1<?php
2
3namespace PhpOffice\PhpSpreadsheet\Calculation;
4
5use Complex\Complex;
6use Complex\Exception as ComplexException;
7
8class Engineering
9{
10    /**
11     * EULER.
12     */
13    const EULER = 2.71828182845904523536;
14
15    /**
16     * Details of the Units of measure that can be used in CONVERTUOM().
17     *
18     * @var mixed[]
19     */
20    private static $conversionUnits = [
21        'g' => ['Group' => 'Mass', 'Unit Name' => 'Gram', 'AllowPrefix' => true],
22        'sg' => ['Group' => 'Mass', 'Unit Name' => 'Slug', 'AllowPrefix' => false],
23        'lbm' => ['Group' => 'Mass', 'Unit Name' => 'Pound mass (avoirdupois)', 'AllowPrefix' => false],
24        'u' => ['Group' => 'Mass', 'Unit Name' => 'U (atomic mass unit)', 'AllowPrefix' => true],
25        'ozm' => ['Group' => 'Mass', 'Unit Name' => 'Ounce mass (avoirdupois)', 'AllowPrefix' => false],
26        'm' => ['Group' => 'Distance', 'Unit Name' => 'Meter', 'AllowPrefix' => true],
27        'mi' => ['Group' => 'Distance', 'Unit Name' => 'Statute mile', 'AllowPrefix' => false],
28        'Nmi' => ['Group' => 'Distance', 'Unit Name' => 'Nautical mile', 'AllowPrefix' => false],
29        'in' => ['Group' => 'Distance', 'Unit Name' => 'Inch', 'AllowPrefix' => false],
30        'ft' => ['Group' => 'Distance', 'Unit Name' => 'Foot', 'AllowPrefix' => false],
31        'yd' => ['Group' => 'Distance', 'Unit Name' => 'Yard', 'AllowPrefix' => false],
32        'ang' => ['Group' => 'Distance', 'Unit Name' => 'Angstrom', 'AllowPrefix' => true],
33        'Pica' => ['Group' => 'Distance', 'Unit Name' => 'Pica (1/72 in)', 'AllowPrefix' => false],
34        'yr' => ['Group' => 'Time', 'Unit Name' => 'Year', 'AllowPrefix' => false],
35        'day' => ['Group' => 'Time', 'Unit Name' => 'Day', 'AllowPrefix' => false],
36        'hr' => ['Group' => 'Time', 'Unit Name' => 'Hour', 'AllowPrefix' => false],
37        'mn' => ['Group' => 'Time', 'Unit Name' => 'Minute', 'AllowPrefix' => false],
38        'sec' => ['Group' => 'Time', 'Unit Name' => 'Second', 'AllowPrefix' => true],
39        'Pa' => ['Group' => 'Pressure', 'Unit Name' => 'Pascal', 'AllowPrefix' => true],
40        'p' => ['Group' => 'Pressure', 'Unit Name' => 'Pascal', 'AllowPrefix' => true],
41        'atm' => ['Group' => 'Pressure', 'Unit Name' => 'Atmosphere', 'AllowPrefix' => true],
42        'at' => ['Group' => 'Pressure', 'Unit Name' => 'Atmosphere', 'AllowPrefix' => true],
43        'mmHg' => ['Group' => 'Pressure', 'Unit Name' => 'mm of Mercury', 'AllowPrefix' => true],
44        'N' => ['Group' => 'Force', 'Unit Name' => 'Newton', 'AllowPrefix' => true],
45        'dyn' => ['Group' => 'Force', 'Unit Name' => 'Dyne', 'AllowPrefix' => true],
46        'dy' => ['Group' => 'Force', 'Unit Name' => 'Dyne', 'AllowPrefix' => true],
47        'lbf' => ['Group' => 'Force', 'Unit Name' => 'Pound force', 'AllowPrefix' => false],
48        'J' => ['Group' => 'Energy', 'Unit Name' => 'Joule', 'AllowPrefix' => true],
49        'e' => ['Group' => 'Energy', 'Unit Name' => 'Erg', 'AllowPrefix' => true],
50        'c' => ['Group' => 'Energy', 'Unit Name' => 'Thermodynamic calorie', 'AllowPrefix' => true],
51        'cal' => ['Group' => 'Energy', 'Unit Name' => 'IT calorie', 'AllowPrefix' => true],
52        'eV' => ['Group' => 'Energy', 'Unit Name' => 'Electron volt', 'AllowPrefix' => true],
53        'ev' => ['Group' => 'Energy', 'Unit Name' => 'Electron volt', 'AllowPrefix' => true],
54        'HPh' => ['Group' => 'Energy', 'Unit Name' => 'Horsepower-hour', 'AllowPrefix' => false],
55        'hh' => ['Group' => 'Energy', 'Unit Name' => 'Horsepower-hour', 'AllowPrefix' => false],
56        'Wh' => ['Group' => 'Energy', 'Unit Name' => 'Watt-hour', 'AllowPrefix' => true],
57        'wh' => ['Group' => 'Energy', 'Unit Name' => 'Watt-hour', 'AllowPrefix' => true],
58        'flb' => ['Group' => 'Energy', 'Unit Name' => 'Foot-pound', 'AllowPrefix' => false],
59        'BTU' => ['Group' => 'Energy', 'Unit Name' => 'BTU', 'AllowPrefix' => false],
60        'btu' => ['Group' => 'Energy', 'Unit Name' => 'BTU', 'AllowPrefix' => false],
61        'HP' => ['Group' => 'Power', 'Unit Name' => 'Horsepower', 'AllowPrefix' => false],
62        'h' => ['Group' => 'Power', 'Unit Name' => 'Horsepower', 'AllowPrefix' => false],
63        'W' => ['Group' => 'Power', 'Unit Name' => 'Watt', 'AllowPrefix' => true],
64        'w' => ['Group' => 'Power', 'Unit Name' => 'Watt', 'AllowPrefix' => true],
65        'T' => ['Group' => 'Magnetism', 'Unit Name' => 'Tesla', 'AllowPrefix' => true],
66        'ga' => ['Group' => 'Magnetism', 'Unit Name' => 'Gauss', 'AllowPrefix' => true],
67        'C' => ['Group' => 'Temperature', 'Unit Name' => 'Celsius', 'AllowPrefix' => false],
68        'cel' => ['Group' => 'Temperature', 'Unit Name' => 'Celsius', 'AllowPrefix' => false],
69        'F' => ['Group' => 'Temperature', 'Unit Name' => 'Fahrenheit', 'AllowPrefix' => false],
70        'fah' => ['Group' => 'Temperature', 'Unit Name' => 'Fahrenheit', 'AllowPrefix' => false],
71        'K' => ['Group' => 'Temperature', 'Unit Name' => 'Kelvin', 'AllowPrefix' => false],
72        'kel' => ['Group' => 'Temperature', 'Unit Name' => 'Kelvin', 'AllowPrefix' => false],
73        'tsp' => ['Group' => 'Liquid', 'Unit Name' => 'Teaspoon', 'AllowPrefix' => false],
74        'tbs' => ['Group' => 'Liquid', 'Unit Name' => 'Tablespoon', 'AllowPrefix' => false],
75        'oz' => ['Group' => 'Liquid', 'Unit Name' => 'Fluid Ounce', 'AllowPrefix' => false],
76        'cup' => ['Group' => 'Liquid', 'Unit Name' => 'Cup', 'AllowPrefix' => false],
77        'pt' => ['Group' => 'Liquid', 'Unit Name' => 'U.S. Pint', 'AllowPrefix' => false],
78        'us_pt' => ['Group' => 'Liquid', 'Unit Name' => 'U.S. Pint', 'AllowPrefix' => false],
79        'uk_pt' => ['Group' => 'Liquid', 'Unit Name' => 'U.K. Pint', 'AllowPrefix' => false],
80        'qt' => ['Group' => 'Liquid', 'Unit Name' => 'Quart', 'AllowPrefix' => false],
81        'gal' => ['Group' => 'Liquid', 'Unit Name' => 'Gallon', 'AllowPrefix' => false],
82        'l' => ['Group' => 'Liquid', 'Unit Name' => 'Litre', 'AllowPrefix' => true],
83        'lt' => ['Group' => 'Liquid', 'Unit Name' => 'Litre', 'AllowPrefix' => true],
84    ];
85
86    /**
87     * Details of the Multiplier prefixes that can be used with Units of Measure in CONVERTUOM().
88     *
89     * @var mixed[]
90     */
91    private static $conversionMultipliers = [
92        'Y' => ['multiplier' => 1E24, 'name' => 'yotta'],
93        'Z' => ['multiplier' => 1E21, 'name' => 'zetta'],
94        'E' => ['multiplier' => 1E18, 'name' => 'exa'],
95        'P' => ['multiplier' => 1E15, 'name' => 'peta'],
96        'T' => ['multiplier' => 1E12, 'name' => 'tera'],
97        'G' => ['multiplier' => 1E9, 'name' => 'giga'],
98        'M' => ['multiplier' => 1E6, 'name' => 'mega'],
99        'k' => ['multiplier' => 1E3, 'name' => 'kilo'],
100        'h' => ['multiplier' => 1E2, 'name' => 'hecto'],
101        'e' => ['multiplier' => 1E1, 'name' => 'deka'],
102        'd' => ['multiplier' => 1E-1, 'name' => 'deci'],
103        'c' => ['multiplier' => 1E-2, 'name' => 'centi'],
104        'm' => ['multiplier' => 1E-3, 'name' => 'milli'],
105        'u' => ['multiplier' => 1E-6, 'name' => 'micro'],
106        'n' => ['multiplier' => 1E-9, 'name' => 'nano'],
107        'p' => ['multiplier' => 1E-12, 'name' => 'pico'],
108        'f' => ['multiplier' => 1E-15, 'name' => 'femto'],
109        'a' => ['multiplier' => 1E-18, 'name' => 'atto'],
110        'z' => ['multiplier' => 1E-21, 'name' => 'zepto'],
111        'y' => ['multiplier' => 1E-24, 'name' => 'yocto'],
112    ];
113
114    /**
115     * Details of the Units of measure conversion factors, organised by group.
116     *
117     * @var mixed[]
118     */
119    private static $unitConversions = [
120        'Mass' => [
121            'g' => [
122                'g' => 1.0,
123                'sg' => 6.85220500053478E-05,
124                'lbm' => 2.20462291469134E-03,
125                'u' => 6.02217000000000E+23,
126                'ozm' => 3.52739718003627E-02,
127            ],
128            'sg' => [
129                'g' => 1.45938424189287E+04,
130                'sg' => 1.0,
131                'lbm' => 3.21739194101647E+01,
132                'u' => 8.78866000000000E+27,
133                'ozm' => 5.14782785944229E+02,
134            ],
135            'lbm' => [
136                'g' => 4.5359230974881148E+02,
137                'sg' => 3.10810749306493E-02,
138                'lbm' => 1.0,
139                'u' => 2.73161000000000E+26,
140                'ozm' => 1.60000023429410E+01,
141            ],
142            'u' => [
143                'g' => 1.66053100460465E-24,
144                'sg' => 1.13782988532950E-28,
145                'lbm' => 3.66084470330684E-27,
146                'u' => 1.0,
147                'ozm' => 5.85735238300524E-26,
148            ],
149            'ozm' => [
150                'g' => 2.83495152079732E+01,
151                'sg' => 1.94256689870811E-03,
152                'lbm' => 6.24999908478882E-02,
153                'u' => 1.70725600000000E+25,
154                'ozm' => 1.0,
155            ],
156        ],
157        'Distance' => [
158            'm' => [
159                'm' => 1.0,
160                'mi' => 6.21371192237334E-04,
161                'Nmi' => 5.39956803455724E-04,
162                'in' => 3.93700787401575E+01,
163                'ft' => 3.28083989501312E+00,
164                'yd' => 1.09361329797891E+00,
165                'ang' => 1.00000000000000E+10,
166                'Pica' => 2.83464566929116E+03,
167            ],
168            'mi' => [
169                'm' => 1.60934400000000E+03,
170                'mi' => 1.0,
171                'Nmi' => 8.68976241900648E-01,
172                'in' => 6.33600000000000E+04,
173                'ft' => 5.28000000000000E+03,
174                'yd' => 1.76000000000000E+03,
175                'ang' => 1.60934400000000E+13,
176                'Pica' => 4.56191999999971E+06,
177            ],
178            'Nmi' => [
179                'm' => 1.85200000000000E+03,
180                'mi' => 1.15077944802354E+00,
181                'Nmi' => 1.0,
182                'in' => 7.29133858267717E+04,
183                'ft' => 6.07611548556430E+03,
184                'yd' => 2.02537182785694E+03,
185                'ang' => 1.85200000000000E+13,
186                'Pica' => 5.24976377952723E+06,
187            ],
188            'in' => [
189                'm' => 2.54000000000000E-02,
190                'mi' => 1.57828282828283E-05,
191                'Nmi' => 1.37149028077754E-05,
192                'in' => 1.0,
193                'ft' => 8.33333333333333E-02,
194                'yd' => 2.77777777686643E-02,
195                'ang' => 2.54000000000000E+08,
196                'Pica' => 7.19999999999955E+01,
197            ],
198            'ft' => [
199                'm' => 3.04800000000000E-01,
200                'mi' => 1.89393939393939E-04,
201                'Nmi' => 1.64578833693305E-04,
202                'in' => 1.20000000000000E+01,
203                'ft' => 1.0,
204                'yd' => 3.33333333223972E-01,
205                'ang' => 3.04800000000000E+09,
206                'Pica' => 8.63999999999946E+02,
207            ],
208            'yd' => [
209                'm' => 9.14400000300000E-01,
210                'mi' => 5.68181818368230E-04,
211                'Nmi' => 4.93736501241901E-04,
212                'in' => 3.60000000118110E+01,
213                'ft' => 3.00000000000000E+00,
214                'yd' => 1.0,
215                'ang' => 9.14400000300000E+09,
216                'Pica' => 2.59200000085023E+03,
217            ],
218            'ang' => [
219                'm' => 1.00000000000000E-10,
220                'mi' => 6.21371192237334E-14,
221                'Nmi' => 5.39956803455724E-14,
222                'in' => 3.93700787401575E-09,
223                'ft' => 3.28083989501312E-10,
224                'yd' => 1.09361329797891E-10,
225                'ang' => 1.0,
226                'Pica' => 2.83464566929116E-07,
227            ],
228            'Pica' => [
229                'm' => 3.52777777777800E-04,
230                'mi' => 2.19205948372629E-07,
231                'Nmi' => 1.90484761219114E-07,
232                'in' => 1.38888888888898E-02,
233                'ft' => 1.15740740740748E-03,
234                'yd' => 3.85802469009251E-04,
235                'ang' => 3.52777777777800E+06,
236                'Pica' => 1.0,
237            ],
238        ],
239        'Time' => [
240            'yr' => [
241                'yr' => 1.0,
242                'day' => 365.25,
243                'hr' => 8766.0,
244                'mn' => 525960.0,
245                'sec' => 31557600.0,
246            ],
247            'day' => [
248                'yr' => 2.73785078713210E-03,
249                'day' => 1.0,
250                'hr' => 24.0,
251                'mn' => 1440.0,
252                'sec' => 86400.0,
253            ],
254            'hr' => [
255                'yr' => 1.14077116130504E-04,
256                'day' => 4.16666666666667E-02,
257                'hr' => 1.0,
258                'mn' => 60.0,
259                'sec' => 3600.0,
260            ],
261            'mn' => [
262                'yr' => 1.90128526884174E-06,
263                'day' => 6.94444444444444E-04,
264                'hr' => 1.66666666666667E-02,
265                'mn' => 1.0,
266                'sec' => 60.0,
267            ],
268            'sec' => [
269                'yr' => 3.16880878140289E-08,
270                'day' => 1.15740740740741E-05,
271                'hr' => 2.77777777777778E-04,
272                'mn' => 1.66666666666667E-02,
273                'sec' => 1.0,
274            ],
275        ],
276        'Pressure' => [
277            'Pa' => [
278                'Pa' => 1.0,
279                'p' => 1.0,
280                'atm' => 9.86923299998193E-06,
281                'at' => 9.86923299998193E-06,
282                'mmHg' => 7.50061707998627E-03,
283            ],
284            'p' => [
285                'Pa' => 1.0,
286                'p' => 1.0,
287                'atm' => 9.86923299998193E-06,
288                'at' => 9.86923299998193E-06,
289                'mmHg' => 7.50061707998627E-03,
290            ],
291            'atm' => [
292                'Pa' => 1.01324996583000E+05,
293                'p' => 1.01324996583000E+05,
294                'atm' => 1.0,
295                'at' => 1.0,
296                'mmHg' => 760.0,
297            ],
298            'at' => [
299                'Pa' => 1.01324996583000E+05,
300                'p' => 1.01324996583000E+05,
301                'atm' => 1.0,
302                'at' => 1.0,
303                'mmHg' => 760.0,
304            ],
305            'mmHg' => [
306                'Pa' => 1.33322363925000E+02,
307                'p' => 1.33322363925000E+02,
308                'atm' => 1.31578947368421E-03,
309                'at' => 1.31578947368421E-03,
310                'mmHg' => 1.0,
311            ],
312        ],
313        'Force' => [
314            'N' => [
315                'N' => 1.0,
316                'dyn' => 1.0E+5,
317                'dy' => 1.0E+5,
318                'lbf' => 2.24808923655339E-01,
319            ],
320            'dyn' => [
321                'N' => 1.0E-5,
322                'dyn' => 1.0,
323                'dy' => 1.0,
324                'lbf' => 2.24808923655339E-06,
325            ],
326            'dy' => [
327                'N' => 1.0E-5,
328                'dyn' => 1.0,
329                'dy' => 1.0,
330                'lbf' => 2.24808923655339E-06,
331            ],
332            'lbf' => [
333                'N' => 4.448222,
334                'dyn' => 4.448222E+5,
335                'dy' => 4.448222E+5,
336                'lbf' => 1.0,
337            ],
338        ],
339        'Energy' => [
340            'J' => [
341                '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' => [
356                'J' => 1.00000048065700E-07,
357                'e' => 1.0,
358                'c' => 2.39006364353494E-08,
359                'cal' => 2.38846305445111E-08,
360                'eV' => 6.24146000000000E+11,
361                'ev' => 6.24146000000000E+11,
362                'HPh' => 3.72506609848824E-14,
363                'hh' => 3.72506609848824E-14,
364                'Wh' => 2.77778049754611E-11,
365                'wh' => 2.77778049754611E-11,
366                'flb' => 2.37304336254586E-06,
367                'BTU' => 9.47815522922962E-11,
368                'btu' => 9.47815522922962E-11,
369            ],
370            'c' => [
371                'J' => 4.18399101363672E+00,
372                'e' => 4.18398900257312E+07,
373                'c' => 1.0,
374                'cal' => 9.99330315287563E-01,
375                'eV' => 2.61142000000000E+19,
376                'ev' => 2.61142000000000E+19,
377                'HPh' => 1.55856355899327E-06,
378                'hh' => 1.55856355899327E-06,
379                'Wh' => 1.16222030532950E-03,
380                'wh' => 1.16222030532950E-03,
381                'flb' => 9.92878733152102E+01,
382                'BTU' => 3.96564972437776E-03,
383                'btu' => 3.96564972437776E-03,
384            ],
385            'cal' => [
386                'J' => 4.18679484613929E+00,
387                'e' => 4.18679283372801E+07,
388                'c' => 1.00067013349059E+00,
389                'cal' => 1.0,
390                'eV' => 2.61317000000000E+19,
391                'ev' => 2.61317000000000E+19,
392                'HPh' => 1.55960800463137E-06,
393                'hh' => 1.55960800463137E-06,
394                'Wh' => 1.16299914807955E-03,
395                'wh' => 1.16299914807955E-03,
396                'flb' => 9.93544094443283E+01,
397                'BTU' => 3.96830723907002E-03,
398                'btu' => 3.96830723907002E-03,
399            ],
400            'eV' => [
401                'J' => 1.60219000146921E-19,
402                'e' => 1.60218923136574E-12,
403                'c' => 3.82933423195043E-20,
404                'cal' => 3.82676978535648E-20,
405                'eV' => 1.0,
406                'ev' => 1.0,
407                'HPh' => 5.96826078912344E-26,
408                'hh' => 5.96826078912344E-26,
409                'Wh' => 4.45053000026614E-23,
410                'wh' => 4.45053000026614E-23,
411                'flb' => 3.80206452103492E-18,
412                'BTU' => 1.51857982414846E-22,
413                'btu' => 1.51857982414846E-22,
414            ],
415            'ev' => [
416                'J' => 1.60219000146921E-19,
417                'e' => 1.60218923136574E-12,
418                'c' => 3.82933423195043E-20,
419                'cal' => 3.82676978535648E-20,
420                'eV' => 1.0,
421                'ev' => 1.0,
422                'HPh' => 5.96826078912344E-26,
423                'hh' => 5.96826078912344E-26,
424                'Wh' => 4.45053000026614E-23,
425                'wh' => 4.45053000026614E-23,
426                'flb' => 3.80206452103492E-18,
427                'BTU' => 1.51857982414846E-22,
428                'btu' => 1.51857982414846E-22,
429            ],
430            'HPh' => [
431                'J' => 2.68451741316170E+06,
432                'e' => 2.68451612283024E+13,
433                'c' => 6.41616438565991E+05,
434                'cal' => 6.41186757845835E+05,
435                'eV' => 1.67553000000000E+25,
436                'ev' => 1.67553000000000E+25,
437                'HPh' => 1.0,
438                'hh' => 1.0,
439                'Wh' => 7.45699653134593E+02,
440                'wh' => 7.45699653134593E+02,
441                'flb' => 6.37047316692964E+07,
442                'BTU' => 2.54442605275546E+03,
443                'btu' => 2.54442605275546E+03,
444            ],
445            'hh' => [
446                'J' => 2.68451741316170E+06,
447                'e' => 2.68451612283024E+13,
448                'c' => 6.41616438565991E+05,
449                'cal' => 6.41186757845835E+05,
450                'eV' => 1.67553000000000E+25,
451                'ev' => 1.67553000000000E+25,
452                'HPh' => 1.0,
453                'hh' => 1.0,
454                'Wh' => 7.45699653134593E+02,
455                'wh' => 7.45699653134593E+02,
456                'flb' => 6.37047316692964E+07,
457                'BTU' => 2.54442605275546E+03,
458                'btu' => 2.54442605275546E+03,
459            ],
460            'Wh' => [
461                'J' => 3.59999820554720E+03,
462                'e' => 3.59999647518369E+10,
463                'c' => 8.60422069219046E+02,
464                'cal' => 8.59845857713046E+02,
465                'eV' => 2.24692340000000E+22,
466                'ev' => 2.24692340000000E+22,
467                'HPh' => 1.34102248243839E-03,
468                'hh' => 1.34102248243839E-03,
469                'Wh' => 1.0,
470                'wh' => 1.0,
471                'flb' => 8.54294774062316E+04,
472                'BTU' => 3.41213254164705E+00,
473                'btu' => 3.41213254164705E+00,
474            ],
475            'wh' => [
476                'J' => 3.59999820554720E+03,
477                'e' => 3.59999647518369E+10,
478                'c' => 8.60422069219046E+02,
479                'cal' => 8.59845857713046E+02,
480                'eV' => 2.24692340000000E+22,
481                'ev' => 2.24692340000000E+22,
482                'HPh' => 1.34102248243839E-03,
483                'hh' => 1.34102248243839E-03,
484                'Wh' => 1.0,
485                'wh' => 1.0,
486                'flb' => 8.54294774062316E+04,
487                'BTU' => 3.41213254164705E+00,
488                'btu' => 3.41213254164705E+00,
489            ],
490            'flb' => [
491                'J' => 4.21400003236424E-02,
492                'e' => 4.21399800687660E+05,
493                'c' => 1.00717234301644E-02,
494                'cal' => 1.00649785509554E-02,
495                'eV' => 2.63015000000000E+17,
496                'ev' => 2.63015000000000E+17,
497                'HPh' => 1.56974211145130E-08,
498                'hh' => 1.56974211145130E-08,
499                'Wh' => 1.17055614802000E-05,
500                'wh' => 1.17055614802000E-05,
501                'flb' => 1.0,
502                'BTU' => 3.99409272448406E-05,
503                'btu' => 3.99409272448406E-05,
504            ],
505            'BTU' => [
506                'J' => 1.05505813786749E+03,
507                'e' => 1.05505763074665E+10,
508                'c' => 2.52165488508168E+02,
509                'cal' => 2.51996617135510E+02,
510                'eV' => 6.58510000000000E+21,
511                'ev' => 6.58510000000000E+21,
512                'HPh' => 3.93015941224568E-04,
513                'hh' => 3.93015941224568E-04,
514                'Wh' => 2.93071851047526E-01,
515                'wh' => 2.93071851047526E-01,
516                'flb' => 2.50369750774671E+04,
517                'BTU' => 1.0,
518                'btu' => 1.0,
519            ],
520            'btu' => [
521                'J' => 1.05505813786749E+03,
522                'e' => 1.05505763074665E+10,
523                'c' => 2.52165488508168E+02,
524                'cal' => 2.51996617135510E+02,
525                'eV' => 6.58510000000000E+21,
526                'ev' => 6.58510000000000E+21,
527                'HPh' => 3.93015941224568E-04,
528                'hh' => 3.93015941224568E-04,
529                'Wh' => 2.93071851047526E-01,
530                'wh' => 2.93071851047526E-01,
531                'flb' => 2.50369750774671E+04,
532                'BTU' => 1.0,
533                'btu' => 1.0,
534            ],
535        ],
536        'Power' => [
537            'HP' => [
538                'HP' => 1.0,
539                'h' => 1.0,
540                'W' => 7.45701000000000E+02,
541                'w' => 7.45701000000000E+02,
542            ],
543            'h' => [
544                'HP' => 1.0,
545                'h' => 1.0,
546                'W' => 7.45701000000000E+02,
547                'w' => 7.45701000000000E+02,
548            ],
549            'W' => [
550                'HP' => 1.34102006031908E-03,
551                'h' => 1.34102006031908E-03,
552                'W' => 1.0,
553                'w' => 1.0,
554            ],
555            'w' => [
556                'HP' => 1.34102006031908E-03,
557                'h' => 1.34102006031908E-03,
558                'W' => 1.0,
559                'w' => 1.0,
560            ],
561        ],
562        'Magnetism' => [
563            'T' => [
564                'T' => 1.0,
565                'ga' => 10000.0,
566            ],
567            'ga' => [
568                'T' => 0.0001,
569                'ga' => 1.0,
570            ],
571        ],
572        'Liquid' => [
573            'tsp' => [
574                'tsp' => 1.0,
575                'tbs' => 3.33333333333333E-01,
576                'oz' => 1.66666666666667E-01,
577                'cup' => 2.08333333333333E-02,
578                'pt' => 1.04166666666667E-02,
579                'us_pt' => 1.04166666666667E-02,
580                'uk_pt' => 8.67558516821960E-03,
581                'qt' => 5.20833333333333E-03,
582                'gal' => 1.30208333333333E-03,
583                'l' => 4.92999408400710E-03,
584                'lt' => 4.92999408400710E-03,
585            ],
586            'tbs' => [
587                'tsp' => 3.00000000000000E+00,
588                'tbs' => 1.0,
589                'oz' => 5.00000000000000E-01,
590                'cup' => 6.25000000000000E-02,
591                'pt' => 3.12500000000000E-02,
592                'us_pt' => 3.12500000000000E-02,
593                'uk_pt' => 2.60267555046588E-02,
594                'qt' => 1.56250000000000E-02,
595                'gal' => 3.90625000000000E-03,
596                'l' => 1.47899822520213E-02,
597                'lt' => 1.47899822520213E-02,
598            ],
599            'oz' => [
600                'tsp' => 6.00000000000000E+00,
601                'tbs' => 2.00000000000000E+00,
602                'oz' => 1.0,
603                'cup' => 1.25000000000000E-01,
604                'pt' => 6.25000000000000E-02,
605                'us_pt' => 6.25000000000000E-02,
606                'uk_pt' => 5.20535110093176E-02,
607                'qt' => 3.12500000000000E-02,
608                'gal' => 7.81250000000000E-03,
609                'l' => 2.95799645040426E-02,
610                'lt' => 2.95799645040426E-02,
611            ],
612            'cup' => [
613                'tsp' => 4.80000000000000E+01,
614                'tbs' => 1.60000000000000E+01,
615                'oz' => 8.00000000000000E+00,
616                'cup' => 1.0,
617                'pt' => 5.00000000000000E-01,
618                'us_pt' => 5.00000000000000E-01,
619                'uk_pt' => 4.16428088074541E-01,
620                'qt' => 2.50000000000000E-01,
621                'gal' => 6.25000000000000E-02,
622                'l' => 2.36639716032341E-01,
623                'lt' => 2.36639716032341E-01,
624            ],
625            'pt' => [
626                'tsp' => 9.60000000000000E+01,
627                'tbs' => 3.20000000000000E+01,
628                'oz' => 1.60000000000000E+01,
629                'cup' => 2.00000000000000E+00,
630                'pt' => 1.0,
631                'us_pt' => 1.0,
632                'uk_pt' => 8.32856176149081E-01,
633                'qt' => 5.00000000000000E-01,
634                'gal' => 1.25000000000000E-01,
635                'l' => 4.73279432064682E-01,
636                'lt' => 4.73279432064682E-01,
637            ],
638            'us_pt' => [
639                'tsp' => 9.60000000000000E+01,
640                'tbs' => 3.20000000000000E+01,
641                'oz' => 1.60000000000000E+01,
642                'cup' => 2.00000000000000E+00,
643                'pt' => 1.0,
644                'us_pt' => 1.0,
645                'uk_pt' => 8.32856176149081E-01,
646                'qt' => 5.00000000000000E-01,
647                'gal' => 1.25000000000000E-01,
648                'l' => 4.73279432064682E-01,
649                'lt' => 4.73279432064682E-01,
650            ],
651            'uk_pt' => [
652                'tsp' => 1.15266000000000E+02,
653                'tbs' => 3.84220000000000E+01,
654                'oz' => 1.92110000000000E+01,
655                'cup' => 2.40137500000000E+00,
656                'pt' => 1.20068750000000E+00,
657                'us_pt' => 1.20068750000000E+00,
658                'uk_pt' => 1.0,
659                'qt' => 6.00343750000000E-01,
660                'gal' => 1.50085937500000E-01,
661                'l' => 5.68260698087162E-01,
662                'lt' => 5.68260698087162E-01,
663            ],
664            'qt' => [
665                'tsp' => 1.92000000000000E+02,
666                'tbs' => 6.40000000000000E+01,
667                'oz' => 3.20000000000000E+01,
668                'cup' => 4.00000000000000E+00,
669                'pt' => 2.00000000000000E+00,
670                'us_pt' => 2.00000000000000E+00,
671                'uk_pt' => 1.66571235229816E+00,
672                'qt' => 1.0,
673                'gal' => 2.50000000000000E-01,
674                'l' => 9.46558864129363E-01,
675                'lt' => 9.46558864129363E-01,
676            ],
677            'gal' => [
678                'tsp' => 7.68000000000000E+02,
679                'tbs' => 2.56000000000000E+02,
680                'oz' => 1.28000000000000E+02,
681                'cup' => 1.60000000000000E+01,
682                'pt' => 8.00000000000000E+00,
683                'us_pt' => 8.00000000000000E+00,
684                'uk_pt' => 6.66284940919265E+00,
685                'qt' => 4.00000000000000E+00,
686                'gal' => 1.0,
687                'l' => 3.78623545651745E+00,
688                'lt' => 3.78623545651745E+00,
689            ],
690            'l' => [
691                'tsp' => 2.02840000000000E+02,
692                'tbs' => 6.76133333333333E+01,
693                'oz' => 3.38066666666667E+01,
694                'cup' => 4.22583333333333E+00,
695                'pt' => 2.11291666666667E+00,
696                'us_pt' => 2.11291666666667E+00,
697                'uk_pt' => 1.75975569552166E+00,
698                'qt' => 1.05645833333333E+00,
699                'gal' => 2.64114583333333E-01,
700                'l' => 1.0,
701                'lt' => 1.0,
702            ],
703            'lt' => [
704                'tsp' => 2.02840000000000E+02,
705                'tbs' => 6.76133333333333E+01,
706                'oz' => 3.38066666666667E+01,
707                'cup' => 4.22583333333333E+00,
708                'pt' => 2.11291666666667E+00,
709                'us_pt' => 2.11291666666667E+00,
710                'uk_pt' => 1.75975569552166E+00,
711                'qt' => 1.05645833333333E+00,
712                'gal' => 2.64114583333333E-01,
713                'l' => 1.0,
714                'lt' => 1.0,
715            ],
716        ],
717    ];
718
719    /**
720     * parseComplex.
721     *
722     * Parses a complex number into its real and imaginary parts, and an I or J suffix
723     *
724     * @deprecated 2.0.0 No longer used by internal code. Please use the Complex\Complex class instead
725     *
726     * @param string $complexNumber The complex number
727     *
728     * @return mixed[] Indexed on "real", "imaginary" and "suffix"
729     */
730    public static function parseComplex($complexNumber)
731    {
732        $complex = new Complex($complexNumber);
733
734        return [
735            'real' => $complex->getReal(),
736            'imaginary' => $complex->getImaginary(),
737            'suffix' => $complex->getSuffix(),
738        ];
739    }
740
741    /**
742     * Formats a number base string value with leading zeroes.
743     *
744     * @param string $xVal The "number" to pad
745     * @param int $places The length that we want to pad this value
746     *
747     * @return string The padded "number"
748     */
749    private static function nbrConversionFormat($xVal, $places)
750    {
751        if ($places !== null) {
752            if (is_numeric($places)) {
753                $places = (int) $places;
754            } else {
755                return Functions::VALUE();
756            }
757            if ($places < 0) {
758                return Functions::NAN();
759            }
760            if (strlen($xVal) <= $places) {
761                return substr(str_pad($xVal, $places, '0', STR_PAD_LEFT), -10);
762            }
763
764            return Functions::NAN();
765        }
766
767        return substr($xVal, -10);
768    }
769
770    /**
771     * BESSELI.
772     *
773     *    Returns the modified Bessel function In(x), which is equivalent to the Bessel function evaluated
774     *        for purely imaginary arguments
775     *
776     *    Excel Function:
777     *        BESSELI(x,ord)
778     *
779     * @category Engineering Functions
780     *
781     * @param float $x The value at which to evaluate the function.
782     *                                If x is nonnumeric, BESSELI returns the #VALUE! error value.
783     * @param int $ord The order of the Bessel function.
784     *                                If ord is not an integer, it is truncated.
785     *                                If $ord is nonnumeric, BESSELI returns the #VALUE! error value.
786     *                                If $ord < 0, BESSELI returns the #NUM! error value.
787     *
788     * @return float
789     */
790    public static function BESSELI($x, $ord)
791    {
792        $x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x);
793        $ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord);
794
795        if ((is_numeric($x)) && (is_numeric($ord))) {
796            $ord = floor($ord);
797            if ($ord < 0) {
798                return Functions::NAN();
799            }
800
801            if (abs($x) <= 30) {
802                $fResult = $fTerm = pow($x / 2, $ord) / MathTrig::FACT($ord);
803                $ordK = 1;
804                $fSqrX = ($x * $x) / 4;
805                do {
806                    $fTerm *= $fSqrX;
807                    $fTerm /= ($ordK * ($ordK + $ord));
808                    $fResult += $fTerm;
809                } while ((abs($fTerm) > 1e-12) && (++$ordK < 100));
810            } else {
811                $f_2_PI = 2 * M_PI;
812
813                $fXAbs = abs($x);
814                $fResult = exp($fXAbs) / sqrt($f_2_PI * $fXAbs);
815                if (($ord & 1) && ($x < 0)) {
816                    $fResult = -$fResult;
817                }
818            }
819
820            return (is_nan($fResult)) ? Functions::NAN() : $fResult;
821        }
822
823        return Functions::VALUE();
824    }
825
826    /**
827     * BESSELJ.
828     *
829     *    Returns the Bessel function
830     *
831     *    Excel Function:
832     *        BESSELJ(x,ord)
833     *
834     * @category Engineering Functions
835     *
836     * @param float $x The value at which to evaluate the function.
837     *                                If x is nonnumeric, BESSELJ returns the #VALUE! error value.
838     * @param int $ord The order of the Bessel function. If n is not an integer, it is truncated.
839     *                                If $ord is nonnumeric, BESSELJ returns the #VALUE! error value.
840     *                                If $ord < 0, BESSELJ returns the #NUM! error value.
841     *
842     * @return float
843     */
844    public static function BESSELJ($x, $ord)
845    {
846        $x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x);
847        $ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord);
848
849        if ((is_numeric($x)) && (is_numeric($ord))) {
850            $ord = floor($ord);
851            if ($ord < 0) {
852                return Functions::NAN();
853            }
854
855            $fResult = 0;
856            if (abs($x) <= 30) {
857                $fResult = $fTerm = pow($x / 2, $ord) / MathTrig::FACT($ord);
858                $ordK = 1;
859                $fSqrX = ($x * $x) / -4;
860                do {
861                    $fTerm *= $fSqrX;
862                    $fTerm /= ($ordK * ($ordK + $ord));
863                    $fResult += $fTerm;
864                } while ((abs($fTerm) > 1e-12) && (++$ordK < 100));
865            } else {
866                $f_PI_DIV_2 = M_PI / 2;
867                $f_PI_DIV_4 = M_PI / 4;
868
869                $fXAbs = abs($x);
870                $fResult = sqrt(Functions::M_2DIVPI / $fXAbs) * cos($fXAbs - $ord * $f_PI_DIV_2 - $f_PI_DIV_4);
871                if (($ord & 1) && ($x < 0)) {
872                    $fResult = -$fResult;
873                }
874            }
875
876            return (is_nan($fResult)) ? Functions::NAN() : $fResult;
877        }
878
879        return Functions::VALUE();
880    }
881
882    private static function besselK0($fNum)
883    {
884        if ($fNum <= 2) {
885            $fNum2 = $fNum * 0.5;
886            $y = ($fNum2 * $fNum2);
887            $fRet = -log($fNum2) * self::BESSELI($fNum, 0) +
888                (-0.57721566 + $y * (0.42278420 + $y * (0.23069756 + $y * (0.3488590e-1 + $y * (0.262698e-2 + $y *
889                                    (0.10750e-3 + $y * 0.74e-5))))));
890        } else {
891            $y = 2 / $fNum;
892            $fRet = exp(-$fNum) / sqrt($fNum) *
893                (1.25331414 + $y * (-0.7832358e-1 + $y * (0.2189568e-1 + $y * (-0.1062446e-1 + $y *
894                                (0.587872e-2 + $y * (-0.251540e-2 + $y * 0.53208e-3))))));
895        }
896
897        return $fRet;
898    }
899
900    private static function besselK1($fNum)
901    {
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
915        return $fRet;
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     * @category Engineering Functions
928     *
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 int $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 $ord < 0, BESSELK returns the #NUM! error value.
934     *
935     * @return float
936     */
937    public static function BESSELK($x, $ord)
938    {
939        $x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x);
940        $ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord);
941
942        if ((is_numeric($x)) && (is_numeric($ord))) {
943            if (($ord < 0) || ($x == 0.0)) {
944                return Functions::NAN();
945            }
946
947            switch (floor($ord)) {
948                case 0:
949                    $fBk = self::besselK0($x);
950
951                    break;
952                case 1:
953                    $fBk = self::besselK1($x);
954
955                    break;
956                default:
957                    $fTox = 2 / $x;
958                    $fBkm = self::besselK0($x);
959                    $fBk = self::besselK1($x);
960                    for ($n = 1; $n < $ord; ++$n) {
961                        $fBkp = $fBkm + $n * $fTox * $fBk;
962                        $fBkm = $fBk;
963                        $fBk = $fBkp;
964                    }
965            }
966
967            return (is_nan($fBk)) ? Functions::NAN() : $fBk;
968        }
969
970        return Functions::VALUE();
971    }
972
973    private static function besselY0($fNum)
974    {
975        if ($fNum < 8.0) {
976            $y = ($fNum * $fNum);
977            $f1 = -2957821389.0 + $y * (7062834065.0 + $y * (-512359803.6 + $y * (10879881.29 + $y * (-86327.92757 + $y * 228.4622733))));
978            $f2 = 40076544269.0 + $y * (745249964.8 + $y * (7189466.438 + $y * (47447.26470 + $y * (226.1030244 + $y))));
979            $fRet = $f1 / $f2 + 0.636619772 * self::BESSELJ($fNum, 0) * log($fNum);
980        } else {
981            $z = 8.0 / $fNum;
982            $y = ($z * $z);
983            $xx = $fNum - 0.785398164;
984            $f1 = 1 + $y * (-0.1098628627e-2 + $y * (0.2734510407e-4 + $y * (-0.2073370639e-5 + $y * 0.2093887211e-6)));
985            $f2 = -0.1562499995e-1 + $y * (0.1430488765e-3 + $y * (-0.6911147651e-5 + $y * (0.7621095161e-6 + $y * (-0.934945152e-7))));
986            $fRet = sqrt(0.636619772 / $fNum) * (sin($xx) * $f1 + $z * cos($xx) * $f2);
987        }
988
989        return $fRet;
990    }
991
992    private static function besselY1($fNum)
993    {
994        if ($fNum < 8.0) {
995            $y = ($fNum * $fNum);
996            $f1 = $fNum * (-0.4900604943e13 + $y * (0.1275274390e13 + $y * (-0.5153438139e11 + $y * (0.7349264551e9 + $y *
997                                (-0.4237922726e7 + $y * 0.8511937935e4)))));
998            $f2 = 0.2499580570e14 + $y * (0.4244419664e12 + $y * (0.3733650367e10 + $y * (0.2245904002e8 + $y *
999                            (0.1020426050e6 + $y * (0.3549632885e3 + $y)))));
1000            $fRet = $f1 / $f2 + 0.636619772 * (self::BESSELJ($fNum, 1) * log($fNum) - 1 / $fNum);
1001        } else {
1002            $fRet = sqrt(0.636619772 / $fNum) * sin($fNum - 2.356194491);
1003        }
1004
1005        return $fRet;
1006    }
1007
1008    /**
1009     * BESSELY.
1010     *
1011     * Returns the Bessel function, which is also called the Weber function or the Neumann function.
1012     *
1013     *    Excel Function:
1014     *        BESSELY(x,ord)
1015     *
1016     * @category Engineering Functions
1017     *
1018     * @param float $x The value at which to evaluate the function.
1019     *                                If x is nonnumeric, BESSELK returns the #VALUE! error value.
1020     * @param int $ord The order of the Bessel function. If n is not an integer, it is truncated.
1021     *                                If $ord is nonnumeric, BESSELK returns the #VALUE! error value.
1022     *                                If $ord < 0, BESSELK returns the #NUM! error value.
1023     *
1024     * @return float
1025     */
1026    public static function BESSELY($x, $ord)
1027    {
1028        $x = ($x === null) ? 0.0 : Functions::flattenSingleValue($x);
1029        $ord = ($ord === null) ? 0.0 : Functions::flattenSingleValue($ord);
1030
1031        if ((is_numeric($x)) && (is_numeric($ord))) {
1032            if (($ord < 0) || ($x == 0.0)) {
1033                return Functions::NAN();
1034            }
1035
1036            switch (floor($ord)) {
1037                case 0:
1038                    $fBy = self::besselY0($x);
1039
1040                    break;
1041                case 1:
1042                    $fBy = self::besselY1($x);
1043
1044                    break;
1045                default:
1046                    $fTox = 2 / $x;
1047                    $fBym = self::besselY0($x);
1048                    $fBy = self::besselY1($x);
1049                    for ($n = 1; $n < $ord; ++$n) {
1050                        $fByp = $n * $fTox * $fBy - $fBym;
1051                        $fBym = $fBy;
1052                        $fBy = $fByp;
1053                    }
1054            }
1055
1056            return (is_nan($fBy)) ? Functions::NAN() : $fBy;
1057        }
1058
1059        return Functions::VALUE();
1060    }
1061
1062    /**
1063     * BINTODEC.
1064     *
1065     * Return a binary value as decimal.
1066     *
1067     * Excel Function:
1068     *        BIN2DEC(x)
1069     *
1070     * @category Engineering Functions
1071     *
1072     * @param string $x The binary number (as a string) that you want to convert. The number
1073     *                                cannot contain more than 10 characters (10 bits). The most significant
1074     *                                bit of number is the sign bit. The remaining 9 bits are magnitude bits.
1075     *                                Negative numbers are represented using two's-complement notation.
1076     *                                If number is not a valid binary number, or if number contains more than
1077     *                                10 characters (10 bits), BIN2DEC returns the #NUM! error value.
1078     *
1079     * @return string
1080     */
1081    public static function BINTODEC($x)
1082    {
1083        $x = Functions::flattenSingleValue($x);
1084
1085        if (is_bool($x)) {
1086            if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) {
1087                $x = (int) $x;
1088            } else {
1089                return Functions::VALUE();
1090            }
1091        }
1092        if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) {
1093            $x = floor($x);
1094        }
1095        $x = (string) $x;
1096        if (strlen($x) > preg_match_all('/[01]/', $x, $out)) {
1097            return Functions::NAN();
1098        }
1099        if (strlen($x) > 10) {
1100            return Functions::NAN();
1101        } elseif (strlen($x) == 10) {
1102            //    Two's Complement
1103            $x = substr($x, -9);
1104
1105            return '-' . (512 - bindec($x));
1106        }
1107
1108        return bindec($x);
1109    }
1110
1111    /**
1112     * BINTOHEX.
1113     *
1114     * Return a binary value as hex.
1115     *
1116     * Excel Function:
1117     *        BIN2HEX(x[,places])
1118     *
1119     * @category Engineering Functions
1120     *
1121     * @param string $x The binary number (as a string) that you want to convert. The number
1122     *                                cannot contain more than 10 characters (10 bits). The most significant
1123     *                                bit of number is the sign bit. The remaining 9 bits are magnitude bits.
1124     *                                Negative numbers are represented using two's-complement notation.
1125     *                                If number is not a valid binary number, or if number contains more than
1126     *                                10 characters (10 bits), BIN2HEX returns the #NUM! error value.
1127     * @param int $places The number of characters to use. If places is omitted, BIN2HEX uses the
1128     *                                minimum number of characters necessary. Places is useful for padding the
1129     *                                return value with leading 0s (zeros).
1130     *                                If places is not an integer, it is truncated.
1131     *                                If places is nonnumeric, BIN2HEX returns the #VALUE! error value.
1132     *                                If places is negative, BIN2HEX returns the #NUM! error value.
1133     *
1134     * @return string
1135     */
1136    public static function BINTOHEX($x, $places = null)
1137    {
1138        $x = Functions::flattenSingleValue($x);
1139        $places = Functions::flattenSingleValue($places);
1140
1141        // Argument X
1142        if (is_bool($x)) {
1143            if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) {
1144                $x = (int) $x;
1145            } else {
1146                return Functions::VALUE();
1147            }
1148        }
1149        if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) {
1150            $x = floor($x);
1151        }
1152        $x = (string) $x;
1153        if (strlen($x) > preg_match_all('/[01]/', $x, $out)) {
1154            return Functions::NAN();
1155        }
1156        if (strlen($x) > 10) {
1157            return Functions::NAN();
1158        } elseif (strlen($x) == 10) {
1159            //    Two's Complement
1160            return str_repeat('F', 8) . substr(strtoupper(dechex(bindec(substr($x, -9)))), -2);
1161        }
1162        $hexVal = (string) strtoupper(dechex(bindec($x)));
1163
1164        return self::nbrConversionFormat($hexVal, $places);
1165    }
1166
1167    /**
1168     * BINTOOCT.
1169     *
1170     * Return a binary value as octal.
1171     *
1172     * Excel Function:
1173     *        BIN2OCT(x[,places])
1174     *
1175     * @category Engineering Functions
1176     *
1177     * @param string $x The binary number (as a string) that you want to convert. The number
1178     *                                cannot contain more than 10 characters (10 bits). The most significant
1179     *                                bit of number is the sign bit. The remaining 9 bits are magnitude bits.
1180     *                                Negative numbers are represented using two's-complement notation.
1181     *                                If number is not a valid binary number, or if number contains more than
1182     *                                10 characters (10 bits), BIN2OCT returns the #NUM! error value.
1183     * @param int $places The number of characters to use. If places is omitted, BIN2OCT uses the
1184     *                                minimum number of characters necessary. Places is useful for padding the
1185     *                                return value with leading 0s (zeros).
1186     *                                If places is not an integer, it is truncated.
1187     *                                If places is nonnumeric, BIN2OCT returns the #VALUE! error value.
1188     *                                If places is negative, BIN2OCT returns the #NUM! error value.
1189     *
1190     * @return string
1191     */
1192    public static function BINTOOCT($x, $places = null)
1193    {
1194        $x = Functions::flattenSingleValue($x);
1195        $places = Functions::flattenSingleValue($places);
1196
1197        if (is_bool($x)) {
1198            if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) {
1199                $x = (int) $x;
1200            } else {
1201                return Functions::VALUE();
1202            }
1203        }
1204        if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) {
1205            $x = floor($x);
1206        }
1207        $x = (string) $x;
1208        if (strlen($x) > preg_match_all('/[01]/', $x, $out)) {
1209            return Functions::NAN();
1210        }
1211        if (strlen($x) > 10) {
1212            return Functions::NAN();
1213        } elseif (strlen($x) == 10) {
1214            //    Two's Complement
1215            return str_repeat('7', 7) . substr(strtoupper(decoct(bindec(substr($x, -9)))), -3);
1216        }
1217        $octVal = (string) decoct(bindec($x));
1218
1219        return self::nbrConversionFormat($octVal, $places);
1220    }
1221
1222    /**
1223     * DECTOBIN.
1224     *
1225     * Return a decimal value as binary.
1226     *
1227     * Excel Function:
1228     *        DEC2BIN(x[,places])
1229     *
1230     * @category Engineering Functions
1231     *
1232     * @param string $x The decimal integer you want to convert. If number is negative,
1233     *                                valid place values are ignored and DEC2BIN returns a 10-character
1234     *                                (10-bit) binary number in which the most significant bit is the sign
1235     *                                bit. The remaining 9 bits are magnitude bits. Negative numbers are
1236     *                                represented using two's-complement notation.
1237     *                                If number < -512 or if number > 511, DEC2BIN returns the #NUM! error
1238     *                                value.
1239     *                                If number is nonnumeric, DEC2BIN returns the #VALUE! error value.
1240     *                                If DEC2BIN requires more than places characters, it returns the #NUM!
1241     *                                error value.
1242     * @param int $places The number of characters to use. If places is omitted, DEC2BIN uses
1243     *                                the minimum number of characters necessary. Places is useful for
1244     *                                padding the return value with leading 0s (zeros).
1245     *                                If places is not an integer, it is truncated.
1246     *                                If places is nonnumeric, DEC2BIN returns the #VALUE! error value.
1247     *                                If places is zero or negative, DEC2BIN returns the #NUM! error value.
1248     *
1249     * @return string
1250     */
1251    public static function DECTOBIN($x, $places = null)
1252    {
1253        $x = Functions::flattenSingleValue($x);
1254        $places = Functions::flattenSingleValue($places);
1255
1256        if (is_bool($x)) {
1257            if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) {
1258                $x = (int) $x;
1259            } else {
1260                return Functions::VALUE();
1261            }
1262        }
1263        $x = (string) $x;
1264        if (strlen($x) > preg_match_all('/[-0123456789.]/', $x, $out)) {
1265            return Functions::VALUE();
1266        }
1267
1268        $x = (string) floor($x);
1269        if ($x < -512 || $x > 511) {
1270            return Functions::NAN();
1271        }
1272
1273        $r = decbin($x);
1274        // Two's Complement
1275        $r = substr($r, -10);
1276        if (strlen($r) >= 11) {
1277            return Functions::NAN();
1278        }
1279
1280        return self::nbrConversionFormat($r, $places);
1281    }
1282
1283    /**
1284     * DECTOHEX.
1285     *
1286     * Return a decimal value as hex.
1287     *
1288     * Excel Function:
1289     *        DEC2HEX(x[,places])
1290     *
1291     * @category Engineering Functions
1292     *
1293     * @param string $x The decimal integer you want to convert. If number is negative,
1294     *                                places is ignored and DEC2HEX returns a 10-character (40-bit)
1295     *                                hexadecimal number in which the most significant bit is the sign
1296     *                                bit. The remaining 39 bits are magnitude bits. Negative numbers
1297     *                                are represented using two's-complement notation.
1298     *                                If number < -549,755,813,888 or if number > 549,755,813,887,
1299     *                                DEC2HEX returns the #NUM! error value.
1300     *                                If number is nonnumeric, DEC2HEX returns the #VALUE! error value.
1301     *                                If DEC2HEX requires more than places characters, it returns the
1302     *                                #NUM! error value.
1303     * @param int $places The number of characters to use. If places is omitted, DEC2HEX uses
1304     *                                the minimum number of characters necessary. Places is useful for
1305     *                                padding the return value with leading 0s (zeros).
1306     *                                If places is not an integer, it is truncated.
1307     *                                If places is nonnumeric, DEC2HEX returns the #VALUE! error value.
1308     *                                If places is zero or negative, DEC2HEX returns the #NUM! error value.
1309     *
1310     * @return string
1311     */
1312    public static function DECTOHEX($x, $places = null)
1313    {
1314        $x = Functions::flattenSingleValue($x);
1315        $places = Functions::flattenSingleValue($places);
1316
1317        if (is_bool($x)) {
1318            if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) {
1319                $x = (int) $x;
1320            } else {
1321                return Functions::VALUE();
1322            }
1323        }
1324        $x = (string) $x;
1325        if (strlen($x) > preg_match_all('/[-0123456789.]/', $x, $out)) {
1326            return Functions::VALUE();
1327        }
1328        $x = (string) floor($x);
1329        $r = strtoupper(dechex($x));
1330        if (strlen($r) == 8) {
1331            //    Two's Complement
1332            $r = 'FF' . $r;
1333        }
1334
1335        return self::nbrConversionFormat($r, $places);
1336    }
1337
1338    /**
1339     * DECTOOCT.
1340     *
1341     * Return an decimal value as octal.
1342     *
1343     * Excel Function:
1344     *        DEC2OCT(x[,places])
1345     *
1346     * @category Engineering Functions
1347     *
1348     * @param string $x The decimal integer you want to convert. If number is negative,
1349     *                                places is ignored and DEC2OCT returns a 10-character (30-bit)
1350     *                                octal number in which the most significant bit is the sign bit.
1351     *                                The remaining 29 bits are magnitude bits. Negative numbers are
1352     *                                represented using two's-complement notation.
1353     *                                If number < -536,870,912 or if number > 536,870,911, DEC2OCT
1354     *                                returns the #NUM! error value.
1355     *                                If number is nonnumeric, DEC2OCT returns the #VALUE! error value.
1356     *                                If DEC2OCT requires more than places characters, it returns the
1357     *                                #NUM! error value.
1358     * @param int $places The number of characters to use. If places is omitted, DEC2OCT uses
1359     *                                the minimum number of characters necessary. Places is useful for
1360     *                                padding the return value with leading 0s (zeros).
1361     *                                If places is not an integer, it is truncated.
1362     *                                If places is nonnumeric, DEC2OCT returns the #VALUE! error value.
1363     *                                If places is zero or negative, DEC2OCT returns the #NUM! error value.
1364     *
1365     * @return string
1366     */
1367    public static function DECTOOCT($x, $places = null)
1368    {
1369        $xorig = $x;
1370        $x = Functions::flattenSingleValue($x);
1371        $places = Functions::flattenSingleValue($places);
1372
1373        if (is_bool($x)) {
1374            if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE) {
1375                $x = (int) $x;
1376            } else {
1377                return Functions::VALUE();
1378            }
1379        }
1380        $x = (string) $x;
1381        if (strlen($x) > preg_match_all('/[-0123456789.]/', $x, $out)) {
1382            return Functions::VALUE();
1383        }
1384        $x = (string) floor($x);
1385        $r = decoct($x);
1386        if (strlen($r) == 11) {
1387            //    Two's Complement
1388            $r = substr($r, -10);
1389        }
1390
1391        return self::nbrConversionFormat($r, $places);
1392    }
1393
1394    /**
1395     * HEXTOBIN.
1396     *
1397     * Return a hex value as binary.
1398     *
1399     * Excel Function:
1400     *        HEX2BIN(x[,places])
1401     *
1402     * @category Engineering Functions
1403     *
1404     * @param string $x the hexadecimal number you want to convert.
1405     *                  Number cannot contain more than 10 characters.
1406     *                  The most significant bit of number is the sign bit (40th bit from the right).
1407     *                  The remaining 9 bits are magnitude bits.
1408     *                  Negative numbers are represented using two's-complement notation.
1409     *                  If number is negative, HEX2BIN ignores places and returns a 10-character binary number.
1410     *                  If number is negative, it cannot be less than FFFFFFFE00,
1411     *                      and if number is positive, it cannot be greater than 1FF.
1412     *                  If number is not a valid hexadecimal number, HEX2BIN returns the #NUM! error value.
1413     *                  If HEX2BIN requires more than places characters, it returns the #NUM! error value.
1414     * @param int $places The number of characters to use. If places is omitted,
1415     *                                    HEX2BIN uses the minimum number of characters necessary. Places
1416     *                                    is useful for padding the return value with leading 0s (zeros).
1417     *                                    If places is not an integer, it is truncated.
1418     *                                    If places is nonnumeric, HEX2BIN returns the #VALUE! error value.
1419     *                                    If places is negative, HEX2BIN returns the #NUM! error value.
1420     *
1421     * @return string
1422     */
1423    public static function HEXTOBIN($x, $places = null)
1424    {
1425        $x = Functions::flattenSingleValue($x);
1426        $places = Functions::flattenSingleValue($places);
1427
1428        if (is_bool($x)) {
1429            return Functions::VALUE();
1430        }
1431        $x = (string) $x;
1432        if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/', strtoupper($x), $out)) {
1433            return Functions::NAN();
1434        }
1435
1436        return self::DECTOBIN(self::HEXTODEC($x), $places);
1437    }
1438
1439    /**
1440     * HEXTODEC.
1441     *
1442     * Return a hex value as decimal.
1443     *
1444     * Excel Function:
1445     *        HEX2DEC(x)
1446     *
1447     * @category Engineering Functions
1448     *
1449     * @param string $x The hexadecimal number you want to convert. This number cannot
1450     *                                contain more than 10 characters (40 bits). The most significant
1451     *                                bit of number is the sign bit. The remaining 39 bits are magnitude
1452     *                                bits. Negative numbers are represented using two's-complement
1453     *                                notation.
1454     *                                If number is not a valid hexadecimal number, HEX2DEC returns the
1455     *                                #NUM! error value.
1456     *
1457     * @return string
1458     */
1459    public static function HEXTODEC($x)
1460    {
1461        $x = Functions::flattenSingleValue($x);
1462
1463        if (is_bool($x)) {
1464            return Functions::VALUE();
1465        }
1466        $x = (string) $x;
1467        if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/', strtoupper($x), $out)) {
1468            return Functions::NAN();
1469        }
1470
1471        if (strlen($x) > 10) {
1472            return Functions::NAN();
1473        }
1474
1475        $binX = '';
1476        foreach (str_split($x) as $char) {
1477            $binX .= str_pad(base_convert($char, 16, 2), 4, '0', STR_PAD_LEFT);
1478        }
1479        if (strlen($binX) == 40 && $binX[0] == '1') {
1480            for ($i = 0; $i < 40; ++$i) {
1481                $binX[$i] = ($binX[$i] == '1' ? '0' : '1');
1482            }
1483
1484            return (bindec($binX) + 1) * -1;
1485        }
1486
1487        return bindec($binX);
1488    }
1489
1490    /**
1491     * HEXTOOCT.
1492     *
1493     * Return a hex value as octal.
1494     *
1495     * Excel Function:
1496     *        HEX2OCT(x[,places])
1497     *
1498     * @category Engineering Functions
1499     *
1500     * @param string $x The hexadecimal number you want to convert. Number cannot
1501     *                                    contain more than 10 characters. The most significant bit of
1502     *                                    number is the sign bit. The remaining 39 bits are magnitude
1503     *                                    bits. Negative numbers are represented using two's-complement
1504     *                                    notation.
1505     *                                    If number is negative, HEX2OCT ignores places and returns a
1506     *                                    10-character octal number.
1507     *                                    If number is negative, it cannot be less than FFE0000000, and
1508     *                                    if number is positive, it cannot be greater than 1FFFFFFF.
1509     *                                    If number is not a valid hexadecimal number, HEX2OCT returns
1510     *                                    the #NUM! error value.
1511     *                                    If HEX2OCT requires more than places characters, it returns
1512     *                                    the #NUM! error value.
1513     * @param int $places The number of characters to use. If places is omitted, HEX2OCT
1514     *                                    uses the minimum number of characters necessary. Places is
1515     *                                    useful for padding the return value with leading 0s (zeros).
1516     *                                    If places is not an integer, it is truncated.
1517     *                                    If places is nonnumeric, HEX2OCT returns the #VALUE! error
1518     *                                    value.
1519     *                                    If places is negative, HEX2OCT returns the #NUM! error value.
1520     *
1521     * @return string
1522     */
1523    public static function HEXTOOCT($x, $places = null)
1524    {
1525        $x = Functions::flattenSingleValue($x);
1526        $places = Functions::flattenSingleValue($places);
1527
1528        if (is_bool($x)) {
1529            return Functions::VALUE();
1530        }
1531        $x = (string) $x;
1532        if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/', strtoupper($x), $out)) {
1533            return Functions::NAN();
1534        }
1535
1536        $decimal = self::HEXTODEC($x);
1537        if ($decimal < -536870912 || $decimal > 536870911) {
1538            return Functions::NAN();
1539        }
1540
1541        return self::DECTOOCT($decimal, $places);
1542    }
1543
1544    /**
1545     * OCTTOBIN.
1546     *
1547     * Return an octal value as binary.
1548     *
1549     * Excel Function:
1550     *        OCT2BIN(x[,places])
1551     *
1552     * @category Engineering Functions
1553     *
1554     * @param string $x The octal number you want to convert. Number may not
1555     *                                    contain more than 10 characters. The most significant
1556     *                                    bit of number is the sign bit. The remaining 29 bits
1557     *                                    are magnitude bits. Negative numbers are represented
1558     *                                    using two's-complement notation.
1559     *                                    If number is negative, OCT2BIN ignores places and returns
1560     *                                    a 10-character binary number.
1561     *                                    If number is negative, it cannot be less than 7777777000,
1562     *                                    and if number is positive, it cannot be greater than 777.
1563     *                                    If number is not a valid octal number, OCT2BIN returns
1564     *                                    the #NUM! error value.
1565     *                                    If OCT2BIN requires more than places characters, it
1566     *                                    returns the #NUM! error value.
1567     * @param int $places The number of characters to use. If places is omitted,
1568     *                                    OCT2BIN uses the minimum number of characters necessary.
1569     *                                    Places is useful for padding the return value with
1570     *                                    leading 0s (zeros).
1571     *                                    If places is not an integer, it is truncated.
1572     *                                    If places is nonnumeric, OCT2BIN returns the #VALUE!
1573     *                                    error value.
1574     *                                    If places is negative, OCT2BIN returns the #NUM! error
1575     *                                    value.
1576     *
1577     * @return string
1578     */
1579    public static function OCTTOBIN($x, $places = null)
1580    {
1581        $x = Functions::flattenSingleValue($x);
1582        $places = Functions::flattenSingleValue($places);
1583
1584        if (is_bool($x)) {
1585            return Functions::VALUE();
1586        }
1587        $x = (string) $x;
1588        if (preg_match_all('/[01234567]/', $x, $out) != strlen($x)) {
1589            return Functions::NAN();
1590        }
1591
1592        return self::DECTOBIN(self::OCTTODEC($x), $places);
1593    }
1594
1595    /**
1596     * OCTTODEC.
1597     *
1598     * Return an octal value as decimal.
1599     *
1600     * Excel Function:
1601     *        OCT2DEC(x)
1602     *
1603     * @category Engineering Functions
1604     *
1605     * @param string $x The octal number you want to convert. Number may not contain
1606     *                                more than 10 octal characters (30 bits). The most significant
1607     *                                bit of number is the sign bit. The remaining 29 bits are
1608     *                                magnitude bits. Negative numbers are represented using
1609     *                                two's-complement notation.
1610     *                                If number is not a valid octal number, OCT2DEC returns the
1611     *                                #NUM! error value.
1612     *
1613     * @return string
1614     */
1615    public static function OCTTODEC($x)
1616    {
1617        $x = Functions::flattenSingleValue($x);
1618
1619        if (is_bool($x)) {
1620            return Functions::VALUE();
1621        }
1622        $x = (string) $x;
1623        if (preg_match_all('/[01234567]/', $x, $out) != strlen($x)) {
1624            return Functions::NAN();
1625        }
1626        $binX = '';
1627        foreach (str_split($x) as $char) {
1628            $binX .= str_pad(decbin((int) $char), 3, '0', STR_PAD_LEFT);
1629        }
1630        if (strlen($binX) == 30 && $binX[0] == '1') {
1631            for ($i = 0; $i < 30; ++$i) {
1632                $binX[$i] = ($binX[$i] == '1' ? '0' : '1');
1633            }
1634
1635            return (bindec($binX) + 1) * -1;
1636        }
1637
1638        return bindec($binX);
1639    }
1640
1641    /**
1642     * OCTTOHEX.
1643     *
1644     * Return an octal value as hex.
1645     *
1646     * Excel Function:
1647     *        OCT2HEX(x[,places])
1648     *
1649     * @category Engineering Functions
1650     *
1651     * @param string $x The octal number you want to convert. Number may not contain
1652     *                                    more than 10 octal characters (30 bits). The most significant
1653     *                                    bit of number is the sign bit. The remaining 29 bits are
1654     *                                    magnitude bits. Negative numbers are represented using
1655     *                                    two's-complement notation.
1656     *                                    If number is negative, OCT2HEX ignores places and returns a
1657     *                                    10-character hexadecimal number.
1658     *                                    If number is not a valid octal number, OCT2HEX returns the
1659     *                                    #NUM! error value.
1660     *                                    If OCT2HEX requires more than places characters, it returns
1661     *                                    the #NUM! error value.
1662     * @param int $places The number of characters to use. If places is omitted, OCT2HEX
1663     *                                    uses the minimum number of characters necessary. Places is useful
1664     *                                    for padding the return value with leading 0s (zeros).
1665     *                                    If places is not an integer, it is truncated.
1666     *                                    If places is nonnumeric, OCT2HEX returns the #VALUE! error value.
1667     *                                    If places is negative, OCT2HEX returns the #NUM! error value.
1668     *
1669     * @return string
1670     */
1671    public static function OCTTOHEX($x, $places = null)
1672    {
1673        $x = Functions::flattenSingleValue($x);
1674        $places = Functions::flattenSingleValue($places);
1675
1676        if (is_bool($x)) {
1677            return Functions::VALUE();
1678        }
1679        $x = (string) $x;
1680        if (preg_match_all('/[01234567]/', $x, $out) != strlen($x)) {
1681            return Functions::NAN();
1682        }
1683        $hexVal = strtoupper(dechex(self::OCTTODEC($x)));
1684
1685        return self::nbrConversionFormat($hexVal, $places);
1686    }
1687
1688    /**
1689     * COMPLEX.
1690     *
1691     * Converts real and imaginary coefficients into a complex number of the form x +/- yi or x +/- yj.
1692     *
1693     * Excel Function:
1694     *        COMPLEX(realNumber,imaginary[,suffix])
1695     *
1696     * @category Engineering Functions
1697     *
1698     * @param float $realNumber the real coefficient of the complex number
1699     * @param float $imaginary the imaginary coefficient of the complex number
1700     * @param string $suffix The suffix for the imaginary component of the complex number.
1701     *                                        If omitted, the suffix is assumed to be "i".
1702     *
1703     * @return string
1704     */
1705    public static function COMPLEX($realNumber = 0.0, $imaginary = 0.0, $suffix = 'i')
1706    {
1707        $realNumber = ($realNumber === null) ? 0.0 : Functions::flattenSingleValue($realNumber);
1708        $imaginary = ($imaginary === null) ? 0.0 : Functions::flattenSingleValue($imaginary);
1709        $suffix = ($suffix === null) ? 'i' : Functions::flattenSingleValue($suffix);
1710
1711        if (((is_numeric($realNumber)) && (is_numeric($imaginary))) &&
1712            (($suffix == 'i') || ($suffix == 'j') || ($suffix == ''))
1713        ) {
1714            $complex = new Complex($realNumber, $imaginary, $suffix);
1715
1716            return (string) $complex;
1717        }
1718
1719        return Functions::VALUE();
1720    }
1721
1722    /**
1723     * IMAGINARY.
1724     *
1725     * Returns the imaginary coefficient of a complex number in x + yi or x + yj text format.
1726     *
1727     * Excel Function:
1728     *        IMAGINARY(complexNumber)
1729     *
1730     * @category Engineering Functions
1731     *
1732     * @param string $complexNumber the complex number for which you want the imaginary
1733     *                                         coefficient
1734     *
1735     * @return float
1736     */
1737    public static function IMAGINARY($complexNumber)
1738    {
1739        $complexNumber = Functions::flattenSingleValue($complexNumber);
1740
1741        return (new Complex($complexNumber))->getImaginary();
1742    }
1743
1744    /**
1745     * IMREAL.
1746     *
1747     * Returns the real coefficient of a complex number in x + yi or x + yj text format.
1748     *
1749     * Excel Function:
1750     *        IMREAL(complexNumber)
1751     *
1752     * @category Engineering Functions
1753     *
1754     * @param string $complexNumber the complex number for which you want the real coefficient
1755     *
1756     * @return float
1757     */
1758    public static function IMREAL($complexNumber)
1759    {
1760        $complexNumber = Functions::flattenSingleValue($complexNumber);
1761
1762        return (new Complex($complexNumber))->getReal();
1763    }
1764
1765    /**
1766     * IMABS.
1767     *
1768     * Returns the absolute value (modulus) of a complex number in x + yi or x + yj text format.
1769     *
1770     * Excel Function:
1771     *        IMABS(complexNumber)
1772     *
1773     * @param string $complexNumber the complex number for which you want the absolute value
1774     *
1775     * @return float
1776     */
1777    public static function IMABS($complexNumber)
1778    {
1779        $complexNumber = Functions::flattenSingleValue($complexNumber);
1780
1781        return (new Complex($complexNumber))->abs();
1782    }
1783
1784    /**
1785     * IMARGUMENT.
1786     *
1787     * Returns the argument theta of a complex number, i.e. the angle in radians from the real
1788     * axis to the representation of the number in polar coordinates.
1789     *
1790     * Excel Function:
1791     *        IMARGUMENT(complexNumber)
1792     *
1793     * @param string $complexNumber the complex number for which you want the argument theta
1794     *
1795     * @return float|string
1796     */
1797    public static function IMARGUMENT($complexNumber)
1798    {
1799        $complexNumber = Functions::flattenSingleValue($complexNumber);
1800
1801        $complex = new Complex($complexNumber);
1802        if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
1803            return Functions::DIV0();
1804        }
1805
1806        return $complex->argument();
1807    }
1808
1809    /**
1810     * IMCONJUGATE.
1811     *
1812     * Returns the complex conjugate of a complex number in x + yi or x + yj text format.
1813     *
1814     * Excel Function:
1815     *        IMCONJUGATE(complexNumber)
1816     *
1817     * @param string $complexNumber the complex number for which you want the conjugate
1818     *
1819     * @return string
1820     */
1821    public static function IMCONJUGATE($complexNumber)
1822    {
1823        $complexNumber = Functions::flattenSingleValue($complexNumber);
1824
1825        return (string) (new Complex($complexNumber))->conjugate();
1826    }
1827
1828    /**
1829     * IMCOS.
1830     *
1831     * Returns the cosine of a complex number in x + yi or x + yj text format.
1832     *
1833     * Excel Function:
1834     *        IMCOS(complexNumber)
1835     *
1836     * @param string $complexNumber the complex number for which you want the cosine
1837     *
1838     * @return float|string
1839     */
1840    public static function IMCOS($complexNumber)
1841    {
1842        $complexNumber = Functions::flattenSingleValue($complexNumber);
1843
1844        return (string) (new Complex($complexNumber))->cos();
1845    }
1846
1847    /**
1848     * IMCOSH.
1849     *
1850     * Returns the hyperbolic cosine of a complex number in x + yi or x + yj text format.
1851     *
1852     * Excel Function:
1853     *        IMCOSH(complexNumber)
1854     *
1855     * @param string $complexNumber the complex number for which you want the hyperbolic cosine
1856     *
1857     * @return float|string
1858     */
1859    public static function IMCOSH($complexNumber)
1860    {
1861        $complexNumber = Functions::flattenSingleValue($complexNumber);
1862
1863        return (string) (new Complex($complexNumber))->cosh();
1864    }
1865
1866    /**
1867     * IMCOT.
1868     *
1869     * Returns the cotangent of a complex number in x + yi or x + yj text format.
1870     *
1871     * Excel Function:
1872     *        IMCOT(complexNumber)
1873     *
1874     * @param string $complexNumber the complex number for which you want the cotangent
1875     *
1876     * @return float|string
1877     */
1878    public static function IMCOT($complexNumber)
1879    {
1880        $complexNumber = Functions::flattenSingleValue($complexNumber);
1881
1882        return (string) (new Complex($complexNumber))->cot();
1883    }
1884
1885    /**
1886     * IMCSC.
1887     *
1888     * Returns the cosecant of a complex number in x + yi or x + yj text format.
1889     *
1890     * Excel Function:
1891     *        IMCSC(complexNumber)
1892     *
1893     * @param string $complexNumber the complex number for which you want the cosecant
1894     *
1895     * @return float|string
1896     */
1897    public static function IMCSC($complexNumber)
1898    {
1899        $complexNumber = Functions::flattenSingleValue($complexNumber);
1900
1901        return (string) (new Complex($complexNumber))->csc();
1902    }
1903
1904    /**
1905     * IMCSCH.
1906     *
1907     * Returns the hyperbolic cosecant of a complex number in x + yi or x + yj text format.
1908     *
1909     * Excel Function:
1910     *        IMCSCH(complexNumber)
1911     *
1912     * @param string $complexNumber the complex number for which you want the hyperbolic cosecant
1913     *
1914     * @return float|string
1915     */
1916    public static function IMCSCH($complexNumber)
1917    {
1918        $complexNumber = Functions::flattenSingleValue($complexNumber);
1919
1920        return (string) (new Complex($complexNumber))->csch();
1921    }
1922
1923    /**
1924     * IMSIN.
1925     *
1926     * Returns the sine of a complex number in x + yi or x + yj text format.
1927     *
1928     * Excel Function:
1929     *        IMSIN(complexNumber)
1930     *
1931     * @param string $complexNumber the complex number for which you want the sine
1932     *
1933     * @return float|string
1934     */
1935    public static function IMSIN($complexNumber)
1936    {
1937        $complexNumber = Functions::flattenSingleValue($complexNumber);
1938
1939        return (string) (new Complex($complexNumber))->sin();
1940    }
1941
1942    /**
1943     * IMSINH.
1944     *
1945     * Returns the hyperbolic sine of a complex number in x + yi or x + yj text format.
1946     *
1947     * Excel Function:
1948     *        IMSINH(complexNumber)
1949     *
1950     * @param string $complexNumber the complex number for which you want the hyperbolic sine
1951     *
1952     * @return float|string
1953     */
1954    public static function IMSINH($complexNumber)
1955    {
1956        $complexNumber = Functions::flattenSingleValue($complexNumber);
1957
1958        return (string) (new Complex($complexNumber))->sinh();
1959    }
1960
1961    /**
1962     * IMSEC.
1963     *
1964     * Returns the secant of a complex number in x + yi or x + yj text format.
1965     *
1966     * Excel Function:
1967     *        IMSEC(complexNumber)
1968     *
1969     * @param string $complexNumber the complex number for which you want the secant
1970     *
1971     * @return float|string
1972     */
1973    public static function IMSEC($complexNumber)
1974    {
1975        $complexNumber = Functions::flattenSingleValue($complexNumber);
1976
1977        return (string) (new Complex($complexNumber))->sec();
1978    }
1979
1980    /**
1981     * IMSECH.
1982     *
1983     * Returns the hyperbolic secant of a complex number in x + yi or x + yj text format.
1984     *
1985     * Excel Function:
1986     *        IMSECH(complexNumber)
1987     *
1988     * @param string $complexNumber the complex number for which you want the hyperbolic secant
1989     *
1990     * @return float|string
1991     */
1992    public static function IMSECH($complexNumber)
1993    {
1994        $complexNumber = Functions::flattenSingleValue($complexNumber);
1995
1996        return (string) (new Complex($complexNumber))->sech();
1997    }
1998
1999    /**
2000     * IMTAN.
2001     *
2002     * Returns the tangent of a complex number in x + yi or x + yj text format.
2003     *
2004     * Excel Function:
2005     *        IMTAN(complexNumber)
2006     *
2007     * @param string $complexNumber the complex number for which you want the tangent
2008     *
2009     * @return float|string
2010     */
2011    public static function IMTAN($complexNumber)
2012    {
2013        $complexNumber = Functions::flattenSingleValue($complexNumber);
2014
2015        return (string) (new Complex($complexNumber))->tan();
2016    }
2017
2018    /**
2019     * IMSQRT.
2020     *
2021     * Returns the square root of a complex number in x + yi or x + yj text format.
2022     *
2023     * Excel Function:
2024     *        IMSQRT(complexNumber)
2025     *
2026     * @param string $complexNumber the complex number for which you want the square root
2027     *
2028     * @return string
2029     */
2030    public static function IMSQRT($complexNumber)
2031    {
2032        $complexNumber = Functions::flattenSingleValue($complexNumber);
2033
2034        $theta = self::IMARGUMENT($complexNumber);
2035        if ($theta === Functions::DIV0()) {
2036            return '0';
2037        }
2038
2039        return (string) (new Complex($complexNumber))->sqrt();
2040    }
2041
2042    /**
2043     * IMLN.
2044     *
2045     * Returns the natural logarithm of a complex number in x + yi or x + yj text format.
2046     *
2047     * Excel Function:
2048     *        IMLN(complexNumber)
2049     *
2050     * @param string $complexNumber the complex number for which you want the natural logarithm
2051     *
2052     * @return string
2053     */
2054    public static function IMLN($complexNumber)
2055    {
2056        $complexNumber = Functions::flattenSingleValue($complexNumber);
2057
2058        $complex = new Complex($complexNumber);
2059        if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
2060            return Functions::NAN();
2061        }
2062
2063        return (string) (new Complex($complexNumber))->ln();
2064    }
2065
2066    /**
2067     * IMLOG10.
2068     *
2069     * Returns the common logarithm (base 10) of a complex number in x + yi or x + yj text format.
2070     *
2071     * Excel Function:
2072     *        IMLOG10(complexNumber)
2073     *
2074     * @param string $complexNumber the complex number for which you want the common logarithm
2075     *
2076     * @return string
2077     */
2078    public static function IMLOG10($complexNumber)
2079    {
2080        $complexNumber = Functions::flattenSingleValue($complexNumber);
2081
2082        $complex = new Complex($complexNumber);
2083        if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
2084            return Functions::NAN();
2085        }
2086
2087        return (string) (new Complex($complexNumber))->log10();
2088    }
2089
2090    /**
2091     * IMLOG2.
2092     *
2093     * Returns the base-2 logarithm of a complex number in x + yi or x + yj text format.
2094     *
2095     * Excel Function:
2096     *        IMLOG2(complexNumber)
2097     *
2098     * @param string $complexNumber the complex number for which you want the base-2 logarithm
2099     *
2100     * @return string
2101     */
2102    public static function IMLOG2($complexNumber)
2103    {
2104        $complexNumber = Functions::flattenSingleValue($complexNumber);
2105
2106        $complex = new Complex($complexNumber);
2107        if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
2108            return Functions::NAN();
2109        }
2110
2111        return (string) (new Complex($complexNumber))->log2();
2112    }
2113
2114    /**
2115     * IMEXP.
2116     *
2117     * Returns the exponential of a complex number in x + yi or x + yj text format.
2118     *
2119     * Excel Function:
2120     *        IMEXP(complexNumber)
2121     *
2122     * @param string $complexNumber the complex number for which you want the exponential
2123     *
2124     * @return string
2125     */
2126    public static function IMEXP($complexNumber)
2127    {
2128        $complexNumber = Functions::flattenSingleValue($complexNumber);
2129
2130        return (string) (new Complex($complexNumber))->exp();
2131    }
2132
2133    /**
2134     * IMPOWER.
2135     *
2136     * Returns a complex number in x + yi or x + yj text format raised to a power.
2137     *
2138     * Excel Function:
2139     *        IMPOWER(complexNumber,realNumber)
2140     *
2141     * @param string $complexNumber the complex number you want to raise to a power
2142     * @param float $realNumber the power to which you want to raise the complex number
2143     *
2144     * @return string
2145     */
2146    public static function IMPOWER($complexNumber, $realNumber)
2147    {
2148        $complexNumber = Functions::flattenSingleValue($complexNumber);
2149        $realNumber = Functions::flattenSingleValue($realNumber);
2150
2151        if (!is_numeric($realNumber)) {
2152            return Functions::VALUE();
2153        }
2154
2155        return (string) (new Complex($complexNumber))->pow($realNumber);
2156    }
2157
2158    /**
2159     * IMDIV.
2160     *
2161     * Returns the quotient of two complex numbers in x + yi or x + yj text format.
2162     *
2163     * Excel Function:
2164     *        IMDIV(complexDividend,complexDivisor)
2165     *
2166     * @param string $complexDividend the complex numerator or dividend
2167     * @param string $complexDivisor the complex denominator or divisor
2168     *
2169     * @return string
2170     */
2171    public static function IMDIV($complexDividend, $complexDivisor)
2172    {
2173        $complexDividend = Functions::flattenSingleValue($complexDividend);
2174        $complexDivisor = Functions::flattenSingleValue($complexDivisor);
2175
2176        try {
2177            return (string) (new Complex($complexDividend))->divideby(new Complex($complexDivisor));
2178        } catch (ComplexException $e) {
2179            return Functions::NAN();
2180        }
2181    }
2182
2183    /**
2184     * IMSUB.
2185     *
2186     * Returns the difference of two complex numbers in x + yi or x + yj text format.
2187     *
2188     * Excel Function:
2189     *        IMSUB(complexNumber1,complexNumber2)
2190     *
2191     * @param string $complexNumber1 the complex number from which to subtract complexNumber2
2192     * @param string $complexNumber2 the complex number to subtract from complexNumber1
2193     *
2194     * @return string
2195     */
2196    public static function IMSUB($complexNumber1, $complexNumber2)
2197    {
2198        $complexNumber1 = Functions::flattenSingleValue($complexNumber1);
2199        $complexNumber2 = Functions::flattenSingleValue($complexNumber2);
2200
2201        try {
2202            return (string) (new Complex($complexNumber1))->subtract(new Complex($complexNumber2));
2203        } catch (ComplexException $e) {
2204            return Functions::NAN();
2205        }
2206    }
2207
2208    /**
2209     * IMSUM.
2210     *
2211     * Returns the sum of two or more complex numbers in x + yi or x + yj text format.
2212     *
2213     * Excel Function:
2214     *        IMSUM(complexNumber[,complexNumber[,...]])
2215     *
2216     * @param string ...$complexNumbers Series of complex numbers to add
2217     *
2218     * @return string
2219     */
2220    public static function IMSUM(...$complexNumbers)
2221    {
2222        // Return value
2223        $returnValue = new Complex(0.0);
2224        $aArgs = Functions::flattenArray($complexNumbers);
2225
2226        try {
2227            // Loop through the arguments
2228            foreach ($aArgs as $complex) {
2229                $returnValue = $returnValue->add(new Complex($complex));
2230            }
2231        } catch (ComplexException $e) {
2232            return Functions::NAN();
2233        }
2234
2235        return (string) $returnValue;
2236    }
2237
2238    /**
2239     * IMPRODUCT.
2240     *
2241     * Returns the product of two or more complex numbers in x + yi or x + yj text format.
2242     *
2243     * Excel Function:
2244     *        IMPRODUCT(complexNumber[,complexNumber[,...]])
2245     *
2246     * @param string ...$complexNumbers Series of complex numbers to multiply
2247     *
2248     * @return string
2249     */
2250    public static function IMPRODUCT(...$complexNumbers)
2251    {
2252        // Return value
2253        $returnValue = new Complex(1.0);
2254        $aArgs = Functions::flattenArray($complexNumbers);
2255
2256        try {
2257            // Loop through the arguments
2258            foreach ($aArgs as $complex) {
2259                $returnValue = $returnValue->multiply(new Complex($complex));
2260            }
2261        } catch (ComplexException $e) {
2262            return Functions::NAN();
2263        }
2264
2265        return (string) $returnValue;
2266    }
2267
2268    /**
2269     * DELTA.
2270     *
2271     * Tests whether two values are equal. Returns 1 if number1 = number2; returns 0 otherwise.
2272     *    Use this function to filter a set of values. For example, by summing several DELTA
2273     *    functions you calculate the count of equal pairs. This function is also known as the
2274     * Kronecker Delta function.
2275     *
2276     *    Excel Function:
2277     *        DELTA(a[,b])
2278     *
2279     * @param float $a the first number
2280     * @param float $b The second number. If omitted, b is assumed to be zero.
2281     *
2282     * @return int
2283     */
2284    public static function DELTA($a, $b = 0)
2285    {
2286        $a = Functions::flattenSingleValue($a);
2287        $b = Functions::flattenSingleValue($b);
2288
2289        return (int) ($a == $b);
2290    }
2291
2292    /**
2293     * GESTEP.
2294     *
2295     *    Excel Function:
2296     *        GESTEP(number[,step])
2297     *
2298     *    Returns 1 if number >= step; returns 0 (zero) otherwise
2299     *    Use this function to filter a set of values. For example, by summing several GESTEP
2300     * functions you calculate the count of values that exceed a threshold.
2301     *
2302     * @param float $number the value to test against step
2303     * @param float $step The threshold value.
2304     *                                    If you omit a value for step, GESTEP uses zero.
2305     *
2306     * @return int
2307     */
2308    public static function GESTEP($number, $step = 0)
2309    {
2310        $number = Functions::flattenSingleValue($number);
2311        $step = Functions::flattenSingleValue($step);
2312
2313        return (int) ($number >= $step);
2314    }
2315
2316    //
2317    //    Private method to calculate the erf value
2318    //
2319    private static $twoSqrtPi = 1.128379167095512574;
2320
2321    public static function erfVal($x)
2322    {
2323        if (abs($x) > 2.2) {
2324            return 1 - self::erfcVal($x);
2325        }
2326        $sum = $term = $x;
2327        $xsqr = ($x * $x);
2328        $j = 1;
2329        do {
2330            $term *= $xsqr / $j;
2331            $sum -= $term / (2 * $j + 1);
2332            ++$j;
2333            $term *= $xsqr / $j;
2334            $sum += $term / (2 * $j + 1);
2335            ++$j;
2336            if ($sum == 0.0) {
2337                break;
2338            }
2339        } while (abs($term / $sum) > Functions::PRECISION);
2340
2341        return self::$twoSqrtPi * $sum;
2342    }
2343
2344    /**
2345     * Validate arguments passed to the bitwise functions.
2346     *
2347     * @param mixed $value
2348     *
2349     * @throws Exception
2350     *
2351     * @return int
2352     */
2353    private static function validateBitwiseArgument($value)
2354    {
2355        $value = Functions::flattenSingleValue($value);
2356
2357        if (is_int($value)) {
2358            return $value;
2359        } elseif (is_numeric($value)) {
2360            if ($value == (int) ($value)) {
2361                $value = (int) ($value);
2362                if (($value > pow(2, 48) - 1) || ($value < 0)) {
2363                    throw new Exception(Functions::NAN());
2364                }
2365
2366                return $value;
2367            }
2368
2369            throw new Exception(Functions::NAN());
2370        }
2371
2372        throw new Exception(Functions::VALUE());
2373    }
2374
2375    /**
2376     * BITAND.
2377     *
2378     * Returns the bitwise AND of two integer values.
2379     *
2380     * Excel Function:
2381     *        BITAND(number1, number2)
2382     *
2383     * @category Engineering Functions
2384     *
2385     * @param int $number1
2386     * @param int $number2
2387     *
2388     * @return int|string
2389     */
2390    public static function BITAND($number1, $number2)
2391    {
2392        try {
2393            $number1 = self::validateBitwiseArgument($number1);
2394            $number2 = self::validateBitwiseArgument($number2);
2395        } catch (Exception $e) {
2396            return $e->getMessage();
2397        }
2398
2399        return $number1 & $number2;
2400    }
2401
2402    /**
2403     * BITOR.
2404     *
2405     * Returns the bitwise OR of two integer values.
2406     *
2407     * Excel Function:
2408     *        BITOR(number1, number2)
2409     *
2410     * @category Engineering Functions
2411     *
2412     * @param int $number1
2413     * @param int $number2
2414     *
2415     * @return int|string
2416     */
2417    public static function BITOR($number1, $number2)
2418    {
2419        try {
2420            $number1 = self::validateBitwiseArgument($number1);
2421            $number2 = self::validateBitwiseArgument($number2);
2422        } catch (Exception $e) {
2423            return $e->getMessage();
2424        }
2425
2426        return $number1 | $number2;
2427    }
2428
2429    /**
2430     * BITXOR.
2431     *
2432     * Returns the bitwise XOR of two integer values.
2433     *
2434     * Excel Function:
2435     *        BITXOR(number1, number2)
2436     *
2437     * @category Engineering Functions
2438     *
2439     * @param int $number1
2440     * @param int $number2
2441     *
2442     * @return int|string
2443     */
2444    public static function BITXOR($number1, $number2)
2445    {
2446        try {
2447            $number1 = self::validateBitwiseArgument($number1);
2448            $number2 = self::validateBitwiseArgument($number2);
2449        } catch (Exception $e) {
2450            return $e->getMessage();
2451        }
2452
2453        return $number1 ^ $number2;
2454    }
2455
2456    /**
2457     * BITLSHIFT.
2458     *
2459     * Returns the number value shifted left by shift_amount bits.
2460     *
2461     * Excel Function:
2462     *        BITLSHIFT(number, shift_amount)
2463     *
2464     * @category Engineering Functions
2465     *
2466     * @param int $number
2467     * @param int $shiftAmount
2468     *
2469     * @return int|string
2470     */
2471    public static function BITLSHIFT($number, $shiftAmount)
2472    {
2473        try {
2474            $number = self::validateBitwiseArgument($number);
2475        } catch (Exception $e) {
2476            return $e->getMessage();
2477        }
2478
2479        $shiftAmount = Functions::flattenSingleValue($shiftAmount);
2480
2481        $result = $number << $shiftAmount;
2482        if ($result > pow(2, 48) - 1) {
2483            return Functions::NAN();
2484        }
2485
2486        return $result;
2487    }
2488
2489    /**
2490     * BITRSHIFT.
2491     *
2492     * Returns the number value shifted right by shift_amount bits.
2493     *
2494     * Excel Function:
2495     *        BITRSHIFT(number, shift_amount)
2496     *
2497     * @category Engineering Functions
2498     *
2499     * @param int $number
2500     * @param int $shiftAmount
2501     *
2502     * @return int|string
2503     */
2504    public static function BITRSHIFT($number, $shiftAmount)
2505    {
2506        try {
2507            $number = self::validateBitwiseArgument($number);
2508        } catch (Exception $e) {
2509            return $e->getMessage();
2510        }
2511
2512        $shiftAmount = Functions::flattenSingleValue($shiftAmount);
2513
2514        return $number >> $shiftAmount;
2515    }
2516
2517    /**
2518     * ERF.
2519     *
2520     * Returns the error function integrated between the lower and upper bound arguments.
2521     *
2522     *    Note: In Excel 2007 or earlier, if you input a negative value for the upper or lower bound arguments,
2523     *            the function would return a #NUM! error. However, in Excel 2010, the function algorithm was
2524     *            improved, so that it can now calculate the function for both positive and negative ranges.
2525     *            PhpSpreadsheet follows Excel 2010 behaviour, and accepts negative arguments.
2526     *
2527     *    Excel Function:
2528     *        ERF(lower[,upper])
2529     *
2530     * @param float $lower lower bound for integrating ERF
2531     * @param float $upper upper bound for integrating ERF.
2532     *                                If omitted, ERF integrates between zero and lower_limit
2533     *
2534     * @return float|string
2535     */
2536    public static function ERF($lower, $upper = null)
2537    {
2538        $lower = Functions::flattenSingleValue($lower);
2539        $upper = Functions::flattenSingleValue($upper);
2540
2541        if (is_numeric($lower)) {
2542            if ($upper === null) {
2543                return self::erfVal($lower);
2544            }
2545            if (is_numeric($upper)) {
2546                return self::erfVal($upper) - self::erfVal($lower);
2547            }
2548        }
2549
2550        return Functions::VALUE();
2551    }
2552
2553    /**
2554     * ERFPRECISE.
2555     *
2556     * Returns the error function integrated between the lower and upper bound arguments.
2557     *
2558     *    Excel Function:
2559     *        ERF.PRECISE(limit)
2560     *
2561     * @param float $limit bound for integrating ERF
2562     *
2563     * @return float|string
2564     */
2565    public static function ERFPRECISE($limit)
2566    {
2567        $limit = Functions::flattenSingleValue($limit);
2568
2569        return self::ERF($limit);
2570    }
2571
2572    //
2573    //    Private method to calculate the erfc value
2574    //
2575    private static $oneSqrtPi = 0.564189583547756287;
2576
2577    private static function erfcVal($x)
2578    {
2579        if (abs($x) < 2.2) {
2580            return 1 - self::erfVal($x);
2581        }
2582        if ($x < 0) {
2583            return 2 - self::ERFC(-$x);
2584        }
2585        $a = $n = 1;
2586        $b = $c = $x;
2587        $d = ($x * $x) + 0.5;
2588        $q1 = $q2 = $b / $d;
2589        $t = 0;
2590        do {
2591            $t = $a * $n + $b * $x;
2592            $a = $b;
2593            $b = $t;
2594            $t = $c * $n + $d * $x;
2595            $c = $d;
2596            $d = $t;
2597            $n += 0.5;
2598            $q1 = $q2;
2599            $q2 = $b / $d;
2600        } while ((abs($q1 - $q2) / $q2) > Functions::PRECISION);
2601
2602        return self::$oneSqrtPi * exp(-$x * $x) * $q2;
2603    }
2604
2605    /**
2606     * ERFC.
2607     *
2608     *    Returns the complementary ERF function integrated between x and infinity
2609     *
2610     *    Note: In Excel 2007 or earlier, if you input a negative value for the lower bound argument,
2611     *        the function would return a #NUM! error. However, in Excel 2010, the function algorithm was
2612     *        improved, so that it can now calculate the function for both positive and negative x values.
2613     *            PhpSpreadsheet follows Excel 2010 behaviour, and accepts nagative arguments.
2614     *
2615     *    Excel Function:
2616     *        ERFC(x)
2617     *
2618     * @param float $x The lower bound for integrating ERFC
2619     *
2620     * @return float|string
2621     */
2622    public static function ERFC($x)
2623    {
2624        $x = Functions::flattenSingleValue($x);
2625
2626        if (is_numeric($x)) {
2627            return self::erfcVal($x);
2628        }
2629
2630        return Functions::VALUE();
2631    }
2632
2633    /**
2634     *    getConversionGroups
2635     * Returns a list of the different conversion groups for UOM conversions.
2636     *
2637     * @return array
2638     */
2639    public static function getConversionGroups()
2640    {
2641        $conversionGroups = [];
2642        foreach (self::$conversionUnits as $conversionUnit) {
2643            $conversionGroups[] = $conversionUnit['Group'];
2644        }
2645
2646        return array_merge(array_unique($conversionGroups));
2647    }
2648
2649    /**
2650     *    getConversionGroupUnits
2651     * Returns an array of units of measure, for a specified conversion group, or for all groups.
2652     *
2653     * @param string $group The group whose units of measure you want to retrieve
2654     *
2655     * @return array
2656     */
2657    public static function getConversionGroupUnits($group = null)
2658    {
2659        $conversionGroups = [];
2660        foreach (self::$conversionUnits as $conversionUnit => $conversionGroup) {
2661            if (($group === null) || ($conversionGroup['Group'] == $group)) {
2662                $conversionGroups[$conversionGroup['Group']][] = $conversionUnit;
2663            }
2664        }
2665
2666        return $conversionGroups;
2667    }
2668
2669    /**
2670     * getConversionGroupUnitDetails.
2671     *
2672     * @param string $group The group whose units of measure you want to retrieve
2673     *
2674     * @return array
2675     */
2676    public static function getConversionGroupUnitDetails($group = null)
2677    {
2678        $conversionGroups = [];
2679        foreach (self::$conversionUnits as $conversionUnit => $conversionGroup) {
2680            if (($group === null) || ($conversionGroup['Group'] == $group)) {
2681                $conversionGroups[$conversionGroup['Group']][] = [
2682                    'unit' => $conversionUnit,
2683                    'description' => $conversionGroup['Unit Name'],
2684                ];
2685            }
2686        }
2687
2688        return $conversionGroups;
2689    }
2690
2691    /**
2692     *    getConversionMultipliers
2693     * Returns an array of the Multiplier prefixes that can be used with Units of Measure in CONVERTUOM().
2694     *
2695     * @return array of mixed
2696     */
2697    public static function getConversionMultipliers()
2698    {
2699        return self::$conversionMultipliers;
2700    }
2701
2702    /**
2703     * CONVERTUOM.
2704     *
2705     * Converts a number from one measurement system to another.
2706     *    For example, CONVERT can translate a table of distances in miles to a table of distances
2707     * in kilometers.
2708     *
2709     *    Excel Function:
2710     *        CONVERT(value,fromUOM,toUOM)
2711     *
2712     * @param float $value the value in fromUOM to convert
2713     * @param string $fromUOM the units for value
2714     * @param string $toUOM the units for the result
2715     *
2716     * @return float
2717     */
2718    public static function CONVERTUOM($value, $fromUOM, $toUOM)
2719    {
2720        $value = Functions::flattenSingleValue($value);
2721        $fromUOM = Functions::flattenSingleValue($fromUOM);
2722        $toUOM = Functions::flattenSingleValue($toUOM);
2723
2724        if (!is_numeric($value)) {
2725            return Functions::VALUE();
2726        }
2727        $fromMultiplier = 1.0;
2728        if (isset(self::$conversionUnits[$fromUOM])) {
2729            $unitGroup1 = self::$conversionUnits[$fromUOM]['Group'];
2730        } else {
2731            $fromMultiplier = substr($fromUOM, 0, 1);
2732            $fromUOM = substr($fromUOM, 1);
2733            if (isset(self::$conversionMultipliers[$fromMultiplier])) {
2734                $fromMultiplier = self::$conversionMultipliers[$fromMultiplier]['multiplier'];
2735            } else {
2736                return Functions::NA();
2737            }
2738            if ((isset(self::$conversionUnits[$fromUOM])) && (self::$conversionUnits[$fromUOM]['AllowPrefix'])) {
2739                $unitGroup1 = self::$conversionUnits[$fromUOM]['Group'];
2740            } else {
2741                return Functions::NA();
2742            }
2743        }
2744        $value *= $fromMultiplier;
2745
2746        $toMultiplier = 1.0;
2747        if (isset(self::$conversionUnits[$toUOM])) {
2748            $unitGroup2 = self::$conversionUnits[$toUOM]['Group'];
2749        } else {
2750            $toMultiplier = substr($toUOM, 0, 1);
2751            $toUOM = substr($toUOM, 1);
2752            if (isset(self::$conversionMultipliers[$toMultiplier])) {
2753                $toMultiplier = self::$conversionMultipliers[$toMultiplier]['multiplier'];
2754            } else {
2755                return Functions::NA();
2756            }
2757            if ((isset(self::$conversionUnits[$toUOM])) && (self::$conversionUnits[$toUOM]['AllowPrefix'])) {
2758                $unitGroup2 = self::$conversionUnits[$toUOM]['Group'];
2759            } else {
2760                return Functions::NA();
2761            }
2762        }
2763        if ($unitGroup1 != $unitGroup2) {
2764            return Functions::NA();
2765        }
2766
2767        if (($fromUOM == $toUOM) && ($fromMultiplier == $toMultiplier)) {
2768            //    We've already factored $fromMultiplier into the value, so we need
2769            //        to reverse it again
2770            return $value / $fromMultiplier;
2771        } elseif ($unitGroup1 == 'Temperature') {
2772            if (($fromUOM == 'F') || ($fromUOM == 'fah')) {
2773                if (($toUOM == 'F') || ($toUOM == 'fah')) {
2774                    return $value;
2775                }
2776                $value = (($value - 32) / 1.8);
2777                if (($toUOM == 'K') || ($toUOM == 'kel')) {
2778                    $value += 273.15;
2779                }
2780
2781                return $value;
2782            } elseif ((($fromUOM == 'K') || ($fromUOM == 'kel')) &&
2783                (($toUOM == 'K') || ($toUOM == 'kel'))
2784            ) {
2785                return $value;
2786            } elseif ((($fromUOM == 'C') || ($fromUOM == 'cel')) &&
2787                (($toUOM == 'C') || ($toUOM == 'cel'))
2788            ) {
2789                return $value;
2790            }
2791            if (($toUOM == 'F') || ($toUOM == 'fah')) {
2792                if (($fromUOM == 'K') || ($fromUOM == 'kel')) {
2793                    $value -= 273.15;
2794                }
2795
2796                return ($value * 1.8) + 32;
2797            }
2798            if (($toUOM == 'C') || ($toUOM == 'cel')) {
2799                return $value - 273.15;
2800            }
2801
2802            return $value + 273.15;
2803        }
2804
2805        return ($value * self::$unitConversions[$unitGroup1][$fromUOM][$toUOM]) / $toMultiplier;
2806    }
2807}
2808