This source file includes following definitions.
- exp2
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17 #include <config.h>
18
19
20 #include <math.h>
21
22 #include <float.h>
23
24
25 #define LOG2 0.693147180559945309417232121458176568075
26
27
28 #define LOG2_INVERSE 1.44269504088896340735992468100189213743
29
30
31 #define LOG2_BY_256 0.00270760617406228636491106297444600221904
32
33
34 #define LOG2_BY_256_INVERSE 369.329930467574632284140718336484387181
35
36 double
37 exp2 (double x)
38 {
39
40
41
42
43
44
45 if (isnand (x))
46 return x;
47
48 if (x > (double) DBL_MAX_EXP)
49
50
51 return HUGE_VAL;
52
53 if (x < (double) (DBL_MIN_EXP - 1 - DBL_MANT_DIG))
54
55
56
57 return 0.0;
58
59
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90 {
91 double nm = round (x * 256.0);
92 double z = (x * 256.0 - nm) * (LOG2_BY_256 * 0.5);
93
94
95 #define TANH_COEFF_1 1.0
96 #define TANH_COEFF_3 -0.333333333333333333333333333333333333334
97 #define TANH_COEFF_5 0.133333333333333333333333333333333333334
98 #define TANH_COEFF_7 -0.053968253968253968253968253968253968254
99 #define TANH_COEFF_9 0.0218694885361552028218694885361552028218
100 #define TANH_COEFF_11 -0.00886323552990219656886323552990219656886
101 #define TANH_COEFF_13 0.00359212803657248101692546136990581435026
102 #define TANH_COEFF_15 -0.00145583438705131826824948518070211191904
103
104 double z2 = z * z;
105 double tanh_z =
106 ((TANH_COEFF_5
107 * z2 + TANH_COEFF_3)
108 * z2 + TANH_COEFF_1)
109 * z;
110
111 double exp_y = (1.0 + tanh_z) / (1.0 - tanh_z);
112
113 int n = (int) round (nm * (1.0 / 256.0));
114 int m = (int) nm - 256 * n;
115
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123
124 static const double exp_table[257] =
125 {
126 0.707106781186547524400844362104849039284,
127 0.709023942160207598920563322257676190836,
128 0.710946301084582779904674297352120049962,
129 0.71287387205274715340350157671438300618,
130 0.714806669195985005617532889137569953044,
131 0.71674470668389442125974978427737336719,
132 0.71868799872449116280161304224785251353,
133 0.720636559564312831364255957304947586072,
134 0.72259040348852331001850312073583545284,
135 0.724549544821017490259402705487111270714,
136 0.726513997924526282423036245842287293786,
137 0.728483777200721910815451524818606761737,
138 0.730458897090323494325651445155310766577,
139 0.732439372073202913296664682112279175616,
140 0.734425216668490963430822513132890712652,
141 0.736416445434683797507470506133110286942,
142 0.738413072969749655693453740187024961962,
143 0.740415113911235885228829945155951253966,
144 0.742422582936376250272386395864403155277,
145 0.744435494762198532693663597314273242753,
146 0.746453864145632424600321765743336770838,
147 0.748477705883617713391824861712720862423,
148 0.750507034813212760132561481529764324813,
149 0.752541865811703272039672277899716132493,
150 0.75458221379671136988300977551659676571,
151 0.756628093726304951096818488157633113612,
152 0.75867952059910734940489114658718937343,
153 0.760736509454407291763130627098242426467,
154 0.762799075372269153425626844758470477304,
155 0.76486723347364351194254345936342587308,
156 0.766940998920478000900300751753859329456,
157 0.769020386915828464216738479594307884331,
158 0.771105412703970411806145931045367420652,
159 0.773196091570510777431255778146135325272,
160 0.77529243884249997956151370535341912283,
161 0.777394469888544286059157168801667390437,
162 0.779502200118918483516864044737428940745,
163 0.781615644985678852072965367573877941354,
164 0.783734819982776446532455855478222575498,
165 0.78585974064617068462428149076570281356,
166 0.787990422553943243227635080090952504452,
167 0.790126881326412263402248482007960521995,
168 0.79226913262624686505993407346567890838,
169 0.794417192158581972116898048814333564685,
170 0.796571075671133448968624321559534367934,
171 0.798730798954313549131410147104316569576,
172 0.800896377841346676896923120795476813684,
173 0.803067828208385462848443946517563571584,
174 0.805245165974627154089760333678700291728,
175 0.807428407102430320039984581575729114268,
176 0.809617567597431874649880866726368203972,
177 0.81181266350866441589760797777344082227,
178 0.814013710928673883424109261007007338614,
179 0.816220725993637535170713864466769240053,
180 0.818433724883482243883852017078007231025,
181 0.82065272382200311435413206848451310067,
182 0.822877739076982422259378362362911222833,
183 0.825108786960308875483586738272485101678,
184 0.827345883828097198786118571797909120834,
185 0.829589046080808042697824787210781231927,
186 0.831838290163368217523168228488195222638,
187 0.834093632565291253329796170708536192903,
188 0.836355089820798286809404612069230711295,
189 0.83862267850893927589613232455870870518,
190 0.84089641525371454303112547623321489504,
191 0.84317631672419664796432298771385230143,
192 0.84546239963465259098692866759361830709,
193 0.84775468074466634749045860363936420312,
194 0.850053176859261734750681286748751167545,
195 0.852357904829025611837203530384718316326,
196 0.854668881550231413551897437515331498025,
197 0.856986123964963019301812477839166009452,
198 0.859309649061238957814672188228156252257,
199 0.861639473873136948607517116872358729753,
200 0.863975615480918781121524414614366207052,
201 0.866318091011155532438509953514163469652,
202 0.868666917636853124497101040936083380124,
203 0.871022112577578221729056715595464682243,
204 0.873383693099584470038708278290226842228,
205 0.875751676515939078050995142767930296012,
206 0.878126080186649741556080309687656610647,
207 0.880506921518791912081045787323636256171,
208 0.882894217966636410521691124969260937028,
209 0.885287987031777386769987907431242017412,
210 0.88768824626326062627527960009966160388,
211 0.89009501325771220447985955243623523504,
212 0.892508305659467490072110281986409916153,
213 0.8949281411607004980029443898876582985,
214 0.897354537501553593213851621063890907178,
215 0.899787512470267546027427696662514569756,
216 0.902227083903311940153838631655504844215,
217 0.904673269685515934269259325789226871994,
218 0.907126087750199378124917300181170171233,
219 0.909585556079304284147971563828178746372,
220 0.91205169270352665549806275316460097744,
221 0.914524515702448671545983912696158354092,
222 0.91700404320467123174354159479414442804,
223 0.919490293387946858856304371174663918816,
224 0.921983284479312962533570386670938449637,
225 0.92448303475522546419252726694739603678,
226 0.92698956254169278419622653516884831976,
227 0.929502886214410192307650717745572682403,
228 0.932023024198894522404814545597236289343,
229 0.934549994970619252444512104439799143264,
230 0.93708381705514995066499947497722326722,
231 0.93962450902828008902058735120448448827,
232 0.942172089516167224843810351983745154882,
233 0.944726577195469551733539267378681531548,
234 0.947287990793482820670109326713462307376,
235 0.949856349088277632361251759806996099924,
236 0.952431670908837101825337466217860725517,
237 0.955013975135194896221170529572799135168,
238 0.957603280698573646936305635147915443924,
239 0.960199606581523736948607188887070611744,
240 0.962802971818062464478519115091191368377,
241 0.965413395493813583952272948264534783197,
242 0.968030896746147225299027952283345762418,
243 0.970655494764320192607710617437589705184,
244 0.973287208789616643172102023321302921373,
245 0.97592605811548914795551023340047499377,
246 0.978572062087700134509161125813435745597,
247 0.981225240104463713381244885057070325016,
248 0.983885611616587889056366801238014683926,
249 0.98655319612761715646797006813220671315,
250 0.989228013193975484129124959065583667775,
251 0.99191008242510968492991311132615581644,
252 0.994599423483633175652477686222166314457,
253 0.997296056085470126257659913847922601123,
254 1.0,
255 1.00271127505020248543074558845036204047,
256 1.0054299011128028213513839559347998147,
257 1.008155898118417515783094890817201039276,
258 1.01088928605170046002040979056186052439,
259 1.013630084951489438840258929063939929597,
260 1.01637831491095303794049311378629406276,
261 1.0191339960777379496848780958207928794,
262 1.02189714865411667823448013478329943978,
263 1.02466779289713564514828907627081492763,
264 1.0274459491187636965388611939222137815,
265 1.030231637686041012871707902453904567093,
266 1.033024879021228422500108283970460918086,
267 1.035825693601957120029983209018081371844,
268 1.03863410196137879061243669795463973258,
269 1.04145012468831614126454607901189312648,
270 1.044273782427413840321966478739929008784,
271 1.04710509587928986612990725022711224056,
272 1.04994408580068726608203812651590790906,
273 1.05279077300462632711989120298074630319,
274 1.05564517836055715880834132515293865216,
275 1.058507322794512690105772109683716645074,
276 1.061377227289262080950567678003883726294,
277 1.06425491288446454978861125700158022068,
278 1.06714040067682361816952112099280916261,
279 1.0700337118202417735424119367576235685,
280 1.072934867525975551385035450873827585343,
281 1.075843889062791037803228648476057074063,
282 1.07876079775711979374068003743848295849,
283 1.081685614993215201942115594422531125643,
284 1.08461836221330923781610517190661434161,
285 1.087559060917769665346797830944039707867,
286 1.09050773266525765920701065576070797899,
287 1.09346439907288585422822014625044716208,
288 1.096429081816376823386138295859248481766,
289 1.09940180263022198546369696823882990404,
290 1.10238258330784094355641420942564685751,
291 1.10537144570174125558827469625695031104,
292 1.108368411723678638009423649426619850137,
293 1.111373503344817603850149254228916637444,
294 1.1143867425958925363088129569196030678,
295 1.11740815156736919905457996308578026665,
296 1.12043775240960668442900387986631301277,
297 1.123475567333019800733729739775321431954,
298 1.12652161860824189979479864378703477763,
299 1.129575928566288145997264988840249825907,
300 1.13263851959871922798707372367762308438,
301 1.13570941415780551424039033067611701343,
302 1.13878863475669165370383028384151125472,
303 1.14187620396956162271229760828788093894,
304 1.14497214443180421939441388822291589579,
305 1.14807647884017900677879966269734268003,
306 1.15118922995298270581775963520198253612,
307 1.154310420590216039548221528724806960684,
308 1.157440073633751029613085766293796821106,
309 1.16057821202749874636945947257609098625,
310 1.16372485877757751381357359909218531234,
311 1.166880036952481570555516298414089287834,
312 1.170043769683250188080259035792738573,
313 1.17321608016363724753480435451324538889,
314 1.176396991650281276284645728483848641054,
315 1.17958652746287594548610056676944051898,
316 1.182784710984341029924457204693850757966,
317 1.18599156566099383137126564953421556374,
318 1.18920711500272106671749997056047591529,
319 1.19243138258315122214272755814543101148,
320 1.195664392039827374583837049865451975705,
321 1.19890616707438048177030255797630020695,
322 1.202156731452703142096396957497765876003,
323 1.205416109005123825604211432558411335666,
324 1.208684323626581577354792255889216998484,
325 1.21196139927680119446816891773249304545,
326 1.215247359980468878116520251338798457624,
327 1.218542229827408361758207148117394510724,
328 1.221846032972757516903891841911570785836,
329 1.225158793637145437709464594384845353707,
330 1.22848053610687000569400895779278184036,
331 1.2318112847340759358845566532127948166,
332 1.235151063936933305692912507415415760294,
333 1.238499898199816567833368865859612431545,
334 1.24185781207348404859367746872659560551,
335 1.24522483017525793277520496748615267417,
336 1.24860097718920473662176609730249554519,
337 1.25198627786631627006020603178920359732,
338 1.255380757024691089579390657442301194595,
339 1.25878443954971644307786044181516261876,
340 1.26219735039425070801401025851841645967,
341 1.265619514578806324196273999873453036296,
342 1.26905095719173322255441908103233800472,
343 1.27249170338940275123669204418460217677,
344 1.27594177839639210038120243475928938891,
345 1.27940120750566922691358797002785254596,
346 1.28287001607877828072666978102151405111,
347 1.286348229546025533601482208069738348355,
348 1.28983587340666581223274729549155218968,
349 1.293332973229089436725559789048704304684,
350 1.296839554651009665933754117792451159835,
351 1.30035564337965065101414056707091779129,
352 1.30388126519193589857452364895199736833,
353 1.30741644593467724479715157747196172848,
354 1.310961211524764341922991786330755849366,
355 1.314515587949354658485983613383997794965,
356 1.318079601266063994690185647066116617664,
357 1.32165327760315751432651181233060922616,
358 1.32523664315974129462953709549872167411,
359 1.32882972420595439547865089632866510792,
360 1.33243254708316144935164337949073577407,
361 1.33604513820414577344262790437186975929,
362 1.33966752405330300536003066972435257602,
363 1.34329973118683526382421714618163087542,
364 1.346941786232945835788173713229537282075,
365 1.35059371589203439140852219606013396004,
366 1.35425554693689272829801474014070280434,
367 1.357927306212901046494536695671766697446,
368 1.36160902063822475558553593883194147464,
369 1.36530071720401181543069836033754285543,
370 1.36900242297459061192960113298219283217,
371 1.37271416508766836928499785714471721579,
372 1.37643597075453010021632280551868696026,
373 1.380167867260238095581945274358283464697,
374 1.383909881963831954872659527265192818,
375 1.387662042298529159042861017950775988896,
376 1.39142437577192618714983552956624344668,
377 1.395196909966200178275574599249220994716,
378 1.398979672538311140209528136715194969206,
379 1.40277269122020470637471352433337881711,
380 1.40657599381901544248361973255451684411,
381 1.410389608217270704414375128268675481145,
382 1.41421356237309504880168872420969807857
383 };
384
385 return ldexp (exp_table[128 + m] * exp_y, n);
386 }
387 }