Prepare for radical source tree reorganization. zack/build-layout-experiment

All top-level files and directories are moved into a temporary storage
directory, REORG.TODO, except for files that will certainly still
exist in their current form at top level when we're done (COPYING,
COPYING.LIB, LICENSES, NEWS, README), all old ChangeLog files (which
are moved to the new directory OldChangeLogs, instead), and the
generated file INSTALL (which is just deleted; in the new order, there
will be no generated files checked into version control).

1 files changed, 961 insertions, 0 deletions

diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_j1l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_j1l.c
new file mode 100644
index 0000000000..6fc69faa3c
--- /dev/null
+++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_j1l.c
@@ -0,0 +1,961 @@
+/*							j1l.c
+ *
+ *	Bessel function of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, j1l();
+ *
+ * y = j1l( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of first kind, order one of the argument.
+ *
+ * The domain is divided into two major intervals [0, 2] and
+ * (2, infinity). In the first interval the rational approximation is
+ * J1(x) = .5x + x x^2 R(x^2)
+ *
+ * The second interval is further partitioned into eight equal segments
+ * of 1/x.
+ * J1(x) = sqrt(2/(pi x)) (P1(x) cos(X) - Q1(x) sin(X)),
+ * X = x - 3 pi / 4,
+ *
+ * and the auxiliary functions are given by
+ *
+ * J1(x)cos(X) + Y1(x)sin(X) = sqrt( 2/(pi x)) P1(x),
+ * P1(x) = 1 + 1/x^2 R(1/x^2)
+ *
+ * Y1(x)cos(X) - J1(x)sin(X) = sqrt( 2/(pi x)) Q1(x),
+ * Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Absolute error:
+ * arithmetic   domain      # trials      peak         rms
+ *    IEEE      0, 30       100000      2.8e-34      2.7e-35
+ *
+ *
+ */
+
+/*							y1l.c
+ *
+ *	Bessel function of the second kind, order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, y1l();
+ *
+ * y = y1l( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind, of order
+ * one, of the argument.
+ *
+ * The domain is divided into two major intervals [0, 2] and
+ * (2, infinity). In the first interval the rational approximation is
+ * Y1(x) = 2/pi * (log(x) * J1(x) - 1/x) + x R(x^2) .
+ * In the second interval the approximation is the same as for J1(x), and
+ * Y1(x) = sqrt(2/(pi x)) (P1(x) sin(X) + Q1(x) cos(X)),
+ * X = x - 3 pi / 4.
+ *
+ * ACCURACY:
+ *
+ *  Absolute error, when y0(x) < 1; else relative error:
+ *
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0, 30       100000      2.7e-34     2.9e-35
+ *
+ */
+
+/* Copyright 2001 by Stephen L. Moshier (moshier@na-net.onrl.gov).
+
+    This library is free software; you can redistribute it and/or
+    modify it under the terms of the GNU Lesser General Public
+    License as published by the Free Software Foundation; either
+    version 2.1 of the License, or (at your option) any later version.
+
+    This library is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+    Lesser General Public License for more details.
+
+    You should have received a copy of the GNU Lesser General Public
+    License along with this library; if not, see
+    <http://www.gnu.org/licenses/>.  */
+
+#include <errno.h>
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+/* 1 / sqrt(pi) */
+static const _Float128 ONEOSQPI = L(5.6418958354775628694807945156077258584405E-1);
+/* 2 / pi */
+static const _Float128 TWOOPI = L(6.3661977236758134307553505349005744813784E-1);
+static const _Float128 zero = 0;
+
+/* J1(x) = .5x + x x^2 R(x^2)
+   Peak relative error 1.9e-35
+   0 <= x <= 2  */
+#define NJ0_2N 6
+static const _Float128 J0_2N[NJ0_2N + 1] = {
+ L(-5.943799577386942855938508697619735179660E16),
+  L(1.812087021305009192259946997014044074711E15),
+ L(-2.761698314264509665075127515729146460895E13),
+  L(2.091089497823600978949389109350658815972E11),
+ L(-8.546413231387036372945453565654130054307E8),
+  L(1.797229225249742247475464052741320612261E6),
+ L(-1.559552840946694171346552770008812083969E3)
+};
+#define NJ0_2D 6
+static const _Float128 J0_2D[NJ0_2D + 1] = {
+  L(9.510079323819108569501613916191477479397E17),
+  L(1.063193817503280529676423936545854693915E16),
+  L(5.934143516050192600795972192791775226920E13),
+  L(2.168000911950620999091479265214368352883E11),
+  L(5.673775894803172808323058205986256928794E8),
+  L(1.080329960080981204840966206372671147224E6),
+  L(1.411951256636576283942477881535283304912E3),
+ /* 1.000000000000000000000000000000000000000E0L */
+};
+
+/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2),
+   0 <= 1/x <= .0625
+   Peak relative error 3.6e-36  */
+#define NP16_IN 9
+static const _Float128 P16_IN[NP16_IN + 1] = {
+  L(5.143674369359646114999545149085139822905E-16),
+  L(4.836645664124562546056389268546233577376E-13),
+  L(1.730945562285804805325011561498453013673E-10),
+  L(3.047976856147077889834905908605310585810E-8),
+  L(2.855227609107969710407464739188141162386E-6),
+  L(1.439362407936705484122143713643023998457E-4),
+  L(3.774489768532936551500999699815873422073E-3),
+  L(4.723962172984642566142399678920790598426E-2),
+  L(2.359289678988743939925017240478818248735E-1),
+  L(3.032580002220628812728954785118117124520E-1),
+};
+#define NP16_ID 9
+static const _Float128 P16_ID[NP16_ID + 1] = {
+  L(4.389268795186898018132945193912677177553E-15),
+  L(4.132671824807454334388868363256830961655E-12),
+  L(1.482133328179508835835963635130894413136E-9),
+  L(2.618941412861122118906353737117067376236E-7),
+  L(2.467854246740858470815714426201888034270E-5),
+  L(1.257192927368839847825938545925340230490E-3),
+  L(3.362739031941574274949719324644120720341E-2),
+  L(4.384458231338934105875343439265370178858E-1),
+  L(2.412830809841095249170909628197264854651E0),
+  L(4.176078204111348059102962617368214856874E0),
+ /* 1.000000000000000000000000000000000000000E0 */
+};
+
+/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2),
+    0.0625 <= 1/x <= 0.125
+    Peak relative error 1.9e-36  */
+#define NP8_16N 11
+static const _Float128 P8_16N[NP8_16N + 1] = {
+  L(2.984612480763362345647303274082071598135E-16),
+  L(1.923651877544126103941232173085475682334E-13),
+  L(4.881258879388869396043760693256024307743E-11),
+  L(6.368866572475045408480898921866869811889E-9),
+  L(4.684818344104910450523906967821090796737E-7),
+  L(2.005177298271593587095982211091300382796E-5),
+  L(4.979808067163957634120681477207147536182E-4),
+  L(6.946005761642579085284689047091173581127E-3),
+  L(5.074601112955765012750207555985299026204E-2),
+  L(1.698599455896180893191766195194231825379E-1),
+  L(1.957536905259237627737222775573623779638E-1),
+  L(2.991314703282528370270179989044994319374E-2),
+};
+#define NP8_16D 10
+static const _Float128 P8_16D[NP8_16D + 1] = {
+  L(2.546869316918069202079580939942463010937E-15),
+  L(1.644650111942455804019788382157745229955E-12),
+  L(4.185430770291694079925607420808011147173E-10),
+  L(5.485331966975218025368698195861074143153E-8),
+  L(4.062884421686912042335466327098932678905E-6),
+  L(1.758139661060905948870523641319556816772E-4),
+  L(4.445143889306356207566032244985607493096E-3),
+  L(6.391901016293512632765621532571159071158E-2),
+  L(4.933040207519900471177016015718145795434E-1),
+  L(1.839144086168947712971630337250761842976E0),
+  L(2.715120873995490920415616716916149586579E0),
+ /* 1.000000000000000000000000000000000000000E0 */
+};
+
+/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2),
+  0.125 <= 1/x <= 0.1875
+  Peak relative error 1.3e-36  */
+#define NP5_8N 10
+static const _Float128 P5_8N[NP5_8N + 1] = {
+  L(2.837678373978003452653763806968237227234E-12),
+  L(9.726641165590364928442128579282742354806E-10),
+  L(1.284408003604131382028112171490633956539E-7),
+  L(8.524624695868291291250573339272194285008E-6),
+  L(3.111516908953172249853673787748841282846E-4),
+  L(6.423175156126364104172801983096596409176E-3),
+  L(7.430220589989104581004416356260692450652E-2),
+  L(4.608315409833682489016656279567605536619E-1),
+  L(1.396870223510964882676225042258855977512E0),
+  L(1.718500293904122365894630460672081526236E0),
+  L(5.465927698800862172307352821870223855365E-1)
+};
+#define NP5_8D 10
+static const _Float128 P5_8D[NP5_8D + 1] = {
+  L(2.421485545794616609951168511612060482715E-11),
+  L(8.329862750896452929030058039752327232310E-9),
+  L(1.106137992233383429630592081375289010720E-6),
+  L(7.405786153760681090127497796448503306939E-5),
+  L(2.740364785433195322492093333127633465227E-3),
+  L(5.781246470403095224872243564165254652198E-2),
+  L(6.927711353039742469918754111511109983546E-1),
+  L(4.558679283460430281188304515922826156690E0),
+  L(1.534468499844879487013168065728837900009E1),
+  L(2.313927430889218597919624843161569422745E1),
+  L(1.194506341319498844336768473218382828637E1),
+ /* 1.000000000000000000000000000000000000000E0 */
+};
+
+/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2),
+   Peak relative error 1.4e-36
+   0.1875 <= 1/x <= 0.25  */
+#define NP4_5N 10
+static const _Float128 P4_5N[NP4_5N + 1] = {
+  L(1.846029078268368685834261260420933914621E-10),
+  L(3.916295939611376119377869680335444207768E-8),
+  L(3.122158792018920627984597530935323997312E-6),
+  L(1.218073444893078303994045653603392272450E-4),
+  L(2.536420827983485448140477159977981844883E-3),
+  L(2.883011322006690823959367922241169171315E-2),
+  L(1.755255190734902907438042414495469810830E-1),
+  L(5.379317079922628599870898285488723736599E-1),
+  L(7.284904050194300773890303361501726561938E-1),
+  L(3.270110346613085348094396323925000362813E-1),
+  L(1.804473805689725610052078464951722064757E-2),
+};
+#define NP4_5D 9
+static const _Float128 P4_5D[NP4_5D + 1] = {
+  L(1.575278146806816970152174364308980863569E-9),
+  L(3.361289173657099516191331123405675054321E-7),
+  L(2.704692281550877810424745289838790693708E-5),
+  L(1.070854930483999749316546199273521063543E-3),
+  L(2.282373093495295842598097265627962125411E-2),
+  L(2.692025460665354148328762368240343249830E-1),
+  L(1.739892942593664447220951225734811133759E0),
+  L(5.890727576752230385342377570386657229324E0),
+  L(9.517442287057841500750256954117735128153E0),
+  L(6.100616353935338240775363403030137736013E0),
+ /* 1.000000000000000000000000000000000000000E0 */
+};
+
+/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2),
+   Peak relative error 3.0e-36
+   0.25 <= 1/x <= 0.3125  */
+#define NP3r2_4N 9
+static const _Float128 P3r2_4N[NP3r2_4N + 1] = {
+  L(8.240803130988044478595580300846665863782E-8),
+  L(1.179418958381961224222969866406483744580E-5),
+  L(6.179787320956386624336959112503824397755E-4),
+  L(1.540270833608687596420595830747166658383E-2),
+  L(1.983904219491512618376375619598837355076E-1),
+  L(1.341465722692038870390470651608301155565E0),
+  L(4.617865326696612898792238245990854646057E0),
+  L(7.435574801812346424460233180412308000587E0),
+  L(4.671327027414635292514599201278557680420E0),
+  L(7.299530852495776936690976966995187714739E-1),
+};
+#define NP3r2_4D 9
+static const _Float128 P3r2_4D[NP3r2_4D + 1] = {
+  L(7.032152009675729604487575753279187576521E-7),
+  L(1.015090352324577615777511269928856742848E-4),
+  L(5.394262184808448484302067955186308730620E-3),
+  L(1.375291438480256110455809354836988584325E-1),
+  L(1.836247144461106304788160919310404376670E0),
+  L(1.314378564254376655001094503090935880349E1),
+  L(4.957184590465712006934452500894672343488E1),
+  L(9.287394244300647738855415178790263465398E1),
+  L(7.652563275535900609085229286020552768399E1),
+  L(2.147042473003074533150718117770093209096E1),
+ /* 1.000000000000000000000000000000000000000E0 */
+};
+
+/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2),
+   Peak relative error 1.0e-35
+   0.3125 <= 1/x <= 0.375  */
+#define NP2r7_3r2N 9
+static const _Float128 P2r7_3r2N[NP2r7_3r2N + 1] = {
+  L(4.599033469240421554219816935160627085991E-7),
+  L(4.665724440345003914596647144630893997284E-5),
+  L(1.684348845667764271596142716944374892756E-3),
+  L(2.802446446884455707845985913454440176223E-2),
+  L(2.321937586453963310008279956042545173930E-1),
+  L(9.640277413988055668692438709376437553804E-1),
+  L(1.911021064710270904508663334033003246028E0),
+  L(1.600811610164341450262992138893970224971E0),
+  L(4.266299218652587901171386591543457861138E-1),
+  L(1.316470424456061252962568223251247207325E-2),
+};
+#define NP2r7_3r2D 8
+static const _Float128 P2r7_3r2D[NP2r7_3r2D + 1] = {
+  L(3.924508608545520758883457108453520099610E-6),
+  L(4.029707889408829273226495756222078039823E-4),
+  L(1.484629715787703260797886463307469600219E-2),
+  L(2.553136379967180865331706538897231588685E-1),
+  L(2.229457223891676394409880026887106228740E0),
+  L(1.005708903856384091956550845198392117318E1),
+  L(2.277082659664386953166629360352385889558E1),
+  L(2.384726835193630788249826630376533988245E1),
+  L(9.700989749041320895890113781610939632410E0),
+ /* 1.000000000000000000000000000000000000000E0 */
+};
+
+/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2),
+   Peak relative error 1.7e-36
+   0.3125 <= 1/x <= 0.4375  */
+#define NP2r3_2r7N 9
+static const _Float128 P2r3_2r7N[NP2r3_2r7N + 1] = {
+  L(3.916766777108274628543759603786857387402E-6),
+  L(3.212176636756546217390661984304645137013E-4),
+  L(9.255768488524816445220126081207248947118E-3),
+  L(1.214853146369078277453080641911700735354E-1),
+  L(7.855163309847214136198449861311404633665E-1),
+  L(2.520058073282978403655488662066019816540E0),
+  L(3.825136484837545257209234285382183711466E0),
+  L(2.432569427554248006229715163865569506873E0),
+  L(4.877934835018231178495030117729800489743E-1),
+  L(1.109902737860249670981355149101343427885E-2),
+};
+#define NP2r3_2r7D 8
+static const _Float128 P2r3_2r7D[NP2r3_2r7D + 1] = {
+  L(3.342307880794065640312646341190547184461E-5),
+  L(2.782182891138893201544978009012096558265E-3),
+  L(8.221304931614200702142049236141249929207E-2),
+  L(1.123728246291165812392918571987858010949E0),
+  L(7.740482453652715577233858317133423434590E0),
+  L(2.737624677567945952953322566311201919139E1),
+  L(4.837181477096062403118304137851260715475E1),
+  L(3.941098643468580791437772701093795299274E1),
+  L(1.245821247166544627558323920382547533630E1),
+ /* 1.000000000000000000000000000000000000000E0 */
+};
+
+/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2),
+   Peak relative error 1.7e-35
+   0.4375 <= 1/x <= 0.5  */
+#define NP2_2r3N 8
+static const _Float128 P2_2r3N[NP2_2r3N + 1] = {
+  L(3.397930802851248553545191160608731940751E-4),
+  L(2.104020902735482418784312825637833698217E-2),
+  L(4.442291771608095963935342749477836181939E-1),
+  L(4.131797328716583282869183304291833754967E0),
+  L(1.819920169779026500146134832455189917589E1),
+  L(3.781779616522937565300309684282401791291E1),
+  L(3.459605449728864218972931220783543410347E1),
+  L(1.173594248397603882049066603238568316561E1),
+  L(9.455702270242780642835086549285560316461E-1),
+};
+#define NP2_2r3D 8
+static const _Float128 P2_2r3D[NP2_2r3D + 1] = {
+  L(2.899568897241432883079888249845707400614E-3),
+  L(1.831107138190848460767699919531132426356E-1),
+  L(3.999350044057883839080258832758908825165E0),
+  L(3.929041535867957938340569419874195303712E1),
+  L(1.884245613422523323068802689915538908291E2),
+  L(4.461469948819229734353852978424629815929E2),
+  L(5.004998753999796821224085972610636347903E2),
+  L(2.386342520092608513170837883757163414100E2),
+  L(3.791322528149347975999851588922424189957E1),
+ /* 1.000000000000000000000000000000000000000E0 */
+};
+
+/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x),
+   Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)),
+   Peak relative error 8.0e-36
+   0 <= 1/x <= .0625  */
+#define NQ16_IN 10
+static const _Float128 Q16_IN[NQ16_IN + 1] = {
+  L(-3.917420835712508001321875734030357393421E-18),
+  L(-4.440311387483014485304387406538069930457E-15),
+  L(-1.951635424076926487780929645954007139616E-12),
+  L(-4.318256438421012555040546775651612810513E-10),
+  L(-5.231244131926180765270446557146989238020E-8),
+  L(-3.540072702902043752460711989234732357653E-6),
+  L(-1.311017536555269966928228052917534882984E-4),
+  L(-2.495184669674631806622008769674827575088E-3),
+  L(-2.141868222987209028118086708697998506716E-2),
+  L(-6.184031415202148901863605871197272650090E-2),
+  L(-1.922298704033332356899546792898156493887E-2),
+};
+#define NQ16_ID 9
+static const _Float128 Q16_ID[NQ16_ID + 1] = {
+  L(3.820418034066293517479619763498400162314E-17),
+  L(4.340702810799239909648911373329149354911E-14),
+  L(1.914985356383416140706179933075303538524E-11),
+  L(4.262333682610888819476498617261895474330E-9),
+  L(5.213481314722233980346462747902942182792E-7),
+  L(3.585741697694069399299005316809954590558E-5),
+  L(1.366513429642842006385029778105539457546E-3),
+  L(2.745282599850704662726337474371355160594E-2),
+  L(2.637644521611867647651200098449903330074E-1),
+  L(1.006953426110765984590782655598680488746E0),
+ /* 1.000000000000000000000000000000000000000E0 */
+ };
+
+/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x),
+   Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)),
+   Peak relative error 1.9e-36
+   0.0625 <= 1/x <= 0.125  */
+#define NQ8_16N 11
+static const _Float128 Q8_16N[NQ8_16N + 1] = {
+  L(-2.028630366670228670781362543615221542291E-17),
+  L(-1.519634620380959966438130374006858864624E-14),
+  L(-4.540596528116104986388796594639405114524E-12),
+  L(-7.085151756671466559280490913558388648274E-10),
+  L(-6.351062671323970823761883833531546885452E-8),
+  L(-3.390817171111032905297982523519503522491E-6),
+  L(-1.082340897018886970282138836861233213972E-4),
+  L(-2.020120801187226444822977006648252379508E-3),
+  L(-2.093169910981725694937457070649605557555E-2),
+  L(-1.092176538874275712359269481414448063393E-1),
+  L(-2.374790947854765809203590474789108718733E-1),
+  L(-1.365364204556573800719985118029601401323E-1),
+};
+#define NQ8_16D 11
+static const _Float128 Q8_16D[NQ8_16D + 1] = {
+  L(1.978397614733632533581207058069628242280E-16),
+  L(1.487361156806202736877009608336766720560E-13),
+  L(4.468041406888412086042576067133365913456E-11),
+  L(7.027822074821007443672290507210594648877E-9),
+  L(6.375740580686101224127290062867976007374E-7),
+  L(3.466887658320002225888644977076410421940E-5),
+  L(1.138625640905289601186353909213719596986E-3),
+  L(2.224470799470414663443449818235008486439E-2),
+  L(2.487052928527244907490589787691478482358E-1),
+  L(1.483927406564349124649083853892380899217E0),
+  L(4.182773513276056975777258788903489507705E0),
+  L(4.419665392573449746043880892524360870944E0),
+ /* 1.000000000000000000000000000000000000000E0 */
+};
+
+/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x),
+   Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)),
+   Peak relative error 1.5e-35
+   0.125 <= 1/x <= 0.1875  */
+#define NQ5_8N 10
+static const _Float128 Q5_8N[NQ5_8N + 1] = {
+  L(-3.656082407740970534915918390488336879763E-13),
+  L(-1.344660308497244804752334556734121771023E-10),
+  L(-1.909765035234071738548629788698150760791E-8),
+  L(-1.366668038160120210269389551283666716453E-6),
+  L(-5.392327355984269366895210704976314135683E-5),
+  L(-1.206268245713024564674432357634540343884E-3),
+  L(-1.515456784370354374066417703736088291287E-2),
+  L(-1.022454301137286306933217746545237098518E-1),
+  L(-3.373438906472495080504907858424251082240E-1),
+  L(-4.510782522110845697262323973549178453405E-1),
+  L(-1.549000892545288676809660828213589804884E-1),
+};
+#define NQ5_8D 10
+static const _Float128 Q5_8D[NQ5_8D + 1] = {
+  L(3.565550843359501079050699598913828460036E-12),
+  L(1.321016015556560621591847454285330528045E-9),
+  L(1.897542728662346479999969679234270605975E-7),
+  L(1.381720283068706710298734234287456219474E-5),
+  L(5.599248147286524662305325795203422873725E-4),
+  L(1.305442352653121436697064782499122164843E-2),
+  L(1.750234079626943298160445750078631894985E-1),
+  L(1.311420542073436520965439883806946678491E0),
+  L(5.162757689856842406744504211089724926650E0),
+  L(9.527760296384704425618556332087850581308E0),
+  L(6.604648207463236667912921642545100248584E0),
+ /* 1.000000000000000000000000000000000000000E0 */
+};
+
+/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x),
+   Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)),
+   Peak relative error 1.3e-35
+   0.1875 <= 1/x <= 0.25  */
+#define NQ4_5N 10
+static const _Float128 Q4_5N[NQ4_5N + 1] = {
+  L(-4.079513568708891749424783046520200903755E-11),
+  L(-9.326548104106791766891812583019664893311E-9),
+  L(-8.016795121318423066292906123815687003356E-7),
+  L(-3.372350544043594415609295225664186750995E-5),
+  L(-7.566238665947967882207277686375417983917E-4),
+  L(-9.248861580055565402130441618521591282617E-3),
+  L(-6.033106131055851432267702948850231270338E-2),
+  L(-1.966908754799996793730369265431584303447E-1),
+  L(-2.791062741179964150755788226623462207560E-1),
+  L(-1.255478605849190549914610121863534191666E-1),
+  L(-4.320429862021265463213168186061696944062E-3),
+};
+#define NQ4_5D 9
+static const _Float128 Q4_5D[NQ4_5D + 1] = {
+  L(3.978497042580921479003851216297330701056E-10),
+  L(9.203304163828145809278568906420772246666E-8),
+  L(8.059685467088175644915010485174545743798E-6),
+  L(3.490187375993956409171098277561669167446E-4),
+  L(8.189109654456872150100501732073810028829E-3),
+  L(1.072572867311023640958725265762483033769E-1),
+  L(7.790606862409960053675717185714576937994E-1),
+  L(3.016049768232011196434185423512777656328E0),
+  L(5.722963851442769787733717162314477949360E0),
+  L(4.510527838428473279647251350931380867663E0),
+ /* 1.000000000000000000000000000000000000000E0 */
+};
+
+/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x),
+   Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)),
+   Peak relative error 2.1e-35
+   0.25 <= 1/x <= 0.3125  */
+#define NQ3r2_4N 9
+static const _Float128 Q3r2_4N[NQ3r2_4N + 1] = {
+  L(-1.087480809271383885936921889040388133627E-8),
+  L(-1.690067828697463740906962973479310170932E-6),
+  L(-9.608064416995105532790745641974762550982E-5),
+  L(-2.594198839156517191858208513873961837410E-3),
+  L(-3.610954144421543968160459863048062977822E-2),
+  L(-2.629866798251843212210482269563961685666E-1),
+  L(-9.709186825881775885917984975685752956660E-1),
+  L(-1.667521829918185121727268867619982417317E0),
+  L(-1.109255082925540057138766105229900943501E0),
+  L(-1.812932453006641348145049323713469043328E-1),
+};
+#define NQ3r2_4D 9
+static const _Float128 Q3r2_4D[NQ3r2_4D + 1] = {
+  L(1.060552717496912381388763753841473407026E-7),
+  L(1.676928002024920520786883649102388708024E-5),
+  L(9.803481712245420839301400601140812255737E-4),
+  L(2.765559874262309494758505158089249012930E-2),
+  L(4.117921827792571791298862613287549140706E-1),
+  L(3.323769515244751267093378361930279161413E0),
+  L(1.436602494405814164724810151689705353670E1),
+  L(3.163087869617098638064881410646782408297E1),
+  L(3.198181264977021649489103980298349589419E1),
+  L(1.203649258862068431199471076202897823272E1),
+ /* 1.000000000000000000000000000000000000000E0  */
+};
+
+/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x),
+   Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)),
+   Peak relative error 1.6e-36
+   0.3125 <= 1/x <= 0.375  */
+#define NQ2r7_3r2N 9
+static const _Float128 Q2r7_3r2N[NQ2r7_3r2N + 1] = {
+  L(-1.723405393982209853244278760171643219530E-7),
+  L(-2.090508758514655456365709712333460087442E-5),
+  L(-9.140104013370974823232873472192719263019E-4),
+  L(-1.871349499990714843332742160292474780128E-2),
+  L(-1.948930738119938669637865956162512983416E-1),
+  L(-1.048764684978978127908439526343174139788E0),
+  L(-2.827714929925679500237476105843643064698E0),
+  L(-3.508761569156476114276988181329773987314E0),
+  L(-1.669332202790211090973255098624488308989E0),
+  L(-1.930796319299022954013840684651016077770E-1),
+};
+#define NQ2r7_3r2D 9
+static const _Float128 Q2r7_3r2D[NQ2r7_3r2D + 1] = {
+  L(1.680730662300831976234547482334347983474E-6),
+  L(2.084241442440551016475972218719621841120E-4),
+  L(9.445316642108367479043541702688736295579E-3),
+  L(2.044637889456631896650179477133252184672E-1),
+  L(2.316091982244297350829522534435350078205E0),
+  L(1.412031891783015085196708811890448488865E1),
+  L(4.583830154673223384837091077279595496149E1),
+  L(7.549520609270909439885998474045974122261E1),
+  L(5.697605832808113367197494052388203310638E1),
+  L(1.601496240876192444526383314589371686234E1),
+  /* 1.000000000000000000000000000000000000000E0 */
+};
+
+/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x),
+   Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)),
+   Peak relative error 9.5e-36
+   0.375 <= 1/x <= 0.4375  */
+#define NQ2r3_2r7N 9
+static const _Float128 Q2r3_2r7N[NQ2r3_2r7N + 1] = {
+  L(-8.603042076329122085722385914954878953775E-7),
+  L(-7.701746260451647874214968882605186675720E-5),
+  L(-2.407932004380727587382493696877569654271E-3),
+  L(-3.403434217607634279028110636919987224188E-2),
+  L(-2.348707332185238159192422084985713102877E-1),
+  L(-7.957498841538254916147095255700637463207E-1),
+  L(-1.258469078442635106431098063707934348577E0),
+  L(-8.162415474676345812459353639449971369890E-1),
+  L(-1.581783890269379690141513949609572806898E-1),
+  L(-1.890595651683552228232308756569450822905E-3),
+};
+#define NQ2r3_2r7D 8
+static const _Float128 Q2r3_2r7D[NQ2r3_2r7D + 1] = {
+  L(8.390017524798316921170710533381568175665E-6),
+  L(7.738148683730826286477254659973968763659E-4),
+  L(2.541480810958665794368759558791634341779E-2),
+  L(3.878879789711276799058486068562386244873E-1),
+  L(3.003783779325811292142957336802456109333E0),
+  L(1.206480374773322029883039064575464497400E1),
+  L(2.458414064785315978408974662900438351782E1),
+  L(2.367237826273668567199042088835448715228E1),
+  L(9.231451197519171090875569102116321676763E0),
+ /* 1.000000000000000000000000000000000000000E0 */
+};
+
+/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x),
+   Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)),
+   Peak relative error 1.4e-36
+   0.4375 <= 1/x <= 0.5  */
+#define NQ2_2r3N 9
+static const _Float128 Q2_2r3N[NQ2_2r3N + 1] = {
+  L(-5.552507516089087822166822364590806076174E-6),
+  L(-4.135067659799500521040944087433752970297E-4),
+  L(-1.059928728869218962607068840646564457980E-2),
+  L(-1.212070036005832342565792241385459023801E-1),
+  L(-6.688350110633603958684302153362735625156E-1),
+  L(-1.793587878197360221340277951304429821582E0),
+  L(-2.225407682237197485644647380483725045326E0),
+  L(-1.123402135458940189438898496348239744403E0),
+  L(-1.679187241566347077204805190763597299805E-1),
+  L(-1.458550613639093752909985189067233504148E-3),
+};
+#define NQ2_2r3D 8
+static const _Float128 Q2_2r3D[NQ2_2r3D + 1] = {
+  L(5.415024336507980465169023996403597916115E-5),
+  L(4.179246497380453022046357404266022870788E-3),
+  L(1.136306384261959483095442402929502368598E-1),
+  L(1.422640343719842213484515445393284072830E0),
+  L(8.968786703393158374728850922289204805764E0),
+  L(2.914542473339246127533384118781216495934E1),
+  L(4.781605421020380669870197378210457054685E1),
+  L(3.693865837171883152382820584714795072937E1),
+  L(1.153220502744204904763115556224395893076E1),
+  /* 1.000000000000000000000000000000000000000E0 */
+};
+
+
+/* Evaluate P[n] x^n  +  P[n-1] x^(n-1)  +  ...  +  P[0] */
+
+static _Float128
+neval (_Float128 x, const _Float128 *p, int n)
+{
+  _Float128 y;
+
+  p += n;
+  y = *p--;
+  do
+    {
+      y = y * x + *p--;
+    }
+  while (--n > 0);
+  return y;
+}
+
+
+/* Evaluate x^n+1  +  P[n] x^(n)  +  P[n-1] x^(n-1)  +  ...  +  P[0] */
+
+static _Float128
+deval (_Float128 x, const _Float128 *p, int n)
+{
+  _Float128 y;
+
+  p += n;
+  y = x + *p--;
+  do
+    {
+      y = y * x + *p--;
+    }
+  while (--n > 0);
+  return y;
+}
+
+
+/* Bessel function of the first kind, order one.  */
+
+_Float128
+__ieee754_j1l (_Float128 x)
+{
+  _Float128 xx, xinv, z, p, q, c, s, cc, ss;
+
+  if (! isfinite (x))
+    {
+      if (x != x)
+	return x + x;
+      else
+	return 0;
+    }
+  if (x == 0)
+    return x;
+  xx = fabsl (x);
+  if (xx <= L(0x1p-58))
+    {
+      _Float128 ret = x * L(0.5);
+      math_check_force_underflow (ret);
+      if (ret == 0)
+	__set_errno (ERANGE);
+      return ret;
+    }
+  if (xx <= 2)
+    {
+      /* 0 <= x <= 2 */
+      z = xx * xx;
+      p = xx * z * neval (z, J0_2N, NJ0_2N) / deval (z, J0_2D, NJ0_2D);
+      p += L(0.5) * xx;
+      if (x < 0)
+	p = -p;
+      return p;
+    }
+
+  /* X = x - 3 pi/4
+     cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4)
+     = 1/sqrt(2) * (-cos(x) + sin(x))
+     sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4)
+     = -1/sqrt(2) * (sin(x) + cos(x))
+     cf. Fdlibm.  */
+  __sincosl (xx, &s, &c);
+  ss = -s - c;
+  cc = s - c;
+  if (xx <= LDBL_MAX / 2)
+    {
+      z = __cosl (xx + xx);
+      if ((s * c) > 0)
+	cc = z / ss;
+      else
+	ss = z / cc;
+    }
+
+  if (xx > L(0x1p256))
+    {
+      z = ONEOSQPI * cc / __ieee754_sqrtl (xx);
+      if (x < 0)
+	z = -z;
+      return z;
+    }
+
+  xinv = 1 / xx;
+  z = xinv * xinv;
+  if (xinv <= 0.25)
+    {
+      if (xinv <= 0.125)
+	{
+	  if (xinv <= 0.0625)
+	    {
+	      p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID);
+	      q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID);
+	    }
+	  else
+	    {
+	      p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D);
+	      q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D);
+	    }
+	}
+      else if (xinv <= 0.1875)
+	{
+	  p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D);
+	  q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D);
+	}
+      else
+	{
+	  p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D);
+	  q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D);
+	}
+    }				/* .25 */
+  else /* if (xinv <= 0.5) */
+    {
+      if (xinv <= 0.375)
+	{
+	  if (xinv <= 0.3125)
+	    {
+	      p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D);
+	      q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D);
+	    }
+	  else
+	    {
+	      p = neval (z, P2r7_3r2N, NP2r7_3r2N)
+		  / deval (z, P2r7_3r2D, NP2r7_3r2D);
+	      q = neval (z, Q2r7_3r2N, NQ2r7_3r2N)
+		  / deval (z, Q2r7_3r2D, NQ2r7_3r2D);
+	    }
+	}
+      else if (xinv <= 0.4375)
+	{
+	  p = neval (z, P2r3_2r7N, NP2r3_2r7N)
+	      / deval (z, P2r3_2r7D, NP2r3_2r7D);
+	  q = neval (z, Q2r3_2r7N, NQ2r3_2r7N)
+	      / deval (z, Q2r3_2r7D, NQ2r3_2r7D);
+	}
+      else
+	{
+	  p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D);
+	  q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D);
+	}
+    }
+  p = 1 + z * p;
+  q = z * q;
+  q = q * xinv + L(0.375) * xinv;
+  z = ONEOSQPI * (p * cc - q * ss) / __ieee754_sqrtl (xx);
+  if (x < 0)
+    z = -z;
+  return z;
+}
+strong_alias (__ieee754_j1l, __j1l_finite)
+
+
+/* Y1(x) = 2/pi * (log(x) * J1(x) - 1/x) + x R(x^2)
+   Peak relative error 6.2e-38
+   0 <= x <= 2   */
+#define NY0_2N 7
+static _Float128 Y0_2N[NY0_2N + 1] = {
+  L(-6.804415404830253804408698161694720833249E19),
+  L(1.805450517967019908027153056150465849237E19),
+  L(-8.065747497063694098810419456383006737312E17),
+  L(1.401336667383028259295830955439028236299E16),
+  L(-1.171654432898137585000399489686629680230E14),
+  L(5.061267920943853732895341125243428129150E11),
+  L(-1.096677850566094204586208610960870217970E9),
+  L(9.541172044989995856117187515882879304461E5),
+};
+#define NY0_2D 7
+static _Float128 Y0_2D[NY0_2D + 1] = {
+  L(3.470629591820267059538637461549677594549E20),
+  L(4.120796439009916326855848107545425217219E18),
+  L(2.477653371652018249749350657387030814542E16),
+  L(9.954678543353888958177169349272167762797E13),
+  L(2.957927997613630118216218290262851197754E11),
+  L(6.748421382188864486018861197614025972118E8),
+  L(1.173453425218010888004562071020305709319E6),
+  L(1.450335662961034949894009554536003377187E3),
+  /* 1.000000000000000000000000000000000000000E0 */
+};
+
+
+/* Bessel function of the second kind, order one.  */
+
+_Float128
+__ieee754_y1l (_Float128 x)
+{
+  _Float128 xx, xinv, z, p, q, c, s, cc, ss;
+
+  if (! isfinite (x))
+    return 1 / (x + x * x);
+  if (x <= 0)
+    {
+      if (x < 0)
+	return (zero / (zero * x));
+      return -1 / zero; /* -inf and divide by zero exception.  */
+    }
+  xx = fabsl (x);
+  if (xx <= 0x1p-114)
+    {
+      z = -TWOOPI / x;
+      if (isinf (z))
+	__set_errno (ERANGE);
+      return z;
+    }
+  if (xx <= 2)
+    {
+      /* 0 <= x <= 2 */
+      SET_RESTORE_ROUNDL (FE_TONEAREST);
+      z = xx * xx;
+      p = xx * neval (z, Y0_2N, NY0_2N) / deval (z, Y0_2D, NY0_2D);
+      p = -TWOOPI / xx + p;
+      p = TWOOPI * __ieee754_logl (x) * __ieee754_j1l (x) + p;
+      return p;
+    }
+
+  /* X = x - 3 pi/4
+     cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4)
+     = 1/sqrt(2) * (-cos(x) + sin(x))
+     sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4)
+     = -1/sqrt(2) * (sin(x) + cos(x))
+     cf. Fdlibm.  */
+  __sincosl (xx, &s, &c);
+  ss = -s - c;
+  cc = s - c;
+  if (xx <= LDBL_MAX / 2)
+    {
+      z = __cosl (xx + xx);
+      if ((s * c) > 0)
+	cc = z / ss;
+      else
+	ss = z / cc;
+    }
+
+  if (xx > L(0x1p256))
+    return ONEOSQPI * ss / __ieee754_sqrtl (xx);
+
+  xinv = 1 / xx;
+  z = xinv * xinv;
+  if (xinv <= 0.25)
+    {
+      if (xinv <= 0.125)
+	{
+	  if (xinv <= 0.0625)
+	    {
+	      p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID);
+	      q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID);
+	    }
+	  else
+	    {
+	      p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D);
+	      q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D);
+	    }
+	}
+      else if (xinv <= 0.1875)
+	{
+	  p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D);
+	  q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D);
+	}
+      else
+	{
+	  p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D);
+	  q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D);
+	}
+    }				/* .25 */
+  else /* if (xinv <= 0.5) */
+    {
+      if (xinv <= 0.375)
+	{
+	  if (xinv <= 0.3125)
+	    {
+	      p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D);
+	      q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D);
+	    }
+	  else
+	    {
+	      p = neval (z, P2r7_3r2N, NP2r7_3r2N)
+		  / deval (z, P2r7_3r2D, NP2r7_3r2D);
+	      q = neval (z, Q2r7_3r2N, NQ2r7_3r2N)
+		  / deval (z, Q2r7_3r2D, NQ2r7_3r2D);
+	    }
+	}
+      else if (xinv <= 0.4375)
+	{
+	  p = neval (z, P2r3_2r7N, NP2r3_2r7N)
+	      / deval (z, P2r3_2r7D, NP2r3_2r7D);
+	  q = neval (z, Q2r3_2r7N, NQ2r3_2r7N)
+	      / deval (z, Q2r3_2r7D, NQ2r3_2r7D);
+	}
+      else
+	{
+	  p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D);
+	  q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D);
+	}
+    }
+  p = 1 + z * p;
+  q = z * q;
+  q = q * xinv + L(0.375) * xinv;
+  z = ONEOSQPI * (p * ss + q * cc) / __ieee754_sqrtl (xx);
+  return z;
+}
+strong_alias (__ieee754_y1l, __y1l_finite)