Lines Matching +full:- +full:e
21 * is J0(x) = 1 - x^2 / 4 + x^4 R(x^2)
25 * J0(x) = sqrt(2/(pi x)) (P0(x) cos(X) - Q0(x) sin(X)),
26 * X = x - pi/4,
33 * Y0(x)cos(X) - J0(x)sin(X) = sqrt( 2/(pi x)) Q0(x),
34 * Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2))
42 * IEEE 0, 30 100000 1.7e-34 2.4e-35
74 * IEEE 0, 30 100000 3.0e-34 2.7e-35
78 /* Copyright 2001 by Stephen L. Moshier (moshier@na-net.ornl.gov).
94 #include "quadmath-imp.h"
97 static const __float128 ONEOSQPI = 5.6418958354775628694807945156077258584405E-1Q;
99 static const __float128 TWOOPI = 6.3661977236758134307553505349005744813784E-1Q;
102 /* J0(x) = 1 - x^2/4 + x^2 x^2 R(x^2)
103 Peak relative error 3.4e-37
108 -5.479944965767990821079467311839107722107E14Q,
110 -3.633750176832769659849028554429106299915E10Q,
112 -2.107485999925074577174305650549367415465E5Q,
129 Peak relative error 3.3e-36 */
132 -1.901689868258117463979611259731176301065E-16Q,
133 -1.798743043824071514483008340803573980931E-13Q,
134 -6.481746687115262291873324132944647438959E-11Q,
135 -1.150651553745409037257197798528294248012E-8Q,
136 -1.088408467297401082271185599507222695995E-6Q,
137 -5.551996725183495852661022587879817546508E-5Q,
138 -1.477286941214245433866838787454880214736E-3Q,
139 -1.882877976157714592017345347609200402472E-2Q,
140 -9.620983176855405325086530374317855880515E-2Q,
141 -1.271468546258855781530458854476627766233E-1Q,
145 2.704625590411544837659891569420764475007E-15Q,
146 2.562526347676857624104306349421985403573E-12Q,
147 9.259137589952741054108665570122085036246E-10Q,
148 1.651044705794378365237454962653430805272E-7Q,
149 1.573561544138733044977714063100859136660E-5Q,
150 8.134482112334882274688298469629884804056E-4Q,
151 2.219259239404080863919375103673593571689E-2Q,
152 2.976990606226596289580242451096393862792E-1Q,
160 Peak relative error 2.4e-35 */
163 -2.335166846111159458466553806683579003632E-15Q,
164 -1.382763674252402720401020004169367089975E-12Q,
165 -3.192160804534716696058987967592784857907E-10Q,
166 -3.744199606283752333686144670572632116899E-8Q,
167 -2.439161236879511162078619292571922772224E-6Q,
168 -9.068436986859420951664151060267045346549E-5Q,
169 -1.905407090637058116299757292660002697359E-3Q,
170 -2.164456143936718388053842376884252978872E-2Q,
171 -1.212178415116411222341491717748696499966E-1Q,
172 -2.782433626588541494473277445959593334494E-1Q,
173 -1.670703190068873186016102289227646035035E-1Q,
177 3.321126181135871232648331450082662856743E-14Q,
178 1.971894594837650840586859228510007703641E-11Q,
179 4.571144364787008285981633719513897281690E-9Q,
180 5.396419143536287457142904742849052402103E-7Q,
181 3.551548222385845912370226756036899901549E-5Q,
182 1.342353874566932014705609788054598013516E-3Q,
183 2.899133293006771317589357444614157734385E-2Q,
184 3.455374978185770197704507681491574261545E-1Q,
193 Peak relative error 2.7e-35 */
196 -1.270478335089770355749591358934012019596E-12Q,
197 -4.007588712145412921057254992155810347245E-10Q,
198 -4.815187822989597568124520080486652009281E-8Q,
199 -2.867070063972764880024598300408284868021E-6Q,
200 -9.218742195161302204046454768106063638006E-5Q,
201 -1.635746821447052827526320629828043529997E-3Q,
202 -1.570376886640308408247709616497261011707E-2Q,
203 -7.656484795303305596941813361786219477807E-2Q,
204 -1.659371030767513274944805479908858628053E-1Q,
205 -1.185340550030955660015841796219919804915E-1Q,
206 -8.920026499909994671248893388013790366712E-3Q,
210 1.806902521016705225778045904631543990314E-11Q,
211 5.728502760243502431663549179135868966031E-9Q,
212 6.938168504826004255287618819550667978450E-7Q,
213 4.183769964807453250763325026573037785902E-5Q,
214 1.372660678476925468014882230851637878587E-3Q,
215 2.516452105242920335873286419212708961771E-2Q,
216 2.550502712902647803796267951846557316182E-1Q,
224 Peak relative error 3.5e-35
228 -9.791405771694098960254468859195175708252E-10Q,
229 -1.917193059944531970421626610188102836352E-7Q,
230 -1.393597539508855262243816152893982002084E-5Q,
231 -4.881863490846771259880606911667479860077E-4Q,
232 -8.946571245022470127331892085881699269853E-3Q,
233 -8.707474232568097513415336886103899434251E-2Q,
234 -4.362042697474650737898551272505525973766E-1Q,
235 -1.032712171267523975431451359962375617386E0Q,
236 -9.630502683169895107062182070514713702346E-1Q,
237 -2.251804386252969656586810309252357233320E-1Q,
241 1.392555487577717669739688337895791213139E-8Q,
242 2.748886559120659027172816051276451376854E-6Q,
243 2.024717710644378047477189849678576659290E-4Q,
244 7.244868609350416002930624752604670292469E-3Q,
245 1.373631762292244371102989739300382152416E-1Q,
255 Peak relative error 2.3e-36
259 -2.589155123706348361249809342508270121788E-8Q,
260 -3.746254369796115441118148490849195516593E-6Q,
261 -1.985595497390808544622893738135529701062E-4Q,
262 -5.008253705202932091290132760394976551426E-3Q,
263 -6.529469780539591572179155511840853077232E-2Q,
264 -4.468736064761814602927408833818990271514E-1Q,
265 -1.556391252586395038089729428444444823380E0Q,
266 -2.533135309840530224072920725976994981638E0Q,
267 -1.605509621731068453869408718565392869560E0Q,
268 -2.518966692256192789269859830255724429375E-1Q,
272 3.682353957237979993646169732962573930237E-7Q,
273 5.386741661883067824698973455566332102029E-5Q,
274 2.906881154171822780345134853794241037053E-3Q,
275 7.545832595801289519475806339863492074126E-2Q,
286 Peak relative error 1.0e-35
290 -1.917322340814391131073820537027234322550E-7Q,
291 -1.966595744473227183846019639723259011906E-5Q,
292 -7.177081163619679403212623526632690465290E-4Q,
293 -1.206467373860974695661544653741899755695E-2Q,
294 -1.008656452188539812154551482286328107316E-1Q,
295 -4.216016116408810856620947307438823892707E-1Q,
296 -8.378631013025721741744285026537009814161E-1Q,
297 -6.973895635309960850033762745957946272579E-1Q,
298 -1.797864718878320770670740413285763554812E-1Q,
299 -4.098025357743657347681137871388402849581E-3Q,
303 2.726858489303036441686496086962545034018E-6Q,
304 2.840430827557109238386808968234848081424E-4Q,
305 1.063826772041781947891481054529454088832E-2Q,
306 1.864775537138364773178044431045514405468E-1Q,
316 Peak relative error 1.3e-36
320 -1.594642785584856746358609622003310312622E-6Q,
321 -1.323238196302221554194031733595194539794E-4Q,
322 -3.856087818696874802689922536987100372345E-3Q,
323 -5.113241710697777193011470733601522047399E-2Q,
324 -3.334229537209911914449990372942022350558E-1Q,
325 -1.075703518198127096179198549659283422832E0Q,
326 -1.634174803414062725476343124267110981807E0Q,
327 -1.030133247434119595616826842367268304880E0Q,
328 -1.989811539080358501229347481000707289391E-1Q,
329 -3.246859189246653459359775001466924610236E-3Q,
333 2.267936634217251403663034189684284173018E-5Q,
334 1.918112982168673386858072491437971732237E-3Q,
335 5.771704085468423159125856786653868219522E-2Q,
336 8.056124451167969333717642810661498890507E-1Q,
346 Peak relative error 1.2e-35
350 -1.001042324337684297465071506097365389123E-4Q,
351 -6.289034524673365824853547252689991418981E-3Q,
352 -1.346527918018624234373664526930736205806E-1Q,
353 -1.268808313614288355444506172560463315102E0Q,
354 -5.654126123607146048354132115649177406163E0Q,
355 -1.186649511267312652171775803270911971693E1Q,
356 -1.094032424931998612551588246779200724257E1Q,
357 -3.728792136814520055025256353193674625267E0Q,
358 -3.000348318524471807839934764596331810608E-1Q,
362 1.423705538269770974803901422532055612980E-3Q,
363 9.171476630091439978533535167485230575894E-2Q,
374 /* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x),
375 Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2))
376 Peak relative error 2.2e-35
380 2.343640834407975740545326632205999437469E-18Q,
381 2.667978112927811452221176781536278257448E-15Q,
382 1.178415018484555397390098879501969116536E-12Q,
383 2.622049767502719728905924701288614016597E-10Q,
384 3.196908059607618864801313380896308968673E-8Q,
385 2.179466154171673958770030655199434798494E-6Q,
386 8.139959091628545225221976413795645177291E-5Q,
387 1.563900725721039825236927137885747138654E-3Q,
388 1.355172364265825167113562519307194840307E-2Q,
389 3.928058355906967977269780046844768588532E-2Q,
390 1.107891967702173292405380993183694932208E-2Q,
394 3.199850952578356211091219295199301766718E-17Q,
395 3.652601488020654842194486058637953363918E-14Q,
396 1.620179741394865258354608590461839031281E-11Q,
397 3.629359209474609630056463248923684371426E-9Q,
398 4.473680923894354600193264347733477363305E-7Q,
399 3.106368086644715743265603656011050476736E-5Q,
400 1.198239259946770604954664925153424252622E-3Q,
401 2.446041004004283102372887804475767568272E-2Q,
402 2.403235525011860603014707768815113698768E-1Q,
403 9.491006790682158612266270665136910927149E-1Q,
407 /* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x),
408 Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2))
409 Peak relative error 5.1e-36
413 1.001954266485599464105669390693597125904E-17Q,
414 7.545499865295034556206475956620160007849E-15Q,
415 2.267838684785673931024792538193202559922E-12Q,
416 3.561909705814420373609574999542459912419E-10Q,
417 3.216201422768092505214730633842924944671E-8Q,
418 1.731194793857907454569364622452058554314E-6Q,
419 5.576944613034537050396518509871004586039E-5Q,
420 1.051787760316848982655967052985391418146E-3Q,
421 1.102852974036687441600678598019883746959E-2Q,
422 5.834647019292460494254225988766702933571E-2Q,
423 1.290281921604364618912425380717127576529E-1Q,
424 7.598886310387075708640370806458926458301E-2Q,
428 1.368001558508338469503329967729951830843E-16Q,
429 1.034454121857542147020549303317348297289E-13Q,
430 3.128109209247090744354764050629381674436E-11Q,
431 4.957795214328501986562102573522064468671E-9Q,
432 4.537872468606711261992676606899273588899E-7Q,
433 2.493639207101727713192687060517509774182E-5Q,
434 8.294957278145328349785532236663051405805E-4Q,
435 1.646471258966713577374948205279380115839E-2Q,
436 1.878910092770966718491814497982191447073E-1Q,
443 /* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x),
444 Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2))
445 Peak relative error 3.9e-35
449 1.750399094021293722243426623211733898747E-13Q,
450 6.483426211748008735242909236490115050294E-11Q,
451 9.279430665656575457141747875716899958373E-9Q,
452 6.696634968526907231258534757736576340266E-7Q,
453 2.666560823798895649685231292142838188061E-5Q,
454 6.025087697259436271271562769707550594540E-4Q,
455 7.652807734168613251901945778921336353485E-3Q,
456 5.226269002589406461622551452343519078905E-2Q,
457 1.748390159751117658969324896330142895079E-1Q,
458 2.378188719097006494782174902213083589660E-1Q,
459 8.383984859679804095463699702165659216831E-2Q,
463 2.389878229704327939008104855942987615715E-12Q,
464 8.926142817142546018703814194987786425099E-10Q,
465 1.294065862406745901206588525833274399038E-7Q,
466 9.524139899457666250828752185212769682191E-6Q,
467 3.908332488377770886091936221573123353489E-4Q,
468 9.250427033957236609624199884089916836748E-3Q,
469 1.263420066165922645975830877751588421451E-1Q,
470 9.692527053860420229711317379861733180654E-1Q,
477 /* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x),
478 Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2))
479 Peak relative error 3.2e-35
483 2.233870042925895644234072357400122854086E-11Q,
484 5.146223225761993222808463878999151699792E-9Q,
485 4.459114531468296461688753521109797474523E-7Q,
486 1.891397692931537975547242165291668056276E-5Q,
487 4.279519145911541776938964806470674565504E-4Q,
488 5.275239415656560634702073291768904783989E-3Q,
489 3.468698403240744801278238473898432608887E-2Q,
490 1.138773146337708415188856882915457888274E-1Q,
491 1.622717518946443013587108598334636458955E-1Q,
492 7.249040006390586123760992346453034628227E-2Q,
493 1.941595365256460232175236758506411486667E-3Q,
497 3.049977232266999249626430127217988047453E-10Q,
498 7.120883230531035857746096928889676144099E-8Q,
499 6.301786064753734446784637919554359588859E-6Q,
500 2.762010530095069598480766869426308077192E-4Q,
501 6.572163250572867859316828886203406361251E-3Q,
502 8.752566114841221958200215255461843397776E-2Q,
503 6.487654992874805093499285311075289932664E-1Q,
510 /* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x),
511 Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2))
512 Peak relative error 1.4e-36
516 6.126167301024815034423262653066023684411E-10Q,
517 1.043969327113173261820028225053598975128E-7Q,
518 6.592927270288697027757438170153763220190E-6Q,
519 2.009103660938497963095652951912071336730E-4Q,
520 3.220543385492643525985862356352195896964E-3Q,
521 2.774405975730545157543417650436941650990E-2Q,
522 1.258114008023826384487378016636555041129E-1Q,
523 2.811724258266902502344701449984698323860E-1Q,
524 2.691837665193548059322831687432415014067E-1Q,
525 7.949087384900985370683770525312735605034E-2Q,
526 1.229509543620976530030153018986910810747E-3Q,
530 8.364260446128475461539941389210166156568E-9Q,
531 1.451301850638956578622154585560759862764E-6Q,
532 9.431830010924603664244578867057141839463E-5Q,
533 3.004105101667433434196388593004526182741E-3Q,
534 5.148157397848271739710011717102773780221E-2Q,
535 4.901089301726939576055285374953887874895E-1Q,
543 /* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x),
544 Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2))
545 Peak relative error 3.8e-36
549 7.584861620402450302063691901886141875454E-8Q,
550 9.300939338814216296064659459966041794591E-6Q,
551 4.112108906197521696032158235392604947895E-4Q,
552 8.515168851578898791897038357239630654431E-3Q,
553 8.971286321017307400142720556749573229058E-2Q,
554 4.885856732902956303343015636331874194498E-1Q,
557 8.165042692571721959157677701625853772271E-1Q,
558 9.805848115375053300608712721986235900715E-2Q,
562 1.035586492113036586458163971239438078160E-6Q,
563 1.301999337731768381683593636500979713689E-4Q,
564 5.993695702564527062553071126719088859654E-3Q,
565 1.321184892887881883489141186815457808785E-1Q,
575 /* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x),
576 Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2))
577 Peak relative error 2.2e-35
581 4.455027774980750211349941766420190722088E-7Q,
582 4.031998274578520170631601850866780366466E-5Q,
583 1.273987274325947007856695677491340636339E-3Q,
584 1.818754543377448509897226554179659122873E-2Q,
585 1.266748858326568264126353051352269875352E-1Q,
586 4.327578594728723821137731555139472880414E-1Q,
587 6.892532471436503074928194969154192615359E-1Q,
588 4.490775818438716873422163588640262036506E-1Q,
589 8.649615949297322440032000346117031581572E-2Q,
590 7.261345286655345047417257611469066147561E-4Q,
594 6.082600739680555266312417978064954793142E-6Q,
595 5.693622538165494742945717226571441747567E-4Q,
596 1.901625907009092204458328768129666975975E-2Q,
597 2.958689532697857335456896889409923371570E-1Q,
606 /* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x),
607 Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2))
608 Peak relative error 3.1e-36
612 2.817566786579768804844367382809101929314E-6Q,
613 2.122772176396691634147024348373539744935E-4Q,
614 5.501378031780457828919593905395747517585E-3Q,
615 6.355374424341762686099147452020466524659E-2Q,
616 3.539652320122661637429658698954748337223E-1Q,
617 9.571721066119617436343740541777014319695E-1Q,
619 6.069388659458926158392384709893753793967E-1Q,
620 9.026746127269713176512359976978248763621E-2Q,
621 5.317668723070450235320878117210807236375E-4Q,
625 3.846924354014260866793741072933159380158E-5Q,
626 3.017562820057704325510067178327449946763E-3Q,
627 8.356305620686867949798885808540444210935E-2Q,
638 /* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */
646 y = *p--; in neval()
649 y = y * x + *p--; in neval()
651 while (--n > 0); in neval()
656 /* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */
664 y = x + *p--; in deval()
667 y = y * x + *p--; in deval()
669 while (--n > 0); in deval()
694 if (xx < 0x1p-57Q) in j0q()
699 p -= 0.25Q * z; in j0q()
704 /* X = x - pi/4 in j0q()
707 sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4) in j0q()
708 = 1/sqrt(2) * (sin(x) - cos(x)) in j0q()
709 sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) in j0q()
712 ss = s - c; in j0q()
716 z = -cosq (xx + xx); in j0q()
786 q = q - 0.125Q * xinv; in j0q()
787 z = ONEOSQPI * (p * cc - q * ss) / sqrtq (xx); in j0q()
794 Peak absolute error 1.7e-36 (relative where Y0 > 1)
798 -1.062023609591350692692296993537002558155E19Q,
800 -1.984190771278515324281415820316054696545E18Q,
802 -5.529326354780295177243773419090123407550E14Q,
804 -7.959436160727126750732203098982718347785E9Q,
820 static const __float128 U0 = -7.3804295108687225274343927948483016310862e-02Q;
835 return -1 / zero; /* -inf and divide by zero exception. */ in y0q()
838 if (xx <= 0x1p-57) in y0q()
849 /* X = x - pi/4 in y0q()
852 sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4) in y0q()
853 = 1/sqrt(2) * (sin(x) - cos(x)) in y0q()
854 sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) in y0q()
857 ss = s - c; in y0q()
861 z = -cosq (x + x); in y0q()
931 q = q - 0.125Q * xinv; in y0q()