1 /* mpn_dcpi1_bdiv_qr -- divide-and-conquer Hensel division with precomputed
2 inverse, returning quotient and remainder.
3
4 Contributed to the GNU project by Niels Möller and Torbjorn Granlund.
5
6 THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
7 SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
8 GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE.
9
10 Copyright 2006, 2007, 2009, 2010, 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
41 /* Computes Hensel binary division of {np, 2*n} by {dp, n}.
42
43 Output:
44
45 q = -n * d^{-1} mod 2^{qn * GMP_NUMB_BITS},
46
47 r = (n + q * d) * 2^{-qn * GMP_NUMB_BITS}
48
49 Stores q at qp. Stores the n least significant limbs of r at the high half
50 of np, and returns the carry from the addition n + q*d.
51
52 d must be odd. dinv is (-d)^-1 mod 2^GMP_NUMB_BITS. */
53
54 mp_size_t
55 mpn_dcpi1_bdiv_qr_n_itch (mp_size_t n)
56 {
57 return n;
58 }
59
60 mp_limb_t
61 mpn_dcpi1_bdiv_qr_n (mp_ptr qp, mp_ptr np, mp_srcptr dp, mp_size_t n,
62 mp_limb_t dinv, mp_ptr tp)
63 {
64 mp_size_t lo, hi;
65 mp_limb_t cy;
66 mp_limb_t rh;
67
68 lo = n >> 1; /* floor(n/2) */
69 hi = n - lo; /* ceil(n/2) */
70
71 if (BELOW_THRESHOLD (lo, DC_BDIV_QR_THRESHOLD))
72 cy = mpn_sbpi1_bdiv_qr (qp, np, 2 * lo, dp, lo, dinv);
73 else
74 cy = mpn_dcpi1_bdiv_qr_n (qp, np, dp, lo, dinv, tp);
75
76 mpn_mul (tp, dp + lo, hi, qp, lo);
77
78 mpn_incr_u (tp + lo, cy);
79 rh = mpn_add (np + lo, np + lo, n + hi, tp, n);
80
81 if (BELOW_THRESHOLD (hi, DC_BDIV_QR_THRESHOLD))
82 cy = mpn_sbpi1_bdiv_qr (qp + lo, np + lo, 2 * hi, dp, hi, dinv);
83 else
84 cy = mpn_dcpi1_bdiv_qr_n (qp + lo, np + lo, dp, hi, dinv, tp);
85
86 mpn_mul (tp, qp + lo, hi, dp + hi, lo);
87
88 mpn_incr_u (tp + hi, cy);
89 rh += mpn_add_n (np + n, np + n, tp, n);
90
91 return rh;
92 }
93
94 mp_limb_t
95 mpn_dcpi1_bdiv_qr (mp_ptr qp, mp_ptr np, mp_size_t nn,
96 mp_srcptr dp, mp_size_t dn, mp_limb_t dinv)
97 {
98 mp_size_t qn;
99 mp_limb_t rr, cy;
100 mp_ptr tp;
101 TMP_DECL;
102
103 TMP_MARK;
104
105 ASSERT (dn >= 2); /* to adhere to mpn_sbpi1_div_qr's limits */
106 ASSERT (nn - dn >= 1); /* to adhere to mpn_sbpi1_div_qr's limits */
107 ASSERT (dp[0] & 1);
108
109 tp = TMP_SALLOC_LIMBS (dn);
110
111 qn = nn - dn;
112
113 if (qn > dn)
114 {
115 /* Reduce qn mod dn without division, optimizing small operations. */
116 do
117 qn -= dn;
118 while (qn > dn);
119
120 /* Perform the typically smaller block first. */
121 if (BELOW_THRESHOLD (qn, DC_BDIV_QR_THRESHOLD))
122 cy = mpn_sbpi1_bdiv_qr (qp, np, 2 * qn, dp, qn, dinv);
123 else
124 cy = mpn_dcpi1_bdiv_qr_n (qp, np, dp, qn, dinv, tp);
125
126 rr = 0;
127 if (qn != dn)
128 {
129 if (qn > dn - qn)
130 mpn_mul (tp, qp, qn, dp + qn, dn - qn);
131 else
132 mpn_mul (tp, dp + qn, dn - qn, qp, qn);
133 mpn_incr_u (tp + qn, cy);
134
135 rr = mpn_add (np + qn, np + qn, nn - qn, tp, dn);
136 cy = 0;
137 }
138
139 np += qn;
140 qp += qn;
141
142 qn = nn - dn - qn;
143 do
144 {
145 rr += mpn_add_1 (np + dn, np + dn, qn, cy);
146 cy = mpn_dcpi1_bdiv_qr_n (qp, np, dp, dn, dinv, tp);
147 qp += dn;
148 np += dn;
149 qn -= dn;
150 }
151 while (qn > 0);
152 TMP_FREE;
153 return rr + cy;
154 }
155
156 if (BELOW_THRESHOLD (qn, DC_BDIV_QR_THRESHOLD))
157 cy = mpn_sbpi1_bdiv_qr (qp, np, 2 * qn, dp, qn, dinv);
158 else
159 cy = mpn_dcpi1_bdiv_qr_n (qp, np, dp, qn, dinv, tp);
160
161 rr = 0;
162 if (qn != dn)
163 {
164 if (qn > dn - qn)
165 mpn_mul (tp, qp, qn, dp + qn, dn - qn);
166 else
167 mpn_mul (tp, dp + qn, dn - qn, qp, qn);
168 mpn_incr_u (tp + qn, cy);
169
170 rr = mpn_add (np + qn, np + qn, nn - qn, tp, dn);
171 cy = 0;
172 }
173
174 TMP_FREE;
175 return rr + cy;
176 }