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, 2012-2014, 2017 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 either:
16
17 * the GNU Lesser General Public License as published by the Free
18 Software Foundation; either version 3 of the License, or (at your
19 option) any later version.
20
21 or
22
23 * the GNU General Public License as published by the Free Software
24 Foundation; either version 2 of the License, or (at your option) any
25 later version.
26
27 or both in parallel, as here.
28
29 The GNU MP Library is distributed in the hope that it will be useful, but
30 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
31 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
32 for more details.
33
34 You should have received copies of the GNU General Public License and the
35 GNU Lesser General Public License along with the GNU MP Library. If not,
36 see https://www.gnu.org/licenses/. */
37
38 #include "gmp-impl.h"
39
40 #if GMP_LIMB_BITS > 50
41 #define LOG 50
42 #else
43 #define LOG GMP_LIMB_BITS
44 #endif
45
46
47 /* Input: U = {up,un}, V = {vp,vn} must be odd, cap
48 Ouput W = {wp,*wn} allocation need is exactly *wn
49
50 Set W = U / V^k, where k is the largest integer <= cap such that the
51 division yields an integer.
52
53 FIXME: We currently allow any operand overlap. This is quite non mpn-ish
54 and might be changed, since it cost significant temporary space.
55 * If we require W to have space for un + 1 limbs, we could save qp or qp2
56 (but we will still need to copy things into wp 50% of the time).
57 * If we allow ourselves to clobber U, we could save the other of qp and qp2,
58 and the initial COPY (but also here we would need un + 1 limbs).
59 */
60
61 /* FIXME: We need to wrap mpn_bdiv_qr due to the itch interface. This need
62 indicates a flaw in the current itch mechanism: Which operands not greater
63 than un,un will incur the worst itch? We need a parallel foo_maxitch set
64 of functions. */
65 static void
66 mpn_bdiv_qr_wrap (mp_ptr qp, mp_ptr rp,
67 mp_srcptr np, mp_size_t nn,
68 mp_srcptr dp, mp_size_t dn)
69 {
70 mp_ptr scratch_out;
71 TMP_DECL;
72
73 TMP_MARK;
74 scratch_out = TMP_ALLOC_LIMBS (mpn_bdiv_qr_itch (nn, dn));
75 mpn_bdiv_qr (qp, rp, np, nn, dp, dn, scratch_out);
76
77 TMP_FREE;
78 }
79
80 mp_bitcnt_t
81 mpn_remove (mp_ptr wp, mp_size_t *wn,
82 mp_srcptr up, mp_size_t un, mp_srcptr vp, mp_size_t vn,
83 mp_bitcnt_t cap)
84 {
85 mp_srcptr pwpsp[LOG];
86 mp_size_t pwpsn[LOG];
87 mp_size_t npowers;
88 mp_ptr tp, qp, np, qp2;
89 mp_srcptr pp;
90 mp_size_t pn, nn, qn, i;
91 mp_bitcnt_t pwr;
92 TMP_DECL;
93
94 ASSERT (un > 0);
95 ASSERT (vn > 0);
96 ASSERT (vp[0] % 2 != 0); /* 2-adic division wants odd numbers */
97 ASSERT (vn > 1 || vp[0] > 1); /* else we would loop indefinitely */
98
99 TMP_MARK;
100
101 TMP_ALLOC_LIMBS_3 (qp, un + 1, /* quotient, alternating */
102 qp2, un + 1, /* quotient, alternating */
103 tp, (un + 1 + vn) / 2); /* remainder */
104 pp = vp;
105 pn = vn;
106
107 MPN_COPY (qp, up, un);
108 qn = un;
109
110 npowers = 0;
111 while (qn >= pn)
112 {
113 qp[qn] = 0;
114 mpn_bdiv_qr_wrap (qp2, tp, qp, qn + 1, pp, pn);
115 if (!mpn_zero_p (tp, pn))
116 {
117 if (mpn_cmp (tp, pp, pn) != 0)
118 break; /* could not divide by V^npowers */
119 }
120
121 MP_PTR_SWAP (qp, qp2);
122 qn = qn - pn;
123 mpn_neg (qp, qp, qn+1);
124
125 qn += qp[qn] != 0;
126
127 pwpsp[npowers] = pp;
128 pwpsn[npowers] = pn;
129 ++npowers;
130
131 if (((mp_bitcnt_t) 2 << npowers) - 1 > cap)
132 break;
133
134 nn = 2 * pn - 1; /* next power will be at least this large */
135 if (nn > qn)
136 break; /* next power would be overlarge */
137
138 if (npowers == 1) /* Alloc once, but only if it's needed */
139 np = TMP_ALLOC_LIMBS (qn + LOG); /* powers of V */
140 else
141 np += pn;
142
143 mpn_sqr (np, pp, pn);
144 pn = nn + (np[nn] != 0);
145 pp = np;
146 }
147
148 pwr = ((mp_bitcnt_t) 1 << npowers) - 1;
149
150 for (i = npowers; --i >= 0;)
151 {
152 pn = pwpsn[i];
153 if (qn < pn)
154 continue;
155
156 if (pwr + ((mp_bitcnt_t) 1 << i) > cap)
157 continue; /* V^i would bring us past cap */
158
159 qp[qn] = 0;
160 mpn_bdiv_qr_wrap (qp2, tp, qp, qn + 1, pwpsp[i], pn);
161 if (!mpn_zero_p (tp, pn))
162 {
163 if (mpn_cmp (tp, pwpsp[i], pn) != 0)
164 continue; /* could not divide by V^i */
165 }
166
167 MP_PTR_SWAP (qp, qp2);
168 qn = qn - pn;
169 mpn_neg (qp, qp, qn+1);
170
171 qn += qp[qn] != 0;
172
173 pwr += (mp_bitcnt_t) 1 << i;
174 }
175
176 MPN_COPY (wp, qp, qn);
177 *wn = qn;
178
179 TMP_FREE;
180
181 return pwr;
182 }