contrib/mpfr/src/subnormal.c

   1 /* mpfr_subnormalize -- Subnormalize a floating point number
   2    emulating sub-normal numbers.
   3
   4 Copyright 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc.
   5 Contributed by the AriC and Caramel projects, INRIA.
   6
   7 This file is part of the GNU MPFR Library.
   8
   9 The GNU MPFR Library is free software; you can redistribute it and/or modify
  10 it under the terms of the GNU Lesser General Public License as published by
  11 the Free Software Foundation; either version 3 of the License, or (at your
  12 option) any later version.
  13
  14 The GNU MPFR Library is distributed in the hope that it will be useful, but
  15 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  16 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
  17 License for more details.
  18
  19 You should have received a copy of the GNU Lesser General Public License
  20 along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
  21 http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
  22 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
  23
  24 #include "mpfr-impl.h"
  25
  26 /* For MPFR_RNDN, we can have a problem of double rounding.
  27    In such a case, this table helps to conclude what to do (y positive):
  28      Rounding Bit |  Sticky Bit | inexact  | Action    | new inexact
  29      0            |   ?         |  ?       | Trunc     | sticky
  30      1            |   0         |  1       | Trunc     |
  31      1            |   0         |  0       | Trunc if even |
  32      1            |   0         | -1       | AddOneUlp |
  33      1            |   1         |  ?       | AddOneUlp |
  34
  35    For other rounding mode, there isn't such a problem.
  36    Just round it again and merge the ternary values.
  37
  38    Set the inexact flag if the returned ternary value is non-zero.
  39    Set the underflow flag if a second rounding occurred (whether this
  40    rounding is exact or not). See
  41      https://sympa.inria.fr/sympa/arc/mpfr/2009-06/msg00000.html
  42      https://sympa.inria.fr/sympa/arc/mpfr/2009-06/msg00008.html
  43      https://sympa.inria.fr/sympa/arc/mpfr/2009-06/msg00010.html
  44 */
  45
  46 int
  47 mpfr_subnormalize (mpfr_ptr y, int old_inexact, mpfr_rnd_t rnd)
  48 {
  49   int sign;
  50
  51   /* The subnormal exponent range is [ emin, emin + MPFR_PREC(y) - 2 ] */
  52   if (MPFR_LIKELY (MPFR_IS_SINGULAR (y)
  53                    || (MPFR_GET_EXP (y) >=
  54                        __gmpfr_emin + (mpfr_exp_t) MPFR_PREC (y) - 1)))
  55     MPFR_RET (old_inexact);
  56
  57   mpfr_set_underflow ();
  58   sign = MPFR_SIGN (y);
  59
  60   /* We have to emulate one bit rounding if EXP(y) = emin */
  61   if (MPFR_GET_EXP (y) == __gmpfr_emin)
  62     {
  63       /* If this is a power of 2, we don't need rounding.
  64          It handles cases when |y| = 0.1 * 2^emin */
  65       if (mpfr_powerof2_raw (y))
  66         MPFR_RET (old_inexact);
  67
  68       /* We keep the same sign for y.
  69          Assuming Y is the real value and y the approximation
  70          and since y is not a power of 2:  0.5*2^emin < Y < 1*2^emin
  71          We also know the direction of the error thanks to ternary value. */
  72
  73       if (rnd == MPFR_RNDN)
  74         {
  75           mp_limb_t *mant, rb ,sb;
  76           mp_size_t s;
  77           /* We need the rounding bit and the sticky bit. Read them
  78              and use the previous table to conclude. */
  79           s = MPFR_LIMB_SIZE (y) - 1;
  80           mant = MPFR_MANT (y) + s;
  81           rb = *mant & (MPFR_LIMB_HIGHBIT >> 1);
  82           if (rb == 0)
  83             goto set_min;
  84           sb = *mant & ((MPFR_LIMB_HIGHBIT >> 1) - 1);
  85           while (sb == 0 && s-- != 0)
  86             sb = *--mant;
  87           if (sb != 0)
  88             goto set_min_p1;
  89           /* Rounding bit is 1 and sticky bit is 0.
  90              We need to examine old inexact flag to conclude. */
  91           if ((old_inexact > 0 && sign > 0) ||
  92               (old_inexact < 0 && sign < 0))
  93             goto set_min;
  94           /* If inexact != 0, return 0.1*2^(emin+1).
  95              Otherwise, rounding bit = 1, sticky bit = 0 and inexact = 0
  96              So we have 0.1100000000000000000000000*2^emin exactly.
  97              We return 0.1*2^(emin+1) according to the even-rounding
  98              rule on subnormals. */
  99           goto set_min_p1;
 100         }
 101       else if (MPFR_IS_LIKE_RNDZ (rnd, MPFR_IS_NEG (y)))
 102         {
 103         set_min:
 104           mpfr_setmin (y, __gmpfr_emin);
 105           MPFR_RET (-sign);
 106         }
 107       else
 108         {
 109         set_min_p1:
 110           /* Note: mpfr_setmin will abort if __gmpfr_emax == __gmpfr_emin. */
 111           mpfr_setmin (y, __gmpfr_emin + 1);
 112           MPFR_RET (sign);
 113         }
 114     }
 115   else /* Hard case: It is more or less the same problem than mpfr_cache */
 116     {
 117       mpfr_t dest;
 118       mpfr_prec_t q;
 119       int inexact, inex2;
 120
 121       MPFR_ASSERTD (MPFR_GET_EXP (y) > __gmpfr_emin);
 122
 123       /* Compute the intermediary precision */
 124       q = (mpfr_uexp_t) MPFR_GET_EXP (y) - __gmpfr_emin + 1;
 125       MPFR_ASSERTD (q >= MPFR_PREC_MIN && q < MPFR_PREC (y));
 126
 127       /* TODO: perform the rounding in place. */
 128       mpfr_init2 (dest, q);
 129       /* Round y in dest */
 130       MPFR_SET_EXP (dest, MPFR_GET_EXP (y));
 131       MPFR_SET_SIGN (dest, sign);
 132       MPFR_RNDRAW_EVEN (inexact, dest,
 133                         MPFR_MANT (y), MPFR_PREC (y), rnd, sign,
 134                         MPFR_SET_EXP (dest, MPFR_GET_EXP (dest) + 1));
 135       if (MPFR_LIKELY (old_inexact != 0))
 136         {
 137           if (MPFR_UNLIKELY (rnd == MPFR_RNDN &&
 138                              (inexact == MPFR_EVEN_INEX ||
 139                               inexact == -MPFR_EVEN_INEX)))
 140             {
 141               /* if both roundings are in the same direction, we have to go
 142                  back in the other direction */
 143               if (SAME_SIGN (inexact, old_inexact))
 144                 {
 145                   if (SAME_SIGN (inexact, MPFR_INT_SIGN (y)))
 146                     mpfr_nexttozero (dest);
 147                   else
 148                     mpfr_nexttoinf (dest);
 149                   inexact = -inexact;
 150                 }
 151             }
 152           else if (MPFR_UNLIKELY (inexact == 0))
 153             inexact = old_inexact;
 154         }
 155
 156       inex2 = mpfr_set (y, dest, rnd);
 157       MPFR_ASSERTN (inex2 == 0);
 158       MPFR_ASSERTN (MPFR_IS_PURE_FP (y));
 159       mpfr_clear (dest);
 160
 161       MPFR_RET (inexact);
 162     }
 163 }