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