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 /* 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved. 24 */ 25 /* 26 * Copyright 2006 Sun Microsystems, Inc. All rights reserved. 27 * Use is subject to license terms. 28 */ 29 30 #include <sys/isa_defs.h> 31 32 #ifdef _LITTLE_ENDIAN 33 #define HI(x) *(1+(int*)x) 34 #define LO(x) *(unsigned*)x 35 #else 36 #define HI(x) *(int*)x 37 #define LO(x) *(1+(unsigned*)x) 38 #endif 39 40 #ifdef __RESTRICT 41 #define restrict _Restrict 42 #else 43 #define restrict 44 #endif 45 46 /* double pow(double x, double y) 47 * 48 * Method : 49 * 1. Special cases: 50 * for (anything) ** 0 => 1 51 * for (anything) ** NaN => QNaN + invalid 52 * for NaN ** (anything) => QNaN + invalid 53 * for +-1 ** +-Inf => QNaN + invalid 54 * for +-(|x| < 1) ** +Inf => +0 55 * for +-(|x| < 1) ** -Inf => +Inf 56 * for +-(|x| > 1) ** +Inf => +Inf 57 * for +-(|x| > 1) ** -Inf => +0 58 * for +Inf ** (negative) => +0 59 * for +Inf ** (positive) => +Inf 60 * for -Inf ** (negative except odd integer) => +0 61 * for -Inf ** (negative odd integer) => -0 62 * for -Inf ** (positive except odd integer) => +Inf 63 * for -Inf ** (positive odd integer) => -Inf 64 * for (negative) ** (non-integer) => QNaN + invalid 65 * for +0 ** (negative) => +Inf + overflow 66 * for +0 ** (positive) => +0 67 * for -0 ** (negative except odd integer) => +Inf + overflow 68 * for -0 ** (negative odd integer) => -Inf + overflow 69 * for -0 ** (positive except odd integer) => +0 70 * for -0 ** (positive odd integer) => -0 71 * 2. Computes x**y from: 72 * x**y = 2**(y*log2(x)) = 2**(w/256), where w = 256*log2(|x|)*y. 73 * 3. Computes w = 256*log2(|x|)*y from 74 * |x| = m * 2**n => log2(|x|) = n + log2(m). 75 * Let m = m0 + dm, where m0 = 1 + k / 256, 76 * k = [0, 255], 77 * dm = [-1/512, 1/512]. 78 * Then 256*log2(m) = 256*log2(m0 + dm) = 256*log2(m0) + 256*log2((1+z)/(1-z)), 79 * where z = (m-m0)/(m+m0), z = [-1/1025, 1/1025]. 80 * Then 81 * 256*log2(m0) is looked up in a table of 256*log2(1), 256*log2(1+1/128), 82 * ..., 256*log2(1+128/128). 83 * 256*log2((1+z)/(1-z)) is computed using 84 * approximation: 256*log2((1+z)/(1-z)) = a0 * z + a1 * z**3 + a1 * z**5. 85 * Perform w = 256*log2(|x|)*y = w1 + w2 by simulating muti-precision arithmetic. 86 * 3. For w >= 262144 87 * then for (negative) ** (odd integer) => -Inf + overflow 88 * else => +Inf + overflow 89 * For w <= -275200 90 * then for (negative) ** (odd integer) => -0 + underflow 91 * else => +0 + underflow 92 * 4. Computes 2 ** (w/256) from: 93 * 2 ** (w/256) = 2**a * 2**(k/256) * 2**(r/256) 94 * Where: 95 * a = int ( w ) >> 8; 96 * k = int ( w ) & 0xFF; 97 * r = frac ( w ). 98 * Note that: 99 * k = 0, 1, ..., 255; 100 * r = (-1, 1). 101 * Then: 102 * 2**(k/256) is looked up in a table of 2**0, 2**1/256, ... 103 * 2**(r/256) is computed using approximation: 104 * 2**(r/256) = ((((b5 * r + b4) * r + b3) * r + b2) * r + b1) * r + b0 105 * Multiplication by 2**a is done by adding "a" to 106 * the biased exponent. 107 * Perform 2 ** (w/256) by simulating muti-precision arithmetic. 108 * 5. For (negative) ** (odd integer) => -(2**(w/256)) 109 * otherwise => 2**(w/256) 110 * 111 * Accuracy: 112 * Max. relative aproximation error < 2**(-67.94) for 256*log2((1+z)/(1-z)). 113 * Max. relative aproximation error < 2**(-63.15) for 2**(r/256). 114 * Maximum error observed: less than 0.761 ulp after 1.300.000.000 115 * results. 116 */ 117 118 static void 119 __vpowx(int n, double * restrict px, double * restrict py, 120 int stridey, double * restrict pz, int stridez); 121 122 static const double __TBL_exp2[] = { 123 /* __TBL_exp2[2*i] = high order bits 2^(i/256), i = [0, 255] */ 124 /* __TBL_exp2[2*i+1] = least bits 2^(i/256), i = [0, 255] */ 125 1.000000000000000000e+00, 0.000000000000000000e+00, 1.002711275050202522e+00, 126 -3.636615928692263944e-17, 1.005429901112802726e+00, 9.499186535455031757e-17, 127 1.008155898118417548e+00,-3.252058756084308061e-17, 1.010889286051700475e+00, 128 -1.523477860336857718e-17, 1.013630084951489430e+00, 9.283599768183567587e-18, 129 1.016378314910953096e+00,-5.772170073199660028e-17, 1.019133996077737914e+00, 130 3.601904982259661106e-17, 1.021897148654116627e+00, 5.109225028973443894e-17, 131 1.024667792897135721e+00,-7.561607868487779440e-17, 1.027445949118763746e+00, 132 -4.956074174645370440e-17, 1.030231637686040980e+00, 3.319830041080812944e-17, 133 1.033024879021228415e+00, 7.600838874027088489e-18, 1.035825693601957198e+00, 134 -7.806782391337636167e-17, 1.038634101961378731e+00, 5.996273788852510618e-17, 135 1.041450124688316103e+00, 3.784830480287576210e-17, 1.044273782427413755e+00, 136 8.551889705537964892e-17, 1.047105095879289793e+00, 7.277077243104314749e-17, 137 1.049944085800687210e+00, 5.592937848127002586e-17, 1.052790773004626423e+00, 138 -9.629482899026935739e-17, 1.055645178360557157e+00, 1.759325738772091599e-18, 139 1.058507322794512762e+00,-7.152651856637780738e-17, 1.061377227289262093e+00, 140 -1.197353708536565756e-17, 1.064254912884464499e+00, 5.078754198611230394e-17, 141 1.067140400676823697e+00,-7.899853966841582122e-17, 1.070033711820241873e+00, 142 -9.937162711288919381e-17, 1.072934867525975555e+00,-3.839668843358823807e-18, 143 1.075843889062791048e+00,-1.000271615114413611e-17, 1.078760797757119860e+00, 144 -6.656660436056592603e-17, 1.081685614993215250e+00,-4.782623902997086266e-17, 145 1.084618362213309206e+00, 3.166152845816346116e-17, 1.087559060917769660e+00, 146 5.409349307820290759e-18, 1.090507732665257690e+00,-3.046782079812471147e-17, 147 1.093464399072885840e+00, 1.441395814726920934e-17, 1.096429081816376883e+00, 148 -5.919933484449315824e-17, 1.099401802630221914e+00, 7.170459599701923225e-17, 149 1.102382583307840891e+00, 5.266036871570694387e-17, 1.105371445701741173e+00, 150 8.239288760500213590e-17, 1.108368411723678726e+00,-8.786813845180526616e-17, 151 1.111373503344817548e+00, 5.563945026669697643e-17, 1.114386742595892432e+00, 152 1.041027845684557095e-16, 1.117408151567369279e+00,-7.976805902628220456e-17, 153 1.120437752409606746e+00,-6.201085906554178750e-17, 1.123475567333019898e+00, 154 -9.699737588987042995e-17, 1.126521618608241848e+00, 5.165856758795456737e-17, 155 1.129575928566288079e+00, 6.712805858726256588e-17, 1.132638519598719196e+00, 156 3.237356166738000264e-17, 1.135709414157805464e+00, 5.066599926126155859e-17, 157 1.138788634756691565e+00, 8.912812676025407778e-17, 1.141876203969561576e+00, 158 4.651091177531412387e-17, 1.144972144431804173e+00, 4.641289892170010657e-17, 159 1.148076478840178938e+00, 6.897740236627191770e-17, 1.151189229952982673e+00, 160 3.250710218863827212e-17, 1.154310420590215935e+00, 1.041712894627326619e-16, 161 1.157440073633751121e+00,-9.123871231134400287e-17, 1.160578212027498779e+00, 162 -3.261040205417393722e-17, 1.163724858777577476e+00, 3.829204836924093499e-17, 163 1.166880036952481658e+00,-8.791879579999169742e-17, 1.170043769683250190e+00, 164 -1.847744201790004694e-18, 1.173216080163637320e+00,-7.287562586584994479e-17, 165 1.176396991650281221e+00, 5.554203254218078963e-17, 1.179586527462875845e+00, 166 1.009231277510039044e-16, 1.182784710984341014e+00, 1.542975430079076058e-17, 167 1.185991565660993841e+00,-9.209506835293105905e-18, 1.189207115002721027e+00, 168 3.982015231465646111e-17, 1.192431382583151178e+00, 4.397551415609721443e-17, 169 1.195664392039827328e+00, 4.616603670481481397e-17, 1.198906167074380580e+00, 170 -9.809193356008423118e-17, 1.202156731452703076e+00, 6.644981499252301245e-17, 171 1.205416109005123859e+00,-3.357272193267529634e-17, 1.208684323626581625e+00, 172 -4.746725945228984097e-17, 1.211961399276801243e+00,-4.890611077521118357e-17, 173 1.215247359980468955e+00,-7.712630692681488131e-17, 1.218542229827408452e+00, 174 -9.006726958363837675e-17, 1.221846032972757623e+00,-1.061102121140269116e-16, 175 1.225158793637145527e+00,-8.903533814269983429e-17, 1.228480536106870025e+00, 176 -1.898781631302529953e-17, 1.231811284734075862e+00, 7.389382471610050247e-17, 177 1.235151063936933413e+00,-1.075524434430784138e-16, 1.238499898199816540e+00, 178 2.767702055573967430e-17, 1.241857812073484002e+00, 4.658027591836936791e-17, 179 1.245224830175257980e+00,-4.677240449846727500e-17, 1.248600977189204819e+00, 180 -8.261810999021963550e-17, 1.251986277866316222e+00, 4.834167152469897600e-17, 181 1.255380757024691096e+00,-6.711389821296878419e-18, 1.258784439549716527e+00, 182 -8.421782587730599357e-17, 1.262197350394250739e+00,-3.084464887473846465e-17, 183 1.265619514578806282e+00, 4.250577003450868637e-17, 1.269050957191733220e+00, 184 2.667932131342186095e-18, 1.272491703389402762e+00,-1.057791626721242103e-17, 185 1.275941778396392001e+00, 9.915430244214290330e-17, 1.279401207505669325e+00, 186 -9.759095008356062210e-17, 1.282870016078778264e+00, 1.713594918243560968e-17, 187 1.286348229546025568e+00,-3.416955706936181976e-17, 1.289835873406665723e+00, 188 8.949257530897591722e-17, 1.293332973229089466e+00,-2.974590443132751646e-17, 189 1.296839554651009641e+00, 2.538250279488831496e-17, 1.300355643379650594e+00, 190 5.678728102802217422e-17, 1.303881265191935812e+00, 8.647675598267871179e-17, 191 1.307416445934677318e+00,-7.336645652878868892e-17, 1.310961211524764414e+00, 192 -7.181536135519453857e-17, 1.314515587949354636e+00, 2.267543315104585645e-17, 193 1.318079601266064049e+00,-5.457955827149153502e-17, 1.321653277603157539e+00, 194 -2.480638245913021742e-17, 1.325236643159741323e+00,-2.858731210038861373e-17, 195 1.328829724205954355e+00, 4.089086223910160052e-17, 1.332432547083161500e+00, 196 -5.101586630916743959e-17, 1.336045138204145832e+00,-5.891866356388801353e-17, 197 1.339667524053302916e+00, 8.927282594831731984e-17, 1.343299731186835322e+00, 198 -5.802580890201437751e-17, 1.346941786232945804e+00, 3.224065101254679169e-17, 199 1.350593715892034474e+00,-8.287110381462416533e-17, 1.354255546936892651e+00, 200 7.700948379802989462e-17, 1.357927306212901142e+00,-9.529635744825188867e-17, 201 1.361609020638224754e+00, 1.533787661270668046e-18, 1.365300717204011915e+00, 202 -1.000536312597476517e-16, 1.369002422974590516e+00, 9.593797919118848773e-17, 203 1.372714165087668414e+00,-4.495960595234841262e-17, 1.376435970754530169e+00, 204 -6.898588935871801042e-17, 1.380167867260237990e+00, 1.051031457996998395e-16, 205 1.383909881963832023e+00,-6.770511658794786287e-17, 1.387662042298529075e+00, 206 8.422984274875415318e-17, 1.391424375771926236e+00,-4.906174865288989325e-17, 207 1.395196909966200272e+00,-9.329336224225496552e-17, 1.398979672538311236e+00, 208 -9.614213209051323072e-17, 1.402772691220204759e+00,-5.295783249407989223e-17, 209 1.406575993819015435e+00, 7.034914812136422188e-18, 1.410389608217270663e+00, 210 4.166548728435062259e-17, 1.414213562373095145e+00,-9.667293313452913451e-17, 211 1.418047884320415175e+00, 2.274438542185529452e-17, 1.421892602169165576e+00, 212 -1.607782891589024413e-17, 1.425747744105494208e+00, 9.880690758500607284e-17, 213 1.429613338391970023e+00,-1.203164248905365518e-17, 1.433489413367788901e+00, 214 -5.802454243926826103e-17, 1.437375997448982368e+00,-4.204034016467556612e-17, 215 1.441273119128625657e+00, 5.602503650878985675e-18, 1.445180806977046650e+00, 216 -3.023758134993987319e-17, 1.449099089642035043e+00,-6.259405000819309254e-17, 217 1.453027995849052623e+00,-5.779948609396106102e-17, 1.456967554401443765e+00, 218 5.648679453876998140e-17, 1.460917794180647045e+00,-5.600377186075215800e-17, 219 1.464878744146405731e+00, 9.530767543587157319e-17, 1.468850433336981842e+00, 220 8.465882756533627608e-17, 1.472832890869367528e+00, 6.691774081940589372e-17, 221 1.476826145939499346e+00,-3.483994556892795796e-17, 1.480830227822471867e+00, 222 -9.686952102630618578e-17, 1.484845165872752393e+00, 1.078008676440748076e-16, 223 1.488870989524397004e+00, 6.155367157742871330e-17, 1.492907728291264835e+00, 224 1.419292015428403577e-17, 1.496955411767235455e+00,-2.861663253899158211e-17, 225 1.501014069626425584e+00,-6.413767275790235039e-17, 1.505083731623406473e+00, 226 7.074710613582846364e-17, 1.509164427593422841e+00,-1.016455327754295039e-16, 227 1.513256187452609813e+00, 8.884497851338712091e-17, 1.517359041198214742e+00, 228 -4.308699472043340801e-17, 1.521473018908814590e+00,-5.996387675945683420e-18, 229 1.525598150744538417e+00,-1.102494171234256094e-16, 1.529734466947286986e+00, 230 3.785792115157219653e-17, 1.533881997840955913e+00, 8.875226844438446141e-17, 231 1.538040773831656827e+00, 1.017467235116135806e-16, 1.542210825407940744e+00, 232 7.949834809697620856e-17, 1.546392183141021448e+00, 1.068396000565721980e-16, 233 1.550584877684999974e+00,-1.460070659068938518e-17, 1.554788939777088652e+00, 234 -8.003161350116035641e-17, 1.559004400237836929e+00, 3.781207053357527502e-17, 235 1.563231289971357629e+00, 7.484777645590734389e-17, 1.567469639965552997e+00, 236 -1.035206176884972199e-16, 1.571719481292341403e+00,-3.342984004687200069e-17, 237 1.575980845107886497e+00,-1.013691647127830398e-17, 1.580253762652824578e+00, 238 -5.163402929554468062e-17, 1.584538265252493749e+00,-1.933771703458570293e-17, 239 1.588834384317163950e+00,-5.994950118824479401e-18, 1.593142151342266999e+00, 240 -1.009440654231196372e-16, 1.597461597908627073e+00, 2.486839279622099613e-17, 241 1.601792755682693414e+00,-6.054917453527784343e-17, 1.606135656416771029e+00, 242 -1.035454528805999526e-16, 1.610490331949254283e+00, 2.470719256979788785e-17, 243 1.614856814204860713e+00,-7.316663399125123263e-17, 1.619235135194863728e+00, 244 2.094133415422909241e-17, 1.623625327017328868e+00,-3.584512851414474710e-17, 245 1.628027421857347834e+00,-6.712955084707084086e-17, 1.632441451987274972e+00, 246 9.852819230429992964e-17, 1.636867449766964411e+00, 7.698325071319875575e-17, 247 1.641305447644006321e+00,-9.247568737640705508e-17, 1.645755478153964946e+00, 248 -1.012567991367477260e-16, 1.650217573920617742e+00, 9.133279588729904190e-18, 249 1.654691767656194301e+00, 9.643294303196028661e-17, 1.659178092161616158e+00, 250 -7.275545550823050654e-17, 1.663676580326736376e+00, 5.890992696713099670e-17, 251 1.668187265130582464e+00, 4.269178019570615091e-17, 1.672710179641596628e+00, 252 -5.476715964599563076e-17, 1.677245357017878469e+00, 8.303949509950732785e-17, 253 1.681792830507429004e+00, 8.199010020581496520e-17, 1.686352633448393368e+00, 254 -7.181463278358010675e-17, 1.690924799269305279e+00,-9.669671474394880166e-17, 255 1.695509361489332623e+00, 7.238416872845166641e-17, 1.700106353718523478e+00, 256 -8.023719370397700246e-18, 1.704715809658051251e+00,-2.728883284797281563e-17, 257 1.709337763100462926e+00,-9.868779456632931076e-17, 1.713972247929925974e+00, 258 6.473975107753367064e-17, 1.718619298122477934e+00,-1.851380418263110988e-17, 259 1.723278947746273992e+00,-9.522123800393799963e-17, 1.727951230961837670e+00, 260 -1.075098186120464245e-16, 1.732636182022311067e+00,-1.698051074315415494e-18, 261 1.737333835273706217e+00, 3.164389299292956947e-17, 1.742044225155156445e+00, 262 -1.525959118950788792e-18, 1.746767386199169048e+00,-1.075229048350751450e-16, 263 1.751503353031878207e+00,-5.124450420596724659e-17, 1.756252160373299454e+00, 264 2.960140695448873307e-17, 1.761013843037583904e+00,-7.943253125039227711e-17, 265 1.765788435933272726e+00, 9.461315018083267867e-17, 1.770575974063554714e+00, 266 5.961794510040555848e-17, 1.775376492526521188e+00, 6.429731796556572034e-17, 267 1.780190026515424462e+00,-5.284627289091617365e-17, 1.785016611318934965e+00, 268 1.533040012103131382e-17, 1.789856282321401038e+00,-4.154354660683350387e-17, 269 1.794709075003107168e+00, 1.822745842791208677e-17, 1.799575024940535117e+00, 270 -2.526889233358897644e-17, 1.804454167806623932e+00,-5.177222408793317883e-17, 271 1.809346539371031959e+00,-9.032641402450029682e-17, 1.814252175500398856e+00, 272 -9.969531538920348820e-17, 1.819171112158608494e+00, 7.402676901145838890e-17, 273 1.824103385407053413e+00,-1.015962786227708306e-16, 1.829049031404897274e+00, 274 6.889192908835695637e-17, 1.834008086409342431e+00, 3.283107224245627204e-17, 275 1.838980586775893711e+00, 6.918969740272511942e-18, 1.843966568958625984e+00, 276 -5.939742026949964550e-17, 1.848966069510450838e+00, 9.027580446261089288e-17, 277 1.853979125083385471e+00, 9.761887490727593538e-17, 1.859005772428820480e+00, 278 -9.528705461989940687e-17, 1.864046048397788979e+00, 6.540912680620571711e-17, 279 1.869099989941238604e+00,-9.938505214255067083e-17, 1.874167634110299963e+00, 280 -6.122763413004142562e-17, 1.879249018056560194e+00,-1.622631555783584478e-17, 281 1.884344179032334532e+00,-8.226593125533710906e-17, 1.889453154390939194e+00, 282 -9.005168285059126718e-17, 1.894575981586965607e+00, 3.403403535216529671e-17, 283 1.899712698176555303e+00,-3.859739769378514323e-17, 1.904863341817674138e+00, 284 6.533857514718278629e-17, 1.910027950270389852e+00,-5.909688006744060237e-17, 285 1.915206561397147400e+00,-1.061994605619596264e-16, 1.920399213163047403e+00, 286 7.116681540630314186e-17, 1.925605943636125028e+00,-9.914963769693740927e-17, 287 1.930826790987627106e+00, 6.167149706169109553e-17, 1.936061793492294347e+00, 288 1.033238596067632574e-16, 1.941310989528640452e+00,-6.638029891621487990e-17, 289 1.946574417579233218e+00, 6.811022349533877184e-17, 1.951852116230978318e+00, 290 -2.199016969979351086e-17, 1.957144124175400179e+00, 8.960767791036667768e-17, 291 1.962450480208927317e+00, 1.097684400091354695e-16, 1.967771223233175881e+00, 292 -1.031492801153113151e-16, 1.973106392255234320e+00,-7.451617863956037486e-18, 293 1.978456026387950928e+00, 4.038875310927816657e-17, 1.983820164850219392e+00, 294 -2.203454412391062657e-17, 1.989198846967266343e+00, 8.205132638369199416e-18, 295 1.994592112170940235e+00, 1.790971035200264509e-17 296 }; 297 298 static const double __TBL_log2[] = { 299 /* __TBL_log2[2*i] = high order rounded 32 bits log2(1+i/256)*256, i = [0, 255] */ 300 /* __TBL_log2[2*i+1] = low order least bits log2(1+i/256)*256, i = [0, 255] */ 301 0.000000000000000000e+00, 0.000000000000000000e+00, 1.439884185791015625e+00, 302 4.078417797464839152e-07, 2.874177932739257812e+00,-5.443862030060025621e-07, 303 4.302921295166015625e+00, 3.525917800357419922e-07, 5.726161956787109375e+00, 304 -1.821502755258614180e-06, 7.143936157226562500e+00,-1.035336134691423741e-06, 305 8.556289672851562500e+00,-1.279264291071495652e-06, 9.963264465332031250e+00, 306 -3.206502629414843101e-06, 1.136489105224609375e+01, 3.503517986289194222e-06, 307 1.276123046875000000e+01,-1.809406249049319022e-06, 1.415230560302734375e+01, 308 -2.114722805833714926e-06, 1.553816223144531250e+01,-3.719431504776986979e-06, 309 1.691883850097656250e+01,-5.743786819670105240e-06, 1.829435729980468750e+01, 310 7.514691093524705578e-06, 1.966479492187500000e+01,-2.076862291588726520e-06, 311 2.103015136718750000e+01, 3.219403619538604258e-06, 2.239048767089843750e+01, 312 -3.108115489869591032e-07, 2.374583435058593750e+01,-6.275103710481114264e-06, 313 2.509620666503906250e+01, 6.572855776743687178e-06, 2.644168090820312500e+01, 314 -1.954725505303359537e-06, 2.778225708007812500e+01, 3.855133152759458770e-06, 315 2.911799621582031250e+01,-1.707228100041815487e-06, 3.044891357421875000e+01, 316 1.042999152333371737e-06, 3.177505493164062500e+01, 8.966313933586820042e-07, 317 3.309646606445312500e+01,-1.372654171244005427e-05, 3.441314697265625000e+01, 318 -8.996099168734074844e-06, 3.572515869140625000e+01,-1.247731510027211536e-05, 319 3.703250122070312500e+01, 8.944258749129049106e-06, 3.833526611328125000e+01, 320 -3.520082642279872716e-06, 3.963342285156250000e+01, 1.306577612991810031e-05, 321 4.092706298828125000e+01,-7.730135593513790229e-07, 4.221618652343750000e+01, 322 -1.329446142304436745e-05, 4.350079345703125000e+01, 6.912200714904314733e-06, 323 4.478097534179687500e+01,-6.216230979739182064e-07, 4.605673217773437500e+01, 324 -5.133911151040936670e-06, 4.732809448242187500e+01,-6.697901206512330627e-06, 325 4.859509277343750000e+01,-5.700153089154811841e-06, 4.985775756835937500e+01, 326 -2.836263919120346801e-06, 5.111611938476562500e+01, 8.933436604624454391e-07, 327 5.237020874023437500e+01, 4.187561748309498307e-06, 5.362005615234375000e+01, 328 5.448667394155597532e-06, 5.486569213867187500e+01, 2.786324169943508531e-06, 329 5.610714721679687500e+01,-5.978483512667373796e-06, 5.734442138671875000e+01, 330 7.207996138368885843e-06, 5.857757568359375000e+01, 9.083351754561760127e-06, 331 5.980664062500000000e+01,-3.374516276140515786e-06, 6.103161621093750000e+01, 332 -2.943717299925017200e-06, 6.225253295898437500e+01, 6.810091060168101732e-06, 333 6.346945190429687500e+01,-8.462738988588859704e-06, 6.468237304687500000e+01, 334 -2.233961135216831566e-05, 6.589129638671875000e+01,-8.657399896582645111e-06, 335 6.709625244140625000e+01, 2.797335967336006296e-05, 6.829736328125000000e+01, 336 -8.863355250907819214e-06, 6.949450683593750000e+01, 2.830758238800374038e-05, 337 7.068786621093750000e+01,-1.846073268549083018e-05, 7.187731933593750000e+01, 338 -2.182503249464459606e-06, 7.306298828125000000e+01,-2.025251442448625989e-05, 339 7.424481201171875000e+01, 1.280303154355201204e-05, 7.542291259765625000e+01, 340 -8.813997363590295654e-07, 7.659722900390625000e+01, 2.370323712746426047e-05, 341 7.776788330078125000e+01,-1.176744290134661421e-05, 7.893481445312500000e+01, 342 -2.273743674288609119e-05, 8.009802246093750000e+01, 1.409185747234803696e-05, 343 8.125762939453125000e+01,-2.707246895087010889e-07, 8.241357421875000000e+01, 344 1.807241476105480180e-05, 8.356597900390625000e+01,-3.030059664889450720e-05, 345 8.471472167968750000e+01,-8.823455531875539245e-07, 8.585992431640625000e+01, 346 6.485238524924182146e-06, 8.700158691406250000e+01, 1.382440142980862947e-05, 347 8.813977050781250000e+01,-1.808136338482881111e-05, 8.927441406250000000e+01, 348 -6.579344146543672011e-06, 9.040557861328125000e+01, 8.714227880222726313e-06, 349 9.153332519531250000e+01,-1.201308307454951138e-05, 9.265759277343750000e+01, 350 1.330278431878087205e-05, 9.377850341796875000e+01,-1.657103990890600482e-05, 351 9.489599609375000000e+01,-1.995110226941163424e-05, 9.601007080078125000e+01, 352 2.362403148762806632e-05, 9.712084960937500000e+01, 1.236086810905991142e-05, 353 9.822827148437500000e+01, 2.738898236946465744e-05, 9.933239746093750000e+01, 354 2.758741700388469572e-05, 1.004332885742187500e+02,-2.834285611604269955e-05, 355 1.015308227539062500e+02, 1.228649517068771375e-06, 1.026251220703125000e+02, 356 1.361792668612316888e-05, 1.037161865234375000e+02, 2.803946653578170389e-05, 357 1.048040771484375000e+02, 2.502814149567842806e-06, 1.058887329101562500e+02, 358 1.692003190104140317e-05, 1.069702148437500000e+02, 2.896703985131545672e-05, 359 1.080485839843750000e+02,-3.844135045484567362e-06, 1.091237792968750000e+02, 360 -2.093137927645659717e-06, 1.101958618164062500e+02,-8.590030211185738579e-06, 361 1.112648315429687500e+02,-5.267967244023324300e-06, 1.123306884765625000e+02, 362 2.578347229232600646e-05, 1.133935546875000000e+02,-1.975022555464358195e-05, 363 1.144533081054687500e+02,-2.195797778964440179e-06, 1.155100708007812500e+02, 364 -2.617170507638525077e-05, 1.165637817382812500e+02,-1.334031370958194516e-05, 365 1.176145019531250000e+02,-7.581976902412963145e-06, 1.186622314453125000e+02, 366 8.112109654298731037e-06, 1.197070312500000000e+02,-1.042875265529314613e-05, 367 1.207488403320312500e+02, 1.455233211877492951e-05, 1.217877807617187500e+02, 368 -2.243432092472914265e-05, 1.228237304687500000e+02, 1.712269952247034061e-05, 369 1.238568115234375000e+02, 2.745621214456745937e-05, 1.248870239257812500e+02, 370 2.473291989440979066e-05, 1.259143676757812500e+02, 2.498461547595911484e-05, 371 1.269389038085937500e+02,-1.692547797717771941e-05, 1.279605712890625000e+02, 372 -2.419576192770340594e-05, 1.289793701171875000e+02, 1.880972467762623192e-05, 373 1.299954833984375000e+02,-5.550757125543327248e-05, 1.310086669921875000e+02, 374 1.237226167189998996e-05, 1.320191650390625000e+02,-6.438347630770959254e-06, 375 1.330268554687500000e+02, 2.525911246920619613e-05, 1.340318603515625000e+02, 376 3.990327953073019333e-07, 1.350340576171875000e+02, 5.593427389035480335e-05, 377 1.360336914062500000e+02,-3.751407409478960320e-05, 1.370305175781250000e+02, 378 -2.116319935859897563e-05, 1.380246582031250000e+02,-2.559468964093475045e-06, 379 1.390161132812500000e+02, 3.270409087092109593e-05, 1.400050048828125000e+02, 380 -2.315157751389992129e-05, 1.409912109375000000e+02,-3.387938973438343638e-05, 381 1.419747314453125000e+02, 1.458416266727572812e-05, 1.429556884765625000e+02, 382 1.412021555596584681e-05, 1.439340820312500000e+02,-2.143065540113838312e-05, 383 1.449097900390625000e+02, 4.373273697503468317e-05, 1.458830566406250000e+02, 384 -2.090790235253405790e-05, 1.468536376953125000e+02, 4.230297794089183646e-05, 385 1.478217773437500000e+02, 2.633401664450247309e-06, 1.487873535156250000e+02, 386 -4.542835986281740771e-06, 1.497503662109375000e+02, 3.397367848245215483e-05, 387 1.507109375000000000e+02, 9.209059510146982590e-06, 1.516689453125000000e+02, 388 5.622812858742714859e-05, 1.526246337890625000e+02,-5.621609346274134244e-05, 389 1.535776367187500000e+02, 5.088115468603551539e-05, 1.545283203125000000e+02, 390 2.400396513473623342e-05, 1.554765625000000000e+02,-2.180099663431456814e-06, 391 1.564223632812500000e+02,-1.517056781617965675e-05, 1.573657226562500000e+02, 392 -2.562756696989711716e-06, 1.583066406250000000e+02, 4.795320325388065854e-05, 393 1.592452392578125000e+02, 2.652301982429665372e-05, 1.601815185546875000e+02, 394 -5.473018439029181240e-05, 1.611152343750000000e+02, 6.036538006249134820e-05, 395 1.620467529296875000e+02, 1.753890969321481711e-05, 1.629759521484375000e+02, 396 -4.928926339732922490e-05, 1.639027099609375000e+02,-6.288016979631557560e-06, 397 1.648271484375000000e+02, 3.614482952210960361e-05, 1.657493896484375000e+02, 398 -3.247597790375142114e-05, 1.666691894531250000e+02, 4.348868072528205213e-05, 399 1.675867919921875000e+02, 3.131097214651595330e-05, 1.685021972656250000e+02, 400 -5.768116554728405733e-05, 1.694151611328125000e+02, 3.189681619086343127e-05, 401 1.703260498046875000e+02,-5.500528238559059116e-05, 1.712344970703125000e+02, 402 5.890184674174263693e-05, 1.721408691406250000e+02, 1.840407787096519837e-05, 403 1.730450439453125000e+02,-4.351222480150346831e-05, 1.739468994140625000e+02, 404 6.059331686505290421e-06, 1.748465576171875000e+02, 5.580532332169584454e-05, 405 1.757441406250000000e+02,-5.666096094448416139e-06, 1.766395263671875000e+02, 406 -4.568380948624016041e-05, 1.775327148437500000e+02,-5.372392273978838048e-05, 407 1.784237060546875000e+02,-1.933871000131713187e-05, 1.793126220703125000e+02, 408 -5.422619290693841471e-05, 1.801993408203125000e+02,-2.601847861521447132e-05, 409 1.810839843750000000e+02,-4.656229401600182454e-05, 1.819664306640625000e+02, 410 1.636297150881445295e-05, 1.828468017578125000e+02, 5.076471489501210225e-05, 411 1.837252197265625000e+02,-5.542156510357154555e-05, 1.846014404296875000e+02, 412 -4.812064810565531807e-05, 1.854755859375000000e+02,-3.953879286781995545e-05, 413 1.863476562500000000e+02,-1.988182101010412125e-05, 1.872176513671875000e+02, 414 2.057522891062264376e-05, 1.880856933593750000e+02,-3.058156040982771239e-05, 415 1.889516601562500000e+02,-4.169340446171797184e-05, 1.898155517578125000e+02, 416 -3.239118881346662872e-06, 1.906774902343750000e+02,-2.783449132689922134e-05, 417 1.915373535156250000e+02, 1.597927683340914293e-05, 1.923952636718750000e+02, 418 1.545493412281261116e-05, 1.932512207031250000e+02,-2.014927705264352875e-05, 419 1.941051025390625000e+02, 4.043097907577914080e-05, 1.949571533203125000e+02, 420 -3.781452579504048975e-05, 1.958071289062500000e+02,-1.677810793588779092e-06, 421 1.966551513671875000e+02, 3.577570564777057149e-05, 1.975013427734375000e+02, 422 -3.858128431828155999e-05, 1.983454589843750000e+02, 2.827352539329734468e-05, 423 1.991877441406250000e+02, 1.020426695132691908e-06, 2.000280761718750000e+02, 424 1.049043785864183866e-05, 2.008665771484375000e+02,-5.668571223208539910e-05, 425 2.017030029296875000e+02, 5.227451898157462205e-05, 2.025377197265625000e+02, 426 -2.025647781341857894e-05, 2.033704833984375000e+02,-2.161281037339224341e-05, 427 2.042012939453125000e+02, 5.667325008632565576e-05, 2.050303955078125000e+02, 428 -2.112821448834358837e-05, 2.058575439453125000e+02,-2.522383155215216853e-06, 429 2.066828613281250000e+02,-1.281378348494855858e-06, 2.075063476562500000e+02, 430 -9.162516382743561384e-06, 2.083280029296875000e+02,-1.797812601298608335e-05, 431 2.091478271484375000e+02,-1.959505997696247453e-05, 2.099658203125000000e+02, 432 -5.934211946670452627e-06, 2.107819824218750000e+02, 3.102996118252714271e-05, 433 2.115964355468750000e+02,-2.280040076415178584e-05, 2.124090576171875000e+02, 434 -3.743515649437846729e-05, 2.132198486328125000e+02,-5.006638631136701490e-06, 435 2.140289306640625000e+02,-3.976919665668718942e-05, 2.148361816406250000e+02, 436 -1.188780735169185652e-05, 2.156417236328125000e+02,-3.571887766413048520e-05, 437 2.164454345703125000e+02, 1.847144755636210490e-05, 2.172474365234375000e+02, 438 3.622647302213163157e-05, 2.180477294921875000e+02, 2.511032323154433900e-05, 439 2.188463134765625000e+02,-7.361941985081681848e-06, 2.196431884765625000e+02, 440 -5.372390403709574017e-05, 2.204382324218750000e+02, 1.551294579696132803e-05, 441 2.212316894531250000e+02,-3.642162925932327343e-05, 2.220233154296875000e+02, 442 4.193598594979618241e-05, 2.228133544921875000e+02, 1.372116405796589833e-05, 443 2.236016845703125000e+02, 8.233623894335039537e-06, 2.243883056640625000e+02, 444 3.265657742833052654e-05, 2.251733398437500000e+02,-2.794287750390687326e-05, 445 2.259566650390625000e+02,-4.440243113774530265e-05, 2.267382812500000000e+02, 446 -9.675114830058622014e-06, 2.275183105468750000e+02,-3.882892066889445600e-05, 447 2.282966308593750000e+02,-2.835487591479255673e-06, 2.290733642578125000e+02, 448 -1.685097895998181422e-05, 2.298483886718750000e+02, 4.806553595480019518e-05, 449 2.306219482421875000e+02,-4.539911586906436716e-05, 2.313937988281250000e+02, 450 -4.631966285757620260e-05, 2.321639404296875000e+02, 5.204609324350696002e-05, 451 2.329326171875000000e+02, 1.225763073721718197e-05, 2.336997070312500000e+02, 452 -3.695637982554016382e-05, 2.344650878906250000e+02, 3.309133292926460016e-05, 453 2.352290039062500000e+02,-1.516395380482592629e-05, 2.359913330078125000e+02, 454 -5.311674305290968619e-05, 2.367519531250000000e+02, 4.779807991226078768e-05, 455 2.375111083984375000e+02, 4.989464209345647548e-05, 2.382687988281250000e+02, 456 -4.041202611322311408e-05, 2.390247802734375000e+02, 2.739433433590848536e-05, 457 2.397792968750000000e+02, 1.550965806406508966e-05, 2.405322265625000000e+02, 458 5.230206142425020257e-05, 2.412836914062500000e+02, 2.196059540790264514e-05, 459 2.420335693359375000e+02, 5.277680785141730338e-05, 2.427819824218750000e+02, 460 2.886380247947272558e-05, 2.435289306640625000e+02,-4.363251767645384661e-05, 461 2.442742919921875000e+02,-3.653314744654563199e-05, 2.450180664062500000e+02, 462 5.623369525922526825e-05, 2.457604980468750000e+02,-3.437446279919778004e-06, 463 2.465013427734375000e+02, 3.459290119679066472e-05, 2.472407226562500000e+02, 464 5.421724428316440202e-05, 2.479787597656250000e+02,-6.070765164808318435e-05, 465 2.487152099609375000e+02,-6.014953987030989107e-05, 2.494501953125000000e+02, 466 -6.032228506450037554e-05, 2.501837158203125000e+02,-5.540433388359054134e-05, 467 2.509157714843750000e+02,-3.960875078622925214e-05, 2.516463623046875000e+02, 468 -7.182944107105660894e-06, 2.523754882812500000e+02, 4.759160516857532540e-05, 469 2.531032714843750000e+02, 8.329299458439681639e-06, 2.538295898437500000e+02, 470 2.751627995643241118e-06, 2.545544433593750000e+02, 3.647649263201999678e-05, 471 2.552779541015625000e+02,-6.981531437649667064e-06 472 }; 473 474 static const unsigned long long LCONST[] = { 475 0x3c90000000000000ULL, /* 2**(-54) = 5.551115123125782702e-17 */ 476 0x3ff0000000000000ULL, /* DONE = 1.0 */ 477 0x4330000000000000ULL, /* DVAIN52 = 2**52 = 4.503599627370496e15 */ 478 0xffffffff00000000ULL, /* 0xffffffff00000000 */ 479 0x000fffffffffffffULL, /* 0x000fffffffffffff */ 480 0x0000080000000000ULL, /* 0x0000080000000000 */ 481 0xfffff00000000000ULL, /* 0xfffff00000000000 */ 482 0x0000000000000000ULL, /* DZERO = 0.0 */ 483 0x4062776d8ce329bdULL, /* KA5 = 5.77078604860893737986e-01*256 */ 484 0x406ec709dc39fc99ULL, /* KA3 = 9.61796693925765549423e-01*256 */ 485 0x3f6d94ae0bf85de6ULL, /* KA1_LO = 1.41052154268147309568e-05*256 */ 486 0x4087154000000000ULL, /* KA1_HI = 2.8853759765625e+00*256 */ 487 0x40871547652b82feULL, /* KA1 = 2.885390081777926774e+00*256 */ 488 0x4110000000000000ULL, /* HTHRESH = 262144.0 */ 489 0xc110cc0000000000ULL, /* LTHRESH = -275200.0 */ 490 0x3cd5d52893bc7fecULL, /* KB5 = 1.21195555854068860923e-15 */ 491 0x3d83b2abc07c93d0ULL, /* KB4 = 2.23939573811855104311e-12 */ 492 0x3e2c6b08d71f5d1eULL, /* KB3 = 3.30830268126604677436e-09 */ 493 0x3ecebfbdff82c4edULL, /* KB2 = 3.66556559691003767877e-06 */ 494 0x3f662e42fefa39efULL, /* KB1 = 2.70760617406228636578e-03 */ 495 0x01a56e1fc2f8f359ULL, /* _TINY = 1.0e-300 */ 496 0x7e37e43c8800759cULL /* _HUGE = 1.0e+300 */ 497 }; 498 499 #define SCALE_ARR ((double*)LCONST + 1) 500 #define _TINY ((double*)LCONST)[20] /* 1.0e-300 */ 501 #define _HUGE ((double*)LCONST)[21] /* 1.0e+300 */ 502 503 #define RET_SC(I) \ 504 px += stridex; \ 505 py += stridey; \ 506 pz += stridez; \ 507 if (--n <= 0) \ 508 break; \ 509 goto start##I; 510 511 #define RETURN(I, ret) \ 512 { \ 513 pz[0] = (ret); \ 514 RET_SC(I) \ 515 } 516 517 #define PREP(I) \ 518 hx = HI(px); \ 519 lx = LO(px); \ 520 hy = HI(py); \ 521 ly = LO(py); \ 522 sx = hx >> 31; \ 523 sy = hy >> 31; \ 524 hx &= 0x7fffffff; \ 525 hy &= 0x7fffffff; \ 526 ull_y0 = *(unsigned long long*)px; \ 527 \ 528 if (hy < 0x3bf00000) /* |Y| < 2^(-64) */ \ 529 { \ 530 y0 = *px; \ 531 if ((hy | ly) == 0) /* pow(X,0) */ \ 532 RETURN (I, DONE) \ 533 if (hx > 0x7ff00000 || (hx == 0x7ff00000 && lx != 0)) /* |X| = Nan */ \ 534 *pz = y0 + y0; \ 535 else if ((hx | lx) == 0 || (hx == 0x7ff00000 && lx == 0)) /* X = 0 or Inf */ \ 536 { \ 537 HI(pz) = hx; \ 538 LO(pz) = lx; \ 539 if (sy) \ 540 *pz = DONE / *pz; \ 541 } \ 542 else \ 543 *pz = (sx) ? DZERO / DZERO : DONE; \ 544 RET_SC(I) \ 545 } \ 546 yisint##I = 0; /* Y - non-integer */ \ 547 exp = hy >> 20; /* Y exponent */ \ 548 ull_y0 &= LMMANT; \ 549 ull_x##I = (ull_y0 | LDONE); \ 550 x##I = *(double*)&ull_x##I; \ 551 ull_ax##I = ((ull_x##I + LMROUND) & LMHI20); \ 552 ax##I = *(double*)&ull_ax##I; \ 553 if (hx >= 0x7ff00000 || exp >= 0x43e) /* X=Inf,Nan or |Y|>2^63,Inf,Nan */ \ 554 { \ 555 y0 = *px; \ 556 if (hx > 0x7ff00000 || (hx == 0x7ff00000 && lx != 0) || \ 557 hy > 0x7ff00000 || (hy == 0x7ff00000 && ly != 0)) /* |X| or |Y| = Nan */ \ 558 RETURN (I, y0 + *py) \ 559 if (hy == 0x7ff00000 && (ly == 0)) /* |Y| = Inf */ \ 560 { \ 561 if (hx == 0x3ff00000 && (lx == 0)) /* +-1 ** +-Inf */ \ 562 *pz = *py - *py; \ 563 else if ((hx < 0x3ff00000) != sy) \ 564 *pz = DZERO; \ 565 else \ 566 { \ 567 HI(pz) = hy; \ 568 LO(pz) = ly; \ 569 } \ 570 RET_SC(I) \ 571 } \ 572 if (exp < 0x43e) /* |Y| < 2^63 */ \ 573 { \ 574 if (sx) /* X = -Inf */ \ 575 { \ 576 if (exp >= 0x434) /* |Y| >= 2^53 */ \ 577 yisint##I = 2; /* Y - even */ \ 578 else \ 579 { \ 580 if (exp >= 0x3ff) /* |Y| >= 1 */ \ 581 { \ 582 if (exp > (20 + 0x3ff)) \ 583 { \ 584 i0 = ly >> (52 - (exp - 0x3ff)); \ 585 if ((i0 << (52 - (exp - 0x3ff))) == ly) \ 586 yisint##I = 2 - (i0 & 1); \ 587 } \ 588 else if (ly == 0) \ 589 { \ 590 i0 = hy >> (20 - (exp - 0x3ff)); \ 591 if ((i0 << (20 - (exp - 0x3ff))) == hy) \ 592 yisint##I = 2 - (i0 & 1); \ 593 } \ 594 } \ 595 } \ 596 } \ 597 if (sy) \ 598 hx = lx = 0; \ 599 hx += yisint##I << 31; \ 600 HI(pz) = hx; \ 601 LO(pz) = lx; \ 602 RET_SC(I) \ 603 } \ 604 else /* |Y| >= 2^63 */ \ 605 { \ 606 /* |X| = 0, 1, Inf */ \ 607 if (lx == 0 && (hx == 0 || hx == 0x3ff00000 || hx == 0x7ff00000)) \ 608 { \ 609 HI(pz) = hx; \ 610 LO(pz) = lx; \ 611 if (sy) \ 612 *pz = DONE / *pz; \ 613 } \ 614 else \ 615 { \ 616 y0 = ((hx < 0x3ff00000) != sy) ? _TINY : _HUGE; \ 617 *pz = y0 * y0; \ 618 } \ 619 RET_SC(I) \ 620 } \ 621 } \ 622 if ((sx || (hx | lx)) == 0) /* X <= 0 */ \ 623 { \ 624 if (exp >= 0x434) /* |Y| >= 2^53 */ \ 625 yisint##I = 2; /* Y - even */ \ 626 else \ 627 { \ 628 if (exp >= 0x3ff) /* |Y| >= 1 */ \ 629 { \ 630 if (exp > (20 + 0x3ff)) \ 631 { \ 632 i0 = ly >> (52 - (exp - 0x3ff)); \ 633 if ((i0 << (52 - (exp - 0x3ff))) == ly) \ 634 yisint##I = 2 - (i0 & 1); \ 635 } \ 636 else if (ly == 0) \ 637 { \ 638 i0 = hy >> (20 - (exp - 0x3ff)); \ 639 if ((i0 << (20 - (exp - 0x3ff))) == hy) \ 640 yisint##I = 2 - (i0 & 1); \ 641 } \ 642 } \ 643 } \ 644 if ((hx | lx) == 0) /* X == 0 */ \ 645 { \ 646 y0 = DZERO; \ 647 if (sy) \ 648 y0 = DONE / y0; \ 649 if (sx & yisint##I) \ 650 y0 = -y0; \ 651 RETURN (I, y0) \ 652 } \ 653 if (yisint##I == 0) /* pow(neg,non-integer) */ \ 654 RETURN (I, DZERO / DZERO) /* NaN */ \ 655 } \ 656 exp = (hx >> 20); \ 657 exp##I = exp - 2046; \ 658 py##I = py; \ 659 pz##I = pz; \ 660 ux##I = x##I + ax##I; \ 661 if (!exp) \ 662 { \ 663 ax##I = (double) ull_y0; \ 664 ull_ax##I = *(unsigned long long*)&ax##I; \ 665 ull_x##I = ((ull_ax##I & LMMANT) | LDONE); \ 666 x##I = *(double*)&ull_x##I; \ 667 exp##I = ((unsigned int*) & ull_ax##I)[0]; \ 668 exp##I = (exp##I >> 20) - (2046 + 1023 + 51); \ 669 ull_ax##I = (ull_x##I + (LMROUND & LMHI20)); \ 670 ax##I = *(double*)&ull_ax##I; \ 671 ux##I = x##I + ax##I; \ 672 } \ 673 ull_x##I = *(unsigned long long *)&ux##I; \ 674 hx##I = HI(&ull_ax##I); \ 675 yd##I = DONE / ux##I; 676 677 void 678 __vpow(int n, double * restrict px, int stridex, double * restrict py, 679 int stridey, double * restrict pz, int stridez) 680 { 681 double *py0 = 0, *py1 = 0, *py2; 682 double *pz0 = 0, *pz1 = 0, *pz2; 683 double y0, yd0 = 0.0L, u0, s0, s_l0, m_h0; 684 double y1, yd1 = 0.0L, u1, s1, s_l1, m_h1; 685 double y2, yd2, u2, s2, s_l2, m_h2; 686 double ax0 = 0.0L, x0 = 0.0L, s_h0, ux0; 687 double ax1 = 0.0L, x1 = 0.0L, s_h1, ux1; 688 double ax2, x2, s_h2, ux2; 689 int eflag0, gflag0, ind0, i0; 690 int eflag1, gflag1, ind1, i1; 691 int eflag2, gflag2, ind2, i2; 692 int hx0 = 0, yisint0 = 0, exp0 = 0; 693 int hx1 = 0, yisint1 = 0, exp1 = 0; 694 int hx2, yisint2, exp2; 695 int exp, i = 0; 696 unsigned hx, lx, sx, hy, ly, sy; 697 unsigned long long ull_y0, ull_x0, ull_x1, ull_x2, ull_ax0, ull_ax1, ull_ax2; 698 unsigned long long LDONE = ((unsigned long long*)LCONST)[1]; /* 1.0 */ 699 unsigned long long LMMANT = ((unsigned long long*)LCONST)[4]; /* 0x000fffffffffffff */ 700 unsigned long long LMROUND = ((unsigned long long*)LCONST)[5]; /* 0x0000080000000000 */ 701 unsigned long long LMHI20 = ((unsigned long long*)LCONST)[6]; /* 0xfffff00000000000 */ 702 double DONE = ((double*)LCONST)[1]; /* 1.0 */ 703 double DZERO = ((double*)LCONST)[7]; /* 0.0 */ 704 double KA5 = ((double*)LCONST)[8]; /* 5.77078604860893737986e-01*256 */ 705 double KA3 = ((double*)LCONST)[9]; /* 9.61796693925765549423e-01*256 */ 706 double KA1_LO = ((double*)LCONST)[10]; /* 1.41052154268147309568e-05*256 */ 707 double KA1_HI = ((double*)LCONST)[11]; /* 2.8853759765625e+00*256 */ 708 double KA1 = ((double*)LCONST)[12]; /* 2.885390081777926774e+00*256 */ 709 double HTHRESH = ((double*)LCONST)[13]; /* 262144.0 */ 710 double LTHRESH = ((double*)LCONST)[14]; /* -275200.0 */ 711 double KB5 = ((double*)LCONST)[15]; /* 1.21195555854068860923e-15 */ 712 double KB4 = ((double*)LCONST)[16]; /* 2.23939573811855104311e-12 */ 713 double KB3 = ((double*)LCONST)[17]; /* 3.30830268126604677436e-09 */ 714 double KB2 = ((double*)LCONST)[18]; /* 3.66556559691003767877e-06 */ 715 double KB1 = ((double*)LCONST)[19]; /* 2.70760617406228636578e-03 */ 716 717 if (stridex == 0) 718 { 719 unsigned hx = HI(px); 720 unsigned lx = LO(px); 721 722 /* if x is a positive normal number not equal to one, 723 call __vpowx */ 724 if (hx >= 0x00100000 && hx < 0x7ff00000 && 725 (hx != 0x3ff00000 || lx != 0)) 726 { 727 __vpowx(n, px, py, stridey, pz, stridez); 728 return; 729 } 730 } 731 732 do 733 { 734 /* perform si + ydi = 256*log2(xi)*yi */ 735 start0: 736 PREP(0) 737 px += stridex; 738 py += stridey; 739 pz += stridez; 740 i = 1; 741 if (--n <= 0) 742 break; 743 744 start1: 745 PREP(1) 746 px += stridex; 747 py += stridey; 748 pz += stridez; 749 i = 2; 750 if (--n <= 0) 751 break; 752 753 start2: 754 PREP(2) 755 756 u0 = x0 - ax0; 757 u1 = x1 - ax1; 758 u2 = x2 - ax2; 759 760 s0 = u0 * yd0; 761 LO(&ux0) = 0; 762 s1 = u1 * yd1; 763 LO(&ux1) = 0; 764 s2 = u2 * yd2; 765 LO(&ux2) = 0; 766 767 y0 = s0 * s0; 768 s_h0 = s0; 769 LO(&s_h0) = 0; 770 y1 = s1 * s1; 771 s_h1 = s1; 772 LO(&s_h1) = 0; 773 y2 = s2 * s2; 774 s_h2 = s2; 775 LO(&s_h2) = 0; 776 777 s0 = (KA5 * y0 + KA3) * y0 * s0; 778 s1 = (KA5 * y1 + KA3) * y1 * s1; 779 s2 = (KA5 * y2 + KA3) * y2 * s2; 780 781 s_l0 = (x0 - (ux0 - ax0)); 782 s_l1 = (x1 - (ux1 - ax1)); 783 s_l2 = (x2 - (ux2 - ax2)); 784 785 s_l0 = u0 - s_h0 * ux0 - s_h0 * s_l0; 786 s_l1 = u1 - s_h1 * ux1 - s_h1 * s_l1; 787 s_l2 = u2 - s_h2 * ux2 - s_h2 * s_l2; 788 789 s_l0 = KA1 * yd0 * s_l0; 790 i0 = (hx0 >> 8) & 0xff0; 791 exp0 += (hx0 >> 20); 792 793 s_l1 = KA1 * yd1 * s_l1; 794 i1 = (hx1 >> 8) & 0xff0; 795 exp1 += (hx1 >> 20); 796 797 s_l2 = KA1 * yd2 * s_l2; 798 i2 = (hx2 >> 8) & 0xff0; 799 exp2 += (hx2 >> 20); 800 801 yd0 = KA1_HI * s_h0; 802 yd1 = KA1_HI * s_h1; 803 yd2 = KA1_HI * s_h2; 804 805 y0 = *(double *)((char*)__TBL_log2 + i0); 806 y1 = *(double *)((char*)__TBL_log2 + i1); 807 y2 = *(double *)((char*)__TBL_log2 + i2); 808 809 y0 += (double)(exp0 << 8); 810 y1 += (double)(exp1 << 8); 811 y2 += (double)(exp2 << 8); 812 813 m_h0 = y0 + yd0; 814 m_h1 = y1 + yd1; 815 m_h2 = y2 + yd2; 816 817 y0 = s0 - ((m_h0 - y0 - yd0) - s_l0); 818 y1 = s1 - ((m_h1 - y1 - yd1) - s_l1); 819 y2 = s2 - ((m_h2 - y2 - yd2) - s_l2); 820 821 y0 += *(double *)((char*)__TBL_log2 + i0 + 8) + KA1_LO * s_h0; 822 y1 += *(double *)((char*)__TBL_log2 + i1 + 8) + KA1_LO * s_h1; 823 y2 += *(double *)((char*)__TBL_log2 + i2 + 8) + KA1_LO * s_h2; 824 825 s_h0 = y0 + m_h0; 826 s_h1 = y1 + m_h1; 827 s_h2 = y2 + m_h2; 828 829 LO(&s_h0) = 0; 830 LO(&s_h1) = 0; 831 LO(&s_h2) = 0; 832 833 yd0 = *py0; 834 yd1 = *py1; 835 yd2 = *py2; 836 s0 = yd0; 837 s1 = yd1; 838 s2 = yd2; 839 LO(&s0) = 0; 840 LO(&s1) = 0; 841 LO(&s2) = 0; 842 843 y0 = y0 - (s_h0 - m_h0); 844 y1 = y1 - (s_h1 - m_h1); 845 y2 = y2 - (s_h2 - m_h2); 846 847 yd0 = (yd0 - s0) * s_h0 + yd0 * y0; 848 yd1 = (yd1 - s1) * s_h1 + yd1 * y1; 849 yd2 = (yd2 - s2) * s_h2 + yd2 * y2; 850 851 s0 = s_h0 * s0; 852 s1 = s_h1 * s1; 853 s2 = s_h2 * s2; 854 855 /* perform 2 ** ((si+ydi)/256) */ 856 if (s0 > HTHRESH) 857 { 858 s0 = HTHRESH; 859 yd0 = DZERO; 860 } 861 if (s1 > HTHRESH) 862 { 863 s1 = HTHRESH; 864 yd1 = DZERO; 865 } 866 if (s2 > HTHRESH) 867 { 868 s2 = HTHRESH; 869 yd2 = DZERO; 870 } 871 872 if (s0 < LTHRESH) 873 { 874 s0 = LTHRESH; 875 yd0 = DZERO; 876 } 877 ind0 = (int) (s0 + yd0); 878 if (s1 < LTHRESH) 879 { 880 s1 = LTHRESH; 881 yd1 = DZERO; 882 } 883 ind1 = (int) (s1 + yd1); 884 if (s2 < LTHRESH) 885 { 886 s2 = LTHRESH; 887 yd2 = DZERO; 888 } 889 ind2 = (int) (s2 + yd2); 890 891 i0 = (ind0 & 0xff) << 4; 892 u0 = (double) ind0; 893 ind0 >>= 8; 894 895 i1 = (ind1 & 0xff) << 4; 896 u1 = (double)ind1; 897 ind1 >>= 8; 898 899 i2 = (ind2 & 0xff) << 4; 900 u2 = (double) ind2; 901 ind2 >>= 8; 902 903 y0 = s0 - u0 + yd0; 904 y1 = s1 - u1 + yd1; 905 y2 = s2 - u2 + yd2; 906 907 u0 = *(double*)((char*)__TBL_exp2 + i0); 908 y0 = ((((KB5 * y0 + KB4) * y0 + KB3) * y0 + KB2) * y0 + KB1) * y0; 909 u1 = *(double*)((char*)__TBL_exp2 + i1); 910 y1 = ((((KB5 * y1 + KB4) * y1 + KB3) * y1 + KB2) * y1 + KB1) * y1; 911 u2 = *(double*)((char*)__TBL_exp2 + i2); 912 y2 = ((((KB5 * y2 + KB4) * y2 + KB3) * y2 + KB2) * y2 + KB1) * y2; 913 914 eflag0 = (ind0 + 1021) >> 31; 915 gflag0 = (1022 - ind0) >> 31; 916 eflag1 = (ind1 + 1021) >> 31; 917 gflag1 = (1022 - ind1) >> 31; 918 eflag2 = (ind2 + 1021) >> 31; 919 gflag2 = (1022 - ind2) >> 31; 920 921 ind0 = (yisint0 << 11) + ind0 + (54 & eflag0) - (52 & gflag0); 922 ind0 <<= 20; 923 ind1 = (yisint1 << 11) + ind1 + (54 & eflag1) - (52 & gflag1); 924 ind1 <<= 20; 925 ind2 = (yisint2 << 11) + ind2 + (54 & eflag2) - (52 & gflag2); 926 ind2 <<= 20; 927 928 u0 = *(double*)((char*)__TBL_exp2 + i0 + 8) + u0 * y0 + u0; 929 u1 = *(double*)((char*)__TBL_exp2 + i1 + 8) + u1 * y1 + u1; 930 u2 = *(double*)((char*)__TBL_exp2 + i2 + 8) + u2 * y2 + u2; 931 932 ull_x0 = *(unsigned long long*)&u0; 933 HI(&ull_x0) += ind0; 934 u0 = *(double*)&ull_x0; 935 936 ull_x1 = *(unsigned long long*)&u1; 937 HI(&ull_x1) += ind1; 938 u1 = *(double*)&ull_x1; 939 940 ull_x2 = *(unsigned long long*)&u2; 941 HI(&ull_x2) += ind2; 942 u2 = *(double*)&ull_x2; 943 944 *pz0 = u0 * SCALE_ARR[eflag0 - gflag0]; 945 *pz1 = u1 * SCALE_ARR[eflag1 - gflag1]; 946 *pz2 = u2 * SCALE_ARR[eflag2 - gflag2]; 947 948 px += stridex; 949 py += stridey; 950 pz += stridez; 951 i = 0; 952 953 } while (--n > 0); 954 955 if (i > 0) 956 { 957 /* perform si + ydi = 256*log2(xi)*yi */ 958 u0 = x0 - ax0; 959 s0 = u0 * yd0; 960 LO(&ux0) = 0; 961 y0 = s0 * s0; 962 s_h0 = s0; 963 LO(&s_h0) = 0; 964 s0 = (KA5 * y0 + KA3) * y0 * s0; 965 s_l0 = (x0 - (ux0 - ax0)); 966 s_l0 = u0 - s_h0 * ux0 - s_h0 * s_l0; 967 s_l0 = KA1 * yd0 * s_l0; 968 i0 = (hx0 >> 8) & 0xff0; 969 exp0 += (hx0 >> 20); 970 yd0 = KA1_HI * s_h0; 971 y0 = *(double *)((char*)__TBL_log2 + i0); 972 y0 += (double)(exp0 << 8); 973 m_h0 = y0 + yd0; 974 y0 = s0 - ((m_h0 - y0 - yd0) - s_l0); 975 y0 += *(double *)((char*)__TBL_log2 + i0 + 8) + KA1_LO * s_h0; 976 s_h0 = y0 + m_h0; 977 LO(&s_h0) = 0; 978 y0 = y0 - (s_h0 - m_h0); 979 s0 = yd0 = *py0; 980 LO(&s0) = 0; 981 yd0 = (yd0 - s0) * s_h0 + yd0 * y0; 982 s0 = s_h0 * s0; 983 984 /* perform 2 ** ((si+ydi)/256) */ 985 if (s0 > HTHRESH) 986 { 987 s0 = HTHRESH; 988 yd0 = DZERO; 989 } 990 if (s0 < LTHRESH) 991 { 992 s0 = LTHRESH; 993 yd0 = DZERO; 994 } 995 ind0 = (int) (s0 + yd0); 996 i0 = (ind0 & 0xff) << 4; 997 u0 = (double) ind0; 998 ind0 >>= 8; 999 y0 = s0 - u0 + yd0; 1000 u0 = *(double*)((char*)__TBL_exp2 + i0); 1001 y0 = ((((KB5 * y0 + KB4) * y0 + KB3) * y0 + KB2) * y0 + KB1) * y0; 1002 eflag0 = (ind0 + 1021) >> 31; 1003 gflag0 = (1022 - ind0) >> 31; 1004 u0 = *(double*)((char*)__TBL_exp2 + i0 + 8) + u0 * y0 + u0; 1005 ind0 = (yisint0 << 11) + ind0 + (54 & eflag0) - (52 & gflag0); 1006 ind0 <<= 20; 1007 ull_x0 = *(unsigned long long*)&u0; 1008 HI(&ull_x0) += ind0; 1009 u0 = *(double*)&ull_x0; 1010 1011 *pz0 = u0 * SCALE_ARR[eflag0 - gflag0]; 1012 1013 if (i > 1) 1014 { 1015 /* perform si + ydi = 256*log2(xi)*yi */ 1016 u0 = x1 - ax1; 1017 s0 = u0 * yd1; 1018 LO(&ux1) = 0; 1019 y0 = s0 * s0; 1020 s_h0 = s0; 1021 LO(&s_h0) = 0; 1022 s0 = (KA5 * y0 + KA3) * y0 * s0; 1023 s_l0 = (x1 - (ux1 - ax1)); 1024 s_l0 = u0 - s_h0 * ux1 - s_h0 * s_l0; 1025 s_l0 = KA1 * yd1 * s_l0; 1026 i0 = (hx1 >> 8) & 0xff0; 1027 exp1 += (hx1 >> 20); 1028 yd0 = KA1_HI * s_h0; 1029 y0 = *(double *)((char*)__TBL_log2 + i0); 1030 y0 += (double)(exp1 << 8); 1031 m_h0 = y0 + yd0; 1032 y0 = s0 - ((m_h0 - y0 - yd0) - s_l0); 1033 y0 += *(double *)((char*)__TBL_log2 + i0 + 8) + KA1_LO * s_h0; 1034 s_h0 = y0 + m_h0; 1035 LO(&s_h0) = 0; 1036 y0 = y0 - (s_h0 - m_h0); 1037 s0 = yd0 = *py1; 1038 LO(&s0) = 0; 1039 yd0 = (yd0 - s0) * s_h0 + yd0 * y0; 1040 s0 = s_h0 * s0; 1041 /* perform 2 ** ((si+ydi)/256) */ 1042 if (s0 > HTHRESH) 1043 { 1044 s0 = HTHRESH; 1045 yd0 = DZERO; 1046 } 1047 if (s0 < LTHRESH) 1048 { 1049 s0 = LTHRESH; 1050 yd0 = DZERO; 1051 } 1052 ind0 = (int) (s0 + yd0); 1053 i0 = (ind0 & 0xff) << 4; 1054 u0 = (double) ind0; 1055 ind0 >>= 8; 1056 y0 = s0 - u0 + yd0; 1057 u0 = *(double*)((char*)__TBL_exp2 + i0); 1058 y0 = ((((KB5 * y0 + KB4) * y0 + KB3) * y0 + KB2) * y0 + KB1) * y0; 1059 eflag0 = (ind0 + 1021) >> 31; 1060 gflag0 = (1022 - ind0) >> 31; 1061 u0 = *(double*)((char*)__TBL_exp2 + i0 + 8) + u0 * y0 + u0; 1062 ind0 = (yisint1 << 11) + ind0 + (54 & eflag0) - (52 & gflag0); 1063 ind0 <<= 20; 1064 ull_x0 = *(unsigned long long*)&u0; 1065 HI(&ull_x0) += ind0; 1066 u0 = *(double*)&ull_x0; 1067 *pz1 = u0 * SCALE_ARR[eflag0 - gflag0]; 1068 } 1069 } 1070 } 1071 1072 #undef RET_SC 1073 #define RET_SC(I) \ 1074 py += stridey; \ 1075 pz += stridez; \ 1076 if (--n <= 0) \ 1077 break; \ 1078 goto start##I; 1079 1080 #define PREP_X(I) \ 1081 hy = HI(py); \ 1082 ly = LO(py); \ 1083 sy = hy >> 31; \ 1084 hy &= 0x7fffffff; \ 1085 py##I = py; \ 1086 \ 1087 if (hy < 0x3bf00000) /* |Y| < 2^(-64) */ \ 1088 RETURN (I, DONE) \ 1089 pz##I = pz; \ 1090 if (hy >= 0x43e00000) /* |Y|>2^63,Inf,Nan */ \ 1091 { \ 1092 if (hy >= 0x7ff00000) /* |Y|=Inf,Nan */ \ 1093 { \ 1094 if (hy == 0x7ff00000 && ly == 0) /* |Y|=Inf */ \ 1095 { \ 1096 if ((hx < 0x3ff00000) != sy) \ 1097 *pz = DZERO; \ 1098 else \ 1099 { \ 1100 HI(pz) = hy; \ 1101 LO(pz) = ly; \ 1102 } \ 1103 } \ 1104 else \ 1105 *pz = *px + *py; /* |Y|=Nan */ \ 1106 } \ 1107 else /* |Y|>2^63 */ \ 1108 { \ 1109 y0 = ((hx < 0x3ff00000) != sy) ? _TINY : _HUGE; \ 1110 *pz = y0 * y0; \ 1111 } \ 1112 RET_SC(I) \ 1113 } \ 1114 1115 #define LMMANT ((unsigned long long*)LCONST)[4] /* 0x000fffffffffffff */ 1116 #define LMROUND ((unsigned long long*)LCONST)[5] /* 0x0000080000000000 */ 1117 #define LMHI20 ((unsigned long long*)LCONST)[6] /* 0xfffff00000000000 */ 1118 #define MMANT ((double*)LCONST)[4] /* 0x000fffffffffffff */ 1119 #define MROUND ((double*)LCONST)[5] /* 0x0000080000000000 */ 1120 #define MHI20 ((double*)LCONST)[6] /* 0xfffff00000000000 */ 1121 #define KA5 ((double*)LCONST)[8] /* 5.77078604860893737986e-01*256 */ 1122 #define KA3 ((double*)LCONST)[9] /* 9.61796693925765549423e-01*256 */ 1123 #define KA1_LO ((double*)LCONST)[10] /* 1.41052154268147309568e-05*256 */ 1124 #define KA1_HI ((double*)LCONST)[11] /* 2.8853759765625e+00*256 */ 1125 #define KA1 ((double*)LCONST)[12] /* 2.885390081777926774e+00*256 */ 1126 1127 1128 static void 1129 __vpowx(int n, double * restrict px, double * restrict py, 1130 int stridey, double * restrict pz, int stridez) 1131 { 1132 double *py0, *py1 = 0, *py2; 1133 double *pz0, *pz1 = 0, *pz2; 1134 double ux0, y0, yd0, u0, s0; 1135 double y1, yd1, u1, s1; 1136 double y2, yd2, u2, s2; 1137 double yr, s_h0, s_l0, m_h0, x0, ax0; 1138 unsigned long long ull_y0, ull_x0, ull_x1, ull_x2, ull_ax0; 1139 int eflag0, gflag0, ind0, i0, exp0; 1140 int eflag1, gflag1, ind1, i1; 1141 int eflag2, gflag2, ind2, i2; 1142 int i = 0; 1143 unsigned hx, hx0, hy, ly, sy; 1144 double DONE = ((double*)LCONST)[1]; /* 1.0 */ 1145 unsigned long long LDONE = ((unsigned long long*)LCONST)[1]; /* 1.0 */ 1146 double DZERO = ((double*)LCONST)[7]; /* 0.0 */ 1147 double HTHRESH = ((double*)LCONST)[13]; /* 262144.0 */ 1148 double LTHRESH = ((double*)LCONST)[14]; /* -275200.0 */ 1149 double KB5 = ((double*)LCONST)[15]; /* 1.21195555854068860923e-15 */ 1150 double KB4 = ((double*)LCONST)[16]; /* 2.23939573811855104311e-12 */ 1151 double KB3 = ((double*)LCONST)[17]; /* 3.30830268126604677436e-09 */ 1152 double KB2 = ((double*)LCONST)[18]; /* 3.66556559691003767877e-06 */ 1153 double KB1 = ((double*)LCONST)[19]; /* 2.70760617406228636578e-03 */ 1154 1155 /* perform s_h + yr = 256*log2(x) */ 1156 ull_y0 = *(unsigned long long*)px; 1157 hx = HI(px); 1158 ull_x0 = (ull_y0 & LMMANT) | LDONE; 1159 x0 = *(double*)&ull_x0; 1160 exp0 = (hx >> 20) - 2046; 1161 ull_ax0 = ull_x0 + (LMROUND & LMHI20); 1162 ax0 = *(double*)&ull_ax0; 1163 hx0 = HI(&ax0); 1164 ux0 = x0 + ax0; 1165 yd0 = DONE / ux0; 1166 u0 = x0 - ax0; 1167 s0 = u0 * yd0; 1168 LO(&ux0) = 0; 1169 y0 = s0 * s0; 1170 s_h0 = s0; 1171 LO(&s_h0) = 0; 1172 s0 = (KA5 * y0 + KA3) * y0 * s0; 1173 s_l0 = (x0 - (ux0 - ax0)); 1174 s_l0 = u0 - s_h0 * ux0 - s_h0 * s_l0; 1175 s_l0 = KA1 * yd0 * s_l0; 1176 i0 = (hx0 >> 8) & 0xff0; 1177 exp0 += (hx0 >> 20); 1178 yd0 = KA1_HI * s_h0; 1179 y0 = *(double *)((char*)__TBL_log2 + i0); 1180 y0 += (double)(exp0 << 8); 1181 m_h0 = y0 + yd0; 1182 y0 = s0 - ((m_h0 - y0 - yd0) - s_l0); 1183 y0 += *(double *)((char*)__TBL_log2 + i0 + 8) + KA1_LO * s_h0; 1184 s_h0 = y0 + m_h0; 1185 LO(&s_h0) = 0; 1186 yr = y0 - (s_h0 - m_h0); 1187 1188 do 1189 { 1190 /* perform 2 ** ((s_h0+yr)*yi/256) */ 1191 start0: 1192 PREP_X(0) 1193 py += stridey; 1194 pz += stridez; 1195 i = 1; 1196 if (--n <= 0) 1197 break; 1198 1199 start1: 1200 PREP_X(1) 1201 py += stridey; 1202 pz += stridez; 1203 i = 2; 1204 if (--n <= 0) 1205 break; 1206 1207 start2: 1208 PREP_X(2) 1209 1210 s0 = yd0 = *py0; 1211 s1 = yd1 = *py1; 1212 s2 = yd2 = *py2; 1213 1214 LO(&s0) = 0; 1215 LO(&s1) = 0; 1216 LO(&s2) = 0; 1217 1218 yd0 = (yd0 - s0) * s_h0 + yd0 * yr; 1219 yd1 = (yd1 - s1) * s_h0 + yd1 * yr; 1220 yd2 = (yd2 - s2) * s_h0 + yd2 * yr; 1221 1222 s0 = s_h0 * s0; 1223 s1 = s_h0 * s1; 1224 s2 = s_h0 * s2; 1225 1226 if (s0 > HTHRESH) 1227 { 1228 s0 = HTHRESH; 1229 yd0 = DZERO; 1230 } 1231 if (s1 > HTHRESH) 1232 { 1233 s1 = HTHRESH; 1234 yd1 = DZERO; 1235 } 1236 if (s2 > HTHRESH) 1237 { 1238 s2 = HTHRESH; 1239 yd2 = DZERO; 1240 } 1241 1242 if (s0 < LTHRESH) 1243 { 1244 s0 = LTHRESH; 1245 yd0 = DZERO; 1246 } 1247 ind0 = (int) (s0 + yd0); 1248 if (s1 < LTHRESH) 1249 { 1250 s1 = LTHRESH; 1251 yd1 = DZERO; 1252 } 1253 ind1 = (int) (s1 + yd1); 1254 if (s2 < LTHRESH) 1255 { 1256 s2 = LTHRESH; 1257 yd2 = DZERO; 1258 } 1259 ind2 = (int) (s2 + yd2); 1260 1261 i0 = (ind0 & 0xff) << 4; 1262 u0 = (double) ind0; 1263 ind0 >>= 8; 1264 1265 i1 = (ind1 & 0xff) << 4; 1266 u1 = (double) ind1; 1267 ind1 >>= 8; 1268 1269 i2 = (ind2 & 0xff) << 4; 1270 u2 = (double) ind2; 1271 ind2 >>= 8; 1272 1273 y0 = s0 - u0 + yd0; 1274 y1 = s1 - u1 + yd1; 1275 y2 = s2 - u2 + yd2; 1276 1277 u0 = *(double*)((char*)__TBL_exp2 + i0); 1278 y0 = ((((KB5 * y0 + KB4) * y0 + KB3) * y0 + KB2) * y0 + KB1) * y0; 1279 u1 = *(double*)((char*)__TBL_exp2 + i1); 1280 y1 = ((((KB5 * y1 + KB4) * y1 + KB3) * y1 + KB2) * y1 + KB1) * y1; 1281 u2 = *(double*)((char*)__TBL_exp2 + i2); 1282 y2 = ((((KB5 * y2 + KB4) * y2 + KB3) * y2 + KB2) * y2 + KB1) * y2; 1283 1284 eflag0 = (ind0 + 1021) >> 31; 1285 gflag0 = (1022 - ind0) >> 31; 1286 eflag1 = (ind1 + 1021) >> 31; 1287 gflag1 = (1022 - ind1) >> 31; 1288 eflag2 = (ind2 + 1021) >> 31; 1289 gflag2 = (1022 - ind2) >> 31; 1290 1291 u0 = *(double*)((char*)__TBL_exp2 + i0 + 8) + u0 * y0 + u0; 1292 ind0 = ind0 + (54 & eflag0) - (52 & gflag0); 1293 ind0 <<= 20; 1294 ull_x0 = *(unsigned long long*)&u0; 1295 HI(&ull_x0) += ind0; 1296 u0 = *(double*)&ull_x0; 1297 1298 u1 = *(double*)((char*)__TBL_exp2 + i1 + 8) + u1 * y1 + u1; 1299 ind1 = ind1 + (54 & eflag1) - (52 & gflag1); 1300 ind1 <<= 20; 1301 ull_x1 = *(unsigned long long*)&u1; 1302 HI(&ull_x1) += ind1; 1303 u1 = *(double*)&ull_x1; 1304 1305 u2 = *(double*)((char*)__TBL_exp2 + i2 + 8) + u2 * y2 + u2; 1306 ind2 = ind2 + (54 & eflag2) - (52 & gflag2); 1307 ind2 <<= 20; 1308 ull_x2 = *(unsigned long long*)&u2; 1309 HI(&ull_x2) += ind2; 1310 u2 = *(double*)&ull_x2; 1311 1312 *pz0 = u0 * SCALE_ARR[eflag0 - gflag0]; 1313 *pz1 = u1 * SCALE_ARR[eflag1 - gflag1]; 1314 *pz2 = u2 * SCALE_ARR[eflag2 - gflag2]; 1315 1316 py += stridey; 1317 pz += stridez; 1318 i = 0; 1319 1320 } while (--n > 0); 1321 1322 if (i > 0) 1323 { 1324 /* perform 2 ** ((s_h0+yr)*yi/256) */ 1325 s0 = y0 = *py0; 1326 LO(&s0) = 0; 1327 yd0 = (y0 - s0) * s_h0 + y0 * yr; 1328 s0 = s_h0 * s0; 1329 if (s0 > HTHRESH) 1330 { 1331 s0 = HTHRESH; 1332 yd0 = DZERO; 1333 } 1334 if (s0 < LTHRESH) 1335 { 1336 s0 = LTHRESH; 1337 yd0 = DZERO; 1338 } 1339 ind0 = (int) (s0 + yd0); 1340 i0 = (ind0 & 0xff) << 4; 1341 u0 = (double) ind0; 1342 ind0 >>= 8; 1343 y0 = s0 - u0 + yd0; 1344 u0 = *(double*)((char*)__TBL_exp2 + i0); 1345 y0 = ((((KB5 * y0 + KB4) * y0 + KB3) * y0 + KB2) * y0 + KB1) * y0; 1346 eflag0 = (ind0 + 1021) >> 31; 1347 gflag0 = (1022 - ind0) >> 31; 1348 u0 = *(double*)((char*)__TBL_exp2 + i0 + 8) + u0 * y0 + u0; 1349 ind0 = ind0 + (54 & eflag0) - (52 & gflag0); 1350 ind0 <<= 20; 1351 ull_x0 = *(unsigned long long*)&u0; 1352 HI(&ull_x0) += ind0; 1353 u0 = *(double*)&ull_x0; 1354 *pz0 = u0 * SCALE_ARR[eflag0 - gflag0]; 1355 1356 if (i > 1) 1357 { 1358 /* perform 2 ** ((s_h0+yr)*yi/256) */ 1359 s0 = y0 = *py1; 1360 LO(&s0) = 0; 1361 yd0 = (y0 - s0) * s_h0 + y0 * yr; 1362 s0 = s_h0 * s0; 1363 if (s0 > HTHRESH) 1364 { 1365 s0 = HTHRESH; 1366 yd0 = DZERO; 1367 } 1368 if (s0 < LTHRESH) 1369 { 1370 s0 = LTHRESH; 1371 yd0 = DZERO; 1372 } 1373 ind0 = (int) (s0 + yd0); 1374 i0 = (ind0 & 0xff) << 4; 1375 u0 = (double) ind0; 1376 ind0 >>= 8; 1377 y0 = s0 - u0 + yd0; 1378 u0 = *(double*)((char*)__TBL_exp2 + i0); 1379 y0 = ((((KB5 * y0 + KB4) * y0 + KB3) * y0 + KB2) * y0 + KB1) * y0; 1380 eflag0 = (ind0 + 1021) >> 31; 1381 gflag0 = (1022 - ind0) >> 31; 1382 u0 = *(double*)((char*)__TBL_exp2 + i0 + 8) + u0 * y0 + u0; 1383 ind0 = ind0 + (54 & eflag0) - (52 & gflag0); 1384 ind0 <<= 20; 1385 ull_x0 = *(unsigned long long*)&u0; 1386 HI(&ull_x0) += ind0; 1387 u0 = *(double*)&ull_x0; 1388 *pz1 = u0 * SCALE_ARR[eflag0 - gflag0]; 1389 } 1390 } 1391 } 1392