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 #ifdef __RESTRICT 31 #define restrict _Restrict 32 #else 33 #define restrict 34 #endif 35 36 /* float powf(float x, float y) 37 * 38 * Method : 39 * 1. Special cases: 40 * for (anything) ** 0 => 1 41 * for (anything) ** NaN => QNaN + invalid 42 * for NaN ** (anything) => QNaN + invalid 43 * for +-1 ** +-Inf => QNaN + invalid 44 * for +-(|x| < 1) ** +Inf => +0 45 * for +-(|x| < 1) ** -Inf => +Inf 46 * for +-(|x| > 1) ** +Inf => +Inf 47 * for +-(|x| > 1) ** -Inf => +0 48 * for +Inf ** (negative) => +0 49 * for +Inf ** (positive) => +Inf 50 * for -Inf ** (negative except odd integer) => +0 51 * for -Inf ** (negative odd integer) => -0 52 * for -Inf ** (positive except odd integer) => +Inf 53 * for -Inf ** (positive odd integer) => -Inf 54 * for (negative) ** (non-integer) => QNaN + invalid 55 * for +0 ** (negative) => +Inf + overflow 56 * for +0 ** (positive) => +0 57 * for -0 ** (negative except odd integer) => +Inf + overflow 58 * for -0 ** (negative odd integer) => -Inf + overflow 59 * for -0 ** (positive except odd integer) => +0 60 * for -0 ** (positive odd integer) => -0 61 * 2. Computes x**y from: 62 * x**y = 2**(y*log2(x)) = 2**(w/256), where w = 256*log2(|x|)*y. 63 * 3. Computes w = 256 * log2(|x|) * y from 64 * |x| = m * 2**n => log2(|x|) = n + log2(m). 65 * Let m = m0 + dm, where m0 = 1 + k / 128, 66 * k = [0, 128], 67 * dm = [-1/256, 1/256]. 68 * Then 256*log2(m) = 256*log2(m0 + dm) = 256*log2(m0) + 256*log2(1+z), 69 * where z = dm*(1/m0), z = [-1/258, 1/256]. 70 * Then 71 * 1/m0 is looked up in a table of 1, 1/(1+1/128), ..., 1/(1+128/128). 72 * 256*log2(m0) is looked up in a table of 256*log2(1), 256*log2(1+1/128), 73 * ..., 256*log2(1+128/128). 74 * 256*log2(1+z) is computed using approximation: 75 * 256*log2(1+z) = (((a3*z + a2)*z + a1)*z + a0)*z. 76 * 3. For w >= 32768 77 * then for (negative) ** (odd integer) => -Inf + overflow 78 * else => +Inf + overflow 79 * For w <= -38400 80 * then for (negative) ** (odd integer) => -0 + underflow 81 * else => +0 + underflow 82 * 4. Computes 2 ** (w/256) from: 83 * 2 ** (w/256) = 2**a * 2**(k/256) * 2**(r/256) 84 * Where: 85 * a = int ( w ) >> 8; 86 * k = int ( w ) & 0xFF; 87 * r = frac ( w ). 88 * Note that: 89 * k = 0, 1, ..., 255; 90 * r = (-1, 1). 91 * Then: 92 * 2**(k/256) is looked up in a table of 2**0, 2**1/256, ... 93 * 2**(r/256) is computed using approximation: 94 * 2**(r/256) = a0 + a1 * r + a2 * r**2 95 * Multiplication by 2**a is done by adding "a" to 96 * the biased exponent. 97 * 5. For (negative) ** (odd integer) => -(2**(w/256)) 98 * otherwise => 2**(w/256) 99 * 100 * Accuracy: 101 * Max. relative aproximation error < 2**(-37.35) for 256*log2(1+z). 102 * Max. relative aproximation error < 2**(-29.18) for 2**(r/256). 103 * All calculations are done in double precision. 104 * Maximum error observed: less than 0.528 ulp after 700.000.000 105 * results. 106 */ 107 108 static void __vpowfx(int n, float * restrict px, float * restrict py, 109 int stridey, float * restrict pz, int stridez); 110 111 static void __vpowf_n(int n, float * restrict px, int stridex, float * restrict py, 112 int stridey, float * restrict pz, int stridez); 113 114 static void __vpowfx_n(int n, double yy, float * restrict py, 115 int stridey, float * restrict pz, int stridez); 116 117 #pragma no_inline(__vpowfx) 118 #pragma no_inline(__vpowf_n) 119 #pragma no_inline(__vpowfx_n) 120 121 static const double __TBL_exp2f[] = { 122 /* 2^(i/256), i = [0, 255] */ 123 1.000000000000000000e+00, 1.002711275050202522e+00, 1.005429901112802726e+00, 124 1.008155898118417548e+00, 1.010889286051700475e+00, 1.013630084951489430e+00, 125 1.016378314910953096e+00, 1.019133996077737914e+00, 1.021897148654116627e+00, 126 1.024667792897135721e+00, 1.027445949118763746e+00, 1.030231637686040980e+00, 127 1.033024879021228415e+00, 1.035825693601957198e+00, 1.038634101961378731e+00, 128 1.041450124688316103e+00, 1.044273782427413755e+00, 1.047105095879289793e+00, 129 1.049944085800687210e+00, 1.052790773004626423e+00, 1.055645178360557157e+00, 130 1.058507322794512762e+00, 1.061377227289262093e+00, 1.064254912884464499e+00, 131 1.067140400676823697e+00, 1.070033711820241873e+00, 1.072934867525975555e+00, 132 1.075843889062791048e+00, 1.078760797757119860e+00, 1.081685614993215250e+00, 133 1.084618362213309206e+00, 1.087559060917769660e+00, 1.090507732665257690e+00, 134 1.093464399072885840e+00, 1.096429081816376883e+00, 1.099401802630221914e+00, 135 1.102382583307840891e+00, 1.105371445701741173e+00, 1.108368411723678726e+00, 136 1.111373503344817548e+00, 1.114386742595892432e+00, 1.117408151567369279e+00, 137 1.120437752409606746e+00, 1.123475567333019898e+00, 1.126521618608241848e+00, 138 1.129575928566288079e+00, 1.132638519598719196e+00, 1.135709414157805464e+00, 139 1.138788634756691565e+00, 1.141876203969561576e+00, 1.144972144431804173e+00, 140 1.148076478840178938e+00, 1.151189229952982673e+00, 1.154310420590215935e+00, 141 1.157440073633751121e+00, 1.160578212027498779e+00, 1.163724858777577476e+00, 142 1.166880036952481658e+00, 1.170043769683250190e+00, 1.173216080163637320e+00, 143 1.176396991650281221e+00, 1.179586527462875845e+00, 1.182784710984341014e+00, 144 1.185991565660993841e+00, 1.189207115002721027e+00, 1.192431382583151178e+00, 145 1.195664392039827328e+00, 1.198906167074380580e+00, 1.202156731452703076e+00, 146 1.205416109005123859e+00, 1.208684323626581625e+00, 1.211961399276801243e+00, 147 1.215247359980468955e+00, 1.218542229827408452e+00, 1.221846032972757623e+00, 148 1.225158793637145527e+00, 1.228480536106870025e+00, 1.231811284734075862e+00, 149 1.235151063936933413e+00, 1.238499898199816540e+00, 1.241857812073484002e+00, 150 1.245224830175257980e+00, 1.248600977189204819e+00, 1.251986277866316222e+00, 151 1.255380757024691096e+00, 1.258784439549716527e+00, 1.262197350394250739e+00, 152 1.265619514578806282e+00, 1.269050957191733220e+00, 1.272491703389402762e+00, 153 1.275941778396392001e+00, 1.279401207505669325e+00, 1.282870016078778264e+00, 154 1.286348229546025568e+00, 1.289835873406665723e+00, 1.293332973229089466e+00, 155 1.296839554651009641e+00, 1.300355643379650594e+00, 1.303881265191935812e+00, 156 1.307416445934677318e+00, 1.310961211524764414e+00, 1.314515587949354636e+00, 157 1.318079601266064049e+00, 1.321653277603157539e+00, 1.325236643159741323e+00, 158 1.328829724205954355e+00, 1.332432547083161500e+00, 1.336045138204145832e+00, 159 1.339667524053302916e+00, 1.343299731186835322e+00, 1.346941786232945804e+00, 160 1.350593715892034474e+00, 1.354255546936892651e+00, 1.357927306212901142e+00, 161 1.361609020638224754e+00, 1.365300717204011915e+00, 1.369002422974590516e+00, 162 1.372714165087668414e+00, 1.376435970754530169e+00, 1.380167867260237990e+00, 163 1.383909881963832023e+00, 1.387662042298529075e+00, 1.391424375771926236e+00, 164 1.395196909966200272e+00, 1.398979672538311236e+00, 1.402772691220204759e+00, 165 1.406575993819015435e+00, 1.410389608217270663e+00, 1.414213562373095145e+00, 166 1.418047884320415175e+00, 1.421892602169165576e+00, 1.425747744105494208e+00, 167 1.429613338391970023e+00, 1.433489413367788901e+00, 1.437375997448982368e+00, 168 1.441273119128625657e+00, 1.445180806977046650e+00, 1.449099089642035043e+00, 169 1.453027995849052623e+00, 1.456967554401443765e+00, 1.460917794180647045e+00, 170 1.464878744146405731e+00, 1.468850433336981842e+00, 1.472832890869367528e+00, 171 1.476826145939499346e+00, 1.480830227822471867e+00, 1.484845165872752393e+00, 172 1.488870989524397004e+00, 1.492907728291264835e+00, 1.496955411767235455e+00, 173 1.501014069626425584e+00, 1.505083731623406473e+00, 1.509164427593422841e+00, 174 1.513256187452609813e+00, 1.517359041198214742e+00, 1.521473018908814590e+00, 175 1.525598150744538417e+00, 1.529734466947286986e+00, 1.533881997840955913e+00, 176 1.538040773831656827e+00, 1.542210825407940744e+00, 1.546392183141021448e+00, 177 1.550584877684999974e+00, 1.554788939777088652e+00, 1.559004400237836929e+00, 178 1.563231289971357629e+00, 1.567469639965552997e+00, 1.571719481292341403e+00, 179 1.575980845107886497e+00, 1.580253762652824578e+00, 1.584538265252493749e+00, 180 1.588834384317163950e+00, 1.593142151342266999e+00, 1.597461597908627073e+00, 181 1.601792755682693414e+00, 1.606135656416771029e+00, 1.610490331949254283e+00, 182 1.614856814204860713e+00, 1.619235135194863728e+00, 1.623625327017328868e+00, 183 1.628027421857347834e+00, 1.632441451987274972e+00, 1.636867449766964411e+00, 184 1.641305447644006321e+00, 1.645755478153964946e+00, 1.650217573920617742e+00, 185 1.654691767656194301e+00, 1.659178092161616158e+00, 1.663676580326736376e+00, 186 1.668187265130582464e+00, 1.672710179641596628e+00, 1.677245357017878469e+00, 187 1.681792830507429004e+00, 1.686352633448393368e+00, 1.690924799269305279e+00, 188 1.695509361489332623e+00, 1.700106353718523478e+00, 1.704715809658051251e+00, 189 1.709337763100462926e+00, 1.713972247929925974e+00, 1.718619298122477934e+00, 190 1.723278947746273992e+00, 1.727951230961837670e+00, 1.732636182022311067e+00, 191 1.737333835273706217e+00, 1.742044225155156445e+00, 1.746767386199169048e+00, 192 1.751503353031878207e+00, 1.756252160373299454e+00, 1.761013843037583904e+00, 193 1.765788435933272726e+00, 1.770575974063554714e+00, 1.775376492526521188e+00, 194 1.780190026515424462e+00, 1.785016611318934965e+00, 1.789856282321401038e+00, 195 1.794709075003107168e+00, 1.799575024940535117e+00, 1.804454167806623932e+00, 196 1.809346539371031959e+00, 1.814252175500398856e+00, 1.819171112158608494e+00, 197 1.824103385407053413e+00, 1.829049031404897274e+00, 1.834008086409342431e+00, 198 1.838980586775893711e+00, 1.843966568958625984e+00, 1.848966069510450838e+00, 199 1.853979125083385471e+00, 1.859005772428820480e+00, 1.864046048397788979e+00, 200 1.869099989941238604e+00, 1.874167634110299963e+00, 1.879249018056560194e+00, 201 1.884344179032334532e+00, 1.889453154390939194e+00, 1.894575981586965607e+00, 202 1.899712698176555303e+00, 1.904863341817674138e+00, 1.910027950270389852e+00, 203 1.915206561397147400e+00, 1.920399213163047403e+00, 1.925605943636125028e+00, 204 1.930826790987627106e+00, 1.936061793492294347e+00, 1.941310989528640452e+00, 205 1.946574417579233218e+00, 1.951852116230978318e+00, 1.957144124175400179e+00, 206 1.962450480208927317e+00, 1.967771223233175881e+00, 1.973106392255234320e+00, 207 1.978456026387950928e+00, 1.983820164850219392e+00, 1.989198846967266343e+00, 208 1.994592112170940235e+00 209 }; 210 211 static const double __TBL_log2f[] = { 212 /* __TBL_log2f[2*i] = 256*log2(1+i/128), i = [0, 128] */ 213 /* __TBL_log2f[2*i+1] = 2**(-23)/(1+i/128), i = [0, 128] */ 214 0.000000000000000000e+00, 1.192092895507812500e-07, 2.874177388353054585e+00, 215 1.182851865310077503e-07, 5.726160135284354524e+00, 1.173753004807692373e-07, 216 8.556288393587271557e+00, 1.164793058206106825e-07, 1.136489455576407970e+01, 217 1.155968868371212153e-07, 1.415230348830453799e+01, 1.147277373120300688e-07, 218 1.691883275718974389e+01, 1.138715601679104456e-07, 1.966479284501270897e+01, 219 1.130280671296296339e-07, 2.239048736008688678e+01, 1.121969784007352926e-07, 220 2.509621323789484038e+01, 1.113780223540145949e-07, 2.778226093521127638e+01, 221 1.105709352355072477e-07, 3.044891461721790193e+01, 1.097754608812949697e-07, 222 3.309645233791141550e+01, 1.089913504464285680e-07, 3.572514621409114710e+01, 223 1.082183621453900683e-07, 3.833526259319860685e+01, 1.074562610035211292e-07, 224 4.092706221526768928e+01, 1.067048186188811188e-07, 4.350080036923196758e+01, 225 1.059638129340277719e-07, 4.605672704382322280e+01, 1.052330280172413778e-07, 226 4.859508707328441091e+01, 1.045122538527397202e-07, 5.111612027810928538e+01, 227 1.038012861394557784e-07, 5.362006160101114460e+01, 1.030999260979729787e-07, 228 5.610714123831336053e+01, 1.024079802852348971e-07, 5.857758476694550609e+01, 229 1.017252604166666732e-07, 6.103161326722020164e+01, 1.010515831953642383e-07, 230 6.346944344155788542e+01, 1.003867701480263102e-07, 6.589128772931884725e+01, 231 9.973064746732026447e-08, 6.829735441789475203e+01, 9.908304586038961692e-08, 232 7.068784775020480993e+01, 9.844380040322580637e-08, 7.306296802873558249e+01, 233 9.781275040064102225e-08, 7.542291171625650748e+01, 9.718973925159236158e-08, 234 7.776787153333835079e+01, 9.657461431962025166e-08, 8.009803655279496581e+01, 235 9.596722680817610579e-08, 8.241359229116476115e+01, 9.536743164062500529e-08, 236 8.471472079734193983e+01, 9.477508734472049048e-08, 8.700160073846393516e+01, 237 9.419005594135801946e-08, 8.927440748315585495e+01, 9.361220283742331508e-08, 238 9.153331318222942059e+01, 9.304139672256097884e-08, 9.377848684692884262e+01, 239 9.247750946969696962e-08, 9.601009442481273481e+01, 9.192041603915663129e-08, 240 9.822829887335737453e+01, 9.136999438622755046e-08, 1.004332602313626381e+02, 241 9.082612537202380448e-08, 1.026251356882391832e+02, 9.028869267751479078e-08, 242 1.048040796512516550e+02, 8.975758272058823405e-08, 1.069702438107898530e+02, 243 8.923268457602338686e-08, 1.091237772037370775e+02, 8.871388989825581272e-08, 244 1.112648262750015107e+02, 8.820109284682080489e-08, 1.133935349372744383e+02, 245 8.769419001436781487e-08, 1.155100446290761766e+02, 8.719308035714285707e-08, 246 1.176144943711480977e+02, 8.669766512784091150e-08, 1.197070208212473403e+02, 247 8.620784781073446298e-08, 1.217877583273978246e+02, 8.572353405898876167e-08, 248 1.238568389796496376e+02, 8.524463163407821503e-08, 1.259143926603967287e+02, 249 8.477105034722222546e-08, 1.279605470933005762e+02, 8.430270200276242743e-08, 250 1.299954278908662388e+02, 8.383950034340659995e-08, 1.320191586007148601e+02, 251 8.338136099726775949e-08, 1.340318607505952855e+02, 8.292820142663043248e-08, 252 1.360336538921758915e+02, 8.247994087837838296e-08, 1.380246556436560468e+02, 253 8.203650033602151192e-08, 1.400049817312349774e+02, 8.159780247326202734e-08, 254 1.419747460294751704e+02, 8.116377160904255122e-08, 1.439340606005945915e+02, 255 8.073433366402115954e-08, 1.458830357327226466e+02, 8.030941611842105082e-08, 256 1.478217799771516638e+02, 7.988894797120419333e-08, 1.497504001846159838e+02, 257 7.947285970052082892e-08, 1.516690015406285852e+02, 7.906108322538860398e-08, 258 1.535776875999046922e+02, 7.865355186855669953e-08, 1.554765603199003294e+02, 259 7.825020032051282044e-08, 1.573657200934933087e+02, 7.785096460459183052e-08, 260 1.592452657808323124e+02, 7.745578204314720208e-08, 1.611152947403800511e+02, 261 7.706459122474748130e-08, 1.629759028591741128e+02, 7.667733197236181018e-08, 262 1.648271845823295223e+02, 7.629394531250000159e-08, 1.666692329418057170e+02, 263 7.591437344527363039e-08, 1.685021395844594565e+02, 7.553855971534653557e-08, 264 1.703259947994051231e+02, 7.516644858374384321e-08, 1.721408875447028777e+02, 265 7.479798560049019504e-08, 1.739469054733941960e+02, 7.443311737804878042e-08, 266 1.757441349589039135e+02, 7.407179156553397416e-08, 1.775326611198272531e+02, 267 7.371395682367149407e-08, 1.793125678441195987e+02, 7.335956280048077330e-08, 268 1.810839378127059831e+02, 7.300856010765549954e-08, 1.828468525225273993e+02, 269 7.266090029761905417e-08, 1.846013923090393973e+02, 7.231653584123223301e-08, 270 1.863476363681789962e+02, 7.197542010613207272e-08, 1.880856627778145764e+02, 271 7.163750733568075279e-08, 1.898155485186936176e+02, 7.130275262850466758e-08, 272 1.915373694949018386e+02, 7.097111191860465018e-08, 1.932512005538479514e+02, 273 7.064254195601851460e-08, 1.949571155057867031e+02, 7.031700028801843312e-08, 274 1.966551871428931406e+02, 6.999444524082569196e-08, 1.983454872579004018e+02, 275 6.967483590182648015e-08, 2.000280866623128588e+02, 6.935813210227272390e-08, 276 2.017030552042064926e+02, 6.904429440045249486e-08, 2.033704617856271284e+02, 277 6.873328406531531472e-08, 2.050303743795980154e+02, 6.842506306053811558e-08, 278 2.066828600467466401e+02, 6.811959402901785336e-08, 2.083279849515614899e+02, 279 6.781684027777777772e-08, 2.099658143782880586e+02, 6.751676576327433535e-08, 280 2.115964127464742432e+02, 6.721933507709251725e-08, 2.132198436261738550e+02, 281 6.692451343201754014e-08, 2.148361697528176535e+02, 6.663226664847161225e-08, 282 2.164454530417600608e+02, 6.634256114130434863e-08, 2.180477546025107358e+02, 283 6.605536390692640687e-08, 2.196431347526584545e+02, 6.577064251077586116e-08, 284 2.212316530314957390e+02, 6.548836507510729591e-08, 2.228133682133515663e+02, 285 6.520850026709402365e-08, 2.243883383206399174e+02, 6.493101728723404362e-08, 286 2.259566206366313565e+02, 6.465588585805084723e-08, 2.275182717179543204e+02, 287 6.438307621308016336e-08, 2.290733474068335340e+02, 6.411255908613445100e-08, 288 2.306219028430716378e+02, 6.384430570083681460e-08, 2.321639924757807307e+02, 289 6.357828776041666578e-08, 2.336996700748701699e+02, 6.331447743775933615e-08, 290 2.352289887422961954e+02, 6.305284736570248109e-08, 2.367520009230799189e+02, 291 6.279337062757202180e-08, 2.382687584160988763e+02, 6.253602074795082293e-08, 292 2.397793123846580556e+02, 6.228077168367347501e-08, 2.412837133668454044e+02, 293 6.202759781504065697e-08, 2.427820112856774699e+02, 6.177647393724696421e-08, 294 2.442742554590400630e+02, 6.152737525201612732e-08, 2.457604946094287186e+02, 295 6.128027735943774537e-08, 2.472407768734942692e+02, 6.103515625000000127e-08, 296 2.487151498113976231e+02, 6.079198829681274795e-08, 2.501836604159786077e+02, 297 6.055075024801586965e-08, 2.516463551217433974e+02, 6.031141921936758485e-08, 298 2.531032798136744475e+02, 6.007397268700787318e-08, 2.545544798358676246e+02, 299 5.983838848039215603e-08, 2.560000000000000000e+02, 5.960464477539062500e-08 300 }; 301 302 static const double __TBL_expfb[] = { 303 7.006492321624085355e-46, 1.401298464324817071e-45, 2.802596928649634142e-45, 304 5.605193857299268284e-45, 1.121038771459853657e-44, 2.242077542919707313e-44, 305 4.484155085839414627e-44, 8.968310171678829254e-44, 1.793662034335765851e-43, 306 3.587324068671531702e-43, 7.174648137343063403e-43, 1.434929627468612681e-42, 307 2.869859254937225361e-42, 5.739718509874450723e-42, 1.147943701974890145e-41, 308 2.295887403949780289e-41, 4.591774807899560578e-41, 9.183549615799121156e-41, 309 1.836709923159824231e-40, 3.673419846319648462e-40, 7.346839692639296925e-40, 310 1.469367938527859385e-39, 2.938735877055718770e-39, 5.877471754111437540e-39, 311 1.175494350822287508e-38, 2.350988701644575016e-38, 4.701977403289150032e-38, 312 9.403954806578300064e-38, 1.880790961315660013e-37, 3.761581922631320025e-37, 313 7.523163845262640051e-37, 1.504632769052528010e-36, 3.009265538105056020e-36, 314 6.018531076210112041e-36, 1.203706215242022408e-35, 2.407412430484044816e-35, 315 4.814824860968089633e-35, 9.629649721936179265e-35, 1.925929944387235853e-34, 316 3.851859888774471706e-34, 7.703719777548943412e-34, 1.540743955509788682e-33, 317 3.081487911019577365e-33, 6.162975822039154730e-33, 1.232595164407830946e-32, 318 2.465190328815661892e-32, 4.930380657631323784e-32, 9.860761315262647568e-32, 319 1.972152263052529514e-31, 3.944304526105059027e-31, 7.888609052210118054e-31, 320 1.577721810442023611e-30, 3.155443620884047222e-30, 6.310887241768094443e-30, 321 1.262177448353618889e-29, 2.524354896707237777e-29, 5.048709793414475555e-29, 322 1.009741958682895111e-28, 2.019483917365790222e-28, 4.038967834731580444e-28, 323 8.077935669463160887e-28, 1.615587133892632177e-27, 3.231174267785264355e-27, 324 6.462348535570528710e-27, 1.292469707114105742e-26, 2.584939414228211484e-26, 325 5.169878828456422968e-26, 1.033975765691284594e-25, 2.067951531382569187e-25, 326 4.135903062765138374e-25, 8.271806125530276749e-25, 1.654361225106055350e-24, 327 3.308722450212110699e-24, 6.617444900424221399e-24, 1.323488980084844280e-23, 328 2.646977960169688560e-23, 5.293955920339377119e-23, 1.058791184067875424e-22, 329 2.117582368135750848e-22, 4.235164736271501695e-22, 8.470329472543003391e-22, 330 1.694065894508600678e-21, 3.388131789017201356e-21, 6.776263578034402713e-21, 331 1.355252715606880543e-20, 2.710505431213761085e-20, 5.421010862427522170e-20, 332 1.084202172485504434e-19, 2.168404344971008868e-19, 4.336808689942017736e-19, 333 8.673617379884035472e-19, 1.734723475976807094e-18, 3.469446951953614189e-18, 334 6.938893903907228378e-18, 1.387778780781445676e-17, 2.775557561562891351e-17, 335 5.551115123125782702e-17, 1.110223024625156540e-16, 2.220446049250313081e-16, 336 4.440892098500626162e-16, 8.881784197001252323e-16, 1.776356839400250465e-15, 337 3.552713678800500929e-15, 7.105427357601001859e-15, 1.421085471520200372e-14, 338 2.842170943040400743e-14, 5.684341886080801487e-14, 1.136868377216160297e-13, 339 2.273736754432320595e-13, 4.547473508864641190e-13, 9.094947017729282379e-13, 340 1.818989403545856476e-12, 3.637978807091712952e-12, 7.275957614183425903e-12, 341 1.455191522836685181e-11, 2.910383045673370361e-11, 5.820766091346740723e-11, 342 1.164153218269348145e-10, 2.328306436538696289e-10, 4.656612873077392578e-10, 343 9.313225746154785156e-10, 1.862645149230957031e-09, 3.725290298461914062e-09, 344 7.450580596923828125e-09, 1.490116119384765625e-08, 2.980232238769531250e-08, 345 5.960464477539062500e-08, 1.192092895507812500e-07, 2.384185791015625000e-07, 346 4.768371582031250000e-07, 9.536743164062500000e-07, 1.907348632812500000e-06, 347 3.814697265625000000e-06, 7.629394531250000000e-06, 1.525878906250000000e-05, 348 3.051757812500000000e-05, 6.103515625000000000e-05, 1.220703125000000000e-04, 349 2.441406250000000000e-04, 4.882812500000000000e-04, 9.765625000000000000e-04, 350 1.953125000000000000e-03, 3.906250000000000000e-03, 7.812500000000000000e-03, 351 1.562500000000000000e-02, 3.125000000000000000e-02, 6.250000000000000000e-02, 352 1.250000000000000000e-01, 2.500000000000000000e-01, 5.000000000000000000e-01, 353 1.000000000000000000e+00, 2.000000000000000000e+00, 4.000000000000000000e+00, 354 8.000000000000000000e+00, 1.600000000000000000e+01, 3.200000000000000000e+01, 355 6.400000000000000000e+01, 1.280000000000000000e+02, 2.560000000000000000e+02, 356 5.120000000000000000e+02, 1.024000000000000000e+03, 2.048000000000000000e+03, 357 4.096000000000000000e+03, 8.192000000000000000e+03, 1.638400000000000000e+04, 358 3.276800000000000000e+04, 6.553600000000000000e+04, 1.310720000000000000e+05, 359 2.621440000000000000e+05, 5.242880000000000000e+05, 1.048576000000000000e+06, 360 2.097152000000000000e+06, 4.194304000000000000e+06, 8.388608000000000000e+06, 361 1.677721600000000000e+07, 3.355443200000000000e+07, 6.710886400000000000e+07, 362 1.342177280000000000e+08, 2.684354560000000000e+08, 5.368709120000000000e+08, 363 1.073741824000000000e+09, 2.147483648000000000e+09, 4.294967296000000000e+09, 364 8.589934592000000000e+09, 1.717986918400000000e+10, 3.435973836800000000e+10, 365 6.871947673600000000e+10, 1.374389534720000000e+11, 2.748779069440000000e+11, 366 5.497558138880000000e+11, 1.099511627776000000e+12, 2.199023255552000000e+12, 367 4.398046511104000000e+12, 8.796093022208000000e+12, 1.759218604441600000e+13, 368 3.518437208883200000e+13, 7.036874417766400000e+13, 1.407374883553280000e+14, 369 2.814749767106560000e+14, 5.629499534213120000e+14, 1.125899906842624000e+15, 370 2.251799813685248000e+15, 4.503599627370496000e+15, 9.007199254740992000e+15, 371 1.801439850948198400e+16, 3.602879701896396800e+16, 7.205759403792793600e+16, 372 1.441151880758558720e+17, 2.882303761517117440e+17, 5.764607523034234880e+17, 373 1.152921504606846976e+18, 2.305843009213693952e+18, 4.611686018427387904e+18, 374 9.223372036854775808e+18, 1.844674407370955162e+19, 3.689348814741910323e+19, 375 7.378697629483820646e+19, 1.475739525896764129e+20, 2.951479051793528259e+20, 376 5.902958103587056517e+20, 1.180591620717411303e+21, 2.361183241434822607e+21, 377 4.722366482869645214e+21, 9.444732965739290427e+21, 1.888946593147858085e+22, 378 3.777893186295716171e+22, 7.555786372591432342e+22, 1.511157274518286468e+23, 379 3.022314549036572937e+23, 6.044629098073145874e+23, 1.208925819614629175e+24, 380 2.417851639229258349e+24, 4.835703278458516699e+24, 9.671406556917033398e+24, 381 1.934281311383406680e+25, 3.868562622766813359e+25, 7.737125245533626718e+25, 382 1.547425049106725344e+26, 3.094850098213450687e+26, 6.189700196426901374e+26, 383 1.237940039285380275e+27, 2.475880078570760550e+27, 4.951760157141521100e+27, 384 9.903520314283042199e+27, 1.980704062856608440e+28, 3.961408125713216880e+28, 385 7.922816251426433759e+28, 1.584563250285286752e+29, 3.169126500570573504e+29, 386 6.338253001141147007e+29, 1.267650600228229401e+30, 2.535301200456458803e+30, 387 5.070602400912917606e+30, 1.014120480182583521e+31, 2.028240960365167042e+31, 388 4.056481920730334085e+31, 8.112963841460668170e+31, 1.622592768292133634e+32, 389 3.245185536584267268e+32, 6.490371073168534536e+32, 1.298074214633706907e+33, 390 2.596148429267413814e+33, 5.192296858534827629e+33, 1.038459371706965526e+34, 391 2.076918743413931051e+34, 4.153837486827862103e+34, 8.307674973655724206e+34, 392 1.661534994731144841e+35, 3.323069989462289682e+35, 6.646139978924579365e+35, 393 1.329227995784915873e+36, 2.658455991569831746e+36, 5.316911983139663492e+36, 394 1.063382396627932698e+37, 2.126764793255865397e+37, 4.253529586511730793e+37, 395 8.507059173023461587e+37, 1.701411834604692317e+38, 3.402823669209384635e+38 396 }; 397 398 static const double 399 KA3 = -3.60659926599003171364e-01*256.0, 400 KA2 = 4.80902715189356683026e-01*256.0, 401 KA1 = -7.21347520569871841065e-01*256.0, 402 KA0 = 1.44269504088069658645e+00*256.0, 403 KB2 = 3.66556671660783833261e-06, 404 KB1 = 2.70760782821392980564e-03, 405 DONE = 1.0, 406 HTHRESH = 32768.0, 407 LTHRESH = -38400.0; 408 409 #define RETURN(ret) \ 410 { \ 411 *pz = (ret); \ 412 px += stridex; \ 413 py += stridey; \ 414 pz += stridez; \ 415 if (n_n == 0) \ 416 { \ 417 spx = px; spy = py; spz = pz; \ 418 continue; \ 419 } \ 420 n--; \ 421 break; \ 422 } 423 424 void 425 __vpowf(int n, float * restrict px, int stridex, float * restrict py, 426 int stridey, float * restrict pz, int stridez) 427 { 428 float *spx, *spy, *spz; 429 double y0, yy0; 430 long long di0; 431 unsigned ux, sx, uy, ay, ax0; 432 int exp, i0, ind0, exp0, yisint0, n_n; 433 434 #ifndef NOPOWFIX 435 if (stridex == 0) 436 { 437 unsigned hx = *(unsigned*)px; 438 439 if ((hx >= 0x00800000) && /* x not zero or subnormal */ 440 (hx < 0x7f800000) && /* x not inf, nan or negative sign bit */ 441 (hx != 0x3f800000)) /* x not 1 */ 442 { 443 __vpowfx(n, px, py, stridey, pz, stridez); 444 return; 445 } 446 } 447 #endif 448 449 while (n > 0) 450 { 451 n_n = 0; 452 spx = px; 453 spy = py; 454 spz = pz; 455 for (; n > 0 ; n--) 456 { 457 uy = *(unsigned int*)py; 458 ux = *(unsigned int*)px; 459 ay = uy & 0x7fffffff; 460 ax0 = ux & 0x7fffffff; 461 sx = ux >> 31; 462 yisint0 = 0; /* Y - non-integer */ 463 464 /* |X| or |Y| = Inf,Nan */ 465 if (ax0 >= 0x7f800000 || ay >= 0x7f800000) 466 { 467 if (ay == 0) 468 RETURN(1.0f) /* pow(X,0) */ 469 /* |X| or |Y| = Nan */ 470 if (ax0 > 0x7f800000 || ay > 0x7f800000) 471 RETURN (*px + *py) 472 if (ay == 0x7f800000) /* |Y| = Inf */ 473 { 474 float fy; 475 if (ax0 == 0x3f800000) 476 fy = *py - *py; /* +-1 ** +-Inf = NaN */ 477 else 478 fy = ((ax0 < 0x3f800000) != (uy >> 31)) ? 0.0f : *(float*) &ay; 479 RETURN(fy) 480 } 481 if (sx) /* X = -Inf */ 482 { 483 exp = ay >> 23; 484 if (exp >= 0x97) /* |Y| >= 2^24 */ 485 yisint0 = 2; /* Y - even */ 486 else if (exp >= 0x7f) /* |Y| >= 1 */ 487 { 488 i0 = ay >> ((0x7f + 23) - exp); 489 if ((i0 << ((0x7f + 23) - exp)) == ay) 490 yisint0 = 2 - (i0 & 1); 491 } 492 } 493 if (uy >> 31) 494 ax0 = 0; 495 ax0 += yisint0 << 31; 496 RETURN(*(float*)&ax0) 497 } 498 499 if ((int)ux < 0x00800000) /* X = denormal or negative */ 500 { 501 if (ay == 0) 502 RETURN(1.0f) /* pow(X,0) */ 503 exp0 = (ax0 >> 23) - 127; 504 505 if ((int)ax0 < 0x00800000) /* X = denormal */ 506 { 507 *((float*) &ax0) = (float) (int)ax0; 508 exp0 = (ax0 >> 23) - (127 + 149); 509 } 510 511 if ((int)ux <= 0) /* X <= 0 */ 512 { 513 exp = ay >> 23; 514 if (exp >= 0x97) /* |Y| >= 2^24 */ 515 yisint0 = 2; /* Y - even */ 516 else if (exp >= 0x7f) /* |Y| >= 1 */ 517 { 518 i0 = ay >> ((0x7f + 23) - exp); 519 if ((i0 << ((0x7f + 23) - exp)) == ay) 520 yisint0 = 2 - (i0 & 1); 521 } 522 523 if (ax0 == 0) /* pow(0,Y) */ 524 { 525 float fy; 526 fy = (uy >> 31) ? 1.0f / 0.0f : 0.0f; 527 if (sx & yisint0) 528 fy = -fy; 529 RETURN(fy) 530 } 531 532 if (yisint0 == 0) /* pow(neg,non-integer) */ 533 RETURN(0.0f / 0.0f) /* NaN */ 534 } 535 536 /* perform yy0 = 256*log2(xi)*yi */ 537 ax0 &= 0x007fffff; 538 i0 = (ax0 + 0x8000) & 0xffff0000; 539 ind0 = i0 >> 15; 540 i0 = ax0 - i0; 541 y0 = (double) i0 * __TBL_log2f[ind0 + 1]; 542 yy0 = __TBL_log2f[ind0] + (double) (exp0 << 8); 543 yy0 += (((KA3 * y0 + KA2) * y0 + KA1) * y0 + KA0) * y0; 544 yy0 = (double)py[0] * yy0; 545 546 /* perform 2 ** (yy0/256) */ 547 if (yy0 >= HTHRESH) 548 yy0 = HTHRESH; 549 if (yy0 <= LTHRESH) 550 yy0 = LTHRESH; 551 ind0 = (int) yy0; 552 y0 = yy0 - (double)ind0; 553 yy0 = (KB2 * y0 + KB1) * y0 + DONE; 554 di0 = ((long long)((ind0 >> 8) + (yisint0 << 11))) << 52; 555 di0 += ((long long*)__TBL_exp2f)[ind0 & 255]; 556 RETURN((float) (yy0 * *(double*)&di0)) 557 } 558 px += stridex; 559 py += stridey; 560 pz += stridez; 561 n_n++; 562 } 563 if (n_n > 0) 564 __vpowf_n(n_n, spx, stridex, spy, stridey, spz, stridez); 565 } 566 } 567 568 569 static void 570 __vpowf_n(int n, float * restrict px, int stridex, float * restrict py, 571 int stridey, float * restrict pz, int stridez) 572 { 573 double y0, yy0; 574 double di0; 575 int ind0, i0, exp0; 576 unsigned ax0; 577 double y1, yy1; 578 double di1; 579 int ind1, i1, exp1; 580 unsigned ax1; 581 double y2, yy2; 582 double di2; 583 int ind2, i2, exp2; 584 unsigned ax2; 585 586 for (; n > 2 ; n -= 3) 587 { 588 /* perform yy0 = 256*log2(xi)*yi */ 589 ax0 = ((int*)px)[0]; 590 px += stridex; 591 ax1 = ((int*)px)[0]; 592 px += stridex; 593 ax2 = ((int*)px)[0]; 594 px += stridex; 595 exp0 = ((ax0 & 0x7fffffff) >> 23) - 127; 596 exp1 = ((ax1 & 0x7fffffff) >> 23) - 127; 597 exp2 = ((ax2 & 0x7fffffff) >> 23) - 127; 598 ax0 &= 0x007fffff; 599 ax1 &= 0x007fffff; 600 ax2 &= 0x007fffff; 601 i0 = (ax0 + 0x8000) & 0xffff0000; 602 i1 = (ax1 + 0x8000) & 0xffff0000; 603 i2 = (ax2 + 0x8000) & 0xffff0000; 604 ind0 = i0 >> 15; 605 ind1 = i1 >> 15; 606 ind2 = i2 >> 15; 607 i0 = ax0 - i0; 608 i1 = ax1 - i1; 609 i2 = ax2 - i2; 610 y0 = (double) i0 * __TBL_log2f[ind0 + 1]; 611 y1 = (double) i1 * __TBL_log2f[ind1 + 1]; 612 y2 = (double) i2 * __TBL_log2f[ind2 + 1]; 613 yy0 = __TBL_log2f[ind0] + (double) (exp0 << 8); 614 yy1 = __TBL_log2f[ind1] + (double) (exp1 << 8); 615 yy2 = __TBL_log2f[ind2] + (double) (exp2 << 8); 616 yy0 += (((KA3 * y0 + KA2) * y0 + KA1) * y0 + KA0) * y0; 617 yy1 += (((KA3 * y1 + KA2) * y1 + KA1) * y1 + KA0) * y1; 618 yy2 += (((KA3 * y2 + KA2) * y2 + KA1) * y2 + KA0) * y2; 619 yy0 = (double)py[0] * yy0; 620 py += stridey; 621 yy1 = (double)py[0] * yy1; 622 py += stridey; 623 yy2 = (double)py[0] * yy2; 624 py += stridey; 625 626 /* perform 2 ** (yy0/256) */ 627 if (yy0 >= HTHRESH) 628 yy0 = HTHRESH; 629 if (yy0 <= LTHRESH) 630 yy0 = LTHRESH; 631 if (yy1 >= HTHRESH) 632 yy1 = HTHRESH; 633 if (yy1 <= LTHRESH) 634 yy1 = LTHRESH; 635 if (yy2 >= HTHRESH) 636 yy2 = HTHRESH; 637 if (yy2 <= LTHRESH) 638 yy2 = LTHRESH; 639 640 ind0 = (int) yy0; 641 ind1 = (int) yy1; 642 ind2 = (int) yy2; 643 y0 = yy0 - (double)ind0; 644 y1 = yy1 - (double)ind1; 645 y2 = yy2 - (double)ind2; 646 yy0 = (KB2 * y0 + KB1) * y0 + DONE; 647 yy1 = (KB2 * y1 + KB1) * y1 + DONE; 648 yy2 = (KB2 * y2 + KB1) * y2 + DONE; 649 di0 = (__TBL_expfb + 150)[ind0 >> 8]; 650 di1 = (__TBL_expfb + 150)[ind1 >> 8]; 651 di2 = (__TBL_expfb + 150)[ind2 >> 8]; 652 di0 *= __TBL_exp2f[ind0 & 255]; 653 di1 *= __TBL_exp2f[ind1 & 255]; 654 di2 *= __TBL_exp2f[ind2 & 255]; 655 pz[0] = (float) (yy0 * di0); 656 pz += stridez; 657 pz[0] = (float) (yy1 * di1); 658 pz += stridez; 659 pz[0] = (float) (yy2 * di2); 660 pz += stridez; 661 } 662 663 for (; n > 0 ; n--) 664 { 665 /* perform yy0 = 256*log2(xi)*yi */ 666 ax0 = ((int*)px)[0]; 667 exp0 = ((ax0 & 0x7fffffff) >> 23) - 127; 668 ax0 &= 0x007fffff; 669 i0 = (ax0 + 0x8000) & 0xffff0000; 670 ind0 = i0 >> 15; 671 i0 = ax0 - i0; 672 y0 = (double) i0 * __TBL_log2f[ind0 + 1]; 673 yy0 = __TBL_log2f[ind0] + (double) (exp0 << 8); 674 yy0 += (((KA3 * y0 + KA2) * y0 + KA1) * y0 + KA0) * y0; 675 yy0 = (double)py[0] * yy0; 676 677 /* perform 2 ** (yy0/256) */ 678 if (yy0 >= HTHRESH) 679 yy0 = HTHRESH; 680 if (yy0 <= LTHRESH) 681 yy0 = LTHRESH; 682 ind0 = (int) yy0; 683 y0 = yy0 - (double)ind0; 684 yy0 = (KB2 * y0 + KB1) * y0 + DONE; 685 di0 = (__TBL_expfb + 150)[ind0 >> 8]; 686 di0 *= __TBL_exp2f[ind0 & 255]; 687 pz[0] = (float) (yy0 * di0); 688 px += stridex; 689 py += stridey; 690 pz += stridez; 691 } 692 } 693 694 695 static void 696 __vpowfx(int n, float * restrict px, float * restrict py, 697 int stridey, float * restrict pz, int stridez) 698 { 699 float *spy, *spz; 700 double yy, y0; 701 int ind0, exp0, i0, n_n; 702 unsigned ux, ax, ax0, uy, ay; 703 704 /* perform yy = 256*log2(xi)*yi */ 705 ux = *(unsigned int*)px; 706 ax = ux & 0x7fffffff; 707 exp0 = (ax >> 23) - 127; 708 ax0 = ux & 0x007fffff; 709 i0 = (ax0 + 0x8000) & 0xffff0000; 710 ind0 = i0 >> 15; 711 i0 = ax0 - i0; 712 y0 = (double) i0 * __TBL_log2f[ind0 + 1]; 713 yy = __TBL_log2f[ind0] + (double) (exp0 << 8); 714 yy += (((KA3 * y0 + KA2) * y0 + KA1) * y0 + KA0) * y0; 715 716 while (n > 0) 717 { 718 n_n = 0; 719 spy = py; 720 spz = pz; 721 for (; n > 0 ; n--) 722 { 723 uy = *(unsigned int*)py; 724 ay = uy & 0x7fffffff; 725 726 if (ay >= 0x7f800000) /* |Y| = Inf or Nan */ 727 { 728 float fy; 729 if (ay > 0x7f800000) 730 fy = *py + *py; /* |Y| = Nan */ 731 else 732 fy = ((ax < 0x3f800000) != (uy >> 31)) ? 0.0f : *(float*)&ay; 733 *pz = fy; 734 py += stridey; 735 pz += stridez; 736 if (n_n == 0) 737 { 738 spy = py; 739 spz = pz; 740 continue; 741 } 742 n--; 743 break; 744 } 745 py += stridey; 746 pz += stridez; 747 n_n++; 748 } 749 if (n_n > 0) 750 __vpowfx_n(n_n, yy, spy, stridey, spz, stridez); 751 } 752 } 753 754 755 static void 756 __vpowfx_n(int n, double yy, float * restrict py, 757 int stridey, float * restrict pz, int stridez) 758 { 759 double y0, yy0, di0; 760 double y1, yy1, di1; 761 double y2, yy2, di2; 762 int ind0, ind1, ind2; 763 764 for (; n > 2 ; n-= 3) 765 { 766 /* perform 2 ** (yy/256) */ 767 yy0 = (double)py[0] * yy; 768 py += stridey; 769 yy1 = (double)py[0] * yy; 770 py += stridey; 771 yy2 = (double)py[0] * yy; 772 py += stridey; 773 if (yy0 >= HTHRESH) 774 yy0 = HTHRESH; 775 if (yy0 <= LTHRESH) 776 yy0 = LTHRESH; 777 if (yy1 >= HTHRESH) 778 yy1 = HTHRESH; 779 if (yy1 <= LTHRESH) 780 yy1 = LTHRESH; 781 if (yy2 >= HTHRESH) 782 yy2 = HTHRESH; 783 if (yy2 <= LTHRESH) 784 yy2 = LTHRESH; 785 ind0 = (int) yy0; 786 ind1 = (int) yy1; 787 ind2 = (int) yy2; 788 y0 = yy0 - (double)ind0; 789 y1 = yy1 - (double)ind1; 790 y2 = yy2 - (double)ind2; 791 yy0 = (KB2 * y0 + KB1) * y0 + DONE; 792 yy1 = (KB2 * y1 + KB1) * y1 + DONE; 793 yy2 = (KB2 * y2 + KB1) * y2 + DONE; 794 di0 = (__TBL_expfb + 150)[ind0 >> 8]; 795 di1 = (__TBL_expfb + 150)[ind1 >> 8]; 796 di2 = (__TBL_expfb + 150)[ind2 >> 8]; 797 di0 *= __TBL_exp2f[ind0 & 255]; 798 di1 *= __TBL_exp2f[ind1 & 255]; 799 di2 *= __TBL_exp2f[ind2 & 255]; 800 pz[0] = (float) (yy0 * di0); 801 pz += stridez; 802 pz[0] = (float) (yy1 * di1); 803 pz += stridez; 804 pz[0] = (float) (yy2 * di2); 805 pz += stridez; 806 } 807 for (; n > 0 ; n--) 808 { 809 /* perform 2 ** (yy/256) */ 810 yy0 = (double)py[0] * yy; 811 if (yy0 >= HTHRESH) 812 yy0 = HTHRESH; 813 if (yy0 <= LTHRESH) 814 yy0 = LTHRESH; 815 ind0 = (int) yy0; 816 y0 = yy0 - (double)ind0; 817 yy0 = (KB2 * y0 + KB1) * y0 + DONE; 818 di0 = (__TBL_expfb + 150)[ind0 >> 8]; 819 di0 *= __TBL_exp2f[ind0 & 255]; 820 pz[0] = (float) (yy0 * di0); 821 py += stridey; 822 pz += stridez; 823 } 824 } 825