1 files changed, 948 insertions, 0 deletions

diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_erfl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_erfl.c
new file mode 100644
index 0000000000..e5dfae9636
--- /dev/null
+++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_erfl.c
@@ -0,0 +1,948 @@
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+/* Modifications and expansions for 128-bit long double are
+   Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
+   and are incorporated herein by permission of the author.  The author
+   reserves the right to distribute this material elsewhere under different
+   copying permissions.  These modifications are distributed here under
+   the following terms:
+
+    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/>.  */
+
+/* double erf(double x)
+ * double erfc(double x)
+ *			     x
+ *		      2      |\
+ *     erf(x)  =  ---------  | exp(-t*t)dt
+ *		   sqrt(pi) \|
+ *			     0
+ *
+ *     erfc(x) =  1-erf(x)
+ *  Note that
+ *		erf(-x) = -erf(x)
+ *		erfc(-x) = 2 - erfc(x)
+ *
+ * Method:
+ *	1.  erf(x)  = x + x*R(x^2) for |x| in [0, 7/8]
+ *	   Remark. The formula is derived by noting
+ *          erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....)
+ *	   and that
+ *          2/sqrt(pi) = 1.128379167095512573896158903121545171688
+ *	   is close to one.
+ *
+ *      1a. erf(x)  = 1 - erfc(x), for |x| > 1.0
+ *          erfc(x) = 1 - erf(x)  if |x| < 1/4
+ *
+ *      2. For |x| in [7/8, 1], let s = |x| - 1, and
+ *         c = 0.84506291151 rounded to single (24 bits)
+ *	erf(s + c)  = sign(x) * (c  + P1(s)/Q1(s))
+ *	   Remark: here we use the taylor series expansion at x=1.
+ *		erf(1+s) = erf(1) + s*Poly(s)
+ *			 = 0.845.. + P1(s)/Q1(s)
+ *	   Note that |P1/Q1|< 0.078 for x in [0.84375,1.25]
+ *
+ *      3. For x in [1/4, 5/4],
+ *	erfc(s + const)  = erfc(const)  + s P1(s)/Q1(s)
+ *              for const = 1/4, 3/8, ..., 9/8
+ *              and 0 <= s <= 1/8 .
+ *
+ *      4. For x in [5/4, 107],
+ *	erfc(x) = (1/x)*exp(-x*x-0.5625 + R(z))
+ *              z=1/x^2
+ *         The interval is partitioned into several segments
+ *         of width 1/8 in 1/x.
+ *
+ *      Note1:
+ *	   To compute exp(-x*x-0.5625+R/S), let s be a single
+ *	   precision number and s := x; then
+ *		-x*x = -s*s + (s-x)*(s+x)
+ *	        exp(-x*x-0.5626+R/S) =
+ *			exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S);
+ *      Note2:
+ *	   Here 4 and 5 make use of the asymptotic series
+ *			  exp(-x*x)
+ *		erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) )
+ *			  x*sqrt(pi)
+ *
+ *      5. For inf > x >= 107
+ *	erf(x)  = sign(x) *(1 - tiny)  (raise inexact)
+ *	erfc(x) = tiny*tiny (raise underflow) if x > 0
+ *			= 2 - tiny if x<0
+ *
+ *      7. Special case:
+ *	erf(0)  = 0, erf(inf)  = 1, erf(-inf) = -1,
+ *	erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2,
+ *		erfc/erf(NaN) is NaN
+ */
+
+#include <errno.h>
+#include <float.h>
+#include <math.h>
+#include <math_private.h>
+
+/* 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;
+}
+
+
+
+static const _Float128
+tiny = L(1e-4931),
+  one = 1,
+  two = 2,
+  /* 2/sqrt(pi) - 1 */
+  efx = L(1.2837916709551257389615890312154517168810E-1);
+
+
+/* erf(x)  = x  + x R(x^2)
+   0 <= x <= 7/8
+   Peak relative error 1.8e-35  */
+#define NTN1 8
+static const _Float128 TN1[NTN1 + 1] =
+{
+ L(-3.858252324254637124543172907442106422373E10),
+  L(9.580319248590464682316366876952214879858E10),
+  L(1.302170519734879977595901236693040544854E10),
+  L(2.922956950426397417800321486727032845006E9),
+  L(1.764317520783319397868923218385468729799E8),
+  L(1.573436014601118630105796794840834145120E7),
+  L(4.028077380105721388745632295157816229289E5),
+  L(1.644056806467289066852135096352853491530E4),
+  L(3.390868480059991640235675479463287886081E1)
+};
+#define NTD1 8
+static const _Float128 TD1[NTD1 + 1] =
+{
+  L(-3.005357030696532927149885530689529032152E11),
+  L(-1.342602283126282827411658673839982164042E11),
+  L(-2.777153893355340961288511024443668743399E10),
+  L(-3.483826391033531996955620074072768276974E9),
+  L(-2.906321047071299585682722511260895227921E8),
+  L(-1.653347985722154162439387878512427542691E7),
+  L(-6.245520581562848778466500301865173123136E5),
+  L(-1.402124304177498828590239373389110545142E4),
+  L(-1.209368072473510674493129989468348633579E2)
+/* 1.0E0 */
+};
+
+
+/* erf(z+1)  = erf_const + P(z)/Q(z)
+   -.125 <= z <= 0
+   Peak relative error 7.3e-36  */
+static const _Float128 erf_const = L(0.845062911510467529296875);
+#define NTN2 8
+static const _Float128 TN2[NTN2 + 1] =
+{
+ L(-4.088889697077485301010486931817357000235E1),
+  L(7.157046430681808553842307502826960051036E3),
+ L(-2.191561912574409865550015485451373731780E3),
+  L(2.180174916555316874988981177654057337219E3),
+  L(2.848578658049670668231333682379720943455E2),
+  L(1.630362490952512836762810462174798925274E2),
+  L(6.317712353961866974143739396865293596895E0),
+  L(2.450441034183492434655586496522857578066E1),
+  L(5.127662277706787664956025545897050896203E-1)
+};
+#define NTD2 8
+static const _Float128 TD2[NTD2 + 1] =
+{
+  L(1.731026445926834008273768924015161048885E4),
+  L(1.209682239007990370796112604286048173750E4),
+  L(1.160950290217993641320602282462976163857E4),
+  L(5.394294645127126577825507169061355698157E3),
+  L(2.791239340533632669442158497532521776093E3),
+  L(8.989365571337319032943005387378993827684E2),
+  L(2.974016493766349409725385710897298069677E2),
+  L(6.148192754590376378740261072533527271947E1),
+  L(1.178502892490738445655468927408440847480E1)
+ /* 1.0E0 */
+};
+
+
+/* erfc(x + 0.25) = erfc(0.25) + x R(x)
+   0 <= x < 0.125
+   Peak relative error 1.4e-35  */
+#define NRNr13 8
+static const _Float128 RNr13[NRNr13 + 1] =
+{
+ L(-2.353707097641280550282633036456457014829E3),
+  L(3.871159656228743599994116143079870279866E2),
+ L(-3.888105134258266192210485617504098426679E2),
+ L(-2.129998539120061668038806696199343094971E1),
+ L(-8.125462263594034672468446317145384108734E1),
+  L(8.151549093983505810118308635926270319660E0),
+ L(-5.033362032729207310462422357772568553670E0),
+ L(-4.253956621135136090295893547735851168471E-2),
+ L(-8.098602878463854789780108161581050357814E-2)
+};
+#define NRDr13 7
+static const _Float128 RDr13[NRDr13 + 1] =
+{
+  L(2.220448796306693503549505450626652881752E3),
+  L(1.899133258779578688791041599040951431383E2),
+  L(1.061906712284961110196427571557149268454E3),
+  L(7.497086072306967965180978101974566760042E1),
+  L(2.146796115662672795876463568170441327274E2),
+  L(1.120156008362573736664338015952284925592E1),
+  L(2.211014952075052616409845051695042741074E1),
+  L(6.469655675326150785692908453094054988938E-1)
+ /* 1.0E0 */
+};
+/* erfc(0.25) = C13a + C13b to extra precision.  */
+static const _Float128 C13a = L(0.723663330078125);
+static const _Float128 C13b = L(1.0279753638067014931732235184287934646022E-5);
+
+
+/* erfc(x + 0.375) = erfc(0.375) + x R(x)
+   0 <= x < 0.125
+   Peak relative error 1.2e-35  */
+#define NRNr14 8
+static const _Float128 RNr14[NRNr14 + 1] =
+{
+ L(-2.446164016404426277577283038988918202456E3),
+  L(6.718753324496563913392217011618096698140E2),
+ L(-4.581631138049836157425391886957389240794E2),
+ L(-2.382844088987092233033215402335026078208E1),
+ L(-7.119237852400600507927038680970936336458E1),
+  L(1.313609646108420136332418282286454287146E1),
+ L(-6.188608702082264389155862490056401365834E0),
+ L(-2.787116601106678287277373011101132659279E-2),
+ L(-2.230395570574153963203348263549700967918E-2)
+};
+#define NRDr14 7
+static const _Float128 RDr14[NRDr14 + 1] =
+{
+  L(2.495187439241869732696223349840963702875E3),
+  L(2.503549449872925580011284635695738412162E2),
+  L(1.159033560988895481698051531263861842461E3),
+  L(9.493751466542304491261487998684383688622E1),
+  L(2.276214929562354328261422263078480321204E2),
+  L(1.367697521219069280358984081407807931847E1),
+  L(2.276988395995528495055594829206582732682E1),
+  L(7.647745753648996559837591812375456641163E-1)
+ /* 1.0E0 */
+};
+/* erfc(0.375) = C14a + C14b to extra precision.  */
+static const _Float128 C14a = L(0.5958709716796875);
+static const _Float128 C14b = L(1.2118885490201676174914080878232469565953E-5);
+
+/* erfc(x + 0.5) = erfc(0.5) + x R(x)
+   0 <= x < 0.125
+   Peak relative error 4.7e-36  */
+#define NRNr15 8
+static const _Float128 RNr15[NRNr15 + 1] =
+{
+ L(-2.624212418011181487924855581955853461925E3),
+  L(8.473828904647825181073831556439301342756E2),
+ L(-5.286207458628380765099405359607331669027E2),
+ L(-3.895781234155315729088407259045269652318E1),
+ L(-6.200857908065163618041240848728398496256E1),
+  L(1.469324610346924001393137895116129204737E1),
+ L(-6.961356525370658572800674953305625578903E0),
+  L(5.145724386641163809595512876629030548495E-3),
+  L(1.990253655948179713415957791776180406812E-2)
+};
+#define NRDr15 7
+static const _Float128 RDr15[NRDr15 + 1] =
+{
+  L(2.986190760847974943034021764693341524962E3),
+  L(5.288262758961073066335410218650047725985E2),
+  L(1.363649178071006978355113026427856008978E3),
+  L(1.921707975649915894241864988942255320833E2),
+  L(2.588651100651029023069013885900085533226E2),
+  L(2.628752920321455606558942309396855629459E1),
+  L(2.455649035885114308978333741080991380610E1),
+  L(1.378826653595128464383127836412100939126E0)
+  /* 1.0E0 */
+};
+/* erfc(0.5) = C15a + C15b to extra precision.  */
+static const _Float128 C15a = L(0.4794921875);
+static const _Float128 C15b = L(7.9346869534623172533461080354712635484242E-6);
+
+/* erfc(x + 0.625) = erfc(0.625) + x R(x)
+   0 <= x < 0.125
+   Peak relative error 5.1e-36  */
+#define NRNr16 8
+static const _Float128 RNr16[NRNr16 + 1] =
+{
+ L(-2.347887943200680563784690094002722906820E3),
+  L(8.008590660692105004780722726421020136482E2),
+ L(-5.257363310384119728760181252132311447963E2),
+ L(-4.471737717857801230450290232600243795637E1),
+ L(-4.849540386452573306708795324759300320304E1),
+  L(1.140885264677134679275986782978655952843E1),
+ L(-6.731591085460269447926746876983786152300E0),
+  L(1.370831653033047440345050025876085121231E-1),
+  L(2.022958279982138755020825717073966576670E-2),
+};
+#define NRDr16 7
+static const _Float128 RDr16[NRDr16 + 1] =
+{
+  L(3.075166170024837215399323264868308087281E3),
+  L(8.730468942160798031608053127270430036627E2),
+  L(1.458472799166340479742581949088453244767E3),
+  L(3.230423687568019709453130785873540386217E2),
+  L(2.804009872719893612081109617983169474655E2),
+  L(4.465334221323222943418085830026979293091E1),
+  L(2.612723259683205928103787842214809134746E1),
+  L(2.341526751185244109722204018543276124997E0),
+  /* 1.0E0 */
+};
+/* erfc(0.625) = C16a + C16b to extra precision.  */
+static const _Float128 C16a = L(0.3767547607421875);
+static const _Float128 C16b = L(4.3570693945275513594941232097252997287766E-6);
+
+/* erfc(x + 0.75) = erfc(0.75) + x R(x)
+   0 <= x < 0.125
+   Peak relative error 1.7e-35  */
+#define NRNr17 8
+static const _Float128 RNr17[NRNr17 + 1] =
+{
+  L(-1.767068734220277728233364375724380366826E3),
+  L(6.693746645665242832426891888805363898707E2),
+  L(-4.746224241837275958126060307406616817753E2),
+  L(-2.274160637728782675145666064841883803196E1),
+  L(-3.541232266140939050094370552538987982637E1),
+  L(6.988950514747052676394491563585179503865E0),
+  L(-5.807687216836540830881352383529281215100E0),
+  L(3.631915988567346438830283503729569443642E-1),
+  L(-1.488945487149634820537348176770282391202E-2)
+};
+#define NRDr17 7
+static const _Float128 RDr17[NRDr17 + 1] =
+{
+  L(2.748457523498150741964464942246913394647E3),
+  L(1.020213390713477686776037331757871252652E3),
+  L(1.388857635935432621972601695296561952738E3),
+  L(3.903363681143817750895999579637315491087E2),
+  L(2.784568344378139499217928969529219886578E2),
+  L(5.555800830216764702779238020065345401144E1),
+  L(2.646215470959050279430447295801291168941E1),
+  L(2.984905282103517497081766758550112011265E0),
+  /* 1.0E0 */
+};
+/* erfc(0.75) = C17a + C17b to extra precision.  */
+static const _Float128 C17a = L(0.2888336181640625);
+static const _Float128 C17b = L(1.0748182422368401062165408589222625794046E-5);
+
+
+/* erfc(x + 0.875) = erfc(0.875) + x R(x)
+   0 <= x < 0.125
+   Peak relative error 2.2e-35  */
+#define NRNr18 8
+static const _Float128 RNr18[NRNr18 + 1] =
+{
+ L(-1.342044899087593397419622771847219619588E3),
+  L(6.127221294229172997509252330961641850598E2),
+ L(-4.519821356522291185621206350470820610727E2),
+  L(1.223275177825128732497510264197915160235E1),
+ L(-2.730789571382971355625020710543532867692E1),
+  L(4.045181204921538886880171727755445395862E0),
+ L(-4.925146477876592723401384464691452700539E0),
+  L(5.933878036611279244654299924101068088582E-1),
+ L(-5.557645435858916025452563379795159124753E-2)
+};
+#define NRDr18 7
+static const _Float128 RDr18[NRDr18 + 1] =
+{
+  L(2.557518000661700588758505116291983092951E3),
+  L(1.070171433382888994954602511991940418588E3),
+  L(1.344842834423493081054489613250688918709E3),
+  L(4.161144478449381901208660598266288188426E2),
+  L(2.763670252219855198052378138756906980422E2),
+  L(5.998153487868943708236273854747564557632E1),
+  L(2.657695108438628847733050476209037025318E1),
+  L(3.252140524394421868923289114410336976512E0),
+  /* 1.0E0 */
+};
+/* erfc(0.875) = C18a + C18b to extra precision.  */
+static const _Float128 C18a = L(0.215911865234375);
+static const _Float128 C18b = L(1.3073705765341685464282101150637224028267E-5);
+
+/* erfc(x + 1.0) = erfc(1.0) + x R(x)
+   0 <= x < 0.125
+   Peak relative error 1.6e-35  */
+#define NRNr19 8
+static const _Float128 RNr19[NRNr19 + 1] =
+{
+ L(-1.139180936454157193495882956565663294826E3),
+  L(6.134903129086899737514712477207945973616E2),
+ L(-4.628909024715329562325555164720732868263E2),
+  L(4.165702387210732352564932347500364010833E1),
+ L(-2.286979913515229747204101330405771801610E1),
+  L(1.870695256449872743066783202326943667722E0),
+ L(-4.177486601273105752879868187237000032364E0),
+  L(7.533980372789646140112424811291782526263E-1),
+ L(-8.629945436917752003058064731308767664446E-2)
+};
+#define NRDr19 7
+static const _Float128 RDr19[NRDr19 + 1] =
+{
+  L(2.744303447981132701432716278363418643778E3),
+  L(1.266396359526187065222528050591302171471E3),
+  L(1.466739461422073351497972255511919814273E3),
+  L(4.868710570759693955597496520298058147162E2),
+  L(2.993694301559756046478189634131722579643E2),
+  L(6.868976819510254139741559102693828237440E1),
+  L(2.801505816247677193480190483913753613630E1),
+  L(3.604439909194350263552750347742663954481E0),
+  /* 1.0E0 */
+};
+/* erfc(1.0) = C19a + C19b to extra precision.  */
+static const _Float128 C19a = L(0.15728759765625);
+static const _Float128 C19b = L(1.1609394035130658779364917390740703933002E-5);
+
+/* erfc(x + 1.125) = erfc(1.125) + x R(x)
+   0 <= x < 0.125
+   Peak relative error 3.6e-36  */
+#define NRNr20 8
+static const _Float128 RNr20[NRNr20 + 1] =
+{
+ L(-9.652706916457973956366721379612508047640E2),
+  L(5.577066396050932776683469951773643880634E2),
+ L(-4.406335508848496713572223098693575485978E2),
+  L(5.202893466490242733570232680736966655434E1),
+ L(-1.931311847665757913322495948705563937159E1),
+ L(-9.364318268748287664267341457164918090611E-2),
+ L(-3.306390351286352764891355375882586201069E0),
+  L(7.573806045289044647727613003096916516475E-1),
+ L(-9.611744011489092894027478899545635991213E-2)
+};
+#define NRDr20 7
+static const _Float128 RDr20[NRDr20 + 1] =
+{
+  L(3.032829629520142564106649167182428189014E3),
+  L(1.659648470721967719961167083684972196891E3),
+  L(1.703545128657284619402511356932569292535E3),
+  L(6.393465677731598872500200253155257708763E2),
+  L(3.489131397281030947405287112726059221934E2),
+  L(8.848641738570783406484348434387611713070E1),
+  L(3.132269062552392974833215844236160958502E1),
+  L(4.430131663290563523933419966185230513168E0)
+ /* 1.0E0 */
+};
+/* erfc(1.125) = C20a + C20b to extra precision.  */
+static const _Float128 C20a = L(0.111602783203125);
+static const _Float128 C20b = L(8.9850951672359304215530728365232161564636E-6);
+
+/* erfc(1/x) = 1/x exp (-1/x^2 - 0.5625 + R(1/x^2))
+   7/8 <= 1/x < 1
+   Peak relative error 1.4e-35  */
+#define NRNr8 9
+static const _Float128 RNr8[NRNr8 + 1] =
+{
+  L(3.587451489255356250759834295199296936784E1),
+  L(5.406249749087340431871378009874875889602E2),
+  L(2.931301290625250886238822286506381194157E3),
+  L(7.359254185241795584113047248898753470923E3),
+  L(9.201031849810636104112101947312492532314E3),
+  L(5.749697096193191467751650366613289284777E3),
+  L(1.710415234419860825710780802678697889231E3),
+  L(2.150753982543378580859546706243022719599E2),
+  L(8.740953582272147335100537849981160931197E0),
+  L(4.876422978828717219629814794707963640913E-2)
+};
+#define NRDr8 8
+static const _Float128 RDr8[NRDr8 + 1] =
+{
+  L(6.358593134096908350929496535931630140282E1),
+  L(9.900253816552450073757174323424051765523E2),
+  L(5.642928777856801020545245437089490805186E3),
+  L(1.524195375199570868195152698617273739609E4),
+  L(2.113829644500006749947332935305800887345E4),
+  L(1.526438562626465706267943737310282977138E4),
+  L(5.561370922149241457131421914140039411782E3),
+  L(9.394035530179705051609070428036834496942E2),
+  L(6.147019596150394577984175188032707343615E1)
+  /* 1.0E0 */
+};
+
+/* erfc(1/x) = 1/x exp (-1/x^2 - 0.5625 + R(1/x^2))
+   0.75 <= 1/x <= 0.875
+   Peak relative error 2.0e-36  */
+#define NRNr7 9
+static const _Float128 RNr7[NRNr7 + 1] =
+{
+ L(1.686222193385987690785945787708644476545E1),
+ L(1.178224543567604215602418571310612066594E3),
+ L(1.764550584290149466653899886088166091093E4),
+ L(1.073758321890334822002849369898232811561E5),
+ L(3.132840749205943137619839114451290324371E5),
+ L(4.607864939974100224615527007793867585915E5),
+ L(3.389781820105852303125270837910972384510E5),
+ L(1.174042187110565202875011358512564753399E5),
+ L(1.660013606011167144046604892622504338313E4),
+ L(6.700393957480661937695573729183733234400E2)
+};
+#define NRDr7 9
+static const _Float128 RDr7[NRDr7 + 1] =
+{
+L(-1.709305024718358874701575813642933561169E3),
+L(-3.280033887481333199580464617020514788369E4),
+L(-2.345284228022521885093072363418750835214E5),
+L(-8.086758123097763971926711729242327554917E5),
+L(-1.456900414510108718402423999575992450138E6),
+L(-1.391654264881255068392389037292702041855E6),
+L(-6.842360801869939983674527468509852583855E5),
+L(-1.597430214446573566179675395199807533371E5),
+L(-1.488876130609876681421645314851760773480E4),
+L(-3.511762950935060301403599443436465645703E2)
+ /* 1.0E0 */
+};
+
+/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2))
+   5/8 <= 1/x < 3/4
+   Peak relative error 1.9e-35  */
+#define NRNr6 9
+static const _Float128 RNr6[NRNr6 + 1] =
+{
+ L(1.642076876176834390623842732352935761108E0),
+ L(1.207150003611117689000664385596211076662E2),
+ L(2.119260779316389904742873816462800103939E3),
+ L(1.562942227734663441801452930916044224174E4),
+ L(5.656779189549710079988084081145693580479E4),
+ L(1.052166241021481691922831746350942786299E5),
+ L(9.949798524786000595621602790068349165758E4),
+ L(4.491790734080265043407035220188849562856E4),
+ L(8.377074098301530326270432059434791287601E3),
+ L(4.506934806567986810091824791963991057083E2)
+};
+#define NRDr6 9
+static const _Float128 RDr6[NRDr6 + 1] =
+{
+L(-1.664557643928263091879301304019826629067E2),
+L(-3.800035902507656624590531122291160668452E3),
+L(-3.277028191591734928360050685359277076056E4),
+L(-1.381359471502885446400589109566587443987E5),
+L(-3.082204287382581873532528989283748656546E5),
+L(-3.691071488256738343008271448234631037095E5),
+L(-2.300482443038349815750714219117566715043E5),
+L(-6.873955300927636236692803579555752171530E4),
+L(-8.262158817978334142081581542749986845399E3),
+L(-2.517122254384430859629423488157361983661E2)
+ /* 1.00 */
+};
+
+/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2))
+   1/2 <= 1/x < 5/8
+   Peak relative error 4.6e-36  */
+#define NRNr5 10
+static const _Float128 RNr5[NRNr5 + 1] =
+{
+L(-3.332258927455285458355550878136506961608E-3),
+L(-2.697100758900280402659586595884478660721E-1),
+L(-6.083328551139621521416618424949137195536E0),
+L(-6.119863528983308012970821226810162441263E1),
+L(-3.176535282475593173248810678636522589861E2),
+L(-8.933395175080560925809992467187963260693E2),
+L(-1.360019508488475978060917477620199499560E3),
+L(-1.075075579828188621541398761300910213280E3),
+L(-4.017346561586014822824459436695197089916E2),
+L(-5.857581368145266249509589726077645791341E1),
+L(-2.077715925587834606379119585995758954399E0)
+};
+#define NRDr5 9
+static const _Float128 RDr5[NRDr5 + 1] =
+{
+ L(3.377879570417399341550710467744693125385E-1),
+ L(1.021963322742390735430008860602594456187E1),
+ L(1.200847646592942095192766255154827011939E2),
+ L(7.118915528142927104078182863387116942836E2),
+ L(2.318159380062066469386544552429625026238E3),
+ L(4.238729853534009221025582008928765281620E3),
+ L(4.279114907284825886266493994833515580782E3),
+ L(2.257277186663261531053293222591851737504E3),
+ L(5.570475501285054293371908382916063822957E2),
+ L(5.142189243856288981145786492585432443560E1)
+ /* 1.0E0 */
+};
+
+/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2))
+   3/8 <= 1/x < 1/2
+   Peak relative error 2.0e-36  */
+#define NRNr4 10
+static const _Float128 RNr4[NRNr4 + 1] =
+{
+ L(3.258530712024527835089319075288494524465E-3),
+ L(2.987056016877277929720231688689431056567E-1),
+ L(8.738729089340199750734409156830371528862E0),
+ L(1.207211160148647782396337792426311125923E2),
+ L(8.997558632489032902250523945248208224445E2),
+ L(3.798025197699757225978410230530640879762E3),
+ L(9.113203668683080975637043118209210146846E3),
+ L(1.203285891339933238608683715194034900149E4),
+ L(8.100647057919140328536743641735339740855E3),
+ L(2.383888249907144945837976899822927411769E3),
+ L(2.127493573166454249221983582495245662319E2)
+};
+#define NRDr4 10
+static const _Float128 RDr4[NRDr4 + 1] =
+{
+L(-3.303141981514540274165450687270180479586E-1),
+L(-1.353768629363605300707949368917687066724E1),
+L(-2.206127630303621521950193783894598987033E2),
+L(-1.861800338758066696514480386180875607204E3),
+L(-8.889048775872605708249140016201753255599E3),
+L(-2.465888106627948210478692168261494857089E4),
+L(-3.934642211710774494879042116768390014289E4),
+L(-3.455077258242252974937480623730228841003E4),
+L(-1.524083977439690284820586063729912653196E4),
+L(-2.810541887397984804237552337349093953857E3),
+L(-1.343929553541159933824901621702567066156E2)
+ /* 1.0E0 */
+};
+
+/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2))
+   1/4 <= 1/x < 3/8
+   Peak relative error 8.4e-37  */
+#define NRNr3 11
+static const _Float128 RNr3[NRNr3 + 1] =
+{
+L(-1.952401126551202208698629992497306292987E-6),
+L(-2.130881743066372952515162564941682716125E-4),
+L(-8.376493958090190943737529486107282224387E-3),
+L(-1.650592646560987700661598877522831234791E-1),
+L(-1.839290818933317338111364667708678163199E0),
+L(-1.216278715570882422410442318517814388470E1),
+L(-4.818759344462360427612133632533779091386E1),
+L(-1.120994661297476876804405329172164436784E2),
+L(-1.452850765662319264191141091859300126931E2),
+L(-9.485207851128957108648038238656777241333E1),
+L(-2.563663855025796641216191848818620020073E1),
+L(-1.787995944187565676837847610706317833247E0)
+};
+#define NRDr3 10
+static const _Float128 RDr3[NRDr3 + 1] =
+{
+ L(1.979130686770349481460559711878399476903E-4),
+ L(1.156941716128488266238105813374635099057E-2),
+ L(2.752657634309886336431266395637285974292E-1),
+ L(3.482245457248318787349778336603569327521E0),
+ L(2.569347069372696358578399521203959253162E1),
+ L(1.142279000180457419740314694631879921561E2),
+ L(3.056503977190564294341422623108332700840E2),
+ L(4.780844020923794821656358157128719184422E2),
+ L(4.105972727212554277496256802312730410518E2),
+ L(1.724072188063746970865027817017067646246E2),
+ L(2.815939183464818198705278118326590370435E1)
+ /* 1.0E0 */
+};
+
+/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2))
+   1/8 <= 1/x < 1/4
+   Peak relative error 1.5e-36  */
+#define NRNr2 11
+static const _Float128 RNr2[NRNr2 + 1] =
+{
+L(-2.638914383420287212401687401284326363787E-8),
+L(-3.479198370260633977258201271399116766619E-6),
+L(-1.783985295335697686382487087502222519983E-4),
+L(-4.777876933122576014266349277217559356276E-3),
+L(-7.450634738987325004070761301045014986520E-2),
+L(-7.068318854874733315971973707247467326619E-1),
+L(-4.113919921935944795764071670806867038732E0),
+L(-1.440447573226906222417767283691888875082E1),
+L(-2.883484031530718428417168042141288943905E1),
+L(-2.990886974328476387277797361464279931446E1),
+L(-1.325283914915104866248279787536128997331E1),
+L(-1.572436106228070195510230310658206154374E0)
+};
+#define NRDr2 10
+static const _Float128 RDr2[NRDr2 + 1] =
+{
+ L(2.675042728136731923554119302571867799673E-6),
+ L(2.170997868451812708585443282998329996268E-4),
+ L(7.249969752687540289422684951196241427445E-3),
+ L(1.302040375859768674620410563307838448508E-1),
+ L(1.380202483082910888897654537144485285549E0),
+ L(8.926594113174165352623847870299170069350E0),
+ L(3.521089584782616472372909095331572607185E1),
+ L(8.233547427533181375185259050330809105570E1),
+ L(1.072971579885803033079469639073292840135E2),
+ L(6.943803113337964469736022094105143158033E1),
+ L(1.775695341031607738233608307835017282662E1)
+ /* 1.0E0 */
+};
+
+/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2))
+   1/128 <= 1/x < 1/8
+   Peak relative error 2.2e-36  */
+#define NRNr1 9
+static const _Float128 RNr1[NRNr1 + 1] =
+{
+L(-4.250780883202361946697751475473042685782E-8),
+L(-5.375777053288612282487696975623206383019E-6),
+L(-2.573645949220896816208565944117382460452E-4),
+L(-6.199032928113542080263152610799113086319E-3),
+L(-8.262721198693404060380104048479916247786E-2),
+L(-6.242615227257324746371284637695778043982E-1),
+L(-2.609874739199595400225113299437099626386E0),
+L(-5.581967563336676737146358534602770006970E0),
+L(-5.124398923356022609707490956634280573882E0),
+L(-1.290865243944292370661544030414667556649E0)
+};
+#define NRDr1 8
+static const _Float128 RDr1[NRDr1 + 1] =
+{
+ L(4.308976661749509034845251315983612976224E-6),
+ L(3.265390126432780184125233455960049294580E-4),
+ L(9.811328839187040701901866531796570418691E-3),
+ L(1.511222515036021033410078631914783519649E-1),
+ L(1.289264341917429958858379585970225092274E0),
+ L(6.147640356182230769548007536914983522270E0),
+ L(1.573966871337739784518246317003956180750E1),
+ L(1.955534123435095067199574045529218238263E1),
+ L(9.472613121363135472247929109615785855865E0)
+  /* 1.0E0 */
+};
+
+
+_Float128
+__erfl (_Float128 x)
+{
+  _Float128 a, y, z;
+  int32_t i, ix, sign;
+  ieee854_long_double_shape_type u;
+
+  u.value = x;
+  sign = u.parts32.w0;
+  ix = sign & 0x7fffffff;
+
+  if (ix >= 0x7fff0000)
+    {				/* erf(nan)=nan */
+      i = ((sign & 0xffff0000) >> 31) << 1;
+      return (_Float128) (1 - i) + one / x;	/* erf(+-inf)=+-1 */
+    }
+
+  if (ix >= 0x3fff0000) /* |x| >= 1.0 */
+    {
+      if (ix >= 0x40030000 && sign > 0)
+	return one; /* x >= 16, avoid spurious underflow from erfc.  */
+      y = __erfcl (x);
+      return (one - y);
+      /*    return (one - __erfcl (x)); */
+    }
+  u.parts32.w0 = ix;
+  a = u.value;
+  z = x * x;
+  if (ix < 0x3ffec000)  /* a < 0.875 */
+    {
+      if (ix < 0x3fc60000) /* |x|<2**-57 */
+	{
+	  if (ix < 0x00080000)
+	    {
+	      /* Avoid spurious underflow.  */
+	      _Float128 ret =  0.0625 * (16.0 * x + (16.0 * efx) * x);
+	      math_check_force_underflow (ret);
+	      return ret;
+	    }
+	  return x + efx * x;
+	}
+      y = a + a * neval (z, TN1, NTN1) / deval (z, TD1, NTD1);
+    }
+  else
+    {
+      a = a - one;
+      y = erf_const + neval (a, TN2, NTN2) / deval (a, TD2, NTD2);
+    }
+
+  if (sign & 0x80000000) /* x < 0 */
+    y = -y;
+  return( y );
+}
+
+weak_alias (__erfl, erfl)
+_Float128
+__erfcl (_Float128 x)
+{
+  _Float128 y, z, p, r;
+  int32_t i, ix, sign;
+  ieee854_long_double_shape_type u;
+
+  u.value = x;
+  sign = u.parts32.w0;
+  ix = sign & 0x7fffffff;
+  u.parts32.w0 = ix;
+
+  if (ix >= 0x7fff0000)
+    {				/* erfc(nan)=nan */
+      /* erfc(+-inf)=0,2 */
+      return (_Float128) (((u_int32_t) sign >> 31) << 1) + one / x;
+    }
+
+  if (ix < 0x3ffd0000) /* |x| <1/4 */
+    {
+      if (ix < 0x3f8d0000) /* |x|<2**-114 */
+	return one - x;
+      return one - __erfl (x);
+    }
+  if (ix < 0x3fff4000) /* 1.25 */
+    {
+      x = u.value;
+      i = 8.0 * x;
+      switch (i)
+	{
+	case 2:
+	  z = x - L(0.25);
+	  y = C13b + z * neval (z, RNr13, NRNr13) / deval (z, RDr13, NRDr13);
+	  y += C13a;
+	  break;
+	case 3:
+	  z = x - L(0.375);
+	  y = C14b + z * neval (z, RNr14, NRNr14) / deval (z, RDr14, NRDr14);
+	  y += C14a;
+	  break;
+	case 4:
+	  z = x - L(0.5);
+	  y = C15b + z * neval (z, RNr15, NRNr15) / deval (z, RDr15, NRDr15);
+	  y += C15a;
+	  break;
+	case 5:
+	  z = x - L(0.625);
+	  y = C16b + z * neval (z, RNr16, NRNr16) / deval (z, RDr16, NRDr16);
+	  y += C16a;
+	  break;
+	case 6:
+	  z = x - L(0.75);
+	  y = C17b + z * neval (z, RNr17, NRNr17) / deval (z, RDr17, NRDr17);
+	  y += C17a;
+	  break;
+	case 7:
+	  z = x - L(0.875);
+	  y = C18b + z * neval (z, RNr18, NRNr18) / deval (z, RDr18, NRDr18);
+	  y += C18a;
+	  break;
+	case 8:
+	  z = x - 1;
+	  y = C19b + z * neval (z, RNr19, NRNr19) / deval (z, RDr19, NRDr19);
+	  y += C19a;
+	  break;
+	default: /* i == 9.  */
+	  z = x - L(1.125);
+	  y = C20b + z * neval (z, RNr20, NRNr20) / deval (z, RDr20, NRDr20);
+	  y += C20a;
+	  break;
+	}
+      if (sign & 0x80000000)
+	y = 2 - y;
+      return y;
+    }
+  /* 1.25 < |x| < 107 */
+  if (ix < 0x4005ac00)
+    {
+      /* x < -9 */
+      if ((ix >= 0x40022000) && (sign & 0x80000000))
+	return two - tiny;
+
+      x = fabsl (x);
+      z = one / (x * x);
+      i = 8.0 / x;
+      switch (i)
+	{
+	default:
+	case 0:
+	  p = neval (z, RNr1, NRNr1) / deval (z, RDr1, NRDr1);
+	  break;
+	case 1:
+	  p = neval (z, RNr2, NRNr2) / deval (z, RDr2, NRDr2);
+	  break;
+	case 2:
+	  p = neval (z, RNr3, NRNr3) / deval (z, RDr3, NRDr3);
+	  break;
+	case 3:
+	  p = neval (z, RNr4, NRNr4) / deval (z, RDr4, NRDr4);
+	  break;
+	case 4:
+	  p = neval (z, RNr5, NRNr5) / deval (z, RDr5, NRDr5);
+	  break;
+	case 5:
+	  p = neval (z, RNr6, NRNr6) / deval (z, RDr6, NRDr6);
+	  break;
+	case 6:
+	  p = neval (z, RNr7, NRNr7) / deval (z, RDr7, NRDr7);
+	  break;
+	case 7:
+	  p = neval (z, RNr8, NRNr8) / deval (z, RDr8, NRDr8);
+	  break;
+	}
+      u.value = x;
+      u.parts32.w3 = 0;
+      u.parts32.w2 &= 0xfe000000;
+      z = u.value;
+      r = __ieee754_expl (-z * z - 0.5625) *
+	__ieee754_expl ((z - x) * (z + x) + p);
+      if ((sign & 0x80000000) == 0)
+	{
+	  _Float128 ret = r / x;
+	  if (ret == 0)
+	    __set_errno (ERANGE);
+	  return ret;
+	}
+      else
+	return two - r / x;
+    }
+  else
+    {
+      if ((sign & 0x80000000) == 0)
+	{
+	  __set_errno (ERANGE);
+	  return tiny * tiny;
+	}
+      else
+	return two - tiny;
+    }
+}
+
+weak_alias (__erfcl, erfcl)