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1 | /* mpn_divrem -- Divide natural numbers, producing both remainder and |
2 | quotient. | |
3 | ||
b168057a | 4 | Copyright (C) 1993-2015 Free Software Foundation, Inc. |
b6ab06ce UD |
5 | |
6 | This file is part of the GNU MP Library. | |
7 | ||
8 | The GNU MP Library is free software; you can redistribute it and/or modify | |
9 | it under the terms of the GNU Lesser General Public License as published by | |
10 | the Free Software Foundation; either version 2.1 of the License, or (at your | |
11 | option) any later version. | |
12 | ||
13 | The GNU MP Library is distributed in the hope that it will be useful, but | |
14 | WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY | |
15 | or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public | |
16 | License for more details. | |
17 | ||
18 | You should have received a copy of the GNU Lesser General Public License | |
59ba27a6 PE |
19 | along with the GNU MP Library; see the file COPYING.LIB. If not, see |
20 | <http://www.gnu.org/licenses/>. */ | |
b6ab06ce UD |
21 | |
22 | #include <gmp.h> | |
23 | #include "gmp-impl.h" | |
24 | #include "longlong.h" | |
25 | ||
26 | /* Divide num (NP/NSIZE) by den (DP/DSIZE) and write | |
27 | the NSIZE-DSIZE least significant quotient limbs at QP | |
28 | and the DSIZE long remainder at NP. If QEXTRA_LIMBS is | |
29 | non-zero, generate that many fraction bits and append them after the | |
30 | other quotient limbs. | |
31 | Return the most significant limb of the quotient, this is always 0 or 1. | |
32 | ||
33 | Preconditions: | |
34 | 0. NSIZE >= DSIZE. | |
35 | 1. The most significant bit of the divisor must be set. | |
36 | 2. QP must either not overlap with the input operands at all, or | |
37 | QP + DSIZE >= NP must hold true. (This means that it's | |
38 | possible to put the quotient in the high part of NUM, right after the | |
39 | remainder in NUM. | |
40 | 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero. */ | |
41 | ||
42 | mp_limb_t | |
43 | #if __STDC__ | |
44 | mpn_divrem (mp_ptr qp, mp_size_t qextra_limbs, | |
45 | mp_ptr np, mp_size_t nsize, | |
46 | mp_srcptr dp, mp_size_t dsize) | |
47 | #else | |
48 | mpn_divrem (qp, qextra_limbs, np, nsize, dp, dsize) | |
49 | mp_ptr qp; | |
50 | mp_size_t qextra_limbs; | |
51 | mp_ptr np; | |
52 | mp_size_t nsize; | |
53 | mp_srcptr dp; | |
54 | mp_size_t dsize; | |
55 | #endif | |
56 | { | |
57 | mp_limb_t most_significant_q_limb = 0; | |
58 | ||
59 | switch (dsize) | |
60 | { | |
61 | case 0: | |
62 | /* We are asked to divide by zero, so go ahead and do it! (To make | |
63 | the compiler not remove this statement, return the value.) */ | |
64 | return 1 / dsize; | |
65 | ||
66 | case 1: | |
67 | { | |
68 | mp_size_t i; | |
69 | mp_limb_t n1; | |
70 | mp_limb_t d; | |
71 | ||
72 | d = dp[0]; | |
73 | n1 = np[nsize - 1]; | |
74 | ||
75 | if (n1 >= d) | |
76 | { | |
77 | n1 -= d; | |
78 | most_significant_q_limb = 1; | |
79 | } | |
80 | ||
81 | qp += qextra_limbs; | |
82 | for (i = nsize - 2; i >= 0; i--) | |
83 | udiv_qrnnd (qp[i], n1, n1, np[i], d); | |
84 | qp -= qextra_limbs; | |
85 | ||
86 | for (i = qextra_limbs - 1; i >= 0; i--) | |
87 | udiv_qrnnd (qp[i], n1, n1, 0, d); | |
88 | ||
89 | np[0] = n1; | |
90 | } | |
91 | break; | |
92 | ||
93 | case 2: | |
94 | { | |
95 | mp_size_t i; | |
96 | mp_limb_t n1, n0, n2; | |
97 | mp_limb_t d1, d0; | |
98 | ||
99 | np += nsize - 2; | |
100 | d1 = dp[1]; | |
101 | d0 = dp[0]; | |
102 | n1 = np[1]; | |
103 | n0 = np[0]; | |
104 | ||
105 | if (n1 >= d1 && (n1 > d1 || n0 >= d0)) | |
106 | { | |
107 | sub_ddmmss (n1, n0, n1, n0, d1, d0); | |
108 | most_significant_q_limb = 1; | |
109 | } | |
110 | ||
111 | for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--) | |
112 | { | |
113 | mp_limb_t q; | |
114 | mp_limb_t r; | |
115 | ||
116 | if (i >= qextra_limbs) | |
117 | np--; | |
118 | else | |
119 | np[0] = 0; | |
120 | ||
121 | if (n1 == d1) | |
122 | { | |
123 | /* Q should be either 111..111 or 111..110. Need special | |
124 | treatment of this rare case as normal division would | |
125 | give overflow. */ | |
126 | q = ~(mp_limb_t) 0; | |
127 | ||
128 | r = n0 + d1; | |
129 | if (r < d1) /* Carry in the addition? */ | |
130 | { | |
131 | add_ssaaaa (n1, n0, r - d0, np[0], 0, d0); | |
132 | qp[i] = q; | |
133 | continue; | |
134 | } | |
135 | n1 = d0 - (d0 != 0); | |
136 | n0 = -d0; | |
137 | } | |
138 | else | |
139 | { | |
140 | udiv_qrnnd (q, r, n1, n0, d1); | |
141 | umul_ppmm (n1, n0, d0, q); | |
142 | } | |
143 | ||
144 | n2 = np[0]; | |
145 | q_test: | |
146 | if (n1 > r || (n1 == r && n0 > n2)) | |
147 | { | |
148 | /* The estimated Q was too large. */ | |
149 | q--; | |
150 | ||
151 | sub_ddmmss (n1, n0, n1, n0, 0, d0); | |
152 | r += d1; | |
153 | if (r >= d1) /* If not carry, test Q again. */ | |
154 | goto q_test; | |
155 | } | |
156 | ||
157 | qp[i] = q; | |
158 | sub_ddmmss (n1, n0, r, n2, n1, n0); | |
159 | } | |
160 | np[1] = n1; | |
161 | np[0] = n0; | |
162 | } | |
163 | break; | |
164 | ||
165 | default: | |
166 | { | |
167 | mp_size_t i; | |
168 | mp_limb_t dX, d1, n0; | |
169 | ||
170 | np += nsize - dsize; | |
171 | dX = dp[dsize - 1]; | |
172 | d1 = dp[dsize - 2]; | |
173 | n0 = np[dsize - 1]; | |
174 | ||
175 | if (n0 >= dX) | |
176 | { | |
177 | if (n0 > dX || mpn_cmp (np, dp, dsize - 1) >= 0) | |
178 | { | |
179 | mpn_sub_n (np, np, dp, dsize); | |
180 | n0 = np[dsize - 1]; | |
181 | most_significant_q_limb = 1; | |
182 | } | |
183 | } | |
184 | ||
185 | for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) | |
186 | { | |
187 | mp_limb_t q; | |
188 | mp_limb_t n1, n2; | |
189 | mp_limb_t cy_limb; | |
190 | ||
191 | if (i >= qextra_limbs) | |
192 | { | |
193 | np--; | |
194 | n2 = np[dsize]; | |
195 | } | |
196 | else | |
197 | { | |
198 | n2 = np[dsize - 1]; | |
199 | MPN_COPY_DECR (np + 1, np, dsize); | |
200 | np[0] = 0; | |
201 | } | |
202 | ||
203 | if (n0 == dX) | |
204 | /* This might over-estimate q, but it's probably not worth | |
205 | the extra code here to find out. */ | |
206 | q = ~(mp_limb_t) 0; | |
207 | else | |
208 | { | |
209 | mp_limb_t r; | |
210 | ||
211 | udiv_qrnnd (q, r, n0, np[dsize - 1], dX); | |
212 | umul_ppmm (n1, n0, d1, q); | |
213 | ||
214 | while (n1 > r || (n1 == r && n0 > np[dsize - 2])) | |
215 | { | |
216 | q--; | |
217 | r += dX; | |
218 | if (r < dX) /* I.e. "carry in previous addition?" */ | |
219 | break; | |
220 | n1 -= n0 < d1; | |
221 | n0 -= d1; | |
222 | } | |
223 | } | |
224 | ||
225 | /* Possible optimization: We already have (q * n0) and (1 * n1) | |
226 | after the calculation of q. Taking advantage of that, we | |
227 | could make this loop make two iterations less. */ | |
228 | ||
229 | cy_limb = mpn_submul_1 (np, dp, dsize, q); | |
230 | ||
231 | if (n2 != cy_limb) | |
232 | { | |
233 | mpn_add_n (np, np, dp, dsize); | |
234 | q--; | |
235 | } | |
236 | ||
237 | qp[i] = q; | |
238 | n0 = np[dsize - 1]; | |
239 | } | |
240 | } | |
241 | } | |
242 | ||
243 | return most_significant_q_limb; | |
244 | } |