contrib/mpfr/log1p.c

   1 /* mpfr_log1p -- Compute log(1+x)
   2
   3 Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
   4 Contributed by the Arenaire and Cacao 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 2.1 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.LIB.  If not, write to
  20 the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
  21 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, mp_rnd_t rnd_mode)
  31 {
  32   int comp, inexact;
  33   mp_exp_t ex;
  34   MPFR_SAVE_EXPO_DECL (expo);
  35
  36   if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
  37     {
  38       if (MPFR_IS_NAN (x))
  39         {
  40           MPFR_SET_NAN (y);
  41           MPFR_RET_NAN;
  42         }
  43       /* check for inf or -inf (result is not defined) */
  44       else if (MPFR_IS_INF (x))
  45         {
  46           if (MPFR_IS_POS (x))
  47             {
  48               MPFR_SET_INF (y);
  49               MPFR_SET_POS (y);
  50               MPFR_RET (0);
  51             }
  52           else
  53             {
  54               MPFR_SET_NAN (y);
  55               MPFR_RET_NAN;
  56             }
  57         }
  58       else /* x is zero */
  59         {
  60           MPFR_ASSERTD (MPFR_IS_ZERO (x));
  61           MPFR_SET_ZERO (y);   /* log1p(+/- 0) = +/- 0 */
  62           MPFR_SET_SAME_SIGN (y, x);
  63           MPFR_RET (0);
  64         }
  65     }
  66
  67   ex = MPFR_GET_EXP (x);
  68   if (ex < 0)  /* -0.5 < x < 0.5 */
  69     {
  70       /* For x > 0,    abs(log(1+x)-x) < x^2/2.
  71          For x > -0.5, abs(log(1+x)-x) < x^2. */
  72       if (MPFR_IS_POS (x))
  73         MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, - ex - 1, 0, 0, rnd_mode, {});
  74       else
  75         MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, - ex, 0, 1, rnd_mode, {});
  76     }
  77
  78   comp = mpfr_cmp_si (x, -1);
  79   /* log1p(x) is undefined for x < -1 */
  80   if (MPFR_UNLIKELY(comp <= 0))
  81     {
  82       if (comp == 0)
  83         /* x=0: log1p(-1)=-inf (division by zero) */
  84         {
  85           MPFR_SET_INF (y);
  86           MPFR_SET_NEG (y);
  87           MPFR_RET (0);
  88         }
  89       MPFR_SET_NAN (y);
  90       MPFR_RET_NAN;
  91     }
  92
  93   MPFR_SAVE_EXPO_MARK (expo);
  94
  95   /* General case */
  96   {
  97     /* Declaration of the intermediary variable */
  98     mpfr_t t;
  99     /* Declaration of the size variable */
 100     mp_prec_t Ny = MPFR_PREC(y);             /* target precision */
 101     mp_prec_t Nt;                            /* working precision */
 102     mp_exp_t err;                            /* error */
 103     MPFR_ZIV_DECL (loop);
 104
 105     /* compute the precision of intermediary variable */
 106     /* the optimal number of bits : see algorithms.tex */
 107     Nt = Ny + MPFR_INT_CEIL_LOG2 (Ny) + 6;
 108
 109     /* if |x| is smaller than 2^(-e), we will loose about e bits
 110        in log(1+x) */
 111     if (MPFR_EXP(x) < 0)
 112       Nt += -MPFR_EXP(x);
 113
 114     /* initialise of intermediary variable */
 115     mpfr_init2 (t, Nt);
 116
 117     /* First computation of log1p */
 118     MPFR_ZIV_INIT (loop, Nt);
 119     for (;;)
 120       {
 121         /* compute log1p */
 122         inexact = mpfr_add_ui (t, x, 1, GMP_RNDN);      /* 1+x */
 123         /* if inexact = 0, then t = x+1, and the result is simply log(t) */
 124         if (inexact == 0)
 125           {
 126             inexact = mpfr_log (y, t, rnd_mode);
 127             goto end;
 128           }
 129         mpfr_log (t, t, GMP_RNDN);        /* log(1+x) */
 130
 131         /* the error is bounded by (1/2+2^(1-EXP(t))*ulp(t) (cf algorithms.tex)
 132            if EXP(t)>=2, then error <= ulp(t)
 133            if EXP(t)<=1, then error <= 2^(2-EXP(t))*ulp(t) */
 134         err = Nt - MAX (0, 2 - MPFR_GET_EXP (t));
 135
 136         if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
 137           break;
 138
 139         /* increase the precision */
 140         MPFR_ZIV_NEXT (loop, Nt);
 141         mpfr_set_prec (t, Nt);
 142       }
 143     inexact = mpfr_set (y, t, rnd_mode);
 144
 145   end:
 146     MPFR_ZIV_FREE (loop);
 147     mpfr_clear (t);
 148   }
 149
 150   MPFR_SAVE_EXPO_FREE (expo);
 151   return mpfr_check_range (y, inexact, rnd_mode);
 152 }