1/* mpfr_log1p -- Compute log(1+x)
2
3Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc.
4Contributed by the AriC and Caramel projects, INRIA.
5
6This file is part of the GNU MPFR Library.
7
8The GNU MPFR Library is free software; you can redistribute it and/or modify
9it under the terms of the GNU Lesser General Public License as published by
10the Free Software Foundation; either version 3 of the License, or (at your
11option) any later version.
12
13The GNU MPFR Library is distributed in the hope that it will be useful, but
14WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
15or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
16License for more details.
17
18You should have received a copy of the GNU Lesser General Public License
19along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
20http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
2151 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
22
23#define MPFR_NEED_LONGLONG_H
24#include "mpfr-impl.h"
25
26 /* The computation of log1p is done by
27    log1p(x)=log(1+x)                      */
28
29int
30mpfr_log1p (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
31{
32  int comp, inexact;
33  mpfr_exp_t ex;
34  MPFR_SAVE_EXPO_DECL (expo);
35
36  MPFR_LOG_FUNC
37    (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode),
38     ("y[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (y), mpfr_log_prec, y,
39      inexact));
40
41  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
42    {
43      if (MPFR_IS_NAN (x))
44        {
45          MPFR_SET_NAN (y);
46          MPFR_RET_NAN;
47        }
48      /* check for inf or -inf (result is not defined) */
49      else if (MPFR_IS_INF (x))
50        {
51          if (MPFR_IS_POS (x))
52            {
53              MPFR_SET_INF (y);
54              MPFR_SET_POS (y);
55              MPFR_RET (0);
56            }
57          else
58            {
59              MPFR_SET_NAN (y);
60              MPFR_RET_NAN;
61            }
62        }
63      else /* x is zero */
64        {
65          MPFR_ASSERTD (MPFR_IS_ZERO (x));
66          MPFR_SET_ZERO (y);   /* log1p(+/- 0) = +/- 0 */
67          MPFR_SET_SAME_SIGN (y, x);
68          MPFR_RET (0);
69        }
70    }
71
72  ex = MPFR_GET_EXP (x);
73  if (ex < 0)  /* -0.5 < x < 0.5 */
74    {
75      /* For x > 0,    abs(log(1+x)-x) < x^2/2.
76         For x > -0.5, abs(log(1+x)-x) < x^2. */
77      if (MPFR_IS_POS (x))
78        MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, - ex - 1, 0, 0, rnd_mode, {});
79      else
80        MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, - ex, 0, 1, rnd_mode, {});
81    }
82
83  comp = mpfr_cmp_si (x, -1);
84  /* log1p(x) is undefined for x < -1 */
85  if (MPFR_UNLIKELY(comp <= 0))
86    {
87      if (comp == 0)
88        /* x=0: log1p(-1)=-inf (divide-by-zero exception) */
89        {
90          MPFR_SET_INF (y);
91          MPFR_SET_NEG (y);
92          mpfr_set_divby0 ();
93          MPFR_RET (0);
94        }
95      MPFR_SET_NAN (y);
96      MPFR_RET_NAN;
97    }
98
99  MPFR_SAVE_EXPO_MARK (expo);
100
101  /* General case */
102  {
103    /* Declaration of the intermediary variable */
104    mpfr_t t;
105    /* Declaration of the size variable */
106    mpfr_prec_t Ny = MPFR_PREC(y);             /* target precision */
107    mpfr_prec_t Nt;                            /* working precision */
108    mpfr_exp_t err;                            /* error */
109    MPFR_ZIV_DECL (loop);
110
111    /* compute the precision of intermediary variable */
112    /* the optimal number of bits : see algorithms.tex */
113    Nt = Ny + MPFR_INT_CEIL_LOG2 (Ny) + 6;
114
115    /* if |x| is smaller than 2^(-e), we will loose about e bits
116       in log(1+x) */
117    if (MPFR_EXP(x) < 0)
118      Nt += -MPFR_EXP(x);
119
120    /* initialise of intermediary variable */
121    mpfr_init2 (t, Nt);
122
123    /* First computation of log1p */
124    MPFR_ZIV_INIT (loop, Nt);
125    for (;;)
126      {
127        /* compute log1p */
128        inexact = mpfr_add_ui (t, x, 1, MPFR_RNDN);      /* 1+x */
129        /* if inexact = 0, then t = x+1, and the result is simply log(t) */
130        if (inexact == 0)
131          {
132            inexact = mpfr_log (y, t, rnd_mode);
133            goto end;
134          }
135        mpfr_log (t, t, MPFR_RNDN);        /* log(1+x) */
136
137        /* the error is bounded by (1/2+2^(1-EXP(t))*ulp(t) (cf algorithms.tex)
138           if EXP(t)>=2, then error <= ulp(t)
139           if EXP(t)<=1, then error <= 2^(2-EXP(t))*ulp(t) */
140        err = Nt - MAX (0, 2 - MPFR_GET_EXP (t));
141
142        if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
143          break;
144
145        /* increase the precision */
146        MPFR_ZIV_NEXT (loop, Nt);
147        mpfr_set_prec (t, Nt);
148      }
149    inexact = mpfr_set (y, t, rnd_mode);
150
151  end:
152    MPFR_ZIV_FREE (loop);
153    mpfr_clear (t);
154  }
155
156  MPFR_SAVE_EXPO_FREE (expo);
157  return mpfr_check_range (y, inexact, rnd_mode);
158}
159