Annotation of OpenXM_contrib/gmp/mpfr/sqrt.c, Revision 1.1
1.1 ! maekawa 1: /* mpfr_sqrt -- square root of a floating-point number
! 2:
! 3: Copyright (C) 1999 PolKA project, Inria Lorraine and Loria
! 4:
! 5: This file is part of the MPFR Library.
! 6:
! 7: The MPFR Library is free software; you can redistribute it and/or modify
! 8: it under the terms of the GNU Library General Public License as published by
! 9: the Free Software Foundation; either version 2 of the License, or (at your
! 10: option) any later version.
! 11:
! 12: The MPFR Library is distributed in the hope that it will be useful, but
! 13: WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
! 14: or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public
! 15: License for more details.
! 16:
! 17: You should have received a copy of the GNU Library General Public License
! 18: along with the MPFR Library; see the file COPYING.LIB. If not, write to
! 19: the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
! 20: MA 02111-1307, USA. */
! 21:
! 22: #include <math.h>
! 23: #include <stdio.h>
! 24: #include <stdlib.h>
! 25: #include "gmp.h"
! 26: #include "gmp-impl.h"
! 27: #include "mpfr.h"
! 28: #include "longlong.h"
! 29:
! 30: /* #define DEBUG */
! 31:
! 32: int
! 33: mpfr_sqrt (mpfr_ptr r, mpfr_srcptr u, unsigned char rnd_mode)
! 34: {
! 35: mp_ptr up, rp, tmp, remp;
! 36: mp_size_t usize, rrsize;
! 37: mp_size_t rsize;
! 38: mp_size_t prec, err;
! 39: mp_limb_t q_limb;
! 40: long rw, nw, k;
! 41: int exact = 0;
! 42: unsigned long cc = 0;
! 43: char can_round = 0;
! 44: TMP_DECL (marker); TMP_DECL(marker0);
! 45:
! 46: if (FLAG_NAN(u) || SIGN(u) == -1) { SET_NAN(r); return 0; }
! 47:
! 48: prec = PREC(r);
! 49:
! 50: if (!NOTZERO(u))
! 51: {
! 52: EXP(r) = 0;
! 53: MPN_ZERO(MANT(r), ABSSIZE(r));
! 54: return 1;
! 55: }
! 56:
! 57: up = MANT(u);
! 58:
! 59: #ifdef DEBUG
! 60: printf("Entering square root : ");
! 61: for(k = usize - 1; k >= 0; k--) { printf("%lu ", up[k]); }
! 62: printf(".\n");
! 63: #endif
! 64:
! 65: /* Compare the mantissas */
! 66:
! 67: usize = (PREC(u) - 1)/BITS_PER_MP_LIMB + 1;
! 68: rsize = ((PREC(r) + 2 + (EXP(u) & 1))/BITS_PER_MP_LIMB + 1) << 1;
! 69: rrsize = (PREC(r) + 2 + (EXP(u) & 1))/BITS_PER_MP_LIMB + 1;
! 70: /* One extra bit is needed in order to get the square root with enough
! 71: precision ; take one extra bit for rrsize in order to solve more
! 72: easily the problem of rounding to nearest.
! 73: Need to have 2*rrsize = rsize...
! 74: Take one extra bit if the exponent of u is odd since we shall have
! 75: to shift then.
! 76: */
! 77:
! 78: TMP_MARK(marker0);
! 79: if (EXP(u) & 1) /* Shift u one bit to the right */
! 80: {
! 81: if (PREC(u) & (BITS_PER_MP_LIMB - 1))
! 82: {
! 83: up = TMP_ALLOC(usize*BYTES_PER_MP_LIMB);
! 84: mpn_rshift(up, u->_mp_d, usize, 1);
! 85: }
! 86: else
! 87: {
! 88: up = TMP_ALLOC((usize + 1)*BYTES_PER_MP_LIMB);
! 89: if (mpn_rshift(up + 1, u->_mp_d, ABSSIZE(u), 1))
! 90: up [0] = ((mp_limb_t) 1) << (BITS_PER_MP_LIMB - 1);
! 91: else up[0] = 0;
! 92: usize++;
! 93: }
! 94: }
! 95:
! 96: EXP(r) = ((EXP(u) + (EXP(u) & 1)) / 2) ;
! 97:
! 98: do
! 99: {
! 100: TMP_MARK (marker);
! 101:
! 102: err = rsize*BITS_PER_MP_LIMB;
! 103: if (rsize < usize) { err--; }
! 104: if (err > rrsize * BITS_PER_MP_LIMB)
! 105: { err = rrsize * BITS_PER_MP_LIMB; }
! 106:
! 107: tmp = (mp_ptr) TMP_ALLOC (rsize * BYTES_PER_MP_LIMB);
! 108: rp = (mp_ptr) TMP_ALLOC (rrsize * BYTES_PER_MP_LIMB);
! 109: remp = (mp_ptr) TMP_ALLOC (rsize * BYTES_PER_MP_LIMB);
! 110:
! 111: if (usize >= rsize) {
! 112: MPN_COPY (tmp, up + usize - rsize, rsize);
! 113: }
! 114: else {
! 115: MPN_COPY (tmp + rsize - usize, up, usize);
! 116: MPN_ZERO (tmp, rsize - usize);
! 117: }
! 118:
! 119: /* Do the real job */
! 120:
! 121: #ifdef DEBUG
! 122: printf("Taking the sqrt of : ");
! 123: for(k = rsize - 1; k >= 0; k--) {
! 124: printf("+%lu*2^%lu",tmp[k],k*mp_bits_per_limb); }
! 125: printf(".\n");
! 126: #endif
! 127:
! 128: q_limb = kara_sqrtrem (rp, remp, tmp, rsize);
! 129:
! 130: #ifdef DEBUG
! 131: printf("The result is : \n");
! 132: printf("sqrt : ");
! 133: for(k = rrsize - 1; k >= 0; k--) { printf("%lu ", rp[k]); }
! 134: printf("(q_limb = %lu)\n", q_limb);
! 135: #endif
! 136:
! 137: can_round = (mpfr_can_round_raw(rp, rrsize, 1, err,
! 138: GMP_RNDZ, rnd_mode, PREC(r)));
! 139:
! 140: /* If we used all the limbs of both the dividend and the divisor,
! 141: then we have the correct RNDZ rounding */
! 142:
! 143: if (!can_round && (rsize < 2*usize))
! 144: {
! 145: #ifdef DEBUG
! 146: printf("Increasing the precision.\n");
! 147: #endif
! 148: TMP_FREE(marker);
! 149: }
! 150: }
! 151: while (!can_round && (rsize < 2*usize)
! 152: && (rsize += 2) && (rrsize ++));
! 153:
! 154:
! 155: /* This part may be deplaced upper to avoid a few mpfr_can_round_raw */
! 156: /* when the square root is exact. It is however very unprobable that */
! 157: /* it would improve the behaviour of the present code on average. */
! 158:
! 159: if (!q_limb) /* possibly exact */
! 160: {
! 161: /* if we have taken into account the whole of up */
! 162: for (k = usize - rsize - 1; k >= 0; k ++)
! 163: if (up[k]) break;
! 164:
! 165: if (k < 0) { exact = 1; goto fin; }
! 166: }
! 167:
! 168: if (can_round)
! 169: {
! 170: cc = mpfr_round_raw(rp, rp, err, 0, PREC(r), rnd_mode);
! 171: rrsize = (PREC(r) - 1)/BITS_PER_MP_LIMB + 1;
! 172: }
! 173: else
! 174: /* Use the return value of sqrtrem to decide of the rounding */
! 175: /* Note that at this point the sqrt has been computed */
! 176: /* EXACTLY. If rounding = GMP_RNDZ, do nothing [comes from */
! 177: /* the fact that the exact square root can end with a bunch of ones, */
! 178: /* and in that case we indeed cannot round if we do not know that */
! 179: /* the computation was exact. */
! 180: switch (rnd_mode)
! 181: {
! 182: case GMP_RNDZ :
! 183: case GMP_RNDD : break;
! 184:
! 185: case GMP_RNDN :
! 186: /* Not in the situation ...0 111111 */
! 187: rw = (PREC(r) + 1) & (BITS_PER_MP_LIMB - 1);
! 188: if (rw) { rw = BITS_PER_MP_LIMB - rw; nw = 0; } else nw = 1;
! 189: if ((rp[nw] >> rw) & 1 && /* Not 0111111111 */
! 190: (q_limb || /* Nonzero remainder */
! 191: (rw ? (rp[nw] >> (rw + 1)) & 1 :
! 192: (rp[nw] >> (BITS_PER_MP_LIMB - 1)) & 1))) /* or even rounding */
! 193: cc = mpn_add_1(rp + nw, rp + nw, rrsize, ((mp_limb_t)1) << rw);
! 194: break;
! 195:
! 196: case GMP_RNDU :
! 197: if (q_limb)
! 198: cc = mpn_add_1(rp, rp, rrsize, 1 << (BITS_PER_MP_LIMB -
! 199: (PREC(r) &
! 200: (BITS_PER_MP_LIMB - 1))));
! 201: }
! 202:
! 203: if (cc) {
! 204: mpn_rshift(rp, rp, rrsize, 1);
! 205: rp[rrsize-1] |= (mp_limb_t) 1 << (BITS_PER_MP_LIMB-1);
! 206: r->_mp_exp++;
! 207: }
! 208:
! 209: fin:
! 210: rsize = rrsize;
! 211: rrsize = (PREC(r) - 1)/BITS_PER_MP_LIMB + 1;
! 212: MPN_COPY(r->_mp_d, rp + rsize - rrsize, rrsize);
! 213:
! 214: if (PREC(r) & (BITS_PER_MP_LIMB - 1))
! 215: MANT(r) [0] &= ~(((mp_limb_t)1 << (BITS_PER_MP_LIMB -
! 216: (PREC(r) & (BITS_PER_MP_LIMB - 1)))) - 1) ;
! 217:
! 218: TMP_FREE(marker0); TMP_FREE (marker);
! 219: return exact;
! 220: }
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