/* mpf_sqrt -- Compute the square root of a float.

Copyright 1993, 1994, 1996, 2000, 2001, 2004, 2005, 2012 Free Software

Foundation, Inc.

This file is part of the GNU MP Library.

The GNU MP Library is free software; you can redistribute it and/or modify

it under the terms of either:

  * 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.

or

  * the GNU General Public License as published by the Free Software

    Foundation; either version 2 of the License, or (at your option) any

    later version.

or both in parallel, as here.

The GNU MP 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 General Public License

for more details.

You should have received copies of the GNU General Public License and the

GNU Lesser General Public License along with the GNU MP Library.  If not,

see https://www.gnu.org/licenses/.  */

#include <stdio.h> /* for NULL */

#include "gmp.h"

#include "gmp-impl.h"

/* As usual, the aim is to produce PREC(r) limbs of result, with the high

   limb non-zero.  This is accomplished by applying mpn_sqrtrem to either

   2*prec or 2*prec-1 limbs, both such sizes resulting in prec limbs.

   The choice between 2*prec or 2*prec-1 limbs is based on the input

   exponent.  With b=2^GMP_NUMB_BITS the limb base then we can think of

   effectively taking out a factor b^(2k), for suitable k, to get to an

   integer input of the desired size ready for mpn_sqrtrem.  It must be an

   even power taken out, ie. an even number of limbs, so the square root

   gives factor b^k and the radix point is still on a limb boundary.  So if

   EXP(r) is even we'll get an even number of input limbs 2*prec, or if

   EXP(r) is odd we get an odd number 2*prec-1.

   Further limbs below the 2*prec or 2*prec-1 used don't affect the result

   and are simply truncated.  This can be seen by considering an integer x,

   with s=floor(sqrt(x)).  s is the unique integer satisfying s^2 <= x <

   (s+1)^2.  Notice that adding a fraction part to x (ie. some further bits)

   doesn't change the inequality, s remains the unique solution.  Working

   suitable factors of 2 into this argument lets it apply to an intended

   precision at any position for any x, not just the integer binary point.

   If the input is smaller than 2*prec or 2*prec-1, then we just pad with

   zeros, that of course being our usual interpretation of short inputs.

   The effect is to extend the root beyond the size of the input (for

   instance into fractional limbs if u is an integer).  */

void

mpf_sqrt (mpf_ptr r, mpf_srcptr u)

{

  mp_size_t usize;

  mp_ptr up, tp;

  mp_size_t prec, tsize;

  mp_exp_t uexp, expodd;

  TMP_DECL;

  usize = u->_mp_size;

  if (UNLIKELY (usize <= 0))

    {

      if (usize < 0)

        SQRT_OF_NEGATIVE;

      r->_mp_size = 0;

      r->_mp_exp = 0;

      return;

    }

  TMP_MARK;

  uexp = u->_mp_exp;

  prec = r->_mp_prec;

  up = u->_mp_d;

  expodd = (uexp & 1);

  tsize = 2 * prec - expodd;

  r->_mp_size = prec;

  r->_mp_exp = (uexp + expodd) / 2;    /* ceil(uexp/2) */

  /* root size is ceil(tsize/2), this will be our desired "prec" limbs */

  ASSERT ((tsize + 1) / 2 == prec);

  tp = TMP_ALLOC_LIMBS (tsize);

  if (usize > tsize)

    {

      up += usize - tsize;

      usize = tsize;

      MPN_COPY (tp, up, tsize);

    }

  else

    {

      MPN_ZERO (tp, tsize - usize);

      MPN_COPY (tp + (tsize - usize), up, usize);

    }

  mpn_sqrtrem (r->_mp_d, NULL, tp, tsize);

  TMP_FREE;

}