Back to index

glibc  2.9
t_exp.c
Go to the documentation of this file.
00001 /* Accurate tables for exp().
00002    Copyright (C) 1998 Free Software Foundation, Inc.
00003    This file is part of the GNU C Library.
00004    Contributed by Geoffrey Keating <geoffk@ozemail.com.au>
00005 
00006    The GNU C Library is free software; you can redistribute it and/or
00007    modify it under the terms of the GNU Lesser General Public
00008    License as published by the Free Software Foundation; either
00009    version 2.1 of the License, or (at your option) any later version.
00010 
00011    The GNU C Library is distributed in the hope that it will be useful,
00012    but WITHOUT ANY WARRANTY; without even the implied warranty of
00013    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
00014    Lesser General Public License for more details.
00015 
00016    You should have received a copy of the GNU Lesser General Public
00017    License along with the GNU C Library; if not, write to the Free
00018    Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
00019    02111-1307 USA.  */
00020 
00021 /* This table has the property that, for all integers -177 <= i <= 177,
00022    exp(i/512.0 + __exp_deltatable[abs(i)]) == __exp_atable[i+177] + r
00023    for some -2^-64 < r < 2^-64 (abs(r) < 2^-65 if i <= 0); and that
00024    __exp_deltatable[abs(i)] == t * 2^-60
00025    for integer t so that abs(t) <= 8847927 * 2^8.  */
00026 
00027 #define W52 (2.22044605e-16)
00028 #define W55 (2.77555756e-17)
00029 #define W58 (3.46944695e-18)
00030 #define W59 (1.73472348e-18)
00031 #define W60 (8.67361738e-19)
00032 const float __exp_deltatable[178] = {
00033          0*W60,  16558714*W60, -10672149*W59,   1441652*W60,
00034  -15787963*W55,    462888*W60,   7291806*W60,   1698880*W60,
00035  -14375103*W58,  -2021016*W60,    728829*W60,  -3759654*W60,
00036    3202123*W60, -10916019*W58,   -251570*W60,  -1043086*W60,
00037    8207536*W60,   -409964*W60,  -5993931*W60,   -475500*W60,
00038    2237522*W60,    324170*W60,   -244117*W60,     32077*W60,
00039     123907*W60,  -1019734*W60,      -143*W60,    813077*W60,
00040     743345*W60,    462461*W60,    629794*W60,   2125066*W60,
00041   -2339121*W60,   -337951*W60,   9922067*W60,   -648704*W60,
00042     149407*W60,  -2687209*W60,   -631608*W60,   2128280*W60,
00043   -4882082*W60,   2001360*W60,    175074*W60,   2923216*W60,
00044    -538947*W60,  -1212193*W60,  -1920926*W60,  -1080577*W60,
00045    3690196*W60,   2643367*W60,   2911937*W60,    671455*W60,
00046   -1128674*W60,    593282*W60,  -5219347*W60,  -1941490*W60,
00047   11007953*W60,    239609*W60,  -2969658*W60,  -1183650*W60,
00048     942998*W60,    699063*W60,    450569*W60,   -329250*W60,
00049   -7257875*W60,   -312436*W60,     51626*W60,    555877*W60,
00050    -641761*W60,   1565666*W60,    884327*W60, -10960035*W60,
00051   -2004679*W60,   -995793*W60,  -2229051*W60,   -146179*W60,
00052    -510327*W60,   1453482*W60,  -3778852*W60,  -2238056*W60,
00053   -4895983*W60,   3398883*W60,   -252738*W60,   1230155*W60,
00054     346918*W60,   1109352*W60,    268941*W60,  -2930483*W60,
00055   -1036263*W60,  -1159280*W60,   1328176*W60,   2937642*W60,
00056   -9371420*W60,  -6902650*W60,  -1419134*W60,   1442904*W60,
00057   -1319056*W60,    -16369*W60,    696555*W60,   -279987*W60,
00058   -7919763*W60,    252741*W60,    459711*W60,  -1709645*W60,
00059     354913*W60,   6025867*W60,   -421460*W60,   -853103*W60,
00060    -338649*W60,    962151*W60,    955965*W60,    784419*W60,
00061   -3633653*W60,   2277133*W60,  -8847927*W52,   1223028*W60,
00062    5907079*W60,    623167*W60,   5142888*W60,   2599099*W60,
00063    1214280*W60,   4870359*W60,    593349*W60,    -57705*W60,
00064    7761209*W60,  -5564097*W60,   2051261*W60,   6216869*W60,
00065    4692163*W60,    601691*W60,  -5264906*W60,   1077872*W60,
00066   -3205949*W60,   1833082*W60,   2081746*W60,   -987363*W60,
00067   -1049535*W60,   2015244*W60,    874230*W60,   2168259*W60,
00068   -1740124*W60, -10068269*W60,    -18242*W60,  -3013583*W60,
00069     580601*W60,  -2547161*W60,   -535689*W60,   2220815*W60,
00070    1285067*W60,   2806933*W60,   -983086*W60,  -1729097*W60,
00071   -1162985*W60,  -2561904*W60,    801988*W60,    244351*W60,
00072    1441893*W60,  -7517981*W60,    271781*W60, -15021588*W60,
00073   -2341588*W60,   -919198*W60,   1642232*W60,   4771771*W60,
00074   -1220099*W60,  -3062372*W60,    628624*W60,   1278114*W60,
00075   13083513*W60, -10521925*W60,   3180310*W60,  -1659307*W60,
00076    3543773*W60,   2501203*W60,      4151*W60,   -340748*W60,
00077   -2285625*W60,   2495202*W60
00078 };
00079 
00080 const double __exp_atable[355] /* __attribute__((mode(DF))) */ = {
00081  0.707722561055888932371, /* 0x0.b52d4e46605c27ffd */
00082  0.709106182438804188967, /* 0x0.b587fb96f75097ffb */
00083  0.710492508843861281234, /* 0x0.b5e2d649899167ffd */
00084  0.711881545564593931623, /* 0x0.b63dde74d36bdfffe */
00085  0.713273297897442870573, /* 0x0.b699142f945f87ffc */
00086  0.714667771153751463236, /* 0x0.b6f477909c4ea0001 */
00087  0.716064970655995725059, /* 0x0.b75008aec758f8004 */
00088  0.717464901723956938193, /* 0x0.b7abc7a0eea7e0002 */
00089  0.718867569715736398602, /* 0x0.b807b47e1586c7ff8 */
00090  0.720272979947266023271, /* 0x0.b863cf5d10e380003 */
00091  0.721681137825144314297, /* 0x0.b8c01855195c37ffb */
00092  0.723092048691992950199, /* 0x0.b91c8f7d213740004 */
00093  0.724505717938892290800, /* 0x0.b97934ec5002d0007 */
00094  0.725922150953176470431, /* 0x0.b9d608b9c92ea7ffc */
00095  0.727341353138962865022, /* 0x0.ba330afcc29e98003 */
00096  0.728763329918453162104, /* 0x0.ba903bcc8618b7ffc */
00097  0.730188086709957051568, /* 0x0.baed9b40591ba0000 */
00098  0.731615628948127705309, /* 0x0.bb4b296f931e30002 */
00099  0.733045962086486091436, /* 0x0.bba8e671a05617ff9 */
00100  0.734479091556371366251, /* 0x0.bc06d25dd49568001 */
00101  0.735915022857225542529, /* 0x0.bc64ed4bce8f6fff9 */
00102  0.737353761441304711410, /* 0x0.bcc33752f915d7ff9 */
00103  0.738795312814142124419, /* 0x0.bd21b08af98e78005 */
00104  0.740239682467211168593, /* 0x0.bd80590b65e9a8000 */
00105  0.741686875913991849885, /* 0x0.bddf30ebec4a10000 */
00106  0.743136898669507939299, /* 0x0.be3e38443c84e0007 */
00107  0.744589756269486091620, /* 0x0.be9d6f2c1d32a0002 */
00108  0.746045454254026796384, /* 0x0.befcd5bb59baf8004 */
00109  0.747503998175051087583, /* 0x0.bf5c6c09ca84c0003 */
00110  0.748965393601880857739, /* 0x0.bfbc322f5b18b7ff8 */
00111  0.750429646104262104698, /* 0x0.c01c2843f776fffff */
00112  0.751896761271877989160, /* 0x0.c07c4e5fa18b88002 */
00113  0.753366744698445112140, /* 0x0.c0dca49a5fb18fffd */
00114  0.754839601988627206827, /* 0x0.c13d2b0c444db0005 */
00115  0.756315338768691947122, /* 0x0.c19de1cd798578006 */
00116  0.757793960659406629066, /* 0x0.c1fec8f623723fffd */
00117  0.759275473314173443536, /* 0x0.c25fe09e8a0f47ff8 */
00118  0.760759882363831851927, /* 0x0.c2c128dedc88f8000 */
00119  0.762247193485956486805, /* 0x0.c322a1cf7d6e7fffa */
00120  0.763737412354726363781, /* 0x0.c3844b88cb9347ffc */
00121  0.765230544649828092739, /* 0x0.c3e626232bd8f7ffc */
00122  0.766726596071518051729, /* 0x0.c44831b719bf18002 */
00123  0.768225572321911687194, /* 0x0.c4aa6e5d12d078001 */
00124  0.769727479119219348810, /* 0x0.c50cdc2da64a37ffb */
00125  0.771232322196981678892, /* 0x0.c56f7b41744490001 */
00126  0.772740107296721268087, /* 0x0.c5d24bb1259e70004 */
00127  0.774250840160724651565, /* 0x0.c6354d95640dd0007 */
00128  0.775764526565368872643, /* 0x0.c6988106fec447fff */
00129  0.777281172269557396602, /* 0x0.c6fbe61eb1bd0ffff */
00130  0.778800783068235302750, /* 0x0.c75f7cf560942fffc */
00131  0.780323364758801041312, /* 0x0.c7c345a3f1983fffe */
00132  0.781848923151573727006, /* 0x0.c8274043594cb0002 */
00133  0.783377464064598849602, /* 0x0.c88b6cec94b3b7ff9 */
00134  0.784908993312207869935, /* 0x0.c8efcbb89cba27ffe */
00135  0.786443516765346961618, /* 0x0.c9545cc0a88c70003 */
00136  0.787981040257604625744, /* 0x0.c9b9201dc643bfffa */
00137  0.789521569657452682047, /* 0x0.ca1e15e92a5410007 */
00138  0.791065110849462849192, /* 0x0.ca833e3c1ae510005 */
00139  0.792611669712891875319, /* 0x0.cae8992fd84667ffd */
00140  0.794161252150049179450, /* 0x0.cb4e26ddbc207fff8 */
00141  0.795713864077794763584, /* 0x0.cbb3e75f301b60003 */
00142  0.797269511407239561694, /* 0x0.cc19dacd978cd8002 */
00143  0.798828200086368567220, /* 0x0.cc8001427e55d7ffb */
00144  0.800389937624300440456, /* 0x0.cce65ade24d360006 */
00145  0.801954725261124767840, /* 0x0.cd4ce7a5de839fffb */
00146  0.803522573691593189330, /* 0x0.cdb3a7c79a678fffd */
00147  0.805093487311204114563, /* 0x0.ce1a9b563965ffffc */
00148  0.806667472122675088819, /* 0x0.ce81c26b838db8000 */
00149  0.808244534127439906441, /* 0x0.cee91d213f8428002 */
00150  0.809824679342317166307, /* 0x0.cf50ab9144d92fff9 */
00151  0.811407913793616542005, /* 0x0.cfb86dd5758c2ffff */
00152  0.812994243520784198882, /* 0x0.d0206407c20e20005 */
00153  0.814583674571603966162, /* 0x0.d0888e4223facfff9 */
00154  0.816176213022088536960, /* 0x0.d0f0ec9eb3f7c8002 */
00155  0.817771864936188586101, /* 0x0.d1597f377d6768002 */
00156  0.819370636400374108252, /* 0x0.d1c24626a46eafff8 */
00157  0.820972533518165570298, /* 0x0.d22b41865ff1e7ff9 */
00158  0.822577562404315121269, /* 0x0.d2947170f32ec7ff9 */
00159  0.824185729164559344159, /* 0x0.d2fdd60097795fff8 */
00160  0.825797039949601741075, /* 0x0.d3676f4fb796d0001 */
00161  0.827411500902565544264, /* 0x0.d3d13d78b5f68fffb */
00162  0.829029118181348834154, /* 0x0.d43b40960546d8001 */
00163  0.830649897953322891022, /* 0x0.d4a578c222a058000 */
00164  0.832273846408250750368, /* 0x0.d50fe617a3ba78005 */
00165  0.833900969738858188772, /* 0x0.d57a88b1218e90002 */
00166  0.835531274148056613016, /* 0x0.d5e560a94048f8006 */
00167  0.837164765846411529371, /* 0x0.d6506e1aac8078003 */
00168  0.838801451086016225394, /* 0x0.d6bbb1204074e0001 */
00169  0.840441336100884561780, /* 0x0.d72729d4c28518004 */
00170  0.842084427144139224814, /* 0x0.d792d8530e12b0001 */
00171  0.843730730487052604790, /* 0x0.d7febcb61273e7fff */
00172  0.845380252404570153833, /* 0x0.d86ad718c308dfff9 */
00173  0.847032999194574087728, /* 0x0.d8d727962c69d7fff */
00174  0.848688977161248581090, /* 0x0.d943ae49621ce7ffb */
00175  0.850348192619261200615, /* 0x0.d9b06b4d832ef8005 */
00176  0.852010651900976245816, /* 0x0.da1d5ebdc22220005 */
00177  0.853676361342631029337, /* 0x0.da8a88b555baa0006 */
00178  0.855345327311054837175, /* 0x0.daf7e94f965f98004 */
00179  0.857017556155879489641, /* 0x0.db6580a7c98f7fff8 */
00180  0.858693054267390953857, /* 0x0.dbd34ed9617befff8 */
00181  0.860371828028939855647, /* 0x0.dc4153ffc8b65fff9 */
00182  0.862053883854957292436, /* 0x0.dcaf90368bfca8004 */
00183  0.863739228154875360306, /* 0x0.dd1e0399328d87ffe */
00184  0.865427867361348468455, /* 0x0.dd8cae435d303fff9 */
00185  0.867119807911702289458, /* 0x0.ddfb9050b1cee8006 */
00186  0.868815056264353846599, /* 0x0.de6aa9dced8448001 */
00187  0.870513618890481399881, /* 0x0.ded9fb03db7320006 */
00188  0.872215502247877139094, /* 0x0.df4983e1380657ff8 */
00189  0.873920712852848668986, /* 0x0.dfb94490ffff77ffd */
00190  0.875629257204025623884, /* 0x0.e0293d2f1cb01fff9 */
00191  0.877341141814212965880, /* 0x0.e0996dd786fff0007 */
00192  0.879056373217612985183, /* 0x0.e109d6a64f5d57ffc */
00193  0.880774957955916648615, /* 0x0.e17a77b78e72a7ffe */
00194  0.882496902590150900078, /* 0x0.e1eb5127722cc7ff8 */
00195  0.884222213673356738383, /* 0x0.e25c63121fb0c8006 */
00196  0.885950897802399772740, /* 0x0.e2cdad93ec5340003 */
00197  0.887682961567391237685, /* 0x0.e33f30c925fb97ffb */
00198  0.889418411575228162725, /* 0x0.e3b0ecce2d05ffff9 */
00199  0.891157254447957902797, /* 0x0.e422e1bf727718006 */
00200  0.892899496816652704641, /* 0x0.e4950fb9713fc7ffe */
00201  0.894645145323828439008, /* 0x0.e50776d8b0e60fff8 */
00202  0.896394206626591749641, /* 0x0.e57a1739c8fadfffc */
00203  0.898146687421414902124, /* 0x0.e5ecf0f97c5798007 */
00204  0.899902594367530173098, /* 0x0.e660043464e378005 */
00205  0.901661934163603406867, /* 0x0.e6d3510747e150006 */
00206  0.903424713533971135418, /* 0x0.e746d78f06cd97ffd */
00207  0.905190939194458810123, /* 0x0.e7ba97e879c91fffc */
00208  0.906960617885092856864, /* 0x0.e82e92309390b0007 */
00209  0.908733756358986566306, /* 0x0.e8a2c6845544afffa */
00210  0.910510361377119825629, /* 0x0.e9173500c8abc7ff8 */
00211  0.912290439722343249336, /* 0x0.e98bddc30f98b0002 */
00212  0.914073998177417412765, /* 0x0.ea00c0e84bc4c7fff */
00213  0.915861043547953501680, /* 0x0.ea75de8db8094fffe */
00214  0.917651582652244779397, /* 0x0.eaeb36d09d3137ffe */
00215  0.919445622318405764159, /* 0x0.eb60c9ce4ed3dffff */
00216  0.921243169397334638073, /* 0x0.ebd697a43995b0007 */
00217  0.923044230737526172328, /* 0x0.ec4ca06fc7768fffa */
00218  0.924848813220121135342, /* 0x0.ecc2e44e865b6fffb */
00219  0.926656923710931002014, /* 0x0.ed39635df34e70006 */
00220  0.928468569126343790092, /* 0x0.edb01dbbc2f5b7ffa */
00221  0.930283756368834757725, /* 0x0.ee2713859aab57ffa */
00222  0.932102492359406786818, /* 0x0.ee9e44d9342870004 */
00223  0.933924784042873379360, /* 0x0.ef15b1d4635438005 */
00224  0.935750638358567643520, /* 0x0.ef8d5a94f60f50007 */
00225  0.937580062297704630580, /* 0x0.f0053f38f345cffff */
00226  0.939413062815381727516, /* 0x0.f07d5fde3a2d98001 */
00227  0.941249646905368053689, /* 0x0.f0f5bca2d481a8004 */
00228  0.943089821583810716806, /* 0x0.f16e55a4e497d7ffe */
00229  0.944933593864477061592, /* 0x0.f1e72b028a2827ffb */
00230  0.946780970781518460559, /* 0x0.f2603cd9fb5430001 */
00231  0.948631959382661205081, /* 0x0.f2d98b497d2a87ff9 */
00232  0.950486566729423554277, /* 0x0.f353166f63e3dffff */
00233  0.952344799896018723290, /* 0x0.f3ccde6a11ae37ffe */
00234  0.954206665969085765512, /* 0x0.f446e357f66120000 */
00235  0.956072172053890279009, /* 0x0.f4c12557964f0fff9 */
00236  0.957941325265908139014, /* 0x0.f53ba48781046fffb */
00237  0.959814132734539637840, /* 0x0.f5b66106555d07ffa */
00238  0.961690601603558903308, /* 0x0.f6315af2c2027fffc */
00239  0.963570739036113010927, /* 0x0.f6ac926b8aeb80004 */
00240  0.965454552202857141381, /* 0x0.f728078f7c5008002 */
00241  0.967342048278315158608, /* 0x0.f7a3ba7d66a908001 */
00242  0.969233234469444204768, /* 0x0.f81fab543e1897ffb */
00243  0.971128118008140250896, /* 0x0.f89bda33122c78007 */
00244  0.973026706099345495256, /* 0x0.f9184738d4cf97ff8 */
00245  0.974929006031422851235, /* 0x0.f994f284d3a5c0008 */
00246  0.976835024947348973265, /* 0x0.fa11dc35bc7820002 */
00247  0.978744770239899142285, /* 0x0.fa8f046b4fb7f8007 */
00248  0.980658249138918636210, /* 0x0.fb0c6b449ab1cfff9 */
00249  0.982575468959622777535, /* 0x0.fb8a10e1088fb7ffa */
00250  0.984496437054508843888, /* 0x0.fc07f5602d79afffc */
00251  0.986421160608523028820, /* 0x0.fc8618e0e55e47ffb */
00252  0.988349647107594098099, /* 0x0.fd047b83571b1fffa */
00253  0.990281903873210800357, /* 0x0.fd831d66f4c018002 */
00254  0.992217938695037382475, /* 0x0.fe01fead3320bfff8 */
00255  0.994157757657894713987, /* 0x0.fe811f703491e8006 */
00256  0.996101369488558541238, /* 0x0.ff007fd5744490005 */
00257  0.998048781093141101932, /* 0x0.ff801ffa9b9280007 */
00258  1.000000000000000000000, /* 0x1.00000000000000000 */
00259  1.001955033605393285965, /* 0x1.0080200565d29ffff */
00260  1.003913889319761887310, /* 0x1.0100802aa0e80fff0 */
00261  1.005876574715736104818, /* 0x1.01812090377240007 */
00262  1.007843096764807100351, /* 0x1.020201541aad7fff6 */
00263  1.009813464316352327214, /* 0x1.0283229c4c9820007 */
00264  1.011787683565730677817, /* 0x1.030484836910a000e */
00265  1.013765762469146736174, /* 0x1.0386272b9c077fffe */
00266  1.015747708536026694351, /* 0x1.04080ab526304fff0 */
00267  1.017733529475172815584, /* 0x1.048a2f412375ffff0 */
00268  1.019723232714418781378, /* 0x1.050c94ef7ad5e000a */
00269  1.021716825883923762690, /* 0x1.058f3be0f1c2d0004 */
00270  1.023714316605201180057, /* 0x1.06122436442e2000e */
00271  1.025715712440059545995, /* 0x1.06954e0fec63afff2 */
00272  1.027721021151397406936, /* 0x1.0718b98f41c92fff6 */
00273  1.029730250269221158939, /* 0x1.079c66d49bb2ffff1 */
00274  1.031743407506447551857, /* 0x1.082056011a9230009 */
00275  1.033760500517691527387, /* 0x1.08a487359ebd50002 */
00276  1.035781537016238873464, /* 0x1.0928fa93490d4fff3 */
00277  1.037806524719013578963, /* 0x1.09adb03b3e5b3000d */
00278  1.039835471338248051878, /* 0x1.0a32a84e9e5760004 */
00279  1.041868384612101516848, /* 0x1.0ab7e2eea5340ffff */
00280  1.043905272300907460835, /* 0x1.0b3d603ca784f0009 */
00281  1.045946142174331239262, /* 0x1.0bc3205a042060000 */
00282  1.047991002016745332165, /* 0x1.0c4923682a086fffe */
00283  1.050039859627715177527, /* 0x1.0ccf698898f3a000d */
00284  1.052092722826109660856, /* 0x1.0d55f2dce5d1dfffb */
00285  1.054149599440827866881, /* 0x1.0ddcbf86b09a5fff6 */
00286  1.056210497317612961855, /* 0x1.0e63cfa7abc97fffd */
00287  1.058275424318780855142, /* 0x1.0eeb23619c146fffb */
00288  1.060344388322010722446, /* 0x1.0f72bad65714bffff */
00289  1.062417397220589476718, /* 0x1.0ffa9627c38d30004 */
00290  1.064494458915699715017, /* 0x1.1082b577d0eef0003 */
00291  1.066575581342167566880, /* 0x1.110b18e893a90000a */
00292  1.068660772440545025953, /* 0x1.1193c09c267610006 */
00293  1.070750040138235936705, /* 0x1.121cacb4959befff6 */
00294  1.072843392435016474095, /* 0x1.12a5dd543cf36ffff */
00295  1.074940837302467588937, /* 0x1.132f529d59552000b */
00296  1.077042382749654914030, /* 0x1.13b90cb250d08fff5 */
00297  1.079148036789447484528, /* 0x1.14430bb58da3dfff9 */
00298  1.081257807444460983297, /* 0x1.14cd4fc984c4a000e */
00299  1.083371702785017154417, /* 0x1.1557d910df9c7000e */
00300  1.085489730853784307038, /* 0x1.15e2a7ae292d30002 */
00301  1.087611899742884524772, /* 0x1.166dbbc422d8c0004 */
00302  1.089738217537583819804, /* 0x1.16f9157586772ffff */
00303  1.091868692357631731528, /* 0x1.1784b4e533cacfff0 */
00304  1.094003332327482702577, /* 0x1.18109a360fc23fff2 */
00305  1.096142145591650907149, /* 0x1.189cc58b155a70008 */
00306  1.098285140311341168136, /* 0x1.1929370751ea50002 */
00307  1.100432324652149906842, /* 0x1.19b5eecdd79cefff0 */
00308  1.102583706811727015711, /* 0x1.1a42ed01dbdba000e */
00309  1.104739294993289488947, /* 0x1.1ad031c69a2eafff0 */
00310  1.106899097422573863281, /* 0x1.1b5dbd3f66e120003 */
00311  1.109063122341542140286, /* 0x1.1beb8f8fa8150000b */
00312  1.111231377994659874592, /* 0x1.1c79a8dac6ad0fff4 */
00313  1.113403872669181282605, /* 0x1.1d0809445a97ffffc */
00314  1.115580614653132185460, /* 0x1.1d96b0effc9db000e */
00315  1.117761612217810673898, /* 0x1.1e25a001332190000 */
00316  1.119946873713312474002, /* 0x1.1eb4d69bdb2a9fff1 */
00317  1.122136407473298902480, /* 0x1.1f4454e3bfae00006 */
00318  1.124330221845670330058, /* 0x1.1fd41afcbb48bfff8 */
00319  1.126528325196519908506, /* 0x1.2064290abc98c0001 */
00320  1.128730725913251964394, /* 0x1.20f47f31c9aa7000f */
00321  1.130937432396844410880, /* 0x1.21851d95f776dfff0 */
00322  1.133148453059692917203, /* 0x1.2216045b6784efffa */
00323  1.135363796355857157764, /* 0x1.22a733a6692ae0004 */
00324  1.137583470716100553249, /* 0x1.2338ab9b3221a0004 */
00325  1.139807484614418608939, /* 0x1.23ca6c5e27aadfff7 */
00326  1.142035846532929888057, /* 0x1.245c7613b7f6c0004 */
00327  1.144268564977221958089, /* 0x1.24eec8e06b035000c */
00328  1.146505648458203463465, /* 0x1.258164e8cea85fff8 */
00329  1.148747105501412235671, /* 0x1.26144a5180d380009 */
00330  1.150992944689175123667, /* 0x1.26a7793f5de2efffa */
00331  1.153243174560058870217, /* 0x1.273af1d712179000d */
00332  1.155497803703682491111, /* 0x1.27ceb43d81d42fff1 */
00333  1.157756840726344771440, /* 0x1.2862c097a3d29000c */
00334  1.160020294239811677834, /* 0x1.28f7170a74cf4fff1 */
00335  1.162288172883275239058, /* 0x1.298bb7bb0faed0004 */
00336  1.164560485298402170388, /* 0x1.2a20a2ce920dffff4 */
00337  1.166837240167474476460, /* 0x1.2ab5d86a4631ffff6 */
00338  1.169118446164539637555, /* 0x1.2b4b58b36d5220009 */
00339  1.171404112007080167155, /* 0x1.2be123cf786790002 */
00340  1.173694246390975415341, /* 0x1.2c7739e3c0aac000d */
00341  1.175988858069749065617, /* 0x1.2d0d9b15deb58fff6 */
00342  1.178287955789017793514, /* 0x1.2da4478b627040002 */
00343  1.180591548323240091978, /* 0x1.2e3b3f69fb794fffc */
00344  1.182899644456603782686, /* 0x1.2ed282d76421d0004 */
00345  1.185212252993012693694, /* 0x1.2f6a11f96c685fff3 */
00346  1.187529382762033236513, /* 0x1.3001ecf60082ffffa */
00347  1.189851042595508889847, /* 0x1.309a13f30f28a0004 */
00348  1.192177241354644978669, /* 0x1.31328716a758cfff7 */
00349  1.194507987909589896687, /* 0x1.31cb4686e1e85fffb */
00350  1.196843291137896336843, /* 0x1.32645269dfd04000a */
00351  1.199183159977805113226, /* 0x1.32fdaae604c39000f */
00352  1.201527603343041317132, /* 0x1.339750219980dfff3 */
00353  1.203876630171082595692, /* 0x1.3431424300e480007 */
00354  1.206230249419600664189, /* 0x1.34cb8170b3fee000e */
00355  1.208588470077065268869, /* 0x1.35660dd14dbd4fffc */
00356  1.210951301134513435915, /* 0x1.3600e78b6bdfc0005 */
00357  1.213318751604272271958, /* 0x1.369c0ec5c38ebfff2 */
00358  1.215690830512196507537, /* 0x1.373783a718d29000f */
00359  1.218067546930756250870, /* 0x1.37d3465662f480007 */
00360  1.220448909901335365929, /* 0x1.386f56fa770fe0008 */
00361  1.222834928513994334780, /* 0x1.390bb5ba5fc540004 */
00362  1.225225611877684750397, /* 0x1.39a862bd3c7a8fff3 */
00363  1.227620969111500981433, /* 0x1.3a455e2a37bcafffd */
00364  1.230021009336254911271, /* 0x1.3ae2a8287dfbefff6 */
00365  1.232425741726685064472, /* 0x1.3b8040df76f39fffa */
00366  1.234835175450728295084, /* 0x1.3c1e287682e48fff1 */
00367  1.237249319699482263931, /* 0x1.3cbc5f151b86bfff8 */
00368  1.239668183679933477545, /* 0x1.3d5ae4e2cc0a8000f */
00369  1.242091776620540377629, /* 0x1.3df9ba07373bf0006 */
00370  1.244520107762172811399, /* 0x1.3e98deaa0d8cafffe */
00371  1.246953186383919165383, /* 0x1.3f3852f32973efff0 */
00372  1.249391019292643401078, /* 0x1.3fd816ffc72b90001 */
00373  1.251833623164381181797, /* 0x1.40782b17863250005 */
00374  1.254280999953110153911, /* 0x1.41188f42caf400000 */
00375  1.256733161434815393410, /* 0x1.41b943b42945bfffd */
00376  1.259190116985283935980, /* 0x1.425a4893e5f10000a */
00377  1.261651875958665236542, /* 0x1.42fb9e0a2df4c0009 */
00378  1.264118447754797758244, /* 0x1.439d443f608c4fff9 */
00379  1.266589841787181258708, /* 0x1.443f3b5bebf850008 */
00380  1.269066067469190262045, /* 0x1.44e183883e561fff7 */
00381  1.271547134259576328224, /* 0x1.45841cecf7a7a0001 */
00382  1.274033051628237434048, /* 0x1.462707b2c43020009 */
00383  1.276523829025464573684, /* 0x1.46ca44023aa410007 */
00384  1.279019475999373156531, /* 0x1.476dd2045d46ffff0 */
00385  1.281520002043128991825, /* 0x1.4811b1e1f1f19000b */
00386  1.284025416692967214122, /* 0x1.48b5e3c3edd74fff4 */
00387  1.286535729509738823464, /* 0x1.495a67d3613c8fff7 */
00388  1.289050950070396384145, /* 0x1.49ff3e396e19d000b */
00389  1.291571087985403654081, /* 0x1.4aa4671f5b401fff1 */
00390  1.294096152842774794011, /* 0x1.4b49e2ae56d19000d */
00391  1.296626154297237043484, /* 0x1.4befb10fd84a3fff4 */
00392  1.299161101984141142272, /* 0x1.4c95d26d41d84fff8 */
00393  1.301701005575179204100, /* 0x1.4d3c46f01d9f0fff3 */
00394  1.304245874766450485904, /* 0x1.4de30ec21097d0003 */
00395  1.306795719266019562007, /* 0x1.4e8a2a0ccce3d0002 */
00396  1.309350548792467483458, /* 0x1.4f3198fa10346fff5 */
00397  1.311910373099227200545, /* 0x1.4fd95bb3be8cffffd */
00398  1.314475201942565174546, /* 0x1.50817263bf0e5fffb */
00399  1.317045045107389400535, /* 0x1.5129dd3418575000e */
00400  1.319619912422941299109, /* 0x1.51d29c4f01c54ffff */
00401  1.322199813675649204855, /* 0x1.527bafde83a310009 */
00402  1.324784758729532718739, /* 0x1.5325180cfb8b3fffd */
00403  1.327374757430096474625, /* 0x1.53ced504b2bd0fff4 */
00404  1.329969819671041886272, /* 0x1.5478e6f02775e0001 */
00405  1.332569955346704748651, /* 0x1.55234df9d8a59fff8 */
00406  1.335175174370685002822, /* 0x1.55ce0a4c5a6a9fff6 */
00407  1.337785486688218616860, /* 0x1.56791c1263abefff7 */
00408  1.340400902247843806217, /* 0x1.57248376aef21fffa */
00409  1.343021431036279800211, /* 0x1.57d040a420c0bfff3 */
00410  1.345647083048053138662, /* 0x1.587c53c5a630f0002 */
00411  1.348277868295411074918, /* 0x1.5928bd063fd7bfff9 */
00412  1.350913796821875845231, /* 0x1.59d57c9110ad60006 */
00413  1.353554878672557082439, /* 0x1.5a8292913d68cfffc */
00414  1.356201123929036356254, /* 0x1.5b2fff3212db00007 */
00415  1.358852542671913132777, /* 0x1.5bddc29edcc06fff3 */
00416  1.361509145047255398051, /* 0x1.5c8bdd032ed16000f */
00417  1.364170941142184734180, /* 0x1.5d3a4e8a5bf61fff4 */
00418  1.366837941171020309735, /* 0x1.5de9176042f1effff */
00419  1.369510155261156381121, /* 0x1.5e9837b062f4e0005 */
00420  1.372187593620959988833, /* 0x1.5f47afa69436cfff1 */
00421  1.374870266463378287715, /* 0x1.5ff77f6eb3f8cfffd */
00422  1.377558184010425845733, /* 0x1.60a7a734a9742fff9 */
00423  1.380251356531521533853, /* 0x1.6158272490016000c */
00424  1.382949794301995272203, /* 0x1.6208ff6a8978a000f */
00425  1.385653507605306700170, /* 0x1.62ba3032c0a280004 */
00426  1.388362506772382154503, /* 0x1.636bb9a994784000f */
00427  1.391076802081129493127, /* 0x1.641d9bfb29a7bfff6 */
00428  1.393796403973427855412, /* 0x1.64cfd7545928b0002 */
00429  1.396521322756352656542, /* 0x1.65826be167badfff8 */
00430  1.399251568859207761660, /* 0x1.663559cf20826000c */
00431  1.401987152677323100733, /* 0x1.66e8a14a29486fffc */
00432  1.404728084651919228815, /* 0x1.679c427f5a4b6000b */
00433  1.407474375243217723560, /* 0x1.68503d9ba0add000f */
00434  1.410226034922914983815, /* 0x1.690492cbf6303fff9 */
00435  1.412983074197955213304, /* 0x1.69b9423d7b548fff6 */
00436 };