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authorZack Weinberg <zackw@panix.com>2017-06-08 15:39:03 -0400
committerZack Weinberg <zackw@panix.com>2017-06-08 15:39:03 -0400
commit5046dbb4a7eba5eccfd258f92f4735c9ffc8d069 (patch)
tree4470480d904b65cf14ca524f96f79eca818c3eaf /REORG.TODO/sysdeps/ieee754/ldbl-128/e_log10l.c
parent199fc19d3aaaf57944ef036e15904febe877fc93 (diff)
downloadglibc-zack/build-layout-experiment.tar.gz
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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).
Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/ldbl-128/e_log10l.c')
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diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/e_log10l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_log10l.c
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index 0000000000..c992f6e5ee
--- /dev/null
+++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/e_log10l.c
@@ -0,0 +1,259 @@
+/*							log10l.c
+ *
+ *	Common logarithm, 128-bit long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, log10l();
+ *
+ * y = log10l( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base 10 logarithm of x.
+ *
+ * The argument 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(x-1)/x+1),
+ *
+ *     log(x) = z + z^3 P(z)/Q(z).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0.5, 2.0     30000      2.3e-34     4.9e-35
+ *    IEEE     exp(+-10000)  30000      1.0e-34     4.1e-35
+ *
+ * In the tests over the interval exp(+-10000), the logarithms
+ * of the random arguments were uniformly distributed over
+ * [-10000, +10000].
+ *
+ */
+
+/*
+   Cephes Math Library Release 2.2:  January, 1991
+   Copyright 1984, 1991 by Stephen L. Moshier
+   Adapted for glibc November, 2001
+
+    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, see <http://www.gnu.org/licenses/>.
+ */
+
+#include <math.h>
+#include <math_private.h>
+
+/* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
+ * 1/sqrt(2) <= x < sqrt(2)
+ * Theoretical peak relative error = 5.3e-37,
+ * relative peak error spread = 2.3e-14
+ */
+static const _Float128 P[13] =
+{
+  L(1.313572404063446165910279910527789794488E4),
+  L(7.771154681358524243729929227226708890930E4),
+  L(2.014652742082537582487669938141683759923E5),
+  L(3.007007295140399532324943111654767187848E5),
+  L(2.854829159639697837788887080758954924001E5),
+  L(1.797628303815655343403735250238293741397E5),
+  L(7.594356839258970405033155585486712125861E4),
+  L(2.128857716871515081352991964243375186031E4),
+  L(3.824952356185897735160588078446136783779E3),
+  L(4.114517881637811823002128927449878962058E2),
+  L(2.321125933898420063925789532045674660756E1),
+  L(4.998469661968096229986658302195402690910E-1),
+  L(1.538612243596254322971797716843006400388E-6)
+};
+static const _Float128 Q[12] =
+{
+  L(3.940717212190338497730839731583397586124E4),
+  L(2.626900195321832660448791748036714883242E5),
+  L(7.777690340007566932935753241556479363645E5),
+  L(1.347518538384329112529391120390701166528E6),
+  L(1.514882452993549494932585972882995548426E6),
+  L(1.158019977462989115839826904108208787040E6),
+  L(6.132189329546557743179177159925690841200E5),
+  L(2.248234257620569139969141618556349415120E5),
+  L(5.605842085972455027590989944010492125825E4),
+  L(9.147150349299596453976674231612674085381E3),
+  L(9.104928120962988414618126155557301584078E2),
+  L(4.839208193348159620282142911143429644326E1)
+/* 1.000000000000000000000000000000000000000E0L, */
+};
+
+/* 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 R[6] =
+{
+  L(1.418134209872192732479751274970992665513E5),
+ L(-8.977257995689735303686582344659576526998E4),
+  L(2.048819892795278657810231591630928516206E4),
+ L(-2.024301798136027039250415126250455056397E3),
+  L(8.057002716646055371965756206836056074715E1),
+ L(-8.828896441624934385266096344596648080902E-1)
+};
+static const _Float128 S[6] =
+{
+  L(1.701761051846631278975701529965589676574E6),
+ L(-1.332535117259762928288745111081235577029E6),
+  L(4.001557694070773974936904547424676279307E5),
+ L(-5.748542087379434595104154610899551484314E4),
+  L(3.998526750980007367835804959888064681098E3),
+ L(-1.186359407982897997337150403816839480438E2)
+/* 1.000000000000000000000000000000000000000E0L, */
+};
+
+static const _Float128
+/* log10(2) */
+L102A = L(0.3125),
+L102B = L(-1.14700043360188047862611052755069732318101185E-2),
+/* log10(e) */
+L10EA = L(0.5),
+L10EB = L(-6.570551809674817234887108108339491770560299E-2),
+/* sqrt(2)/2 */
+SQRTH = L(7.071067811865475244008443621048490392848359E-1);
+
+
+
+/* Evaluate P[n] x^n  +  P[n-1] x^(n-1)  +  ...  +  P[0] */
+
+static _Float128
+neval (_Float128 x, const _Float128 *p, int n)
+{
+  _Float128 y;
+
+  p += n;
+  y = *p--;
+  do
+    {
+      y = y * x + *p--;
+    }
+  while (--n > 0);
+  return y;
+}
+
+
+/* Evaluate x^n+1  +  P[n] x^(n)  +  P[n-1] x^(n-1)  +  ...  +  P[0] */
+
+static _Float128
+deval (_Float128 x, const _Float128 *p, int n)
+{
+  _Float128 y;
+
+  p += n;
+  y = x + *p--;
+  do
+    {
+      y = y * x + *p--;
+    }
+  while (--n > 0);
+  return y;
+}
+
+
+
+_Float128
+__ieee754_log10l (_Float128 x)
+{
+  _Float128 z;
+  _Float128 y;
+  int e;
+  int64_t hx, lx;
+
+/* Test for domain */
+  GET_LDOUBLE_WORDS64 (hx, lx, x);
+  if (((hx & 0x7fffffffffffffffLL) | lx) == 0)
+    return (-1 / __fabsl (x));		/* log10l(+-0)=-inf  */
+  if (hx < 0)
+    return (x - x) / (x - x);
+  if (hx >= 0x7fff000000000000LL)
+    return (x + x);
+
+  if (x == 1)
+    return 0;
+
+/* separate mantissa from exponent */
+
+/* Note, frexp is used so that denormal numbers
+ * will be handled properly.
+ */
+  x = __frexpl (x, &e);
+
+
+/* logarithm using log(x) = z + z**3 P(z)/Q(z),
+ * where z = 2(x-1)/x+1)
+ */
+  if ((e > 2) || (e < -2))
+    {
+      if (x < SQRTH)
+	{			/* 2( 2x-1 )/( 2x+1 ) */
+	  e -= 1;
+	  z = x - L(0.5);
+	  y = L(0.5) * z + L(0.5);
+	}
+      else
+	{			/*  2 (x-1)/(x+1)   */
+	  z = x - L(0.5);
+	  z -= L(0.5);
+	  y = L(0.5) * x + L(0.5);
+	}
+      x = z / y;
+      z = x * x;
+      y = x * (z * neval (z, R, 5) / deval (z, S, 5));
+      goto done;
+    }
+
+
+/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
+
+  if (x < SQRTH)
+    {
+      e -= 1;
+      x = 2.0 * x - 1;	/*  2x - 1  */
+    }
+  else
+    {
+      x = x - 1;
+    }
+  z = x * x;
+  y = x * (z * neval (x, P, 12) / deval (x, Q, 11));
+  y = y - 0.5 * z;
+
+done:
+
+  /* Multiply log of fraction by log10(e)
+   * and base 2 exponent by log10(2).
+   */
+  z = y * L10EB;
+  z += x * L10EB;
+  z += e * L102B;
+  z += y * L10EA;
+  z += x * L10EA;
+  z += e * L102A;
+  return (z);
+}
+strong_alias (__ieee754_log10l, __log10l_finite)