-/* logll.c
+/* Copyright 2001 by Stephen L. Moshier <moshier@na-net.ornl.gov>
+
+ This program is free software: you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation; either version 3 of the License, or
+ (at your option) any later version.
+
+ This program 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 General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program. If not, see <http://www.gnu.org/licenses/>. */
+
+#include <config.h>
+
+/* Specification. */
+#include <math.h>
+
+/* logll.c
*
* Natural logarithm for 128-bit long double precision.
*
*
*/
-#include <math.h>
-
-#include "mathl.h"
-
-/* Copyright 2001 by Stephen L. Moshier <moshier@na-net.ornl.gov> */
-
/* log(1+x) = x - .5 x^2 + x^3 l(x)
-.0078125 <= x <= +.0078125
peak relative error 1.2e-37 */
long double
logl(long double x)
{
- long double z, y, w, u, t;
- unsigned int m;
+ long double z, y, w;
+ long double t;
int k, e;
/* Check for IEEE special cases. */
+ /* log(NaN) = NaN. */
+ if (isnanl (x))
+ {
+ return x;
+ }
/* log(0) = -infinity. */
if (x == 0.0L)
- return -0.5L / 0.0L;
-
+ {
+ return -0.5L / ZERO;
+ }
/* log ( x < 0 ) = NaN */
if (x < 0.0L)
- return (x - x) / (x - x);
-
- /* log (infinity or NaN) */
- if (x + x == x || x != x)
- return x + x;
+ {
+ return (x - x) / ZERO;
+ }
+ /* log (infinity) */
+ if (x + x == x)
+ {
+ return x + x;
+ }
/* Extract exponent and reduce domain to 0.703125 <= u < 1.40625 */
x = frexpl(x, &e);
/* On this interval the table is not used due to cancellation error. */
if ((x <= 1.0078125L) && (x >= 0.9921875L))
{
+ z = x - 1.0L;
k = 64;
t = 1.0L;
- z = x - 1.0L;
}
else
{
- k = floorl((x - 0.5L) * 128.0L);
+ k = floorl ((x - 0.5L) * 128.0L);
t = 0.5L + k / 128.0L;
z = (x - t) / t;
}
/* Series expansion of log(1+z). */
w = z * z;
y = ((((((((((((l15 * z
- + l14) * z
- + l13) * z
- + l12) * z
- + l11) * z
- + l10) * z
- + l9) * z
- + l8) * z
- + l7) * z
- + l6) * z
- + l5) * z
- + l4) * z
+ + l14) * z
+ + l13) * z
+ + l12) * z
+ + l11) * z
+ + l10) * z
+ + l9) * z
+ + l8) * z
+ + l7) * z
+ + l6) * z
+ + l5) * z
+ + l4) * z
+ l3) * z * w;
y -= 0.5 * w;
y += e * ln2b; /* Base 2 exponent offset times ln(2). */