2.5-18.1

1 files changed, 441 insertions, 0 deletions

diff --git a/sysdeps/ieee754/ldbl-128ibm/e_powl.c b/sysdeps/ieee754/ldbl-128ibm/e_powl.c
new file mode 100644
index 0000000000..feeaa8ce21
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-128ibm/e_powl.c
@@ -0,0 +1,441 @@
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+/* Expansions and 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_powl(x,y) return x**y
+ *
+ *		      n
+ * Method:  Let x =  2   * (1+f)
+ *	1. Compute and return log2(x) in two pieces:
+ *		log2(x) = w1 + w2,
+ *	   where w1 has 113-53 = 60 bit trailing zeros.
+ *	2. Perform y*log2(x) = n+y' by simulating muti-precision
+ *	   arithmetic, where |y'|<=0.5.
+ *	3. Return x**y = 2**n*exp(y'*log2)
+ *
+ * Special cases:
+ *	1.  (anything) ** 0  is 1
+ *	2.  (anything) ** 1  is itself
+ *	3.  (anything) ** NAN is NAN
+ *	4.  NAN ** (anything except 0) is NAN
+ *	5.  +-(|x| > 1) **  +INF is +INF
+ *	6.  +-(|x| > 1) **  -INF is +0
+ *	7.  +-(|x| < 1) **  +INF is +0
+ *	8.  +-(|x| < 1) **  -INF is +INF
+ *	9.  +-1         ** +-INF is NAN
+ *	10. +0 ** (+anything except 0, NAN)               is +0
+ *	11. -0 ** (+anything except 0, NAN, odd integer)  is +0
+ *	12. +0 ** (-anything except 0, NAN)               is +INF
+ *	13. -0 ** (-anything except 0, NAN, odd integer)  is +INF
+ *	14. -0 ** (odd integer) = -( +0 ** (odd integer) )
+ *	15. +INF ** (+anything except 0,NAN) is +INF
+ *	16. +INF ** (-anything except 0,NAN) is +0
+ *	17. -INF ** (anything)  = -0 ** (-anything)
+ *	18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
+ *	19. (-anything except 0 and inf) ** (non-integer) is NAN
+ *
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const long double bp[] = {
+  1.0L,
+  1.5L,
+};
+
+/* log_2(1.5) */
+static const long double dp_h[] = {
+  0.0,
+  5.8496250072115607565592654282227158546448E-1L
+};
+
+/* Low part of log_2(1.5) */
+static const long double dp_l[] = {
+  0.0,
+  1.0579781240112554492329533686862998106046E-16L
+};
+
+static const long double zero = 0.0L,
+  one = 1.0L,
+  two = 2.0L,
+  two113 = 1.0384593717069655257060992658440192E34L,
+  huge = 1.0e3000L,
+  tiny = 1.0e-3000L;
+
+/* 3/2 log x = 3 z + z^3 + z^3 (z^2 R(z^2))
+   z = (x-1)/(x+1)
+   1 <= x <= 1.25
+   Peak relative error 2.3e-37 */
+static const long double LN[] =
+{
+ -3.0779177200290054398792536829702930623200E1L,
+  6.5135778082209159921251824580292116201640E1L,
+ -4.6312921812152436921591152809994014413540E1L,
+  1.2510208195629420304615674658258363295208E1L,
+ -9.9266909031921425609179910128531667336670E-1L
+};
+static const long double LD[] =
+{
+ -5.129862866715009066465422805058933131960E1L,
+  1.452015077564081884387441590064272782044E2L,
+ -1.524043275549860505277434040464085593165E2L,
+  7.236063513651544224319663428634139768808E1L,
+ -1.494198912340228235853027849917095580053E1L
+  /* 1.0E0 */
+};
+
+/* exp(x) = 1 + x - x / (1 - 2 / (x - x^2 R(x^2)))
+   0 <= x <= 0.5
+   Peak relative error 5.7e-38  */
+static const long double PN[] =
+{
+  5.081801691915377692446852383385968225675E8L,
+  9.360895299872484512023336636427675327355E6L,
+  4.213701282274196030811629773097579432957E4L,
+  5.201006511142748908655720086041570288182E1L,
+  9.088368420359444263703202925095675982530E-3L,
+};
+static const long double PD[] =
+{
+  3.049081015149226615468111430031590411682E9L,
+  1.069833887183886839966085436512368982758E8L,
+  8.259257717868875207333991924545445705394E5L,
+  1.872583833284143212651746812884298360922E3L,
+  /* 1.0E0 */
+};
+
+static const long double
+  /* ln 2 */
+  lg2 = 6.9314718055994530941723212145817656807550E-1L,
+  lg2_h = 6.9314718055994528622676398299518041312695E-1L,
+  lg2_l = 2.3190468138462996154948554638754786504121E-17L,
+  ovt = 8.0085662595372944372e-0017L,
+  /* 2/(3*log(2)) */
+  cp = 9.6179669392597560490661645400126142495110E-1L,
+  cp_h = 9.6179669392597555432899980587535537779331E-1L,
+  cp_l = 5.0577616648125906047157785230014751039424E-17L;
+
+#ifdef __STDC__
+long double
+__ieee754_powl (long double x, long double y)
+#else
+long double
+__ieee754_powl (x, y)
+     long double x, y;
+#endif
+{
+  long double z, ax, z_h, z_l, p_h, p_l;
+  long double y1, t1, t2, r, s, t, u, v, w;
+  long double s2, s_h, s_l, t_h, t_l;
+  int32_t i, j, k, yisint, n;
+  u_int32_t ix, iy;
+  int32_t hx, hy;
+  ieee854_long_double_shape_type o, p, q;
+
+  p.value = x;
+  hx = p.parts32.w0;
+  ix = hx & 0x7fffffff;
+
+  q.value = y;
+  hy = q.parts32.w0;
+  iy = hy & 0x7fffffff;
+
+
+  /* y==zero: x**0 = 1 */
+  if ((iy | q.parts32.w1 | (q.parts32.w2 & 0x7fffffff) | q.parts32.w3) == 0)
+    return one;
+
+  /* 1.0**y = 1; -1.0**+-Inf = 1 */
+  if (x == one)
+    return one;
+  if (x == -1.0L && iy == 0x7ff00000
+      && (q.parts32.w1 | (q.parts32.w2 & 0x7fffffff) | q.parts32.w3) == 0)
+    return one;
+
+  /* +-NaN return x+y */
+  if ((ix > 0x7ff00000)
+      || ((ix == 0x7ff00000)
+	  && ((p.parts32.w1 | (p.parts32.w2 & 0x7fffffff) | p.parts32.w3) != 0))
+      || (iy > 0x7ff00000)
+      || ((iy == 0x7ff00000)
+	  && ((q.parts32.w1 | (q.parts32.w2 & 0x7fffffff) | q.parts32.w3) != 0)))
+    return x + y;
+
+  /* determine if y is an odd int when x < 0
+   * yisint = 0       ... y is not an integer
+   * yisint = 1       ... y is an odd int
+   * yisint = 2       ... y is an even int
+   */
+  yisint = 0;
+  if (hx < 0)
+    {
+      if ((q.parts32.w2 & 0x7fffffff) >= 0x43400000)	/* Low part >= 2^53 */
+	yisint = 2;		/* even integer y */
+      else if (iy >= 0x3ff00000)	/* 1.0 */
+	{
+	  if (__floorl (y) == y)
+	    {
+	      z = 0.5 * y;
+	      if (__floorl (z) == z)
+		yisint = 2;
+	      else
+		yisint = 1;
+	    }
+	}
+    }
+
+  /* special value of y */
+  if ((q.parts32.w1 | (q.parts32.w2 & 0x7fffffff) | q.parts32.w3) == 0)
+    {
+      if (iy == 0x7ff00000 && q.parts32.w1 == 0)	/* y is +-inf */
+	{
+	  if (((ix - 0x3ff00000) | p.parts32.w1
+	       | (p.parts32.w2 & 0x7fffffff) | p.parts32.w3) == 0)
+	    return y - y;	/* inf**+-1 is NaN */
+	  else if (ix > 0x3ff00000 || fabsl (x) > 1.0L)
+	    /* (|x|>1)**+-inf = inf,0 */
+	    return (hy >= 0) ? y : zero;
+	  else
+	    /* (|x|<1)**-,+inf = inf,0 */
+	    return (hy < 0) ? -y : zero;
+	}
+      if (iy == 0x3ff00000)
+	{			/* y is  +-1 */
+	  if (hy < 0)
+	    return one / x;
+	  else
+	    return x;
+	}
+      if (hy == 0x40000000)
+	return x * x;		/* y is  2 */
+      if (hy == 0x3fe00000)
+	{			/* y is  0.5 */
+	  if (hx >= 0)		/* x >= +0 */
+	    return __ieee754_sqrtl (x);
+	}
+    }
+
+  ax = fabsl (x);
+  /* special value of x */
+  if ((p.parts32.w1 | (p.parts32.w2 & 0x7fffffff) | p.parts32.w3) == 0)
+    {
+      if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000)
+	{
+	  z = ax;		/*x is +-0,+-inf,+-1 */
+	  if (hy < 0)
+	    z = one / z;	/* z = (1/|x|) */
+	  if (hx < 0)
+	    {
+	      if (((ix - 0x3ff00000) | yisint) == 0)
+		{
+		  z = (z - z) / (z - z);	/* (-1)**non-int is NaN */
+		}
+	      else if (yisint == 1)
+		z = -z;		/* (x<0)**odd = -(|x|**odd) */
+	    }
+	  return z;
+	}
+    }
+
+  /* (x<0)**(non-int) is NaN */
+  if (((((u_int32_t) hx >> 31) - 1) | yisint) == 0)
+    return (x - x) / (x - x);
+
+  /* |y| is huge.
+     2^-16495 = 1/2 of smallest representable value.
+     If (1 - 1/131072)^y underflows, y > 1.4986e9 */
+  if (iy > 0x41d654b0)
+    {
+      /* if (1 - 2^-113)^y underflows, y > 1.1873e38 */
+      if (iy > 0x47d654b0)
+	{
+	  if (ix <= 0x3fefffff)
+	    return (hy < 0) ? huge * huge : tiny * tiny;
+	  if (ix >= 0x3ff00000)
+	    return (hy > 0) ? huge * huge : tiny * tiny;
+	}
+      /* over/underflow if x is not close to one */
+      if (ix < 0x3fefffff)
+	return (hy < 0) ? huge * huge : tiny * tiny;
+      if (ix > 0x3ff00000)
+	return (hy > 0) ? huge * huge : tiny * tiny;
+    }
+
+  n = 0;
+  /* take care subnormal number */
+  if (ix < 0x00100000)
+    {
+      ax *= two113;
+      n -= 113;
+      o.value = ax;
+      ix = o.parts32.w0;
+    }
+  n += ((ix) >> 20) - 0x3ff;
+  j = ix & 0x000fffff;
+  /* determine interval */
+  ix = j | 0x3ff00000;		/* normalize ix */
+  if (j <= 0x39880)
+    k = 0;			/* |x|<sqrt(3/2) */
+  else if (j < 0xbb670)
+    k = 1;			/* |x|<sqrt(3)   */
+  else
+    {
+      k = 0;
+      n += 1;
+      ix -= 0x00100000;
+    }
+
+  o.value = ax;
+  o.value = __scalbnl (o.value, ((int) ((ix - o.parts32.w0) * 2)) >> 21);
+  ax = o.value;
+
+  /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
+  u = ax - bp[k];		/* bp[0]=1.0, bp[1]=1.5 */
+  v = one / (ax + bp[k]);
+  s = u * v;
+  s_h = s;
+
+  o.value = s_h;
+  o.parts32.w3 = 0;
+  o.parts32.w2 &= 0xffff8000;
+  s_h = o.value;
+  /* t_h=ax+bp[k] High */
+  t_h = ax + bp[k];
+  o.value = t_h;
+  o.parts32.w3 = 0;
+  o.parts32.w2 &= 0xffff8000;
+  t_h = o.value;
+  t_l = ax - (t_h - bp[k]);
+  s_l = v * ((u - s_h * t_h) - s_h * t_l);
+  /* compute log(ax) */
+  s2 = s * s;
+  u = LN[0] + s2 * (LN[1] + s2 * (LN[2] + s2 * (LN[3] + s2 * LN[4])));
+  v = LD[0] + s2 * (LD[1] + s2 * (LD[2] + s2 * (LD[3] + s2 * (LD[4] + s2))));
+  r = s2 * s2 * u / v;
+  r += s_l * (s_h + s);
+  s2 = s_h * s_h;
+  t_h = 3.0 + s2 + r;
+  o.value = t_h;
+  o.parts32.w3 = 0;
+  o.parts32.w2 &= 0xffff8000;
+  t_h = o.value;
+  t_l = r - ((t_h - 3.0) - s2);
+  /* u+v = s*(1+...) */
+  u = s_h * t_h;
+  v = s_l * t_h + t_l * s;
+  /* 2/(3log2)*(s+...) */
+  p_h = u + v;
+  o.value = p_h;
+  o.parts32.w3 = 0;
+  o.parts32.w2 &= 0xffff8000;
+  p_h = o.value;
+  p_l = v - (p_h - u);
+  z_h = cp_h * p_h;		/* cp_h+cp_l = 2/(3*log2) */
+  z_l = cp_l * p_h + p_l * cp + dp_l[k];
+  /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
+  t = (long double) n;
+  t1 = (((z_h + z_l) + dp_h[k]) + t);
+  o.value = t1;
+  o.parts32.w3 = 0;
+  o.parts32.w2 &= 0xffff8000;
+  t1 = o.value;
+  t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
+
+  /* s (sign of result -ve**odd) = -1 else = 1 */
+  s = one;
+  if (((((u_int32_t) hx >> 31) - 1) | (yisint - 1)) == 0)
+    s = -one;			/* (-ve)**(odd int) */
+
+  /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
+  y1 = y;
+  o.value = y1;
+  o.parts32.w3 = 0;
+  o.parts32.w2 &= 0xffff8000;
+  y1 = o.value;
+  p_l = (y - y1) * t1 + y * t2;
+  p_h = y1 * t1;
+  z = p_l + p_h;
+  o.value = z;
+  j = o.parts32.w0;
+  if (j >= 0x40d00000) /* z >= 16384 */
+    {
+      /* if z > 16384 */
+      if (((j - 0x40d00000) | o.parts32.w1
+        | (o.parts32.w2 & 0x7fffffff) | o.parts32.w3) != 0)
+	return s * huge * huge;	/* overflow */
+      else
+	{
+	  if (p_l + ovt > z - p_h)
+	    return s * huge * huge;	/* overflow */
+	}
+    }
+  else if ((j & 0x7fffffff) >= 0x40d01b90)	/* z <= -16495 */
+    {
+      /* z < -16495 */
+      if (((j - 0xc0d01bc0) | o.parts32.w1
+         | (o.parts32.w2 & 0x7fffffff) | o.parts32.w3) != 0)
+	return s * tiny * tiny;	/* underflow */
+      else
+	{
+	  if (p_l <= z - p_h)
+	    return s * tiny * tiny;	/* underflow */
+	}
+    }
+  /* compute 2**(p_h+p_l) */
+  i = j & 0x7fffffff;
+  k = (i >> 20) - 0x3ff;
+  n = 0;
+  if (i > 0x3fe00000)
+    {				/* if |z| > 0.5, set n = [z+0.5] */
+      n = __floorl (z + 0.5L);
+      t = n;
+      p_h -= t;
+    }
+  t = p_l + p_h;
+  o.value = t;
+  o.parts32.w3 = 0;
+  o.parts32.w2 &= 0xffff8000;
+  t = o.value;
+  u = t * lg2_h;
+  v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
+  z = u + v;
+  w = v - (z - u);
+  /*  exp(z) */
+  t = z * z;
+  u = PN[0] + t * (PN[1] + t * (PN[2] + t * (PN[3] + t * PN[4])));
+  v = PD[0] + t * (PD[1] + t * (PD[2] + t * (PD[3] + t)));
+  t1 = z - t * u / v;
+  r = (z * t1) / (t1 - two) - (w + z * w);
+  z = one - (r - z);
+  z = __scalbnl (z, n);
+  return s * z;
+}