/* * CDDL HEADER START * * The contents of this file are subject to the terms of the * Common Development and Distribution License (the "License"). * You may not use this file except in compliance with the License. * * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE * or http://www.opensolaris.org/os/licensing. * See the License for the specific language governing permissions * and limitations under the License. * * When distributing Covered Code, include this CDDL HEADER in each * file and include the License file at usr/src/OPENSOLARIS.LICENSE. * If applicable, add the following below this CDDL HEADER, with the * fields enclosed by brackets "[]" replaced with your own identifying * information: Portions Copyright [yyyy] [name of copyright owner] * * CDDL HEADER END */ /* * Copyright 2011 Nexenta Systems, Inc. All rights reserved. */ /* * Copyright 2006 Sun Microsystems, Inc. All rights reserved. * Use is subject to license terms. */ #include #ifdef _LITTLE_ENDIAN #define HI(x) *(1+(int*)x) #define LO(x) *(unsigned*)x #else #define HI(x) *(int*)x #define LO(x) *(1+(unsigned*)x) #endif #ifdef __RESTRICT #define restrict _Restrict #else #define restrict #endif /* double pow(double x, double y) * * Method : * 1. Special cases: * for (anything) ** 0 => 1 * for (anything) ** NaN => QNaN + invalid * for NaN ** (anything) => QNaN + invalid * for +-1 ** +-Inf => QNaN + invalid * for +-(|x| < 1) ** +Inf => +0 * for +-(|x| < 1) ** -Inf => +Inf * for +-(|x| > 1) ** +Inf => +Inf * for +-(|x| > 1) ** -Inf => +0 * for +Inf ** (negative) => +0 * for +Inf ** (positive) => +Inf * for -Inf ** (negative except odd integer) => +0 * for -Inf ** (negative odd integer) => -0 * for -Inf ** (positive except odd integer) => +Inf * for -Inf ** (positive odd integer) => -Inf * for (negative) ** (non-integer) => QNaN + invalid * for +0 ** (negative) => +Inf + overflow * for +0 ** (positive) => +0 * for -0 ** (negative except odd integer) => +Inf + overflow * for -0 ** (negative odd integer) => -Inf + overflow * for -0 ** (positive except odd integer) => +0 * for -0 ** (positive odd integer) => -0 * 2. Computes x**y from: * x**y = 2**(y*log2(x)) = 2**(w/256), where w = 256*log2(|x|)*y. * 3. Computes w = 256*log2(|x|)*y from * |x| = m * 2**n => log2(|x|) = n + log2(m). * Let m = m0 + dm, where m0 = 1 + k / 256, * k = [0, 255], * dm = [-1/512, 1/512]. * Then 256*log2(m) = 256*log2(m0 + dm) = 256*log2(m0) + 256*log2((1+z)/(1-z)), * where z = (m-m0)/(m+m0), z = [-1/1025, 1/1025]. * Then * 256*log2(m0) is looked up in a table of 256*log2(1), 256*log2(1+1/128), * ..., 256*log2(1+128/128). * 256*log2((1+z)/(1-z)) is computed using * approximation: 256*log2((1+z)/(1-z)) = a0 * z + a1 * z**3 + a1 * z**5. * Perform w = 256*log2(|x|)*y = w1 + w2 by simulating muti-precision arithmetic. * 3. For w >= 262144 * then for (negative) ** (odd integer) => -Inf + overflow * else => +Inf + overflow * For w <= -275200 * then for (negative) ** (odd integer) => -0 + underflow * else => +0 + underflow * 4. Computes 2 ** (w/256) from: * 2 ** (w/256) = 2**a * 2**(k/256) * 2**(r/256) * Where: * a = int ( w ) >> 8; * k = int ( w ) & 0xFF; * r = frac ( w ). * Note that: * k = 0, 1, ..., 255; * r = (-1, 1). * Then: * 2**(k/256) is looked up in a table of 2**0, 2**1/256, ... * 2**(r/256) is computed using approximation: * 2**(r/256) = ((((b5 * r + b4) * r + b3) * r + b2) * r + b1) * r + b0 * Multiplication by 2**a is done by adding "a" to * the biased exponent. * Perform 2 ** (w/256) by simulating muti-precision arithmetic. * 5. For (negative) ** (odd integer) => -(2**(w/256)) * otherwise => 2**(w/256) * * Accuracy: * Max. relative aproximation error < 2**(-67.94) for 256*log2((1+z)/(1-z)). * Max. relative aproximation error < 2**(-63.15) for 2**(r/256). * Maximum error observed: less than 0.761 ulp after 1.300.000.000 * results. */ static void __vpowx(int n, double * restrict px, double * restrict py, int stridey, double * restrict pz, int stridez); static const double __TBL_exp2[] = { /* __TBL_exp2[2*i] = high order bits 2^(i/256), i = [0, 255] */ /* __TBL_exp2[2*i+1] = least bits 2^(i/256), i = [0, 255] */ 1.000000000000000000e+00, 0.000000000000000000e+00, 1.002711275050202522e+00, -3.636615928692263944e-17, 1.005429901112802726e+00, 9.499186535455031757e-17, 1.008155898118417548e+00,-3.252058756084308061e-17, 1.010889286051700475e+00, -1.523477860336857718e-17, 1.013630084951489430e+00, 9.283599768183567587e-18, 1.016378314910953096e+00,-5.772170073199660028e-17, 1.019133996077737914e+00, 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1.704715809658051251e+00,-2.728883284797281563e-17, 1.709337763100462926e+00,-9.868779456632931076e-17, 1.713972247929925974e+00, 6.473975107753367064e-17, 1.718619298122477934e+00,-1.851380418263110988e-17, 1.723278947746273992e+00,-9.522123800393799963e-17, 1.727951230961837670e+00, -1.075098186120464245e-16, 1.732636182022311067e+00,-1.698051074315415494e-18, 1.737333835273706217e+00, 3.164389299292956947e-17, 1.742044225155156445e+00, -1.525959118950788792e-18, 1.746767386199169048e+00,-1.075229048350751450e-16, 1.751503353031878207e+00,-5.124450420596724659e-17, 1.756252160373299454e+00, 2.960140695448873307e-17, 1.761013843037583904e+00,-7.943253125039227711e-17, 1.765788435933272726e+00, 9.461315018083267867e-17, 1.770575974063554714e+00, 5.961794510040555848e-17, 1.775376492526521188e+00, 6.429731796556572034e-17, 1.780190026515424462e+00,-5.284627289091617365e-17, 1.785016611318934965e+00, 1.533040012103131382e-17, 1.789856282321401038e+00,-4.154354660683350387e-17, 1.794709075003107168e+00, 1.822745842791208677e-17, 1.799575024940535117e+00, -2.526889233358897644e-17, 1.804454167806623932e+00,-5.177222408793317883e-17, 1.809346539371031959e+00,-9.032641402450029682e-17, 1.814252175500398856e+00, -9.969531538920348820e-17, 1.819171112158608494e+00, 7.402676901145838890e-17, 1.824103385407053413e+00,-1.015962786227708306e-16, 1.829049031404897274e+00, 6.889192908835695637e-17, 1.834008086409342431e+00, 3.283107224245627204e-17, 1.838980586775893711e+00, 6.918969740272511942e-18, 1.843966568958625984e+00, -5.939742026949964550e-17, 1.848966069510450838e+00, 9.027580446261089288e-17, 1.853979125083385471e+00, 9.761887490727593538e-17, 1.859005772428820480e+00, -9.528705461989940687e-17, 1.864046048397788979e+00, 6.540912680620571711e-17, 1.869099989941238604e+00,-9.938505214255067083e-17, 1.874167634110299963e+00, -6.122763413004142562e-17, 1.879249018056560194e+00,-1.622631555783584478e-17, 1.884344179032334532e+00,-8.226593125533710906e-17, 1.889453154390939194e+00, -9.005168285059126718e-17, 1.894575981586965607e+00, 3.403403535216529671e-17, 1.899712698176555303e+00,-3.859739769378514323e-17, 1.904863341817674138e+00, 6.533857514718278629e-17, 1.910027950270389852e+00,-5.909688006744060237e-17, 1.915206561397147400e+00,-1.061994605619596264e-16, 1.920399213163047403e+00, 7.116681540630314186e-17, 1.925605943636125028e+00,-9.914963769693740927e-17, 1.930826790987627106e+00, 6.167149706169109553e-17, 1.936061793492294347e+00, 1.033238596067632574e-16, 1.941310989528640452e+00,-6.638029891621487990e-17, 1.946574417579233218e+00, 6.811022349533877184e-17, 1.951852116230978318e+00, -2.199016969979351086e-17, 1.957144124175400179e+00, 8.960767791036667768e-17, 1.962450480208927317e+00, 1.097684400091354695e-16, 1.967771223233175881e+00, -1.031492801153113151e-16, 1.973106392255234320e+00,-7.451617863956037486e-18, 1.978456026387950928e+00, 4.038875310927816657e-17, 1.983820164850219392e+00, -2.203454412391062657e-17, 1.989198846967266343e+00, 8.205132638369199416e-18, 1.994592112170940235e+00, 1.790971035200264509e-17 }; static const double __TBL_log2[] = { /* __TBL_log2[2*i] = high order rounded 32 bits log2(1+i/256)*256, i = [0, 255] */ /* __TBL_log2[2*i+1] = low order least bits log2(1+i/256)*256, i = [0, 255] */ 0.000000000000000000e+00, 0.000000000000000000e+00, 1.439884185791015625e+00, 4.078417797464839152e-07, 2.874177932739257812e+00,-5.443862030060025621e-07, 4.302921295166015625e+00, 3.525917800357419922e-07, 5.726161956787109375e+00, -1.821502755258614180e-06, 7.143936157226562500e+00,-1.035336134691423741e-06, 8.556289672851562500e+00,-1.279264291071495652e-06, 9.963264465332031250e+00, -3.206502629414843101e-06, 1.136489105224609375e+01, 3.503517986289194222e-06, 1.276123046875000000e+01,-1.809406249049319022e-06, 1.415230560302734375e+01, -2.114722805833714926e-06, 1.553816223144531250e+01,-3.719431504776986979e-06, 1.691883850097656250e+01,-5.743786819670105240e-06, 1.829435729980468750e+01, 7.514691093524705578e-06, 1.966479492187500000e+01,-2.076862291588726520e-06, 2.103015136718750000e+01, 3.219403619538604258e-06, 2.239048767089843750e+01, -3.108115489869591032e-07, 2.374583435058593750e+01,-6.275103710481114264e-06, 2.509620666503906250e+01, 6.572855776743687178e-06, 2.644168090820312500e+01, -1.954725505303359537e-06, 2.778225708007812500e+01, 3.855133152759458770e-06, 2.911799621582031250e+01,-1.707228100041815487e-06, 3.044891357421875000e+01, 1.042999152333371737e-06, 3.177505493164062500e+01, 8.966313933586820042e-07, 3.309646606445312500e+01,-1.372654171244005427e-05, 3.441314697265625000e+01, -8.996099168734074844e-06, 3.572515869140625000e+01,-1.247731510027211536e-05, 3.703250122070312500e+01, 8.944258749129049106e-06, 3.833526611328125000e+01, -3.520082642279872716e-06, 3.963342285156250000e+01, 1.306577612991810031e-05, 4.092706298828125000e+01,-7.730135593513790229e-07, 4.221618652343750000e+01, -1.329446142304436745e-05, 4.350079345703125000e+01, 6.912200714904314733e-06, 4.478097534179687500e+01,-6.216230979739182064e-07, 4.605673217773437500e+01, -5.133911151040936670e-06, 4.732809448242187500e+01,-6.697901206512330627e-06, 4.859509277343750000e+01,-5.700153089154811841e-06, 4.985775756835937500e+01, -2.836263919120346801e-06, 5.111611938476562500e+01, 8.933436604624454391e-07, 5.237020874023437500e+01, 4.187561748309498307e-06, 5.362005615234375000e+01, 5.448667394155597532e-06, 5.486569213867187500e+01, 2.786324169943508531e-06, 5.610714721679687500e+01,-5.978483512667373796e-06, 5.734442138671875000e+01, 7.207996138368885843e-06, 5.857757568359375000e+01, 9.083351754561760127e-06, 5.980664062500000000e+01,-3.374516276140515786e-06, 6.103161621093750000e+01, -2.943717299925017200e-06, 6.225253295898437500e+01, 6.810091060168101732e-06, 6.346945190429687500e+01,-8.462738988588859704e-06, 6.468237304687500000e+01, -2.233961135216831566e-05, 6.589129638671875000e+01,-8.657399896582645111e-06, 6.709625244140625000e+01, 2.797335967336006296e-05, 6.829736328125000000e+01, -8.863355250907819214e-06, 6.949450683593750000e+01, 2.830758238800374038e-05, 7.068786621093750000e+01,-1.846073268549083018e-05, 7.187731933593750000e+01, -2.182503249464459606e-06, 7.306298828125000000e+01,-2.025251442448625989e-05, 7.424481201171875000e+01, 1.280303154355201204e-05, 7.542291259765625000e+01, -8.813997363590295654e-07, 7.659722900390625000e+01, 2.370323712746426047e-05, 7.776788330078125000e+01,-1.176744290134661421e-05, 7.893481445312500000e+01, -2.273743674288609119e-05, 8.009802246093750000e+01, 1.409185747234803696e-05, 8.125762939453125000e+01,-2.707246895087010889e-07, 8.241357421875000000e+01, 1.807241476105480180e-05, 8.356597900390625000e+01,-3.030059664889450720e-05, 8.471472167968750000e+01,-8.823455531875539245e-07, 8.585992431640625000e+01, 6.485238524924182146e-06, 8.700158691406250000e+01, 1.382440142980862947e-05, 8.813977050781250000e+01,-1.808136338482881111e-05, 8.927441406250000000e+01, -6.579344146543672011e-06, 9.040557861328125000e+01, 8.714227880222726313e-06, 9.153332519531250000e+01,-1.201308307454951138e-05, 9.265759277343750000e+01, 1.330278431878087205e-05, 9.377850341796875000e+01,-1.657103990890600482e-05, 9.489599609375000000e+01,-1.995110226941163424e-05, 9.601007080078125000e+01, 2.362403148762806632e-05, 9.712084960937500000e+01, 1.236086810905991142e-05, 9.822827148437500000e+01, 2.738898236946465744e-05, 9.933239746093750000e+01, 2.758741700388469572e-05, 1.004332885742187500e+02,-2.834285611604269955e-05, 1.015308227539062500e+02, 1.228649517068771375e-06, 1.026251220703125000e+02, 1.361792668612316888e-05, 1.037161865234375000e+02, 2.803946653578170389e-05, 1.048040771484375000e+02, 2.502814149567842806e-06, 1.058887329101562500e+02, 1.692003190104140317e-05, 1.069702148437500000e+02, 2.896703985131545672e-05, 1.080485839843750000e+02,-3.844135045484567362e-06, 1.091237792968750000e+02, -2.093137927645659717e-06, 1.101958618164062500e+02,-8.590030211185738579e-06, 1.112648315429687500e+02,-5.267967244023324300e-06, 1.123306884765625000e+02, 2.578347229232600646e-05, 1.133935546875000000e+02,-1.975022555464358195e-05, 1.144533081054687500e+02,-2.195797778964440179e-06, 1.155100708007812500e+02, -2.617170507638525077e-05, 1.165637817382812500e+02,-1.334031370958194516e-05, 1.176145019531250000e+02,-7.581976902412963145e-06, 1.186622314453125000e+02, 8.112109654298731037e-06, 1.197070312500000000e+02,-1.042875265529314613e-05, 1.207488403320312500e+02, 1.455233211877492951e-05, 1.217877807617187500e+02, -2.243432092472914265e-05, 1.228237304687500000e+02, 1.712269952247034061e-05, 1.238568115234375000e+02, 2.745621214456745937e-05, 1.248870239257812500e+02, 2.473291989440979066e-05, 1.259143676757812500e+02, 2.498461547595911484e-05, 1.269389038085937500e+02,-1.692547797717771941e-05, 1.279605712890625000e+02, -2.419576192770340594e-05, 1.289793701171875000e+02, 1.880972467762623192e-05, 1.299954833984375000e+02,-5.550757125543327248e-05, 1.310086669921875000e+02, 1.237226167189998996e-05, 1.320191650390625000e+02,-6.438347630770959254e-06, 1.330268554687500000e+02, 2.525911246920619613e-05, 1.340318603515625000e+02, 3.990327953073019333e-07, 1.350340576171875000e+02, 5.593427389035480335e-05, 1.360336914062500000e+02,-3.751407409478960320e-05, 1.370305175781250000e+02, -2.116319935859897563e-05, 1.380246582031250000e+02,-2.559468964093475045e-06, 1.390161132812500000e+02, 3.270409087092109593e-05, 1.400050048828125000e+02, -2.315157751389992129e-05, 1.409912109375000000e+02,-3.387938973438343638e-05, 1.419747314453125000e+02, 1.458416266727572812e-05, 1.429556884765625000e+02, 1.412021555596584681e-05, 1.439340820312500000e+02,-2.143065540113838312e-05, 1.449097900390625000e+02, 4.373273697503468317e-05, 1.458830566406250000e+02, -2.090790235253405790e-05, 1.468536376953125000e+02, 4.230297794089183646e-05, 1.478217773437500000e+02, 2.633401664450247309e-06, 1.487873535156250000e+02, -4.542835986281740771e-06, 1.497503662109375000e+02, 3.397367848245215483e-05, 1.507109375000000000e+02, 9.209059510146982590e-06, 1.516689453125000000e+02, 5.622812858742714859e-05, 1.526246337890625000e+02,-5.621609346274134244e-05, 1.535776367187500000e+02, 5.088115468603551539e-05, 1.545283203125000000e+02, 2.400396513473623342e-05, 1.554765625000000000e+02,-2.180099663431456814e-06, 1.564223632812500000e+02,-1.517056781617965675e-05, 1.573657226562500000e+02, -2.562756696989711716e-06, 1.583066406250000000e+02, 4.795320325388065854e-05, 1.592452392578125000e+02, 2.652301982429665372e-05, 1.601815185546875000e+02, -5.473018439029181240e-05, 1.611152343750000000e+02, 6.036538006249134820e-05, 1.620467529296875000e+02, 1.753890969321481711e-05, 1.629759521484375000e+02, -4.928926339732922490e-05, 1.639027099609375000e+02,-6.288016979631557560e-06, 1.648271484375000000e+02, 3.614482952210960361e-05, 1.657493896484375000e+02, -3.247597790375142114e-05, 1.666691894531250000e+02, 4.348868072528205213e-05, 1.675867919921875000e+02, 3.131097214651595330e-05, 1.685021972656250000e+02, -5.768116554728405733e-05, 1.694151611328125000e+02, 3.189681619086343127e-05, 1.703260498046875000e+02,-5.500528238559059116e-05, 1.712344970703125000e+02, 5.890184674174263693e-05, 1.721408691406250000e+02, 1.840407787096519837e-05, 1.730450439453125000e+02,-4.351222480150346831e-05, 1.739468994140625000e+02, 6.059331686505290421e-06, 1.748465576171875000e+02, 5.580532332169584454e-05, 1.757441406250000000e+02,-5.666096094448416139e-06, 1.766395263671875000e+02, -4.568380948624016041e-05, 1.775327148437500000e+02,-5.372392273978838048e-05, 1.784237060546875000e+02,-1.933871000131713187e-05, 1.793126220703125000e+02, -5.422619290693841471e-05, 1.801993408203125000e+02,-2.601847861521447132e-05, 1.810839843750000000e+02,-4.656229401600182454e-05, 1.819664306640625000e+02, 1.636297150881445295e-05, 1.828468017578125000e+02, 5.076471489501210225e-05, 1.837252197265625000e+02,-5.542156510357154555e-05, 1.846014404296875000e+02, -4.812064810565531807e-05, 1.854755859375000000e+02,-3.953879286781995545e-05, 1.863476562500000000e+02,-1.988182101010412125e-05, 1.872176513671875000e+02, 2.057522891062264376e-05, 1.880856933593750000e+02,-3.058156040982771239e-05, 1.889516601562500000e+02,-4.169340446171797184e-05, 1.898155517578125000e+02, -3.239118881346662872e-06, 1.906774902343750000e+02,-2.783449132689922134e-05, 1.915373535156250000e+02, 1.597927683340914293e-05, 1.923952636718750000e+02, 1.545493412281261116e-05, 1.932512207031250000e+02,-2.014927705264352875e-05, 1.941051025390625000e+02, 4.043097907577914080e-05, 1.949571533203125000e+02, -3.781452579504048975e-05, 1.958071289062500000e+02,-1.677810793588779092e-06, 1.966551513671875000e+02, 3.577570564777057149e-05, 1.975013427734375000e+02, -3.858128431828155999e-05, 1.983454589843750000e+02, 2.827352539329734468e-05, 1.991877441406250000e+02, 1.020426695132691908e-06, 2.000280761718750000e+02, 1.049043785864183866e-05, 2.008665771484375000e+02,-5.668571223208539910e-05, 2.017030029296875000e+02, 5.227451898157462205e-05, 2.025377197265625000e+02, -2.025647781341857894e-05, 2.033704833984375000e+02,-2.161281037339224341e-05, 2.042012939453125000e+02, 5.667325008632565576e-05, 2.050303955078125000e+02, -2.112821448834358837e-05, 2.058575439453125000e+02,-2.522383155215216853e-06, 2.066828613281250000e+02,-1.281378348494855858e-06, 2.075063476562500000e+02, -9.162516382743561384e-06, 2.083280029296875000e+02,-1.797812601298608335e-05, 2.091478271484375000e+02,-1.959505997696247453e-05, 2.099658203125000000e+02, -5.934211946670452627e-06, 2.107819824218750000e+02, 3.102996118252714271e-05, 2.115964355468750000e+02,-2.280040076415178584e-05, 2.124090576171875000e+02, -3.743515649437846729e-05, 2.132198486328125000e+02,-5.006638631136701490e-06, 2.140289306640625000e+02,-3.976919665668718942e-05, 2.148361816406250000e+02, -1.188780735169185652e-05, 2.156417236328125000e+02,-3.571887766413048520e-05, 2.164454345703125000e+02, 1.847144755636210490e-05, 2.172474365234375000e+02, 3.622647302213163157e-05, 2.180477294921875000e+02, 2.511032323154433900e-05, 2.188463134765625000e+02,-7.361941985081681848e-06, 2.196431884765625000e+02, -5.372390403709574017e-05, 2.204382324218750000e+02, 1.551294579696132803e-05, 2.212316894531250000e+02,-3.642162925932327343e-05, 2.220233154296875000e+02, 4.193598594979618241e-05, 2.228133544921875000e+02, 1.372116405796589833e-05, 2.236016845703125000e+02, 8.233623894335039537e-06, 2.243883056640625000e+02, 3.265657742833052654e-05, 2.251733398437500000e+02,-2.794287750390687326e-05, 2.259566650390625000e+02,-4.440243113774530265e-05, 2.267382812500000000e+02, -9.675114830058622014e-06, 2.275183105468750000e+02,-3.882892066889445600e-05, 2.282966308593750000e+02,-2.835487591479255673e-06, 2.290733642578125000e+02, -1.685097895998181422e-05, 2.298483886718750000e+02, 4.806553595480019518e-05, 2.306219482421875000e+02,-4.539911586906436716e-05, 2.313937988281250000e+02, -4.631966285757620260e-05, 2.321639404296875000e+02, 5.204609324350696002e-05, 2.329326171875000000e+02, 1.225763073721718197e-05, 2.336997070312500000e+02, -3.695637982554016382e-05, 2.344650878906250000e+02, 3.309133292926460016e-05, 2.352290039062500000e+02,-1.516395380482592629e-05, 2.359913330078125000e+02, -5.311674305290968619e-05, 2.367519531250000000e+02, 4.779807991226078768e-05, 2.375111083984375000e+02, 4.989464209345647548e-05, 2.382687988281250000e+02, -4.041202611322311408e-05, 2.390247802734375000e+02, 2.739433433590848536e-05, 2.397792968750000000e+02, 1.550965806406508966e-05, 2.405322265625000000e+02, 5.230206142425020257e-05, 2.412836914062500000e+02, 2.196059540790264514e-05, 2.420335693359375000e+02, 5.277680785141730338e-05, 2.427819824218750000e+02, 2.886380247947272558e-05, 2.435289306640625000e+02,-4.363251767645384661e-05, 2.442742919921875000e+02,-3.653314744654563199e-05, 2.450180664062500000e+02, 5.623369525922526825e-05, 2.457604980468750000e+02,-3.437446279919778004e-06, 2.465013427734375000e+02, 3.459290119679066472e-05, 2.472407226562500000e+02, 5.421724428316440202e-05, 2.479787597656250000e+02,-6.070765164808318435e-05, 2.487152099609375000e+02,-6.014953987030989107e-05, 2.494501953125000000e+02, -6.032228506450037554e-05, 2.501837158203125000e+02,-5.540433388359054134e-05, 2.509157714843750000e+02,-3.960875078622925214e-05, 2.516463623046875000e+02, -7.182944107105660894e-06, 2.523754882812500000e+02, 4.759160516857532540e-05, 2.531032714843750000e+02, 8.329299458439681639e-06, 2.538295898437500000e+02, 2.751627995643241118e-06, 2.545544433593750000e+02, 3.647649263201999678e-05, 2.552779541015625000e+02,-6.981531437649667064e-06 }; static const unsigned long long LCONST[] = { 0x3c90000000000000ULL, /* 2**(-54) = 5.551115123125782702e-17 */ 0x3ff0000000000000ULL, /* DONE = 1.0 */ 0x4330000000000000ULL, /* DVAIN52 = 2**52 = 4.503599627370496e15 */ 0xffffffff00000000ULL, /* 0xffffffff00000000 */ 0x000fffffffffffffULL, /* 0x000fffffffffffff */ 0x0000080000000000ULL, /* 0x0000080000000000 */ 0xfffff00000000000ULL, /* 0xfffff00000000000 */ 0x0000000000000000ULL, /* DZERO = 0.0 */ 0x4062776d8ce329bdULL, /* KA5 = 5.77078604860893737986e-01*256 */ 0x406ec709dc39fc99ULL, /* KA3 = 9.61796693925765549423e-01*256 */ 0x3f6d94ae0bf85de6ULL, /* KA1_LO = 1.41052154268147309568e-05*256 */ 0x4087154000000000ULL, /* KA1_HI = 2.8853759765625e+00*256 */ 0x40871547652b82feULL, /* KA1 = 2.885390081777926774e+00*256 */ 0x4110000000000000ULL, /* HTHRESH = 262144.0 */ 0xc110cc0000000000ULL, /* LTHRESH = -275200.0 */ 0x3cd5d52893bc7fecULL, /* KB5 = 1.21195555854068860923e-15 */ 0x3d83b2abc07c93d0ULL, /* KB4 = 2.23939573811855104311e-12 */ 0x3e2c6b08d71f5d1eULL, /* KB3 = 3.30830268126604677436e-09 */ 0x3ecebfbdff82c4edULL, /* KB2 = 3.66556559691003767877e-06 */ 0x3f662e42fefa39efULL, /* KB1 = 2.70760617406228636578e-03 */ 0x01a56e1fc2f8f359ULL, /* _TINY = 1.0e-300 */ 0x7e37e43c8800759cULL /* _HUGE = 1.0e+300 */ }; #define SCALE_ARR ((double*)LCONST + 1) #define _TINY ((double*)LCONST)[20] /* 1.0e-300 */ #define _HUGE ((double*)LCONST)[21] /* 1.0e+300 */ #define RET_SC(I) \ px += stridex; \ py += stridey; \ pz += stridez; \ if (--n <= 0) \ break; \ goto start##I; #define RETURN(I, ret) \ { \ pz[0] = (ret); \ RET_SC(I) \ } #define PREP(I) \ hx = HI(px); \ lx = LO(px); \ hy = HI(py); \ ly = LO(py); \ sx = hx >> 31; \ sy = hy >> 31; \ hx &= 0x7fffffff; \ hy &= 0x7fffffff; \ ull_y0 = *(unsigned long long*)px; \ \ if (hy < 0x3bf00000) /* |Y| < 2^(-64) */ \ { \ y0 = *px; \ if ((hy | ly) == 0) /* pow(X,0) */ \ RETURN (I, DONE) \ if (hx > 0x7ff00000 || (hx == 0x7ff00000 && lx != 0)) /* |X| = Nan */ \ *pz = y0 + y0; \ else if ((hx | lx) == 0 || (hx == 0x7ff00000 && lx == 0)) /* X = 0 or Inf */ \ { \ HI(pz) = hx; \ LO(pz) = lx; \ if (sy) \ *pz = DONE / *pz; \ } \ else \ *pz = (sx) ? DZERO / DZERO : DONE; \ RET_SC(I) \ } \ yisint##I = 0; /* Y - non-integer */ \ exp = hy >> 20; /* Y exponent */ \ ull_y0 &= LMMANT; \ ull_x##I = (ull_y0 | LDONE); \ x##I = *(double*)&ull_x##I; \ ull_ax##I = ((ull_x##I + LMROUND) & LMHI20); \ ax##I = *(double*)&ull_ax##I; \ if (hx >= 0x7ff00000 || exp >= 0x43e) /* X=Inf,Nan or |Y|>2^63,Inf,Nan */ \ { \ y0 = *px; \ if (hx > 0x7ff00000 || (hx == 0x7ff00000 && lx != 0) || \ hy > 0x7ff00000 || (hy == 0x7ff00000 && ly != 0)) /* |X| or |Y| = Nan */ \ RETURN (I, y0 + *py) \ if (hy == 0x7ff00000 && (ly == 0)) /* |Y| = Inf */ \ { \ if (hx == 0x3ff00000 && (lx == 0)) /* +-1 ** +-Inf */ \ *pz = *py - *py; \ else if ((hx < 0x3ff00000) != sy) \ *pz = DZERO; \ else \ { \ HI(pz) = hy; \ LO(pz) = ly; \ } \ RET_SC(I) \ } \ if (exp < 0x43e) /* |Y| < 2^63 */ \ { \ if (sx) /* X = -Inf */ \ { \ if (exp >= 0x434) /* |Y| >= 2^53 */ \ yisint##I = 2; /* Y - even */ \ else \ { \ if (exp >= 0x3ff) /* |Y| >= 1 */ \ { \ if (exp > (20 + 0x3ff)) \ { \ i0 = ly >> (52 - (exp - 0x3ff)); \ if ((i0 << (52 - (exp - 0x3ff))) == ly) \ yisint##I = 2 - (i0 & 1); \ } \ else if (ly == 0) \ { \ i0 = hy >> (20 - (exp - 0x3ff)); \ if ((i0 << (20 - (exp - 0x3ff))) == hy) \ yisint##I = 2 - (i0 & 1); \ } \ } \ } \ } \ if (sy) \ hx = lx = 0; \ hx += yisint##I << 31; \ HI(pz) = hx; \ LO(pz) = lx; \ RET_SC(I) \ } \ else /* |Y| >= 2^63 */ \ { \ /* |X| = 0, 1, Inf */ \ if (lx == 0 && (hx == 0 || hx == 0x3ff00000 || hx == 0x7ff00000)) \ { \ HI(pz) = hx; \ LO(pz) = lx; \ if (sy) \ *pz = DONE / *pz; \ } \ else \ { \ y0 = ((hx < 0x3ff00000) != sy) ? _TINY : _HUGE; \ *pz = y0 * y0; \ } \ RET_SC(I) \ } \ } \ if ((sx || (hx | lx)) == 0) /* X <= 0 */ \ { \ if (exp >= 0x434) /* |Y| >= 2^53 */ \ yisint##I = 2; /* Y - even */ \ else \ { \ if (exp >= 0x3ff) /* |Y| >= 1 */ \ { \ if (exp > (20 + 0x3ff)) \ { \ i0 = ly >> (52 - (exp - 0x3ff)); \ if ((i0 << (52 - (exp - 0x3ff))) == ly) \ yisint##I = 2 - (i0 & 1); \ } \ else if (ly == 0) \ { \ i0 = hy >> (20 - (exp - 0x3ff)); \ if ((i0 << (20 - (exp - 0x3ff))) == hy) \ yisint##I = 2 - (i0 & 1); \ } \ } \ } \ if ((hx | lx) == 0) /* X == 0 */ \ { \ y0 = DZERO; \ if (sy) \ y0 = DONE / y0; \ if (sx & yisint##I) \ y0 = -y0; \ RETURN (I, y0) \ } \ if (yisint##I == 0) /* pow(neg,non-integer) */ \ RETURN (I, DZERO / DZERO) /* NaN */ \ } \ exp = (hx >> 20); \ exp##I = exp - 2046; \ py##I = py; \ pz##I = pz; \ ux##I = x##I + ax##I; \ if (!exp) \ { \ ax##I = (double) ull_y0; \ ull_ax##I = *(unsigned long long*)&ax##I; \ ull_x##I = ((ull_ax##I & LMMANT) | LDONE); \ x##I = *(double*)&ull_x##I; \ exp##I = ((unsigned int*) & ull_ax##I)[0]; \ exp##I = (exp##I >> 20) - (2046 + 1023 + 51); \ ull_ax##I = (ull_x##I + (LMROUND & LMHI20)); \ ax##I = *(double*)&ull_ax##I; \ ux##I = x##I + ax##I; \ } \ ull_x##I = *(unsigned long long *)&ux##I; \ hx##I = HI(&ull_ax##I); \ yd##I = DONE / ux##I; void __vpow(int n, double * restrict px, int stridex, double * restrict py, int stridey, double * restrict pz, int stridez) { double *py0 = 0, *py1 = 0, *py2; double *pz0 = 0, *pz1 = 0, *pz2; double y0, yd0 = 0.0L, u0, s0, s_l0, m_h0; double y1, yd1 = 0.0L, u1, s1, s_l1, m_h1; double y2, yd2, u2, s2, s_l2, m_h2; double ax0 = 0.0L, x0 = 0.0L, s_h0, ux0; double ax1 = 0.0L, x1 = 0.0L, s_h1, ux1; double ax2, x2, s_h2, ux2; int eflag0, gflag0, ind0, i0; int eflag1, gflag1, ind1, i1; int eflag2, gflag2, ind2, i2; int hx0 = 0, yisint0 = 0, exp0 = 0; int hx1 = 0, yisint1 = 0, exp1 = 0; int hx2, yisint2, exp2; int exp, i = 0; unsigned hx, lx, sx, hy, ly, sy; unsigned long long ull_y0, ull_x0, ull_x1, ull_x2, ull_ax0, ull_ax1, ull_ax2; unsigned long long LDONE = ((unsigned long long*)LCONST)[1]; /* 1.0 */ unsigned long long LMMANT = ((unsigned long long*)LCONST)[4]; /* 0x000fffffffffffff */ unsigned long long LMROUND = ((unsigned long long*)LCONST)[5]; /* 0x0000080000000000 */ unsigned long long LMHI20 = ((unsigned long long*)LCONST)[6]; /* 0xfffff00000000000 */ double DONE = ((double*)LCONST)[1]; /* 1.0 */ double DZERO = ((double*)LCONST)[7]; /* 0.0 */ double KA5 = ((double*)LCONST)[8]; /* 5.77078604860893737986e-01*256 */ double KA3 = ((double*)LCONST)[9]; /* 9.61796693925765549423e-01*256 */ double KA1_LO = ((double*)LCONST)[10]; /* 1.41052154268147309568e-05*256 */ double KA1_HI = ((double*)LCONST)[11]; /* 2.8853759765625e+00*256 */ double KA1 = ((double*)LCONST)[12]; /* 2.885390081777926774e+00*256 */ double HTHRESH = ((double*)LCONST)[13]; /* 262144.0 */ double LTHRESH = ((double*)LCONST)[14]; /* -275200.0 */ double KB5 = ((double*)LCONST)[15]; /* 1.21195555854068860923e-15 */ double KB4 = ((double*)LCONST)[16]; /* 2.23939573811855104311e-12 */ double KB3 = ((double*)LCONST)[17]; /* 3.30830268126604677436e-09 */ double KB2 = ((double*)LCONST)[18]; /* 3.66556559691003767877e-06 */ double KB1 = ((double*)LCONST)[19]; /* 2.70760617406228636578e-03 */ if (stridex == 0) { unsigned hx = HI(px); unsigned lx = LO(px); /* if x is a positive normal number not equal to one, call __vpowx */ if (hx >= 0x00100000 && hx < 0x7ff00000 && (hx != 0x3ff00000 || lx != 0)) { __vpowx(n, px, py, stridey, pz, stridez); return; } } do { /* perform si + ydi = 256*log2(xi)*yi */ start0: PREP(0) px += stridex; py += stridey; pz += stridez; i = 1; if (--n <= 0) break; start1: PREP(1) px += stridex; py += stridey; pz += stridez; i = 2; if (--n <= 0) break; start2: PREP(2) u0 = x0 - ax0; u1 = x1 - ax1; u2 = x2 - ax2; s0 = u0 * yd0; LO(&ux0) = 0; s1 = u1 * yd1; LO(&ux1) = 0; s2 = u2 * yd2; LO(&ux2) = 0; y0 = s0 * s0; s_h0 = s0; LO(&s_h0) = 0; y1 = s1 * s1; s_h1 = s1; LO(&s_h1) = 0; y2 = s2 * s2; s_h2 = s2; LO(&s_h2) = 0; s0 = (KA5 * y0 + KA3) * y0 * s0; s1 = (KA5 * y1 + KA3) * y1 * s1; s2 = (KA5 * y2 + KA3) * y2 * s2; s_l0 = (x0 - (ux0 - ax0)); s_l1 = (x1 - (ux1 - ax1)); s_l2 = (x2 - (ux2 - ax2)); s_l0 = u0 - s_h0 * ux0 - s_h0 * s_l0; s_l1 = u1 - s_h1 * ux1 - s_h1 * s_l1; s_l2 = u2 - s_h2 * ux2 - s_h2 * s_l2; s_l0 = KA1 * yd0 * s_l0; i0 = (hx0 >> 8) & 0xff0; exp0 += (hx0 >> 20); s_l1 = KA1 * yd1 * s_l1; i1 = (hx1 >> 8) & 0xff0; exp1 += (hx1 >> 20); s_l2 = KA1 * yd2 * s_l2; i2 = (hx2 >> 8) & 0xff0; exp2 += (hx2 >> 20); yd0 = KA1_HI * s_h0; yd1 = KA1_HI * s_h1; yd2 = KA1_HI * s_h2; y0 = *(double *)((char*)__TBL_log2 + i0); y1 = *(double *)((char*)__TBL_log2 + i1); y2 = *(double *)((char*)__TBL_log2 + i2); y0 += (double)(exp0 << 8); y1 += (double)(exp1 << 8); y2 += (double)(exp2 << 8); m_h0 = y0 + yd0; m_h1 = y1 + yd1; m_h2 = y2 + yd2; y0 = s0 - ((m_h0 - y0 - yd0) - s_l0); y1 = s1 - ((m_h1 - y1 - yd1) - s_l1); y2 = s2 - ((m_h2 - y2 - yd2) - s_l2); y0 += *(double *)((char*)__TBL_log2 + i0 + 8) + KA1_LO * s_h0; y1 += *(double *)((char*)__TBL_log2 + i1 + 8) + KA1_LO * s_h1; y2 += *(double *)((char*)__TBL_log2 + i2 + 8) + KA1_LO * s_h2; s_h0 = y0 + m_h0; s_h1 = y1 + m_h1; s_h2 = y2 + m_h2; LO(&s_h0) = 0; LO(&s_h1) = 0; LO(&s_h2) = 0; yd0 = *py0; yd1 = *py1; yd2 = *py2; s0 = yd0; s1 = yd1; s2 = yd2; LO(&s0) = 0; LO(&s1) = 0; LO(&s2) = 0; y0 = y0 - (s_h0 - m_h0); y1 = y1 - (s_h1 - m_h1); y2 = y2 - (s_h2 - m_h2); yd0 = (yd0 - s0) * s_h0 + yd0 * y0; yd1 = (yd1 - s1) * s_h1 + yd1 * y1; yd2 = (yd2 - s2) * s_h2 + yd2 * y2; s0 = s_h0 * s0; s1 = s_h1 * s1; s2 = s_h2 * s2; /* perform 2 ** ((si+ydi)/256) */ if (s0 > HTHRESH) { s0 = HTHRESH; yd0 = DZERO; } if (s1 > HTHRESH) { s1 = HTHRESH; yd1 = DZERO; } if (s2 > HTHRESH) { s2 = HTHRESH; yd2 = DZERO; } if (s0 < LTHRESH) { s0 = LTHRESH; yd0 = DZERO; } ind0 = (int) (s0 + yd0); if (s1 < LTHRESH) { s1 = LTHRESH; yd1 = DZERO; } ind1 = (int) (s1 + yd1); if (s2 < LTHRESH) { s2 = LTHRESH; yd2 = DZERO; } ind2 = (int) (s2 + yd2); i0 = (ind0 & 0xff) << 4; u0 = (double) ind0; ind0 >>= 8; i1 = (ind1 & 0xff) << 4; u1 = (double)ind1; ind1 >>= 8; i2 = (ind2 & 0xff) << 4; u2 = (double) ind2; ind2 >>= 8; y0 = s0 - u0 + yd0; y1 = s1 - u1 + yd1; y2 = s2 - u2 + yd2; u0 = *(double*)((char*)__TBL_exp2 + i0); y0 = ((((KB5 * y0 + KB4) * y0 + KB3) * y0 + KB2) * y0 + KB1) * y0; u1 = *(double*)((char*)__TBL_exp2 + i1); y1 = ((((KB5 * y1 + KB4) * y1 + KB3) * y1 + KB2) * y1 + KB1) * y1; u2 = *(double*)((char*)__TBL_exp2 + i2); y2 = ((((KB5 * y2 + KB4) * y2 + KB3) * y2 + KB2) * y2 + KB1) * y2; eflag0 = (ind0 + 1021) >> 31; gflag0 = (1022 - ind0) >> 31; eflag1 = (ind1 + 1021) >> 31; gflag1 = (1022 - ind1) >> 31; eflag2 = (ind2 + 1021) >> 31; gflag2 = (1022 - ind2) >> 31; ind0 = (yisint0 << 11) + ind0 + (54 & eflag0) - (52 & gflag0); ind0 <<= 20; ind1 = (yisint1 << 11) + ind1 + (54 & eflag1) - (52 & gflag1); ind1 <<= 20; ind2 = (yisint2 << 11) + ind2 + (54 & eflag2) - (52 & gflag2); ind2 <<= 20; u0 = *(double*)((char*)__TBL_exp2 + i0 + 8) + u0 * y0 + u0; u1 = *(double*)((char*)__TBL_exp2 + i1 + 8) + u1 * y1 + u1; u2 = *(double*)((char*)__TBL_exp2 + i2 + 8) + u2 * y2 + u2; ull_x0 = *(unsigned long long*)&u0; HI(&ull_x0) += ind0; u0 = *(double*)&ull_x0; ull_x1 = *(unsigned long long*)&u1; HI(&ull_x1) += ind1; u1 = *(double*)&ull_x1; ull_x2 = *(unsigned long long*)&u2; HI(&ull_x2) += ind2; u2 = *(double*)&ull_x2; *pz0 = u0 * SCALE_ARR[eflag0 - gflag0]; *pz1 = u1 * SCALE_ARR[eflag1 - gflag1]; *pz2 = u2 * SCALE_ARR[eflag2 - gflag2]; px += stridex; py += stridey; pz += stridez; i = 0; } while (--n > 0); if (i > 0) { /* perform si + ydi = 256*log2(xi)*yi */ u0 = x0 - ax0; s0 = u0 * yd0; LO(&ux0) = 0; y0 = s0 * s0; s_h0 = s0; LO(&s_h0) = 0; s0 = (KA5 * y0 + KA3) * y0 * s0; s_l0 = (x0 - (ux0 - ax0)); s_l0 = u0 - s_h0 * ux0 - s_h0 * s_l0; s_l0 = KA1 * yd0 * s_l0; i0 = (hx0 >> 8) & 0xff0; exp0 += (hx0 >> 20); yd0 = KA1_HI * s_h0; y0 = *(double *)((char*)__TBL_log2 + i0); y0 += (double)(exp0 << 8); m_h0 = y0 + yd0; y0 = s0 - ((m_h0 - y0 - yd0) - s_l0); y0 += *(double *)((char*)__TBL_log2 + i0 + 8) + KA1_LO * s_h0; s_h0 = y0 + m_h0; LO(&s_h0) = 0; y0 = y0 - (s_h0 - m_h0); s0 = yd0 = *py0; LO(&s0) = 0; yd0 = (yd0 - s0) * s_h0 + yd0 * y0; s0 = s_h0 * s0; /* perform 2 ** ((si+ydi)/256) */ if (s0 > HTHRESH) { s0 = HTHRESH; yd0 = DZERO; } if (s0 < LTHRESH) { s0 = LTHRESH; yd0 = DZERO; } ind0 = (int) (s0 + yd0); i0 = (ind0 & 0xff) << 4; u0 = (double) ind0; ind0 >>= 8; y0 = s0 - u0 + yd0; u0 = *(double*)((char*)__TBL_exp2 + i0); y0 = ((((KB5 * y0 + KB4) * y0 + KB3) * y0 + KB2) * y0 + KB1) * y0; eflag0 = (ind0 + 1021) >> 31; gflag0 = (1022 - ind0) >> 31; u0 = *(double*)((char*)__TBL_exp2 + i0 + 8) + u0 * y0 + u0; ind0 = (yisint0 << 11) + ind0 + (54 & eflag0) - (52 & gflag0); ind0 <<= 20; ull_x0 = *(unsigned long long*)&u0; HI(&ull_x0) += ind0; u0 = *(double*)&ull_x0; *pz0 = u0 * SCALE_ARR[eflag0 - gflag0]; if (i > 1) { /* perform si + ydi = 256*log2(xi)*yi */ u0 = x1 - ax1; s0 = u0 * yd1; LO(&ux1) = 0; y0 = s0 * s0; s_h0 = s0; LO(&s_h0) = 0; s0 = (KA5 * y0 + KA3) * y0 * s0; s_l0 = (x1 - (ux1 - ax1)); s_l0 = u0 - s_h0 * ux1 - s_h0 * s_l0; s_l0 = KA1 * yd1 * s_l0; i0 = (hx1 >> 8) & 0xff0; exp1 += (hx1 >> 20); yd0 = KA1_HI * s_h0; y0 = *(double *)((char*)__TBL_log2 + i0); y0 += (double)(exp1 << 8); m_h0 = y0 + yd0; y0 = s0 - ((m_h0 - y0 - yd0) - s_l0); y0 += *(double *)((char*)__TBL_log2 + i0 + 8) + KA1_LO * s_h0; s_h0 = y0 + m_h0; LO(&s_h0) = 0; y0 = y0 - (s_h0 - m_h0); s0 = yd0 = *py1; LO(&s0) = 0; yd0 = (yd0 - s0) * s_h0 + yd0 * y0; s0 = s_h0 * s0; /* perform 2 ** ((si+ydi)/256) */ if (s0 > HTHRESH) { s0 = HTHRESH; yd0 = DZERO; } if (s0 < LTHRESH) { s0 = LTHRESH; yd0 = DZERO; } ind0 = (int) (s0 + yd0); i0 = (ind0 & 0xff) << 4; u0 = (double) ind0; ind0 >>= 8; y0 = s0 - u0 + yd0; u0 = *(double*)((char*)__TBL_exp2 + i0); y0 = ((((KB5 * y0 + KB4) * y0 + KB3) * y0 + KB2) * y0 + KB1) * y0; eflag0 = (ind0 + 1021) >> 31; gflag0 = (1022 - ind0) >> 31; u0 = *(double*)((char*)__TBL_exp2 + i0 + 8) + u0 * y0 + u0; ind0 = (yisint1 << 11) + ind0 + (54 & eflag0) - (52 & gflag0); ind0 <<= 20; ull_x0 = *(unsigned long long*)&u0; HI(&ull_x0) += ind0; u0 = *(double*)&ull_x0; *pz1 = u0 * SCALE_ARR[eflag0 - gflag0]; } } } #undef RET_SC #define RET_SC(I) \ py += stridey; \ pz += stridez; \ if (--n <= 0) \ break; \ goto start##I; #define PREP_X(I) \ hy = HI(py); \ ly = LO(py); \ sy = hy >> 31; \ hy &= 0x7fffffff; \ py##I = py; \ \ if (hy < 0x3bf00000) /* |Y| < 2^(-64) */ \ RETURN (I, DONE) \ pz##I = pz; \ if (hy >= 0x43e00000) /* |Y|>2^63,Inf,Nan */ \ { \ if (hy >= 0x7ff00000) /* |Y|=Inf,Nan */ \ { \ if (hy == 0x7ff00000 && ly == 0) /* |Y|=Inf */ \ { \ if ((hx < 0x3ff00000) != sy) \ *pz = DZERO; \ else \ { \ HI(pz) = hy; \ LO(pz) = ly; \ } \ } \ else \ *pz = *px + *py; /* |Y|=Nan */ \ } \ else /* |Y|>2^63 */ \ { \ y0 = ((hx < 0x3ff00000) != sy) ? _TINY : _HUGE; \ *pz = y0 * y0; \ } \ RET_SC(I) \ } \ #define LMMANT ((unsigned long long*)LCONST)[4] /* 0x000fffffffffffff */ #define LMROUND ((unsigned long long*)LCONST)[5] /* 0x0000080000000000 */ #define LMHI20 ((unsigned long long*)LCONST)[6] /* 0xfffff00000000000 */ #define MMANT ((double*)LCONST)[4] /* 0x000fffffffffffff */ #define MROUND ((double*)LCONST)[5] /* 0x0000080000000000 */ #define MHI20 ((double*)LCONST)[6] /* 0xfffff00000000000 */ #define KA5 ((double*)LCONST)[8] /* 5.77078604860893737986e-01*256 */ #define KA3 ((double*)LCONST)[9] /* 9.61796693925765549423e-01*256 */ #define KA1_LO ((double*)LCONST)[10] /* 1.41052154268147309568e-05*256 */ #define KA1_HI ((double*)LCONST)[11] /* 2.8853759765625e+00*256 */ #define KA1 ((double*)LCONST)[12] /* 2.885390081777926774e+00*256 */ static void __vpowx(int n, double * restrict px, double * restrict py, int stridey, double * restrict pz, int stridez) { double *py0, *py1 = 0, *py2; double *pz0, *pz1 = 0, *pz2; double ux0, y0, yd0, u0, s0; double y1, yd1, u1, s1; double y2, yd2, u2, s2; double yr, s_h0, s_l0, m_h0, x0, ax0; unsigned long long ull_y0, ull_x0, ull_x1, ull_x2, ull_ax0; int eflag0, gflag0, ind0, i0, exp0; int eflag1, gflag1, ind1, i1; int eflag2, gflag2, ind2, i2; int i = 0; unsigned hx, hx0, hy, ly, sy; double DONE = ((double*)LCONST)[1]; /* 1.0 */ unsigned long long LDONE = ((unsigned long long*)LCONST)[1]; /* 1.0 */ double DZERO = ((double*)LCONST)[7]; /* 0.0 */ double HTHRESH = ((double*)LCONST)[13]; /* 262144.0 */ double LTHRESH = ((double*)LCONST)[14]; /* -275200.0 */ double KB5 = ((double*)LCONST)[15]; /* 1.21195555854068860923e-15 */ double KB4 = ((double*)LCONST)[16]; /* 2.23939573811855104311e-12 */ double KB3 = ((double*)LCONST)[17]; /* 3.30830268126604677436e-09 */ double KB2 = ((double*)LCONST)[18]; /* 3.66556559691003767877e-06 */ double KB1 = ((double*)LCONST)[19]; /* 2.70760617406228636578e-03 */ /* perform s_h + yr = 256*log2(x) */ ull_y0 = *(unsigned long long*)px; hx = HI(px); ull_x0 = (ull_y0 & LMMANT) | LDONE; x0 = *(double*)&ull_x0; exp0 = (hx >> 20) - 2046; ull_ax0 = ull_x0 + (LMROUND & LMHI20); ax0 = *(double*)&ull_ax0; hx0 = HI(&ax0); ux0 = x0 + ax0; yd0 = DONE / ux0; u0 = x0 - ax0; s0 = u0 * yd0; LO(&ux0) = 0; y0 = s0 * s0; s_h0 = s0; LO(&s_h0) = 0; s0 = (KA5 * y0 + KA3) * y0 * s0; s_l0 = (x0 - (ux0 - ax0)); s_l0 = u0 - s_h0 * ux0 - s_h0 * s_l0; s_l0 = KA1 * yd0 * s_l0; i0 = (hx0 >> 8) & 0xff0; exp0 += (hx0 >> 20); yd0 = KA1_HI * s_h0; y0 = *(double *)((char*)__TBL_log2 + i0); y0 += (double)(exp0 << 8); m_h0 = y0 + yd0; y0 = s0 - ((m_h0 - y0 - yd0) - s_l0); y0 += *(double *)((char*)__TBL_log2 + i0 + 8) + KA1_LO * s_h0; s_h0 = y0 + m_h0; LO(&s_h0) = 0; yr = y0 - (s_h0 - m_h0); do { /* perform 2 ** ((s_h0+yr)*yi/256) */ start0: PREP_X(0) py += stridey; pz += stridez; i = 1; if (--n <= 0) break; start1: PREP_X(1) py += stridey; pz += stridez; i = 2; if (--n <= 0) break; start2: PREP_X(2) s0 = yd0 = *py0; s1 = yd1 = *py1; s2 = yd2 = *py2; LO(&s0) = 0; LO(&s1) = 0; LO(&s2) = 0; yd0 = (yd0 - s0) * s_h0 + yd0 * yr; yd1 = (yd1 - s1) * s_h0 + yd1 * yr; yd2 = (yd2 - s2) * s_h0 + yd2 * yr; s0 = s_h0 * s0; s1 = s_h0 * s1; s2 = s_h0 * s2; if (s0 > HTHRESH) { s0 = HTHRESH; yd0 = DZERO; } if (s1 > HTHRESH) { s1 = HTHRESH; yd1 = DZERO; } if (s2 > HTHRESH) { s2 = HTHRESH; yd2 = DZERO; } if (s0 < LTHRESH) { s0 = LTHRESH; yd0 = DZERO; } ind0 = (int) (s0 + yd0); if (s1 < LTHRESH) { s1 = LTHRESH; yd1 = DZERO; } ind1 = (int) (s1 + yd1); if (s2 < LTHRESH) { s2 = LTHRESH; yd2 = DZERO; } ind2 = (int) (s2 + yd2); i0 = (ind0 & 0xff) << 4; u0 = (double) ind0; ind0 >>= 8; i1 = (ind1 & 0xff) << 4; u1 = (double) ind1; ind1 >>= 8; i2 = (ind2 & 0xff) << 4; u2 = (double) ind2; ind2 >>= 8; y0 = s0 - u0 + yd0; y1 = s1 - u1 + yd1; y2 = s2 - u2 + yd2; u0 = *(double*)((char*)__TBL_exp2 + i0); y0 = ((((KB5 * y0 + KB4) * y0 + KB3) * y0 + KB2) * y0 + KB1) * y0; u1 = *(double*)((char*)__TBL_exp2 + i1); y1 = ((((KB5 * y1 + KB4) * y1 + KB3) * y1 + KB2) * y1 + KB1) * y1; u2 = *(double*)((char*)__TBL_exp2 + i2); y2 = ((((KB5 * y2 + KB4) * y2 + KB3) * y2 + KB2) * y2 + KB1) * y2; eflag0 = (ind0 + 1021) >> 31; gflag0 = (1022 - ind0) >> 31; eflag1 = (ind1 + 1021) >> 31; gflag1 = (1022 - ind1) >> 31; eflag2 = (ind2 + 1021) >> 31; gflag2 = (1022 - ind2) >> 31; u0 = *(double*)((char*)__TBL_exp2 + i0 + 8) + u0 * y0 + u0; ind0 = ind0 + (54 & eflag0) - (52 & gflag0); ind0 <<= 20; ull_x0 = *(unsigned long long*)&u0; HI(&ull_x0) += ind0; u0 = *(double*)&ull_x0; u1 = *(double*)((char*)__TBL_exp2 + i1 + 8) + u1 * y1 + u1; ind1 = ind1 + (54 & eflag1) - (52 & gflag1); ind1 <<= 20; ull_x1 = *(unsigned long long*)&u1; HI(&ull_x1) += ind1; u1 = *(double*)&ull_x1; u2 = *(double*)((char*)__TBL_exp2 + i2 + 8) + u2 * y2 + u2; ind2 = ind2 + (54 & eflag2) - (52 & gflag2); ind2 <<= 20; ull_x2 = *(unsigned long long*)&u2; HI(&ull_x2) += ind2; u2 = *(double*)&ull_x2; *pz0 = u0 * SCALE_ARR[eflag0 - gflag0]; *pz1 = u1 * SCALE_ARR[eflag1 - gflag1]; *pz2 = u2 * SCALE_ARR[eflag2 - gflag2]; py += stridey; pz += stridez; i = 0; } while (--n > 0); if (i > 0) { /* perform 2 ** ((s_h0+yr)*yi/256) */ s0 = y0 = *py0; LO(&s0) = 0; yd0 = (y0 - s0) * s_h0 + y0 * yr; s0 = s_h0 * s0; if (s0 > HTHRESH) { s0 = HTHRESH; yd0 = DZERO; } if (s0 < LTHRESH) { s0 = LTHRESH; yd0 = DZERO; } ind0 = (int) (s0 + yd0); i0 = (ind0 & 0xff) << 4; u0 = (double) ind0; ind0 >>= 8; y0 = s0 - u0 + yd0; u0 = *(double*)((char*)__TBL_exp2 + i0); y0 = ((((KB5 * y0 + KB4) * y0 + KB3) * y0 + KB2) * y0 + KB1) * y0; eflag0 = (ind0 + 1021) >> 31; gflag0 = (1022 - ind0) >> 31; u0 = *(double*)((char*)__TBL_exp2 + i0 + 8) + u0 * y0 + u0; ind0 = ind0 + (54 & eflag0) - (52 & gflag0); ind0 <<= 20; ull_x0 = *(unsigned long long*)&u0; HI(&ull_x0) += ind0; u0 = *(double*)&ull_x0; *pz0 = u0 * SCALE_ARR[eflag0 - gflag0]; if (i > 1) { /* perform 2 ** ((s_h0+yr)*yi/256) */ s0 = y0 = *py1; LO(&s0) = 0; yd0 = (y0 - s0) * s_h0 + y0 * yr; s0 = s_h0 * s0; if (s0 > HTHRESH) { s0 = HTHRESH; yd0 = DZERO; } if (s0 < LTHRESH) { s0 = LTHRESH; yd0 = DZERO; } ind0 = (int) (s0 + yd0); i0 = (ind0 & 0xff) << 4; u0 = (double) ind0; ind0 >>= 8; y0 = s0 - u0 + yd0; u0 = *(double*)((char*)__TBL_exp2 + i0); y0 = ((((KB5 * y0 + KB4) * y0 + KB3) * y0 + KB2) * y0 + KB1) * y0; eflag0 = (ind0 + 1021) >> 31; gflag0 = (1022 - ind0) >> 31; u0 = *(double*)((char*)__TBL_exp2 + i0 + 8) + u0 * y0 + u0; ind0 = ind0 + (54 & eflag0) - (52 & gflag0); ind0 <<= 20; ull_x0 = *(unsigned long long*)&u0; HI(&ull_x0) += ind0; u0 = *(double*)&ull_x0; *pz1 = u0 * SCALE_ARR[eflag0 - gflag0]; } } }