xref: /dragonfly/contrib/mpfr/src/sqrt.c (revision ab6d115f)

/* mpfr_sqrt -- square root of a floating-point number

Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc.
Contributed by the AriC and Caramel projects, INRIA.

This file is part of the GNU MPFR Library.

The GNU MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

The GNU MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */

#include "mpfr-impl.h"

int
mpfr_sqrt (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
{
  mp_size_t rsize; /* number of limbs of r (plus 1 if exact limb multiple) */
  mp_size_t rrsize;
  mp_size_t usize; /* number of limbs of u */
  mp_size_t tsize; /* number of limbs of the sqrtrem remainder */
  mp_size_t k;
  mp_size_t l;
  mpfr_limb_ptr rp, rp0;
  mpfr_limb_ptr up;
  mpfr_limb_ptr sp;
  mp_limb_t sticky0; /* truncated part of input */
  mp_limb_t sticky1; /* truncated part of rp[0] */
  mp_limb_t sticky;
  int odd_exp;
  int sh; /* number of extra bits in rp[0] */
  int inexact; /* return ternary flag */
  mpfr_exp_t expr;
  MPFR_TMP_DECL(marker);

  MPFR_LOG_FUNC
    (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (u), mpfr_log_prec, u, rnd_mode),
     ("y[%Pu]=%.*Rg inexact=%d",
      mpfr_get_prec (r), mpfr_log_prec, r, inexact));

  if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(u)))
    {
      if (MPFR_IS_NAN(u))
        {
          MPFR_SET_NAN(r);
          MPFR_RET_NAN;
        }
      else if (MPFR_IS_ZERO(u))
        {
          /* 0+ or 0- */
          MPFR_SET_SAME_SIGN(r, u);
          MPFR_SET_ZERO(r);
          MPFR_RET(0); /* zero is exact */
        }
      else
        {
          MPFR_ASSERTD(MPFR_IS_INF(u));
          /* sqrt(-Inf) = NAN */
          if (MPFR_IS_NEG(u))
            {
              MPFR_SET_NAN(r);
              MPFR_RET_NAN;
            }
          MPFR_SET_POS(r);
          MPFR_SET_INF(r);
          MPFR_RET(0);
        }
    }
  if (MPFR_UNLIKELY(MPFR_IS_NEG(u)))
    {
      MPFR_SET_NAN(r);
      MPFR_RET_NAN;
    }
  MPFR_SET_POS(r);

  MPFR_TMP_MARK (marker);
  MPFR_UNSIGNED_MINUS_MODULO(sh,MPFR_PREC(r));
  if (sh == 0 && rnd_mode == MPFR_RNDN)
    sh = GMP_NUMB_BITS; /* ugly case */
  rsize = MPFR_LIMB_SIZE(r) + (sh == GMP_NUMB_BITS);
  /* rsize is the number of limbs of r + 1 if exact limb multiple and rounding
     to nearest, this is the number of wanted limbs for the square root */
  rrsize = rsize + rsize;
  usize = MPFR_LIMB_SIZE(u); /* number of limbs of u */
  rp0 = MPFR_MANT(r);
  rp = (sh < GMP_NUMB_BITS) ? rp0 : MPFR_TMP_LIMBS_ALLOC (rsize);
  up = MPFR_MANT(u);
  sticky0 = MPFR_LIMB_ZERO; /* truncated part of input */
  sticky1 = MPFR_LIMB_ZERO; /* truncated part of rp[0] */
  odd_exp = (unsigned int) MPFR_GET_EXP (u) & 1;
  inexact = -1; /* return ternary flag */

  sp = MPFR_TMP_LIMBS_ALLOC (rrsize);

  /* copy the most significant limbs of u to {sp, rrsize} */
  if (MPFR_LIKELY(usize <= rrsize)) /* in case r and u have the same precision,
                                       we have indeed rrsize = 2 * usize */
    {
      k = rrsize - usize;
      if (MPFR_LIKELY(k))
        MPN_ZERO (sp, k);
      if (odd_exp)
        {
          if (MPFR_LIKELY(k))
            sp[k - 1] = mpn_rshift (sp + k, up, usize, 1);
          else
            sticky0 = mpn_rshift (sp, up, usize, 1);
        }
      else
        MPN_COPY (sp + rrsize - usize, up, usize);
    }
  else /* usize > rrsize: truncate the input */
    {
      k = usize - rrsize;
      if (odd_exp)
        sticky0 = mpn_rshift (sp, up + k, rrsize, 1);
      else
        MPN_COPY (sp, up + k, rrsize);
      l = k;
      while (sticky0 == MPFR_LIMB_ZERO && l != 0)
        sticky0 = up[--l];
    }

  /* sticky0 is non-zero iff the truncated part of the input is non-zero */

  /* mpn_rootrem with NULL 2nd argument is faster than mpn_sqrtrem, thus use
     it if available and if the user asked to use GMP internal functions */
#if defined(WANT_GMP_INTERNALS) && defined(HAVE___GMPN_ROOTREM)
  tsize = __gmpn_rootrem (rp, NULL, sp, rrsize, 2);
#else
  tsize = mpn_sqrtrem (rp, NULL, sp, rrsize);
#endif

  /* a return value of zero in mpn_sqrtrem indicates a perfect square */
  sticky = sticky0 || tsize != 0;

  /* truncate low bits of rp[0] */
  sticky1 = rp[0] & ((sh < GMP_NUMB_BITS) ? MPFR_LIMB_MASK(sh)
                     : ~MPFR_LIMB_ZERO);
  rp[0] -= sticky1;

  sticky = sticky || sticky1;

  expr = (MPFR_GET_EXP(u) + odd_exp) / 2;  /* exact */

  if (rnd_mode == MPFR_RNDZ || rnd_mode == MPFR_RNDD || sticky == MPFR_LIMB_ZERO)
    {
      inexact = (sticky == MPFR_LIMB_ZERO) ? 0 : -1;
      goto truncate;
    }
  else if (rnd_mode == MPFR_RNDN)
    {
      /* if sh < GMP_NUMB_BITS, the round bit is bit (sh-1) of sticky1
                  and the sticky bit is formed by the low sh-1 bits from
                  sticky1, together with the sqrtrem remainder and sticky0. */
      if (sh < GMP_NUMB_BITS)
        {
          if (sticky1 & (MPFR_LIMB_ONE << (sh - 1)))
            { /* round bit is set */
              if (sticky1 == (MPFR_LIMB_ONE << (sh - 1)) && tsize == 0
                  && sticky0 == 0)
                goto even_rule;
              else
                goto add_one_ulp;
            }
          else /* round bit is zero */
            goto truncate; /* with the default inexact=-1 */
        }
      else /* sh = GMP_NUMB_BITS: the round bit is the most significant bit
              of rp[0], and the remaining GMP_NUMB_BITS-1 bits contribute to
              the sticky bit */
        {
          if (sticky1 & MPFR_LIMB_HIGHBIT)
            { /* round bit is set */
              if (sticky1 == MPFR_LIMB_HIGHBIT && tsize == 0 && sticky0 == 0)
                goto even_rule;
              else
                goto add_one_ulp;
            }
          else /* round bit is zero */
            goto truncate; /* with the default inexact=-1 */
        }
    }
  else /* rnd_mode=GMP_RDNU, necessarily sticky <> 0, thus add 1 ulp */
    goto add_one_ulp;

 even_rule: /* has to set inexact */
  if (sh < GMP_NUMB_BITS)
    inexact = (rp[0] & (MPFR_LIMB_ONE << sh)) ? 1 : -1;
  else
    inexact = (rp[1] & MPFR_LIMB_ONE) ? 1 : -1;
  if (inexact == -1)
    goto truncate;
  /* else go through add_one_ulp */

 add_one_ulp:
  inexact = 1; /* always here */
  if (sh == GMP_NUMB_BITS)
    {
      rp ++;
      rsize --;
      sh = 0;
    }
  if (mpn_add_1 (rp0, rp, rsize, MPFR_LIMB_ONE << sh))
    {
      expr ++;
      rp[rsize - 1] = MPFR_LIMB_HIGHBIT;
    }
  goto end;

 truncate: /* inexact = 0 or -1 */
  if (sh == GMP_NUMB_BITS)
    MPN_COPY (rp0, rp + 1, rsize - 1);

 end:
  MPFR_ASSERTN (expr >= MPFR_EMIN_MIN && expr <= MPFR_EMAX_MAX);
  MPFR_EXP (r) = expr;
  MPFR_TMP_FREE(marker);

  return mpfr_check_range (r, inexact, rnd_mode);
}