Annotation of OpenXM_contrib/gmp/mpfr/div.c, Revision 1.1.1.1
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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