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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/dbl-64/e_exp2.c
parent199fc19d3aaaf57944ef036e15904febe877fc93 (diff)
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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/dbl-64/e_exp2.c')
-rw-r--r--REORG.TODO/sysdeps/ieee754/dbl-64/e_exp2.c133
1 files changed, 133 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_exp2.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_exp2.c
new file mode 100644
index 0000000000..9efda23f06
--- /dev/null
+++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_exp2.c
@@ -0,0 +1,133 @@
+/* Double-precision floating point 2^x.
+   Copyright (C) 1997-2017 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+   Contributed by Geoffrey Keating <geoffk@ozemail.com.au>
+
+   The GNU C 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.
+
+   The GNU C 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 the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+/* The basic design here is from
+   Shmuel Gal and Boris Bachelis, "An Accurate Elementary Mathematical
+   Library for the IEEE Floating Point Standard", ACM Trans. Math. Soft.,
+   17 (1), March 1991, pp. 26-45.
+   It has been slightly modified to compute 2^x instead of e^x.
+   */
+#include <stdlib.h>
+#include <float.h>
+#include <ieee754.h>
+#include <math.h>
+#include <fenv.h>
+#include <inttypes.h>
+#include <math_private.h>
+
+#include "t_exp2.h"
+
+static const double TWO1023 = 8.988465674311579539e+307;
+static const double TWOM1000 = 9.3326361850321887899e-302;
+
+double
+__ieee754_exp2 (double x)
+{
+  static const double himark = (double) DBL_MAX_EXP;
+  static const double lomark = (double) (DBL_MIN_EXP - DBL_MANT_DIG - 1);
+
+  /* Check for usual case.  */
+  if (__glibc_likely (isless (x, himark)))
+    {
+      /* Exceptional cases:  */
+      if (__glibc_unlikely (!isgreaterequal (x, lomark)))
+	{
+	  if (isinf (x))
+	    /* e^-inf == 0, with no error.  */
+	    return 0;
+	  else
+	    /* Underflow */
+	    return TWOM1000 * TWOM1000;
+	}
+
+      static const double THREEp42 = 13194139533312.0;
+      int tval, unsafe;
+      double rx, x22, result;
+      union ieee754_double ex2_u, scale_u;
+
+      if (fabs (x) < DBL_EPSILON / 4.0)
+	return 1.0 + x;
+
+      {
+	SET_RESTORE_ROUND_NOEX (FE_TONEAREST);
+
+	/* 1. Argument reduction.
+	   Choose integers ex, -256 <= t < 256, and some real
+	   -1/1024 <= x1 <= 1024 so that
+	   x = ex + t/512 + x1.
+
+	   First, calculate rx = ex + t/512.  */
+	rx = x + THREEp42;
+	rx -= THREEp42;
+	x -= rx;  /* Compute x=x1. */
+	/* Compute tval = (ex*512 + t)+256.
+	   Now, t = (tval mod 512)-256 and ex=tval/512  [that's mod, NOT %;
+	   and /-round-to-nearest not the usual c integer /].  */
+	tval = (int) (rx * 512.0 + 256.0);
+
+	/* 2. Adjust for accurate table entry.
+	   Find e so that
+	   x = ex + t/512 + e + x2
+	   where -1e6 < e < 1e6, and
+	   (double)(2^(t/512+e))
+	   is accurate to one part in 2^-64.  */
+
+	/* 'tval & 511' is the same as 'tval%512' except that it's always
+	   positive.
+	   Compute x = x2.  */
+	x -= exp2_deltatable[tval & 511];
+
+	/* 3. Compute ex2 = 2^(t/512+e+ex).  */
+	ex2_u.d = exp2_accuratetable[tval & 511];
+	tval >>= 9;
+	/* x2 is an integer multiple of 2^-54; avoid intermediate
+	   underflow from the calculation of x22 * x.  */
+	unsafe = abs (tval) >= -DBL_MIN_EXP - 56;
+	ex2_u.ieee.exponent += tval >> unsafe;
+	scale_u.d = 1.0;
+	scale_u.ieee.exponent += tval - (tval >> unsafe);
+
+	/* 4. Approximate 2^x2 - 1, using a fourth-degree polynomial,
+	   with maximum error in [-2^-10-2^-30,2^-10+2^-30]
+	   less than 10^-19.  */
+
+	x22 = (((.0096181293647031180
+		 * x + .055504110254308625)
+		* x + .240226506959100583)
+	       * x + .69314718055994495) * ex2_u.d;
+	math_opt_barrier (x22);
+      }
+
+      /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex).  */
+      result = x22 * x + ex2_u.d;
+
+      if (!unsafe)
+	return result;
+      else
+	{
+	  result *= scale_u.d;
+	  math_check_force_underflow_nonneg (result);
+	  return result;
+	}
+    }
+  else
+    /* Return x, if x is a NaN or Inf; or overflow, otherwise.  */
+    return TWO1023 * x;
+}
+strong_alias (__ieee754_exp2, __exp2_finite)