ILIAS  release_5-3 Revision v5.3.23-19-g915713cf615
Engineering.php
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1 <?php
30 if (!defined('PHPEXCEL_ROOT')) {
34  define('PHPEXCEL_ROOT', dirname(__FILE__) . '/../../');
35  require(PHPEXCEL_ROOT . 'PHPExcel/Autoloader.php');
36 }
37 
38 
40 define('EULER', 2.71828182845904523536);
41 
42 
50 class PHPExcel_Calculation_Engineering {
51 
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 
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 
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 
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' => $suffix
739  );
740  } // function _parseComplex()
741 
742 
749  private static function _cleanComplex($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 $complexNumber;
755  }
756 
764  private static function _nbrConversionFormat($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 
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() : $fResult;
825  }
826  return PHPExcel_Calculation_Functions::VALUE();
827  } // function BESSELI()
828 
829 
848  public static function BESSELJ($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 $fRet;
915  } // function _Besselk1()
916 
917 
937  public static function BESSELK($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 $fRet;
996  } // function _Bessely1()
997 
998 
1017  public static function BESSELY($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() : $fBy;
1041  }
1042  return PHPExcel_Calculation_Functions::VALUE();
1043  } // function BESSELY()
1044 
1045 
1064  public static function BINTODEC($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 
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 
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 
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,$places);
1253  } // function DECTOBIN()
1254 
1255 
1284  public static function DECTOHEX($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 
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 
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 
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($x);
1442  } // function HEXTODEC()
1443 
1444 
1477  public static function HEXTOOCT($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 
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 
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($x);
1575  } // function OCTTODEC()
1576 
1577 
1607  public static function OCTTOHEX($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 
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.$suffix;
1669  }
1670 
1671  return PHPExcel_Calculation_Functions::VALUE();
1672  } // function COMPLEX()
1673 
1674 
1689  public static function IMAGINARY($complexNumber) {
1690  $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1691 
1692  $parsedComplex = self::_parseComplex($complexNumber);
1693  return $parsedComplex['imaginary'];
1694  } // function IMAGINARY()
1695 
1696 
1710  public static function IMREAL($complexNumber) {
1711  $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1712 
1713  $parsedComplex = self::_parseComplex($complexNumber);
1714  return $parsedComplex['real'];
1715  } // function IMREAL()
1716 
1717 
1729  public static function IMABS($complexNumber) {
1730  $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1731 
1732  $parsedComplex = self::_parseComplex($complexNumber);
1733 
1734  return sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary']));
1735  } // function IMABS()
1736 
1737 
1750  public static function IMARGUMENT($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 
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  $parsedComplex['suffix']
1795  )
1796  );
1797  }
1798  } // function IMCONJUGATE()
1799 
1800 
1812  public static function IMCOS($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']),$parsedComplex['suffix']));
1821  }
1822  } // function IMCOS()
1823 
1824 
1836  public static function IMSIN($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']),$parsedComplex['suffix']);
1845  }
1846  } // function IMSIN()
1847 
1848 
1860  public static function IMSQRT($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 
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 
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 
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 
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 
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),$parsedComplex['suffix']);
2024  }
2025  } // function IMPOWER()
2026 
2027 
2040  public static function IMDIV($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 $r;
2068  }
2069  } // function IMDIV()
2070 
2071 
2084  public static function IMSUB($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 
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 
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 
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 == $b);
2197  } // function DELTA()
2198 
2199 
2215  public static function GESTEP($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 * $sum;
2247  } // function _erfVal()
2248 
2249 
2268  public static function ERF($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) * $q2;
2313  } // function _erfcVal()
2314 
2315 
2332  public static function ERFC($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 
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 
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 $conversionGroups;
2372  } // function getConversionGroupUnits()
2373 
2374 
2381  public static function getConversionGroupUnitDetails($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 $conversionGroups;
2391  } // function getConversionGroupUnitDetails()
2392 
2393 
2400  public static function getConversionMultipliers() {
2401  return self::$_conversionMultipliers;
2402  } // function getConversionGroups()
2403 
2404 
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]) / $toMultiplier;
2503  } // function CONVERTUOM()
2504 
2505 } // class PHPExcel_Calculation_Engineering
PHPExcel_Calculation_Engineering\IMAGINARY
static IMAGINARY($complexNumber)
Definition: Engineering.php:1689
PHPExcel_Calculation_Engineering\BESSELY
static BESSELY($x, $ord)
Definition: Engineering.php:1017
PHPExcel_Calculation_Engineering\BESSELI
static BESSELI($x, $ord)
Definition: Engineering.php:796
string
Add rich text string
Definition: 05featuredemo.inc.php:117
PHPExcel_Calculation_Engineering\_erfcVal
static _erfcVal($x)
Definition: Engineering.php:2289
PHPExcel_Calculation_Engineering\IMARGUMENT
static IMARGUMENT($complexNumber)
IMARGUMENT.
Definition: Engineering.php:1750
PHPExcel_Calculation_Engineering\IMCOS
static IMCOS($complexNumber)
IMCOS.
Definition: Engineering.php:1812
PHPExcel_Calculation_Functions\flattenSingleValue
static flattenSingleValue($value='')
Convert an array to a single scalar value by extracting the first element.
Definition: Functions.php:662
PHPExcel_Calculation_Engineering\HEXTOBIN
static HEXTOBIN($x, $places=null)
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PHPExcel_Calculation_Engineering\_Besselk1
static _Besselk1($fNum)
Definition: Engineering.php:901
PHPExcel_Calculation_MathTrig\FACT
static FACT($factVal)
Definition: MathTrig.php:240
PHPExcel_Calculation_Engineering\_parseComplex
static _parseComplex($complexNumber)
_parseComplex
Definition: Engineering.php:696
PHPExcel_Calculation_Engineering\$_conversionMultipliers
static $_conversionMultipliers
Definition: Engineering.php:127
$x
$x
Definition: example_009.php:98
PHPExcel_Calculation_Engineering\IMSUM
static IMSUM()
IMSUM.
Definition: Engineering.php:2116
PRECISION
const PRECISION
PRECISION.
Definition: Functions.php:49
PHPExcel_Calculation_Engineering\_erfVal
static _erfVal($x)
Definition: Engineering.php:2228
PHPExcel_Calculation_Engineering\IMLOG10
static IMLOG10($complexNumber)
IMLOG10.
Definition: Engineering.php:1920
PHPExcel_Calculation_Engineering\IMEXP
static IMEXP($complexNumber)
IMEXP.
Definition: Engineering.php:1972
PHPExcel_Calculation_Engineering\COMPLEX
static COMPLEX($realNumber=0.0, $imaginary=0.0, $suffix='i')
Definition: Engineering.php:1640
PHPExcel_Calculation_Engineering\_cleanComplex
static _cleanComplex($complexNumber)
Cleans the leading characters in a complex number string.
Definition: Engineering.php:749
PHPExcel_Calculation_Functions\flattenArray
static flattenArray($array)
Convert a multi-dimensional array to a simple 1-dimensional array.
Definition: Functions.php:598
PHPExcel_Calculation_Engineering\IMLOG2
static IMLOG2($complexNumber)
IMLOG2.
Definition: Engineering.php:1946
PHPExcel_Calculation_Engineering\GESTEP
static GESTEP($number, $step=0)
GESTEP.
Definition: Engineering.php:2215
PHPExcel_Calculation_Functions\VALUE
static VALUE()
Definition: Functions.php:289
PHPExcel_Calculation_Engineering\_Besselk0
static _Besselk0($fNum)
Definition: Engineering.php:884
PHPExcel_Calculation_Engineering\DECTOBIN
static DECTOBIN($x, $places=NULL)
Definition: Engineering.php:1228
PHPExcel_Calculation_Engineering\IMSQRT
static IMSQRT($complexNumber)
IMSQRT.
Definition: Engineering.php:1860
PHPExcel_Calculation_Engineering\_nbrConversionFormat
static _nbrConversionFormat($xVal, $places)
Formats a number base string value with leading zeroes.
Definition: Engineering.php:764
PHPExcel_Calculation_Engineering\IMPOWER
static IMPOWER($complexNumber, $realNumber)
IMPOWER.
Definition: Engineering.php:2005
$r
$r
Definition: example_031.php:79
PHPExcel_Calculation_Engineering\$_unitConversions
static $_unitConversions
Definition: Engineering.php:154
PHPExcel_Calculation_Engineering\ERFC
static ERFC($x)
ERFC.
Definition: Engineering.php:2332
$y
$y
Definition: example_007.php:83
PHPExcel_Calculation_Engineering\$_one_sqrtpi
static $_one_sqrtpi
Definition: Engineering.php:2287
PHPExcel_Calculation_Engineering\BESSELJ
static BESSELJ($x, $ord)
Definition: Engineering.php:848
e
e($cmd)
Definition: flush.php:14
PHPExcel_Calculation_Engineering\DELTA
static DELTA($a, $b=0)
DELTA.
Definition: Engineering.php:2192
PHPExcel_Calculation_Engineering\getConversionMultipliers
static getConversionMultipliers()
getConversionMultipliers Returns an array of the Multiplier prefixes that can be used with Units of M...
Definition: Engineering.php:2400
PHPExcel_Calculation_Engineering\OCTTOHEX
static OCTTOHEX($x, $places=null)
Definition: Engineering.php:1607
PHPExcel_Calculation_Engineering
Definition: Engineering.php:50
PHPExcel_Calculation_Engineering\OCTTOBIN
static OCTTOBIN($x, $places=null)
Definition: Engineering.php:1528
PHPExcel_Calculation_Engineering\IMREAL
static IMREAL($complexNumber)
Definition: Engineering.php:1710
$n
$n
Definition: RandomTest.php:85
PHPExcel_Calculation_Engineering\IMPRODUCT
static IMPRODUCT()
IMPRODUCT.
Definition: Engineering.php:2152
PHPExcel_Calculation_Functions\NA
static NA()
Definition: Functions.php:219
PHPExcel_Calculation_Functions\COMPATIBILITY_OPENOFFICE
const COMPATIBILITY_OPENOFFICE
Definition: Functions.php:64
PHPExcel_Calculation_Engineering\IMABS
static IMABS($complexNumber)
IMABS.
Definition: Engineering.php:1729
PHPExcel_Calculation_Engineering\IMSUB
static IMSUB($complexNumber1, $complexNumber2)
IMSUB.
Definition: Engineering.php:2084
array
Create styles array
The data for the language used.
Definition: 40duplicateStyle.php:19
PHPExcel_Calculation_Functions\getCompatibilityMode
static getCompatibilityMode()
Definition: Functions.php:138
PHPExcel_Calculation_Engineering\IMCONJUGATE
static IMCONJUGATE($complexNumber)
IMCONJUGATE.
Definition: Engineering.php:1784
PHPExcel_Calculation_Engineering\getConversionGroupUnits
static getConversionGroupUnits($group=NULL)
getConversionGroupUnits Returns an array of units of measure, for a specified conversion group...
Definition: Engineering.php:2364
PHPExcel_Calculation_Engineering\$_conversionUnits
static $_conversionUnits
Definition: Engineering.php:57
EULER
const EULER(!defined('PHPEXCEL_ROOT'))
PHPExcel root directory.
Definition: Engineering.php:40
PHPExcel_Calculation_Engineering\IMLN
static IMLN($complexNumber)
IMLN.
Definition: Engineering.php:1889
PHPExcel_Calculation_Engineering\_Bessely0
static _Bessely0($fNum)
Definition: Engineering.php:966
PHPExcel_Calculation_Engineering\getConversionGroupUnitDetails
static getConversionGroupUnitDetails($group=NULL)
getConversionGroupUnitDetails
Definition: Engineering.php:2381
PHPExcel_Calculation_Functions\NaN
static NaN()
Definition: Functions.php:233
PHPExcel_Calculation_Engineering\BINTOOCT
static BINTOOCT($x, $places=NULL)
Definition: Engineering.php:1170
PHPExcel_Calculation_Engineering\DECTOOCT
static DECTOOCT($x, $places=null)
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PHPExcel_Calculation_Engineering\getConversionGroups
static getConversionGroups()
getConversionGroups Returns a list of the different conversion groups for UOM conversions ...
Definition: Engineering.php:2348
PHPExcel_Calculation_Engineering\ERF
static ERF($lower, $upper=NULL)
ERF.
Definition: Engineering.php:2268
PHPExcel_Calculation_Engineering\BINTOHEX
static BINTOHEX($x, $places=NULL)
Definition: Engineering.php:1116
PHPExcel_Calculation_Engineering\DECTOHEX
static DECTOHEX($x, $places=null)
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$i
$i
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PHPExcel_Calculation_Engineering\CONVERTUOM
static CONVERTUOM($value, $fromUOM, $toUOM)
CONVERTUOM.
Definition: Engineering.php:2421
M_2DIVPI
const M_2DIVPI
2 / PI
Definition: Functions.php:43
PHPExcel_Calculation_Engineering\OCTTODEC
static OCTTODEC($x)
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PHPExcel_Calculation_Engineering\IMSIN
static IMSIN($complexNumber)
IMSIN.
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PHPExcel_Calculation_Functions\COMPATIBILITY_GNUMERIC
const COMPATIBILITY_GNUMERIC
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PHPExcel_Calculation_Engineering\BESSELK
static BESSELK($x, $ord)
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defined
defined( 'APPLICATION_ENV')||define( 'APPLICATION_ENV'
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PHPExcel_Calculation_Engineering\HEXTODEC
static HEXTODEC($x)
Definition: Engineering.php:1431
PHPExcel_Calculation_Engineering\BINTODEC
static BINTODEC($x)
Definition: Engineering.php:1064
PHPExcel_Calculation_Engineering\IMDIV
static IMDIV($complexDividend, $complexDivisor)
IMDIV.
Definition: Engineering.php:2040
PHPExcel_Calculation_Engineering\$_two_sqrtpi
static $_two_sqrtpi
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$d
for($i=6; $i< 13; $i++) for($i=1; $i< 13; $i++) $d
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PHPExcel_Calculation_Engineering\HEXTOOCT
static HEXTOOCT($x, $places=null)
Definition: Engineering.php:1477
PHPExcel_Calculation_Engineering\_Bessely1
static _Bessely1($fNum)
Definition: Engineering.php:984