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authorUlrich Drepper <drepper@redhat.com>2004-12-22 20:10:10 +0000
committerUlrich Drepper <drepper@redhat.com>2004-12-22 20:10:10 +0000
commita334319f6530564d22e775935d9c91663623a1b4 (patch)
treeb5877475619e4c938e98757d518bb1e9cbead751 /sysdeps/ieee754/ldbl-128ibm/e_jnl.c
parent0ecb606cb6cf65de1d9fc8a919bceb4be476c602 (diff)
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(CFLAGS-tst-align.c): Add -mpreferred-stack-boundary=4.
Diffstat (limited to 'sysdeps/ieee754/ldbl-128ibm/e_jnl.c')
-rw-r--r--sysdeps/ieee754/ldbl-128ibm/e_jnl.c402
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diff --git a/sysdeps/ieee754/ldbl-128ibm/e_jnl.c b/sysdeps/ieee754/ldbl-128ibm/e_jnl.c
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index 0eea745676..0000000000
--- a/sysdeps/ieee754/ldbl-128ibm/e_jnl.c
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@@ -1,402 +0,0 @@
-/*
- * ====================================================
- * 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 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, write to the Free Software
-    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307  USA */
-
-/*
- * __ieee754_jn(n, x), __ieee754_yn(n, x)
- * floating point Bessel's function of the 1st and 2nd kind
- * of order n
- *
- * Special cases:
- *	y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
- *	y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
- * Note 2. About jn(n,x), yn(n,x)
- *	For n=0, j0(x) is called,
- *	for n=1, j1(x) is called,
- *	for n<x, forward recursion us used starting
- *	from values of j0(x) and j1(x).
- *	for n>x, a continued fraction approximation to
- *	j(n,x)/j(n-1,x) is evaluated and then backward
- *	recursion is used starting from a supposed value
- *	for j(n,x). The resulting value of j(0,x) is
- *	compared with the actual value to correct the
- *	supposed value of j(n,x).
- *
- *	yn(n,x) is similar in all respects, except
- *	that forward recursion is used for all
- *	values of n>1.
- *
- */
-
-#include "math.h"
-#include "math_private.h"
-
-#ifdef __STDC__
-static const long double
-#else
-static long double
-#endif
-  invsqrtpi = 5.6418958354775628694807945156077258584405E-1L,
-  two = 2.0e0L,
-  one = 1.0e0L,
-  zero = 0.0L;
-
-
-#ifdef __STDC__
-long double
-__ieee754_jnl (int n, long double x)
-#else
-long double
-__ieee754_jnl (n, x)
-     int n;
-     long double x;
-#endif
-{
-  u_int32_t se;
-  int32_t i, ix, sgn;
-  long double a, b, temp, di;
-  long double z, w;
-  ieee854_long_double_shape_type u;
-
-
-  /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
-   * Thus, J(-n,x) = J(n,-x)
-   */
-
-  u.value = x;
-  se = u.parts32.w0;
-  ix = se & 0x7fffffff;
-
-  /* if J(n,NaN) is NaN */
-  if (ix >= 0x7ff00000)
-    {
-      if ((u.parts32.w0 & 0xfffff) | u.parts32.w1
-	  | (u.parts32.w2 & 0x7fffffff) | u.parts32.w3)
-	return x + x;
-    }
-
-  if (n < 0)
-    {
-      n = -n;
-      x = -x;
-      se ^= 0x80000000;
-    }
-  if (n == 0)
-    return (__ieee754_j0l (x));
-  if (n == 1)
-    return (__ieee754_j1l (x));
-  sgn = (n & 1) & (se >> 31);	/* even n -- 0, odd n -- sign(x) */
-  x = fabsl (x);
-
-  if (x == 0.0L || ix >= 0x7ff00000)	/* if x is 0 or inf */
-    b = zero;
-  else if ((long double) n <= x)
-    {
-      /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
-      if (ix >= 0x52d00000)
-	{			/* x > 2**302 */
-
-	  /* ??? Could use an expansion for large x here.  */
-
-	  /* (x >> n**2)
-	   *      Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
-	   *      Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
-	   *      Let s=sin(x), c=cos(x),
-	   *          xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
-	   *
-	   *             n    sin(xn)*sqt2    cos(xn)*sqt2
-	   *          ----------------------------------
-	   *             0     s-c             c+s
-	   *             1    -s-c            -c+s
-	   *             2    -s+c            -c-s
-	   *             3     s+c             c-s
-	   */
-	  long double s;
-	  long double c;
-	  __sincosl (x, &s, &c);
-	  switch (n & 3)
-	    {
-	    case 0:
-	      temp = c + s;
-	      break;
-	    case 1:
-	      temp = -c + s;
-	      break;
-	    case 2:
-	      temp = -c - s;
-	      break;
-	    case 3:
-	      temp = c - s;
-	      break;
-	    }
-	  b = invsqrtpi * temp / __ieee754_sqrtl (x);
-	}
-      else
-	{
-	  a = __ieee754_j0l (x);
-	  b = __ieee754_j1l (x);
-	  for (i = 1; i < n; i++)
-	    {
-	      temp = b;
-	      b = b * ((long double) (i + i) / x) - a;	/* avoid underflow */
-	      a = temp;
-	    }
-	}
-    }
-  else
-    {
-      if (ix < 0x3e100000)
-	{			/* x < 2**-29 */
-	  /* x is tiny, return the first Taylor expansion of J(n,x)
-	   * J(n,x) = 1/n!*(x/2)^n  - ...
-	   */
-	  if (n >= 33)		/* underflow, result < 10^-300 */
-	    b = zero;
-	  else
-	    {
-	      temp = x * 0.5;
-	      b = temp;
-	      for (a = one, i = 2; i <= n; i++)
-		{
-		  a *= (long double) i;	/* a = n! */
-		  b *= temp;	/* b = (x/2)^n */
-		}
-	      b = b / a;
-	    }
-	}
-      else
-	{
-	  /* use backward recurrence */
-	  /*                      x      x^2      x^2
-	   *  J(n,x)/J(n-1,x) =  ----   ------   ------   .....
-	   *                      2n  - 2(n+1) - 2(n+2)
-	   *
-	   *                      1      1        1
-	   *  (for large x)   =  ----  ------   ------   .....
-	   *                      2n   2(n+1)   2(n+2)
-	   *                      -- - ------ - ------ -
-	   *                       x     x         x
-	   *
-	   * Let w = 2n/x and h=2/x, then the above quotient
-	   * is equal to the continued fraction:
-	   *                  1
-	   *      = -----------------------
-	   *                     1
-	   *         w - -----------------
-	   *                        1
-	   *              w+h - ---------
-	   *                     w+2h - ...
-	   *
-	   * To determine how many terms needed, let
-	   * Q(0) = w, Q(1) = w(w+h) - 1,
-	   * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
-	   * When Q(k) > 1e4      good for single
-	   * When Q(k) > 1e9      good for double
-	   * When Q(k) > 1e17     good for quadruple
-	   */
-	  /* determine k */
-	  long double t, v;
-	  long double q0, q1, h, tmp;
-	  int32_t k, m;
-	  w = (n + n) / (long double) x;
-	  h = 2.0L / (long double) x;
-	  q0 = w;
-	  z = w + h;
-	  q1 = w * z - 1.0L;
-	  k = 1;
-	  while (q1 < 1.0e17L)
-	    {
-	      k += 1;
-	      z += h;
-	      tmp = z * q1 - q0;
-	      q0 = q1;
-	      q1 = tmp;
-	    }
-	  m = n + n;
-	  for (t = zero, i = 2 * (n + k); i >= m; i -= 2)
-	    t = one / (i / x - t);
-	  a = t;
-	  b = one;
-	  /*  estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
-	   *  Hence, if n*(log(2n/x)) > ...
-	   *  single 8.8722839355e+01
-	   *  double 7.09782712893383973096e+02
-	   *  long double 1.1356523406294143949491931077970765006170e+04
-	   *  then recurrent value may overflow and the result is
-	   *  likely underflow to zero
-	   */
-	  tmp = n;
-	  v = two / x;
-	  tmp = tmp * __ieee754_logl (fabsl (v * tmp));
-
-	  if (tmp < 1.1356523406294143949491931077970765006170e+04L)
-	    {
-	      for (i = n - 1, di = (long double) (i + i); i > 0; i--)
-		{
-		  temp = b;
-		  b *= di;
-		  b = b / x - a;
-		  a = temp;
-		  di -= two;
-		}
-	    }
-	  else
-	    {
-	      for (i = n - 1, di = (long double) (i + i); i > 0; i--)
-		{
-		  temp = b;
-		  b *= di;
-		  b = b / x - a;
-		  a = temp;
-		  di -= two;
-		  /* scale b to avoid spurious overflow */
-		  if (b > 1e100L)
-		    {
-		      a /= b;
-		      t /= b;
-		      b = one;
-		    }
-		}
-	    }
-	  b = (t * __ieee754_j0l (x) / b);
-	}
-    }
-  if (sgn == 1)
-    return -b;
-  else
-    return b;
-}
-
-#ifdef __STDC__
-long double
-__ieee754_ynl (int n, long double x)
-#else
-long double
-__ieee754_ynl (n, x)
-     int n;
-     long double x;
-#endif
-{
-  u_int32_t se;
-  int32_t i, ix;
-  int32_t sign;
-  long double a, b, temp;
-  ieee854_long_double_shape_type u;
-
-  u.value = x;
-  se = u.parts32.w0;
-  ix = se & 0x7fffffff;
-
-  /* if Y(n,NaN) is NaN */
-  if (ix >= 0x7ff00000)
-    {
-      if ((u.parts32.w0 & 0xfffff) | u.parts32.w1
-	  | (u.parts32.w2 & 0x7fffffff) | u.parts32.w3)
-	return x + x;
-    }
-  if (x <= 0.0L)
-    {
-      if (x == 0.0L)
-	return -HUGE_VALL + x;
-      if (se & 0x80000000)
-	return zero / (zero * x);
-    }
-  sign = 1;
-  if (n < 0)
-    {
-      n = -n;
-      sign = 1 - ((n & 1) << 1);
-    }
-  if (n == 0)
-    return (__ieee754_y0l (x));
-  if (n == 1)
-    return (sign * __ieee754_y1l (x));
-  if (ix >= 0x7ff00000)
-    return zero;
-  if (ix >= 0x52D00000)
-    {				/* x > 2**302 */
-
-      /* ??? See comment above on the possible futility of this.  */
-
-      /* (x >> n**2)
-       *      Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
-       *      Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
-       *      Let s=sin(x), c=cos(x),
-       *          xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
-       *
-       *             n    sin(xn)*sqt2    cos(xn)*sqt2
-       *          ----------------------------------
-       *             0     s-c             c+s
-       *             1    -s-c            -c+s
-       *             2    -s+c            -c-s
-       *             3     s+c             c-s
-       */
-      long double s;
-      long double c;
-      __sincosl (x, &s, &c);
-      switch (n & 3)
-	{
-	case 0:
-	  temp = s - c;
-	  break;
-	case 1:
-	  temp = -s - c;
-	  break;
-	case 2:
-	  temp = -s + c;
-	  break;
-	case 3:
-	  temp = s + c;
-	  break;
-	}
-      b = invsqrtpi * temp / __ieee754_sqrtl (x);
-    }
-  else
-    {
-      a = __ieee754_y0l (x);
-      b = __ieee754_y1l (x);
-      /* quit if b is -inf */
-      u.value = b;
-      se = u.parts32.w0 & 0xfff00000;
-      for (i = 1; i < n && se != 0xfff00000; i++)
-	{
-	  temp = b;
-	  b = ((long double) (i + i) / x) * b - a;
-	  u.value = b;
-	  se = u.parts32.w0 & 0xfff00000;
-	  a = temp;
-	}
-    }
-  if (sign > 0)
-    return b;
-  else
-    return -b;
-}