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6b628d36 | 1 | /* mpn_mod_1(dividend_ptr, dividend_size, divisor_limb) -- |
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2 | Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB. |
3 | Return the single-limb remainder. | |
4 | There are no constraints on the value of the divisor. | |
5 | ||
d614a753 | 6 | Copyright (C) 1991-2020 Free Software Foundation, Inc. |
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7 | |
8 | This file is part of the GNU MP Library. | |
9 | ||
10 | The GNU MP Library is free software; you can redistribute it and/or modify | |
6d84f89a AJ |
11 | it under the terms of the GNU Lesser General Public License as published by |
12 | the Free Software Foundation; either version 2.1 of the License, or (at your | |
28f540f4 RM |
13 | option) any later version. |
14 | ||
15 | The GNU MP Library is distributed in the hope that it will be useful, but | |
16 | WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY | |
6d84f89a | 17 | or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public |
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18 | License for more details. |
19 | ||
6d84f89a | 20 | You should have received a copy of the GNU Lesser General Public License |
59ba27a6 | 21 | along with the GNU MP Library; see the file COPYING.LIB. If not, see |
5a82c748 | 22 | <https://www.gnu.org/licenses/>. */ |
28f540f4 | 23 | |
9d13fb24 | 24 | #include <gmp.h> |
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25 | #include "gmp-impl.h" |
26 | #include "longlong.h" | |
27 | ||
28 | #ifndef UMUL_TIME | |
29 | #define UMUL_TIME 1 | |
30 | #endif | |
31 | ||
32 | #ifndef UDIV_TIME | |
33 | #define UDIV_TIME UMUL_TIME | |
34 | #endif | |
35 | ||
36 | /* FIXME: We should be using invert_limb (or invert_normalized_limb) | |
37 | here (not udiv_qrnnd). */ | |
38 | ||
b928942e | 39 | mp_limb_t |
6b628d36 | 40 | mpn_mod_1 (mp_srcptr dividend_ptr, mp_size_t dividend_size, |
b928942e | 41 | mp_limb_t divisor_limb) |
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42 | { |
43 | mp_size_t i; | |
b928942e | 44 | mp_limb_t n1, n0, r; |
db1ee0a8 | 45 | mp_limb_t dummy __attribute__ ((unused)); |
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46 | |
47 | /* Botch: Should this be handled at all? Rely on callers? */ | |
48 | if (dividend_size == 0) | |
49 | return 0; | |
50 | ||
51 | /* If multiplication is much faster than division, and the | |
52 | dividend is large, pre-invert the divisor, and use | |
53 | only multiplications in the inner loop. */ | |
54 | ||
55 | /* This test should be read: | |
56 | Does it ever help to use udiv_qrnnd_preinv? | |
57 | && Does what we save compensate for the inversion overhead? */ | |
58 | if (UDIV_TIME > (2 * UMUL_TIME + 6) | |
59 | && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) | |
60 | { | |
61 | int normalization_steps; | |
62 | ||
63 | count_leading_zeros (normalization_steps, divisor_limb); | |
64 | if (normalization_steps != 0) | |
65 | { | |
b928942e | 66 | mp_limb_t divisor_limb_inverted; |
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67 | |
68 | divisor_limb <<= normalization_steps; | |
69 | ||
70 | /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The | |
71 | result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the | |
72 | most significant bit (with weight 2**N) implicit. */ | |
73 | ||
74 | /* Special case for DIVISOR_LIMB == 100...000. */ | |
75 | if (divisor_limb << 1 == 0) | |
b928942e | 76 | divisor_limb_inverted = ~(mp_limb_t) 0; |
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77 | else |
78 | udiv_qrnnd (divisor_limb_inverted, dummy, | |
79 | -divisor_limb, 0, divisor_limb); | |
80 | ||
81 | n1 = dividend_ptr[dividend_size - 1]; | |
82 | r = n1 >> (BITS_PER_MP_LIMB - normalization_steps); | |
83 | ||
84 | /* Possible optimization: | |
85 | if (r == 0 | |
86 | && divisor_limb > ((n1 << normalization_steps) | |
87 | | (dividend_ptr[dividend_size - 2] >> ...))) | |
88 | ...one division less... */ | |
89 | ||
90 | for (i = dividend_size - 2; i >= 0; i--) | |
91 | { | |
92 | n0 = dividend_ptr[i]; | |
93 | udiv_qrnnd_preinv (dummy, r, r, | |
94 | ((n1 << normalization_steps) | |
95 | | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))), | |
96 | divisor_limb, divisor_limb_inverted); | |
97 | n1 = n0; | |
98 | } | |
99 | udiv_qrnnd_preinv (dummy, r, r, | |
100 | n1 << normalization_steps, | |
101 | divisor_limb, divisor_limb_inverted); | |
102 | return r >> normalization_steps; | |
103 | } | |
104 | else | |
105 | { | |
b928942e | 106 | mp_limb_t divisor_limb_inverted; |
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107 | |
108 | /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The | |
109 | result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the | |
110 | most significant bit (with weight 2**N) implicit. */ | |
111 | ||
112 | /* Special case for DIVISOR_LIMB == 100...000. */ | |
113 | if (divisor_limb << 1 == 0) | |
b928942e | 114 | divisor_limb_inverted = ~(mp_limb_t) 0; |
28f540f4 RM |
115 | else |
116 | udiv_qrnnd (divisor_limb_inverted, dummy, | |
117 | -divisor_limb, 0, divisor_limb); | |
118 | ||
119 | i = dividend_size - 1; | |
120 | r = dividend_ptr[i]; | |
121 | ||
122 | if (r >= divisor_limb) | |
123 | r = 0; | |
124 | else | |
125 | i--; | |
126 | ||
127 | for (; i >= 0; i--) | |
128 | { | |
129 | n0 = dividend_ptr[i]; | |
130 | udiv_qrnnd_preinv (dummy, r, r, | |
131 | n0, divisor_limb, divisor_limb_inverted); | |
132 | } | |
133 | return r; | |
134 | } | |
135 | } | |
136 | else | |
137 | { | |
138 | if (UDIV_NEEDS_NORMALIZATION) | |
139 | { | |
140 | int normalization_steps; | |
141 | ||
142 | count_leading_zeros (normalization_steps, divisor_limb); | |
143 | if (normalization_steps != 0) | |
144 | { | |
145 | divisor_limb <<= normalization_steps; | |
146 | ||
147 | n1 = dividend_ptr[dividend_size - 1]; | |
148 | r = n1 >> (BITS_PER_MP_LIMB - normalization_steps); | |
149 | ||
150 | /* Possible optimization: | |
151 | if (r == 0 | |
152 | && divisor_limb > ((n1 << normalization_steps) | |
153 | | (dividend_ptr[dividend_size - 2] >> ...))) | |
154 | ...one division less... */ | |
155 | ||
156 | for (i = dividend_size - 2; i >= 0; i--) | |
157 | { | |
158 | n0 = dividend_ptr[i]; | |
159 | udiv_qrnnd (dummy, r, r, | |
160 | ((n1 << normalization_steps) | |
161 | | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))), | |
162 | divisor_limb); | |
163 | n1 = n0; | |
164 | } | |
165 | udiv_qrnnd (dummy, r, r, | |
166 | n1 << normalization_steps, | |
167 | divisor_limb); | |
168 | return r >> normalization_steps; | |
169 | } | |
170 | } | |
171 | /* No normalization needed, either because udiv_qrnnd doesn't require | |
172 | it, or because DIVISOR_LIMB is already normalized. */ | |
173 | ||
174 | i = dividend_size - 1; | |
175 | r = dividend_ptr[i]; | |
176 | ||
177 | if (r >= divisor_limb) | |
178 | r = 0; | |
179 | else | |
180 | i--; | |
181 | ||
182 | for (; i >= 0; i--) | |
183 | { | |
184 | n0 = dividend_ptr[i]; | |
185 | udiv_qrnnd (dummy, r, r, n0, divisor_limb); | |
186 | } | |
187 | return r; | |
188 | } | |
189 | } |