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<li class="navelem"><a class="el" href="dir_dc43877d82dd332f9fb2071fcca799d6.html">kernel</a></li><li class="navelem"><a class="el" href="dir_7ab5cd9d6a44db3bf3b807f89e50cefe.html">util</a></li> </ul>
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<div class="title">bessel_i0.c</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/*</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment"> * Copyright (c) 2002, 2016 Jens Keiner, Stefan Kunis, Daniel Potts</span></div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> *</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> * This program is free software; you can redistribute it and/or modify it under</span></div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> * the terms of the GNU General Public License as published by the Free Software</span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> * Foundation; either version 2 of the License, or (at your option) any later</span></div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> * version.</span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> *</span></div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> * This program is distributed in the hope that it will be useful, but WITHOUT</span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS</span></div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more</span></div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"> * details.</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment"> *</span></div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment"> * You should have received a copy of the GNU General Public License along with</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"> * this program; if not, write to the Free Software Foundation, Inc., 51</span></div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"> * Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.</span></div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"> */</span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> </div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="preprocessor">#include "infft.h"</span></div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> </div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#if defined(NFFT_LDOUBLE)</span></div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor"> #if LDBL_MANT_DIG > 64</span></div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  <span class="comment">/* long double 128 bit wide */</span></div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  <span class="keyword">static</span> <span class="keyword">const</span> R P1[] =</div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  {</div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  K(0.9999999999999999999999999999999999962027889818871465625924752326583154315551642695323965510694779151206544639605419513240736857),</div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  K(0.25000000000000000000000000000000012196714800029501487764875563265263401524033425368818847175854607800541392646833606522273821246),</div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  K(0.027777777777777777777777777777777144587988290342214362953013414854374623029362784740516243952857824585136440104808521394795213943),</div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  K(0.0017361111111111111111111111111123869249041395763984631620599418268304349163419724426016945727467811299651660803976432220176426406),</div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  K(0.000069444444444444444444444444443107647328522467237563132750155356213911633630315806134293192377451924142086027094615621024770286162),</div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  K(1.9290123456790123456790123465252951528964587234675843733257549721655185850604449629037749798050593867815808367493607761074167203e-6),</div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  K(3.9367598891408415217939027108074887847673564509601917363278330920730719763184952569786096533271821267912464336083679709264700463e-8),</div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  K(6.1511873267825648778029740886343589006492244222098376295896480615672663845071908228080782331139431967897922330634666102008303163e-10),</div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  K(7.5940584281266233059295735665953083409170414099680216865037645091739362117435423650805312126318743025058577203204754258976678014e-12),</div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  K(7.5940584281266233059299735717776013802752093873942144943735559285381124771290874275774972580263377448832380260417572227398010273e-14),</div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  K(6.2760813455591928148129664638468741352313877508511272487605818260638787040214741939853005199347727650099145873785771162609470873e-16),</div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  K(4.3583898233049950103405756560043488004237104566659409254314063662323845080352835082013472245469229428130314480254874472462460891e-18),</div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  K(2.5789288895295828459033545114345754110126610917070986842981263284383138335900724842812739092696462831628856077304156728937367615e-20),</div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  K(1.3157800456783585979726388980387458854840810376002467594059415767303181634829326622143751699233015215909660383669969973896437826e-22),</div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  K(5.8479113141260380335975041071277913723234662896226038462639284334574178411617861304919195972489113065590753369218560772342930726e-25),</div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  K(2.2843403570804844741559425131287256347316408180969139215424927280400161659234508601992572475246984021932920101195981533775809011e-27),</div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  K(7.9042918930120215557655530936488590704671411306518762754706457865191035559604608171265261834240025123226121413351951869227469481e-30),</div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  K(2.439596263275438744691212721375550679559038036180973780451914524892069264667965537779114429543772487937962814842584430315822309e-32),</div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  K(6.7578843858008565460738956555556721994562125360817163818492848944114465748014992064357014275747373903974186259850477923287772269e-35),</div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  K(1.6894710964596677914300599135928934608666852785592175435009841929849562545281838798552390215907162912732614665877854602723350365e-37),</div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  K(3.8310002185198913939699183167260082132386992335359252310560205887083199288222921373551164604122527855575096799590794332372889982e-40),</div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  K(7.9152897117050638868250808160461112764395266893341033364145136187242187903457065607810464366513129569605469553757332577108931927e-43),</div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  K(1.4962740408949741994371775249428502243459110838196377209217623910923455903816887608569441907818721649385471112081388662207931364e-45),</div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  K(2.5976980842076886545162534185856248239556535520445635413487233605795098016339073754464291911162237045775316398305220029774563812e-48),</div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  K(4.1563157246970089177790104414625258959749615665778227563200792024682955941012716142727278222955329547858593509607233532321977384e-51),</div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  K(6.1484091972930398448317003607725995381550723813563853679777776077080177504939862858361387931698777740352242553154617386041598546e-54),</div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  K(8.4339079896649387396805165150345921345758626392364604080732341511582436140021851014611248449264294960348295127030417414763783526e-57),</div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  K(1.0758542181237264915749101505104765885049322002226174095616335030835886896108338436649327399785636341219913669804985122152824265e-59),</div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  K(1.2785524522454856200134470274184700289665086209215001086254221172250431156408812081801869424331341843840158057362920094547656938e-62),</div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  K(1.4248179766163819508194806049285708797690012879420281636927945272874304904429404793261110930103216776338690899423424418356698994e-65),</div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  K(1.4613184522449821802557940850011777432583484917091332887731152191646500305736827143107335993192474581511762327392034830200299768e-68),</div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  K(1.517919158523286579991864653430437909257242986598610110778281992820044480031975647280367518640551811313326095597412581231791542e-71),</div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  K(1.0730639360074958234700168111189609812309927776575154251790558216554191498594054258151950239282462897703667491995027177113192561e-74),</div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  K(1.849733759307828545234442543657764632352967627228530812064253357302934215881683992754041627944673908746817007111464947383730042e-77),</div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  K(-5.8729229858051647671731463714537532835823360515481187134639456051237156797256723676348818396781843804444226329124520413341278697e-81),</div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  K(3.1842186240879590225313774846938043014439524114338193689962549518448769929496194164836586422709285896399036894999980974150749013e-83),</div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  K(-2.1881719673472495157660923989130852804625696106789978549832744474725166266000647439983140838502086580706730083730364920779307716e-86),</div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  K(2.0535558773071560722118718580083555594558665120203432096590057810260358624306996796538168725229696967831406758396551788353456152e-89),</div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  };</div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keyword">static</span> <span class="keyword">const</span> R Q1[] =</div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  {</div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  K(1),</div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  };</div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="keyword">static</span> <span class="keyword">const</span> R P2[] =</div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  {</div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  K(0.39894228040143267793994605993438189141018035442705729869804407689568381581734064686884602636060801485954621762740457550454120697),</div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  K(0.049867785050179084742493257490426145214512545591609659268248950196534280305961469882423461068790635445162491599891668241427694247),</div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  K(0.028050629090725735167652470998240899244071027169401361478749442415263988321141666521103085221687123192693334717091473761538817597),</div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  K(0.029219405302839307466250377876541919632987444632087277804127165783408826159066976653503074036487303121478723913535606767065816568),</div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  K(0.044742214369972689672757506995683668911838579935127513656738903414493578300728048844259081530992294260985826760124616165540729805),</div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  K(0.090602984099194545717108245690464709907435886237578028801057472781356468016933973445902282489417082489842418887592185592440521463),</div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  K(0.22839502241685343551568202900938534408323646867712940217756161458845324824124440104346632880269277474229622722857526929839330408),</div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  K(0.68926354970839797649853996399096479758550548316271823261307182611573812144139459011679425469995979044875363036072019650427109275),</div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  K(2.423192207724660758719355443491407013949377273831782675793140405839150024194700004683477388942832249119599378305563068242785029),</div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  K(9.7264091894977322855634221908603466759090961796678318811908721617317858636550474385646395183519977007947556596807399846944242623),</div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  K(43.894849749018396087574371484153328058059670508806822372081594668827438357942108803133491029755284933660373288867373132032368835),</div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  K(218.92224061880098667718426029789638820474517627422355720085391021586878854687601367885067299893531247137789283401227975375634307),</div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  K(1411.0714378841016321410168079012058915863951925541781772306639164464058932052840516833410793638465388787557712463940136004684829),</div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  K(-24669.417143852155941925922310645066937535848529101153480534808775058200117108762353716556845844109846670042694143992197668096542),</div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  K(4.3456187215737626225180053878439968236045760017182272244210822162169787026396322773165192567887238575971635413521445809876980004e6),</div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  K(-4.8794244314757594930125129712472496055896630924509326926769483634245544755261389240465702901747116533723557473550656594631532836e8),</div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  K(4.7135622802198833573595004986499079081107263879749738524409185091193774357674279922423541892450668395500169866908527469556459572e10),</div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  K(-3.8845767816711551934241716931447885535253872729659980739269139137736111723828410537289978592243029663663867611966517996124536087e12),</div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  K(2.7431597072135274612373797235764178284960675893163510470039767771950309546569261187500692221566731027281621740913265115102310496e14),</div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  K(-1.6636598713596741944604248189852920881501346018142892635481495198437840156774926185383215014490693563834394957950230048940030269e16),</div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  K(8.6761557906756247348638118281136603405500414721831534457612925481123322024593371759387146931591096846424375193986594474897877506e17),</div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  K(-3.8913176955569588730031997156307239438827348326480575220510931691527300070325174335141194550785118636626722266446637917200705305e19),</div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  K(1.4994387859623891999511364539836016709264090275867767459706869909005029610415881414010795232967045454552995180823348444416265002e21),</div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  K(-4.9526316726474597668971927656830715565011030190318549395742059758921820863775022631233335917983607537011812481817492614325105297e22),</div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  K(1.397064884652902423392749086230445982786614531772675459975976690233879103001760917728872951577136897092365891622780984709402973e24),</div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  K(-3.3476761876177350335523912452608780785827233458182277101687250287742574272022970793769978972224508627617386323901820464201569753e25),</div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  K(6.7638961792609295046405395451813410863531398189017078811550463864945380021979484321848645213471320221939039055909450745691397385e26),</div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  K(-1.14079573340166931747184530752445311008079545441036388481953511060965509254548158980345036081716115934507061629230171580151953e28),</div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  K(1.5843626737066263794105803441416923917274696837109592895480698389316466299714783209728565162325083868829306539854083641550288868e29),</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  K(-1.7782859979199278216778586806675418350823245944594339589914373884037721073371915283109990177929377444043444423433544695887093251e30),</div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  K(1.5708853802374339215889671052352242220779637148891880270680676413885516142759102997242314905431899904918009952268613041942043472e31),</div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  K(-1.0500350399986598062815891870047338843859846801171623906896291522399576189691430301012749176131933567692272239383081900006983104e32),</div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  K(4.9857172763962740855781912335959709090990833630483482545791462951647915758552039690361109105750366582497609235282417166004295666e32),</div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  K(-1.4964974779697884725668300877703598873484331649647945507167852672912478283006052834187237212505395652815341504129608210970635177e33),</div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  K(2.1318910685882714113074231521717786024327977165170135019860427349218908241618243742167588675566067235117191319364522120898974407e33),</div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  };</div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="keyword">static</span> <span class="keyword">const</span> R Q2[] =</div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  {</div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  K(1.0),</div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  };</div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="preprocessor"> #elif LDBL_MANT_DIG == 64</span></div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="comment">/* long double 96 bit wide */</span></div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keyword">static</span> <span class="keyword">const</span> R P1[] =</div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  {</div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  K(1.00696388290874250231638626673686646317801154370159972703168538),</div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  K(0.243352848727738955738908687369450214577920342918851509272408866),</div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  K(0.006964401160721188186398281247079919082283450941469460164590432),</div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  K(0.000083047334117897959145500056901191736030823531931380263686302),</div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  K(5.18256420384764810882467760619532575731801821889985626099e-7),</div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  K(1.90790611016475818883461118145629029943434891680660527e-9),</div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  K(4.44170587990105074420754325358582895345307949815573e-12),</div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  K(6.805150196466153819995090798791966304827558189423e-15),</div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  K(6.985104315031938858779570788468047860794936128e-18),</div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  K(4.785507068734939741097928056648844894386614e-21),</div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  K(2.117077490896605677726199140622837572025e-24),</div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  K(5.52919580174986488729896702518475621e-28),</div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  K(6.5666588969169003434516942087381e-32),</div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  };</div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="keyword">static</span> <span class="keyword">const</span> R Q1[] =</div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  {</div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  K(1.000011863675914860400478598182318948452642744176732473923183795358),</div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  K(-0.006896324225185339751945118908659032102601115341265224641280055928),</div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  K(0.00001186368725103095674191039208189536570056102297912907572890034),</div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  K(-1.3496696876875206170114218872940978330152830864048922600366e-8),</div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  K(1.1336174449932022007831556161183407392648142591512923821e-11),</div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  K(-7.422841655569707018644701823047396523966712871897812e-15),</div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  K(3.893669273036094904159100761627937282479044304922e-18),</div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  K(-1.651720545895290413869725701665259282787265642e-21),</div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  K(5.6323805635535562808481781647661895955232e-25),</div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  K(-1.50728066570923164846664348266414336373e-28),</div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  K(3.006044492319661074666639642233229e-32),</div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  K(-4.010148023149017379419706572721e-36),</div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  K(2.70282874465984817539266054e-40),</div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  };</div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="keyword">static</span> <span class="keyword">const</span> R P2[] =</div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  {</div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  K( 1.30090423521760256476093919023146864017751590623897710895862681),</div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  K(-1.981041925270972574120174940817336830170017871902975653312750388),</div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  K( 0.956892580228917795561363651877698243164566364537052353014543669),</div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  K(-0.295476285312266394050596510402082979039773201845265239542019439),</div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  K( 0.056978837924988815165935230495950981635872574537538384147033652),</div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  K(-0.006299149197554616295736173514236214970859775932020376086036399),</div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  K( 0.000353716966863384475462973243411450895641022763240331882363443),</div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  K(-8.707624424632528381900923003415938761710942641810978203625e-6),</div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  K( 7.283705999222063845686558855093093825421931939071318202e-8),</div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  K(-9.7967727386492889920273780071218382357131320542055799e-11)</div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  };</div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keyword">static</span> <span class="keyword">const</span> R Q2[] =</div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  {</div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  K( 3.257608431020108786259398271424889402309379351594793640349460063),</div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  K(-4.96363276525502538609792324882976732173260916421950408693842731),</div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  K( 2.400495835659089927333294199555080092801133193497330702140754591),</div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  K(-0.742868968166381852162379299256973953894545292197384361382965225),</div><div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  K( 0.143801810439830068463911726822151703498931831272162081681231077),</div><div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  K(-0.016019224718850575023820322478614758671031103220377245057110662),</div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  K( 0.000914623505897601721718970098041677534130323750396506936364887),</div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  K(-0.000023411644633126949191317085153966622167096685843127825287574),</div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  K( 2.17705048674331703171406080664526952334380771487046428339e-7),</div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  K(-4.47580289731041130181939560179689655281441839562189718e-10)</div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  };</div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="preprocessor"> #else</span></div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="preprocessor"> #error Unsupported size of long double</span></div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="preprocessor"> #endif</span></div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span> <span class="preprocessor">#elif defined(NFFT_SINGLE)</span></div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <span class="comment">/* float */</span></div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <span class="keyword">static</span> <span class="keyword">const</span> R P1[] =</div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  {</div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  K(1.006634511033311726164163027592274220828216885723379609007274761),</div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  K(0.240606487720090757394176928596156553834296465200311569457994763),</div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  K(0.006634921274522227156198202198389031672287220144321235665461021),</div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  K(0.000073749622820821337100502174723273851941734199062726870961819),</div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  K(4.10243517822171814488230564074819973544765129449450710122e-7),</div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  K(1.262110026222369902633819303536802438120823461060572684e-9),</div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  K(2.218532296437410634454463125960648541194468552527652e-12),</div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  K(2.141504045536019682125761418851096299425878119158e-15),</div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  K(9.19584570350722374435337612379408707845677156e-19),</div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  };</div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="keyword">static</span> <span class="keyword">const</span> R Q1[] =</div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  {</div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  K(1.000022624782705275228334312456728477812835742762369533496905023937),</div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  K(-0.009614857078745003693609489751018087358244444264456521971379273084),</div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  K(0.000022624818652773047747424411495054891627754515915461183178099877),</div><div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  K(-3.4080521639954323706277061786236961377055349443081338572762e-8),</div><div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  K(3.5947512112800645225066705862453058797853924958888263259e-11),</div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  K(-2.7149805873212658218594464017972758572144265290831215e-14),</div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  K(1.4293388301569282795540255590126107486209476445158e-17),</div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  K(-4.771887851505849942903948600229238419570937509e-21),</div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  K(7.68298982666756594543081799488936861257839e-25),</div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  };</div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="keyword">static</span> <span class="keyword">const</span> R P2[] =</div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  {</div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  K( 0.400758393969643840397216812932361963736749407866811083462461),</div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  K(-0.0312216150704950438088565774064329777860642477326179964345542),</div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  K( 0.0001215451718646727844117193541329442989170354233955281424116)</div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  };</div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <span class="keyword">static</span> <span class="keyword">const</span> R Q2[] =</div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  {</div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  K( 1.00043733569136882353241680221279480297575523819814430369272934),</div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  K(-0.0822433017391967535749382764476705160129315137731445852657631),</div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  K( 0.00043733569136882353241680221279480297575523819814430369272934)</div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  };</div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span> <span class="preprocessor">#else</span></div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="comment">/* double */</span></div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="keyword">static</span> <span class="keyword">const</span> R P1[] =</div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  {</div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  K(1.006897990143384859657820271920512961153421109156614230747188622),</div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  K(0.242805341483041870658834102275462978674549112393424086979586278),</div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  K(0.006898486035482686938510112687043665965094733332210445239567379),</div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  K(0.000081165067173822070066416843139523709162208390998449005642346),</div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  K(4.95896034564955471201271060753697747487292805350402943964e-7),</div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  K(1.769262324717844587819564151110983803173733141412266849e-9),</div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  K(3.936742942676484111899247866083681245613312522754135e-12),</div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  K(5.65030097981781148787580946077568408874044779529e-15),</div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  K(5.267856044117588097078633338366456262960465052e-18),</div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  K(3.111192981528832405775039015470693622536939e-21),</div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  K(1.071238669051606108411504195862449904664e-24),</div><div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  K(1.66685455020362122704904175079692613e-28),</div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  };</div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <span class="keyword">static</span> <span class="keyword">const</span> R Q1[] =</div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  {</div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  K(1.000013770640886533569435896302721489503868900260448440877422679934),</div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  K(-0.007438195256024963574139196893944950727405523418354136393367554385),</div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  K(0.000013770655915064256304772604385297068669909609091264440116789601),</div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  K(-1.6794623118559896441239590667288215019925076196457659206142e-8),</div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  K(1.50285363491992136130760477001818578470292828225498818e-11),</div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  K(-1.0383232801211938342796582949062551517465351830706356e-14),</div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  K(5.66233115275307483428203764087829782195312564006e-18),</div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  K(-2.44062252162491829675666639093292109472275754e-21),</div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  K(8.15441695513966815222186223740016719597617e-25),</div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  K(-2.01117218503954384746303760121365911698e-28),</div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  K(3.2919820158429806312377323449729691e-32),</div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  K(-2.70343047912331415988664032397e-36),</div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  };</div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  <span class="keyword">static</span> <span class="keyword">const</span> R P2[] =</div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  {</div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  K( 0.4305671332839579065931339658100499864903788418438938270811),</div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  K(-0.2897224581554843285637983312103876003389911968369470222427),</div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  K( 0.0299419330186508349765969995362253891383950029259740306077),</div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  K(-0.0010756807437990349677633120240742396555192749710627626584),</div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  K( 0.0000116485185631252780743187413946316104574410146692335443),</div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  K(-1.89995137955806752293614125586568854200245376235433e-08)</div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  };</div><div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  <span class="keyword">static</span> <span class="keyword">const</span> R Q2[] =</div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  {</div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  K(1.0762291019783101702628805159947862543863829764738274558421),</div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  K(-0.7279167074883770739509279847502106137135422309409220238564),</div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  K(0.0762629142282649564822465976300194596092279190843683614797),</div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  K(-0.0028345107938479082322784040228834113914746923069059932628),</div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  K(0.0000338122499547862193660816352332052228449426105409056376),</div><div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  K(-8.28850093512263912295888947693700479250899073022595e-08)</div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  };</div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span> </div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span> <span class="keyword">static</span> <span class="keyword">const</span> INT N1 = <span class="keyword">sizeof</span>(P1)/<span class="keyword">sizeof</span>(P1[0]);</div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span> <span class="keyword">static</span> <span class="keyword">const</span> INT M1 = <span class="keyword">sizeof</span>(Q1)/<span class="keyword">sizeof</span>(Q1[0]);</div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span> <span class="keyword">static</span> <span class="keyword">const</span> INT N2 = <span class="keyword">sizeof</span>(P2)/<span class="keyword">sizeof</span>(P2[0]);</div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span> <span class="keyword">static</span> <span class="keyword">const</span> INT M2 = <span class="keyword">sizeof</span>(Q2)/<span class="keyword">sizeof</span>(Q2[0]);</div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span> </div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span> <span class="keyword">static</span> <span class="keyword">inline</span> R evaluate_chebyshev(<span class="keyword">const</span> INT n, <span class="keyword">const</span> R *c, <span class="keyword">const</span> R x)</div><div class="line"><a name="l00270"></a><span class="lineno"> 270</span> {</div><div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  R a = c[n-2], b = c[n-1], t;</div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  INT j;</div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  </div><div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  A(n >= 2);</div><div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  </div><div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  <span class="keywordflow">for</span> (j = n - 2; j > 0; j--)</div><div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  {</div><div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  t = c[j-1] - b;</div><div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  b = a + K(2.0) * x * b;</div><div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  a = t;</div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  }</div><div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="keywordflow">return</span> a + x * b;</div><div class="line"><a name="l00283"></a><span class="lineno"> 283</span> }</div><div class="line"><a name="l00284"></a><span class="lineno"> 284</span> </div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span> <span class="keyword">static</span> <span class="keyword">inline</span> R evaluate_polynomial(<span class="keyword">const</span> INT n, <span class="keyword">const</span> R *c, <span class="keyword">const</span> R x)</div><div class="line"><a name="l00286"></a><span class="lineno"> 286</span> {</div><div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  R r = c[n-1];</div><div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  INT j;</div><div class="line"><a name="l00289"></a><span class="lineno"> 289</span> </div><div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  A(n >= 2);</div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span> </div><div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  <span class="keywordflow">for</span> (j = n - 2; j >= 0; j--)</div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  {</div><div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  r = r * x + c[j];</div><div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  }</div><div class="line"><a name="l00296"></a><span class="lineno"> 296</span> </div><div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <span class="keywordflow">return</span> r;</div><div class="line"><a name="l00298"></a><span class="lineno"> 298</span> }</div><div class="line"><a name="l00299"></a><span class="lineno"> 299</span> </div><div class="line"><a name="l00300"></a><span class="lineno"> 300</span> R Y(bessel_i0)(R x)</div><div class="line"><a name="l00301"></a><span class="lineno"> 301</span> {</div><div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <span class="keywordflow">if</span> (x < 0)</div><div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  {</div><div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="comment">/* even function */</span></div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  x = -x;</div><div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  }</div><div class="line"><a name="l00307"></a><span class="lineno"> 307</span> </div><div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  <span class="keywordflow">if</span> (x == K(0.0))</div><div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  <span class="keywordflow">return</span> K(1.0);</div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span> </div><div class="line"><a name="l00311"></a><span class="lineno"> 311</span> <span class="preprocessor">#if defined(NFFT_LDOUBLE) && LDBL_MANT_DIG > 64</span></div><div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="keywordflow">if</span> (x <= K(25.0))</div><div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  {</div><div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  R y = (x / K(2.0));</div><div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  y = y * y;</div><div class="line"><a name="l00316"></a><span class="lineno"> 316</span> </div><div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <span class="keywordflow">return</span> (K(1.0) + y * evaluate_polynomial(N1, P1, y));</div><div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  }</div><div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  {</div><div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <span class="keywordflow">return</span> (EXP(x) / SQRT(x)) * evaluate_polynomial(N2, P2, 1 / x);</div><div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  }</div><div class="line"><a name="l00323"></a><span class="lineno"> 323</span> <span class="preprocessor">#else</span></div><div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  <span class="keywordflow">if</span> (x <= K(15.0))</div><div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  {</div><div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  <span class="comment">/* x in (0, 15] */</span></div><div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  <span class="keyword">const</span> R y = x * x;</div><div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  <span class="keywordflow">return</span> evaluate_chebyshev(N1, P1, y) / evaluate_chebyshev(M1, Q1, y);</div><div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  }</div><div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  {</div><div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  <span class="comment">/* x in (15, \infty) */</span></div><div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  <span class="keyword">const</span> R y = (K(30.0) - x) / x;</div><div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <span class="keywordflow">return</span> (EXP(x) / SQRT(x)) * (evaluate_chebyshev(N2, P2, y) /</div><div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  evaluate_chebyshev(M2, Q2, y));</div><div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  }</div><div class="line"><a name="l00337"></a><span class="lineno"> 337</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00338"></a><span class="lineno"> 338</span> }</div></div><!-- fragment --></div><!-- contents -->
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