--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/libquadmath/math/log1pq.c	Sun Aug 21 07:07:55 2011 +0900
@@ -0,0 +1,244 @@
+/*							log1pl.c
+ *
+ *      Relative error logarithm
+ *	Natural logarithm of 1+x, 128-bit long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, log1pl();
+ *
+ * y = log1pl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base e (2.718...) logarithm of 1+x.
+ *
+ * The argument 1+x is separated into its exponent and fractional
+ * parts.  If the exponent is between -1 and +1, the logarithm
+ * of the fraction is approximated by
+ *
+ *     log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x).
+ *
+ * Otherwise, setting  z = 2(w-1)/(w+1),
+ *
+ *     log(w) = z + z^3 P(z)/Q(z).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      -1, 8       100000      1.9e-34     4.3e-35
+ */
+
+/* Copyright 2001 by Stephen L. Moshier 
+
+    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 */
+
+
+#include "quadmath-imp.h"
+
+/* Coefficients for log(1+x) = x - x^2 / 2 + x^3 P(x)/Q(x)
+ * 1/sqrt(2) <= 1+x < sqrt(2)
+ * Theoretical peak relative error = 5.3e-37,
+ * relative peak error spread = 2.3e-14
+ */
+static const __float128
+  P12 = 1.538612243596254322971797716843006400388E-6Q,
+  P11 = 4.998469661968096229986658302195402690910E-1Q,
+  P10 = 2.321125933898420063925789532045674660756E1Q,
+  P9 = 4.114517881637811823002128927449878962058E2Q,
+  P8 = 3.824952356185897735160588078446136783779E3Q,
+  P7 = 2.128857716871515081352991964243375186031E4Q,
+  P6 = 7.594356839258970405033155585486712125861E4Q,
+  P5 = 1.797628303815655343403735250238293741397E5Q,
+  P4 = 2.854829159639697837788887080758954924001E5Q,
+  P3 = 3.007007295140399532324943111654767187848E5Q,
+  P2 = 2.014652742082537582487669938141683759923E5Q,
+  P1 = 7.771154681358524243729929227226708890930E4Q,
+  P0 = 1.313572404063446165910279910527789794488E4Q,
+  /* Q12 = 1.000000000000000000000000000000000000000E0Q, */
+  Q11 = 4.839208193348159620282142911143429644326E1Q,
+  Q10 = 9.104928120962988414618126155557301584078E2Q,
+  Q9 = 9.147150349299596453976674231612674085381E3Q,
+  Q8 = 5.605842085972455027590989944010492125825E4Q,
+  Q7 = 2.248234257620569139969141618556349415120E5Q,
+  Q6 = 6.132189329546557743179177159925690841200E5Q,
+  Q5 = 1.158019977462989115839826904108208787040E6Q,
+  Q4 = 1.514882452993549494932585972882995548426E6Q,
+  Q3 = 1.347518538384329112529391120390701166528E6Q,
+  Q2 = 7.777690340007566932935753241556479363645E5Q,
+  Q1 = 2.626900195321832660448791748036714883242E5Q,
+  Q0 = 3.940717212190338497730839731583397586124E4Q;
+
+/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
+ * where z = 2(x-1)/(x+1)
+ * 1/sqrt(2) <= x < sqrt(2)
+ * Theoretical peak relative error = 1.1e-35,
+ * relative peak error spread 1.1e-9
+ */
+static const __float128
+  R5 = -8.828896441624934385266096344596648080902E-1Q,
+  R4 = 8.057002716646055371965756206836056074715E1Q,
+  R3 = -2.024301798136027039250415126250455056397E3Q,
+  R2 = 2.048819892795278657810231591630928516206E4Q,
+  R1 = -8.977257995689735303686582344659576526998E4Q,
+  R0 = 1.418134209872192732479751274970992665513E5Q,
+  /* S6 = 1.000000000000000000000000000000000000000E0Q, */
+  S5 = -1.186359407982897997337150403816839480438E2Q,
+  S4 = 3.998526750980007367835804959888064681098E3Q,
+  S3 = -5.748542087379434595104154610899551484314E4Q,
+  S2 = 4.001557694070773974936904547424676279307E5Q,
+  S1 = -1.332535117259762928288745111081235577029E6Q,
+  S0 = 1.701761051846631278975701529965589676574E6Q;
+
+/* C1 + C2 = ln 2 */
+static const __float128 C1 = 6.93145751953125E-1Q;
+static const __float128 C2 = 1.428606820309417232121458176568075500134E-6Q;
+
+static const __float128 sqrth = 0.7071067811865475244008443621048490392848Q;
+static const __float128 zero = 0.0Q;
+
+
+__float128
+log1pq (__float128 xm1)
+{
+  __float128 x, y, z, r, s;
+  ieee854_float128 u;
+  int32_t hx;
+  int e;
+
+  /* Test for NaN or infinity input. */
+  u.value = xm1;
+  hx = u.words32.w0;
+  if (hx >= 0x7fff0000)
+    return xm1;
+
+  /* log1p(+- 0) = +- 0.  */
+  if (((hx & 0x7fffffff) == 0)
+      && (u.words32.w1 | u.words32.w2 | u.words32.w3) == 0)
+    return xm1;
+
+  x = xm1 + 1.0Q;
+
+  /* log1p(-1) = -inf */
+  if (x <= 0.0Q)
+    {
+      if (x == 0.0Q)
+	return (-1.0Q / (x - x));
+      else
+	return (zero / (x - x));
+    }
+
+  /* Separate mantissa from exponent.  */
+
+  /* Use frexp used so that denormal numbers will be handled properly.  */
+  x = frexpq (x, &e);
+
+  /* Logarithm using log(x) = z + z^3 P(z^2)/Q(z^2),
+     where z = 2(x-1)/x+1).  */
+  if ((e > 2) || (e < -2))
+    {
+      if (x < sqrth)
+	{			/* 2( 2x-1 )/( 2x+1 ) */
+	  e -= 1;
+	  z = x - 0.5Q;
+	  y = 0.5Q * z + 0.5Q;
+	}
+      else
+	{			/*  2 (x-1)/(x+1)   */
+	  z = x - 0.5Q;
+	  z -= 0.5Q;
+	  y = 0.5Q * x + 0.5Q;
+	}
+      x = z / y;
+      z = x * x;
+      r = ((((R5 * z
+	      + R4) * z
+	     + R3) * z
+	    + R2) * z
+	   + R1) * z
+	+ R0;
+      s = (((((z
+	       + S5) * z
+	      + S4) * z
+	     + S3) * z
+	    + S2) * z
+	   + S1) * z
+	+ S0;
+      z = x * (z * r / s);
+      z = z + e * C2;
+      z = z + x;
+      z = z + e * C1;
+      return (z);
+    }
+
+
+  /* Logarithm using log(1+x) = x - .5x^2 + x^3 P(x)/Q(x). */
+
+  if (x < sqrth)
+    {
+      e -= 1;
+      if (e != 0)
+	x = 2.0Q * x - 1.0Q;	/*  2x - 1  */
+      else
+	x = xm1;
+    }
+  else
+    {
+      if (e != 0)
+	x = x - 1.0Q;
+      else
+	x = xm1;
+    }
+  z = x * x;
+  r = (((((((((((P12 * x
+		 + P11) * x
+		+ P10) * x
+	       + P9) * x
+	      + P8) * x
+	     + P7) * x
+	    + P6) * x
+	   + P5) * x
+	  + P4) * x
+	 + P3) * x
+	+ P2) * x
+       + P1) * x
+    + P0;
+  s = (((((((((((x
+		 + Q11) * x
+		+ Q10) * x
+	       + Q9) * x
+	      + Q8) * x
+	     + Q7) * x
+	    + Q6) * x
+	   + Q5) * x
+	  + Q4) * x
+	 + Q3) * x
+	+ Q2) * x
+       + Q1) * x
+    + Q0;
+  y = x * (z * r / s);
+  y = y + e * C2;
+  z = y - 0.5Q * z;
+  z = z + x;
+  z = z + e * C1;
+  return (z);
+}