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