1 /* 2 * CDDL HEADER START 3 * 4 * The contents of this file are subject to the terms of the 5 * Common Development and Distribution License (the "License"). 6 * You may not use this file except in compliance with the License. 7 * 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 9 * or http://www.opensolaris.org/os/licensing. 10 * See the License for the specific language governing permissions 11 * and limitations under the License. 12 * 13 * When distributing Covered Code, include this CDDL HEADER in each 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 15 * If applicable, add the following below this CDDL HEADER, with the 16 * fields enclosed by brackets "[]" replaced with your own identifying 17 * information: Portions Copyright [yyyy] [name of copyright owner] 18 * 19 * CDDL HEADER END 20 */ 21 /* 22 * Copyright 2011 Nexenta Systems, Inc. All rights reserved. 23 */ 24 /* 25 * Copyright 2006 Sun Microsystems, Inc. All rights reserved. 26 * Use is subject to license terms. 27 */ 28 29 #pragma weak __atan2 = atan2 30 31 #include "libm.h" 32 33 /* 34 * Let t(0) = 1 and for i = 1, ..., 160, let t(i) be the slope of 35 * the line bisecting the conical hull of the set of points (x,y) 36 * where x and y are positive normal floating point numbers and 37 * the high order words hx and hy of their binary representations 38 * satisfy |hx - hy - i * 0x8000| <= 0x4000. Then: 39 * 40 * TBL[4*i+2] is t(i) rounded to 21 significant bits (i.e., the 41 * low order word is zero), and 42 * 43 * TBL[4*i] + TBL[4*i+1] form a doubled-double approximation to 44 * atan(TBL[4*i+2]). 45 * 46 * Finally, TBL[4*161] = TBL[4*161+1] = TBL[4*161+2] = 0. 47 * 48 * Now for any (x,y) with 0 < y <= x and any 0 < t <= 1, we have 49 * atan(y/x) = atan(t) + atan((y-t*x)/(x+t*y)). By choosing t = 50 * TBL[4*i+2], where i is the multiple of 0x8000 nearest hx - hy, 51 * if this multiple is less than 161, and i = 161 otherwise, we 52 * find that |(y-t*x)/(x+t*y)| <~ 2^-5. 53 */ 54 static const double TBL[] = { 55 7.8539816339744827900e-01, +3.0616169978683830179e-17, 56 1.0000000000000000000e+00, +0, 57 7.7198905126506112140e-01, +2.6989956960083153652e-16, 58 9.7353506088256835938e-01, +0, 59 7.6068143954461309164e-01, -3.5178810518941914972e-16, 60 9.5174932479858398438e-01, +0, 61 7.4953661876353638860e-01, -3.2548100004524337476e-16, 62 9.3073129653930664062e-01, +0, 63 7.3854614984728339522e-01, -2.0775571023910406668e-16, 64 9.1042709350585937500e-01, +0, 65 7.2770146962041337702e-01, +3.8883249403168348802e-16, 66 8.9078664779663085938e-01, +0, 67 7.1699492488093774512e-01, -4.0468841511547224071e-16, 68 8.7176513671875000000e-01, +0, 69 7.0641813488653149022e-01, +5.6902424353981484031e-17, 70 8.5331964492797851562e-01, +0, 71 6.9596351101035658360e-01, +2.8245513321075021303e-16, 72 8.3541154861450195312e-01, +0, 73 6.8562363680534943455e-01, -4.2316970721658854064e-16, 74 8.1800508499145507812e-01, +0, 75 6.7539055666438230219e-01, +4.3535917281300047233e-16, 76 8.0106592178344726562e-01, +0, 77 6.6525763346931832132e-01, +1.1830431602404727977e-17, 78 7.8456401824951171875e-01, +0, 79 6.5521767574310185722e-01, -1.7435923100651044208e-16, 80 7.6847028732299804688e-01, +0, 81 6.4526390999481897381e-01, -1.4741927403093983947e-16, 82 7.5275802612304687500e-01, +0, 83 6.3538979894204850041e-01, +1.5734535069995660853e-16, 84 7.3740243911743164062e-01, +0, 85 6.2558914346942717799e-01, -2.8175588856316910960e-16, 86 7.2238063812255859375e-01, +0, 87 6.1585586476157949676e-01, -4.3056167357725226449e-16, 88 7.0767116546630859375e-01, +0, 89 6.0618408027576098362e-01, +1.5018013918429320289e-16, 90 6.9325399398803710938e-01, +0, 91 5.9656817827486730010e-01, +5.5271942033557644157e-17, 92 6.7911052703857421875e-01, +0, 93 5.8700289083426504533e-01, -8.2411369282676383293e-17, 94 6.6522359848022460938e-01, +0, 95 5.7748303053627658699e-01, +4.9400383775709159558e-17, 96 6.5157699584960937500e-01, +0, 97 5.6800353968303252117e-01, +2.9924431103311109543e-16, 98 6.3815546035766601562e-01, +0, 99 5.5855953863493823519e-01, -2.0306003403868777403e-16, 100 6.2494468688964843750e-01, +0, 101 5.4914706708329674711e-01, +2.8255378613779667461e-17, 102 6.1193227767944335938e-01, +0, 103 5.3976176660618069292e-01, +1.6370248781078747995e-16, 104 5.9910583496093750000e-01, +0, 105 5.3039888601412332747e-01, -7.6196097360093680134e-17, 106 5.8645296096801757812e-01, +0, 107 5.2105543924318808990e-01, -2.2400815668154739561e-16, 108 5.7396411895751953125e-01, +0, 109 5.1172778873967050828e-01, -3.6888136019899681185e-16, 110 5.6162929534912109375e-01, +0, 111 5.0241199666452196482e-01, -2.5412891474397011281e-16, 112 5.4943847656250000000e-01, +0, 113 4.9310493954293743712e-01, +4.4132186128251152229e-16, 114 5.3738307952880859375e-01, +0, 115 4.8380436844750995817e-01, -2.7844387907776656488e-16, 116 5.2545595169067382812e-01, +0, 117 4.7450670361463753721e-01, -2.0494355197368286028e-16, 118 5.1364850997924804688e-01, +0, 119 4.6367660027976320691e-01, +3.1709878607954760668e-16, 120 5.0003623962402343750e-01, +0, 121 4.5304753104003925301e-01, +3.3593436122420574865e-16, 122 4.8681926727294921875e-01, +0, 123 4.4423658037407065535e-01, +2.1987183192008082015e-17, 124 4.7596645355224609375e-01, +0, 125 4.3567016972500294258e-01, +3.0118422805369552650e-16, 126 4.6550178527832031250e-01, +0, 127 4.2733152672544871820e-01, -3.2667693224866479909e-16, 128 4.5539522171020507812e-01, +0, 129 4.1920540176693954493e-01, -2.2454273841113897647e-16, 130 4.4561982154846191406e-01, +0, 131 4.1127722812701872357e-01, -3.1620568973494653391e-16, 132 4.3615055084228515625e-01, +0, 133 4.0353384063084263289e-01, -3.5932009901481421723e-16, 134 4.2696499824523925781e-01, +0, 135 3.9596319345246833166e-01, -4.0281533417458698585e-16, 136 4.1804289817810058594e-01, +0, 137 3.8855405220339722661e-01, +1.6132231486045176674e-16, 138 4.0936565399169921875e-01, +0, 139 3.8129566313738116889e-01, +1.7684657060650804570e-16, 140 4.0091586112976074219e-01, +0, 141 3.7417884791401867517e-01, +2.6897604227426977619e-16, 142 3.9267849922180175781e-01, +0, 143 3.6719421967585041955e-01, -4.5886151448673745001e-17, 144 3.8463878631591796875e-01, +0, 145 3.6033388248727771241e-01, +1.5804115573136074946e-16, 146 3.7678408622741699219e-01, +0, 147 3.5358982224579182940e-01, +1.2624619863035782939e-16, 148 3.6910200119018554688e-01, +0, 149 3.4695498404186952968e-01, +9.3221684607372865177e-17, 150 3.6158156394958496094e-01, +0, 151 3.4042268308109679964e-01, +2.7697913559445449137e-16, 152 3.5421252250671386719e-01, +0, 153 3.3398684598563566084e-01, +3.6085337449716011085e-16, 154 3.4698557853698730469e-01, +0, 155 3.2764182824591436827e-01, +2.0581506352606456186e-16, 156 3.3989214897155761719e-01, +0, 157 3.2138200938788497041e-01, -1.9015787485430693661e-16, 158 3.3292388916015625000e-01, +0, 159 3.1520245348069497737e-01, +2.6961839659264087022e-16, 160 3.2607340812683105469e-01, +0, 161 3.0909871873117023000e-01, -1.5641891686756272625e-16, 162 3.1933403015136718750e-01, +0, 163 3.0306644308947827682e-01, +2.8801634211591956223e-16, 164 3.1269931793212890625e-01, +0, 165 2.9710135482774191473e-01, -4.3148994478973365819e-16, 166 3.0616307258605957031e-01, +0, 167 2.9120015759141004708e-01, -6.8539854790808585159e-17, 168 2.9972028732299804688e-01, +0, 169 2.8535879880370362827e-01, -1.2231638445300492682e-16, 170 2.9336524009704589844e-01, +0, 171 2.7957422506893880865e-01, -4.6707752931043135528e-17, 172 2.8709340095520019531e-01, +0, 173 2.7384352102802367313e-01, -4.1215636366229625876e-16, 174 2.8090047836303710938e-01, +0, 175 2.6816369484161040049e-01, -2.3700583122400495333e-16, 176 2.7478218078613281250e-01, +0, 177 2.6253212627627764419e-01, +2.3123213692190889610e-16, 178 2.6873469352722167969e-01, +0, 179 2.5694635355759309903e-01, -4.0638513814701264145e-16, 180 2.6275444030761718750e-01, +0, 181 2.5140385572454615470e-01, -3.4795333793554943723e-16, 182 2.5683784484863281250e-01, +0, 183 2.4500357070096612233e-01, +6.6542334848010259289e-17, 184 2.5002646446228027344e-01, +0, 185 2.3877766609573036760e-01, -2.7756633678549343650e-16, 186 2.4342155456542968750e-01, +0, 187 2.3365669377188336142e-01, +3.2700803838522067998e-16, 188 2.3800384998321533203e-01, +0, 189 2.2870810463931334766e-01, -4.4279127662219799521e-16, 190 2.3278105258941650391e-01, +0, 191 2.2391820542294382790e-01, +3.7558889374284208052e-16, 192 2.2773718833923339844e-01, +0, 193 2.1927501815429550902e-01, -1.4829838176513811186e-16, 194 2.2285830974578857422e-01, +0, 195 2.1476740847367459253e-01, -2.0535381496063397578e-17, 196 2.1813154220581054688e-01, +0, 197 2.1038568111737454558e-01, -4.2826767738736168650e-16, 198 2.1354568004608154297e-01, +0, 199 2.0612057974373865221e-01, +4.2108051749502232359e-16, 200 2.0909011363983154297e-01, +0, 201 2.0196410359405447821e-01, +3.5157118083511092869e-16, 202 2.0475566387176513672e-01, +0, 203 1.9790861144712756925e-01, +3.7894950972257700994e-16, 204 2.0053362846374511719e-01, +0, 205 1.9394752160084305359e-01, +2.8270367403478935534e-16, 206 1.9641649723052978516e-01, +0, 207 1.9007440763641536563e-01, -2.0842758095683676397e-16, 208 1.9239699840545654297e-01, +0, 209 1.8628369629742813629e-01, +3.4710917040399448932e-16, 210 1.8846881389617919922e-01, +0, 211 1.8256998712939509488e-01, +1.1053834120570125251e-16, 212 1.8462586402893066406e-01, +0, 213 1.7892875067284830237e-01, +3.0486232913366680305e-16, 214 1.8086302280426025391e-01, +0, 215 1.7535529778449010507e-01, -2.3810135019970148624e-16, 216 1.7717504501342773438e-01, +0, 217 1.7184559192514736736e-01, +5.1432582846210893916e-17, 218 1.7355740070343017578e-01, +0, 219 1.6839590847744290159e-01, +3.1605623296041433586e-18, 220 1.7000591754913330078e-01, +0, 221 1.6500283902547518977e-01, +1.5405422268770998251e-16, 222 1.6651678085327148438e-01, +0, 223 1.6166306303174859949e-01, +4.0042241517254928672e-16, 224 1.6308629512786865234e-01, +0, 225 1.5837358268281231943e-01, -2.2786616251622967291e-16, 226 1.5971112251281738281e-01, +0, 227 1.5513160990288810126e-01, -3.7547723514797166336e-16, 228 1.5638816356658935547e-01, +0, 229 1.5193468535499299321e-01, +4.3497510505554267446e-16, 230 1.5311467647552490234e-01, +0, 231 1.4878033155427861089e-01, -2.3102860235324261895e-16, 232 1.4988791942596435547e-01, +0, 233 1.4566628729590647140e-01, +9.9227592950040279415e-17, 234 1.4670538902282714844e-01, +0, 235 1.4259050967286590605e-01, -3.3869909683813096906e-18, 236 1.4356482028961181641e-01, +0, 237 1.3955105903633846509e-01, +1.5500435650773331566e-17, 238 1.4046406745910644531e-01, +0, 239 1.3654610022831903393e-01, +3.3965918616682805753e-16, 240 1.3740110397338867188e-01, +0, 241 1.3357402082462854764e-01, +2.7572431581527535421e-16, 242 1.3437414169311523438e-01, +0, 243 1.3063319828908959153e-01, -3.4667213797076707331e-16, 244 1.3138139247894287109e-01, +0, 245 1.2772200049776749609e-01, +3.1089261947725651968e-16, 246 1.2842106819152832031e-01, +0, 247 1.2436931430778752627e-01, -4.0654251891464630059e-16, 248 1.2501454353332519531e-01, +0, 249 1.2111683701666819957e-01, -3.9381654342464836012e-16, 250 1.2171256542205810547e-01, +0, 251 1.1844801833536511282e-01, -3.6673155595150283444e-16, 252 1.1900508403778076172e-01, +0, 253 1.1587365536613614125e-01, -1.5026628801318421951e-16, 254 1.1639505624771118164e-01, +0, 255 1.1338607085741525538e-01, +1.2886806274050538880e-16, 256 1.1387449502944946289e-01, +0, 257 1.1097844020819369604e-01, +2.3848343623577768044e-16, 258 1.1143630743026733398e-01, +0, 259 1.0864456107308662069e-01, +4.2065430313285469408e-16, 260 1.0907405614852905273e-01, +0, 261 1.0637891628473727934e-01, -4.6883543790348472687e-18, 262 1.0678201913833618164e-01, +0, 263 1.0417650062205296990e-01, +1.4774925414624453292e-16, 264 1.0455501079559326172e-01, +0, 265 1.0203276464730581807e-01, -1.5677032794816452332e-16, 266 1.0238832235336303711e-01, +0, 267 9.9943617083734892503e-02, +3.4511310907979792828e-16, 268 1.0027772188186645508e-01, +0, 269 9.7905249824711049200e-02, +3.4489485563461708496e-16, 270 9.8219275474548339844e-02, +0, 271 9.5914316649349906641e-02, -1.3214510886789011569e-17, 272 9.6209526062011718750e-02, +0, 273 9.3967698614664918466e-02, +1.1048427091217964090e-16, 274 9.4245254993438720703e-02, +0, 275 9.2062564267554769515e-02, -3.7297463814697759309e-16, 276 9.2323541641235351562e-02, +0, 277 9.0196252506350660383e-02, -3.5280143043576718079e-16, 278 9.0441644191741943359e-02, +0, 279 8.8366391663268650802e-02, -6.1140673227541621183e-17, 280 8.8597118854522705078e-02, +0, 281 8.6570782100201526532e-02, -2.0998844594957629702e-16, 282 8.6787700653076171875e-02, +0, 283 8.4807337678923566671e-02, +3.9530981588194673068e-16, 284 8.5011243820190429688e-02, +0, 285 8.3074323040850828193e-02, -4.3022503210464894539e-17, 286 8.3265960216522216797e-02, +0, 287 8.1369880712663267275e-02, -6.3063867569127169744e-18, 288 8.1549942493438720703e-02, +0, 289 7.9692445771216036121e-02, -5.0787623072962671502e-17, 290 7.9861581325531005859e-02, +0, 291 7.8040568735575632786e-02, -3.8810063021216721741e-16, 292 7.8199386596679687500e-02, +0, 293 7.6412797391314235540e-02, +4.1246529500495762995e-16, 294 7.6561868190765380859e-02, +0, 295 7.4807854772808823896e-02, -3.7025599052186724156e-16, 296 7.4947714805603027344e-02, +0, 297 7.3224639528778112663e-02, +4.2209138483206712401e-17, 298 7.3355793952941894531e-02, +0, 299 7.1661929761571485642e-02, -3.2074473649855177622e-16, 300 7.1784853935241699219e-02, +0, 301 7.0118738881148168218e-02, -2.5371257235753296804e-16, 302 7.0233881473541259766e-02, +0, 303 6.8594137996416115755e-02, +3.3796987842548399135e-16, 304 6.8701922893524169922e-02, +0, 305 6.7087137393172291411e-02, +5.5061492696328852397e-17, 306 6.7187964916229248047e-02, +0, 307 6.5596983299946565182e-02, -2.1580863111502565280e-16, 308 6.5691232681274414062e-02, +0, 309 6.4122802037412718335e-02, -3.1315661827469233434e-16, 310 6.4210832118988037109e-02, +0, 311 6.2426231582525915087e-02, -2.5758980071296622188e-16, 312 6.2507450580596923828e-02, +0, 313 6.0781559928021700046e-02, +1.3736899336217710591e-16, 314 6.0856521129608154297e-02, +0, 315 5.9432882624005145544e-02, +2.2246097394328856474e-16, 316 5.9502959251403808594e-02, +0, 317 5.8132551274581167888e-02, -6.2525053236379489390e-18, 318 5.8198124170303344727e-02, +0, 319 5.6876611930681164608e-02, -2.6589930995607417149e-16, 320 5.6938022375106811523e-02, +0, 321 5.5661522654748551986e-02, -4.2736362859832186197e-16, 322 5.5719077587127685547e-02, +0, 323 5.4484124463757943602e-02, -1.6708067365310384253e-16, 324 5.4538100957870483398e-02, +0, 325 5.3341582449436764080e-02, +3.3271673004611311850e-17, 326 5.3392231464385986328e-02, +0, 327 5.2231267345892007370e-02, -3.5593396674200571616e-16, 328 5.2278816699981689453e-02, +0, 329 5.1150874758829623090e-02, +1.4432815841187114832e-16, 330 5.1195532083511352539e-02, +0, 331 5.0098306612679444072e-02, +9.4680943793589404083e-17, 332 5.0140261650085449219e-02, +0, 333 4.9071641675614507960e-02, +2.1131168520301896817e-16, 334 4.9111068248748779297e-02, +0, 335 4.8069135772851545596e-02, +1.6035336741307516296e-16, 336 4.8106193542480468750e-02, +0, 337 4.7089192241088539959e-02, -2.2491738698796901479e-16, 338 4.7124028205871582031e-02, +0, 339 4.6130362086062248750e-02, -1.5111423469578965206e-16, 340 4.6163111925125122070e-02, +0, 341 4.5191314382707403752e-02, +4.1989325207399786612e-16, 342 4.5222103595733642578e-02, +0, 343 4.4270836390474244126e-02, -4.1432635292331004454e-16, 344 4.4299781322479248047e-02, +0, 345 4.3367774164955186222e-02, -3.0615383054587355892e-16, 346 4.3394982814788818359e-02, +0, 347 4.2481121875321825598e-02, -3.6730166956273555173e-16, 348 4.2506694793701171875e-02, +0, 349 4.1609902899457651415e-02, -4.4226425958068821782e-16, 350 4.1633933782577514648e-02, +0, 351 4.0753259129372665370e-02, +1.9801161516527046872e-16, 352 4.0775835514068603516e-02, +0, 353 3.9910361780060910064e-02, +8.2560620036613164573e-18, 354 3.9931565523147583008e-02, +0, 355 3.9080441183869218946e-02, +3.9908991939242971628e-17, 356 3.9100348949432373047e-02, +0, 357 3.8262816593271686827e-02, +9.5182237812195590276e-17, 358 3.8281500339508056641e-02, +0, 359 3.7456806948784837630e-02, +1.5213508760679563439e-16, 360 3.7474334239959716797e-02, +0, 361 3.6661849947035918262e-02, +7.3335516005184616486e-17, 362 3.6678284406661987305e-02, +0, 363 3.5877353272533163420e-02, -1.3007348019891714540e-16, 364 3.5892754793167114258e-02, +0, 365 3.5102754135096780885e-02, -2.9903662298950558656e-16, 366 3.5117179155349731445e-02, +0, 367 3.4337638360670830195e-02, +2.9656295131966114331e-16, 368 3.4351140260696411133e-02, +0, 369 3.3581472523789734907e-02, +3.4810947205572817820e-16, 370 3.3594101667404174805e-02, +0, 371 3.2833871859357266487e-02, -3.8885440174405159838e-16, 372 3.2845675945281982422e-02, +0, 373 3.2094421679560447558e-02, +5.8805134853032009978e-17, 374 3.2105445861816406250e-02, +0, 375 3.1243584858944295490e-02, +2.8737383773884313066e-17, 376 3.1253755092620849609e-02, +0, 377 0, 0, 0, 0 378 }; 379 380 static const double C[] = { 381 0.0, 382 0.125, 383 1.2980742146337069071e+33, 384 7.8539816339744827900e-01, 385 1.5707963267948965580e+00, 386 6.1232339957367658860e-17, 387 -3.1415926535897931160e+00, 388 -1.2246467991473531772e-16, 389 -3.33333333333327571893331786354179101074860633009e-0001, 390 +1.99999999942671624230086497610394721817438631379e-0001, 391 -1.42856965565428636896183013324727205980484158356e-0001, 392 +1.10894981496317081405107718475040168084164825641e-0001, 393 }; 394 395 #define zero C[0] 396 #define twom3 C[1] 397 #define two110 C[2] 398 #define pio4 C[3] 399 #define pio2 C[4] 400 #define pio2_lo C[5] 401 #define mpi C[6] 402 #define mpi_lo C[7] 403 #define p1 C[8] 404 #define p2 C[9] 405 #define p3 C[10] 406 #define p4 C[11] 407 408 double 409 atan2(double oy, double ox) { 410 double ah, al, t, xh, x, y, z; 411 int i, k, hx, hy, sx, sy; 412 #ifndef lint 413 volatile int inexact __unused; 414 #endif 415 416 hy = ((int *)&oy)[HIWORD]; 417 sy = hy & 0x80000000; 418 hy &= ~0x80000000; 419 420 hx = ((int *)&ox)[HIWORD]; 421 sx = hx & 0x80000000; 422 hx &= ~0x80000000; 423 424 if (hy > hx || (hy == hx && ((unsigned *)&oy)[LOWORD] > 425 ((unsigned *)&ox)[LOWORD])) { 426 i = hx; 427 hx = hy; 428 hy = i; 429 x = fabs(oy); 430 y = fabs(ox); 431 if (sx) { 432 ah = pio2; 433 al = pio2_lo; 434 } else { 435 ah = -pio2; 436 al = -pio2_lo; 437 sy ^= 0x80000000; 438 } 439 } else { 440 x = fabs(ox); 441 y = fabs(oy); 442 if (sx) { 443 ah = mpi; 444 al = mpi_lo; 445 sy ^= 0x80000000; 446 } else { 447 ah = al = zero; 448 } 449 } 450 451 if (hx >= 0x7fe00000 || hx - hy >= 0x03600000) { 452 if (hx >= 0x7ff00000) { 453 if (((hx ^ 0x7ff00000) | ((int *)&x)[LOWORD]) != 0) 454 return (ox * oy); 455 if (hy >= 0x7ff00000) 456 ah += pio4; 457 #ifndef lint 458 inexact = (int)ah; /* inexact if ah != 0 */ 459 #endif 460 return ((sy)? -ah : ah); 461 } 462 if (hx - hy >= 0x03600000) { 463 if ((int)ah == 0) 464 ah = y / x; 465 return ((sy)? -ah : ah); 466 } 467 y *= twom3; 468 x *= twom3; 469 hy -= 0x00300000; 470 hx -= 0x00300000; 471 } else if (hy < 0x00100000) { 472 if ((hy | ((int *)&y)[LOWORD]) == 0) { 473 if ((hx | ((int *)&x)[LOWORD]) == 0) 474 return (_SVID_libm_err(ox, oy, 3)); 475 #ifndef lint 476 inexact = (int)ah; /* inexact if ah != 0 */ 477 #endif 478 return ((sy)? -ah : ah); 479 } 480 y *= two110; 481 x *= two110; 482 hy = ((int *)&y)[HIWORD]; 483 hx = ((int *)&x)[HIWORD]; 484 } 485 486 k = (((hx - hy) + 0x00004000) >> 13) & ~0x3; 487 if (k > 644) 488 k = 644; 489 ah += TBL[k]; 490 al += TBL[k+1]; 491 t = TBL[k+2]; 492 493 xh = x; 494 ((int *)&xh)[LOWORD] = 0; 495 z = ((y - t * xh) - t * (x - xh)) / (x + y * t); 496 x = z * z; 497 t = ah + (z + (al + (z * x) * (p1 + x * (p2 + x * (p3 + x * p4))))); 498 return ((sy)? -t : t); 499 } 500