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b6ab06ce UD |
1 | /* mpn_divmod_1(quot_ptr, dividend_ptr, dividend_size, divisor_limb) -- |
2 | Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB. | |
3 | Write DIVIDEND_SIZE limbs of quotient at QUOT_PTR. | |
4 | Return the single-limb remainder. | |
5 | There are no constraints on the value of the divisor. | |
6 | ||
7 | QUOT_PTR and DIVIDEND_PTR might point to the same limb. | |
8 | ||
6d7e8eda | 9 | Copyright (C) 1991-2023 Free Software Foundation, Inc. |
b6ab06ce UD |
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 the GNU Lesser General Public License as published by | |
15 | the Free Software Foundation; either version 2.1 of the License, or (at your | |
16 | option) any later version. | |
17 | ||
18 | The GNU MP Library is distributed in the hope that it will be useful, but | |
19 | WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY | |
20 | or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public | |
21 | License for more details. | |
22 | ||
23 | You should have received a copy of the GNU Lesser General Public License | |
59ba27a6 | 24 | along with the GNU MP Library; see the file COPYING.LIB. If not, see |
5a82c748 | 25 | <https://www.gnu.org/licenses/>. */ |
b6ab06ce UD |
26 | |
27 | #include <gmp.h> | |
28 | #include "gmp-impl.h" | |
29 | #include "longlong.h" | |
30 | ||
31 | #ifndef UMUL_TIME | |
32 | #define UMUL_TIME 1 | |
33 | #endif | |
34 | ||
35 | #ifndef UDIV_TIME | |
36 | #define UDIV_TIME UMUL_TIME | |
37 | #endif | |
38 | ||
39 | /* FIXME: We should be using invert_limb (or invert_normalized_limb) | |
40 | here (not udiv_qrnnd). */ | |
41 | ||
42 | mp_limb_t | |
b6ab06ce UD |
43 | mpn_divmod_1 (mp_ptr quot_ptr, |
44 | mp_srcptr dividend_ptr, mp_size_t dividend_size, | |
45 | mp_limb_t divisor_limb) | |
b6ab06ce UD |
46 | { |
47 | mp_size_t i; | |
48 | mp_limb_t n1, n0, r; | |
db1ee0a8 | 49 | mp_limb_t dummy __attribute__ ((unused)); |
b6ab06ce UD |
50 | |
51 | /* ??? Should this be handled at all? Rely on callers? */ | |
52 | if (dividend_size == 0) | |
53 | return 0; | |
54 | ||
55 | /* If multiplication is much faster than division, and the | |
56 | dividend is large, pre-invert the divisor, and use | |
57 | only multiplications in the inner loop. */ | |
58 | ||
59 | /* This test should be read: | |
60 | Does it ever help to use udiv_qrnnd_preinv? | |
61 | && Does what we save compensate for the inversion overhead? */ | |
62 | if (UDIV_TIME > (2 * UMUL_TIME + 6) | |
63 | && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) | |
64 | { | |
65 | int normalization_steps; | |
66 | ||
67 | count_leading_zeros (normalization_steps, divisor_limb); | |
68 | if (normalization_steps != 0) | |
69 | { | |
70 | mp_limb_t divisor_limb_inverted; | |
71 | ||
72 | divisor_limb <<= normalization_steps; | |
73 | ||
74 | /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The | |
75 | result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the | |
76 | most significant bit (with weight 2**N) implicit. */ | |
77 | ||
78 | /* Special case for DIVISOR_LIMB == 100...000. */ | |
79 | if (divisor_limb << 1 == 0) | |
80 | divisor_limb_inverted = ~(mp_limb_t) 0; | |
81 | else | |
82 | udiv_qrnnd (divisor_limb_inverted, dummy, | |
83 | -divisor_limb, 0, divisor_limb); | |
84 | ||
85 | n1 = dividend_ptr[dividend_size - 1]; | |
86 | r = n1 >> (BITS_PER_MP_LIMB - normalization_steps); | |
87 | ||
88 | /* Possible optimization: | |
89 | if (r == 0 | |
90 | && divisor_limb > ((n1 << normalization_steps) | |
91 | | (dividend_ptr[dividend_size - 2] >> ...))) | |
92 | ...one division less... */ | |
93 | ||
94 | for (i = dividend_size - 2; i >= 0; i--) | |
95 | { | |
96 | n0 = dividend_ptr[i]; | |
97 | udiv_qrnnd_preinv (quot_ptr[i + 1], r, r, | |
98 | ((n1 << normalization_steps) | |
99 | | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))), | |
100 | divisor_limb, divisor_limb_inverted); | |
101 | n1 = n0; | |
102 | } | |
103 | udiv_qrnnd_preinv (quot_ptr[0], r, r, | |
104 | n1 << normalization_steps, | |
105 | divisor_limb, divisor_limb_inverted); | |
106 | return r >> normalization_steps; | |
107 | } | |
108 | else | |
109 | { | |
110 | mp_limb_t divisor_limb_inverted; | |
111 | ||
112 | /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The | |
113 | result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the | |
114 | most significant bit (with weight 2**N) implicit. */ | |
115 | ||
116 | /* Special case for DIVISOR_LIMB == 100...000. */ | |
117 | if (divisor_limb << 1 == 0) | |
118 | divisor_limb_inverted = ~(mp_limb_t) 0; | |
119 | else | |
120 | udiv_qrnnd (divisor_limb_inverted, dummy, | |
121 | -divisor_limb, 0, divisor_limb); | |
122 | ||
123 | i = dividend_size - 1; | |
124 | r = dividend_ptr[i]; | |
125 | ||
126 | if (r >= divisor_limb) | |
127 | r = 0; | |
128 | else | |
129 | { | |
130 | quot_ptr[i] = 0; | |
131 | i--; | |
132 | } | |
133 | ||
134 | for (; i >= 0; i--) | |
135 | { | |
136 | n0 = dividend_ptr[i]; | |
137 | udiv_qrnnd_preinv (quot_ptr[i], r, r, | |
138 | n0, divisor_limb, divisor_limb_inverted); | |
139 | } | |
140 | return r; | |
141 | } | |
142 | } | |
143 | else | |
144 | { | |
145 | if (UDIV_NEEDS_NORMALIZATION) | |
146 | { | |
147 | int normalization_steps; | |
148 | ||
149 | count_leading_zeros (normalization_steps, divisor_limb); | |
150 | if (normalization_steps != 0) | |
151 | { | |
152 | divisor_limb <<= normalization_steps; | |
153 | ||
154 | n1 = dividend_ptr[dividend_size - 1]; | |
155 | r = n1 >> (BITS_PER_MP_LIMB - normalization_steps); | |
156 | ||
157 | /* Possible optimization: | |
158 | if (r == 0 | |
159 | && divisor_limb > ((n1 << normalization_steps) | |
160 | | (dividend_ptr[dividend_size - 2] >> ...))) | |
161 | ...one division less... */ | |
162 | ||
163 | for (i = dividend_size - 2; i >= 0; i--) | |
164 | { | |
165 | n0 = dividend_ptr[i]; | |
166 | udiv_qrnnd (quot_ptr[i + 1], r, r, | |
167 | ((n1 << normalization_steps) | |
168 | | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))), | |
169 | divisor_limb); | |
170 | n1 = n0; | |
171 | } | |
172 | udiv_qrnnd (quot_ptr[0], r, r, | |
173 | n1 << normalization_steps, | |
174 | divisor_limb); | |
175 | return r >> normalization_steps; | |
176 | } | |
177 | } | |
178 | /* No normalization needed, either because udiv_qrnnd doesn't require | |
179 | it, or because DIVISOR_LIMB is already normalized. */ | |
180 | ||
181 | i = dividend_size - 1; | |
182 | r = dividend_ptr[i]; | |
183 | ||
184 | if (r >= divisor_limb) | |
185 | r = 0; | |
186 | else | |
187 | { | |
188 | quot_ptr[i] = 0; | |
189 | i--; | |
190 | } | |
191 | ||
192 | for (; i >= 0; i--) | |
193 | { | |
194 | n0 = dividend_ptr[i]; | |
195 | udiv_qrnnd (quot_ptr[i], r, r, n0, divisor_limb); | |
196 | } | |
197 | return r; | |
198 | } | |
199 | } |