllowPrefix'])) {
2460				$unitGroup2 = self::$_conversionUnits[$toUOM]['Group'];
2461			} else {
2462				return PHPExcel_Calculation_Functions::NA();
2463			}
2464		}
2465		if ($unitGroup1 != $unitGroup2) {
2466			return PHPExcel_Calculation_Functions::NA();
2467		}
2468
2469		if (($fromUOM == $toUOM) && ($fromMultiplier == $toMultiplier)) {
2470			//	We've already factored $fromMultiplier into the value, so we need
2471			//		to reverse it again
2472			return $value / $fromMultiplier;
2473		} elseif ($unitGroup1 == 'Temperature') {
2474			if (($fromUOM == 'F') || ($fromUOM == 'fah')) {
2475				if (($toUOM == 'F') || ($toUOM == 'fah')) {
2476					return $value;
2477				} else {
2478					$value = (($value - 32) / 1.8);
2479					if (($toUOM == 'K') || ($toUOM == 'kel')) {
2480						$value += 273.15;
2481					}
2482					return $value;
2483				}
2484			} elseif ((($fromUOM == 'K') || ($fromUOM == 'kel')) &&
2485					  (($toUOM == 'K') || ($toUOM == 'kel'))) {
2486						return $value;
2487			} elseif ((($fromUOM == 'C') || ($fromUOM == 'cel')) &&
2488					  (($toUOM == 'C') || ($toUOM == 'cel'))) {
2489					return $value;
2490			}
2491			if (($toUOM == 'F') || ($toUOM == 'fah')) {
2492				if (($fromUOM == 'K') || ($fromUOM == 'kel')) {
2493					$value -= 273.15;
2494				}
2495				return ($value * 1.8) + 32;
2496			}
2497			if (($toUOM == 'C') || ($toUOM == 'cel')) {
2498				return $value - 273.15;
2499			}
2500			return $value + 273.15;
2501		}
2502		return ($value * self::$_unitConversions[$unitGroup1][$fromUOM][$toUOM]) / $toMultiplier;
2503	}	//	function CONVERTUOM()
2504
2505}	//	class PHPExcel_Calculation_Engineering
2506