source/libs/mpfr/mpfr-3.1.3/src/log1p.c

   1 /* mpfr_log1p -- Compute log(1+x)
   2
   3 Copyright 2001-2015 Free Software Foundation, Inc.
   4 Contributed by the AriC and Caramel projects, INRIA.
   5
   6 This file is part of the GNU MPFR Library.
   7
   8 The GNU MPFR Library is free software; you can redistribute it and/or modify
   9 it under the terms of the GNU Lesser General Public License as published by
  10 the Free Software Foundation; either version 3 of the License, or (at your
  11 option) any later version.
  12
  13 The GNU MPFR Library is distributed in the hope that it will be useful, but
  14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  15 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
  16 License for more details.
  17
  18 You should have received a copy of the GNU Lesser General Public License
  19 along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
  20 http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
  21 51 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
  29 int
  30 mpfr_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 }