Annotation of OpenXM_contrib/gmp/mpfr/div.c, Revision 1.1
1.1 ! maekawa 1: /* mpfr_div -- divide two floating-point numbers
! 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: void
! 33: mpfr_div (mpfr_ptr r, mpfr_srcptr u, mpfr_srcptr v, unsigned char rnd_mode)
! 34: {
! 35: mp_srcptr up, vp;
! 36: mp_ptr rp, tp, tp0, tmp;
! 37: mp_size_t usize, vsize, rrsize;
! 38: mp_size_t rsize;
! 39: mp_size_t sign_quotient;
! 40: mp_size_t prec, err;
! 41: mp_limb_t q_limb;
! 42: mp_exp_t rexp;
! 43: long k, mult, vn;
! 44: unsigned long cc = 0, rw, nw;
! 45: char can_round = 0;
! 46: TMP_DECL (marker);
! 47:
! 48: if (FLAG_NAN(u) || FLAG_NAN(v)) { SET_NAN(r); return; }
! 49:
! 50: usize = (PREC(u) - 1)/BITS_PER_MP_LIMB + 1;
! 51: vsize = (PREC(v) - 1)/BITS_PER_MP_LIMB + 1;
! 52: sign_quotient = (SIGN(u) == SIGN(v) ? 1 : -1);
! 53: prec = PREC(r);
! 54:
! 55: if (!NOTZERO(u)) { SET_ZERO(r); return; }
! 56:
! 57: if (!NOTZERO(v))
! 58: vsize = 1 / v->_mp_d[vsize - 1]; /* Gestion des infinis ? */
! 59:
! 60: if (!NOTZERO(v))
! 61: {
! 62: r->_mp_exp = 0;
! 63: MPN_ZERO(r->_mp_d, r->_mp_size);
! 64: return;
! 65: }
! 66:
! 67: up = u->_mp_d;
! 68: vp = v->_mp_d;
! 69:
! 70: #ifdef DEBUG
! 71: printf("Entering division : ");
! 72: for(k = usize - 1; k >= 0; k--) { printf("%lu ", up[k]); }
! 73: printf(" by ");
! 74: for(k = vsize - 1; k >= 0; k--) { printf("%lu ", vp[k]); }
! 75: printf(".\n");
! 76: #endif
! 77:
! 78: /* Compare the mantissas */
! 79: mult = mpn_cmp(up, vp, (usize > vsize ? vsize : usize));
! 80: if (mult == 0 && vsize > usize)
! 81: {
! 82: vn = vsize - usize;
! 83: while (vn >= 0) if (vp[vn--]) { mult = 1; break; }
! 84: /* On peut diagnostiquer ici pour pas cher le cas u = v */
! 85: }
! 86: else { mult = (mult < 0 ? 1 : 0); }
! 87:
! 88: rsize = (PREC(r) + 3)/BITS_PER_MP_LIMB + 1;
! 89: rrsize = PREC(r)/BITS_PER_MP_LIMB + 1;
! 90: /* Three extra bits are needed in order to get the quotient with enough
! 91: precision ; take one extra bit for rrsize in order to solve more
! 92: easily the problem of rounding to nearest. */
! 93:
! 94: /* ATTENTION, USIZE DOIT RESTER > A VSIZE !!!!!!!! */
! 95:
! 96: do
! 97: {
! 98: TMP_MARK (marker);
! 99:
! 100: rexp = u->_mp_exp - v->_mp_exp;
! 101:
! 102: err = rsize*BITS_PER_MP_LIMB;
! 103: if (rsize < vsize) { err-=2; }
! 104: if (rsize < usize) { err--; }
! 105: if (err > rrsize * BITS_PER_MP_LIMB)
! 106: { err = rrsize * BITS_PER_MP_LIMB; }
! 107:
! 108: tp0 = (mp_ptr) TMP_ALLOC ((rsize+rrsize) * BYTES_PER_MP_LIMB);
! 109: /* fill by zero rrsize low limbs of t */
! 110: MPN_ZERO(tp0, rrsize); tp = tp0 + rrsize;
! 111: tmp = (mp_ptr) TMP_ALLOC (rsize * BYTES_PER_MP_LIMB);
! 112: rp = (mp_ptr) TMP_ALLOC (rrsize * BYTES_PER_MP_LIMB);
! 113:
! 114: if (vsize >= rsize) {
! 115: MPN_COPY (tmp, vp + vsize - rsize, rsize);
! 116: }
! 117: else {
! 118: MPN_COPY (tmp + rsize - vsize, vp, vsize);
! 119: MPN_ZERO (tmp, rsize - vsize);
! 120: }
! 121:
! 122: if (usize >= rsize) {
! 123: MPN_COPY (tp, up + usize - rsize, rsize);
! 124: }
! 125: else {
! 126: MPN_COPY (tp + rsize - usize, up, usize);
! 127: MPN_ZERO (tp, rsize - usize);
! 128: }
! 129:
! 130: /* Do the real job */
! 131:
! 132: #ifdef DEBUG
! 133: printf("Dividing : ");
! 134: for(k = rsize - 1; k >= 0; k--) { printf("%lu ", tp[k]); }
! 135: printf(" by ");
! 136: for(k = rsize - 1; k >= 0; k--) { printf("%lu ", tmp[k]); }
! 137: printf(".\n");
! 138: #endif
! 139:
! 140: q_limb = (rsize==rrsize) /* use Burnikel-Ziegler algorithm */
! 141: ? mpn_divrem_n (rp, tp0, tmp, rsize)
! 142: : mpn_divrem (rp, 0, tp0, rsize+rrsize, tmp, rsize);
! 143: tp = tp0; /* location of remainder */
! 144:
! 145: #ifdef DEBUG
! 146: printf("The result is : \n");
! 147: printf("Quotient : ");
! 148: for(k = rrsize - 1; k >= 0; k--) { printf("%lu ", rp[k]); }
! 149: printf("Remainder : ");
! 150: for(k = rsize - 1; k >= 0; k--) { printf("%lu ", tp[k]); }
! 151: printf("(q_limb = %lu)\n", q_limb);
! 152: #endif
! 153:
! 154: /* msb-normalize the result */
! 155:
! 156: if (q_limb)
! 157: {
! 158: count_leading_zeros(k, q_limb);
! 159: mpn_rshift(rp, rp, rrsize, BITS_PER_MP_LIMB - k);
! 160: rp[rrsize - 1] |= (q_limb << k);
! 161: rexp += BITS_PER_MP_LIMB - k;
! 162: }
! 163: else
! 164: {
! 165: count_leading_zeros(k, rp[rrsize - 1]);
! 166: if (k) { mpn_lshift(rp, rp, rrsize, k); }
! 167: rexp -= k;
! 168: }
! 169:
! 170: can_round = (mpfr_can_round_raw(rp, rrsize, sign_quotient, err,
! 171: GMP_RNDN, rnd_mode, PREC(r))
! 172: || (usize == rsize && vsize == rsize &&
! 173: mpfr_can_round_raw(rp, rrsize, sign_quotient, err,
! 174: GMP_RNDZ, rnd_mode, PREC(r))));
! 175:
! 176: /* If we used all the limbs of both the dividend and the divisor,
! 177: then we have the correct RNDZ rounding */
! 178:
! 179: if (!can_round && (rsize < usize || rsize < vsize))
! 180: {
! 181: #ifdef DEBUG
! 182: printf("Increasing the precision.\n");
! 183: #endif
! 184: printf("#");
! 185: TMP_FREE(marker);
! 186: }
! 187: }
! 188: while (!can_round && (rsize < usize || rsize < vsize)
! 189: && (rsize++) && (rrsize++));
! 190:
! 191: /* ON PEUT PROBABLEMENT SE DEBROUILLER DES QUE rsize >= vsize */
! 192: /* MAIS IL FAUT AJOUTER LE BOUT QUI MANQUE DE usize A rsize */
! 193:
! 194: if (can_round)
! 195: {
! 196: cc = mpfr_round_raw(rp, rp, err, (sign_quotient == -1 ? 1 : 0),
! 197: PREC(r), rnd_mode);
! 198: rrsize = (PREC(r) - 1)/BITS_PER_MP_LIMB + 1;
! 199: }
! 200: else
! 201: /* Use the remainder to find out the correct rounding */
! 202: /* Note that at this point the division has been done */
! 203: /* EXACTLY. */
! 204: if ((rnd_mode == GMP_RNDD && sign_quotient == -1)
! 205: || (rnd_mode == GMP_RNDU && sign_quotient == 1)
! 206: || (rnd_mode == GMP_RNDN))
! 207: {
! 208: /* We cannot round, so that the last bits of the quotient
! 209: have to be zero; just look if the remainder is nonzero */
! 210: k = rsize - 1;
! 211: while (k >= 0) { if (tp[k]) break; k--; }
! 212: if (k >= 0)
! 213: cc = mpn_add_1(rp, rp, rrsize, (mp_limb_t)1 << (BITS_PER_MP_LIMB -
! 214: (PREC(r) &
! 215: (BITS_PER_MP_LIMB - 1))));
! 216: else
! 217: if (rnd_mode == GMP_RNDN) /* even rounding */
! 218: {
! 219: rw = (PREC(r) + 1) & (BITS_PER_MP_LIMB - 1);
! 220: if (rw) { rw = BITS_PER_MP_LIMB - rw; nw = 0; } else nw = 1;
! 221: if ((rw ? (rp[nw] >> (rw + 1)) & 1 :
! 222: (rp[nw] >> (BITS_PER_MP_LIMB - 1)) & 1))
! 223: {
! 224: cc = mpn_add_1(rp + nw, rp + nw, rrsize,
! 225: ((mp_limb_t)1) << rw);
! 226: }
! 227: }
! 228: /* cas 0111111 */
! 229: }
! 230:
! 231: if (sign_quotient != SIGN(r)) { CHANGE_SIGN(r); }
! 232: r->_mp_exp = rexp;
! 233:
! 234: if (cc) {
! 235: mpn_rshift(rp, rp, rrsize, 1);
! 236: rp[rrsize-1] |= (mp_limb_t) 1 << (BITS_PER_MP_LIMB-1);
! 237: r->_mp_exp++;
! 238: }
! 239:
! 240: rsize = rrsize;
! 241: rrsize = (PREC(r) - 1)/BITS_PER_MP_LIMB + 1;
! 242: MPN_COPY(r->_mp_d, rp + rsize - rrsize, rrsize);
! 243: MANT(r) [0] &= ~(((mp_limb_t)1 << (BITS_PER_MP_LIMB -
! 244: (PREC(r) & (BITS_PER_MP_LIMB - 1)))) - 1) ;
! 245:
! 246: TMP_FREE (marker);
! 247: }
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