contrib/mpfr/src/sqr.c

   1 /* mpfr_sqr -- Floating square
   2
   3 Copyright 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 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 #include "mpfr-impl.h"
  24
  25 int
  26 mpfr_sqr (mpfr_ptr a, mpfr_srcptr b, mpfr_rnd_t rnd_mode)
  27 {
  28   int cc, inexact;
  29   mpfr_exp_t ax;
  30   mp_limb_t *tmp;
  31   mp_limb_t b1;
  32   mpfr_prec_t bq;
  33   mp_size_t bn, tn;
  34   MPFR_TMP_DECL(marker);
  35
  36   MPFR_LOG_FUNC
  37     (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (b), mpfr_log_prec, b, rnd_mode),
  38      ("y[%Pu]=%.*Rg inexact=%d",
  39       mpfr_get_prec (a), mpfr_log_prec, a, inexact));
  40
  41   /* deal with special cases */
  42   if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(b)))
  43     {
  44       if (MPFR_IS_NAN(b))
  45         {
  46           MPFR_SET_NAN(a);
  47           MPFR_RET_NAN;
  48         }
  49       MPFR_SET_POS (a);
  50       if (MPFR_IS_INF(b))
  51         MPFR_SET_INF(a);
  52       else
  53         ( MPFR_ASSERTD(MPFR_IS_ZERO(b)), MPFR_SET_ZERO(a) );
  54       MPFR_RET(0);
  55     }
  56   ax = 2 * MPFR_GET_EXP (b);
  57   bq = MPFR_PREC(b);
  58
  59   MPFR_ASSERTN (2 * (mpfr_uprec_t) bq <= MPFR_PREC_MAX);
  60
  61   bn = MPFR_LIMB_SIZE (b); /* number of limbs of b */
  62   tn = MPFR_PREC2LIMBS (2 * bq); /* number of limbs of square,
  63                                     2*bn or 2*bn-1 */
  64
  65   if (MPFR_UNLIKELY(bn > MPFR_SQR_THRESHOLD))
  66     return mpfr_mul (a, b, b, rnd_mode);
  67
  68   MPFR_TMP_MARK(marker);
  69   tmp = MPFR_TMP_LIMBS_ALLOC (2 * bn);
  70
  71   /* Multiplies the mantissa in temporary allocated space */
  72   mpn_sqr_n (tmp, MPFR_MANT(b), bn);
  73   b1 = tmp[2 * bn - 1];
  74
  75   /* now tmp[0]..tmp[2*bn-1] contains the product of both mantissa,
  76      with tmp[2*bn-1]>=2^(GMP_NUMB_BITS-2) */
  77   b1 >>= GMP_NUMB_BITS - 1; /* msb from the product */
  78
  79   /* if the mantissas of b and c are uniformly distributed in ]1/2, 1],
  80      then their product is in ]1/4, 1/2] with probability 2*ln(2)-1 ~ 0.386
  81      and in [1/2, 1] with probability 2-2*ln(2) ~ 0.614 */
  82   tmp += 2 * bn - tn; /* +0 or +1 */
  83   if (MPFR_UNLIKELY(b1 == 0))
  84     mpn_lshift (tmp, tmp, tn, 1); /* tn <= k, so no stack corruption */
  85
  86   cc = mpfr_round_raw (MPFR_MANT (a), tmp, 2 * bq, 0,
  87                        MPFR_PREC (a), rnd_mode, &inexact);
  88   /* cc = 1 ==> result is a power of two */
  89   if (MPFR_UNLIKELY(cc))
  90     MPFR_MANT(a)[MPFR_LIMB_SIZE(a)-1] = MPFR_LIMB_HIGHBIT;
  91
  92   MPFR_TMP_FREE(marker);
  93   {
  94     mpfr_exp_t ax2 = ax + (mpfr_exp_t) (b1 - 1 + cc);
  95     if (MPFR_UNLIKELY( ax2 > __gmpfr_emax))
  96       return mpfr_overflow (a, rnd_mode, MPFR_SIGN_POS);
  97     if (MPFR_UNLIKELY( ax2 < __gmpfr_emin))
  98       {
  99         /* In the rounding to the nearest mode, if the exponent of the exact
 100            result (i.e. before rounding, i.e. without taking cc into account)
 101            is < __gmpfr_emin - 1 or the exact result is a power of 2 (i.e. if
 102            both arguments are powers of 2), then round to zero. */
 103         if (rnd_mode == MPFR_RNDN &&
 104             (ax + (mpfr_exp_t) b1 < __gmpfr_emin || mpfr_powerof2_raw (b)))
 105           rnd_mode = MPFR_RNDZ;
 106         return mpfr_underflow (a, rnd_mode, MPFR_SIGN_POS);
 107       }
 108     MPFR_SET_EXP (a, ax2);
 109     MPFR_SET_POS (a);
 110   }
 111   MPFR_RET (inexact);
 112 }