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

   1 /* mpfr_frac -- Fractional part of a floating-point number.
   2
   3 Copyright 2002-2004, 2006-2015 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
  24 #define MPFR_NEED_LONGLONG_H
  25 #include "mpfr-impl.h"
  26
  27 /* Optimization note: it is not a good idea to call mpfr_integer_p,
  28    as some cases will take longer (the number may be parsed twice). */
  29
  30 int
  31 mpfr_frac (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
  32 {
  33   mpfr_exp_t re, ue;
  34   mpfr_prec_t uq;
  35   mp_size_t un, tn, t0;
  36   mp_limb_t *up, *tp, k;
  37   int sh;
  38   mpfr_t tmp;
  39   mpfr_ptr t;
  40   int inex;
  41   MPFR_SAVE_EXPO_DECL (expo);
  42
  43   /* Special cases */
  44   if (MPFR_UNLIKELY(MPFR_IS_NAN(u)))
  45     {
  46       MPFR_SET_NAN(r);
  47       MPFR_RET_NAN;
  48     }
  49   else if (MPFR_UNLIKELY(MPFR_IS_INF(u) || mpfr_integer_p (u)))
  50     {
  51       MPFR_SET_SAME_SIGN(r, u);
  52       MPFR_SET_ZERO(r);
  53       MPFR_RET(0);  /* zero is exact */
  54     }
  55
  56   ue = MPFR_GET_EXP (u);
  57   if (ue <= 0)  /* |u| < 1 */
  58     return mpfr_set (r, u, rnd_mode);
  59
  60   /* Now |u| >= 1, meaning that an overflow is not possible. */
  61
  62   uq = MPFR_PREC(u);
  63   un = (uq - 1) / GMP_NUMB_BITS;  /* index of most significant limb */
  64   un -= (mp_size_t) (ue / GMP_NUMB_BITS);
  65   /* now the index of the MSL containing bits of the fractional part */
  66
  67   up = MPFR_MANT(u);
  68   sh = ue % GMP_NUMB_BITS;
  69   k = up[un] << sh;
  70   /* the first bit of the fractional part is the MSB of k */
  71
  72   if (k != 0)
  73     {
  74       int cnt;
  75
  76       count_leading_zeros(cnt, k);
  77       /* first bit 1 of the fractional part -> MSB of the number */
  78       re = -cnt;
  79       sh += cnt;
  80       MPFR_ASSERTN (sh < GMP_NUMB_BITS);
  81       k <<= cnt;
  82     }
  83   else
  84     {
  85       re = sh - GMP_NUMB_BITS;
  86       /* searching for the first bit 1 (exists since u isn't an integer) */
  87       while (up[--un] == 0)
  88         re -= GMP_NUMB_BITS;
  89       MPFR_ASSERTN(un >= 0);
  90       k = up[un];
  91       count_leading_zeros(sh, k);
  92       re -= sh;
  93       k <<= sh;
  94     }
  95   /* The exponent of r will be re */
  96   /* un: index of the limb of u that contains the first bit 1 of the FP */
  97
  98   t = (mp_size_t) (MPFR_PREC(r) - 1) / GMP_NUMB_BITS < un ?
  99     (mpfr_init2 (tmp, (un + 1) * GMP_NUMB_BITS), tmp) : r;
 100   /* t has enough precision to contain the fractional part of u */
 101   /* If we use a temporary variable, we take the non-significant bits
 102      of u into account, because of the mpn_lshift below. */
 103   MPFR_SET_SAME_SIGN(t, u);
 104
 105   /* Put the fractional part of u into t */
 106   tn = (MPFR_PREC(t) - 1) / GMP_NUMB_BITS;
 107   MPFR_ASSERTN(tn >= un);
 108   t0 = tn - un;
 109   tp = MPFR_MANT(t);
 110   if (sh == 0)
 111     MPN_COPY_DECR(tp + t0, up, un + 1);
 112   else /* warning: un may be 0 here */
 113     tp[tn] = k | ((un) ? mpn_lshift (tp + t0, up, un, sh) : (mp_limb_t) 0);
 114   if (t0 > 0)
 115     MPN_ZERO(tp, t0);
 116
 117   MPFR_SAVE_EXPO_MARK (expo);
 118
 119   if (t != r)
 120     { /* t is tmp */
 121       MPFR_EXP (t) = 0;  /* should be re, but not necessarily in the range */
 122       inex = mpfr_set (r, t, rnd_mode);  /* no underflow */
 123       mpfr_clear (t);
 124       MPFR_EXP (r) += re;
 125     }
 126   else
 127     { /* There may be remaining non-significant bits in t (= r). */
 128       int carry;
 129
 130       MPFR_EXP (r) = re;
 131       carry = mpfr_round_raw (tp, tp,
 132                               (mpfr_prec_t) (tn + 1) * GMP_NUMB_BITS,
 133                               MPFR_IS_NEG (r), MPFR_PREC (r), rnd_mode,
 134                               &inex);
 135       if (carry)
 136         {
 137           tp[tn] = MPFR_LIMB_HIGHBIT;
 138           MPFR_EXP (r) ++;
 139         }
 140     }
 141
 142   MPFR_SAVE_EXPO_FREE (expo);
 143   return mpfr_check_range (r, inex, rnd_mode);
 144 }