1 /* mpn_mu_div_q.
2
3 Contributed to the GNU project by Torbjorn Granlund and Marco Bodrato.
4
5 THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
6 SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
7 GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE.
8
9 Copyright 2005-2007, 2009, 2010, 2013 Free Software Foundation, Inc.
10
11 This file is part of the GNU MP Library.
12
13 The GNU MP Library is free software; you can redistribute it and/or modify
14 it under the terms of either:
15
16 * the GNU Lesser General Public License as published by the Free
17 Software Foundation; either version 3 of the License, or (at your
18 option) any later version.
19
20 or
21
22 * the GNU General Public License as published by the Free Software
23 Foundation; either version 2 of the License, or (at your option) any
24 later version.
25
26 or both in parallel, as here.
27
28 The GNU MP Library is distributed in the hope that it will be useful, but
29 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
30 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
31 for more details.
32
33 You should have received copies of the GNU General Public License and the
34 GNU Lesser General Public License along with the GNU MP Library. If not,
35 see https://www.gnu.org/licenses/. */
36
37
38 /*
39 The idea of the algorithm used herein is to compute a smaller inverted value
40 than used in the standard Barrett algorithm, and thus save time in the
41 Newton iterations, and pay just a small price when using the inverted value
42 for developing quotient bits. This algorithm was presented at ICMS 2006.
43 */
44
45 /*
46 Things to work on:
47
48 1. This is a rudimentary implementation of mpn_mu_div_q. The algorithm is
49 probably close to optimal, except when mpn_mu_divappr_q fails.
50
51 2. We used to fall back to mpn_mu_div_qr when we detect a possible
52 mpn_mu_divappr_q rounding problem, now we multiply and compare.
53 Unfortunately, since mpn_mu_divappr_q does not return the partial
54 remainder, this also doesn't become optimal. A mpn_mu_divappr_qr could
55 solve that.
56
57 3. The allocations done here should be made from the scratch area, which
58 then would need to be amended.
59 */
60
61 #include <stdlib.h> /* for NULL */
62 #include "gmp-impl.h"
63
64
65 mp_limb_t
66 mpn_mu_div_q (mp_ptr qp,
67 mp_srcptr np, mp_size_t nn,
68 mp_srcptr dp, mp_size_t dn,
69 mp_ptr scratch)
70 {
71 mp_ptr tp, rp;
72 mp_size_t qn;
73 mp_limb_t cy, qh;
74 TMP_DECL;
75
76 TMP_MARK;
77
78 qn = nn - dn;
79
80 tp = TMP_BALLOC_LIMBS (qn + 1);
81
82 if (qn >= dn) /* nn >= 2*dn + 1 */
83 {
84 /* |_______________________| dividend
85 |________| divisor */
86
87 rp = TMP_BALLOC_LIMBS (nn + 1);
88 MPN_COPY (rp + 1, np, nn);
89 rp[0] = 0;
90
91 qh = mpn_cmp (rp + 1 + nn - dn, dp, dn) >= 0;
92 if (qh != 0)
93 mpn_sub_n (rp + 1 + nn - dn, rp + 1 + nn - dn, dp, dn);
94
95 cy = mpn_mu_divappr_q (tp, rp, nn + 1, dp, dn, scratch);
96
97 if (UNLIKELY (cy != 0))
98 {
99 /* Since the partial remainder fed to mpn_preinv_mu_divappr_q was
100 canonically reduced, replace the returned value of B^(qn-dn)+eps
101 by the largest possible value. */
102 mp_size_t i;
103 for (i = 0; i < qn + 1; i++)
104 tp[i] = GMP_NUMB_MAX;
105 }
106
107 /* The max error of mpn_mu_divappr_q is +4. If the low quotient limb is
108 smaller than the max error, we cannot trust the quotient. */
109 if (tp[0] > 4)
110 {
111 MPN_COPY (qp, tp + 1, qn);
112 }
113 else
114 {
115 mp_limb_t cy;
116 mp_ptr pp;
117
118 pp = rp;
119 mpn_mul (pp, tp + 1, qn, dp, dn);
120
121 cy = (qh != 0) ? mpn_add_n (pp + qn, pp + qn, dp, dn) : 0;
122
123 if (cy || mpn_cmp (pp, np, nn) > 0) /* At most is wrong by one, no cycle. */
124 qh -= mpn_sub_1 (qp, tp + 1, qn, 1);
125 else /* Same as above */
126 MPN_COPY (qp, tp + 1, qn);
127 }
128 }
129 else
130 {
131 /* |_______________________| dividend
132 |________________| divisor */
133
134 /* FIXME: When nn = 2dn-1, qn becomes dn-1, and the numerator size passed
135 here becomes 2dn, i.e., more than nn. This shouldn't hurt, since only
136 the most significant dn-1 limbs will actually be read, but it is not
137 pretty. */
138
139 qh = mpn_mu_divappr_q (tp, np + nn - (2 * qn + 2), 2 * qn + 2,
140 dp + dn - (qn + 1), qn + 1, scratch);
141
142 /* The max error of mpn_mu_divappr_q is +4, but we get an additional
143 error from the divisor truncation. */
144 if (tp[0] > 6)
145 {
146 MPN_COPY (qp, tp + 1, qn);
147 }
148 else
149 {
150 mp_limb_t cy;
151
152 /* FIXME: a shorter product should be enough; we may use already
153 allocated space... */
154 rp = TMP_BALLOC_LIMBS (nn);
155 mpn_mul (rp, dp, dn, tp + 1, qn);
156
157 cy = (qh != 0) ? mpn_add_n (rp + qn, rp + qn, dp, dn) : 0;
158
159 if (cy || mpn_cmp (rp, np, nn) > 0) /* At most is wrong by one, no cycle. */
160 qh -= mpn_sub_1 (qp, tp + 1, qn, 1);
161 else /* Same as above */
162 MPN_COPY (qp, tp + 1, qn);
163 }
164 }
165
166 TMP_FREE;
167 return qh;
168 }
169
170 mp_size_t
171 mpn_mu_div_q_itch (mp_size_t nn, mp_size_t dn, int mua_k)
172 {
173 mp_size_t qn;
174
175 qn = nn - dn;
176 if (qn >= dn)
177 {
178 return mpn_mu_divappr_q_itch (nn + 1, dn, mua_k);
179 }
180 else
181 {
182 return mpn_mu_divappr_q_itch (2 * qn + 2, qn + 1, mua_k);
183 }
184 }