1 /* mpn_sbpi1_divappr_q -- Schoolbook division using the Möller-Granlund 3/2
2 division algorithm, returning approximate quotient. The quotient returned
3 is either correct, or one too large.
4
5 Contributed to the GNU project by Torbjorn Granlund.
6
7 THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY
8 SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
9 GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE.
10
11 Copyright 2007, 2009 Free Software Foundation, Inc.
12
13 This file is part of the GNU MP Library.
14
15 The GNU MP Library is free software; you can redistribute it and/or modify
16 it under the terms of either:
17
18 * the GNU Lesser General Public License as published by the Free
19 Software Foundation; either version 3 of the License, or (at your
20 option) any later version.
21
22 or
23
24 * the GNU General Public License as published by the Free Software
25 Foundation; either version 2 of the License, or (at your option) any
26 later version.
27
28 or both in parallel, as here.
29
30 The GNU MP Library is distributed in the hope that it will be useful, but
31 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
32 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
33 for more details.
34
35 You should have received copies of the GNU General Public License and the
36 GNU Lesser General Public License along with the GNU MP Library. If not,
37 see https://www.gnu.org/licenses/. */
38
39
40 #include "gmp-impl.h"
41 #include "longlong.h"
42
43 mp_limb_t
44 mpn_sbpi1_divappr_q (mp_ptr qp,
45 mp_ptr np, mp_size_t nn,
46 mp_srcptr dp, mp_size_t dn,
47 mp_limb_t dinv)
48 {
49 mp_limb_t qh;
50 mp_size_t qn, i;
51 mp_limb_t n1, n0;
52 mp_limb_t d1, d0;
53 mp_limb_t cy, cy1;
54 mp_limb_t q;
55 mp_limb_t flag;
56
57 ASSERT (dn > 2);
58 ASSERT (nn >= dn);
59 ASSERT ((dp[dn-1] & GMP_NUMB_HIGHBIT) != 0);
60
61 np += nn;
62
63 qn = nn - dn;
64 if (qn + 1 < dn)
65 {
66 dp += dn - (qn + 1);
67 dn = qn + 1;
68 }
69
70 qh = mpn_cmp (np - dn, dp, dn) >= 0;
71 if (qh != 0)
72 mpn_sub_n (np - dn, np - dn, dp, dn);
73
74 qp += qn;
75
76 dn -= 2; /* offset dn by 2 for main division loops,
77 saving two iterations in mpn_submul_1. */
78 d1 = dp[dn + 1];
79 d0 = dp[dn + 0];
80
81 np -= 2;
82
83 n1 = np[1];
84
85 for (i = qn - (dn + 2); i >= 0; i--)
86 {
87 np--;
88 if (UNLIKELY (n1 == d1) && np[1] == d0)
89 {
90 q = GMP_NUMB_MASK;
91 mpn_submul_1 (np - dn, dp, dn + 2, q);
92 n1 = np[1]; /* update n1, last loop's value will now be invalid */
93 }
94 else
95 {
96 udiv_qr_3by2 (q, n1, n0, n1, np[1], np[0], d1, d0, dinv);
97
98 cy = mpn_submul_1 (np - dn, dp, dn, q);
99
100 cy1 = n0 < cy;
101 n0 = (n0 - cy) & GMP_NUMB_MASK;
102 cy = n1 < cy1;
103 n1 -= cy1;
104 np[0] = n0;
105
106 if (UNLIKELY (cy != 0))
107 {
108 n1 += d1 + mpn_add_n (np - dn, np - dn, dp, dn + 1);
109 q--;
110 }
111 }
112
113 *--qp = q;
114 }
115
116 flag = ~CNST_LIMB(0);
117
118 if (dn >= 0)
119 {
120 for (i = dn; i > 0; i--)
121 {
122 np--;
123 if (UNLIKELY (n1 >= (d1 & flag)))
124 {
125 q = GMP_NUMB_MASK;
126 cy = mpn_submul_1 (np - dn, dp, dn + 2, q);
127
128 if (UNLIKELY (n1 != cy))
129 {
130 if (n1 < (cy & flag))
131 {
132 q--;
133 mpn_add_n (np - dn, np - dn, dp, dn + 2);
134 }
135 else
136 flag = 0;
137 }
138 n1 = np[1];
139 }
140 else
141 {
142 udiv_qr_3by2 (q, n1, n0, n1, np[1], np[0], d1, d0, dinv);
143
144 cy = mpn_submul_1 (np - dn, dp, dn, q);
145
146 cy1 = n0 < cy;
147 n0 = (n0 - cy) & GMP_NUMB_MASK;
148 cy = n1 < cy1;
149 n1 -= cy1;
150 np[0] = n0;
151
152 if (UNLIKELY (cy != 0))
153 {
154 n1 += d1 + mpn_add_n (np - dn, np - dn, dp, dn + 1);
155 q--;
156 }
157 }
158
159 *--qp = q;
160
161 /* Truncate operands. */
162 dn--;
163 dp++;
164 }
165
166 np--;
167 if (UNLIKELY (n1 >= (d1 & flag)))
168 {
169 q = GMP_NUMB_MASK;
170 cy = mpn_submul_1 (np, dp, 2, q);
171
172 if (UNLIKELY (n1 != cy))
173 {
174 if (n1 < (cy & flag))
175 {
176 q--;
177 add_ssaaaa (np[1], np[0], np[1], np[0], dp[1], dp[0]);
178 }
179 else
180 flag = 0;
181 }
182 n1 = np[1];
183 }
184 else
185 {
186 udiv_qr_3by2 (q, n1, n0, n1, np[1], np[0], d1, d0, dinv);
187
188 np[1] = n1;
189 np[0] = n0;
190 }
191
192 *--qp = q;
193 }
194
195 ASSERT_ALWAYS (np[1] == n1);
196
197 return qh;
198 }