1 /* mpn_remove -- divide out all multiples of odd mpn number from another mpn
2 number.
3
4 Contributed to the GNU project by Torbjorn Granlund.
5
6 THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY
7 SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
8 GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE.
9
10 Copyright 2009 Free Software Foundation, Inc.
11
12 This file is part of the GNU MP Library.
13
14 The GNU MP Library is free software; you can redistribute it and/or modify
15 it under the terms of the GNU Lesser General Public License as published by
16 the Free Software Foundation; either version 3 of the License, or (at your
17 option) any later version.
18
19 The GNU MP Library is distributed in the hope that it will be useful, but
20 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
21 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
22 License for more details.
23
24 You should have received a copy of the GNU Lesser General Public License
25 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
26
27 #include "gmp.h"
28 #include "gmp-impl.h"
29
30 #if GMP_LIMB_BITS > 50
31 #define LOG 50
32 #else
33 #define LOG GMP_LIMB_BITS
34 #endif
35
36
37 /* Input: U = {up,un}, V = {vp,vn} must be odd, cap
38 Ouput W = {wp,*wn} allocation need is exactly *wn
39
40 Set W = U / V^k, where k is the largest integer <= cap such that the
41 division yields an integer.
42
43 FIXME: We currently allow any operand overlap. This is quite non mpn-ish
44 and might be changed, since it cost significant temporary space.
45 * If we require W to have space for un limbs, we could save qp or qp2 (but
46 we will still need to copy things into wp 50% of the time).
47 * If we allow ourselves to clobber U, we could save the other of qp and qp2.
48 */
49
50 mp_bitcnt_t
mpn_remove(mp_ptr wp,mp_size_t * wn,mp_ptr up,mp_size_t un,mp_ptr vp,mp_size_t vn,mp_bitcnt_t cap)51 mpn_remove (mp_ptr wp, mp_size_t *wn,
52 mp_ptr up, mp_size_t un, mp_ptr vp, mp_size_t vn,
53 mp_bitcnt_t cap)
54 {
55 mp_ptr pwpsp[LOG];
56 mp_size_t pwpsn[LOG];
57 mp_size_t npowers;
58 mp_ptr tp, qp, np, pp, qp2, scratch_out;
59 mp_size_t pn, nn, qn, i;
60 mp_bitcnt_t pwr;
61 TMP_DECL;
62
63 ASSERT (un > 0);
64 ASSERT (vn > 0);
65 ASSERT (vp[0] % 2 != 0); /* 2-adic division wants odd numbers */
66 ASSERT (vn > 1 || vp[0] > 1); /* else we would loop indefinitely */
67
68 TMP_MARK;
69
70 tp = TMP_ALLOC_LIMBS ((un + vn) / 2); /* remainder */
71 qp = TMP_ALLOC_LIMBS (un); /* quotient, alternating */
72 qp2 = TMP_ALLOC_LIMBS (un); /* quotient, alternating */
73 np = TMP_ALLOC_LIMBS (un + LOG); /* powers of V */
74 pp = vp;
75 pn = vn;
76
77 /* FIXME: This allocation need indicate a flaw in the current itch mechanism:
78 Which operands not greater than un,un will incur the worst itch? We need
79 a parallel foo_maxitch set of functions. */
80 scratch_out = TMP_ALLOC_LIMBS (mpn_bdiv_qr_itch (un, un >> 1));
81
82 MPN_COPY (qp, up, un);
83 qn = un;
84
85 npowers = 0;
86 while (qn >= pn)
87 {
88 mpn_bdiv_qr (qp2, tp, qp, qn, pp, pn, scratch_out);
89 if (!mpn_zero_p (tp, pn))
90 break; /* could not divide by V^npowers */
91
92 MP_PTR_SWAP (qp, qp2);
93 qn = qn - pn;
94 qn += qp[qn] != 0;
95
96 pwpsp[npowers] = pp;
97 pwpsn[npowers] = pn;
98 npowers++;
99
100 if (((mp_bitcnt_t) 2 << npowers) - 1 > cap)
101 break;
102
103 nn = 2 * pn - 1; /* next power will be at least this many limbs */
104 if (nn > qn)
105 break; /* next power would be overlarge */
106
107 mpn_sqr (np, pp, pn);
108 nn += np[nn] != 0;
109 pp = np;
110 pn = nn;
111 np += nn;
112 }
113
114 pwr = ((mp_bitcnt_t) 1 << npowers) - 1;
115
116 for (i = npowers - 1; i >= 0; i--)
117 {
118 pp = pwpsp[i];
119 pn = pwpsn[i];
120 if (qn < pn)
121 continue;
122
123 if (pwr + ((mp_bitcnt_t) 1 << i) > cap)
124 continue; /* V^i would bring us past cap */
125
126 mpn_bdiv_qr (qp2, tp, qp, qn, pp, pn, scratch_out);
127 if (!mpn_zero_p (tp, pn))
128 continue; /* could not divide by V^i */
129
130 MP_PTR_SWAP (qp, qp2);
131 qn = qn - pn;
132 qn += qp[qn] != 0;
133
134 pwr += (mp_bitcnt_t) 1 << i;
135 }
136
137 MPN_COPY (wp, qp, qn);
138 *wn = qn;
139
140 TMP_FREE;
141
142 return pwr;
143 }
144