_TBL_sin.c revision 25c28e83beb90e7c80452a7c818c5e6f73a07dc8
/*
* 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
* 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 2005 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
#include "libm_protos.h"
/*
* Table of constants for x[i],sin(x[i]),cos(x[i]), where
* x[i] ~ (i+10.5)/64 chosen to make the value of sine and
* cosine nearly representable in double (with error less
* than 2**-8 ulp)
* By K.C. Ng, May 5, 1995
*
* For each i, _TBL_sincosx[i] := x[i], _TBL_sincos[2*i] :=
* sin(x[i]), and _TBL_sincos[2*i+1] := cos(x[i]).
*/
const double _TBL_sincos[] = {
1.63327491736778435127e-01, 9.86571908399470176576e-01,
1.78722113534634630128e-01, 9.83899591489758251761e-01,
1.94073102892906523831e-01, 9.80987069605669836925e-01,
2.09376712086097482857e-01, 9.77835053797937558961e-01,
2.24629204957583178404e-01, 9.74444313586017130113e-01,
2.39826857830661321902e-01, 9.70815676770349522684e-01,
2.54965960415442560727e-01, 9.66950029230792762469e-01,
2.70042816718758793559e-01, 9.62848314709330965755e-01,
2.85053745940880454146e-01, 9.58511534581129587274e-01,
2.99995083378835347698e-01, 9.53940747608846839611e-01,
3.14863181320744367486e-01, 9.49137069684131584602e-01,
3.29654409930721814526e-01, 9.44101673557052656349e-01,
3.44365158144533722862e-01, 9.38835788546692695533e-01,
3.58991834544317267586e-01, 9.33340700243220688925e-01,
3.73530868238515501023e-01, 9.27617750192923362640e-01,
3.87978709726743087316e-01, 9.21668335573470609567e-01,
4.02331831777567594521e-01, 9.15493908848391546584e-01,
4.16586730281922223984e-01, 9.09095977415485534401e-01,
4.30739925110786514573e-01, 9.02476103237949467406e-01,
4.44787960958008266044e-01, 8.95635902466408118094e-01,
4.58727408216676513231e-01, 8.88577045028066558885e-01,
4.72554863751536879946e-01, 8.81301254251215970825e-01,
4.86266951795427115890e-01, 8.73810306411857196096e-01,
4.99860324731856597857e-01, 8.66106030321324382726e-01,
5.13331663943585647658e-01, 8.58190306862591900661e-01,
5.26677680590333596733e-01, 8.50065068549453184410e-01,
5.39895116435048061376e-01, 8.41732299041438647436e-01,
5.52980744632255882820e-01, 8.33194032663434169805e-01,
5.65931370507619768695e-01, 8.24452353914625679643e-01,
5.78743832357296650315e-01, 8.15509396946711651033e-01,
5.91415002201596706755e-01, 8.06367345054898265744e-01,
6.03941786558566895415e-01, 7.97028430138126520177e-01,
6.16321127179607297641e-01, 7.87494932169127248578e-01,
6.28550001844884853597e-01, 7.77769178600434929471e-01,
6.40625425044079821468e-01, 7.67853543839638774671e-01,
6.52544448725672743272e-01, 7.57750448655299613243e-01,
6.64304163044103668234e-01, 7.47462359562187539375e-01,
6.75901697026429104653e-01, 7.36991788256011193248e-01,
6.87334219302880855551e-01, 7.26341290975047959577e-01,
6.98598938789923074033e-01, 7.15513467882745946014e-01,
7.09693105361432152733e-01, 7.04510962443060329008e-01,
7.20614010544995853280e-01, 6.93336460750663685637e-01,
7.31358988151144640000e-01, 6.81992690906972898190e-01,
7.41925414945620254059e-01, 6.70482422333180339002e-01,
7.52310711296420575600e-01, 6.58808465085774175307e-01,
7.62512341773335489137e-01, 6.46973669204044199432e-01,
7.72527815799416095466e-01, 6.34980923978180178402e-01,
7.82354688238184881044e-01, 6.22833157267443926486e-01,
7.91990560000511156780e-01, 6.10533334773848967991e-01,
8.01433078627164507957e-01, 5.98084459321745920413e-01,
8.10679938859144910701e-01, 5.85489570130274028514e-01,
8.19728883213368231253e-01, 5.72751742053888568407e-01,
8.28577702516849257108e-01, 5.59874084854710574177e-01,
8.37224236455711978699e-01, 5.46859742430497508536e-01,
8.45666374107491569667e-01, 5.33711892039036461810e-01,
8.53902054441761149128e-01, 5.20433743544881588505e-01,
8.61929266833302509809e-01, 5.07028538621057900393e-01,
8.69746051561515076678e-01, 4.93499549942200410602e-01,
8.77350500260862697921e-01, 4.79850080433476600117e-01,
8.84740756420631879742e-01, 4.66083462405874393575e-01,
8.91915015812867362222e-01, 4.52203056787028545571e-01,
8.98871526946913745881e-01, 4.38212252275223035358e-01,
9.05608591487805036913e-01, 4.24114464529888268718e-01,
9.12124564678846838639e-01, 4.09913135321892496687e-01,
9.18417855741508804002e-01, 3.95611731695571844369e-01,
9.24486928255549345046e-01, 3.81213745141251114656e-01,
9.30330300545781363475e-01, 3.66722690716563270996e-01,
9.35946546034209125864e-01, 3.52142106210879102246e-01,
9.41334293596668869597e-01, 3.37475551260917883134e-01,
9.46492227896101323559e-01, 3.22726606483374089951e-01,
9.51419089686698082886e-01, 3.07898872650964328113e-01,
9.56113676155394554002e-01, 2.92995969713948978264e-01,
9.60574841181938254842e-01, 2.78021536015277237475e-01,
9.64801495637480077683e-01, 2.62979227346346711158e-01,
9.68792607644664016675e-01, 2.47872716072285947941e-01,
9.72547202831614887586e-01, 2.32705690227810568782e-01,
9.76064364566613607010e-01, 2.17481852629530458820e-01,
9.79343234187565414572e-01, 2.02204919947659544910e-01,
9.82383011202836109454e-01, 1.86878621837941599759e-01,
9.85182953494231017366e-01, 1.71506699998524386741e-01,
9.87742377497998091940e-01, 1.56092907252707135957e-01,
9.90060658366647028394e-01, 1.40641006660935985462e-01,
9.92137230124395808062e-01, 1.25154770588626285122e-01,
9.93971585806359803072e-01, 1.09637979777038541140e-01,
9.95563277581850036846e-01, 9.40944224196323536491e-02,
9.96911916861350277941e-01, 7.85278932598362233719e-02,
9.98017174394052908326e-01, 6.29421926414276133865e-02,
9.98878780347215333713e-01, 4.73411255892753485286e-02,
9.99496524372108563483e-01, 3.17285008797294557081e-02,
9.99870255655346151791e-01, 1.61081301122361006395e-02,
9.99999882955821872699e-01, 4.83826769160181427432e-04,
9.99885374626887313276e-01, -1.51405946795101862407e-02,
9.99526758624139421983e-01, -3.07613197753498594789e-02,
9.98924122498464628350e-01, -4.63745349375326090802e-02,
9.98077613374894423437e-01, -6.19764284214149308028e-02,
9.96987437916807328619e-01, -7.75631912448182664344e-02,
9.95653862273598311283e-01, -9.31310181393209396417e-02,
9.94077212020575529117e-01, -1.08676108420387079745e-01,
9.92257872072439317535e-01, -1.24194666996109981394e-01,
9.90196286596708996619e-01, -1.39682905217811598186e-01,
9.87892958898728967831e-01, -1.55137041864005509328e-01,
9.85348451302295424981e-01, -1.70553304031812708041e-01,
9.82563385014030843401e-01, -1.85927928052160545969e-01,
9.79538439968065888230e-01, -2.01257160431443482551e-01,
9.76274354660002341433e-01, -2.16537258764389006771e-01,
9.72771925969731610095e-01, -2.31764492632368090952e-01,
9.69032008956924317822e-01, -2.46935144556029828600e-01,
9.65055516693764658953e-01, -2.62045510739892129060e-01,
9.60843419958733790942e-01, -2.77091902303196746526e-01,
9.56396747083171572257e-01, -2.92070645852553878452e-01,
9.51716583658057113659e-01, -3.06978084543891138747e-01,
9.46804072278775166183e-01, -3.21810578937871294425e-01,
9.41660412264228252610e-01, -3.36564507894643705210e-01,
9.36286859366077139910e-01, -3.51236269451786098372e-01,
9.30684725460523609719e-01, -3.65822281708577445869e-01,
9.24855378224429758305e-01, -3.80318983708869018390e-01,
9.18800240811794344253e-01, -3.94722836284130795814e-01,
9.12520791499566663596e-01, -4.09030322935848345001e-01,
9.06018563323250702979e-01, -4.23237950701107090712e-01,
8.99295143708603639254e-01, -4.37342250991282488481e-01,
8.92352174084417359978e-01, -4.51339780439098559039e-01,
8.85191349474114597129e-01, -4.65227121754735961634e-01,
8.77814418087698666859e-01, -4.79000884547570504601e-01,
8.70223180902864101860e-01, -4.92657706140177065190e-01,
8.62419491209962973954e-01, -5.06194252418129098103e-01,
8.54405254167239447405e-01, -5.19607218629047684644e-01,
8.46182426332270809510e-01, -5.32893330195106762481e-01,
8.37753015193838712626e-01, -5.46049343497116423940e-01,
8.29119078677651999421e-01, -5.59072046674417011403e-01,
8.20282724626069215113e-01, -5.71958260435175724901e-01,
8.11246110312714763246e-01, -5.84704838788333125521e-01,
8.02011441899084687179e-01, -5.97308669837422590021e-01,
7.92580973890125495274e-01, -6.09766676547169317324e-01,
7.82957008603788473522e-01, -6.22075817467780289860e-01,
7.73141895594474215514e-01, -6.34233087497477643346e-01,
7.63138031079152456826e-01, -6.46235518615801973752e-01,
7.52947857359473227135e-01, -6.58080180599429964694e-01,
7.42573862219235825144e-01, -6.69764181745192588302e-01,
7.32018578314804879703e-01, -6.81284669577975954269e-01,
7.21284582577006005977e-01, -6.92638831525286491342e-01,
7.10374495555637031075e-01, -7.03823895633044149811e-01,
6.99290980797484418297e-01, -7.14837131223114541356e-01,
6.88036744157449198234e-01, -7.25675849597612554476e-01,
6.76614533221899572268e-01, -7.36337404613476742554e-01,
6.65027136549188546688e-01, -7.46819193415104276568e-01,
6.53277383052505156158e-01, -7.57118657009633100330e-01,
6.41368141233487065733e-01, -7.67233280958732777322e-01,
6.29302318589868403542e-01, -7.77160595898567008177e-01,
6.17082860810903133242e-01, -7.86898178224750721732e-01,
6.04712751105658807838e-01, -7.96443650643424705393e-01,
5.92195009450509846083e-01, -8.05794682770934245220e-01,
5.79532691867931770702e-01, -8.14948991689853463605e-01,
5.66728889706594629594e-01, -8.23904342488817387213e-01,
5.53786728799491090314e-01, -8.32658548869558479133e-01,
5.40709368819720759269e-01, -8.41209473597735457595e-01,
5.27500002380493770993e-01, -8.49555029111463189118e-01,
5.14161854409658891640e-01, -8.57693177931374672873e-01,
5.00698181184736190730e-01, -8.65621933270118271153e-01,
4.87112269682015319727e-01, -8.73339359427499739574e-01,
4.73407436683839610847e-01, -8.80843572317148937323e-01,
4.59587028080454429446e-01, -8.88132739865035936155e-01,
4.45654417892204612883e-01, -8.95205082544307417791e-01,
4.31613007576607476956e-01, -9.02058873738668665077e-01,
4.17466225094956511210e-01, -9.08692440215591923369e-01,
4.03217524247773739798e-01, -9.15104162453376668296e-01,
3.88870383625079307777e-01, -9.21292475134407928827e-01,
3.74428305866518040812e-01, -9.27255867474522488259e-01,
3.59894816812003803808e-01, -9.32992883591217014860e-01,
3.45273464602750546071e-01, -9.38502122875176647554e-01,
3.30567818825136694461e-01, -9.43782240327286303661e-01,
3.15781469657649860316e-01, -9.48831946880402399280e-01,
3.00918026974915431282e-01, -9.53650009721346392233e-01,
2.85981119468962208252e-01, -9.58235252590552089025e-01,
2.70974393771316324209e-01, -9.62586556066657106356e-01,
2.55901513568614069616e-01, -9.66702857838587559236e-01,
2.40766158683884484715e-01, -9.70583152971761897732e-01,
2.25572024178931879179e-01, -9.74226494152062860721e-01,
2.10322819513115238932e-01, -9.77631991902911057224e-01,
1.95022267545207572681e-01, -9.80798814824694553671e-01,
1.79674103687683967001e-01, -9.83726189782516358129e-01,
1.64282074965636487596e-01, -9.86413402101261493904e-01,
1.48849939140241666058e-01, -9.88859795733422641817e-01,
1.33381463740289751829e-01, -9.91064773428305123559e-01,
1.17880425165185737102e-01, -9.93027796873216961338e-01,
1.02350607771443738447e-01, -9.94748386823932517764e-01,
8.67958029390951818494e-02, -9.96226123223115322958e-01,
7.12198081674702832000e-02, -9.97460645301151083153e-01,
5.56264261071372570489e-02, -9.98451651667994988237e-01,
4.00194636390110436430e-02, -9.99198900384726140800e-01,
2.44027309972172715136e-02, -9.99702209020204901613e-01,
8.78004077991816241078e-03, -9.99961454699081375708e-01,
-6.84479296391702837776e-03, -9.99976574130254869388e-01,
-2.24679556394218951643e-02, -9.99747563622630175395e-01,
-3.80856331006515710924e-02, -9.99274479085362488107e-01,
-5.36940124898220294547e-02, -9.98557436015947375019e-01,
-6.92892832575160572128e-02, -9.97596609469809547655e-01,
-8.48676380386628043118e-02, -9.96392234019183087312e-01,
-1.00425273601341916163e-01, -9.94944603695148255262e-01,
-1.15958391781735684067e-01, -9.93254071914831615508e-01,
-1.31463200384306394541e-01, -9.91321051397939245753e-01,
-1.46935914119801724897e-01, -9.89146014065556578032e-01,
-1.62372755568482129984e-01, -9.86729490918913376696e-01,
-1.77769956039573850948e-01, -9.84072071918356994225e-01,
-1.93123756521520834051e-01, -9.81174405835688490107e-01,
-2.08430408606563005725e-01, -9.78037200094199477007e-01,
-2.23686175400125447643e-01, -9.74661220596605204491e-01,
-2.38887332428331961021e-01, -9.71047291539024692852e-01,
-2.54030168529570332669e-01, -9.67196295214595047618e-01,
-2.69110986809851404633e-01, -9.63109171785954898404e-01,
-2.84126105504238113397e-01, -9.58786919065437892584e-01,
-2.99071858881536201125e-01, -9.54230592270622235418e-01,
-3.13944598143160502612e-01, -9.49441303765919730751e-01,
-3.28740692363219233485e-01, -9.44420222774031481450e-01,
-3.43456529243486463621e-01, -9.39168575134420757777e-01,
-3.58088516132365641820e-01, -9.33687642958886176991e-01,
-3.72633080853157161449e-01, -9.27978764333475703019e-01,
-3.87086672547184373894e-01, -9.22043333003578990947e-01,
-4.01445762590873223008e-01, -9.15882798013933796533e-01,
-4.15706845395529489551e-01, -9.09498663380709615467e-01,
-4.29866439353555507275e-01, -9.02892487684716527063e-01,
-4.43921087571260808424e-01, -8.96065883743795366101e-01,
-4.57867358817895864220e-01, -8.89020518171051099543e-01,
-4.71701848327647499381e-01, -8.81758110982984399939e-01,
-4.85421178579811707365e-01, -8.74280435207254624785e-01,
-4.99022000232008211551e-01, -8.66589316391822128693e-01,
-5.12500992809901023683e-01, -8.58686632229048840692e-01,
-5.25854865641323332426e-01, -8.50574312027670975667e-01,
-5.39080358520030999969e-01, -8.42254336324791408330e-01,
-5.52174242663304060130e-01, -8.33728736304085060738e-01,
-5.65133321393192722404e-01, -8.24999593364201810886e-01,
-5.77954430931352902689e-01, -8.16069038603239760299e-01,
-5.90634441175508673183e-01, -8.06939252296785092256e-01,
-6.03170256463835929850e-01, -7.97612463366358381833e-01,
-6.15558816459891189332e-01, -7.88090948735295393490e-01,
-6.27797096543907584554e-01, -7.78377033044423516372e-01,
-6.39882108993420795073e-01, -7.68473087746169514212e-01,
-6.51810903392718188343e-01, -7.58381530773507561705e-01,
-6.63580567511655061708e-01, -7.48104825823834529430e-01,
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9.99997073896832011641e-01, 2.41913161566219324719e-03,
9.99912803818512774257e-01, -1.32054821873487954892e-02,
9.99584419370001642235e-01, -2.88268720595330242562e-02,
9.99012000721555049054e-01, -4.44412242666163900817e-02,
9.98195687620527460915e-01, -6.00447267941353959864e-02,
9.97135679355775073063e-01, -7.56335702958476074897e-02,
9.95832234722008102779e-01, -9.12039488650100010902e-02,
9.94285671925894676271e-01, -1.06752061351864019345e-01,
9.92496368545773943737e-01, -1.22274111828511194977e-01,
9.90464761404806215417e-01, -1.37766310886661608182e-01
};
const double _TBL_sincosx[] = {
1.64062500000167837966e-01, 1.79687499999472477530e-01,
1.95312499999996669331e-01, 2.10937500000106192832e-01,
2.26562499999874683576e-01, 2.42187499999999750200e-01,
2.57812499999549193941e-01, 2.73437500000180466753e-01,
2.89062500000347444296e-01, 3.04687500000159650071e-01,
3.20312500001052657961e-01, 3.35937499999853450561e-01,
3.51562499998759436792e-01, 3.67187499998127386824e-01,
3.82812499999808708573e-01, 3.98437499999694078046e-01,
4.14062499999775512904e-01, 4.29687499999869215728e-01,
4.45312499999981514787e-01, 4.60937499992721433362e-01,
4.76562499999932387418e-01, 4.92187500000263733479e-01,
5.07812500002462252624e-01, 5.23437499998664290679e-01,
5.39062500000133337785e-01, 5.54687499999937494444e-01,
5.70312499999814259688e-01, 5.85937500002074562744e-01,
6.01562499999652833260e-01, 6.17187499999419131314e-01,
6.32812500000347721851e-01, 6.48437500005533351555e-01,
6.64062499997531863194e-01, 6.79687499999813815599e-01,
6.95312500005013212068e-01, 7.10937499999876987289e-01,
7.26562500001548428052e-01, 7.42187500000339617223e-01,
7.57812499998633315457e-01, 7.73437500000337285755e-01,
7.89062499996497468402e-01, 8.04687500000179967152e-01,
8.20312500001350475287e-01, 8.35937499996779354028e-01,
8.51562500000668243239e-01, 8.67187499999485522650e-01,
8.82812500000538014078e-01, 8.98437500000525690602e-01,
9.14062500000757727214e-01, 9.29687500002357114504e-01,
9.45312499999430455588e-01, 9.60937500000796696042e-01,
9.76562500001389000026e-01, 9.92187499998313238159e-01,
1.00781250000027000624e+00, 1.02343750000073119288e+00,
1.03906249999567279474e+00, 1.05468750000121480603e+00,
1.07031249999813948826e+00, 1.08593749999936250994e+00,
1.10156249999885291757e+00, 1.11718750000074029671e+00,
1.13281249999926680871e+00, 1.14843749999650057703e+00,
1.16406249999956079577e+00, 1.17968749999995736744e+00,
1.19531250000235189646e+00, 1.21093750000001554312e+00,
1.22656249999714606069e+00, 1.24218750000679789558e+00,
1.25781249999789324079e+00, 1.27343750000030864200e+00,
1.28906250000041366910e+00, 1.30468750000013344881e+00,
1.32031249999823008245e+00, 1.33593749999817146268e+00,
1.35156249999504352033e+00, 1.36718750000051336713e+00,
1.38281250000255573340e+00, 1.39843749999889488400e+00,
1.41406250000066702199e+00, 1.42968750000377853304e+00,
1.44531250000268074452e+00, 1.46093749999857935862e+00,
1.47656250000000177636e+00, 1.49218750000007549517e+00,
1.50781249999986965982e+00, 1.52343749999979238829e+00,
1.53906250000026356695e+00, 1.55468750000024247271e+00,
1.57031250000686006807e+00, 1.58593749999970379250e+00,
1.60156249999876076906e+00, 1.61718749999920530236e+00,
1.63281249999894950697e+00, 1.64843749999433342168e+00,
1.66406250000158717484e+00, 1.67968749999775224246e+00,
1.69531250000185917948e+00, 1.71093749999863442568e+00,
1.72656249999789279670e+00, 1.74218750000263478128e+00,
1.75781250000296740410e+00, 1.77343749999920641258e+00,
1.78906249999844191301e+00, 1.80468749999888578017e+00,
1.82031250003296385387e+00, 1.83593749999912847493e+00,
1.85156249999896371783e+00, 1.86718749999873900869e+00,
1.88281249999986122212e+00, 1.89843750000025601743e+00,
1.91406250000089750429e+00, 1.92968749999936717288e+00,
1.94531249999502553472e+00, 1.96093749999814637164e+00,
1.97656250000163713487e+00, 1.99218750000058819616e+00,
2.00781250000015099033e+00, 2.02343750000025890401e+00,
2.03906249999571986820e+00, 2.05468749999347455315e+00,
2.07031249999880184731e+00, 2.08593749999950617280e+00,
2.10156249999859534583e+00, 2.11718749999749178414e+00,
2.13281250000269562150e+00, 2.14843750000770983277e+00,
2.16406250000204325445e+00, 2.17968750000288169488e+00,
2.19531250000207567297e+00, 2.21093749999685940111e+00,
2.22656249999882449586e+00, 2.24218750000040500936e+00,
2.25781249999956967756e+00, 2.27343749999970867748e+00,
2.28906249999833111275e+00, 2.30468749999696020936e+00,
2.32031250000405675493e+00, 2.33593750000527755617e+00,
2.35156250000277511347e+00, 2.36718749998901101250e+00,
2.38281250000068833828e+00, 2.39843750000151390012e+00,
2.41406250000618571860e+00, 2.42968749999278221807e+00,
2.44531250000394617672e+00, 2.46093750000379341003e+00,
2.47656250000329514194e+00, 2.49218749999781508109e+00,
2.50781249999807354101e+00, 2.52343750000954214485e+00,
2.53906250000098099306e+00, 2.55468750001107025582e+00,
2.57031250000341415785e+00, 2.58593750002171240965e+00,
2.60156250000635891340e+00, 2.61718750000451771953e+00,
2.63281250000028421709e+00, 2.64843750001994493459e+00,
2.66406250000455235849e+00, 2.67968749999316235844e+00,
2.69531249997396704643e+00, 2.71093749999957500663e+00,
2.72656249999638511383e+00, 2.74218749999314947985e+00,
2.75781249999954258811e+00, 2.77343750000063726802e+00,
2.78906249999834177089e+00, 2.80468750000019895197e+00,
2.82031249999983835153e+00, 2.83593749999777511306e+00,
2.85156249999855315735e+00, 2.86718750000235678144e+00,
2.88281249999902611236e+00, 2.89843749999328359479e+00,
2.91406250000365130148e+00, 2.92968749999994892974e+00,
2.94531249999847322130e+00, 2.96093749999701350006e+00,
2.97656250000468292072e+00, 2.99218750000308997272e+00,
3.00781249999819877416e+00, 3.02343749999709299203e+00,
3.03906249999948618878e+00, 3.05468750000752597984e+00,
3.07031250000433075797e+00, 3.08593749999511279825e+00,
3.10156249999957589480e+00, 3.11718749999961186603e+00,
3.13281249999836441944e+00, 3.14843750000262057043e+00,
3.16406249999657873673e+00, 3.17968750000540190115e+00,
3.19531250000325739435e+00, 3.21093750000270583556e+00,
3.22656250000035882408e+00, 3.24218749999618305324e+00,
3.25781250000001199041e+00, 3.27343750000431255032e+00,
3.28906249999634914261e+00, 3.30468749999773381276e+00,
3.32031250000108801856e+00, 3.33593750000042854609e+00,
3.35156249999819699781e+00, 3.36718749999951061369e+00,
3.38281250000727817806e+00, 3.39843750000385558252e+00,
3.41406250000184297022e+00, 3.42968750000183808524e+00,
3.44531249999830135877e+00, 3.46093749998354383024e+00,
3.47656249999984101606e+00, 3.49218750000081934459e+00,
3.50781249999577759979e+00, 3.52343749999866640010e+00,
3.53906249999683852892e+00, 3.55468750000498978636e+00,
3.57031249999826005848e+00, 3.58593750001092637092e+00,
3.60156250000782085507e+00, 3.61718749999987299049e+00,
3.63281250000544186918e+00, 3.64843749999226352188e+00,
3.66406250000062438943e+00, 3.67968749999757616109e+00,
3.69531250001872235700e+00, 3.71093750000574784664e+00,
3.72656249999563016218e+00, 3.74218749999581179466e+00,
3.75781250000033528735e+00, 3.77343749999415045693e+00,
3.78906249995283994636e+00, 3.80468750000592104143e+00,
3.82031249998920063859e+00, 3.83593750000164934733e+00,
3.85156250000057731597e+00, 3.86718750000405053768e+00,
3.88281249997192157153e+00, 3.89843749998371702503e+00,
3.91406249999986277643e+00, 3.92968749999597033451e+00,
3.94531249999519229021e+00, 3.96093749997563104870e+00,
3.97656250000223510099e+00, 3.99218750000022870594e+00,
4.00781250004454392410e+00, 4.02343749999355093649e+00,
4.03906249999698196973e+00, 4.05468749999250022142e+00,
4.07031249994990851349e+00, 4.08593749999590372113e+00,
4.10156249999066258027e+00, 4.11718749999303490483e+00,
4.13281249999853184107e+00, 4.14843749998088373587e+00,
4.16406249999834177089e+00, 4.17968749999662758654e+00,
4.19531249999891109326e+00, 4.21093749999872102308e+00,
4.22656249999120881000e+00, 4.24218750000338129524e+00,
4.25781250000494537744e+00, 4.27343749997698019172e+00,
4.28906250000330668826e+00, 4.30468749999959232611e+00,
4.32031250000562039304e+00, 4.33593749999550670537e+00,
4.35156250000948219281e+00, 4.36718750000763922259e+00,
4.38281249999987476684e+00, 4.39843750000314237525e+00,
4.41406250000408473255e+00, 4.42968750000079314333e+00,
4.44531249998868371875e+00, 4.46093750000322319949e+00,
4.47656249999480770896e+00, 4.49218749997964028609e+00,
4.50781250000320810045e+00, 4.52343749999724753508e+00,
4.53906249999181721222e+00, 4.55468750000258193467e+00,
4.57031249999976196818e+00, 4.58593750000821920310e+00,
4.60156250004601385939e+00, 4.61718750000444977388e+00,
4.63281249999695177166e+00, 4.64843749999638600201e+00,
4.66406250000544897460e+00, 4.67968749999663469197e+00,
4.69531249998381028377e+00, 4.71093749999796340688e+00,
4.72656250000119992905e+00, 4.74218750001258992910e+00,
4.75781250000492050845e+00, 4.77343750000340971695e+00,
4.78906250000747402140e+00, 4.80468749998990762862e+00,
4.82031250001256594828e+00, 4.83593750000031530334e+00,
4.85156250000026023628e+00, 4.86718750000094679820e+00,
4.88281250000185362836e+00, 4.89843749997600141910e+00,
4.91406249999471889112e+00, 4.92968749998860822359e+00,
4.94531250000475353090e+00, 4.96093749999659205940e+00,
4.97656250000856825721e+00, 4.99218750002637179364e+00,
5.00781249999760014191e+00, 5.02343749998691091463e+00,
5.03906249999699618058e+00, 5.05468750000537525580e+00,
5.07031250000353406193e+00, 5.08593749999286881547e+00,
5.10156249998831601289e+00, 5.11718750000479172257e+00,
5.13281250001085087575e+00, 5.14843750000346744855e+00,
5.16406250000581845683e+00, 5.17968750000350119933e+00,
5.19531249999482636071e+00, 5.21093750000432454073e+00,
5.22656250000434585701e+00, 5.24218750001077093970e+00,
5.25781249998869881779e+00, 5.27343750002139977084e+00,
5.28906249999702104958e+00, 5.30468749998945909851e+00,
5.32031249999385913441e+00, 5.33593749999546851370e+00,
5.35156250001908162517e+00, 5.36718749999724487054e+00,
5.38281249999679634044e+00, 5.39843750001770139590e+00,
5.41406249999678212959e+00, 5.42968749999906563630e+00,
5.44531250000517097476e+00, 5.46093749999811794993e+00,
5.47656250001082511858e+00, 5.49218749999457500621e+00,
5.50781250001214406353e+00, 5.52343750001415045858e+00,
5.53906250000498356911e+00, 5.55468750000498889818e+00,
5.57031250000316013882e+00, 5.58593750000908428888e+00,
5.60156250002763478335e+00, 5.61718749999503863535e+00,
5.63281250000129496414e+00, 5.64843750001081890133e+00,
5.66406250000738609174e+00, 5.67968750000023270275e+00,
5.69531249998335997731e+00, 5.71093749999160404940e+00,
5.72656250000217958984e+00, 5.74218750000474997819e+00,
5.75781250000163868918e+00, 5.77343749999750688318e+00,
5.78906249999925304195e+00, 5.80468749999988631316e+00,
5.82031249999487254598e+00, 5.83593749999551025809e+00,
5.85156249999513455862e+00, 5.86718749999803179662e+00,
5.88281250000295141689e+00, 5.89843750000985433957e+00,
5.91406249999845634591e+00, 5.92968750000455990801e+00,
5.94531250000243982612e+00, 5.96093750000733901828e+00,
5.97656249999234212567e+00, 5.99218749999141753193e+00,
6.00781250000843591863e+00, 6.02343749999880984092e+00,
6.03906249999745359247e+00, 6.05468750000370548037e+00,
6.07031250001220445967e+00, 6.08593750001188915633e+00,
6.10156249999290700714e+00, 6.11718749998957456171e+00,
6.13281249999975663911e+00, 6.14843749999015098950e+00,
6.16406250000358646446e+00, 6.17968750000026467717e+00,
6.19531249998414246249e+00, 6.21093749998937294521e+00,
6.22656249999281197205e+00, 6.24218750000707967018e+00,
6.25781250000234834374e+00, 6.27343749999462829692e+00,
6.28906250001052136156e+00, 6.30468750000171862524e+00,
6.32031250000594013727e+00, 6.33593750000045385917e+00,
6.35156250000499689179e+00, 6.36718749999230215764e+00,
6.38281249999868105505e+00, 6.39843749999853628196e+00,
6.41406249999377564563e+00, 6.42968750000876010375e+00,
6.44531250002396838283e+00, 6.46093750000062527761e+00,
6.47656249999929212180e+00, 6.49218750000642064180e+00,
6.50781249999003996720e+00, 6.52343750000912248055e+00,
6.53906249998720845440e+00, 6.55468749999868371958e+00,
6.57031249998638067211e+00, 6.58593750000546407364e+00,
6.60156249994729282804e+00, 6.61718749997319211076e+00,
6.63281249997879296387e+00, 6.64843749999244426618e+00,
6.66406249999900524017e+00, 6.67968749999884092716e+00,
6.69531249999227373593e+00, 6.71093749999063504674e+00,
6.72656249999940136775e+00, 6.74218749999563193853e+00,
6.75781249999463895506e+00, 6.77343750001427569174e+00,
6.78906249999704858311e+00, 6.80468750000215738538e+00,
6.82031250000341859874e+00, 6.83593749999844302323e+00,
6.85156250001598987609e+00, 6.86718750000203925765e+00,
6.88281250000989430760e+00, 6.89843750000604671868e+00,
6.91406249999750777135e+00, 6.92968749999960120789e+00,
6.94531249995244071016e+00, 6.96093750002739852789e+00,
6.97656249999430233544e+00, 6.99218749999911892701e+00,
7.00781250000804245559e+00, 7.02343750000080380147e+00,
7.03906249999665778461e+00, 7.05468749999575539533e+00,
7.07031250001700328767e+00, 7.08593750000647215614e+00,
7.10156249997034372257e+00, 7.11718749999698641062e+00,
7.13281250000188915550e+00, 7.14843750000192734717e+00,
7.16406250000996358551e+00, 7.17968750005667022407e+00,
7.19531250000950883816e+00, 7.21093749995827248966e+00,
7.22656250000638511466e+00, 7.24218750002578115499e+00,
7.25781249999116351290e+00, 7.27343749999614619384e+00,
7.28906249998626343256e+00, 7.30468749998397015588e+00,
7.32031249998488320330e+00, 7.33593749999550048813e+00,
7.35156249998663557932e+00, 7.36718750000183675297e+00,
7.38281249999652722238e+00, 7.39843750007829115134e+00,
7.41406250000048494542e+00, 7.42968750000089794838e+00,
7.44531249999165467557e+00, 7.46093749999333422096e+00,
7.47656250000219557705e+00, 7.49218750000104360964e+00,
7.50781249999853983468e+00, 7.52343749999573585541e+00,
7.53906249999752819946e+00, 7.55468749999868549594e+00,
7.57031250024692781153e+00, 7.58593750000690736357e+00,
7.60156249999365662973e+00, 7.61718749999451283372e+00,
7.63281249995806998498e+00, 7.64843749997276400876e+00,
7.66406249998022381931e+00, 7.67968750000013145041e+00,
7.69531249999808597551e+00, 7.71093750001158539931e+00,
7.72656249999979038989e+00, 7.74218750000620037355e+00,
7.75781249999318234245e+00, 7.77343750001715427800e+00,
7.78906250000142730272e+00, 7.80468749997501465288e+00,
7.82031249999300381859e+00, 7.83593750003314948316e+00,
7.85156249999927524641e+00, 7.86718749999776001403e+00,
7.88281249999449951105e+00, 7.89843749999351540936e+00,
7.91406250000050803806e+00, 7.92968750004068656523e+00,
7.94531249999952127183e+00, 7.96093750001230571200e+00,
7.97656249999947331020e+00, 7.99218750003934363946e+00
};