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Diffstat (limited to 'lib/log1p.c')
-rw-r--r-- | lib/log1p.c | 518 |
1 files changed, 518 insertions, 0 deletions
diff --git a/lib/log1p.c b/lib/log1p.c new file mode 100644 index 000000000..d266290ac --- /dev/null +++ b/lib/log1p.c @@ -0,0 +1,518 @@ +/* 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, + 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