1: <?php
2: /**
3: * PHPExcel
4: *
5: * Copyright (c) 2006 - 2014 PHPExcel
6: *
7: * This library is free software; you can redistribute it and/or
8: * modify it under the terms of the GNU Lesser General Public
9: * License as published by the Free Software Foundation; either
10: * version 2.1 of the License, or (at your option) any later version.
11: *
12: * This library is distributed in the hope that it will be useful,
13: * but WITHOUT ANY WARRANTY; without even the implied warranty of
14: * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
15: * Lesser General Public License for more details.
16: *
17: * You should have received a copy of the GNU Lesser General Public
18: * License along with this library; if not, write to the Free Software
19: * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
20: *
21: * @category PHPExcel
22: * @package PHPExcel_Calculation
23: * @copyright Copyright (c) 2006 - 2014 PHPExcel (http://www.codeplex.com/PHPExcel)
24: * @license http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt LGPL
25: * @version 1.8.0, 2014-03-02
26: */
27:
28:
29: /** PHPExcel root directory */
30: if (!defined('PHPEXCEL_ROOT')) {
31: /**
32: * @ignore
33: */
34: define('PHPEXCEL_ROOT', dirname(__FILE__) . '/../../');
35: require(PHPEXCEL_ROOT . 'PHPExcel/Autoloader.php');
36: }
37:
38:
39: /** EULER */
40: define('EULER', 2.71828182845904523536);
41:
42:
43: /**
44: * PHPExcel_Calculation_Engineering
45: *
46: * @category PHPExcel
47: * @package PHPExcel_Calculation
48: * @copyright Copyright (c) 2006 - 2014 PHPExcel (http://www.codeplex.com/PHPExcel)
49: */
50: class PHPExcel_Calculation_Engineering {
51:
52: /**
53: * Details of the Units of measure that can be used in CONVERTUOM()
54: *
55: * @var mixed[]
56: */
57: private static $_conversionUnits = array( 'g' => array( 'Group' => 'Mass', 'Unit Name' => 'Gram', 'AllowPrefix' => True ),
58: 'sg' => array( 'Group' => 'Mass', 'Unit Name' => 'Slug', 'AllowPrefix' => False ),
59: 'lbm' => array( 'Group' => 'Mass', 'Unit Name' => 'Pound mass (avoirdupois)', 'AllowPrefix' => False ),
60: 'u' => array( 'Group' => 'Mass', 'Unit Name' => 'U (atomic mass unit)', 'AllowPrefix' => True ),
61: 'ozm' => array( 'Group' => 'Mass', 'Unit Name' => 'Ounce mass (avoirdupois)', 'AllowPrefix' => False ),
62: 'm' => array( 'Group' => 'Distance', 'Unit Name' => 'Meter', 'AllowPrefix' => True ),
63: 'mi' => array( 'Group' => 'Distance', 'Unit Name' => 'Statute mile', 'AllowPrefix' => False ),
64: 'Nmi' => array( 'Group' => 'Distance', 'Unit Name' => 'Nautical mile', 'AllowPrefix' => False ),
65: 'in' => array( 'Group' => 'Distance', 'Unit Name' => 'Inch', 'AllowPrefix' => False ),
66: 'ft' => array( 'Group' => 'Distance', 'Unit Name' => 'Foot', 'AllowPrefix' => False ),
67: 'yd' => array( 'Group' => 'Distance', 'Unit Name' => 'Yard', 'AllowPrefix' => False ),
68: 'ang' => array( 'Group' => 'Distance', 'Unit Name' => 'Angstrom', 'AllowPrefix' => True ),
69: 'Pica' => array( 'Group' => 'Distance', 'Unit Name' => 'Pica (1/72 in)', 'AllowPrefix' => False ),
70: 'yr' => array( 'Group' => 'Time', 'Unit Name' => 'Year', 'AllowPrefix' => False ),
71: 'day' => array( 'Group' => 'Time', 'Unit Name' => 'Day', 'AllowPrefix' => False ),
72: 'hr' => array( 'Group' => 'Time', 'Unit Name' => 'Hour', 'AllowPrefix' => False ),
73: 'mn' => array( 'Group' => 'Time', 'Unit Name' => 'Minute', 'AllowPrefix' => False ),
74: 'sec' => array( 'Group' => 'Time', 'Unit Name' => 'Second', 'AllowPrefix' => True ),
75: 'Pa' => array( 'Group' => 'Pressure', 'Unit Name' => 'Pascal', 'AllowPrefix' => True ),
76: 'p' => array( 'Group' => 'Pressure', 'Unit Name' => 'Pascal', 'AllowPrefix' => True ),
77: 'atm' => array( 'Group' => 'Pressure', 'Unit Name' => 'Atmosphere', 'AllowPrefix' => True ),
78: 'at' => array( 'Group' => 'Pressure', 'Unit Name' => 'Atmosphere', 'AllowPrefix' => True ),
79: 'mmHg' => array( 'Group' => 'Pressure', 'Unit Name' => 'mm of Mercury', 'AllowPrefix' => True ),
80: 'N' => array( 'Group' => 'Force', 'Unit Name' => 'Newton', 'AllowPrefix' => True ),
81: 'dyn' => array( 'Group' => 'Force', 'Unit Name' => 'Dyne', 'AllowPrefix' => True ),
82: 'dy' => array( 'Group' => 'Force', 'Unit Name' => 'Dyne', 'AllowPrefix' => True ),
83: 'lbf' => array( 'Group' => 'Force', 'Unit Name' => 'Pound force', 'AllowPrefix' => False ),
84: 'J' => array( 'Group' => 'Energy', 'Unit Name' => 'Joule', 'AllowPrefix' => True ),
85: 'e' => array( 'Group' => 'Energy', 'Unit Name' => 'Erg', 'AllowPrefix' => True ),
86: 'c' => array( 'Group' => 'Energy', 'Unit Name' => 'Thermodynamic calorie', 'AllowPrefix' => True ),
87: 'cal' => array( 'Group' => 'Energy', 'Unit Name' => 'IT calorie', 'AllowPrefix' => True ),
88: 'eV' => array( 'Group' => 'Energy', 'Unit Name' => 'Electron volt', 'AllowPrefix' => True ),
89: 'ev' => array( 'Group' => 'Energy', 'Unit Name' => 'Electron volt', 'AllowPrefix' => True ),
90: 'HPh' => array( 'Group' => 'Energy', 'Unit Name' => 'Horsepower-hour', 'AllowPrefix' => False ),
91: 'hh' => array( 'Group' => 'Energy', 'Unit Name' => 'Horsepower-hour', 'AllowPrefix' => False ),
92: 'Wh' => array( 'Group' => 'Energy', 'Unit Name' => 'Watt-hour', 'AllowPrefix' => True ),
93: 'wh' => array( 'Group' => 'Energy', 'Unit Name' => 'Watt-hour', 'AllowPrefix' => True ),
94: 'flb' => array( 'Group' => 'Energy', 'Unit Name' => 'Foot-pound', 'AllowPrefix' => False ),
95: 'BTU' => array( 'Group' => 'Energy', 'Unit Name' => 'BTU', 'AllowPrefix' => False ),
96: 'btu' => array( 'Group' => 'Energy', 'Unit Name' => 'BTU', 'AllowPrefix' => False ),
97: 'HP' => array( 'Group' => 'Power', 'Unit Name' => 'Horsepower', 'AllowPrefix' => False ),
98: 'h' => array( 'Group' => 'Power', 'Unit Name' => 'Horsepower', 'AllowPrefix' => False ),
99: 'W' => array( 'Group' => 'Power', 'Unit Name' => 'Watt', 'AllowPrefix' => True ),
100: 'w' => array( 'Group' => 'Power', 'Unit Name' => 'Watt', 'AllowPrefix' => True ),
101: 'T' => array( 'Group' => 'Magnetism', 'Unit Name' => 'Tesla', 'AllowPrefix' => True ),
102: 'ga' => array( 'Group' => 'Magnetism', 'Unit Name' => 'Gauss', 'AllowPrefix' => True ),
103: 'C' => array( 'Group' => 'Temperature', 'Unit Name' => 'Celsius', 'AllowPrefix' => False ),
104: 'cel' => array( 'Group' => 'Temperature', 'Unit Name' => 'Celsius', 'AllowPrefix' => False ),
105: 'F' => array( 'Group' => 'Temperature', 'Unit Name' => 'Fahrenheit', 'AllowPrefix' => False ),
106: 'fah' => array( 'Group' => 'Temperature', 'Unit Name' => 'Fahrenheit', 'AllowPrefix' => False ),
107: 'K' => array( 'Group' => 'Temperature', 'Unit Name' => 'Kelvin', 'AllowPrefix' => False ),
108: 'kel' => array( 'Group' => 'Temperature', 'Unit Name' => 'Kelvin', 'AllowPrefix' => False ),
109: 'tsp' => array( 'Group' => 'Liquid', 'Unit Name' => 'Teaspoon', 'AllowPrefix' => False ),
110: 'tbs' => array( 'Group' => 'Liquid', 'Unit Name' => 'Tablespoon', 'AllowPrefix' => False ),
111: 'oz' => array( 'Group' => 'Liquid', 'Unit Name' => 'Fluid Ounce', 'AllowPrefix' => False ),
112: 'cup' => array( 'Group' => 'Liquid', 'Unit Name' => 'Cup', 'AllowPrefix' => False ),
113: 'pt' => array( 'Group' => 'Liquid', 'Unit Name' => 'U.S. Pint', 'AllowPrefix' => False ),
114: 'us_pt' => array( 'Group' => 'Liquid', 'Unit Name' => 'U.S. Pint', 'AllowPrefix' => False ),
115: 'uk_pt' => array( 'Group' => 'Liquid', 'Unit Name' => 'U.K. Pint', 'AllowPrefix' => False ),
116: 'qt' => array( 'Group' => 'Liquid', 'Unit Name' => 'Quart', 'AllowPrefix' => False ),
117: 'gal' => array( 'Group' => 'Liquid', 'Unit Name' => 'Gallon', 'AllowPrefix' => False ),
118: 'l' => array( 'Group' => 'Liquid', 'Unit Name' => 'Litre', 'AllowPrefix' => True ),
119: 'lt' => array( 'Group' => 'Liquid', 'Unit Name' => 'Litre', 'AllowPrefix' => True )
120: );
121:
122: /**
123: * Details of the Multiplier prefixes that can be used with Units of Measure in CONVERTUOM()
124: *
125: * @var mixed[]
126: */
127: private static $_conversionMultipliers = array( 'Y' => array( 'multiplier' => 1E24, 'name' => 'yotta' ),
128: 'Z' => array( 'multiplier' => 1E21, 'name' => 'zetta' ),
129: 'E' => array( 'multiplier' => 1E18, 'name' => 'exa' ),
130: 'P' => array( 'multiplier' => 1E15, 'name' => 'peta' ),
131: 'T' => array( 'multiplier' => 1E12, 'name' => 'tera' ),
132: 'G' => array( 'multiplier' => 1E9, 'name' => 'giga' ),
133: 'M' => array( 'multiplier' => 1E6, 'name' => 'mega' ),
134: 'k' => array( 'multiplier' => 1E3, 'name' => 'kilo' ),
135: 'h' => array( 'multiplier' => 1E2, 'name' => 'hecto' ),
136: 'e' => array( 'multiplier' => 1E1, 'name' => 'deka' ),
137: 'd' => array( 'multiplier' => 1E-1, 'name' => 'deci' ),
138: 'c' => array( 'multiplier' => 1E-2, 'name' => 'centi' ),
139: 'm' => array( 'multiplier' => 1E-3, 'name' => 'milli' ),
140: 'u' => array( 'multiplier' => 1E-6, 'name' => 'micro' ),
141: 'n' => array( 'multiplier' => 1E-9, 'name' => 'nano' ),
142: 'p' => array( 'multiplier' => 1E-12, 'name' => 'pico' ),
143: 'f' => array( 'multiplier' => 1E-15, 'name' => 'femto' ),
144: 'a' => array( 'multiplier' => 1E-18, 'name' => 'atto' ),
145: 'z' => array( 'multiplier' => 1E-21, 'name' => 'zepto' ),
146: 'y' => array( 'multiplier' => 1E-24, 'name' => 'yocto' )
147: );
148:
149: /**
150: * Details of the Units of measure conversion factors, organised by group
151: *
152: * @var mixed[]
153: */
154: private static $_unitConversions = array( 'Mass' => array( 'g' => array( 'g' => 1.0,
155: 'sg' => 6.85220500053478E-05,
156: 'lbm' => 2.20462291469134E-03,
157: 'u' => 6.02217000000000E+23,
158: 'ozm' => 3.52739718003627E-02
159: ),
160: 'sg' => array( 'g' => 1.45938424189287E+04,
161: 'sg' => 1.0,
162: 'lbm' => 3.21739194101647E+01,
163: 'u' => 8.78866000000000E+27,
164: 'ozm' => 5.14782785944229E+02
165: ),
166: 'lbm' => array( 'g' => 4.5359230974881148E+02,
167: 'sg' => 3.10810749306493E-02,
168: 'lbm' => 1.0,
169: 'u' => 2.73161000000000E+26,
170: 'ozm' => 1.60000023429410E+01
171: ),
172: 'u' => array( 'g' => 1.66053100460465E-24,
173: 'sg' => 1.13782988532950E-28,
174: 'lbm' => 3.66084470330684E-27,
175: 'u' => 1.0,
176: 'ozm' => 5.85735238300524E-26
177: ),
178: 'ozm' => array( 'g' => 2.83495152079732E+01,
179: 'sg' => 1.94256689870811E-03,
180: 'lbm' => 6.24999908478882E-02,
181: 'u' => 1.70725600000000E+25,
182: 'ozm' => 1.0
183: )
184: ),
185: 'Distance' => array( 'm' => array( 'm' => 1.0,
186: 'mi' => 6.21371192237334E-04,
187: 'Nmi' => 5.39956803455724E-04,
188: 'in' => 3.93700787401575E+01,
189: 'ft' => 3.28083989501312E+00,
190: 'yd' => 1.09361329797891E+00,
191: 'ang' => 1.00000000000000E+10,
192: 'Pica' => 2.83464566929116E+03
193: ),
194: 'mi' => array( 'm' => 1.60934400000000E+03,
195: 'mi' => 1.0,
196: 'Nmi' => 8.68976241900648E-01,
197: 'in' => 6.33600000000000E+04,
198: 'ft' => 5.28000000000000E+03,
199: 'yd' => 1.76000000000000E+03,
200: 'ang' => 1.60934400000000E+13,
201: 'Pica' => 4.56191999999971E+06
202: ),
203: 'Nmi' => array( 'm' => 1.85200000000000E+03,
204: 'mi' => 1.15077944802354E+00,
205: 'Nmi' => 1.0,
206: 'in' => 7.29133858267717E+04,
207: 'ft' => 6.07611548556430E+03,
208: 'yd' => 2.02537182785694E+03,
209: 'ang' => 1.85200000000000E+13,
210: 'Pica' => 5.24976377952723E+06
211: ),
212: 'in' => array( 'm' => 2.54000000000000E-02,
213: 'mi' => 1.57828282828283E-05,
214: 'Nmi' => 1.37149028077754E-05,
215: 'in' => 1.0,
216: 'ft' => 8.33333333333333E-02,
217: 'yd' => 2.77777777686643E-02,
218: 'ang' => 2.54000000000000E+08,
219: 'Pica' => 7.19999999999955E+01
220: ),
221: 'ft' => array( 'm' => 3.04800000000000E-01,
222: 'mi' => 1.89393939393939E-04,
223: 'Nmi' => 1.64578833693305E-04,
224: 'in' => 1.20000000000000E+01,
225: 'ft' => 1.0,
226: 'yd' => 3.33333333223972E-01,
227: 'ang' => 3.04800000000000E+09,
228: 'Pica' => 8.63999999999946E+02
229: ),
230: 'yd' => array( 'm' => 9.14400000300000E-01,
231: 'mi' => 5.68181818368230E-04,
232: 'Nmi' => 4.93736501241901E-04,
233: 'in' => 3.60000000118110E+01,
234: 'ft' => 3.00000000000000E+00,
235: 'yd' => 1.0,
236: 'ang' => 9.14400000300000E+09,
237: 'Pica' => 2.59200000085023E+03
238: ),
239: 'ang' => array( 'm' => 1.00000000000000E-10,
240: 'mi' => 6.21371192237334E-14,
241: 'Nmi' => 5.39956803455724E-14,
242: 'in' => 3.93700787401575E-09,
243: 'ft' => 3.28083989501312E-10,
244: 'yd' => 1.09361329797891E-10,
245: 'ang' => 1.0,
246: 'Pica' => 2.83464566929116E-07
247: ),
248: 'Pica' => array( 'm' => 3.52777777777800E-04,
249: 'mi' => 2.19205948372629E-07,
250: 'Nmi' => 1.90484761219114E-07,
251: 'in' => 1.38888888888898E-02,
252: 'ft' => 1.15740740740748E-03,
253: 'yd' => 3.85802469009251E-04,
254: 'ang' => 3.52777777777800E+06,
255: 'Pica' => 1.0
256: )
257: ),
258: 'Time' => array( 'yr' => array( 'yr' => 1.0,
259: 'day' => 365.25,
260: 'hr' => 8766.0,
261: 'mn' => 525960.0,
262: 'sec' => 31557600.0
263: ),
264: 'day' => array( 'yr' => 2.73785078713210E-03,
265: 'day' => 1.0,
266: 'hr' => 24.0,
267: 'mn' => 1440.0,
268: 'sec' => 86400.0
269: ),
270: 'hr' => array( 'yr' => 1.14077116130504E-04,
271: 'day' => 4.16666666666667E-02,
272: 'hr' => 1.0,
273: 'mn' => 60.0,
274: 'sec' => 3600.0
275: ),
276: 'mn' => array( 'yr' => 1.90128526884174E-06,
277: 'day' => 6.94444444444444E-04,
278: 'hr' => 1.66666666666667E-02,
279: 'mn' => 1.0,
280: 'sec' => 60.0
281: ),
282: 'sec' => array( 'yr' => 3.16880878140289E-08,
283: 'day' => 1.15740740740741E-05,
284: 'hr' => 2.77777777777778E-04,
285: 'mn' => 1.66666666666667E-02,
286: 'sec' => 1.0
287: )
288: ),
289: 'Pressure' => array( 'Pa' => array( 'Pa' => 1.0,
290: 'p' => 1.0,
291: 'atm' => 9.86923299998193E-06,
292: 'at' => 9.86923299998193E-06,
293: 'mmHg' => 7.50061707998627E-03
294: ),
295: 'p' => array( 'Pa' => 1.0,
296: 'p' => 1.0,
297: 'atm' => 9.86923299998193E-06,
298: 'at' => 9.86923299998193E-06,
299: 'mmHg' => 7.50061707998627E-03
300: ),
301: 'atm' => array( 'Pa' => 1.01324996583000E+05,
302: 'p' => 1.01324996583000E+05,
303: 'atm' => 1.0,
304: 'at' => 1.0,
305: 'mmHg' => 760.0
306: ),
307: 'at' => array( 'Pa' => 1.01324996583000E+05,
308: 'p' => 1.01324996583000E+05,
309: 'atm' => 1.0,
310: 'at' => 1.0,
311: 'mmHg' => 760.0
312: ),
313: 'mmHg' => array( 'Pa' => 1.33322363925000E+02,
314: 'p' => 1.33322363925000E+02,
315: 'atm' => 1.31578947368421E-03,
316: 'at' => 1.31578947368421E-03,
317: 'mmHg' => 1.0
318: )
319: ),
320: 'Force' => array( 'N' => array( 'N' => 1.0,
321: 'dyn' => 1.0E+5,
322: 'dy' => 1.0E+5,
323: 'lbf' => 2.24808923655339E-01
324: ),
325: 'dyn' => array( 'N' => 1.0E-5,
326: 'dyn' => 1.0,
327: 'dy' => 1.0,
328: 'lbf' => 2.24808923655339E-06
329: ),
330: 'dy' => array( 'N' => 1.0E-5,
331: 'dyn' => 1.0,
332: 'dy' => 1.0,
333: 'lbf' => 2.24808923655339E-06
334: ),
335: 'lbf' => array( 'N' => 4.448222,
336: 'dyn' => 4.448222E+5,
337: 'dy' => 4.448222E+5,
338: 'lbf' => 1.0
339: )
340: ),
341: 'Energy' => array( 'J' => array( 'J' => 1.0,
342: 'e' => 9.99999519343231E+06,
343: 'c' => 2.39006249473467E-01,
344: 'cal' => 2.38846190642017E-01,
345: 'eV' => 6.24145700000000E+18,
346: 'ev' => 6.24145700000000E+18,
347: 'HPh' => 3.72506430801000E-07,
348: 'hh' => 3.72506430801000E-07,
349: 'Wh' => 2.77777916238711E-04,
350: 'wh' => 2.77777916238711E-04,
351: 'flb' => 2.37304222192651E+01,
352: 'BTU' => 9.47815067349015E-04,
353: 'btu' => 9.47815067349015E-04
354: ),
355: 'e' => array( 'J' => 1.00000048065700E-07,
356: 'e' => 1.0,
357: 'c' => 2.39006364353494E-08,
358: 'cal' => 2.38846305445111E-08,
359: 'eV' => 6.24146000000000E+11,
360: 'ev' => 6.24146000000000E+11,
361: 'HPh' => 3.72506609848824E-14,
362: 'hh' => 3.72506609848824E-14,
363: 'Wh' => 2.77778049754611E-11,
364: 'wh' => 2.77778049754611E-11,
365: 'flb' => 2.37304336254586E-06,
366: 'BTU' => 9.47815522922962E-11,
367: 'btu' => 9.47815522922962E-11
368: ),
369: 'c' => array( 'J' => 4.18399101363672E+00,
370: 'e' => 4.18398900257312E+07,
371: 'c' => 1.0,
372: 'cal' => 9.99330315287563E-01,
373: 'eV' => 2.61142000000000E+19,
374: 'ev' => 2.61142000000000E+19,
375: 'HPh' => 1.55856355899327E-06,
376: 'hh' => 1.55856355899327E-06,
377: 'Wh' => 1.16222030532950E-03,
378: 'wh' => 1.16222030532950E-03,
379: 'flb' => 9.92878733152102E+01,
380: 'BTU' => 3.96564972437776E-03,
381: 'btu' => 3.96564972437776E-03
382: ),
383: 'cal' => array( 'J' => 4.18679484613929E+00,
384: 'e' => 4.18679283372801E+07,
385: 'c' => 1.00067013349059E+00,
386: 'cal' => 1.0,
387: 'eV' => 2.61317000000000E+19,
388: 'ev' => 2.61317000000000E+19,
389: 'HPh' => 1.55960800463137E-06,
390: 'hh' => 1.55960800463137E-06,
391: 'Wh' => 1.16299914807955E-03,
392: 'wh' => 1.16299914807955E-03,
393: 'flb' => 9.93544094443283E+01,
394: 'BTU' => 3.96830723907002E-03,
395: 'btu' => 3.96830723907002E-03
396: ),
397: 'eV' => array( 'J' => 1.60219000146921E-19,
398: 'e' => 1.60218923136574E-12,
399: 'c' => 3.82933423195043E-20,
400: 'cal' => 3.82676978535648E-20,
401: 'eV' => 1.0,
402: 'ev' => 1.0,
403: 'HPh' => 5.96826078912344E-26,
404: 'hh' => 5.96826078912344E-26,
405: 'Wh' => 4.45053000026614E-23,
406: 'wh' => 4.45053000026614E-23,
407: 'flb' => 3.80206452103492E-18,
408: 'BTU' => 1.51857982414846E-22,
409: 'btu' => 1.51857982414846E-22
410: ),
411: 'ev' => array( 'J' => 1.60219000146921E-19,
412: 'e' => 1.60218923136574E-12,
413: 'c' => 3.82933423195043E-20,
414: 'cal' => 3.82676978535648E-20,
415: 'eV' => 1.0,
416: 'ev' => 1.0,
417: 'HPh' => 5.96826078912344E-26,
418: 'hh' => 5.96826078912344E-26,
419: 'Wh' => 4.45053000026614E-23,
420: 'wh' => 4.45053000026614E-23,
421: 'flb' => 3.80206452103492E-18,
422: 'BTU' => 1.51857982414846E-22,
423: 'btu' => 1.51857982414846E-22
424: ),
425: 'HPh' => array( 'J' => 2.68451741316170E+06,
426: 'e' => 2.68451612283024E+13,
427: 'c' => 6.41616438565991E+05,
428: 'cal' => 6.41186757845835E+05,
429: 'eV' => 1.67553000000000E+25,
430: 'ev' => 1.67553000000000E+25,
431: 'HPh' => 1.0,
432: 'hh' => 1.0,
433: 'Wh' => 7.45699653134593E+02,
434: 'wh' => 7.45699653134593E+02,
435: 'flb' => 6.37047316692964E+07,
436: 'BTU' => 2.54442605275546E+03,
437: 'btu' => 2.54442605275546E+03
438: ),
439: 'hh' => array( 'J' => 2.68451741316170E+06,
440: 'e' => 2.68451612283024E+13,
441: 'c' => 6.41616438565991E+05,
442: 'cal' => 6.41186757845835E+05,
443: 'eV' => 1.67553000000000E+25,
444: 'ev' => 1.67553000000000E+25,
445: 'HPh' => 1.0,
446: 'hh' => 1.0,
447: 'Wh' => 7.45699653134593E+02,
448: 'wh' => 7.45699653134593E+02,
449: 'flb' => 6.37047316692964E+07,
450: 'BTU' => 2.54442605275546E+03,
451: 'btu' => 2.54442605275546E+03
452: ),
453: 'Wh' => array( 'J' => 3.59999820554720E+03,
454: 'e' => 3.59999647518369E+10,
455: 'c' => 8.60422069219046E+02,
456: 'cal' => 8.59845857713046E+02,
457: 'eV' => 2.24692340000000E+22,
458: 'ev' => 2.24692340000000E+22,
459: 'HPh' => 1.34102248243839E-03,
460: 'hh' => 1.34102248243839E-03,
461: 'Wh' => 1.0,
462: 'wh' => 1.0,
463: 'flb' => 8.54294774062316E+04,
464: 'BTU' => 3.41213254164705E+00,
465: 'btu' => 3.41213254164705E+00
466: ),
467: 'wh' => array( 'J' => 3.59999820554720E+03,
468: 'e' => 3.59999647518369E+10,
469: 'c' => 8.60422069219046E+02,
470: 'cal' => 8.59845857713046E+02,
471: 'eV' => 2.24692340000000E+22,
472: 'ev' => 2.24692340000000E+22,
473: 'HPh' => 1.34102248243839E-03,
474: 'hh' => 1.34102248243839E-03,
475: 'Wh' => 1.0,
476: 'wh' => 1.0,
477: 'flb' => 8.54294774062316E+04,
478: 'BTU' => 3.41213254164705E+00,
479: 'btu' => 3.41213254164705E+00
480: ),
481: 'flb' => array( 'J' => 4.21400003236424E-02,
482: 'e' => 4.21399800687660E+05,
483: 'c' => 1.00717234301644E-02,
484: 'cal' => 1.00649785509554E-02,
485: 'eV' => 2.63015000000000E+17,
486: 'ev' => 2.63015000000000E+17,
487: 'HPh' => 1.56974211145130E-08,
488: 'hh' => 1.56974211145130E-08,
489: 'Wh' => 1.17055614802000E-05,
490: 'wh' => 1.17055614802000E-05,
491: 'flb' => 1.0,
492: 'BTU' => 3.99409272448406E-05,
493: 'btu' => 3.99409272448406E-05
494: ),
495: 'BTU' => array( 'J' => 1.05505813786749E+03,
496: 'e' => 1.05505763074665E+10,
497: 'c' => 2.52165488508168E+02,
498: 'cal' => 2.51996617135510E+02,
499: 'eV' => 6.58510000000000E+21,
500: 'ev' => 6.58510000000000E+21,
501: 'HPh' => 3.93015941224568E-04,
502: 'hh' => 3.93015941224568E-04,
503: 'Wh' => 2.93071851047526E-01,
504: 'wh' => 2.93071851047526E-01,
505: 'flb' => 2.50369750774671E+04,
506: 'BTU' => 1.0,
507: 'btu' => 1.0,
508: ),
509: 'btu' => array( 'J' => 1.05505813786749E+03,
510: 'e' => 1.05505763074665E+10,
511: 'c' => 2.52165488508168E+02,
512: 'cal' => 2.51996617135510E+02,
513: 'eV' => 6.58510000000000E+21,
514: 'ev' => 6.58510000000000E+21,
515: 'HPh' => 3.93015941224568E-04,
516: 'hh' => 3.93015941224568E-04,
517: 'Wh' => 2.93071851047526E-01,
518: 'wh' => 2.93071851047526E-01,
519: 'flb' => 2.50369750774671E+04,
520: 'BTU' => 1.0,
521: 'btu' => 1.0,
522: )
523: ),
524: 'Power' => array( 'HP' => array( 'HP' => 1.0,
525: 'h' => 1.0,
526: 'W' => 7.45701000000000E+02,
527: 'w' => 7.45701000000000E+02
528: ),
529: 'h' => array( 'HP' => 1.0,
530: 'h' => 1.0,
531: 'W' => 7.45701000000000E+02,
532: 'w' => 7.45701000000000E+02
533: ),
534: 'W' => array( 'HP' => 1.34102006031908E-03,
535: 'h' => 1.34102006031908E-03,
536: 'W' => 1.0,
537: 'w' => 1.0
538: ),
539: 'w' => array( 'HP' => 1.34102006031908E-03,
540: 'h' => 1.34102006031908E-03,
541: 'W' => 1.0,
542: 'w' => 1.0
543: )
544: ),
545: 'Magnetism' => array( 'T' => array( 'T' => 1.0,
546: 'ga' => 10000.0
547: ),
548: 'ga' => array( 'T' => 0.0001,
549: 'ga' => 1.0
550: )
551: ),
552: 'Liquid' => array( 'tsp' => array( 'tsp' => 1.0,
553: 'tbs' => 3.33333333333333E-01,
554: 'oz' => 1.66666666666667E-01,
555: 'cup' => 2.08333333333333E-02,
556: 'pt' => 1.04166666666667E-02,
557: 'us_pt' => 1.04166666666667E-02,
558: 'uk_pt' => 8.67558516821960E-03,
559: 'qt' => 5.20833333333333E-03,
560: 'gal' => 1.30208333333333E-03,
561: 'l' => 4.92999408400710E-03,
562: 'lt' => 4.92999408400710E-03
563: ),
564: 'tbs' => array( 'tsp' => 3.00000000000000E+00,
565: 'tbs' => 1.0,
566: 'oz' => 5.00000000000000E-01,
567: 'cup' => 6.25000000000000E-02,
568: 'pt' => 3.12500000000000E-02,
569: 'us_pt' => 3.12500000000000E-02,
570: 'uk_pt' => 2.60267555046588E-02,
571: 'qt' => 1.56250000000000E-02,
572: 'gal' => 3.90625000000000E-03,
573: 'l' => 1.47899822520213E-02,
574: 'lt' => 1.47899822520213E-02
575: ),
576: 'oz' => array( 'tsp' => 6.00000000000000E+00,
577: 'tbs' => 2.00000000000000E+00,
578: 'oz' => 1.0,
579: 'cup' => 1.25000000000000E-01,
580: 'pt' => 6.25000000000000E-02,
581: 'us_pt' => 6.25000000000000E-02,
582: 'uk_pt' => 5.20535110093176E-02,
583: 'qt' => 3.12500000000000E-02,
584: 'gal' => 7.81250000000000E-03,
585: 'l' => 2.95799645040426E-02,
586: 'lt' => 2.95799645040426E-02
587: ),
588: 'cup' => array( 'tsp' => 4.80000000000000E+01,
589: 'tbs' => 1.60000000000000E+01,
590: 'oz' => 8.00000000000000E+00,
591: 'cup' => 1.0,
592: 'pt' => 5.00000000000000E-01,
593: 'us_pt' => 5.00000000000000E-01,
594: 'uk_pt' => 4.16428088074541E-01,
595: 'qt' => 2.50000000000000E-01,
596: 'gal' => 6.25000000000000E-02,
597: 'l' => 2.36639716032341E-01,
598: 'lt' => 2.36639716032341E-01
599: ),
600: 'pt' => array( 'tsp' => 9.60000000000000E+01,
601: 'tbs' => 3.20000000000000E+01,
602: 'oz' => 1.60000000000000E+01,
603: 'cup' => 2.00000000000000E+00,
604: 'pt' => 1.0,
605: 'us_pt' => 1.0,
606: 'uk_pt' => 8.32856176149081E-01,
607: 'qt' => 5.00000000000000E-01,
608: 'gal' => 1.25000000000000E-01,
609: 'l' => 4.73279432064682E-01,
610: 'lt' => 4.73279432064682E-01
611: ),
612: 'us_pt' => array( 'tsp' => 9.60000000000000E+01,
613: 'tbs' => 3.20000000000000E+01,
614: 'oz' => 1.60000000000000E+01,
615: 'cup' => 2.00000000000000E+00,
616: 'pt' => 1.0,
617: 'us_pt' => 1.0,
618: 'uk_pt' => 8.32856176149081E-01,
619: 'qt' => 5.00000000000000E-01,
620: 'gal' => 1.25000000000000E-01,
621: 'l' => 4.73279432064682E-01,
622: 'lt' => 4.73279432064682E-01
623: ),
624: 'uk_pt' => array( 'tsp' => 1.15266000000000E+02,
625: 'tbs' => 3.84220000000000E+01,
626: 'oz' => 1.92110000000000E+01,
627: 'cup' => 2.40137500000000E+00,
628: 'pt' => 1.20068750000000E+00,
629: 'us_pt' => 1.20068750000000E+00,
630: 'uk_pt' => 1.0,
631: 'qt' => 6.00343750000000E-01,
632: 'gal' => 1.50085937500000E-01,
633: 'l' => 5.68260698087162E-01,
634: 'lt' => 5.68260698087162E-01
635: ),
636: 'qt' => array( 'tsp' => 1.92000000000000E+02,
637: 'tbs' => 6.40000000000000E+01,
638: 'oz' => 3.20000000000000E+01,
639: 'cup' => 4.00000000000000E+00,
640: 'pt' => 2.00000000000000E+00,
641: 'us_pt' => 2.00000000000000E+00,
642: 'uk_pt' => 1.66571235229816E+00,
643: 'qt' => 1.0,
644: 'gal' => 2.50000000000000E-01,
645: 'l' => 9.46558864129363E-01,
646: 'lt' => 9.46558864129363E-01
647: ),
648: 'gal' => array( 'tsp' => 7.68000000000000E+02,
649: 'tbs' => 2.56000000000000E+02,
650: 'oz' => 1.28000000000000E+02,
651: 'cup' => 1.60000000000000E+01,
652: 'pt' => 8.00000000000000E+00,
653: 'us_pt' => 8.00000000000000E+00,
654: 'uk_pt' => 6.66284940919265E+00,
655: 'qt' => 4.00000000000000E+00,
656: 'gal' => 1.0,
657: 'l' => 3.78623545651745E+00,
658: 'lt' => 3.78623545651745E+00
659: ),
660: 'l' => array( 'tsp' => 2.02840000000000E+02,
661: 'tbs' => 6.76133333333333E+01,
662: 'oz' => 3.38066666666667E+01,
663: 'cup' => 4.22583333333333E+00,
664: 'pt' => 2.11291666666667E+00,
665: 'us_pt' => 2.11291666666667E+00,
666: 'uk_pt' => 1.75975569552166E+00,
667: 'qt' => 1.05645833333333E+00,
668: 'gal' => 2.64114583333333E-01,
669: 'l' => 1.0,
670: 'lt' => 1.0
671: ),
672: 'lt' => array( 'tsp' => 2.02840000000000E+02,
673: 'tbs' => 6.76133333333333E+01,
674: 'oz' => 3.38066666666667E+01,
675: 'cup' => 4.22583333333333E+00,
676: 'pt' => 2.11291666666667E+00,
677: 'us_pt' => 2.11291666666667E+00,
678: 'uk_pt' => 1.75975569552166E+00,
679: 'qt' => 1.05645833333333E+00,
680: 'gal' => 2.64114583333333E-01,
681: 'l' => 1.0,
682: 'lt' => 1.0
683: )
684: )
685: );
686:
687:
688: /**
689: * _parseComplex
690: *
691: * Parses a complex number into its real and imaginary parts, and an I or J suffix
692: *
693: * @param string $complexNumber The complex number
694: * @return string[] Indexed on "real", "imaginary" and "suffix"
695: */
696: public static function _parseComplex($complexNumber) {
697: $workString = (string) $complexNumber;
698:
699: $realNumber = $imaginary = 0;
700: // Extract the suffix, if there is one
701: $suffix = substr($workString,-1);
702: if (!is_numeric($suffix)) {
703: $workString = substr($workString,0,-1);
704: } else {
705: $suffix = '';
706: }
707:
708: // Split the input into its Real and Imaginary components
709: $leadingSign = 0;
710: if (strlen($workString) > 0) {
711: $leadingSign = (($workString{0} == '+') || ($workString{0} == '-')) ? 1 : 0;
712: }
713: $power = '';
714: $realNumber = strtok($workString, '+-');
715: if (strtoupper(substr($realNumber,-1)) == 'E') {
716: $power = strtok('+-');
717: ++$leadingSign;
718: }
719:
720: $realNumber = substr($workString,0,strlen($realNumber)+strlen($power)+$leadingSign);
721:
722: if ($suffix != '') {
723: $imaginary = substr($workString,strlen($realNumber));
724:
725: if (($imaginary == '') && (($realNumber == '') || ($realNumber == '+') || ($realNumber == '-'))) {
726: $imaginary = $realNumber.'1';
727: $realNumber = '0';
728: } else if ($imaginary == '') {
729: $imaginary = $realNumber;
730: $realNumber = '0';
731: } elseif (($imaginary == '+') || ($imaginary == '-')) {
732: $imaginary .= '1';
733: }
734: }
735:
736: return array( 'real' => $realNumber,
737: 'imaginary' => $imaginary,
738: 'suffix' => $suffix
739: );
740: } // function _parseComplex()
741:
742:
743: /**
744: * Cleans the leading characters in a complex number string
745: *
746: * @param string $complexNumber The complex number to clean
747: * @return string The "cleaned" complex number
748: */
749: private static function _cleanComplex($complexNumber) {
750: if ($complexNumber{0} == '+') $complexNumber = substr($complexNumber,1);
751: if ($complexNumber{0} == '0') $complexNumber = substr($complexNumber,1);
752: if ($complexNumber{0} == '.') $complexNumber = '0'.$complexNumber;
753: if ($complexNumber{0} == '+') $complexNumber = substr($complexNumber,1);
754: return $complexNumber;
755: }
756:
757: /**
758: * Formats a number base string value with leading zeroes
759: *
760: * @param string $xVal The "number" to pad
761: * @param integer $places The length that we want to pad this value
762: * @return string The padded "number"
763: */
764: private static function _nbrConversionFormat($xVal, $places) {
765: if (!is_null($places)) {
766: if (strlen($xVal) <= $places) {
767: return substr(str_pad($xVal, $places, '0', STR_PAD_LEFT), -10);
768: } else {
769: return PHPExcel_Calculation_Functions::NaN();
770: }
771: }
772:
773: return substr($xVal, -10);
774: } // function _nbrConversionFormat()
775:
776: /**
777: * BESSELI
778: *
779: * Returns the modified Bessel function In(x), which is equivalent to the Bessel function evaluated
780: * for purely imaginary arguments
781: *
782: * Excel Function:
783: * BESSELI(x,ord)
784: *
785: * @access public
786: * @category Engineering Functions
787: * @param float $x The value at which to evaluate the function.
788: * If x is nonnumeric, BESSELI returns the #VALUE! error value.
789: * @param integer $ord The order of the Bessel function.
790: * If ord is not an integer, it is truncated.
791: * If $ord is nonnumeric, BESSELI returns the #VALUE! error value.
792: * If $ord < 0, BESSELI returns the #NUM! error value.
793: * @return float
794: *
795: */
796: public static function BESSELI($x, $ord) {
797: $x = (is_null($x)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($x);
798: $ord = (is_null($ord)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($ord);
799:
800: if ((is_numeric($x)) && (is_numeric($ord))) {
801: $ord = floor($ord);
802: if ($ord < 0) {
803: return PHPExcel_Calculation_Functions::NaN();
804: }
805:
806: if (abs($x) <= 30) {
807: $fResult = $fTerm = pow($x / 2, $ord) / PHPExcel_Calculation_MathTrig::FACT($ord);
808: $ordK = 1;
809: $fSqrX = ($x * $x) / 4;
810: do {
811: $fTerm *= $fSqrX;
812: $fTerm /= ($ordK * ($ordK + $ord));
813: $fResult += $fTerm;
814: } while ((abs($fTerm) > 1e-12) && (++$ordK < 100));
815: } else {
816: $f_2_PI = 2 * M_PI;
817:
818: $fXAbs = abs($x);
819: $fResult = exp($fXAbs) / sqrt($f_2_PI * $fXAbs);
820: if (($ord & 1) && ($x < 0)) {
821: $fResult = -$fResult;
822: }
823: }
824: return (is_nan($fResult)) ? PHPExcel_Calculation_Functions::NaN() : $fResult;
825: }
826: return PHPExcel_Calculation_Functions::VALUE();
827: } // function BESSELI()
828:
829:
830: /**
831: * BESSELJ
832: *
833: * Returns the Bessel function
834: *
835: * Excel Function:
836: * BESSELJ(x,ord)
837: *
838: * @access public
839: * @category Engineering Functions
840: * @param float $x The value at which to evaluate the function.
841: * If x is nonnumeric, BESSELJ returns the #VALUE! error value.
842: * @param integer $ord The order of the Bessel function. If n is not an integer, it is truncated.
843: * If $ord is nonnumeric, BESSELJ returns the #VALUE! error value.
844: * If $ord < 0, BESSELJ returns the #NUM! error value.
845: * @return float
846: *
847: */
848: public static function BESSELJ($x, $ord) {
849: $x = (is_null($x)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($x);
850: $ord = (is_null($ord)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($ord);
851:
852: if ((is_numeric($x)) && (is_numeric($ord))) {
853: $ord = floor($ord);
854: if ($ord < 0) {
855: return PHPExcel_Calculation_Functions::NaN();
856: }
857:
858: $fResult = 0;
859: if (abs($x) <= 30) {
860: $fResult = $fTerm = pow($x / 2, $ord) / PHPExcel_Calculation_MathTrig::FACT($ord);
861: $ordK = 1;
862: $fSqrX = ($x * $x) / -4;
863: do {
864: $fTerm *= $fSqrX;
865: $fTerm /= ($ordK * ($ordK + $ord));
866: $fResult += $fTerm;
867: } while ((abs($fTerm) > 1e-12) && (++$ordK < 100));
868: } else {
869: $f_PI_DIV_2 = M_PI / 2;
870: $f_PI_DIV_4 = M_PI / 4;
871:
872: $fXAbs = abs($x);
873: $fResult = sqrt(M_2DIVPI / $fXAbs) * cos($fXAbs - $ord * $f_PI_DIV_2 - $f_PI_DIV_4);
874: if (($ord & 1) && ($x < 0)) {
875: $fResult = -$fResult;
876: }
877: }
878: return (is_nan($fResult)) ? PHPExcel_Calculation_Functions::NaN() : $fResult;
879: }
880: return PHPExcel_Calculation_Functions::VALUE();
881: } // function BESSELJ()
882:
883:
884: private static function _Besselk0($fNum) {
885: if ($fNum <= 2) {
886: $fNum2 = $fNum * 0.5;
887: $y = ($fNum2 * $fNum2);
888: $fRet = -log($fNum2) * self::BESSELI($fNum, 0) +
889: (-0.57721566 + $y * (0.42278420 + $y * (0.23069756 + $y * (0.3488590e-1 + $y * (0.262698e-2 + $y *
890: (0.10750e-3 + $y * 0.74e-5))))));
891: } else {
892: $y = 2 / $fNum;
893: $fRet = exp(-$fNum) / sqrt($fNum) *
894: (1.25331414 + $y * (-0.7832358e-1 + $y * (0.2189568e-1 + $y * (-0.1062446e-1 + $y *
895: (0.587872e-2 + $y * (-0.251540e-2 + $y * 0.53208e-3))))));
896: }
897: return $fRet;
898: } // function _Besselk0()
899:
900:
901: private static function _Besselk1($fNum) {
902: if ($fNum <= 2) {
903: $fNum2 = $fNum * 0.5;
904: $y = ($fNum2 * $fNum2);
905: $fRet = log($fNum2) * self::BESSELI($fNum, 1) +
906: (1 + $y * (0.15443144 + $y * (-0.67278579 + $y * (-0.18156897 + $y * (-0.1919402e-1 + $y *
907: (-0.110404e-2 + $y * (-0.4686e-4))))))) / $fNum;
908: } else {
909: $y = 2 / $fNum;
910: $fRet = exp(-$fNum) / sqrt($fNum) *
911: (1.25331414 + $y * (0.23498619 + $y * (-0.3655620e-1 + $y * (0.1504268e-1 + $y * (-0.780353e-2 + $y *
912: (0.325614e-2 + $y * (-0.68245e-3)))))));
913: }
914: return $fRet;
915: } // function _Besselk1()
916:
917:
918: /**
919: * BESSELK
920: *
921: * Returns the modified Bessel function Kn(x), which is equivalent to the Bessel functions evaluated
922: * for purely imaginary arguments.
923: *
924: * Excel Function:
925: * BESSELK(x,ord)
926: *
927: * @access public
928: * @category Engineering Functions
929: * @param float $x The value at which to evaluate the function.
930: * If x is nonnumeric, BESSELK returns the #VALUE! error value.
931: * @param integer $ord The order of the Bessel function. If n is not an integer, it is truncated.
932: * If $ord is nonnumeric, BESSELK returns the #VALUE! error value.
933: * If $ord < 0, BESSELK returns the #NUM! error value.
934: * @return float
935: *
936: */
937: public static function BESSELK($x, $ord) {
938: $x = (is_null($x)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($x);
939: $ord = (is_null($ord)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($ord);
940:
941: if ((is_numeric($x)) && (is_numeric($ord))) {
942: if (($ord < 0) || ($x == 0.0)) {
943: return PHPExcel_Calculation_Functions::NaN();
944: }
945:
946: switch(floor($ord)) {
947: case 0 : return self::_Besselk0($x);
948: break;
949: case 1 : return self::_Besselk1($x);
950: break;
951: default : $fTox = 2 / $x;
952: $fBkm = self::_Besselk0($x);
953: $fBk = self::_Besselk1($x);
954: for ($n = 1; $n < $ord; ++$n) {
955: $fBkp = $fBkm + $n * $fTox * $fBk;
956: $fBkm = $fBk;
957: $fBk = $fBkp;
958: }
959: }
960: return (is_nan($fBk)) ? PHPExcel_Calculation_Functions::NaN() : $fBk;
961: }
962: return PHPExcel_Calculation_Functions::VALUE();
963: } // function BESSELK()
964:
965:
966: private static function _Bessely0($fNum) {
967: if ($fNum < 8.0) {
968: $y = ($fNum * $fNum);
969: $f1 = -2957821389.0 + $y * (7062834065.0 + $y * (-512359803.6 + $y * (10879881.29 + $y * (-86327.92757 + $y * 228.4622733))));
970: $f2 = 40076544269.0 + $y * (745249964.8 + $y * (7189466.438 + $y * (47447.26470 + $y * (226.1030244 + $y))));
971: $fRet = $f1 / $f2 + 0.636619772 * self::BESSELJ($fNum, 0) * log($fNum);
972: } else {
973: $z = 8.0 / $fNum;
974: $y = ($z * $z);
975: $xx = $fNum - 0.785398164;
976: $f1 = 1 + $y * (-0.1098628627e-2 + $y * (0.2734510407e-4 + $y * (-0.2073370639e-5 + $y * 0.2093887211e-6)));
977: $f2 = -0.1562499995e-1 + $y * (0.1430488765e-3 + $y * (-0.6911147651e-5 + $y * (0.7621095161e-6 + $y * (-0.934945152e-7))));
978: $fRet = sqrt(0.636619772 / $fNum) * (sin($xx) * $f1 + $z * cos($xx) * $f2);
979: }
980: return $fRet;
981: } // function _Bessely0()
982:
983:
984: private static function _Bessely1($fNum) {
985: if ($fNum < 8.0) {
986: $y = ($fNum * $fNum);
987: $f1 = $fNum * (-0.4900604943e13 + $y * (0.1275274390e13 + $y * (-0.5153438139e11 + $y * (0.7349264551e9 + $y *
988: (-0.4237922726e7 + $y * 0.8511937935e4)))));
989: $f2 = 0.2499580570e14 + $y * (0.4244419664e12 + $y * (0.3733650367e10 + $y * (0.2245904002e8 + $y *
990: (0.1020426050e6 + $y * (0.3549632885e3 + $y)))));
991: $fRet = $f1 / $f2 + 0.636619772 * ( self::BESSELJ($fNum, 1) * log($fNum) - 1 / $fNum);
992: } else {
993: $fRet = sqrt(0.636619772 / $fNum) * sin($fNum - 2.356194491);
994: }
995: return $fRet;
996: } // function _Bessely1()
997:
998:
999: /**
1000: * BESSELY
1001: *
1002: * Returns the Bessel function, which is also called the Weber function or the Neumann function.
1003: *
1004: * Excel Function:
1005: * BESSELY(x,ord)
1006: *
1007: * @access public
1008: * @category Engineering Functions
1009: * @param float $x The value at which to evaluate the function.
1010: * If x is nonnumeric, BESSELK returns the #VALUE! error value.
1011: * @param integer $ord The order of the Bessel function. If n is not an integer, it is truncated.
1012: * If $ord is nonnumeric, BESSELK returns the #VALUE! error value.
1013: * If $ord < 0, BESSELK returns the #NUM! error value.
1014: *
1015: * @return float
1016: */
1017: public static function BESSELY($x, $ord) {
1018: $x = (is_null($x)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($x);
1019: $ord = (is_null($ord)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($ord);
1020:
1021: if ((is_numeric($x)) && (is_numeric($ord))) {
1022: if (($ord < 0) || ($x == 0.0)) {
1023: return PHPExcel_Calculation_Functions::NaN();
1024: }
1025:
1026: switch(floor($ord)) {
1027: case 0 : return self::_Bessely0($x);
1028: break;
1029: case 1 : return self::_Bessely1($x);
1030: break;
1031: default: $fTox = 2 / $x;
1032: $fBym = self::_Bessely0($x);
1033: $fBy = self::_Bessely1($x);
1034: for ($n = 1; $n < $ord; ++$n) {
1035: $fByp = $n * $fTox * $fBy - $fBym;
1036: $fBym = $fBy;
1037: $fBy = $fByp;
1038: }
1039: }
1040: return (is_nan($fBy)) ? PHPExcel_Calculation_Functions::NaN() : $fBy;
1041: }
1042: return PHPExcel_Calculation_Functions::VALUE();
1043: } // function BESSELY()
1044:
1045:
1046: /**
1047: * BINTODEC
1048: *
1049: * Return a binary value as decimal.
1050: *
1051: * Excel Function:
1052: * BIN2DEC(x)
1053: *
1054: * @access public
1055: * @category Engineering Functions
1056: * @param string $x The binary number (as a string) that you want to convert. The number
1057: * cannot contain more than 10 characters (10 bits). The most significant
1058: * bit of number is the sign bit. The remaining 9 bits are magnitude bits.
1059: * Negative numbers are represented using two's-complement notation.
1060: * If number is not a valid binary number, or if number contains more than
1061: * 10 characters (10 bits), BIN2DEC returns the #NUM! error value.
1062: * @return string
1063: */
1064: public static function BINTODEC($x) {
1065: $x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
1066:
1067: if (is_bool($x)) {
1068: if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
1069: $x = (int) $x;
1070: } else {
1071: return PHPExcel_Calculation_Functions::VALUE();
1072: }
1073: }
1074: if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
1075: $x = floor($x);
1076: }
1077: $x = (string) $x;
1078: if (strlen($x) > preg_match_all('/[01]/',$x,$out)) {
1079: return PHPExcel_Calculation_Functions::NaN();
1080: }
1081: if (strlen($x) > 10) {
1082: return PHPExcel_Calculation_Functions::NaN();
1083: } elseif (strlen($x) == 10) {
1084: // Two's Complement
1085: $x = substr($x,-9);
1086: return '-'.(512-bindec($x));
1087: }
1088: return bindec($x);
1089: } // function BINTODEC()
1090:
1091:
1092: /**
1093: * BINTOHEX
1094: *
1095: * Return a binary value as hex.
1096: *
1097: * Excel Function:
1098: * BIN2HEX(x[,places])
1099: *
1100: * @access public
1101: * @category Engineering Functions
1102: * @param string $x The binary number (as a string) that you want to convert. The number
1103: * cannot contain more than 10 characters (10 bits). The most significant
1104: * bit of number is the sign bit. The remaining 9 bits are magnitude bits.
1105: * Negative numbers are represented using two's-complement notation.
1106: * If number is not a valid binary number, or if number contains more than
1107: * 10 characters (10 bits), BIN2HEX returns the #NUM! error value.
1108: * @param integer $places The number of characters to use. If places is omitted, BIN2HEX uses the
1109: * minimum number of characters necessary. Places is useful for padding the
1110: * return value with leading 0s (zeros).
1111: * If places is not an integer, it is truncated.
1112: * If places is nonnumeric, BIN2HEX returns the #VALUE! error value.
1113: * If places is negative, BIN2HEX returns the #NUM! error value.
1114: * @return string
1115: */
1116: public static function BINTOHEX($x, $places=NULL) {
1117: $x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
1118: $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
1119:
1120: if (is_bool($x)) {
1121: if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
1122: $x = (int) $x;
1123: } else {
1124: return PHPExcel_Calculation_Functions::VALUE();
1125: }
1126: }
1127: if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
1128: $x = floor($x);
1129: }
1130: $x = (string) $x;
1131: if (strlen($x) > preg_match_all('/[01]/',$x,$out)) {
1132: return PHPExcel_Calculation_Functions::NaN();
1133: }
1134: if (strlen($x) > 10) {
1135: return PHPExcel_Calculation_Functions::NaN();
1136: } elseif (strlen($x) == 10) {
1137: // Two's Complement
1138: return str_repeat('F',8).substr(strtoupper(dechex(bindec(substr($x,-9)))),-2);
1139: }
1140: $hexVal = (string) strtoupper(dechex(bindec($x)));
1141:
1142: return self::_nbrConversionFormat($hexVal,$places);
1143: } // function BINTOHEX()
1144:
1145:
1146: /**
1147: * BINTOOCT
1148: *
1149: * Return a binary value as octal.
1150: *
1151: * Excel Function:
1152: * BIN2OCT(x[,places])
1153: *
1154: * @access public
1155: * @category Engineering Functions
1156: * @param string $x The binary number (as a string) that you want to convert. The number
1157: * cannot contain more than 10 characters (10 bits). The most significant
1158: * bit of number is the sign bit. The remaining 9 bits are magnitude bits.
1159: * Negative numbers are represented using two's-complement notation.
1160: * If number is not a valid binary number, or if number contains more than
1161: * 10 characters (10 bits), BIN2OCT returns the #NUM! error value.
1162: * @param integer $places The number of characters to use. If places is omitted, BIN2OCT uses the
1163: * minimum number of characters necessary. Places is useful for padding the
1164: * return value with leading 0s (zeros).
1165: * If places is not an integer, it is truncated.
1166: * If places is nonnumeric, BIN2OCT returns the #VALUE! error value.
1167: * If places is negative, BIN2OCT returns the #NUM! error value.
1168: * @return string
1169: */
1170: public static function BINTOOCT($x, $places=NULL) {
1171: $x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
1172: $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
1173:
1174: if (is_bool($x)) {
1175: if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
1176: $x = (int) $x;
1177: } else {
1178: return PHPExcel_Calculation_Functions::VALUE();
1179: }
1180: }
1181: if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
1182: $x = floor($x);
1183: }
1184: $x = (string) $x;
1185: if (strlen($x) > preg_match_all('/[01]/',$x,$out)) {
1186: return PHPExcel_Calculation_Functions::NaN();
1187: }
1188: if (strlen($x) > 10) {
1189: return PHPExcel_Calculation_Functions::NaN();
1190: } elseif (strlen($x) == 10) {
1191: // Two's Complement
1192: return str_repeat('7',7).substr(strtoupper(decoct(bindec(substr($x,-9)))),-3);
1193: }
1194: $octVal = (string) decoct(bindec($x));
1195:
1196: return self::_nbrConversionFormat($octVal,$places);
1197: } // function BINTOOCT()
1198:
1199:
1200: /**
1201: * DECTOBIN
1202: *
1203: * Return a decimal value as binary.
1204: *
1205: * Excel Function:
1206: * DEC2BIN(x[,places])
1207: *
1208: * @access public
1209: * @category Engineering Functions
1210: * @param string $x The decimal integer you want to convert. If number is negative,
1211: * valid place values are ignored and DEC2BIN returns a 10-character
1212: * (10-bit) binary number in which the most significant bit is the sign
1213: * bit. The remaining 9 bits are magnitude bits. Negative numbers are
1214: * represented using two's-complement notation.
1215: * If number < -512 or if number > 511, DEC2BIN returns the #NUM! error
1216: * value.
1217: * If number is nonnumeric, DEC2BIN returns the #VALUE! error value.
1218: * If DEC2BIN requires more than places characters, it returns the #NUM!
1219: * error value.
1220: * @param integer $places The number of characters to use. If places is omitted, DEC2BIN uses
1221: * the minimum number of characters necessary. Places is useful for
1222: * padding the return value with leading 0s (zeros).
1223: * If places is not an integer, it is truncated.
1224: * If places is nonnumeric, DEC2BIN returns the #VALUE! error value.
1225: * If places is zero or negative, DEC2BIN returns the #NUM! error value.
1226: * @return string
1227: */
1228: public static function DECTOBIN($x, $places=NULL) {
1229: $x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
1230: $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
1231:
1232: if (is_bool($x)) {
1233: if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
1234: $x = (int) $x;
1235: } else {
1236: return PHPExcel_Calculation_Functions::VALUE();
1237: }
1238: }
1239: $x = (string) $x;
1240: if (strlen($x) > preg_match_all('/[-0123456789.]/',$x,$out)) {
1241: return PHPExcel_Calculation_Functions::VALUE();
1242: }
1243: $x = (string) floor($x);
1244: $r = decbin($x);
1245: if (strlen($r) == 32) {
1246: // Two's Complement
1247: $r = substr($r,-10);
1248: } elseif (strlen($r) > 11) {
1249: return PHPExcel_Calculation_Functions::NaN();
1250: }
1251:
1252: return self::_nbrConversionFormat($r,$places);
1253: } // function DECTOBIN()
1254:
1255:
1256: /**
1257: * DECTOHEX
1258: *
1259: * Return a decimal value as hex.
1260: *
1261: * Excel Function:
1262: * DEC2HEX(x[,places])
1263: *
1264: * @access public
1265: * @category Engineering Functions
1266: * @param string $x The decimal integer you want to convert. If number is negative,
1267: * places is ignored and DEC2HEX returns a 10-character (40-bit)
1268: * hexadecimal number in which the most significant bit is the sign
1269: * bit. The remaining 39 bits are magnitude bits. Negative numbers
1270: * are represented using two's-complement notation.
1271: * If number < -549,755,813,888 or if number > 549,755,813,887,
1272: * DEC2HEX returns the #NUM! error value.
1273: * If number is nonnumeric, DEC2HEX returns the #VALUE! error value.
1274: * If DEC2HEX requires more than places characters, it returns the
1275: * #NUM! error value.
1276: * @param integer $places The number of characters to use. If places is omitted, DEC2HEX uses
1277: * the minimum number of characters necessary. Places is useful for
1278: * padding the return value with leading 0s (zeros).
1279: * If places is not an integer, it is truncated.
1280: * If places is nonnumeric, DEC2HEX returns the #VALUE! error value.
1281: * If places is zero or negative, DEC2HEX returns the #NUM! error value.
1282: * @return string
1283: */
1284: public static function DECTOHEX($x, $places=null) {
1285: $x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
1286: $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
1287:
1288: if (is_bool($x)) {
1289: if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
1290: $x = (int) $x;
1291: } else {
1292: return PHPExcel_Calculation_Functions::VALUE();
1293: }
1294: }
1295: $x = (string) $x;
1296: if (strlen($x) > preg_match_all('/[-0123456789.]/',$x,$out)) {
1297: return PHPExcel_Calculation_Functions::VALUE();
1298: }
1299: $x = (string) floor($x);
1300: $r = strtoupper(dechex($x));
1301: if (strlen($r) == 8) {
1302: // Two's Complement
1303: $r = 'FF'.$r;
1304: }
1305:
1306: return self::_nbrConversionFormat($r,$places);
1307: } // function DECTOHEX()
1308:
1309:
1310: /**
1311: * DECTOOCT
1312: *
1313: * Return an decimal value as octal.
1314: *
1315: * Excel Function:
1316: * DEC2OCT(x[,places])
1317: *
1318: * @access public
1319: * @category Engineering Functions
1320: * @param string $x The decimal integer you want to convert. If number is negative,
1321: * places is ignored and DEC2OCT returns a 10-character (30-bit)
1322: * octal number in which the most significant bit is the sign bit.
1323: * The remaining 29 bits are magnitude bits. Negative numbers are
1324: * represented using two's-complement notation.
1325: * If number < -536,870,912 or if number > 536,870,911, DEC2OCT
1326: * returns the #NUM! error value.
1327: * If number is nonnumeric, DEC2OCT returns the #VALUE! error value.
1328: * If DEC2OCT requires more than places characters, it returns the
1329: * #NUM! error value.
1330: * @param integer $places The number of characters to use. If places is omitted, DEC2OCT uses
1331: * the minimum number of characters necessary. Places is useful for
1332: * padding the return value with leading 0s (zeros).
1333: * If places is not an integer, it is truncated.
1334: * If places is nonnumeric, DEC2OCT returns the #VALUE! error value.
1335: * If places is zero or negative, DEC2OCT returns the #NUM! error value.
1336: * @return string
1337: */
1338: public static function DECTOOCT($x, $places=null) {
1339: $x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
1340: $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
1341:
1342: if (is_bool($x)) {
1343: if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
1344: $x = (int) $x;
1345: } else {
1346: return PHPExcel_Calculation_Functions::VALUE();
1347: }
1348: }
1349: $x = (string) $x;
1350: if (strlen($x) > preg_match_all('/[-0123456789.]/',$x,$out)) {
1351: return PHPExcel_Calculation_Functions::VALUE();
1352: }
1353: $x = (string) floor($x);
1354: $r = decoct($x);
1355: if (strlen($r) == 11) {
1356: // Two's Complement
1357: $r = substr($r,-10);
1358: }
1359:
1360: return self::_nbrConversionFormat($r,$places);
1361: } // function DECTOOCT()
1362:
1363:
1364: /**
1365: * HEXTOBIN
1366: *
1367: * Return a hex value as binary.
1368: *
1369: * Excel Function:
1370: * HEX2BIN(x[,places])
1371: *
1372: * @access public
1373: * @category Engineering Functions
1374: * @param string $x the hexadecimal number you want to convert. Number cannot
1375: * contain more than 10 characters. The most significant bit of
1376: * number is the sign bit (40th bit from the right). The remaining
1377: * 9 bits are magnitude bits. Negative numbers are represented
1378: * using two's-complement notation.
1379: * If number is negative, HEX2BIN ignores places and returns a
1380: * 10-character binary number.
1381: * If number is negative, it cannot be less than FFFFFFFE00, and
1382: * if number is positive, it cannot be greater than 1FF.
1383: * If number is not a valid hexadecimal number, HEX2BIN returns
1384: * the #NUM! error value.
1385: * If HEX2BIN requires more than places characters, it returns
1386: * the #NUM! error value.
1387: * @param integer $places The number of characters to use. If places is omitted,
1388: * HEX2BIN uses the minimum number of characters necessary. Places
1389: * is useful for padding the return value with leading 0s (zeros).
1390: * If places is not an integer, it is truncated.
1391: * If places is nonnumeric, HEX2BIN returns the #VALUE! error value.
1392: * If places is negative, HEX2BIN returns the #NUM! error value.
1393: * @return string
1394: */
1395: public static function HEXTOBIN($x, $places=null) {
1396: $x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
1397: $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
1398:
1399: if (is_bool($x)) {
1400: return PHPExcel_Calculation_Functions::VALUE();
1401: }
1402: $x = (string) $x;
1403: if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/',strtoupper($x),$out)) {
1404: return PHPExcel_Calculation_Functions::NaN();
1405: }
1406: $binVal = decbin(hexdec($x));
1407:
1408: return substr(self::_nbrConversionFormat($binVal,$places),-10);
1409: } // function HEXTOBIN()
1410:
1411:
1412: /**
1413: * HEXTODEC
1414: *
1415: * Return a hex value as decimal.
1416: *
1417: * Excel Function:
1418: * HEX2DEC(x)
1419: *
1420: * @access public
1421: * @category Engineering Functions
1422: * @param string $x The hexadecimal number you want to convert. This number cannot
1423: * contain more than 10 characters (40 bits). The most significant
1424: * bit of number is the sign bit. The remaining 39 bits are magnitude
1425: * bits. Negative numbers are represented using two's-complement
1426: * notation.
1427: * If number is not a valid hexadecimal number, HEX2DEC returns the
1428: * #NUM! error value.
1429: * @return string
1430: */
1431: public static function HEXTODEC($x) {
1432: $x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
1433:
1434: if (is_bool($x)) {
1435: return PHPExcel_Calculation_Functions::VALUE();
1436: }
1437: $x = (string) $x;
1438: if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/',strtoupper($x),$out)) {
1439: return PHPExcel_Calculation_Functions::NaN();
1440: }
1441: return hexdec($x);
1442: } // function HEXTODEC()
1443:
1444:
1445: /**
1446: * HEXTOOCT
1447: *
1448: * Return a hex value as octal.
1449: *
1450: * Excel Function:
1451: * HEX2OCT(x[,places])
1452: *
1453: * @access public
1454: * @category Engineering Functions
1455: * @param string $x The hexadecimal number you want to convert. Number cannot
1456: * contain more than 10 characters. The most significant bit of
1457: * number is the sign bit. The remaining 39 bits are magnitude
1458: * bits. Negative numbers are represented using two's-complement
1459: * notation.
1460: * If number is negative, HEX2OCT ignores places and returns a
1461: * 10-character octal number.
1462: * If number is negative, it cannot be less than FFE0000000, and
1463: * if number is positive, it cannot be greater than 1FFFFFFF.
1464: * If number is not a valid hexadecimal number, HEX2OCT returns
1465: * the #NUM! error value.
1466: * If HEX2OCT requires more than places characters, it returns
1467: * the #NUM! error value.
1468: * @param integer $places The number of characters to use. If places is omitted, HEX2OCT
1469: * uses the minimum number of characters necessary. Places is
1470: * useful for padding the return value with leading 0s (zeros).
1471: * If places is not an integer, it is truncated.
1472: * If places is nonnumeric, HEX2OCT returns the #VALUE! error
1473: * value.
1474: * If places is negative, HEX2OCT returns the #NUM! error value.
1475: * @return string
1476: */
1477: public static function HEXTOOCT($x, $places=null) {
1478: $x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
1479: $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
1480:
1481: if (is_bool($x)) {
1482: return PHPExcel_Calculation_Functions::VALUE();
1483: }
1484: $x = (string) $x;
1485: if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/',strtoupper($x),$out)) {
1486: return PHPExcel_Calculation_Functions::NaN();
1487: }
1488: $octVal = decoct(hexdec($x));
1489:
1490: return self::_nbrConversionFormat($octVal,$places);
1491: } // function HEXTOOCT()
1492:
1493:
1494: /**
1495: * OCTTOBIN
1496: *
1497: * Return an octal value as binary.
1498: *
1499: * Excel Function:
1500: * OCT2BIN(x[,places])
1501: *
1502: * @access public
1503: * @category Engineering Functions
1504: * @param string $x The octal number you want to convert. Number may not
1505: * contain more than 10 characters. The most significant
1506: * bit of number is the sign bit. The remaining 29 bits
1507: * are magnitude bits. Negative numbers are represented
1508: * using two's-complement notation.
1509: * If number is negative, OCT2BIN ignores places and returns
1510: * a 10-character binary number.
1511: * If number is negative, it cannot be less than 7777777000,
1512: * and if number is positive, it cannot be greater than 777.
1513: * If number is not a valid octal number, OCT2BIN returns
1514: * the #NUM! error value.
1515: * If OCT2BIN requires more than places characters, it
1516: * returns the #NUM! error value.
1517: * @param integer $places The number of characters to use. If places is omitted,
1518: * OCT2BIN uses the minimum number of characters necessary.
1519: * Places is useful for padding the return value with
1520: * leading 0s (zeros).
1521: * If places is not an integer, it is truncated.
1522: * If places is nonnumeric, OCT2BIN returns the #VALUE!
1523: * error value.
1524: * If places is negative, OCT2BIN returns the #NUM! error
1525: * value.
1526: * @return string
1527: */
1528: public static function OCTTOBIN($x, $places=null) {
1529: $x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
1530: $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
1531:
1532: if (is_bool($x)) {
1533: return PHPExcel_Calculation_Functions::VALUE();
1534: }
1535: $x = (string) $x;
1536: if (preg_match_all('/[01234567]/',$x,$out) != strlen($x)) {
1537: return PHPExcel_Calculation_Functions::NaN();
1538: }
1539: $r = decbin(octdec($x));
1540:
1541: return self::_nbrConversionFormat($r,$places);
1542: } // function OCTTOBIN()
1543:
1544:
1545: /**
1546: * OCTTODEC
1547: *
1548: * Return an octal value as decimal.
1549: *
1550: * Excel Function:
1551: * OCT2DEC(x)
1552: *
1553: * @access public
1554: * @category Engineering Functions
1555: * @param string $x The octal number you want to convert. Number may not contain
1556: * more than 10 octal characters (30 bits). The most significant
1557: * bit of number is the sign bit. The remaining 29 bits are
1558: * magnitude bits. Negative numbers are represented using
1559: * two's-complement notation.
1560: * If number is not a valid octal number, OCT2DEC returns the
1561: * #NUM! error value.
1562: * @return string
1563: */
1564: public static function OCTTODEC($x) {
1565: $x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
1566:
1567: if (is_bool($x)) {
1568: return PHPExcel_Calculation_Functions::VALUE();
1569: }
1570: $x = (string) $x;
1571: if (preg_match_all('/[01234567]/',$x,$out) != strlen($x)) {
1572: return PHPExcel_Calculation_Functions::NaN();
1573: }
1574: return octdec($x);
1575: } // function OCTTODEC()
1576:
1577:
1578: /**
1579: * OCTTOHEX
1580: *
1581: * Return an octal value as hex.
1582: *
1583: * Excel Function:
1584: * OCT2HEX(x[,places])
1585: *
1586: * @access public
1587: * @category Engineering Functions
1588: * @param string $x The octal number you want to convert. Number may not contain
1589: * more than 10 octal characters (30 bits). The most significant
1590: * bit of number is the sign bit. The remaining 29 bits are
1591: * magnitude bits. Negative numbers are represented using
1592: * two's-complement notation.
1593: * If number is negative, OCT2HEX ignores places and returns a
1594: * 10-character hexadecimal number.
1595: * If number is not a valid octal number, OCT2HEX returns the
1596: * #NUM! error value.
1597: * If OCT2HEX requires more than places characters, it returns
1598: * the #NUM! error value.
1599: * @param integer $places The number of characters to use. If places is omitted, OCT2HEX
1600: * uses the minimum number of characters necessary. Places is useful
1601: * for padding the return value with leading 0s (zeros).
1602: * If places is not an integer, it is truncated.
1603: * If places is nonnumeric, OCT2HEX returns the #VALUE! error value.
1604: * If places is negative, OCT2HEX returns the #NUM! error value.
1605: * @return string
1606: */
1607: public static function OCTTOHEX($x, $places=null) {
1608: $x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
1609: $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
1610:
1611: if (is_bool($x)) {
1612: return PHPExcel_Calculation_Functions::VALUE();
1613: }
1614: $x = (string) $x;
1615: if (preg_match_all('/[01234567]/',$x,$out) != strlen($x)) {
1616: return PHPExcel_Calculation_Functions::NaN();
1617: }
1618: $hexVal = strtoupper(dechex(octdec($x)));
1619:
1620: return self::_nbrConversionFormat($hexVal,$places);
1621: } // function OCTTOHEX()
1622:
1623:
1624: /**
1625: * COMPLEX
1626: *
1627: * Converts real and imaginary coefficients into a complex number of the form x + yi or x + yj.
1628: *
1629: * Excel Function:
1630: * COMPLEX(realNumber,imaginary[,places])
1631: *
1632: * @access public
1633: * @category Engineering Functions
1634: * @param float $realNumber The real coefficient of the complex number.
1635: * @param float $imaginary The imaginary coefficient of the complex number.
1636: * @param string $suffix The suffix for the imaginary component of the complex number.
1637: * If omitted, the suffix is assumed to be "i".
1638: * @return string
1639: */
1640: public static function COMPLEX($realNumber=0.0, $imaginary=0.0, $suffix='i') {
1641: $realNumber = (is_null($realNumber)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($realNumber);
1642: $imaginary = (is_null($imaginary)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($imaginary);
1643: $suffix = (is_null($suffix)) ? 'i' : PHPExcel_Calculation_Functions::flattenSingleValue($suffix);
1644:
1645: if (((is_numeric($realNumber)) && (is_numeric($imaginary))) &&
1646: (($suffix == 'i') || ($suffix == 'j') || ($suffix == ''))) {
1647: $realNumber = (float) $realNumber;
1648: $imaginary = (float) $imaginary;
1649:
1650: if ($suffix == '') $suffix = 'i';
1651: if ($realNumber == 0.0) {
1652: if ($imaginary == 0.0) {
1653: return (string) '0';
1654: } elseif ($imaginary == 1.0) {
1655: return (string) $suffix;
1656: } elseif ($imaginary == -1.0) {
1657: return (string) '-'.$suffix;
1658: }
1659: return (string) $imaginary.$suffix;
1660: } elseif ($imaginary == 0.0) {
1661: return (string) $realNumber;
1662: } elseif ($imaginary == 1.0) {
1663: return (string) $realNumber.'+'.$suffix;
1664: } elseif ($imaginary == -1.0) {
1665: return (string) $realNumber.'-'.$suffix;
1666: }
1667: if ($imaginary > 0) { $imaginary = (string) '+'.$imaginary; }
1668: return (string) $realNumber.$imaginary.$suffix;
1669: }
1670:
1671: return PHPExcel_Calculation_Functions::VALUE();
1672: } // function COMPLEX()
1673:
1674:
1675: /**
1676: * IMAGINARY
1677: *
1678: * Returns the imaginary coefficient of a complex number in x + yi or x + yj text format.
1679: *
1680: * Excel Function:
1681: * IMAGINARY(complexNumber)
1682: *
1683: * @access public
1684: * @category Engineering Functions
1685: * @param string $complexNumber The complex number for which you want the imaginary
1686: * coefficient.
1687: * @return float
1688: */
1689: public static function IMAGINARY($complexNumber) {
1690: $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1691:
1692: $parsedComplex = self::_parseComplex($complexNumber);
1693: return $parsedComplex['imaginary'];
1694: } // function IMAGINARY()
1695:
1696:
1697: /**
1698: * IMREAL
1699: *
1700: * Returns the real coefficient of a complex number in x + yi or x + yj text format.
1701: *
1702: * Excel Function:
1703: * IMREAL(complexNumber)
1704: *
1705: * @access public
1706: * @category Engineering Functions
1707: * @param string $complexNumber The complex number for which you want the real coefficient.
1708: * @return float
1709: */
1710: public static function IMREAL($complexNumber) {
1711: $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1712:
1713: $parsedComplex = self::_parseComplex($complexNumber);
1714: return $parsedComplex['real'];
1715: } // function IMREAL()
1716:
1717:
1718: /**
1719: * IMABS
1720: *
1721: * Returns the absolute value (modulus) of a complex number in x + yi or x + yj text format.
1722: *
1723: * Excel Function:
1724: * IMABS(complexNumber)
1725: *
1726: * @param string $complexNumber The complex number for which you want the absolute value.
1727: * @return float
1728: */
1729: public static function IMABS($complexNumber) {
1730: $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1731:
1732: $parsedComplex = self::_parseComplex($complexNumber);
1733:
1734: return sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary']));
1735: } // function IMABS()
1736:
1737:
1738: /**
1739: * IMARGUMENT
1740: *
1741: * Returns the argument theta of a complex number, i.e. the angle in radians from the real
1742: * axis to the representation of the number in polar coordinates.
1743: *
1744: * Excel Function:
1745: * IMARGUMENT(complexNumber)
1746: *
1747: * @param string $complexNumber The complex number for which you want the argument theta.
1748: * @return float
1749: */
1750: public static function IMARGUMENT($complexNumber) {
1751: $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1752:
1753: $parsedComplex = self::_parseComplex($complexNumber);
1754:
1755: if ($parsedComplex['real'] == 0.0) {
1756: if ($parsedComplex['imaginary'] == 0.0) {
1757: return 0.0;
1758: } elseif($parsedComplex['imaginary'] < 0.0) {
1759: return M_PI / -2;
1760: } else {
1761: return M_PI / 2;
1762: }
1763: } elseif ($parsedComplex['real'] > 0.0) {
1764: return atan($parsedComplex['imaginary'] / $parsedComplex['real']);
1765: } elseif ($parsedComplex['imaginary'] < 0.0) {
1766: return 0 - (M_PI - atan(abs($parsedComplex['imaginary']) / abs($parsedComplex['real'])));
1767: } else {
1768: return M_PI - atan($parsedComplex['imaginary'] / abs($parsedComplex['real']));
1769: }
1770: } // function IMARGUMENT()
1771:
1772:
1773: /**
1774: * IMCONJUGATE
1775: *
1776: * Returns the complex conjugate of a complex number in x + yi or x + yj text format.
1777: *
1778: * Excel Function:
1779: * IMCONJUGATE(complexNumber)
1780: *
1781: * @param string $complexNumber The complex number for which you want the conjugate.
1782: * @return string
1783: */
1784: public static function IMCONJUGATE($complexNumber) {
1785: $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1786:
1787: $parsedComplex = self::_parseComplex($complexNumber);
1788:
1789: if ($parsedComplex['imaginary'] == 0.0) {
1790: return $parsedComplex['real'];
1791: } else {
1792: return self::_cleanComplex( self::COMPLEX( $parsedComplex['real'],
1793: 0 - $parsedComplex['imaginary'],
1794: $parsedComplex['suffix']
1795: )
1796: );
1797: }
1798: } // function IMCONJUGATE()
1799:
1800:
1801: /**
1802: * IMCOS
1803: *
1804: * Returns the cosine of a complex number in x + yi or x + yj text format.
1805: *
1806: * Excel Function:
1807: * IMCOS(complexNumber)
1808: *
1809: * @param string $complexNumber The complex number for which you want the cosine.
1810: * @return string|float
1811: */
1812: public static function IMCOS($complexNumber) {
1813: $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1814:
1815: $parsedComplex = self::_parseComplex($complexNumber);
1816:
1817: if ($parsedComplex['imaginary'] == 0.0) {
1818: return cos($parsedComplex['real']);
1819: } else {
1820: return self::IMCONJUGATE(self::COMPLEX(cos($parsedComplex['real']) * cosh($parsedComplex['imaginary']),sin($parsedComplex['real']) * sinh($parsedComplex['imaginary']),$parsedComplex['suffix']));
1821: }
1822: } // function IMCOS()
1823:
1824:
1825: /**
1826: * IMSIN
1827: *
1828: * Returns the sine of a complex number in x + yi or x + yj text format.
1829: *
1830: * Excel Function:
1831: * IMSIN(complexNumber)
1832: *
1833: * @param string $complexNumber The complex number for which you want the sine.
1834: * @return string|float
1835: */
1836: public static function IMSIN($complexNumber) {
1837: $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1838:
1839: $parsedComplex = self::_parseComplex($complexNumber);
1840:
1841: if ($parsedComplex['imaginary'] == 0.0) {
1842: return sin($parsedComplex['real']);
1843: } else {
1844: return self::COMPLEX(sin($parsedComplex['real']) * cosh($parsedComplex['imaginary']),cos($parsedComplex['real']) * sinh($parsedComplex['imaginary']),$parsedComplex['suffix']);
1845: }
1846: } // function IMSIN()
1847:
1848:
1849: /**
1850: * IMSQRT
1851: *
1852: * Returns the square root of a complex number in x + yi or x + yj text format.
1853: *
1854: * Excel Function:
1855: * IMSQRT(complexNumber)
1856: *
1857: * @param string $complexNumber The complex number for which you want the square root.
1858: * @return string
1859: */
1860: public static function IMSQRT($complexNumber) {
1861: $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1862:
1863: $parsedComplex = self::_parseComplex($complexNumber);
1864:
1865: $theta = self::IMARGUMENT($complexNumber);
1866: $d1 = cos($theta / 2);
1867: $d2 = sin($theta / 2);
1868: $r = sqrt(sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary'])));
1869:
1870: if ($parsedComplex['suffix'] == '') {
1871: return self::COMPLEX($d1 * $r,$d2 * $r);
1872: } else {
1873: return self::COMPLEX($d1 * $r,$d2 * $r,$parsedComplex['suffix']);
1874: }
1875: } // function IMSQRT()
1876:
1877:
1878: /**
1879: * IMLN
1880: *
1881: * Returns the natural logarithm of a complex number in x + yi or x + yj text format.
1882: *
1883: * Excel Function:
1884: * IMLN(complexNumber)
1885: *
1886: * @param string $complexNumber The complex number for which you want the natural logarithm.
1887: * @return string
1888: */
1889: public static function IMLN($complexNumber) {
1890: $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1891:
1892: $parsedComplex = self::_parseComplex($complexNumber);
1893:
1894: if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
1895: return PHPExcel_Calculation_Functions::NaN();
1896: }
1897:
1898: $logR = log(sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary'])));
1899: $t = self::IMARGUMENT($complexNumber);
1900:
1901: if ($parsedComplex['suffix'] == '') {
1902: return self::COMPLEX($logR,$t);
1903: } else {
1904: return self::COMPLEX($logR,$t,$parsedComplex['suffix']);
1905: }
1906: } // function IMLN()
1907:
1908:
1909: /**
1910: * IMLOG10
1911: *
1912: * Returns the common logarithm (base 10) of a complex number in x + yi or x + yj text format.
1913: *
1914: * Excel Function:
1915: * IMLOG10(complexNumber)
1916: *
1917: * @param string $complexNumber The complex number for which you want the common logarithm.
1918: * @return string
1919: */
1920: public static function IMLOG10($complexNumber) {
1921: $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1922:
1923: $parsedComplex = self::_parseComplex($complexNumber);
1924:
1925: if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
1926: return PHPExcel_Calculation_Functions::NaN();
1927: } elseif (($parsedComplex['real'] > 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
1928: return log10($parsedComplex['real']);
1929: }
1930:
1931: return self::IMPRODUCT(log10(EULER),self::IMLN($complexNumber));
1932: } // function IMLOG10()
1933:
1934:
1935: /**
1936: * IMLOG2
1937: *
1938: * Returns the base-2 logarithm of a complex number in x + yi or x + yj text format.
1939: *
1940: * Excel Function:
1941: * IMLOG2(complexNumber)
1942: *
1943: * @param string $complexNumber The complex number for which you want the base-2 logarithm.
1944: * @return string
1945: */
1946: public static function IMLOG2($complexNumber) {
1947: $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1948:
1949: $parsedComplex = self::_parseComplex($complexNumber);
1950:
1951: if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
1952: return PHPExcel_Calculation_Functions::NaN();
1953: } elseif (($parsedComplex['real'] > 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
1954: return log($parsedComplex['real'],2);
1955: }
1956:
1957: return self::IMPRODUCT(log(EULER,2),self::IMLN($complexNumber));
1958: } // function IMLOG2()
1959:
1960:
1961: /**
1962: * IMEXP
1963: *
1964: * Returns the exponential of a complex number in x + yi or x + yj text format.
1965: *
1966: * Excel Function:
1967: * IMEXP(complexNumber)
1968: *
1969: * @param string $complexNumber The complex number for which you want the exponential.
1970: * @return string
1971: */
1972: public static function IMEXP($complexNumber) {
1973: $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
1974:
1975: $parsedComplex = self::_parseComplex($complexNumber);
1976:
1977: if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
1978: return '1';
1979: }
1980:
1981: $e = exp($parsedComplex['real']);
1982: $eX = $e * cos($parsedComplex['imaginary']);
1983: $eY = $e * sin($parsedComplex['imaginary']);
1984:
1985: if ($parsedComplex['suffix'] == '') {
1986: return self::COMPLEX($eX,$eY);
1987: } else {
1988: return self::COMPLEX($eX,$eY,$parsedComplex['suffix']);
1989: }
1990: } // function IMEXP()
1991:
1992:
1993: /**
1994: * IMPOWER
1995: *
1996: * Returns a complex number in x + yi or x + yj text format raised to a power.
1997: *
1998: * Excel Function:
1999: * IMPOWER(complexNumber,realNumber)
2000: *
2001: * @param string $complexNumber The complex number you want to raise to a power.
2002: * @param float $realNumber The power to which you want to raise the complex number.
2003: * @return string
2004: */
2005: public static function IMPOWER($complexNumber,$realNumber) {
2006: $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
2007: $realNumber = PHPExcel_Calculation_Functions::flattenSingleValue($realNumber);
2008:
2009: if (!is_numeric($realNumber)) {
2010: return PHPExcel_Calculation_Functions::VALUE();
2011: }
2012:
2013: $parsedComplex = self::_parseComplex($complexNumber);
2014:
2015: $r = sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary']));
2016: $rPower = pow($r,$realNumber);
2017: $theta = self::IMARGUMENT($complexNumber) * $realNumber;
2018: if ($theta == 0) {
2019: return 1;
2020: } elseif ($parsedComplex['imaginary'] == 0.0) {
2021: return self::COMPLEX($rPower * cos($theta),$rPower * sin($theta),$parsedComplex['suffix']);
2022: } else {
2023: return self::COMPLEX($rPower * cos($theta),$rPower * sin($theta),$parsedComplex['suffix']);
2024: }
2025: } // function IMPOWER()
2026:
2027:
2028: /**
2029: * IMDIV
2030: *
2031: * Returns the quotient of two complex numbers in x + yi or x + yj text format.
2032: *
2033: * Excel Function:
2034: * IMDIV(complexDividend,complexDivisor)
2035: *
2036: * @param string $complexDividend The complex numerator or dividend.
2037: * @param string $complexDivisor The complex denominator or divisor.
2038: * @return string
2039: */
2040: public static function IMDIV($complexDividend,$complexDivisor) {
2041: $complexDividend = PHPExcel_Calculation_Functions::flattenSingleValue($complexDividend);
2042: $complexDivisor = PHPExcel_Calculation_Functions::flattenSingleValue($complexDivisor);
2043:
2044: $parsedComplexDividend = self::_parseComplex($complexDividend);
2045: $parsedComplexDivisor = self::_parseComplex($complexDivisor);
2046:
2047: if (($parsedComplexDividend['suffix'] != '') && ($parsedComplexDivisor['suffix'] != '') &&
2048: ($parsedComplexDividend['suffix'] != $parsedComplexDivisor['suffix'])) {
2049: return PHPExcel_Calculation_Functions::NaN();
2050: }
2051: if (($parsedComplexDividend['suffix'] != '') && ($parsedComplexDivisor['suffix'] == '')) {
2052: $parsedComplexDivisor['suffix'] = $parsedComplexDividend['suffix'];
2053: }
2054:
2055: $d1 = ($parsedComplexDividend['real'] * $parsedComplexDivisor['real']) + ($parsedComplexDividend['imaginary'] * $parsedComplexDivisor['imaginary']);
2056: $d2 = ($parsedComplexDividend['imaginary'] * $parsedComplexDivisor['real']) - ($parsedComplexDividend['real'] * $parsedComplexDivisor['imaginary']);
2057: $d3 = ($parsedComplexDivisor['real'] * $parsedComplexDivisor['real']) + ($parsedComplexDivisor['imaginary'] * $parsedComplexDivisor['imaginary']);
2058:
2059: $r = $d1/$d3;
2060: $i = $d2/$d3;
2061:
2062: if ($i > 0.0) {
2063: return self::_cleanComplex($r.'+'.$i.$parsedComplexDivisor['suffix']);
2064: } elseif ($i < 0.0) {
2065: return self::_cleanComplex($r.$i.$parsedComplexDivisor['suffix']);
2066: } else {
2067: return $r;
2068: }
2069: } // function IMDIV()
2070:
2071:
2072: /**
2073: * IMSUB
2074: *
2075: * Returns the difference of two complex numbers in x + yi or x + yj text format.
2076: *
2077: * Excel Function:
2078: * IMSUB(complexNumber1,complexNumber2)
2079: *
2080: * @param string $complexNumber1 The complex number from which to subtract complexNumber2.
2081: * @param string $complexNumber2 The complex number to subtract from complexNumber1.
2082: * @return string
2083: */
2084: public static function IMSUB($complexNumber1,$complexNumber2) {
2085: $complexNumber1 = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber1);
2086: $complexNumber2 = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber2);
2087:
2088: $parsedComplex1 = self::_parseComplex($complexNumber1);
2089: $parsedComplex2 = self::_parseComplex($complexNumber2);
2090:
2091: if ((($parsedComplex1['suffix'] != '') && ($parsedComplex2['suffix'] != '')) &&
2092: ($parsedComplex1['suffix'] != $parsedComplex2['suffix'])) {
2093: return PHPExcel_Calculation_Functions::NaN();
2094: } elseif (($parsedComplex1['suffix'] == '') && ($parsedComplex2['suffix'] != '')) {
2095: $parsedComplex1['suffix'] = $parsedComplex2['suffix'];
2096: }
2097:
2098: $d1 = $parsedComplex1['real'] - $parsedComplex2['real'];
2099: $d2 = $parsedComplex1['imaginary'] - $parsedComplex2['imaginary'];
2100:
2101: return self::COMPLEX($d1,$d2,$parsedComplex1['suffix']);
2102: } // function IMSUB()
2103:
2104:
2105: /**
2106: * IMSUM
2107: *
2108: * Returns the sum of two or more complex numbers in x + yi or x + yj text format.
2109: *
2110: * Excel Function:
2111: * IMSUM(complexNumber[,complexNumber[,...]])
2112: *
2113: * @param string $complexNumber,... Series of complex numbers to add
2114: * @return string
2115: */
2116: public static function IMSUM() {
2117: // Return value
2118: $returnValue = self::_parseComplex('0');
2119: $activeSuffix = '';
2120:
2121: // Loop through the arguments
2122: $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
2123: foreach ($aArgs as $arg) {
2124: $parsedComplex = self::_parseComplex($arg);
2125:
2126: if ($activeSuffix == '') {
2127: $activeSuffix = $parsedComplex['suffix'];
2128: } elseif (($parsedComplex['suffix'] != '') && ($activeSuffix != $parsedComplex['suffix'])) {
2129: return PHPExcel_Calculation_Functions::VALUE();
2130: }
2131:
2132: $returnValue['real'] += $parsedComplex['real'];
2133: $returnValue['imaginary'] += $parsedComplex['imaginary'];
2134: }
2135:
2136: if ($returnValue['imaginary'] == 0.0) { $activeSuffix = ''; }
2137: return self::COMPLEX($returnValue['real'],$returnValue['imaginary'],$activeSuffix);
2138: } // function IMSUM()
2139:
2140:
2141: /**
2142: * IMPRODUCT
2143: *
2144: * Returns the product of two or more complex numbers in x + yi or x + yj text format.
2145: *
2146: * Excel Function:
2147: * IMPRODUCT(complexNumber[,complexNumber[,...]])
2148: *
2149: * @param string $complexNumber,... Series of complex numbers to multiply
2150: * @return string
2151: */
2152: public static function IMPRODUCT() {
2153: // Return value
2154: $returnValue = self::_parseComplex('1');
2155: $activeSuffix = '';
2156:
2157: // Loop through the arguments
2158: $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
2159: foreach ($aArgs as $arg) {
2160: $parsedComplex = self::_parseComplex($arg);
2161:
2162: $workValue = $returnValue;
2163: if (($parsedComplex['suffix'] != '') && ($activeSuffix == '')) {
2164: $activeSuffix = $parsedComplex['suffix'];
2165: } elseif (($parsedComplex['suffix'] != '') && ($activeSuffix != $parsedComplex['suffix'])) {
2166: return PHPExcel_Calculation_Functions::NaN();
2167: }
2168: $returnValue['real'] = ($workValue['real'] * $parsedComplex['real']) - ($workValue['imaginary'] * $parsedComplex['imaginary']);
2169: $returnValue['imaginary'] = ($workValue['real'] * $parsedComplex['imaginary']) + ($workValue['imaginary'] * $parsedComplex['real']);
2170: }
2171:
2172: if ($returnValue['imaginary'] == 0.0) { $activeSuffix = ''; }
2173: return self::COMPLEX($returnValue['real'],$returnValue['imaginary'],$activeSuffix);
2174: } // function IMPRODUCT()
2175:
2176:
2177: /**
2178: * DELTA
2179: *
2180: * Tests whether two values are equal. Returns 1 if number1 = number2; returns 0 otherwise.
2181: * Use this function to filter a set of values. For example, by summing several DELTA
2182: * functions you calculate the count of equal pairs. This function is also known as the
2183: * Kronecker Delta function.
2184: *
2185: * Excel Function:
2186: * DELTA(a[,b])
2187: *
2188: * @param float $a The first number.
2189: * @param float $b The second number. If omitted, b is assumed to be zero.
2190: * @return int
2191: */
2192: public static function DELTA($a, $b=0) {
2193: $a = PHPExcel_Calculation_Functions::flattenSingleValue($a);
2194: $b = PHPExcel_Calculation_Functions::flattenSingleValue($b);
2195:
2196: return (int) ($a == $b);
2197: } // function DELTA()
2198:
2199:
2200: /**
2201: * GESTEP
2202: *
2203: * Excel Function:
2204: * GESTEP(number[,step])
2205: *
2206: * Returns 1 if number >= step; returns 0 (zero) otherwise
2207: * Use this function to filter a set of values. For example, by summing several GESTEP
2208: * functions you calculate the count of values that exceed a threshold.
2209: *
2210: * @param float $number The value to test against step.
2211: * @param float $step The threshold value.
2212: * If you omit a value for step, GESTEP uses zero.
2213: * @return int
2214: */
2215: public static function GESTEP($number, $step=0) {
2216: $number = PHPExcel_Calculation_Functions::flattenSingleValue($number);
2217: $step = PHPExcel_Calculation_Functions::flattenSingleValue($step);
2218:
2219: return (int) ($number >= $step);
2220: } // function GESTEP()
2221:
2222:
2223: //
2224: // Private method to calculate the erf value
2225: //
2226: private static $_two_sqrtpi = 1.128379167095512574;
2227:
2228: public static function _erfVal($x) {
2229: if (abs($x) > 2.2) {
2230: return 1 - self::_erfcVal($x);
2231: }
2232: $sum = $term = $x;
2233: $xsqr = ($x * $x);
2234: $j = 1;
2235: do {
2236: $term *= $xsqr / $j;
2237: $sum -= $term / (2 * $j + 1);
2238: ++$j;
2239: $term *= $xsqr / $j;
2240: $sum += $term / (2 * $j + 1);
2241: ++$j;
2242: if ($sum == 0.0) {
2243: break;
2244: }
2245: } while (abs($term / $sum) > PRECISION);
2246: return self::$_two_sqrtpi * $sum;
2247: } // function _erfVal()
2248:
2249:
2250: /**
2251: * ERF
2252: *
2253: * Returns the error function integrated between the lower and upper bound arguments.
2254: *
2255: * Note: In Excel 2007 or earlier, if you input a negative value for the upper or lower bound arguments,
2256: * the function would return a #NUM! error. However, in Excel 2010, the function algorithm was
2257: * improved, so that it can now calculate the function for both positive and negative ranges.
2258: * PHPExcel follows Excel 2010 behaviour, and accepts nagative arguments.
2259: *
2260: * Excel Function:
2261: * ERF(lower[,upper])
2262: *
2263: * @param float $lower lower bound for integrating ERF
2264: * @param float $upper upper bound for integrating ERF.
2265: * If omitted, ERF integrates between zero and lower_limit
2266: * @return float
2267: */
2268: public static function ERF($lower, $upper = NULL) {
2269: $lower = PHPExcel_Calculation_Functions::flattenSingleValue($lower);
2270: $upper = PHPExcel_Calculation_Functions::flattenSingleValue($upper);
2271:
2272: if (is_numeric($lower)) {
2273: if (is_null($upper)) {
2274: return self::_erfVal($lower);
2275: }
2276: if (is_numeric($upper)) {
2277: return self::_erfVal($upper) - self::_erfVal($lower);
2278: }
2279: }
2280: return PHPExcel_Calculation_Functions::VALUE();
2281: } // function ERF()
2282:
2283:
2284: //
2285: // Private method to calculate the erfc value
2286: //
2287: private static $_one_sqrtpi = 0.564189583547756287;
2288:
2289: private static function _erfcVal($x) {
2290: if (abs($x) < 2.2) {
2291: return 1 - self::_erfVal($x);
2292: }
2293: if ($x < 0) {
2294: return 2 - self::ERFC(-$x);
2295: }
2296: $a = $n = 1;
2297: $b = $c = $x;
2298: $d = ($x * $x) + 0.5;
2299: $q1 = $q2 = $b / $d;
2300: $t = 0;
2301: do {
2302: $t = $a * $n + $b * $x;
2303: $a = $b;
2304: $b = $t;
2305: $t = $c * $n + $d * $x;
2306: $c = $d;
2307: $d = $t;
2308: $n += 0.5;
2309: $q1 = $q2;
2310: $q2 = $b / $d;
2311: } while ((abs($q1 - $q2) / $q2) > PRECISION);
2312: return self::$_one_sqrtpi * exp(-$x * $x) * $q2;
2313: } // function _erfcVal()
2314:
2315:
2316: /**
2317: * ERFC
2318: *
2319: * Returns the complementary ERF function integrated between x and infinity
2320: *
2321: * Note: In Excel 2007 or earlier, if you input a negative value for the lower bound argument,
2322: * the function would return a #NUM! error. However, in Excel 2010, the function algorithm was
2323: * improved, so that it can now calculate the function for both positive and negative x values.
2324: * PHPExcel follows Excel 2010 behaviour, and accepts nagative arguments.
2325: *
2326: * Excel Function:
2327: * ERFC(x)
2328: *
2329: * @param float $x The lower bound for integrating ERFC
2330: * @return float
2331: */
2332: public static function ERFC($x) {
2333: $x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
2334:
2335: if (is_numeric($x)) {
2336: return self::_erfcVal($x);
2337: }
2338: return PHPExcel_Calculation_Functions::VALUE();
2339: } // function ERFC()
2340:
2341:
2342: /**
2343: * getConversionGroups
2344: * Returns a list of the different conversion groups for UOM conversions
2345: *
2346: * @return array
2347: */
2348: public static function getConversionGroups() {
2349: $conversionGroups = array();
2350: foreach(self::$_conversionUnits as $conversionUnit) {
2351: $conversionGroups[] = $conversionUnit['Group'];
2352: }
2353: return array_merge(array_unique($conversionGroups));
2354: } // function getConversionGroups()
2355:
2356:
2357: /**
2358: * getConversionGroupUnits
2359: * Returns an array of units of measure, for a specified conversion group, or for all groups
2360: *
2361: * @param string $group The group whose units of measure you want to retrieve
2362: * @return array
2363: */
2364: public static function getConversionGroupUnits($group = NULL) {
2365: $conversionGroups = array();
2366: foreach(self::$_conversionUnits as $conversionUnit => $conversionGroup) {
2367: if ((is_null($group)) || ($conversionGroup['Group'] == $group)) {
2368: $conversionGroups[$conversionGroup['Group']][] = $conversionUnit;
2369: }
2370: }
2371: return $conversionGroups;
2372: } // function getConversionGroupUnits()
2373:
2374:
2375: /**
2376: * getConversionGroupUnitDetails
2377: *
2378: * @param string $group The group whose units of measure you want to retrieve
2379: * @return array
2380: */
2381: public static function getConversionGroupUnitDetails($group = NULL) {
2382: $conversionGroups = array();
2383: foreach(self::$_conversionUnits as $conversionUnit => $conversionGroup) {
2384: if ((is_null($group)) || ($conversionGroup['Group'] == $group)) {
2385: $conversionGroups[$conversionGroup['Group']][] = array( 'unit' => $conversionUnit,
2386: 'description' => $conversionGroup['Unit Name']
2387: );
2388: }
2389: }
2390: return $conversionGroups;
2391: } // function getConversionGroupUnitDetails()
2392:
2393:
2394: /**
2395: * getConversionMultipliers
2396: * Returns an array of the Multiplier prefixes that can be used with Units of Measure in CONVERTUOM()
2397: *
2398: * @return array of mixed
2399: */
2400: public static function getConversionMultipliers() {
2401: return self::$_conversionMultipliers;
2402: } // function getConversionGroups()
2403:
2404:
2405: /**
2406: * CONVERTUOM
2407: *
2408: * Converts a number from one measurement system to another.
2409: * For example, CONVERT can translate a table of distances in miles to a table of distances
2410: * in kilometers.
2411: *
2412: * Excel Function:
2413: * CONVERT(value,fromUOM,toUOM)
2414: *
2415: * @param float $value The value in fromUOM to convert.
2416: * @param string $fromUOM The units for value.
2417: * @param string $toUOM The units for the result.
2418: *
2419: * @return float
2420: */
2421: public static function CONVERTUOM($value, $fromUOM, $toUOM) {
2422: $value = PHPExcel_Calculation_Functions::flattenSingleValue($value);
2423: $fromUOM = PHPExcel_Calculation_Functions::flattenSingleValue($fromUOM);
2424: $toUOM = PHPExcel_Calculation_Functions::flattenSingleValue($toUOM);
2425:
2426: if (!is_numeric($value)) {
2427: return PHPExcel_Calculation_Functions::VALUE();
2428: }
2429: $fromMultiplier = 1.0;
2430: if (isset(self::$_conversionUnits[$fromUOM])) {
2431: $unitGroup1 = self::$_conversionUnits[$fromUOM]['Group'];
2432: } else {
2433: $fromMultiplier = substr($fromUOM,0,1);
2434: $fromUOM = substr($fromUOM,1);
2435: if (isset(self::$_conversionMultipliers[$fromMultiplier])) {
2436: $fromMultiplier = self::$_conversionMultipliers[$fromMultiplier]['multiplier'];
2437: } else {
2438: return PHPExcel_Calculation_Functions::NA();
2439: }
2440: if ((isset(self::$_conversionUnits[$fromUOM])) && (self::$_conversionUnits[$fromUOM]['AllowPrefix'])) {
2441: $unitGroup1 = self::$_conversionUnits[$fromUOM]['Group'];
2442: } else {
2443: return PHPExcel_Calculation_Functions::NA();
2444: }
2445: }
2446: $value *= $fromMultiplier;
2447:
2448: $toMultiplier = 1.0;
2449: if (isset(self::$_conversionUnits[$toUOM])) {
2450: $unitGroup2 = self::$_conversionUnits[$toUOM]['Group'];
2451: } else {
2452: $toMultiplier = substr($toUOM,0,1);
2453: $toUOM = substr($toUOM,1);
2454: if (isset(self::$_conversionMultipliers[$toMultiplier])) {
2455: $toMultiplier = self::$_conversionMultipliers[$toMultiplier]['multiplier'];
2456: } else {
2457: return PHPExcel_Calculation_Functions::NA();
2458: }
2459: if ((isset(self::$_conversionUnits[$toUOM])) && (self::$_conversionUnits[$toUOM]['AllowPrefix'])) {
2460: $unitGroup2 = self::$_conversionUnits[$toUOM]['Group'];
2461: } else {
2462: return PHPExcel_Calculation_Functions::NA();
2463: }
2464: }
2465: if ($unitGroup1 != $unitGroup2) {
2466: return PHPExcel_Calculation_Functions::NA();
2467: }
2468:
2469: if (($fromUOM == $toUOM) && ($fromMultiplier == $toMultiplier)) {
2470: // We've already factored $fromMultiplier into the value, so we need
2471: // to reverse it again
2472: return $value / $fromMultiplier;
2473: } elseif ($unitGroup1 == 'Temperature') {
2474: if (($fromUOM == 'F') || ($fromUOM == 'fah')) {
2475: if (($toUOM == 'F') || ($toUOM == 'fah')) {
2476: return $value;
2477: } else {
2478: $value = (($value - 32) / 1.8);
2479: if (($toUOM == 'K') || ($toUOM == 'kel')) {
2480: $value += 273.15;
2481: }
2482: return $value;
2483: }
2484: } elseif ((($fromUOM == 'K') || ($fromUOM == 'kel')) &&
2485: (($toUOM == 'K') || ($toUOM == 'kel'))) {
2486: return $value;
2487: } elseif ((($fromUOM == 'C') || ($fromUOM == 'cel')) &&
2488: (($toUOM == 'C') || ($toUOM == 'cel'))) {
2489: return $value;
2490: }
2491: if (($toUOM == 'F') || ($toUOM == 'fah')) {
2492: if (($fromUOM == 'K') || ($fromUOM == 'kel')) {
2493: $value -= 273.15;
2494: }
2495: return ($value * 1.8) + 32;
2496: }
2497: if (($toUOM == 'C') || ($toUOM == 'cel')) {
2498: return $value - 273.15;
2499: }
2500: return $value + 273.15;
2501: }
2502: return ($value * self::$_unitConversions[$unitGroup1][$fromUOM][$toUOM]) / $toMultiplier;
2503: } // function CONVERTUOM()
2504:
2505: } // class PHPExcel_Calculation_Engineering
2506: