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/* mpfr_sqrt -- square root of a floating-point number
Copyright 1999, 2000, 2001, 2002, 2003 Free Software Foundation, Inc.
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 Lesser General Public License as published by
the Free Software Foundation; either version 2.1 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 Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser 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 "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* #define DEBUG */
int
mpfr_sqrt (mpfr_ptr r, mpfr_srcptr u, mp_rnd_t rnd_mode)
{
mp_ptr up, rp, tmp, remp;
mp_size_t usize, rrsize;
mp_size_t rsize;
mp_size_t err;
mp_limb_t q_limb;
int odd_exp_u;
long rw, nw, k;
int inexact = 0, t;
unsigned long cc = 0;
int can_round = 0;
TMP_DECL(marker);
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 if (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_CLEAR_FLAGS(r);
MPFR_SET_POS(r);
up = MPFR_MANT(u);
usize = MPFR_LIMB_SIZE(u);
#ifdef DEBUG
printf("Entering square root : ");
for(k = usize - 1; k >= 0; k--) { printf("%lu ", up[k]); }
printf(".\n");
#endif
/* Compare the mantissas */
odd_exp_u = (unsigned int) MPFR_GET_EXP (u) & 1;
MPFR_ASSERTN(MPFR_PREC(r) <= MPFR_INTPREC_MAX - 3);
rrsize = (MPFR_PREC(r) + 2 + odd_exp_u) / BITS_PER_MP_LIMB + 1;
MPFR_ASSERTN(rrsize <= MP_SIZE_T_MAX/2);
rsize = rrsize << 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(marker);
if (odd_exp_u) /* 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] = MPFR_LIMB_HIGHBIT;
else
up[0] = 0;
usize++;
}
}
MPFR_SET_EXP(r, MPFR_GET_EXP(u) != MPFR_EMAX_MAX
? (MPFR_GET_EXP(u) + odd_exp_u) / 2
: (MPFR_EMAX_MAX - 1) / 2 + 1);
do
{
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 ("(inexact = %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
}
}
while (!can_round && (rsize < 2*usize) && (rsize += 2) && (rrsize++));
#ifdef DEBUG
printf ("can_round = %d\n", can_round);
#endif
/* 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) /* the sqrtrem call was exact, possible exact square root */
{
/* if we have taken into account the whole of up */
for (k = usize - rsize - 1; k >= 0; k++)
if (up[k] != 0)
break;
if (k < 0)
goto fin; /* exact square root ==> inexact = 0 */
}
if (can_round)
{
cc = mpfr_round_raw (rp, rp, err, 0, MPFR_PREC(r), rnd_mode, &inexact);
if (inexact == 0) /* exact high part: inex flag depends on remainder */
inexact = -q_limb;
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. */
switch (rnd_mode)
{
case GMP_RNDZ :
case GMP_RNDD :
inexact = -1; /* result is truncated */
break;
case GMP_RNDN :
/* Not in the situation ...0 111111 */
rw = (MPFR_PREC(r) + 1) & (BITS_PER_MP_LIMB - 1);
if (rw != 0)
{
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 r. */
{
cc = mpn_add_1 (rp + nw, rp + nw, rrsize, MP_LIMB_T_ONE << rw);
inexact = 1;
}
else
inexact = -1;
break;
case GMP_RNDU:
/* we should arrive here only when the result is inexact, i.e.
either q_limb > 0 (the remainder from mpn_sqrtrem is non-zero)
or up[0..usize-rsize-1] is non zero, thus we have to add one
ulp, and inexact = 1 */
inexact = 1;
t = MPFR_PREC(r) & (BITS_PER_MP_LIMB - 1);
rsize = (MPFR_PREC(r) - 1)/BITS_PER_MP_LIMB + 1;
cc = mpn_add_1 (rp + rrsize - rsize, rp + rrsize - rsize, rsize,
t != 0 ?
MP_LIMB_T_ONE << (BITS_PER_MP_LIMB - t) :
MP_LIMB_T_ONE);
}
}
if (cc)
{
/* Is a shift necessary here? Isn't the result 1.0000...? */
mpn_rshift (rp, rp, rrsize, 1);
rp[rrsize-1] |= MPFR_LIMB_HIGHBIT;
MPFR_SET_EXP (r, MPFR_GET_EXP (r) + 1);
}
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_ONE <<
(BITS_PER_MP_LIMB -
(MPFR_PREC(r) & (BITS_PER_MP_LIMB - 1)))) - 1);
TMP_FREE(marker);
return inexact;
}
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