Update.

2001-02-12  Ulrich Drepper  <drepper@redhat.com>

	* sysdeps/ieee754/ldbl-96/e_j0l.c: New file.
	Contributed by Stephen L. Moshier <moshier@na-net.ornl.gov>.

2001-02-11  Jakub Jelinek  <jakub@redhat.com>

	* sysdeps/generic/strtoll.c (__strtoq_internal): Ressurect alias
	which was exported from libc.
	* sysdeps/generic/strtoull.c (__strtouq_internal): Likewise.

3 files changed, 632 insertions, 0 deletions

diff --git a/sysdeps/generic/strtoll.c b/sysdeps/generic/strtoll.c
index e507abb703..cfa98c841f 100644
--- a/sysdeps/generic/strtoll.c
+++ b/sysdeps/generic/strtoll.c
@@ -21,4 +21,5 @@
 
 #include <strtol.c>
 
+strong_alias (__strtoll_internal, __strtoq_internal)
 weak_alias (strtoll, strtoq)
diff --git a/sysdeps/generic/strtoull.c b/sysdeps/generic/strtoull.c
index 5ec375679d..80ccf91c5e 100644
--- a/sysdeps/generic/strtoull.c
+++ b/sysdeps/generic/strtoull.c
@@ -22,5 +22,6 @@
 #include <strtoul.c>
 
 #ifdef _LIBC
+strong_alias (__strtoull_internal, __strtouq_internal)
 weak_alias (strtoull, strtouq)
 #endif
diff --git a/sysdeps/ieee754/ldbl-96/e_j0l.c b/sysdeps/ieee754/ldbl-96/e_j0l.c
new file mode 100644
index 0000000000..bec0f74470
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-96/e_j0l.c
@@ -0,0 +1,630 @@
+/*
+ * ====================================================
+ * 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 contributed by
+   Stephen L. Moshier <moshier@na-net.ornl.gov>  */
+
+/* __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"
+
+#ifdef __STDC__
+static long double pzero (long double), qzero (long double);
+#else
+static long double pzero (), qzero ();
+#endif
+
+#ifdef __STDC__
+static const long double
+#else
+static long double
+#endif
+  huge = 1e4930L,
+  one = 1.0L,
+  invsqrtpi = 5.6418958354775628694807945156077258584405e-1L,
+  tpi = 6.3661977236758134307553505349005744813784e-1L,
+  j0z1 = 2.40482555769577276862163187932650662155139L,
+  j0z2 = 5.520078110286310649596604112813027425221865L,
+
+  /* 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,*/
+};
+
+#ifdef __STDC__
+static const long double zero = 0.0;
+#else
+static long double zero = 0.0;
+#endif
+
+#ifdef __STDC__
+long double
+__ieee754_j0l (long double x)
+#else
+long double
+__ieee754_j0l (x)
+     long double x;
+#endif
+{
+  long double z, s, c, ss, cc, r, u, v;
+  int32_t ix;
+  u_int32_t se, i0, i1;
+
+  GET_LDOUBLE_WORDS (se, i0, i1, x);
+  ix = se & 0x7fff;
+  if (ix >= 0x7fff)
+    return one / (x * x);
+  x = fabsl (x);
+  if (ix >= 0x4000)		/* |x| >= 2.0 */
+    {
+      s = __sinl (x);
+      c = __cosl (x);
+      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 (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 (ix < 0x3fef) /* |x| < 2**-16 */
+    {
+      if (huge + x > one)
+	{			/* raise inexact if x != 0 */
+	  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));
+    }
+}
+
+
+/* y0(x) = 2/pi ln(x) J0(x) + U(x^2)/V(x^2)
+   0 < x <= 2
+   peak relative error 1.7e-21 */
+#ifdef __STDC__
+static const long double
+#else
+static long double
+#endif
+U[6] = {
+  -1.054912306975785573710813351985351350861E10L,
+  2.520192609749295139432773849576523636127E10L,
+  -1.856426071075602001239955451329519093395E9L,
+  4.079209129698891442683267466276785956784E7L,
+  -3.440684087134286610316661166492641011539E5L,
+  1.005524356159130626192144663414848383774E3L,
+};
+#ifdef __STDC__
+static const long double
+#else
+static long double
+#endif
+V[5] = {
+  1.429337283720789610137291929228082613676E11L,
+  2.492593075325119157558811370165695013002E9L,
+  2.186077620785925464237324417623665138376E7L,
+  1.238407896366385175196515057064384929222E5L,
+  4.693924035211032457494368947123233101664E2L,
+  /*  1.000000000000000000000000000000000000000E0L */
+};
+
+#ifdef __STDC__
+long double
+__ieee754_y0l (long double x)
+#else
+long double
+__ieee754_y0l (x)
+     long double x;
+#endif
+{
+  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 (se & 0x8000)
+    return zero / zero;
+  if (ix >= 0x7fff)
+    return one / (x + x * x);
+  if ((i0 | i1) == 0)
+    return -one / zero;
+  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.
+       */
+      s = __sinl (x);
+      c = __cosl (x);
+      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 (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 (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)));
+}
+
+/* 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)
+ */
+#ifdef __STDC__
+static const long double pR8[7] = {
+#else
+static long double pR8[7] = {
+#endif
+  /* 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,
+};
+#ifdef __STDC__
+static const long double pS8[6] = {
+#else
+static long double pS8[6] = {
+#endif
+  5.823145095287749230197031108839653988393E-8L,
+  1.279281986035060320477759999428992730280E-5L,
+  9.132668954726626677174825517150228961304E-4L,
+  2.606019379433060585351880541545146252534E-2L,
+  2.956262215119520464228467583516287175244E-1L,
+  1.149498145388256448535563278632697465675E0L,
+  /* 1.000000000000000000000000000000000000000E0L, */
+};
+
+#ifdef __STDC__
+static const long double pR5[7] = {
+#else
+static long double pR5[7] = {
+#endif
+  /* 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,
+};
+#ifdef __STDC__
+static const long double pS5[6] = {
+#else
+static long double pS5[6] = {
+#endif
+  2.903078099681108697057258628212823545290E-6L,
+  3.253948449946735405975737677123673867321E-4L,
+  1.181269751723085006534147920481582279979E-2L,
+  1.719212057790143888884745200257619469363E-1L,
+  1.006306498779212467670654535430694221924E0L,
+  2.069568808688074324555596301126375951502E0L,
+  /* 1.000000000000000000000000000000000000000E0L, */
+};
+
+#ifdef __STDC__
+static const long double pR3[7] = {
+#else
+static long double pR3[7] = {
+#endif
+  /* 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,
+};
+#ifdef __STDC__
+static const long double pS3[6] = {
+#else
+static long double pS3[6] = {
+#endif
+  8.185931139070086158103309281525036712419E-5L,
+  5.398016943778891093520574483111255476787E-3L,
+  1.130589193590489566669164765853409621081E-1L,
+  9.358652328786413274673192987670237145071E-1L,
+  3.091711512598349056276917907005098085273E0L,
+  3.594602474737921977972586821673124231111E0L,
+  /* 1.000000000000000000000000000000000000000E0L, */
+};
+
+#ifdef __STDC__
+static const long double pR2[7] = {
+#else
+static long double pR2[7] = {
+#endif
+  /* 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,
+};
+#ifdef __STDC__
+static const long double pS2[6] = {
+#else
+static long double pS2[6] = {
+#endif
+  1.734442793664291412489066256138894953823E-3L,
+  7.158111826468626405416300895617986926008E-2L,
+  9.153839713992138340197264669867993552641E-1L,
+  4.539209519433011393525841956702487797582E0L,
+  8.868932430625331650266067101752626253644E0L,
+  6.067161890196324146320763844772857713502E0L,
+  /* 1.000000000000000000000000000000000000000E0L, */
+};
+
+#ifdef __STDC__
+static long double
+pzero (long double x)
+#else
+static long double
+pzero (x)
+     long double x;
+#endif
+{
+#ifdef __STDC__
+  const long double *p, *q;
+#else
+  long double *p, *q;
+#endif
+  long double z, r, s;
+  int32_t ix;
+  u_int32_t se, i0, i1;
+
+  GET_LDOUBLE_WORDS (se, i0, i1, x);
+  ix = se & 0x7fff;
+  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 if (ix >= 0x4000)	/* x better be >= 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))
+ */
+#ifdef __STDC__
+static const long double qR8[7] = {
+#else
+static long double qR8[7] = {
+#endif
+  /* 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,
+};
+#ifdef __STDC__
+static const long double qS8[7] = {
+#else
+static long double qS8[7] = {
+#endif
+  4.097730123753051126914971174076227600212E-9L,
+  1.199615869122646109596153392152131139306E-6L,
+  1.196337580514532207793107149088168946451E-4L,
+  5.099074440112045094341500497767181211104E-3L,
+  9.577420799632372483249761659674764460583E-2L,
+  7.385243015344292267061953461563695918646E-1L,
+  1.917266424391428937962682301561699055943E0L,
+  /* 1.000000000000000000000000000000000000000E0L, */
+};
+
+#ifdef __STDC__
+static const long double qR5[7] = {
+#else
+static long double qR5[7] = {
+#endif
+  /* 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,
+};
+#ifdef __STDC__
+static const long double qS5[7] = {
+#else
+static long double qS5[7] = {
+#endif
+  4.650675622764245276538207123618745150785E-7L,
+  6.773573292521412265840260065635377164455E-5L,
+  3.340711249876192721980146877577806687714E-3L,
+  7.036218046856839214741678375536970613501E-2L,
+  6.569599559163872573895171876511377891143E-1L,
+  2.557525022583599204591036677199171155186E0L,
+  3.457237396120935674982927714210361269133E0L,
+  /* 1.000000000000000000000000000000000000000E0L,*/
+};
+
+#ifdef __STDC__
+static const long double qR3[7] = {
+#else
+static long double qR3[7] = {
+#endif
+  /* 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,
+};
+#ifdef __STDC__
+static const long double qS3[7] = {
+#else
+static long double qS3[7] = {
+#endif
+  2.388596091707517488372313710647510488042E-5L,
+  2.048679968058758616370095132104333998147E-3L,
+  5.824663198201417760864458765259945181513E-2L,
+  6.953906394693328750931617748038994763958E-1L,
+  3.638186936390881159685868764832961092476E0L,
+  7.900169524705757837298990558459547842607E0L,
+  5.992718532451026507552820701127504582907E0L,
+  /* 1.000000000000000000000000000000000000000E0L, */
+};
+
+#ifdef __STDC__
+static const long double qR2[7] = {
+#else
+static long double qR2[7] = {
+#endif
+  /* 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,
+};
+#ifdef __STDC__
+static const long double qS2[7] = {
+#else
+static long double qS2[7] = {
+#endif
+  8.610579901936193494609755345106129102676E-4L,
+  4.649054352710496997203474853066665869047E-2L,
+  8.104282924459837407218042945106320388339E-1L,
+  5.807730930825886427048038146088828206852E0L,
+  1.795310145936848873627710102199881642939E1L,
+  2.281313316875375733663657188888110605044E1L,
+  1.011242067883822301487154844458322200143E1L,
+  /* 1.000000000000000000000000000000000000000E0L, */
+};
+
+#ifdef __STDC__
+static long double
+qzero (long double x)
+#else
+static long double
+qzero (x)
+     long double x;
+#endif
+{
+#ifdef __STDC__
+  const long double *p, *q;
+#else
+  long double *p, *q;
+#endif
+  long double s, r, z;
+  int32_t ix;
+  u_int32_t se, i0, i1;
+
+  GET_LDOUBLE_WORDS (se, i0, i1, x);
+  ix = se & 0x7fff;
+  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 if (ix >= 0x4000)	/* x better be >= 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;
+}