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diff --git a/lib/log1p.c b/lib/log1p.c
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+/* Natural logarithm of 1 plus argument.
+ Copyright (C) 2012-2017 Free Software Foundation, Inc.
+
+ This program 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 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 Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public License
+ along with this program. If not, see <http://www.gnu.org/licenses/>. */
+
+#include <config.h>
+
+/* Specification. */
+#include <math.h>
+
+double
+log1p (double x)
+{
+ if (isnand (x))
+ return x;
+
+ if (x <= -1.0)
+ {
+ if (x == -1.0)
+ /* Return -Infinity. */
+ return - HUGE_VAL;
+ else
+ {
+ /* Return NaN. */
+#if defined _MSC_VER || (defined __sgi && !defined __GNUC__)
+ static double zero;
+ return zero / zero;
+#else
+ return 0.0 / 0.0;
+#endif
+ }
+ }
+
+ if (x < -0.5 || x > 1.0)
+ return log (1.0 + x);
+ /* Here -0.5 <= x <= 1.0. */
+
+ if (x == 0.0)
+ /* Return a zero with the same sign as x. */
+ return x;
+
+ /* Decompose x into
+ 1 + x = (1 + m/256) * (1 + y)
+ where
+ m is an integer, -128 <= m <= 256,
+ y is a number, |y| <= 1/256.
+ y is computed as
+ y = (256 * x - m) / (256 + m).
+ Then
+ log(1+x) = log(m/256) + log(1+y)
+ The first summand is a table lookup.
+ The second summand is computed
+ - either through the power series
+ log(1+y) = y
+ - 1/2 * y^2
+ + 1/3 * y^3
+ - 1/4 * y^4
+ + 1/5 * y^5
+ - 1/6 * y^6
+ + 1/7 * y^7
+ - 1/8 * y^8
+ + 1/9 * y^9
+ - 1/10 * y^10
+ + 1/11 * y^11
+ - 1/12 * y^12
+ + 1/13 * y^13
+ - 1/14 * y^14
+ + 1/15 * y^15
+ - ...
+ - or as log(1+y) = log((1+z)/(1-z)) = 2 * atanh(z)
+ where z = y/(2+y)
+ and atanh(z) is computed through its power series:
+ atanh(z) = z
+ + 1/3 * z^3
+ + 1/5 * z^5
+ + 1/7 * z^7
+ + 1/9 * z^9
+ + 1/11 * z^11
+ + 1/13 * z^13
+ + 1/15 * z^15
+ + ...
+ Since |z| <= 1/511 < 0.002, the relative contribution of the z^9
+ term is < 1/9*0.002^8 < 2^-60 <= 2^-DBL_MANT_DIG, therefore we
+ can truncate the series after the z^7 term. */
+
+ {
+ double m = round (x * 256.0);
+ double y = ((x * 256.0) - m) / (m + 256.0);
+ double z = y / (2.0 + y);
+
+/* Coefficients of the power series for atanh(z). */
+#define ATANH_COEFF_1 1.0
+#define ATANH_COEFF_3 0.333333333333333333333333333333333333334
+#define ATANH_COEFF_5 0.2
+#define ATANH_COEFF_7 0.142857142857142857142857142857142857143
+#define ATANH_COEFF_9 0.1111111111111111111111111111111111111113
+#define ATANH_COEFF_11 0.090909090909090909090909090909090909091
+#define ATANH_COEFF_13 0.076923076923076923076923076923076923077
+#define ATANH_COEFF_15 0.066666666666666666666666666666666666667
+
+ double z2 = z * z;
+ double atanh_z =
+ (((ATANH_COEFF_7
+ * z2 + ATANH_COEFF_5)
+ * z2 + ATANH_COEFF_3)
+ * z2 + ATANH_COEFF_1)
+ * z;
+
+ /* log_table[i] = log((i + 128) / 256).
+ Computed in GNU clisp through
+ (setf (long-float-digits) 128)
+ (setq a 0L0)
+ (setf (long-float-digits) 256)
+ (dotimes (i 385)
+ (format t " ~D,~%"
+ (float (log (* (/ (+ i 128) 256) 1L0)) a))) */
+ static const double log_table[385] =
+ {
+ -0.693147180559945309417232121458176568075,
+ -0.6853650401178903604697692213970398044,
+ -0.677642994023980055266378075415729732197,
+ -0.669980121278410931188432960495886651496,
+ -0.662375521893191621046203913861404403985,
+ -0.65482831625780871022347679633437927773,
+ -0.647337644528651106250552853843513225963,
+ -0.639902666041133026551361927671647791137,
+ -0.632522558743510466836625989417756304788,
+ -0.625196518651437560022666843685547154042,
+ -0.617923759322357783718626781474514153438,
+ -0.61070351134887071814907205278986876216,
+ -0.60353502187025817679728065207969203929,
+ -0.59641755410139419712166106497071313106,
+ -0.58935038687830174459117031769420187977,
+ -0.582332814219655195222425952134964639978,
+ -0.575364144903561854878438011987654863008,
+ -0.568443702058988073553825606077313299585,
+ -0.561570822771226036828515992768693405624,
+ -0.554744857700826173731906247856527380683,
+ -0.547965170715447412135297057717612244552,
+ -0.541231138534103334345428696561292056747,
+ -0.534542150383306725323860946832334992828,
+ -0.527897607664638146541620672180936254347,
+ -0.52129692363328608707713317540302930314,
+ -0.514739523087127012297831879947234599722,
+ -0.50822484206593331675332852879892694707,
+ -0.50175232756031585480793331389686769463,
+ -0.495321437230025429054660050261215099,
+ -0.488931639131254417913411735261937295862,
+ -0.482582411452595671747679308725825054355,
+ -0.476273242259330949798142595713829069596,
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+ -0.43923197057898186527990882355156990061,
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+ -0.427183632062807368078106194920633178807,
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+ 0.667428651271956189947234166318980478403,
+ 0.669430653942629267298885270929503510123,
+ 0.67142865660530232331713904200189252584,
+ 0.67342267521216672029796038880101726475,
+ 0.67541272562017673108090414397019748722,
+ 0.677398823591806140809682609997348298556,
+ 0.67938098479579735014710062847376425181,
+ 0.681359224807903068948071559568089441735,
+ 0.683333559111620688164363148387750369654,
+ 0.68530400309891941654404807896723298642,
+ 0.687270572070960267497006884394346103924,
+ 0.689233281238808980324914337814603903233,
+ 0.691192145724141958859604629216309755938,
+ 0.693147180559945309417232121458176568075
+ };
+ return log_table[128 + (int)m] + 2.0 * atanh_z;
+ }
+}