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, 466 insertions, 0 deletions

diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_j1.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_j1.c
new file mode 100644
index 0000000000..eb446fd102
--- /dev/null
+++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_j1.c
@@ -0,0 +1,466 @@
+/* @(#)e_j1.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/26,
+   for performance improvement on pipelined processors.
+ */
+
+/* __ieee754_j1(x), __ieee754_y1(x)
+ * Bessel function of the first and second kinds of order zero.
+ * Method -- j1(x):
+ *	1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ...
+ *	2. Reduce x to |x| since j1(x)=-j1(-x),  and
+ *	   for x in (0,2)
+ *		j1(x) = x/2 + x*z*R0/S0,  where z = x*x;
+ *	   (precision:  |j1/x - 1/2 - R0/S0 |<2**-61.51 )
+ *	   for x in (2,inf)
+ *		j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1))
+ *		y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
+ *	   where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
+ *	   as follow:
+ *		cos(x1) =  cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
+ *			=  1/sqrt(2) * (sin(x) - cos(x))
+ *		sin(x1) =  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.)
+ *
+ *	3 Special cases
+ *		j1(nan)= nan
+ *		j1(0) = 0
+ *		j1(inf) = 0
+ *
+ * Method -- y1(x):
+ *	1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN
+ *	2. For x<2.
+ *	   Since
+ *		y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...)
+ *	   therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function.
+ *	   We use the following function to approximate y1,
+ *		y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2
+ *	   where for x in [0,2] (abs err less than 2**-65.89)
+ *		U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4
+ *		V(z) = 1  + v0[0]*z + ... + v0[4]*z^5
+ *	   Note: For tiny x, 1/x dominate y1 and hence
+ *		y1(tiny) = -2/pi/tiny, (choose tiny<2**-54)
+ *	3. For x>=2.
+ *		y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
+ *	   where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
+ *	   by method mentioned above.
+ */
+
+#include <errno.h>
+#include <float.h>
+#include <math.h>
+#include <math_private.h>
+
+static double pone (double), qone (double);
+
+static const double
+  huge = 1e300,
+  one = 1.0,
+  invsqrtpi = 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
+  tpi = 6.36619772367581382433e-01,     /* 0x3FE45F30, 0x6DC9C883 */
+/* R0/S0 on [0,2] */
+  R[] = { -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */
+	  1.40705666955189706048e-03,   /* 0x3F570D9F, 0x98472C61 */
+	  -1.59955631084035597520e-05,  /* 0xBEF0C5C6, 0xBA169668 */
+	  4.96727999609584448412e-08 }, /* 0x3E6AAAFA, 0x46CA0BD9 */
+  S[] = { 0.0, 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */
+	  1.85946785588630915560e-04,   /* 0x3F285F56, 0xB9CDF664 */
+	  1.17718464042623683263e-06,   /* 0x3EB3BFF8, 0x333F8498 */
+	  5.04636257076217042715e-09,   /* 0x3E35AC88, 0xC97DFF2C */
+	  1.23542274426137913908e-11 }; /* 0x3DAB2ACF, 0xCFB97ED8 */
+
+static const double zero = 0.0;
+
+double
+__ieee754_j1 (double x)
+{
+  double z, s, c, ss, cc, r, u, v, y, r1, r2, s1, s2, s3, z2, z4;
+  int32_t hx, ix;
+
+  GET_HIGH_WORD (hx, x);
+  ix = hx & 0x7fffffff;
+  if (__glibc_unlikely (ix >= 0x7ff00000))
+    return one / x;
+  y = fabs (x);
+  if (ix >= 0x40000000)         /* |x| >= 2.0 */
+    {
+      __sincos (y, &s, &c);
+      ss = -s - c;
+      cc = s - c;
+      if (ix < 0x7fe00000)           /* make sure y+y not overflow */
+	{
+	  z = __cos (y + y);
+	  if ((s * c) > zero)
+	    cc = z / ss;
+	  else
+	    ss = z / cc;
+	}
+      /*
+       * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
+       * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
+       */
+      if (ix > 0x48000000)
+	z = (invsqrtpi * cc) / __ieee754_sqrt (y);
+      else
+	{
+	  u = pone (y); v = qone (y);
+	  z = invsqrtpi * (u * cc - v * ss) / __ieee754_sqrt (y);
+	}
+      if (hx < 0)
+	return -z;
+      else
+	return z;
+    }
+  if (__glibc_unlikely (ix < 0x3e400000))                  /* |x|<2**-27 */
+    {
+      if (huge + x > one)                 /* inexact if x!=0 necessary */
+	{
+	  double ret = math_narrow_eval (0.5 * x);
+	  math_check_force_underflow (ret);
+	  if (ret == 0 && x != 0)
+	    __set_errno (ERANGE);
+	  return ret;
+	}
+    }
+  z = x * x;
+  r1 = z * R[0]; z2 = z * z;
+  r2 = R[1] + z * R[2]; z4 = z2 * z2;
+  r = r1 + z2 * r2 + z4 * R[3];
+  r *= x;
+  s1 = one + z * S[1];
+  s2 = S[2] + z * S[3];
+  s3 = S[4] + z * S[5];
+  s = s1 + z2 * s2 + z4 * s3;
+  return (x * 0.5 + r / s);
+}
+strong_alias (__ieee754_j1, __j1_finite)
+
+static const double U0[5] = {
+ -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */
+  5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */
+ -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */
+  2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */
+ -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */
+};
+static const double V0[5] = {
+  1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */
+  2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */
+  1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */
+  6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */
+  1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */
+};
+
+double
+__ieee754_y1 (double x)
+{
+  double z, s, c, ss, cc, u, v, u1, u2, v1, v2, v3, z2, z4;
+  int32_t hx, ix, lx;
+
+  EXTRACT_WORDS (hx, lx, x);
+  ix = 0x7fffffff & hx;
+  /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
+  if (__glibc_unlikely (ix >= 0x7ff00000))
+    return one / (x + x * x);
+  if (__glibc_unlikely ((ix | lx) == 0))
+    return -1 / zero; /* -inf and divide by zero exception.  */
+  /* -inf and overflow exception.  */;
+  if (__glibc_unlikely (hx < 0))
+    return zero / (zero * x);
+  if (ix >= 0x40000000)         /* |x| >= 2.0 */
+    {
+      __sincos (x, &s, &c);
+      ss = -s - c;
+      cc = s - c;
+      if (ix < 0x7fe00000)           /* make sure x+x not overflow */
+	{
+	  z = __cos (x + x);
+	  if ((s * c) > zero)
+	    cc = z / ss;
+	  else
+	    ss = z / cc;
+	}
+      /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
+       * where x0 = x-3pi/4
+       *      Better formula:
+       *              cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
+       *                      =  1/sqrt(2) * (sin(x) - cos(x))
+       *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
+       *                      = -1/sqrt(2) * (cos(x) + sin(x))
+       * To avoid cancellation, use
+       *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+       * to compute the worse one.
+       */
+      if (ix > 0x48000000)
+	z = (invsqrtpi * ss) / __ieee754_sqrt (x);
+      else
+	{
+	  u = pone (x); v = qone (x);
+	  z = invsqrtpi * (u * ss + v * cc) / __ieee754_sqrt (x);
+	}
+      return z;
+    }
+  if (__glibc_unlikely (ix <= 0x3c900000))              /* x < 2**-54 */
+    {
+      z = -tpi / x;
+      if (isinf (z))
+	__set_errno (ERANGE);
+      return z;
+    }
+  z = x * x;
+  u1 = U0[0] + z * U0[1]; z2 = z * z;
+  u2 = U0[2] + z * U0[3]; z4 = z2 * z2;
+  u = u1 + z2 * u2 + z4 * U0[4];
+  v1 = one + z * V0[0];
+  v2 = V0[1] + z * V0[2];
+  v3 = V0[3] + z * V0[4];
+  v = v1 + z2 * v2 + z4 * v3;
+  return (x * (u / v) + tpi * (__ieee754_j1 (x) * __ieee754_log (x) - one / x));
+}
+strong_alias (__ieee754_y1, __y1_finite)
+
+/* For x >= 8, the asymptotic expansions of pone is
+ *	1 + 15/128 s^2 - 4725/2^15 s^4 - ...,	where s = 1/x.
+ * We approximate pone by
+ *	pone(x) = 1 + (R/S)
+ * where  R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
+ *	  S = 1 + ps0*s^2 + ... + ps4*s^10
+ * and
+ *	| pone(x)-1-R/S | <= 2  ** ( -60.06)
+ */
+
+static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
+  1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */
+  1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */
+  4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */
+  3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */
+  7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */
+};
+static const double ps8[5] = {
+  1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */
+  3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */
+  3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */
+  9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */
+  3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */
+};
+
+static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+  1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */
+  1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */
+  6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */
+  1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */
+  5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */
+  5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */
+};
+static const double ps5[5] = {
+  5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */
+  9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */
+  5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */
+  7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */
+  1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */
+};
+
+static const double pr3[6] = {
+  3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */
+  1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */
+  3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */
+  3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */
+  9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */
+  4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */
+};
+static const double ps3[5] = {
+  3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */
+  3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */
+  1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */
+  8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */
+  1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */
+};
+
+static const double pr2[6] = { /* for x in [2.8570,2]=1/[0.3499,0.5] */
+  1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */
+  1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */
+  2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */
+  1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */
+  1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */
+  5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */
+};
+static const double ps2[5] = {
+  2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */
+  1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */
+  2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */
+  1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */
+  8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */
+};
+
+static double
+pone (double x)
+{
+  const double *p, *q;
+  double z, r, s, r1, r2, r3, s1, s2, s3, z2, z4;
+  int32_t ix;
+  GET_HIGH_WORD (ix, x);
+  ix &= 0x7fffffff;
+  /* ix >= 0x40000000 for all calls to this function.  */
+  if (ix >= 0x41b00000)
+    {
+      return one;
+    }
+  else if (ix >= 0x40200000)
+    {
+      p = pr8; q = ps8;
+    }
+  else if (ix >= 0x40122E8B)
+    {
+      p = pr5; q = ps5;
+    }
+  else if (ix >= 0x4006DB6D)
+    {
+      p = pr3; q = ps3;
+    }
+  else
+    {
+      p = pr2; q = ps2;
+    }
+  z = one / (x * x);
+  r1 = p[0] + z * p[1]; z2 = z * z;
+  r2 = p[2] + z * p[3]; z4 = z2 * z2;
+  r3 = p[4] + z * p[5];
+  r = r1 + z2 * r2 + z4 * r3;
+  s1 = one + z * q[0];
+  s2 = q[1] + z * q[2];
+  s3 = q[3] + z * q[4];
+  s = s1 + z2 * s2 + z4 * s3;
+  return one + r / s;
+}
+
+
+/* For x >= 8, the asymptotic expansions of qone is
+ *	3/8 s - 105/1024 s^3 - ..., where s = 1/x.
+ * We approximate pone by
+ *	qone(x) = s*(0.375 + (R/S))
+ * where  R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
+ *	  S = 1 + qs1*s^2 + ... + qs6*s^12
+ * and
+ *	| qone(x)/s -0.375-R/S | <= 2  ** ( -61.13)
+ */
+
+static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
+ -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */
+ -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */
+ -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */
+ -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */
+ -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */
+};
+static const double qs8[6] = {
+  1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */
+  7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */
+  1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */
+  7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */
+  6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */
+ -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */
+};
+
+static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+ -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */
+ -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */
+ -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */
+ -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */
+ -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */
+ -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */
+};
+static const double qs5[6] = {
+  8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */
+  1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */
+  1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */
+  4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */
+  2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */
+ -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */
+};
+
+static const double qr3[6] = {
+ -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */
+ -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */
+ -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */
+ -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */
+ -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */
+ -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */
+};
+static const double qs3[6] = {
+  4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */
+  6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */
+  3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */
+  5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */
+  1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */
+ -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */
+};
+
+static const double qr2[6] = { /* for x in [2.8570,2]=1/[0.3499,0.5] */
+ -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */
+ -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */
+ -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */
+ -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */
+ -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */
+ -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */
+};
+static const double qs2[6] = {
+  2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */
+  2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */
+  7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */
+  7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */
+  1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */
+ -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */
+};
+
+static double
+qone (double x)
+{
+  const double *p, *q;
+  double s, r, z, r1, r2, r3, s1, s2, s3, z2, z4, z6;
+  int32_t ix;
+  GET_HIGH_WORD (ix, x);
+  ix &= 0x7fffffff;
+  /* ix >= 0x40000000 for all calls to this function.  */
+  if (ix >= 0x41b00000)
+    {
+      return .375 / x;
+    }
+  else if (ix >= 0x40200000)
+    {
+      p = qr8; q = qs8;
+    }
+  else if (ix >= 0x40122E8B)
+    {
+      p = qr5; q = qs5;
+    }
+  else if (ix >= 0x4006DB6D)
+    {
+      p = qr3; q = qs3;
+    }
+  else
+    {
+      p = qr2; q = qs2;
+    }
+  z = one / (x * x);
+  r1 = p[0] + z * p[1]; z2 = z * z;
+  r2 = p[2] + z * p[3]; z4 = z2 * z2;
+  r3 = p[4] + z * p[5]; z6 = z4 * z2;
+  r = r1 + z2 * r2 + z4 * r3;
+  s1 = one + z * q[0];
+  s2 = q[1] + z * q[2];
+  s3 = q[3] + z * q[4];
+  s = s1 + z2 * s2 + z4 * s3 + z6 * q[5];
+  return (.375 + r / s) / x;
+}