| /* mpfr_log1p -- Compute log(1+x) |
| |
| Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc. |
| Contributed by the Arenaire and Cacao projects, INRIA. |
| |
| This file is part of the GNU MPFR Library. |
| |
| The GNU MPFR 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 MPFR 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 MPFR Library; see the file COPYING.LIB. If not, write to |
| the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, |
| MA 02110-1301, USA. */ |
| |
| #define MPFR_NEED_LONGLONG_H |
| #include "mpfr-impl.h" |
| |
| /* The computation of log1p is done by |
| log1p(x)=log(1+x) */ |
| |
| int |
| mpfr_log1p (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode) |
| { |
| int comp, inexact; |
| mp_exp_t ex; |
| MPFR_SAVE_EXPO_DECL (expo); |
| |
| if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) |
| { |
| if (MPFR_IS_NAN (x)) |
| { |
| MPFR_SET_NAN (y); |
| MPFR_RET_NAN; |
| } |
| /* check for inf or -inf (result is not defined) */ |
| else if (MPFR_IS_INF (x)) |
| { |
| if (MPFR_IS_POS (x)) |
| { |
| MPFR_SET_INF (y); |
| MPFR_SET_POS (y); |
| MPFR_RET (0); |
| } |
| else |
| { |
| MPFR_SET_NAN (y); |
| MPFR_RET_NAN; |
| } |
| } |
| else /* x is zero */ |
| { |
| MPFR_ASSERTD (MPFR_IS_ZERO (x)); |
| MPFR_SET_ZERO (y); /* log1p(+/- 0) = +/- 0 */ |
| MPFR_SET_SAME_SIGN (y, x); |
| MPFR_RET (0); |
| } |
| } |
| |
| ex = MPFR_GET_EXP (x); |
| if (ex < 0) /* -0.5 < x < 0.5 */ |
| { |
| /* For x > 0, abs(log(1+x)-x) < x^2/2. |
| For x > -0.5, abs(log(1+x)-x) < x^2. */ |
| if (MPFR_IS_POS (x)) |
| MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, - ex - 1, 0, 0, rnd_mode, {}); |
| else |
| MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, - ex, 0, 1, rnd_mode, {}); |
| } |
| |
| comp = mpfr_cmp_si (x, -1); |
| /* log1p(x) is undefined for x < -1 */ |
| if (MPFR_UNLIKELY(comp <= 0)) |
| { |
| if (comp == 0) |
| /* x=0: log1p(-1)=-inf (division by zero) */ |
| { |
| MPFR_SET_INF (y); |
| MPFR_SET_NEG (y); |
| MPFR_RET (0); |
| } |
| MPFR_SET_NAN (y); |
| MPFR_RET_NAN; |
| } |
| |
| MPFR_SAVE_EXPO_MARK (expo); |
| |
| /* General case */ |
| { |
| /* Declaration of the intermediary variable */ |
| mpfr_t t; |
| /* Declaration of the size variable */ |
| mp_prec_t Ny = MPFR_PREC(y); /* target precision */ |
| mp_prec_t Nt; /* working precision */ |
| mp_exp_t err; /* error */ |
| MPFR_ZIV_DECL (loop); |
| |
| /* compute the precision of intermediary variable */ |
| /* the optimal number of bits : see algorithms.tex */ |
| Nt = Ny + MPFR_INT_CEIL_LOG2 (Ny) + 6; |
| |
| /* if |x| is smaller than 2^(-e), we will loose about e bits |
| in log(1+x) */ |
| if (MPFR_EXP(x) < 0) |
| Nt += -MPFR_EXP(x); |
| |
| /* initialise of intermediary variable */ |
| mpfr_init2 (t, Nt); |
| |
| /* First computation of log1p */ |
| MPFR_ZIV_INIT (loop, Nt); |
| for (;;) |
| { |
| /* compute log1p */ |
| inexact = mpfr_add_ui (t, x, 1, GMP_RNDN); /* 1+x */ |
| /* if inexact = 0, then t = x+1, and the result is simply log(t) */ |
| if (inexact == 0) |
| { |
| inexact = mpfr_log (y, t, rnd_mode); |
| goto end; |
| } |
| mpfr_log (t, t, GMP_RNDN); /* log(1+x) */ |
| |
| /* the error is bounded by (1/2+2^(1-EXP(t))*ulp(t) (cf algorithms.tex) |
| if EXP(t)>=2, then error <= ulp(t) |
| if EXP(t)<=1, then error <= 2^(2-EXP(t))*ulp(t) */ |
| err = Nt - MAX (0, 2 - MPFR_GET_EXP (t)); |
| |
| if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode))) |
| break; |
| |
| /* increase the precision */ |
| MPFR_ZIV_NEXT (loop, Nt); |
| mpfr_set_prec (t, Nt); |
| } |
| inexact = mpfr_set (y, t, rnd_mode); |
| |
| end: |
| MPFR_ZIV_FREE (loop); |
| mpfr_clear (t); |
| } |
| |
| MPFR_SAVE_EXPO_FREE (expo); |
| return mpfr_check_range (y, inexact, rnd_mode); |
| } |