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/* mpfr_sqrt -- square root of a floating-point number
Copyright (C) 1999, 2001 Free Software Foundation.
This file is part of the MPFR Library.
The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Library General Public License as published by
the Free Software Foundation; either version 2 of the License, or (at your
option) any later version.
The 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 Library General Public
License for more details.
You should have received a copy of the GNU Library General Public License
along with the MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include <stdio.h>
#include <stdlib.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* #define DEBUG */
int
#if __STDC__
mpfr_sqrt (mpfr_ptr r, mpfr_srcptr u, mp_rnd_t rnd_mode)
#else
mpfr_sqrt (r, u, rnd_mode)
mpfr_ptr r;
mpfr_srcptr u;
mp_rnd_t rnd_mode;
#endif
{
mp_ptr up, rp, tmp, remp;
mp_size_t usize, rrsize;
mp_size_t rsize;
mp_size_t prec, err;
mp_limb_t q_limb;
long rw, nw, k;
int exact = 0, t;
unsigned long cc = 0;
char can_round = 0;
TMP_DECL(marker0);
if (MPFR_IS_NAN(u)) {
MPFR_SET_NAN(r);
return 1;
}
if (MPFR_SIGN(u) < 0) {
if (MPFR_IS_INF(u) || MPFR_NOTZERO(u)) {
MPFR_SET_NAN(r);
return 1;
}
else { /* sqrt(-0) = -0 */
MPFR_SET_ZERO(r);
if (MPFR_SIGN(r) > 0) MPFR_CHANGE_SIGN(r);
return 0;
}
}
MPFR_CLEAR_NAN(r);
if (MPFR_SIGN(r) < 0) MPFR_CHANGE_SIGN(r);
if (MPFR_IS_INF(u))
{
MPFR_SET_INF(r);
return 1;
}
MPFR_CLEAR_INF(r);
prec = MPFR_PREC(r);
if (!MPFR_NOTZERO(u))
{
MPFR_EXP(r) = 0;
rsize = (prec-1)/BITS_PER_MP_LIMB + 1;
MPN_ZERO(MPFR_MANT(r), rsize);
return 0;
}
up = MPFR_MANT(u);
usize = (MPFR_PREC(u) - 1)/BITS_PER_MP_LIMB + 1;
#ifdef DEBUG
printf("Entering square root : ");
for(k = usize - 1; k >= 0; k--) { printf("%lu ", up[k]); }
printf(".\n");
#endif
/* Compare the mantissas */
rsize = ((MPFR_PREC(r) + 2 + (MPFR_EXP(u) & 1))/BITS_PER_MP_LIMB + 1) << 1;
rrsize = (MPFR_PREC(r) + 2 + (MPFR_EXP(u) & 1))/BITS_PER_MP_LIMB + 1;
/* One extra bit is needed in order to get the square root with enough
precision ; take one extra bit for rrsize in order to solve more
easily the problem of rounding to nearest.
Need to have 2*rrsize = rsize...
Take one extra bit if the exponent of u is odd since we shall have
to shift then.
*/
TMP_MARK(marker0);
if (MPFR_EXP(u) & 1) /* Shift u one bit to the right */
{
if (MPFR_PREC(u) & (BITS_PER_MP_LIMB - 1))
{
up = TMP_ALLOC(usize*BYTES_PER_MP_LIMB);
mpn_rshift(up, MPFR_MANT(u), usize, 1);
}
else
{
up = TMP_ALLOC((usize + 1)*BYTES_PER_MP_LIMB);
if (mpn_rshift(up + 1, MPFR_MANT(u), usize, 1))
up [0] = ((mp_limb_t) 1) << (BITS_PER_MP_LIMB - 1);
else up[0] = 0;
usize++;
}
}
MPFR_EXP(r) = ((MPFR_EXP(u) + (MPFR_EXP(u) & 1)) / 2) ;
{
TMP_DECL (marker);
do
{
TMP_MARK (marker);
err = rsize*BITS_PER_MP_LIMB;
if (rsize < usize) { err--; }
if (err > rrsize * BITS_PER_MP_LIMB)
{ err = rrsize * BITS_PER_MP_LIMB; }
tmp = (mp_ptr) TMP_ALLOC (rsize * BYTES_PER_MP_LIMB);
rp = (mp_ptr) TMP_ALLOC (rrsize * BYTES_PER_MP_LIMB);
remp = (mp_ptr) TMP_ALLOC (rsize * BYTES_PER_MP_LIMB);
if (usize >= rsize) {
MPN_COPY (tmp, up + usize - rsize, rsize);
}
else {
MPN_COPY (tmp + rsize - usize, up, usize);
MPN_ZERO (tmp, rsize - usize);
}
/* Do the real job */
#ifdef DEBUG
printf("Taking the sqrt of : ");
for(k = rsize - 1; k >= 0; k--) {
printf("+%lu*2^%lu",tmp[k],k*BITS_PER_MP_LIMB); }
printf(".\n");
#endif
q_limb = mpn_sqrtrem (rp, remp, tmp, rsize);
#ifdef DEBUG
printf("The result is : \n");
printf("sqrt : ");
for(k = rrsize - 1; k >= 0; k--) { printf("%lu ", rp[k]); }
printf("(q_limb = %lu)\n", q_limb);
#endif
can_round = (mpfr_can_round_raw(rp, rrsize, 1, err,
GMP_RNDZ, rnd_mode, MPFR_PREC(r)));
/* If we used all the limbs of both the dividend and the divisor,
then we have the correct RNDZ rounding */
if (!can_round && (rsize < 2*usize))
{
#ifdef DEBUG
printf("Increasing the precision.\n");
#endif
TMP_FREE(marker);
}
}
while (!can_round && (rsize < 2*usize)
&& (rsize += 2) && (rrsize ++));
/* This part may be deplaced upper to avoid a few mpfr_can_round_raw */
/* when the square root is exact. It is however very unprobable that */
/* it would improve the behaviour of the present code on average. */
if (!q_limb) /* possibly exact */
{
/* if we have taken into account the whole of up */
for (k = usize - rsize - 1; k >= 0; k ++)
if (up[k]) break;
if (k < 0) { exact = 1; goto fin; }
}
if (can_round)
{
cc = mpfr_round_raw(rp, rp, err, 0, MPFR_PREC(r), rnd_mode);
rrsize = (MPFR_PREC(r) - 1)/BITS_PER_MP_LIMB + 1;
}
else
/* Use the return value of sqrtrem to decide of the rounding */
/* Note that at this point the sqrt has been computed */
/* EXACTLY. If rounding = GMP_RNDZ, do nothing [comes from */
/* the fact that the exact square root can end with a bunch of ones, */
/* and in that case we indeed cannot round if we do not know that */
/* the computation was exact. */
switch (rnd_mode)
{
case GMP_RNDZ :
case GMP_RNDD : break;
case GMP_RNDN :
/* Not in the situation ...0 111111 */
rw = (MPFR_PREC(r) + 1) & (BITS_PER_MP_LIMB - 1);
if (rw) { rw = BITS_PER_MP_LIMB - rw; nw = 0; } else nw = 1;
if ((rp[nw] >> rw) & 1 && /* Not 0111111111 */
(q_limb || /* Nonzero remainder */
(rw ? (rp[nw] >> (rw + 1)) & 1 :
(rp[nw] >> (BITS_PER_MP_LIMB - 1)) & 1))) /* or even rounding */
cc = mpn_add_1(rp + nw, rp + nw, rrsize, ((mp_limb_t)1) << rw);
break;
case GMP_RNDU :
if (q_limb)
{
t = MPFR_PREC(r) & (BITS_PER_MP_LIMB - 1);
if (t)
{
cc = mpn_add_1(rp, rp, rrsize, 1 << (BITS_PER_MP_LIMB - t));
}
else
cc = mpn_add_1 (rp, rp, rrsize, 1);
}
}
if (cc) {
mpn_rshift(rp, rp, rrsize, 1);
rp[rrsize-1] |= (mp_limb_t) 1 << (BITS_PER_MP_LIMB-1);
MPFR_EXP(r)++;
}
fin:
rsize = rrsize;
rrsize = (MPFR_PREC(r) - 1)/BITS_PER_MP_LIMB + 1;
MPN_COPY(MPFR_MANT(r), rp + rsize - rrsize, rrsize);
if (MPFR_PREC(r) & (BITS_PER_MP_LIMB - 1))
MPFR_MANT(r) [0] &= ~(((mp_limb_t)1 << (BITS_PER_MP_LIMB -
(MPFR_PREC(r) & (BITS_PER_MP_LIMB - 1)))) - 1) ;
TMP_FREE (marker);
}
TMP_FREE(marker0);
return exact;
}
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