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lammps/src/math_inline.h
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math_inline.h
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#ifndef LMP_MATH_INLINE
#define LMP_MATH_INLINE
#include <stdint.h>
#include <math.h>
namespace LAMMPS_NS {
namespace MathInline {
// set to 0 for using pade approximation
#define FM_USE_SPLINE_TABLE 1
// IEEE 754 double precision floating point data manipulation
typedef union
{
double f;
uint64_t u;
struct {int32_t i0,i1;} s;
} udi_t;
#define FM_DOUBLE_BIAS 1023
#define FM_DOUBLE_EMASK 2146435072
#define FM_DOUBLE_MBITS 20
#define FM_DOUBLE_MMASK 1048575
#define FM_DOUBLE_EZERO 1072693248
// generate 2**num in floating point by bitshifting
#define FM_DOUBLE_INIT_EXP(var,num) \
var.i0 = 0; \
var.i1 = (((int) num) + FM_DOUBLE_BIAS) << 20
// double precision constants
#define FM_DOUBLE_LOGEOF2 6.9314718055994530942e-1
#define FM_DOUBLE_SQRT2 1.41421356237309504880
#if FM_USE_SPLINE_TABLE
/* optimizer friendly implementation of log2(x).
*
* strategy:
*
* split the argument into a product, 2**ipart * fpart
* by using bitmasks and integer math and then approximate
* log_2(fpart) from a spline table of log(x) in [1.0:2.0[
*/
#define FM_SPLINE_SHIFT 8
static const double fm_log_dinv = 4.09600000000000000000e+03;
static const double fm_log_dsq6 = 9.93410746256510361521e-09;
static const double fm_log_q1[] = {
0.00000000000000000000e+00, 2.44110827527362707389e-04,
4.88162079501351187181e-04, 7.32153784993847520958e-04,
9.76085973055458924752e-04, 1.21995867271553880967e-03,
1.46377191298220740885e-03, 1.70752572284237243150e-03,
1.95122013126174933748e-03, 2.19485516718488302135e-03,
2.43843085953516754485e-03, 2.68194723721486717044e-03,
2.92540432910513587689e-03, 3.16880216406604034440e-03,
3.41214077093657773554e-03, 3.65542017853469781291e-03,
3.89864041565732288852e-03, 4.14180151108036864044e-03,
4.38490349355876492948e-03, 4.62794639182647314646e-03,
4.87093023459651223300e-03, 5.11385505056097429410e-03,
5.35672086839104454742e-03, 5.59952771673702821148e-03,
5.84227562422836091405e-03, 6.08496461947363731504e-03,
6.32759473106062758641e-03, 6.57016598755629822881e-03,
6.81267841750683115359e-03, 7.05513204943764623417e-03,
7.29752691185341952063e-03, 7.53986303323810405641e-03,
7.78214044205494896028e-03, 8.02435916674652111036e-03,
8.26651923573472682816e-03, 8.50862067742082402166e-03,
8.75066352018545254299e-03, 8.99264779238864719879e-03,
9.23457352236985856697e-03, 9.47644073844797554806e-03,
9.71824946892134618193e-03, 9.95999974206778979080e-03,
1.02016915861446264696e-02, 1.04433250293886909638e-02,
1.06849001000163534858e-02, 1.09264168262235422668e-02,
1.11678752361857574343e-02, 1.14092753580580970330e-02,
1.16506172199752743718e-02, 1.18919008500516353716e-02,
1.21331262763811845856e-02, 1.23742935270375938733e-02,
1.26154026300742353600e-02, 1.28564536135241883757e-02,
1.30974465054002689457e-02, 1.33383813336950454026e-02,
1.35792581263808539993e-02, 1.38200769114098266643e-02,
1.40608377167139014102e-02, 1.43015405702048535586e-02,
1.45421854997742992094e-02, 1.47827725332937282010e-02,
1.50233016986145197225e-02, 1.52637730235679579260e-02,
1.55041865359652544787e-02, 1.57445422635975676440e-02,
1.59848402342360230988e-02, 1.62250804756317243416e-02,
1.64652630155157908565e-02, 1.67053878815993511742e-02,
1.69454551015735914443e-02, 1.71854647031097450272e-02,
1.74254167138591341268e-02, 1.76653111614531801998e-02,
1.79051480735034213021e-02, 1.81449274776015329058e-02,
1.83846494013193521855e-02, 1.86243138722088884263e-02,
1.88639209178023438407e-02, 1.91034705656121447936e-02,
1.93429628431309348635e-02, 1.95823977778316234144e-02,
1.98217753971673821267e-02, 2.00610957285716796916e-02,
2.03003587994582852805e-02, 2.05395646372212997699e-02,
2.07787132692351730889e-02, 2.10178047228547111580e-02,
2.12568390254151175223e-02, 2.14958162042319829432e-02,
2.17347362866013270322e-02, 2.19735992997996155973e-02,
2.22124052710837606439e-02, 2.24511542276911585381e-02,
2.26898461968397004151e-02, 2.29284812057277964659e-02,
2.31670592815343794058e-02, 2.34055804514189426391e-02,
2.36440447425215437283e-02, 2.38824521819628390884e-02,
2.41208027968440805178e-02, 2.43590966142471533618e-02,
2.45973336612345834518e-02, 2.48355139648495648608e-02,
2.50736375521159599034e-02, 2.53117044500383477079e-02,
2.55497146856020138084e-02, 2.57876682857729813692e-02,
2.60255652774980320019e-02, 2.62634056877047161738e-02,
2.65011895433013774936e-02, 2.67389168711771700593e-02,
2.69765876982020758046e-02, 2.72142020512269183774e-02,
2.74517599570833874256e-02, 2.76892614425840594139e-02,
2.79267065345224080319e-02, 2.81640952596728215418e-02,
2.84014276447906305334e-02, 2.86387037166121183329e-02,
2.88759235018545418194e-02, 2.91130870272161487722e-02,
2.93501943193761917483e-02, 2.95872454049949593080e-02,
2.98242403107137760143e-02, 3.00611790631550336583e-02,
3.02980616889222051369e-02, 3.05348882145998617998e-02,
3.07716586667536873279e-02, 3.10083730719305089574e-02,
3.12450314566582974807e-02, 3.14816338474461984709e-02,
3.17181802707845392209e-02, 3.19546707531448703765e-02,
3.21911053209799416508e-02, 3.24274840007237608042e-02,
3.26638068187915936447e-02, 3.29000738015799848446e-02,
3.31362849754667510016e-02, 3.33724403668110569665e-02,
3.36085400019533672711e-02, 3.38445839072155085780e-02,
3.40805721089006696811e-02, 3.43165046332934153828e-02,
3.45523815066597350665e-02, 3.47882027552470010634e-02,
3.50239684052840449802e-02, 3.52596784829811438211e-02,
3.54953330145300408049e-02, 3.57309320261039800593e-02,
3.59664755438576927427e-02, 3.62019635939274456171e-02,
3.64373962024310479868e-02, 3.66727733954678516981e-02,
3.69080951991187997119e-02, 3.71433616394464122257e-02,
3.73785727424948352460e-02, 3.76137285342898197715e-02,
3.78488290408387842434e-02, 3.80838742881307937282e-02,
3.83188643021366015518e-02, 3.85537991088086354208e-02,
3.87886787340810668123e-02, 3.90235032038697762791e-02,
3.92582725440723950827e-02, 3.94929867805683190718e-02,
3.97276459392187364372e-02, 3.99622500458666138345e-02,
4.01967991263367518950e-02, 4.04312932064357782869e-02,
4.06657323119521615928e-02, 4.09001164686562529438e-02,
4.11344457023002721408e-02, 4.13687200386183492884e-02,
4.16029395033265247950e-02, 4.18371041221227840667e-02,
4.20712139206870575081e-02, 4.23052689246812343993e-02,
4.25392691597492184075e-02, 4.27732146515168790146e-02,
4.30071054255921278453e-02, 4.32409415075649117277e-02,
4.34747229230072265715e-02, 4.37084496974731243069e-02,
4.39421218564987614563e-02, 4.41757394256023921963e-02,
4.44093024302843961126e-02, 4.46428108960272643224e-02,
4.48762648482956758023e-02, 4.51096643125364488158e-02,
4.53430093141786172417e-02, 4.55762998786333820012e-02,
4.58095360312942012637e-02, 4.60427177975367488139e-02,
4.62758452027189418065e-02, 4.65089182721809893395e-02,
4.67419370312453785754e-02, 4.69749015052168886197e-02,
4.72078117193826252151e-02, 4.74406676990120346193e-02,
4.76734694693569036050e-02, 4.79062170556513941544e-02,
4.81389104831120573369e-02, 4.83715497769378263704e-02,
4.86041349623100790711e-02, 4.88366660643926031593e-02,
4.90691431083316448314e-02, 4.93015661192559226378e-02,
4.95339351222766274829e-02, 4.97662501424874642586e-02,
4.99985112049646240884e-02, 5.02307183347668675943e-02,
5.04628715569354693860e-02, 5.06949708964942874490e-02,
5.09270163784497562065e-02, 5.11590080277909073359e-02,
5.13909458694893697683e-02, 5.16228299284994252005e-02,
5.18546602297579733998e-02, 5.20864367981846085320e-02,
5.23181596586815636507e-02, 5.25498288361337939634e-02,
5.27814443554089490762e-02, 5.30130062413574076885e-02,
5.32445145188122845314e-02, 5.34759692125894581238e-02,
5.37073703474875707720e-02, 5.39387179482880632642e-02,
5.41700120397551818097e-02, 5.44012526466359849775e-02,
5.46324397936603645132e-02, 5.48635735055410730943e-02,
5.50946538069737382082e-02, 5.53256807226368482744e-02,
5.55566542771918150945e-02, 5.57875744952829599743e-02,
5.60184414015375206630e-02, 5.62492550205656929863e-02,
5.64800153769606447240e-02, 5.67107224952985156108e-02,
5.69413764001384242741e-02, 5.71719771160225237461e-02,
5.74025246674759737076e-02, 5.76330190790069890605e-02,
5.78634603751068329891e-02, 5.80938485802498377764e-02,
5.83241837188934394987e-02, 5.85544658154781641479e-02,
5.87846948944276553872e-02, 5.90148709801487023063e-02,
5.92449940970312324828e-02, 5.94750642694483605544e-02,
5.97050815217563465853e-02, 5.99350458782946862724e-02,
6.01649573633860623723e-02, 6.03948160013363932741e-02,
6.06246218164348399382e-02, 6.08543748329538267128e-02,
6.10840750751490343951e-02, 6.13137225672594557424e-02,
6.15433173335073746557e-02, 6.17728593980984008738e-02,
6.20023487852214699734e-02, 6.22317855190488850026e-02,
6.24611696237362887252e-02, 6.26905011234227399486e-02,
6.29197800422306580126e-02, 6.31490064042658921784e-02,
6.33781802336177285673e-02, 6.36073015543588693443e-02,
6.38363703905454882293e-02, 6.40653867662172443742e-02,
6.42943507053972546084e-02, 6.45232622320921628267e-02,
6.47521213702921261124e-02, 6.49809281439708147365e-02,
6.52096825770854676696e-02, 6.54383846935768787034e-02,
6.56670345173694380847e-02, 6.58956320723710908815e-02,
6.61241773824734202503e-02, 6.63526704715516196798e-02,
6.65811113634645346249e-02, 6.68095000820546486286e-02,
6.70378366511480972001e-02, 6.72661210945547510809e-02,
6.74943534360681191009e-02, 6.77225336994654592004e-02,
6.79506619085077506748e-02, 6.81787380869397080518e-02,
6.84067622584897949700e-02, 6.86347344468702658116e-02,
6.88626546757771518248e-02, 6.90905229688902888796e-02,
6.93183393498733174676e-02, 6.95461038423737382130e-02,
6.97738164700228424842e-02, 7.00014772564358511708e-02,
7.02290862252118036624e-02, 7.04566433999336549920e-02,
7.06841488041682619592e-02, 7.09116024614664108849e-02,
7.11390043953627759787e-02, 7.13663546293760442385e-02,
7.15936531870088183060e-02, 7.18209000917476997339e-02,
7.20480953670632612296e-02, 7.22752390364101160447e-02,
7.25023311232268624638e-02, 7.27293716509361670708e-02,
7.29563606429447231161e-02, 7.31832981226432782718e-02,
7.34101841134067040207e-02, 7.36370186385939123896e-02,
7.38638017215479669719e-02, 7.40905333855960135381e-02,
7.43172136540493771806e-02, 7.45438425502034929249e-02,
7.47704200973380028739e-02, 7.49969463187166729412e-02,
7.52234212375875316292e-02, 7.54498448771827451287e-02,
7.56762172607187699747e-02, 7.59025384113962420241e-02,
7.61288083524001013558e-02, 7.63550271068994951262e-02,
7.65811946980478885916e-02, 7.68073111489830512300e-02,
7.70333764828270151082e-02, 7.72593907226861720261e-02,
7.74853538916512596391e-02, 7.77112660127973059465e-02,
7.79371271091837819478e-02, 7.81629372038544767420e-02,
7.83886963198376085504e-02, 7.86144044801457830829e-02,
7.88400617077760212936e-02, 7.90656680257098148923e-02,
7.92912234569130569550e-02, 7.95167280243361529468e-02,
7.97421817509139374547e-02, 7.99675846595657713323e-02,
8.01929367731955139442e-02, 8.04182381146915231662e-02,
8.06434887069267247739e-02, 8.08686885727585569317e-02,
8.10938377350290395817e-02, 8.13189362165647605662e-02,
8.15439840401769033829e-02, 8.17689812286612333070e-02,
8.19939278047981806585e-02, 8.22188237913527297795e-02,
8.24436692110745855677e-02, 8.26684640866980763318e-02,
8.28932084409421815474e-02, 8.31179022965106151233e-02,
8.33425456760917421350e-02, 8.35671386023586620917e-02,
8.37916810979692228134e-02, 8.40161731855659649204e-02,
8.42406148877762328553e-02, 8.44650062272121054940e-02,
8.46893472264704516572e-02, 8.49136379081329439877e-02,
8.51378782947660450731e-02, 8.53620684089210490786e-02,
8.55862082731341095032e-02, 8.58102979099261975460e-02,
8.60343373418031576172e-02, 8.62583265912557073385e-02,
8.64822656807594791761e-02, 8.67061546327749649299e-02,
8.69299934697476128775e-02, 8.71537822141077861415e-02,
8.73775208882708043223e-02, 8.76012095146369157428e-02,
8.78248481155913807150e-02, 8.80484367135044021513e-02,
8.82719753307312088308e-02, 8.84954639896120276443e-02,
8.87189027124721391049e-02, 8.89422915216218218371e-02,
8.91656304393564219657e-02, 8.93889194879563669938e-02,
8.96121586896871380468e-02, 8.98353480667993115061e-02,
9.00584876415286006424e-02, 9.02815774360957862266e-02,
9.05046174727068136745e-02, 9.07276077735527791690e-02,
9.09505483608099157822e-02, 9.11734392566396351087e-02,
9.13962804831885272661e-02, 9.16190720625884025274e-02,
9.18418140169562635666e-02, 9.20645063683943332133e-02,
9.22871491389900822089e-02, 9.25097423508162430839e-02,
9.27322860259307685249e-02, 9.29547801863769285191e-02,
9.31772248541832964763e-02, 9.33996200513636798402e-02,
9.36219657999172727436e-02, 9.38442621218285727425e-02,
9.40665090390674085707e-02, 9.42887065735889817741e-02,
9.45108547473338389544e-02, 9.47329535822279272805e-02,
9.49550031001825944887e-02, 9.51770033230945750047e-02,
9.53989542728460315768e-02, 9.56208559713045552764e-02,
9.58427084403232071308e-02, 9.60645117017404626125e-02,
9.62862657773803226613e-02, 9.65079706890522165397e-02,
9.67296264585511128553e-02, 9.69512331076574779276e-02,
9.71727906581372896655e-02, 9.73942991317420792008e-02,
9.76157585502089170104e-02, 9.78371689352604545498e-02,
9.80585303086048687415e-02, 9.82798426919359729981e-02,
9.85011061069331617102e-02, 9.87223205752614380026e-02,
9.89434861185714414900e-02, 9.91646027584994482762e-02,
9.93856705166673570773e-02, 9.96066894146827863654e-02,
9.98276594741389772247e-02, 1.00048580716614876618e-01,
1.00269453163675151264e-01, 1.00490276836870159882e-01,
1.00711051757735994827e-01, 1.00931777947794482087e-01,
1.01152455428553222916e-01, 1.01373084221505552205e-01,
1.01593664348130593988e-01, 1.01814195829893261447e-01,
1.02034678688244284661e-01, 1.02255112944620182858e-01,
1.02475498620443319919e-01, 1.02695835737121890507e-01,
1.02916124316049961696e-01, 1.03136364378607417458e-01,
1.03356555946160069692e-01, 1.03576699040059588830e-01,
1.03796793681643559348e-01, 1.04016839892235493648e-01,
1.04236837693144804295e-01, 1.04456787105666845661e-01,
1.04676688151082941669e-01, 1.04896540850660371924e-01,
1.05116345225652385587e-01, 1.05336101297298229129e-01,
1.05555809086823132459e-01, 1.05775468615438378306e-01,
1.05995079904341218957e-01, 1.06214642974714987278e-01,
1.06434157847729041202e-01, 1.06653624544538833119e-01,
1.06873043086285854364e-01, 1.07092413494097690729e-01,
1.07311735789088050219e-01, 1.07531009992356721416e-01,
1.07750236124989628994e-01, 1.07969414208058833715e-01,
1.08188544262622546310e-01, 1.08407626309725127478e-01,
1.08626660370397129518e-01, 1.08845646465655254698e-01,
1.09064584616502438519e-01, 1.09283474843927794207e-01,
1.09502317168906668221e-01, 1.09721111612400654134e-01,
1.09939858195357564874e-01, 1.10158556938711474360e-01,
1.10377207863382731379e-01, 1.10595810990277973462e-01,
1.10814366340290113011e-01, 1.11032873934298378926e-01,
1.11251333793168288855e-01, 1.11469745937751746334e-01,
1.11688110388886929769e-01, 1.11906427167398417333e-01,
1.12124696294097117577e-01, 1.12342917789780338822e-01,
1.12561091675231775278e-01, 1.12779217971221507044e-01,
1.12997296698506041746e-01, 1.13215327877828272896e-01,
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6.33025972048829377314e-01, 6.33155598077917547428e-01,
6.33285207306276021200e-01, 6.33414799738259315376e-01,
6.33544375378220392392e-01, 6.33673934230510105259e-01,
6.33803476299478196765e-01, 6.33933001589472078230e-01,
6.34062510104837939728e-01, 6.34192001849920194978e-01,
6.34321476829061370317e-01, 6.34450935046602548795e-01,
6.34580376506882926080e-01, 6.34709801214240143530e-01,
6.34839209173010177167e-01, 6.34968600387527226658e-01,
6.35097974862123937356e-01, 6.35227332601131067236e-01,
6.35356673608877819959e-01, 6.35485997889691733853e-01,
6.35615305447898681912e-01, 6.35744596287822760772e-01,
6.35873870413786512756e-01, 6.36003127830110703833e-01,
6.36132368541114545657e-01, 6.36261592551115362504e-01,
6.36390799864429035360e-01, 6.36519990485369668853e-01,
6.36649164418249702280e-01, 6.36778321667379798576e-01,
6.36907462237069177391e-01, 6.37036586131625282015e-01,
6.37165693355353779381e-01, 6.37294783912558782113e-01,
6.37423857807542737497e-01, 6.37552915044606427486e-01,
6.37681955628048968698e-01, 6.37810979562167701395e-01,
6.37939986851258411527e-01, 6.38068977499615330728e-01,
6.38197951511530692237e-01, 6.38326908891295508042e-01,
6.38455849643198680710e-01, 6.38584773771527891562e-01,
6.38713681280568712495e-01, 6.38842572174605605184e-01,
6.38971446457920699835e-01, 6.39100304134795127453e-01,
6.39229145209507909620e-01, 6.39357969686336624626e-01,
6.39486777569557185430e-01, 6.39615568863443728631e-01,
6.39744343572268947540e-01, 6.39873101700303648087e-01,
6.40001843251817081892e-01, 6.40130568231077057284e-01,
6.40259276642349384190e-01, 6.40387968489898540270e-01,
6.40516643777987004782e-01, 6.40645302510875924717e-01,
6.40773944692824781733e-01, 6.40902570328091170104e-01,
6.41031179420931240820e-01, 6.41159771975599590554e-01,
6.41288347996348928604e-01, 6.41416907487430409951e-01,
6.41545450453093524246e-01, 6.41673976897586428869e-01,
6.41802486825155171779e-01, 6.41930980240044468665e-01,
6.42059457146497258861e-01, 6.42187917548755038410e-01,
6.42316361451057304954e-01, 6.42444788857642334889e-01,
6.42573199772746628256e-01, 6.42701594200604797713e-01,
6.42829972145450234677e-01, 6.42958333611514443184e-01,
6.43086678603027261936e-01, 6.43215007124217197365e-01,
6.43343319179310868527e-01, 6.43471614772533229143e-01,
6.43599893908107678620e-01, 6.43728156590256284098e-01,
6.43856402823198892271e-01, 6.43984632611154350634e-01,
6.44112845958339397257e-01, 6.44241042868969437940e-01,
6.44369223347258102130e-01, 6.44497387397417575983e-01,
6.44625535023658158273e-01, 6.44753666230188704489e-01,
6.44881781021216515803e-01, 6.45009879400947228056e-01,
6.45137961373584700731e-01, 6.45266026943331350019e-01,
6.45394076114387926779e-01, 6.45522108890953627558e-01,
6.45650125277225872544e-01, 6.45778125277400638637e-01,
6.45906108895672126380e-01, 6.46034076136233315069e-01,
6.46162027003274963555e-01, 6.46289961500986720466e-01,
6.46417879633556458074e-01, 6.46545781405170272294e-01,
6.46673666820013037793e-01, 6.46801535882267741862e-01,
6.46929388596115706456e-01, 6.47057224965736921263e-01,
6.47185044995309599614e-01, 6.47312848689010289505e-01,
6.47440636051014095642e-01, 6.47568407085494457398e-01,
6.47696161796623148810e-01, 6.47823900188570500625e-01,
6.47951622265505067233e-01, 6.48079328031593959736e-01,
6.48207017491002623899e-01, 6.48334690647894840154e-01,
6.48462347506432945643e-01, 6.48589988070777501150e-01,
6.48717612345087624171e-01, 6.48845220333520877887e-01,
6.48972812040233049125e-01, 6.49100387469378481420e-01,
6.49227946625109852974e-01, 6.49355489511578287676e-01,
6.49483016132933244080e-01, 6.49610526493322737451e-01,
6.49738020596893228742e-01, 6.49865498447789291525e-01,
6.49992960050154167106e-01, 6.50120405408129542479e-01,
6.50247834525855328280e-01, 6.50375247407469991856e-01,
6.50502644057110446241e-01, 6.50630024478911828112e-01,
6.50757388677007941880e-01, 6.50884736655530926619e-01,
6.51012068418611256071e-01, 6.51139383970377849664e-01,
6.51266683314958072515e-01, 6.51393966456477846450e-01,
6.51521233399061316938e-01, 6.51648484146831186159e-01,
6.51775718703908490959e-01, 6.51902937074412824892e-01,
6.52030139262461894134e-01, 6.52157325272172294639e-01,
6.52284495107658734980e-01, 6.52411648773034480442e-01,
6.52538786272411130973e-01, 6.52665907609898732211e-01,
6.52793012789605997526e-01, 6.52920101815639641885e-01,
6.53047174692105159011e-01, 6.53174231423106488315e-01,
6.53301272012745681828e-01, 6.53428296465123459313e-01,
6.53555304784339097246e-01, 6.53682296974490095742e-01,
6.53809273039672400607e-01, 6.53936232983980625377e-01,
6.54063176811507496211e-01, 6.54190104526344406999e-01,
6.54317016132581086296e-01, 6.54443911634305819369e-01,
6.54570791035605337171e-01, 6.54697654340564483277e-01,
6.54824501553267102061e-01, 6.54951332677795039494e-01,
6.55078147718228809282e-01, 6.55204946678647148772e-01,
6.55331729563127685090e-01, 6.55458496375745935936e-01,
6.55585247120576197766e-01, 6.55711981801691323746e-01,
6.55838700423162279662e-01, 6.55965402989058699035e-01,
6.56092089503448661070e-01, 6.56218759970398801684e-01,
6.56345414393973758393e-01, 6.56472052778237280535e-01,
6.56598675127251008021e-01, 6.56725281445075359521e-01,
6.56851871735769199390e-01, 6.56978446003389615626e-01,
6.57105004251992363962e-01, 6.57231546485631645815e-01,
6.57358072708359997272e-01, 6.57484582924228733170e-01,
6.57611077137287058925e-01, 6.57737555351583291774e-01,
6.57864017571163861575e-01, 6.57990463800073532852e-01,
6.58116894042355848882e-01, 6.58243308302052687608e-01,
6.58369706583204372663e-01, 6.58496088889849673365e-01,
6.58622455226025915742e-01, 6.58748805595768760490e-01,
6.58875140003112647058e-01, 6.59001458452090016493e-01,
6.59127760946732199621e-01, 6.59254047491068750908e-01,
6.59380318089127781533e-01, 6.59506572744935959385e-01,
6.59632811462518287016e-01, 6.59759034245898212667e-01,
6.59885241099097852313e-01, 6.60011432026137656592e-01,
6.60137607031036632854e-01, 6.60263766117812123113e-01,
6.60389909290480248139e-01, 6.60516036553055130298e-01,
6.60642147909550003781e-01, 6.60768243363975882332e-01,
6.60894322920342891514e-01, 6.61020386582659269514e-01,
6.61146434354931700206e-01, 6.61272466241165757239e-01,
6.61398482245365015864e-01, 6.61524482371531830083e-01,
6.61650466623666999588e-01, 6.61776435005769658737e-01,
6.61902387521837720641e-01, 6.62028324175867211032e-01,
6.62154244971853045421e-01, 6.62280149913788362959e-01,
6.62406039005664859509e-01, 6.62531912251472676623e-01,
6.62657769655200512560e-01, 6.62783611220835733313e-01,
6.62909436952363706475e-01, 6.63035246853768911457e-01,
6.63161040929033829272e-01, 6.63286819182139719686e-01,
6.63412581617066288153e-01, 6.63538328237791463771e-01,
6.63664059048292176435e-01, 6.63789774052543579685e-01,
6.63915473254519050705e-01, 6.64041156658191078499e-01,
6.64166824267530264692e-01, 6.64292476086505656596e-01,
6.64418112119084969258e-01, 6.64543732369234474433e-01,
6.64669336840918778542e-01, 6.64794925538101155738e-01,
6.64920498464743214839e-01, 6.65046055624805232398e-01,
6.65171597022245819630e-01, 6.65297122661022366508e-01,
6.65422632545090486644e-01, 6.65548126678404461387e-01,
6.65673605064917017771e-01, 6.65799067708579439540e-01,
6.65924514613341678171e-01, 6.66049945783151686740e-01,
6.66175361221956641167e-01, 6.66300760933701607946e-01,
6.66426144922330543352e-01, 6.66551513191785738321e-01,
6.66676865746008262548e-01, 6.66802202588937187322e-01,
6.66927523724510695757e-01, 6.67052829156665194610e-01,
6.67178118889335536323e-01, 6.67303392926455130052e-01,
6.67428651271956163704e-01, 6.67553893929769048832e-01,
6.67679120903822864719e-01, 6.67804332198045247360e-01,
6.67929527816362167414e-01, 6.68054707762698263274e-01,
6.68179872040976619019e-01, 6.68305020655119097484e-01,
6.68430153609045785146e-01, 6.68555270906675325193e-01,
6.68680372551925139568e-01, 6.68805458548710873856e-01,
6.68930528900946952398e-01, 6.69055583612546245220e-01,
6.69180622687419957018e-01, 6.69305646129478182260e-01,
6.69430653942629239062e-01, 6.69555646130780224290e-01,
6.69680622697836569479e-01, 6.69805583647702484917e-01,
6.69930528984280293514e-01, 6.70055458711471318978e-01,
6.70180372833175219682e-01, 6.70305271353290099690e-01,
6.70430154275712841816e-01, 6.70555021604338552521e-01,
6.70679873343061228042e-01, 6.70804709495773088257e-01,
6.70929530066365131802e-01, 6.71054335058726802998e-01,
6.71179124476746102879e-01, 6.71303898324309589185e-01,
6.71428656605302376370e-01, 6.71553399323607913551e-01,
6.71678126483108539624e-01, 6.71802838087684928148e-01,
6.71927534141216420416e-01, 6.72052214647580803408e-01,
6.72176879610654420816e-01, 6.72301529034312284061e-01,
6.72426162922427739232e-01, 6.72550781278872911173e-01,
6.72675384107518370413e-01, 6.72799971412233133172e-01,
6.72924543196884994423e-01, 6.73049099465340305848e-01,
6.73173640221463642774e-01, 6.73298165469118470305e-01,
6.73422675212166699232e-01, 6.73547169454468797056e-01,
6.73671648199883787989e-01, 6.73796111452269252950e-01,
6.73920559215481329574e-01, 6.74044991493374712199e-01,
6.74169408289802651879e-01, 6.74293809608617067397e-01,
6.74418195453668323225e-01, 6.74542565828805340544e-01,
6.74666920737875597247e-01, 6.74791260184725238958e-01,
6.74915584173198968010e-01, 6.75039892707139821404e-01,
6.75164185790389836939e-01, 6.75288463426789165034e-01,
6.75412725620176734864e-01, 6.75536972374390143337e-01,
6.75661203693265322023e-01, 6.75785419580636981252e-01,
6.75909620040338388058e-01, 6.76033805076201144146e-01,
6.76157974692055740995e-01, 6.76282128891731004749e-01,
6.76406267679054540309e-01, 6.76530391057852287240e-01,
6.76654499031948852839e-01, 6.76778591605167623158e-01,
6.76902668781330207892e-01, 6.77026730564257217537e-01,
6.77150776957767375208e-01, 6.77274807965678293797e-01,
6.77398823591806142908e-01, 6.77522823839965537829e-01,
6.77646808713969761584e-01, 6.77770778217630653906e-01,
6.77894732354758722259e-01, 6.78018671129162808775e-01,
6.78142594544650756383e-01, 6.78266502605028631656e-01,
6.78390395314101168900e-01, 6.78514272675671770152e-01,
6.78638134693542394160e-01, 6.78761981371513556383e-01,
6.78885812713384440009e-01, 6.79009628722952562896e-01,
6.79133429404014443698e-01, 6.79257214760364935735e-01,
6.79380984795797338016e-01, 6.79504739514103950349e-01,
6.79628478919075296183e-01, 6.79752203014500677725e-01,
6.79875911804167953889e-01, 6.79999605291863540302e-01,
6.80123283481372520320e-01, 6.80246946376478422991e-01,
6.80370593980963667136e-01, 6.80494226298608895220e-01,
6.80617843333193639488e-01, 6.80741445088495988891e-01,
6.80865031568292367048e-01, 6.80988602776358198376e-01,
6.81112158716467130937e-01, 6.81235699392391813589e-01,
6.81359224807903118837e-01, 6.81482734966770586915e-01,
6.81606229872762758859e-01, 6.81729709529646177302e-01,
6.81853173941186385676e-01, 6.81976623111147484124e-01,
6.82100057043292129499e-01, 6.82223475741381535364e-01,
6.82346879209175583014e-01, 6.82470267450432710454e-01,
6.82593640468910134445e-01, 6.82716998268363406410e-01,
6.82840340852546967554e-01, 6.82963668225213593743e-01,
6.83086980390114839601e-01, 6.83210277351001038504e-01,
6.83333559111620636450e-01, 6.83456825675721302282e-01,
6.83580077047048817462e-01, 6.83703313229347853230e-01,
6.83826534226361637536e-01, 6.83949740041831955040e-01,
6.84072930679499369155e-01, 6.84196106143102777963e-01,
6.84319266436379969321e-01, 6.84442411563067176772e-01,
6.84565541526899412617e-01, 6.84688656331610134842e-01,
6.84811755980931580190e-01, 6.84934840478594542112e-01,
6.85057909828328370772e-01, 6.85180964033861084062e-01,
6.85304003098919367609e-01, 6.85427027027228574774e-01,
6.85550035822512615624e-01, 6.85673029488493845918e-01,
6.85796008028893511188e-01, 6.85918971447431524702e-01,
6.86041919747826134390e-01, 6.86164852933794477963e-01,
6.86287771009052138815e-01, 6.86410673977313590122e-01,
6.86533561842291528698e-01, 6.86656434607697763184e-01,
6.86779292277242214837e-01, 6.86902134854634027761e-01,
6.87024962343580458679e-01, 6.87147774747787654093e-01,
6.87270572070960317212e-01, 6.87393354316801818982e-01,
6.87516121489014198076e-01, 6.87638873591298049881e-01,
6.87761610627352748537e-01, 6.87884332600876113872e-01,
6.88007039515564633447e-01, 6.88129731375113684599e-01,
6.88252408183216979332e-01, 6.88375069943567119424e-01,
6.88497716659855041321e-01, 6.88620348335770571246e-01,
6.88742964975002092132e-01, 6.88865566581236654642e-01,
6.88988153158160088196e-01, 6.89110724709456445858e-01,
6.89233281238809003533e-01, 6.89355822749899149748e-01,
6.89478349246407273831e-01, 6.89600860732012321819e-01,
6.89723357210391685435e-01, 6.89845838685221757203e-01,
6.89968305160177375335e-01, 6.90090756638931934752e-01,
6.90213193125157720154e-01, 6.90335614622525572948e-01,
6.90458021134704891253e-01, 6.90580412665363740921e-01,
6.90702789218168966556e-01, 6.90825150796785969476e-01,
6.90947497404878929750e-01, 6.91069829046110473136e-01,
6.91192145724142004148e-01, 6.91314447442633595031e-01,
6.91436734205243874740e-01, 6.91559006015630362008e-01,
6.91681262877449021254e-01, 6.91803504794354484631e-01,
6.91925731770000163046e-01, 6.92047943808038024116e-01,
6.92170140912118703191e-01, 6.92292323085891614376e-01,
6.92414490333004617462e-01, 6.92536642657104462018e-01,
6.92658780061836454323e-01, 6.92780902550844568388e-01,
6.92903010127771445958e-01, 6.93025102796258285487e-01,
6.93147180559945286227e-01
};
static const double fm_log_q2[] = {
-9.99999970204339394542e-01, -9.99511867731007974669e-01,
-9.99024122545299819720e-01, -9.98536734292937211421e-01,
-9.98049702617656908643e-01, -9.97563027181486594586e-01,
-9.97076707618930857535e-01, -9.96590743612639662352e-01,
-9.96105134789343704682e-01, -9.95619880820340474870e-01,
-9.95134981341887603357e-01, -9.94650436042181285146e-01,
-9.94166244524016029516e-01, -9.93682406505230209071e-01,
-9.93198921590821237615e-01, -9.92715789460176134540e-01,
-9.92233009782583330605e-01, -9.91750582106026845608e-01,
-9.91268506386495218408e-01, -9.90786781855067077984e-01,
-9.90305408488223459784e-01, -9.89824385926602934305e-01,
-9.89343713535692392824e-01, -9.88863391418940196331e-01,
-9.88383418923948875445e-01, -9.87903795762894443300e-01,
-9.87424521643993191589e-01, -9.86945596275973890954e-01,
-9.86467019194852801078e-01, -9.85988790103114798313e-01,
-9.85510908733950863336e-01, -9.85033374705881481503e-01,
-9.84556187716159159073e-01, -9.84079347261778369926e-01,
-9.83602853387407938257e-01, -9.83126705195018768535e-01,
-9.82650902914219859241e-01, -9.82175445826114934533e-01,
-9.81700333782709821939e-01, -9.81225566348648436943e-01,
-9.80751143317876161731e-01, -9.80277064203733838887e-01,
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// computes sqrt(-log(x*x)/x)
//
// strategy for log(x):
// split the argument into a product, 2**ipart * fpart
// by using bitmasks and integer math and then approximate
// log(fpart) from a spline table in [1.0:2.0[
// for maximum speed, argument validity is not checked.
static double sqrtlgx2byx(const double x)
{
udi_t val;
double a,b,y,z;
int32_t hx, ipart;
val.f = x*x;
hx = val.s.i1;
/* extract exponent and subtract bias */
ipart = (((hx & FM_DOUBLE_EMASK) >> FM_DOUBLE_MBITS) - FM_DOUBLE_BIAS);
/* mask out exponent to get the prefactor to 2**ipart */
hx &= FM_DOUBLE_MMASK;
val.s.i1 = hx | FM_DOUBLE_EZERO;
z = val.f;
/* table index */
hx >>= FM_SPLINE_SHIFT;
/* compute x value matching table index */
val.s.i0 = 0;
val.s.i1 = FM_DOUBLE_EZERO | (hx << FM_SPLINE_SHIFT);
b = (z - val.f) * fm_log_dinv;
a = 1.0 - b;
/* evaluate spline */
y = a * fm_log_q1[hx] + b * fm_log_q1[hx+1];
a = (a*a*a-a) * fm_log_q2[hx];
b = (b*b*b-b) * fm_log_q2[hx+1];
y += (a + b) * fm_log_dsq6;
return sqrt(-(((double)ipart)*FM_DOUBLE_LOGEOF2 + y)/x);
}
#else
/* optimizer friendly implementation of sqrt(-log(x*x)/x).
*
* strategy:
*
* split the argument into a product, 2**ipart * fpart
* by using bitmasks and integer math and then approximate
* log_2(fpart) with a rational function in [1.0:2.0[
*/
static const double fm_log2_p[] = {
1.01875663804580931796e-4,
4.97494994976747001425e-1,
4.70579119878881725854e0,
1.44989225341610930846e1,
1.79368678507819816313e1,
7.70838733755885391666e0
};
static const double fm_log2_q[] = {
/* 1.00000000000000000000e0, */
1.12873587189167450590e1,
4.52279145837532221105e1,
8.29875266912776603211e1,
7.11544750618563894466e1,
2.31251620126765340583e1
};
// computes sqrt(-log(x*x)/x)
// log(x) follows the strategy outlined in the Cephes math library.
// for maximum speed, argument validity is not checked.
static double sqrtlgx2byx(const double x)
{
udi_t val;
double y,z,px,qx;
int32_t ipart,fpart;
/* compute log(x*x) */
val.f = x*x;
/* extract exponent and part of the mantissa */
fpart = val.s.i1 & FM_DOUBLE_MMASK;
ipart = val.s.i1 & FM_DOUBLE_EMASK;
/* set exponent to 0 to get the prefactor to 2**ipart */
fpart |= FM_DOUBLE_EZERO;
val.s.i1 = fpart;
y = val.f;
/* convert exponent bits to integer */
ipart >>= FM_DOUBLE_MBITS;
ipart -= FM_DOUBLE_BIAS;
/* the polynomial is computed for sqrt(0.5) < x < sqrt(2),
but we have the mantissa in the interval 1 < x < 2.
adjust by dividing x by 2 and incrementing ipart, if needed. */
if (y > FM_DOUBLE_SQRT2) {
y *= 0.5;
++ipart;
}
/* use polynomial approximation for log(1+x) */
y -= 1.0;
px = fm_log2_p[0];
px = px*y + fm_log2_p[1];
px = px*y + fm_log2_p[2];
px = px*y + fm_log2_p[3];
px = px*y + fm_log2_p[4];
px = px*y + fm_log2_p[5];
qx = y + fm_log2_q[0];
qx = qx*y + fm_log2_q[1];
qx = qx*y + fm_log2_q[2];
qx = qx*y + fm_log2_q[3];
qx = qx*y + fm_log2_q[4];
z = y*y;
z = y*(z*px/qx) - 0.5*z + y;
z += ((double)ipart)*FM_DOUBLE_LOGEOF2;
return sqrt(-z/x);
}
#endif
}
}
#endif
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