105 lines
3.6 KiB
C
105 lines
3.6 KiB
C
/* mpf_sqrt -- Compute the square root of a float.
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Copyright 1993, 1994, 1996, 2000, 2001, 2004, 2005 Free Software Foundation,
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Inc.
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 2.1 of the License, or (at your
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option) any later version.
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The GNU MP Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MP Library; see the file COPYING.LIB. If not, write to
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the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
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MA 02110-1301, USA. */
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#include <stdio.h> /* for NULL */
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#include "gmp.h"
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#include "gmp-impl.h"
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/* As usual, the aim is to produce PREC(r) limbs of result, with the high
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limb non-zero. This is accomplished by applying mpn_sqrtrem to either
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2*prec or 2*prec-1 limbs, both such sizes resulting in prec limbs.
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The choice between 2*prec or 2*prec-1 limbs is based on the input
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exponent. With b=2^GMP_NUMB_BITS the limb base then we can think of
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effectively taking out a factor b^(2k), for suitable k, to get to an
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integer input of the desired size ready for mpn_sqrtrem. It must be an
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even power taken out, ie. an even number of limbs, so the square root
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gives factor b^k and the radix point is still on a limb boundary. So if
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EXP(r) is even we'll get an even number of input limbs 2*prec, or if
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EXP(r) is odd we get an odd number 2*prec-1.
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Further limbs below the 2*prec or 2*prec-1 used don't affect the result
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and are simply truncated. This can be seen by considering an integer x,
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with s=floor(sqrt(x)). s is the unique integer satisfying s^2 <= x <
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(s+1)^2. Notice that adding a fraction part to x (ie. some further bits)
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doesn't change the inequality, s remains the unique solution. Working
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suitable factors of 2 into this argument lets it apply to an intended
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precision at any position for any x, not just the integer binary point.
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If the input is smaller than 2*prec or 2*prec-1, then we just pad with
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zeros, that of course being our usual interpretation of short inputs.
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The effect is to extend the root beyond the size of the input (for
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instance into fractional limbs if u is an integer). */
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void
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mpf_sqrt (mpf_ptr r, mpf_srcptr u)
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{
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mp_size_t usize;
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mp_ptr up, tp;
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mp_size_t prec, tsize;
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mp_exp_t uexp, expodd;
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TMP_DECL;
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usize = u->_mp_size;
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if (usize <= 0)
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{
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if (usize < 0)
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SQRT_OF_NEGATIVE;
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r->_mp_size = 0;
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r->_mp_exp = 0;
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return;
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}
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TMP_MARK;
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uexp = u->_mp_exp;
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prec = r->_mp_prec;
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up = u->_mp_d;
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expodd = (uexp & 1);
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tsize = 2 * prec - expodd;
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r->_mp_size = prec;
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r->_mp_exp = (uexp + expodd) / 2; /* ceil(uexp/2) */
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/* root size is ceil(tsize/2), this will be our desired "prec" limbs */
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ASSERT ((tsize + 1) / 2 == prec);
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tp = (mp_ptr) TMP_ALLOC (tsize * BYTES_PER_MP_LIMB);
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if (usize > tsize)
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{
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up += usize - tsize;
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usize = tsize;
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MPN_COPY (tp, up, tsize);
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}
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else
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{
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MPN_ZERO (tp, tsize - usize);
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MPN_COPY (tp + (tsize - usize), up, usize);
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}
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mpn_sqrtrem (r->_mp_d, NULL, tp, tsize);
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TMP_FREE;
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}
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