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, 531 insertions, 0 deletions

diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-96/e_j0l.c b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_j0l.c
new file mode 100644
index 0000000000..a536054cde
--- /dev/null
+++ b/REORG.TODO/sysdeps/ieee754/ldbl-96/e_j0l.c
@@ -0,0 +1,531 @@
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+/* Long double expansions 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/>.  */
+
+/* __ieee754_j0(x), __ieee754_y0(x)
+ * Bessel function of the first and second kinds of order zero.
+ * Method -- j0(x):
+ *	1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ...
+ *	2. Reduce x to |x| since j0(x)=j0(-x),  and
+ *	   for x in (0,2)
+ *		j0(x) = 1 - z/4 + z^2*R0/S0,  where z = x*x;
+ *	   for x in (2,inf)
+ *		j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0))
+ *	   where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
+ *	   as follow:
+ *		cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
+ *			= 1/sqrt(2) * (cos(x) + sin(x))
+ *		sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4)
+ *			= 1/sqrt(2) * (sin(x) - cos(x))
+ *	   (To avoid cancellation, use
+ *		sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+ *	    to compute the worse one.)
+ *
+ *	3 Special cases
+ *		j0(nan)= nan
+ *		j0(0) = 1
+ *		j0(inf) = 0
+ *
+ * Method -- y0(x):
+ *	1. For x<2.
+ *	   Since
+ *		y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...)
+ *	   therefore y0(x)-2/pi*j0(x)*ln(x) is an even function.
+ *	   We use the following function to approximate y0,
+ *		y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2
+ *
+ *	   Note: For tiny x, U/V = u0 and j0(x)~1, hence
+ *		y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27)
+ *	2. For x>=2.
+ *		y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0))
+ *	   where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
+ *	   by the method mentioned above.
+ *	3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0.
+ */
+
+#include <math.h>
+#include <math_private.h>
+
+static long double pzero (long double), qzero (long double);
+
+static const long double
+  huge = 1e4930L,
+  one = 1.0L,
+  invsqrtpi = 5.6418958354775628694807945156077258584405e-1L,
+  tpi = 6.3661977236758134307553505349005744813784e-1L,
+
+  /* J0(x) = 1 - x^2 / 4 + x^4 R0(x^2) / S0(x^2)
+     0 <= x <= 2
+     peak relative error 1.41e-22 */
+  R[5] = {
+  4.287176872744686992880841716723478740566E7L,
+  -6.652058897474241627570911531740907185772E5L,
+  7.011848381719789863458364584613651091175E3L,
+  -3.168040850193372408702135490809516253693E1L,
+  6.030778552661102450545394348845599300939E-2L,
+},
+
+ S[4] = {
+   2.743793198556599677955266341699130654342E9L,
+   3.364330079384816249840086842058954076201E7L,
+   1.924119649412510777584684927494642526573E5L,
+   6.239282256012734914211715620088714856494E2L,
+   /*   1.000000000000000000000000000000000000000E0L,*/
+};
+
+static const long double zero = 0.0;
+
+long double
+__ieee754_j0l (long double x)
+{
+  long double z, s, c, ss, cc, r, u, v;
+  int32_t ix;
+  u_int32_t se;
+
+  GET_LDOUBLE_EXP (se, x);
+  ix = se & 0x7fff;
+  if (__glibc_unlikely (ix >= 0x7fff))
+    return one / (x * x);
+  x = fabsl (x);
+  if (ix >= 0x4000)		/* |x| >= 2.0 */
+    {
+      __sincosl (x, &s, &c);
+      ss = s - c;
+      cc = s + c;
+      if (ix < 0x7ffe)
+	{			/* make sure x+x not overflow */
+	  z = -__cosl (x + x);
+	  if ((s * c) < zero)
+	    cc = z / ss;
+	  else
+	    ss = z / cc;
+	}
+      /*
+       * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
+       * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
+       */
+      if (__glibc_unlikely (ix > 0x4080))      	/* 2^129 */
+	z = (invsqrtpi * cc) / __ieee754_sqrtl (x);
+      else
+	{
+	  u = pzero (x);
+	  v = qzero (x);
+	  z = invsqrtpi * (u * cc - v * ss) / __ieee754_sqrtl (x);
+	}
+      return z;
+    }
+  if (__glibc_unlikely (ix < 0x3fef))       /* |x| < 2**-16 */
+    {
+      /* raise inexact if x != 0 */
+      math_force_eval (huge + x);
+      if (ix < 0x3fde) /* |x| < 2^-33 */
+	return one;
+      else
+	return one - 0.25 * x * x;
+    }
+  z = x * x;
+  r = z * (R[0] + z * (R[1] + z * (R[2] + z * (R[3] + z * R[4]))));
+  s = S[0] + z * (S[1] + z * (S[2] + z * (S[3] + z)));
+  if (ix < 0x3fff)
+    {				/* |x| < 1.00 */
+      return (one - 0.25 * z + z * (r / s));
+    }
+  else
+    {
+      u = 0.5 * x;
+      return ((one + u) * (one - u) + z * (r / s));
+    }
+}
+strong_alias (__ieee754_j0l, __j0l_finite)
+
+
+/* y0(x) = 2/pi ln(x) J0(x) + U(x^2)/V(x^2)
+   0 < x <= 2
+   peak relative error 1.7e-21 */
+static const long double
+U[6] = {
+  -1.054912306975785573710813351985351350861E10L,
+  2.520192609749295139432773849576523636127E10L,
+  -1.856426071075602001239955451329519093395E9L,
+  4.079209129698891442683267466276785956784E7L,
+  -3.440684087134286610316661166492641011539E5L,
+  1.005524356159130626192144663414848383774E3L,
+};
+static const long double
+V[5] = {
+  1.429337283720789610137291929228082613676E11L,
+  2.492593075325119157558811370165695013002E9L,
+  2.186077620785925464237324417623665138376E7L,
+  1.238407896366385175196515057064384929222E5L,
+  4.693924035211032457494368947123233101664E2L,
+  /*  1.000000000000000000000000000000000000000E0L */
+};
+
+long double
+__ieee754_y0l (long double x)
+{
+  long double z, s, c, ss, cc, u, v;
+  int32_t ix;
+  u_int32_t se, i0, i1;
+
+  GET_LDOUBLE_WORDS (se, i0, i1, x);
+  ix = se & 0x7fff;
+  /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0  */
+  if (__glibc_unlikely (se & 0x8000))
+    return zero / (zero * x);
+  if (__glibc_unlikely (ix >= 0x7fff))
+    return one / (x + x * x);
+  if (__glibc_unlikely ((i0 | i1) == 0))
+    return -HUGE_VALL + x;  /* -inf and overflow exception.  */
+  if (ix >= 0x4000)
+    {				/* |x| >= 2.0 */
+
+      /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
+       * where x0 = x-pi/4
+       *      Better formula:
+       *              cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
+       *                      =  1/sqrt(2) * (sin(x) + cos(x))
+       *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
+       *                      =  1/sqrt(2) * (sin(x) - cos(x))
+       * To avoid cancellation, use
+       *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+       * to compute the worse one.
+       */
+      __sincosl (x, &s, &c);
+      ss = s - c;
+      cc = s + c;
+      /*
+       * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
+       * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
+       */
+      if (ix < 0x7ffe)
+	{			/* make sure x+x not overflow */
+	  z = -__cosl (x + x);
+	  if ((s * c) < zero)
+	    cc = z / ss;
+	  else
+	    ss = z / cc;
+	}
+      if (__glibc_unlikely (ix > 0x4080))      	/* 1e39 */
+	z = (invsqrtpi * ss) / __ieee754_sqrtl (x);
+      else
+	{
+	  u = pzero (x);
+	  v = qzero (x);
+	  z = invsqrtpi * (u * ss + v * cc) / __ieee754_sqrtl (x);
+	}
+      return z;
+    }
+  if (__glibc_unlikely (ix <= 0x3fde))       /* x < 2^-33 */
+    {
+      z = -7.380429510868722527629822444004602747322E-2L
+	+ tpi * __ieee754_logl (x);
+      return z;
+    }
+  z = x * x;
+  u = U[0] + z * (U[1] + z * (U[2] + z * (U[3] + z * (U[4] + z * U[5]))));
+  v = V[0] + z * (V[1] + z * (V[2] + z * (V[3] + z * (V[4] + z))));
+  return (u / v + tpi * (__ieee754_j0l (x) * __ieee754_logl (x)));
+}
+strong_alias (__ieee754_y0l, __y0l_finite)
+
+/* The asymptotic expansions of pzero is
+ *	1 - 9/128 s^2 + 11025/98304 s^4 - ...,	where s = 1/x.
+ * For x >= 2, We approximate pzero by
+ *	pzero(x) = 1 + s^2 R(s^2) / S(s^2)
+ */
+static const long double pR8[7] = {
+  /* 8 <= x <= inf
+     Peak relative error 4.62 */
+  -4.094398895124198016684337960227780260127E-9L,
+  -8.929643669432412640061946338524096893089E-7L,
+  -6.281267456906136703868258380673108109256E-5L,
+  -1.736902783620362966354814353559382399665E-3L,
+  -1.831506216290984960532230842266070146847E-2L,
+  -5.827178869301452892963280214772398135283E-2L,
+  -2.087563267939546435460286895807046616992E-2L,
+};
+static const long double pS8[6] = {
+  5.823145095287749230197031108839653988393E-8L,
+  1.279281986035060320477759999428992730280E-5L,
+  9.132668954726626677174825517150228961304E-4L,
+  2.606019379433060585351880541545146252534E-2L,
+  2.956262215119520464228467583516287175244E-1L,
+  1.149498145388256448535563278632697465675E0L,
+  /* 1.000000000000000000000000000000000000000E0L, */
+};
+
+static const long double pR5[7] = {
+  /* 4.54541015625 <= x <= 8
+     Peak relative error 6.51E-22 */
+  -2.041226787870240954326915847282179737987E-7L,
+  -2.255373879859413325570636768224534428156E-5L,
+  -7.957485746440825353553537274569102059990E-4L,
+  -1.093205102486816696940149222095559439425E-2L,
+  -5.657957849316537477657603125260701114646E-2L,
+  -8.641175552716402616180994954177818461588E-2L,
+  -1.354654710097134007437166939230619726157E-2L,
+};
+static const long double pS5[6] = {
+  2.903078099681108697057258628212823545290E-6L,
+  3.253948449946735405975737677123673867321E-4L,
+  1.181269751723085006534147920481582279979E-2L,
+  1.719212057790143888884745200257619469363E-1L,
+  1.006306498779212467670654535430694221924E0L,
+  2.069568808688074324555596301126375951502E0L,
+  /* 1.000000000000000000000000000000000000000E0L, */
+};
+
+static const long double pR3[7] = {
+  /* 2.85711669921875 <= x <= 4.54541015625
+     peak relative error 5.25e-21 */
+  -5.755732156848468345557663552240816066802E-6L,
+  -3.703675625855715998827966962258113034767E-4L,
+  -7.390893350679637611641350096842846433236E-3L,
+  -5.571922144490038765024591058478043873253E-2L,
+  -1.531290690378157869291151002472627396088E-1L,
+  -1.193350853469302941921647487062620011042E-1L,
+  -8.567802507331578894302991505331963782905E-3L,
+};
+static const long double pS3[6] = {
+  8.185931139070086158103309281525036712419E-5L,
+  5.398016943778891093520574483111255476787E-3L,
+  1.130589193590489566669164765853409621081E-1L,
+  9.358652328786413274673192987670237145071E-1L,
+  3.091711512598349056276917907005098085273E0L,
+  3.594602474737921977972586821673124231111E0L,
+  /* 1.000000000000000000000000000000000000000E0L, */
+};
+
+static const long double pR2[7] = {
+  /* 2 <= x <= 2.85711669921875
+     peak relative error 2.64e-21 */
+  -1.219525235804532014243621104365384992623E-4L,
+  -4.838597135805578919601088680065298763049E-3L,
+  -5.732223181683569266223306197751407418301E-2L,
+  -2.472947430526425064982909699406646503758E-1L,
+  -3.753373645974077960207588073975976327695E-1L,
+  -1.556241316844728872406672349347137975495E-1L,
+  -5.355423239526452209595316733635519506958E-3L,
+};
+static const long double pS2[6] = {
+  1.734442793664291412489066256138894953823E-3L,
+  7.158111826468626405416300895617986926008E-2L,
+  9.153839713992138340197264669867993552641E-1L,
+  4.539209519433011393525841956702487797582E0L,
+  8.868932430625331650266067101752626253644E0L,
+  6.067161890196324146320763844772857713502E0L,
+  /* 1.000000000000000000000000000000000000000E0L, */
+};
+
+static long double
+pzero (long double x)
+{
+  const long double *p, *q;
+  long double z, r, s;
+  int32_t ix;
+  u_int32_t se, i0, i1;
+
+  GET_LDOUBLE_WORDS (se, i0, i1, x);
+  ix = se & 0x7fff;
+  /* ix >= 0x4000 for all calls to this function.  */
+  if (ix >= 0x4002)
+    {
+      p = pR8;
+      q = pS8;
+    }				/* x >= 8 */
+  else
+    {
+      i1 = (ix << 16) | (i0 >> 16);
+      if (i1 >= 0x40019174)	/* x >= 4.54541015625 */
+	{
+	  p = pR5;
+	  q = pS5;
+	}
+      else if (i1 >= 0x4000b6db)	/* x >= 2.85711669921875 */
+	{
+	  p = pR3;
+	  q = pS3;
+	}
+      else	/* x >= 2 */
+	{
+	  p = pR2;
+	  q = pS2;
+	}
+    }
+  z = one / (x * x);
+  r =
+    p[0] + z * (p[1] +
+		z * (p[2] + z * (p[3] + z * (p[4] + z * (p[5] + z * p[6])))));
+  s =
+    q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * (q[5] + z)))));
+  return (one + z * r / s);
+}
+
+
+/* For x >= 8, the asymptotic expansions of qzero is
+ *	-1/8 s + 75/1024 s^3 - ..., where s = 1/x.
+ * We approximate qzero by
+ *	qzero(x) = s*(-.125 + R(s^2) / S(s^2))
+ */
+static const long double qR8[7] = {
+  /* 8 <= x <= inf
+     peak relative error 2.23e-21 */
+  3.001267180483191397885272640777189348008E-10L,
+  8.693186311430836495238494289942413810121E-8L,
+  8.496875536711266039522937037850596580686E-6L,
+  3.482702869915288984296602449543513958409E-4L,
+  6.036378380706107692863811938221290851352E-3L,
+  3.881970028476167836382607922840452192636E-2L,
+  6.132191514516237371140841765561219149638E-2L,
+};
+static const long double qS8[7] = {
+  4.097730123753051126914971174076227600212E-9L,
+  1.199615869122646109596153392152131139306E-6L,
+  1.196337580514532207793107149088168946451E-4L,
+  5.099074440112045094341500497767181211104E-3L,
+  9.577420799632372483249761659674764460583E-2L,
+  7.385243015344292267061953461563695918646E-1L,
+  1.917266424391428937962682301561699055943E0L,
+  /* 1.000000000000000000000000000000000000000E0L, */
+};
+
+static const long double qR5[7] = {
+  /* 4.54541015625 <= x <= 8
+     peak relative error 1.03e-21 */
+  3.406256556438974327309660241748106352137E-8L,
+  4.855492710552705436943630087976121021980E-6L,
+  2.301011739663737780613356017352912281980E-4L,
+  4.500470249273129953870234803596619899226E-3L,
+  3.651376459725695502726921248173637054828E-2L,
+  1.071578819056574524416060138514508609805E-1L,
+  7.458950172851611673015774675225656063757E-2L,
+};
+static const long double qS5[7] = {
+  4.650675622764245276538207123618745150785E-7L,
+  6.773573292521412265840260065635377164455E-5L,
+  3.340711249876192721980146877577806687714E-3L,
+  7.036218046856839214741678375536970613501E-2L,
+  6.569599559163872573895171876511377891143E-1L,
+  2.557525022583599204591036677199171155186E0L,
+  3.457237396120935674982927714210361269133E0L,
+  /* 1.000000000000000000000000000000000000000E0L,*/
+};
+
+static const long double qR3[7] = {
+  /* 2.85711669921875 <= x <= 4.54541015625
+     peak relative error 5.24e-21 */
+  1.749459596550816915639829017724249805242E-6L,
+  1.446252487543383683621692672078376929437E-4L,
+  3.842084087362410664036704812125005761859E-3L,
+  4.066369994699462547896426554180954233581E-2L,
+  1.721093619117980251295234795188992722447E-1L,
+  2.538595333972857367655146949093055405072E-1L,
+  8.560591367256769038905328596020118877936E-2L,
+};
+static const long double qS3[7] = {
+  2.388596091707517488372313710647510488042E-5L,
+  2.048679968058758616370095132104333998147E-3L,
+  5.824663198201417760864458765259945181513E-2L,
+  6.953906394693328750931617748038994763958E-1L,
+  3.638186936390881159685868764832961092476E0L,
+  7.900169524705757837298990558459547842607E0L,
+  5.992718532451026507552820701127504582907E0L,
+  /* 1.000000000000000000000000000000000000000E0L, */
+};
+
+static const long double qR2[7] = {
+  /* 2 <= x <= 2.85711669921875
+     peak relative error 1.58e-21  */
+  6.306524405520048545426928892276696949540E-5L,
+  3.209606155709930950935893996591576624054E-3L,
+  5.027828775702022732912321378866797059604E-2L,
+  3.012705561838718956481911477587757845163E-1L,
+  6.960544893905752937420734884995688523815E-1L,
+  5.431871999743531634887107835372232030655E-1L,
+  9.447736151202905471899259026430157211949E-2L,
+};
+static const long double qS2[7] = {
+  8.610579901936193494609755345106129102676E-4L,
+  4.649054352710496997203474853066665869047E-2L,
+  8.104282924459837407218042945106320388339E-1L,
+  5.807730930825886427048038146088828206852E0L,
+  1.795310145936848873627710102199881642939E1L,
+  2.281313316875375733663657188888110605044E1L,
+  1.011242067883822301487154844458322200143E1L,
+  /* 1.000000000000000000000000000000000000000E0L, */
+};
+
+static long double
+qzero (long double x)
+{
+  const long double *p, *q;
+  long double s, r, z;
+  int32_t ix;
+  u_int32_t se, i0, i1;
+
+  GET_LDOUBLE_WORDS (se, i0, i1, x);
+  ix = se & 0x7fff;
+  /* ix >= 0x4000 for all calls to this function.  */
+  if (ix >= 0x4002)		/* x >= 8 */
+    {
+      p = qR8;
+      q = qS8;
+    }
+  else
+    {
+      i1 = (ix << 16) | (i0 >> 16);
+      if (i1 >= 0x40019174)	/* x >= 4.54541015625 */
+	{
+	  p = qR5;
+	  q = qS5;
+	}
+      else if (i1 >= 0x4000b6db)	/* x >= 2.85711669921875 */
+	{
+	  p = qR3;
+	  q = qS3;
+	}
+      else	/* x >= 2 */
+	{
+	  p = qR2;
+	  q = qS2;
+	}
+    }
+  z = one / (x * x);
+  r =
+    p[0] + z * (p[1] +
+		z * (p[2] + z * (p[3] + z * (p[4] + z * (p[5] + z * p[6])))));
+  s =
+    q[0] + z * (q[1] +
+		z * (q[2] +
+		     z * (q[3] + z * (q[4] + z * (q[5] + z * (q[6] + z))))));
+  return (-.125 + z * r / s) / x;
+}