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6b628d36 | 1 | /* mpn_divmod_1(quot_ptr, dividend_ptr, dividend_size, divisor_limb) -- |
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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 | ||
6b628d36 | 9 | Copyright (C) 1991, 1993, 1994, 1996 Free Software Foundation, Inc. |
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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 | |
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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 | |
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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 | |
6d84f89a | 20 | or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public |
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21 | License for more details. |
22 | ||
6d84f89a | 23 | You should have received a copy of the GNU Lesser General Public License |
28f540f4 | 24 | along with the GNU MP Library; see the file COPYING.LIB. If not, write to |
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25 | the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
26 | MA 02111-1307, USA. */ | |
28f540f4 | 27 | |
a334319f | 28 | #include "gmp.h" |
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29 | #include "gmp-impl.h" |
30 | #include "longlong.h" | |
31 | ||
32 | #ifndef UMUL_TIME | |
33 | #define UMUL_TIME 1 | |
34 | #endif | |
35 | ||
36 | #ifndef UDIV_TIME | |
37 | #define UDIV_TIME UMUL_TIME | |
38 | #endif | |
39 | ||
40 | /* FIXME: We should be using invert_limb (or invert_normalized_limb) | |
41 | here (not udiv_qrnnd). */ | |
42 | ||
b928942e | 43 | mp_limb_t |
28f540f4 | 44 | #if __STDC__ |
6b628d36 | 45 | mpn_divmod_1 (mp_ptr quot_ptr, |
28f540f4 | 46 | mp_srcptr dividend_ptr, mp_size_t dividend_size, |
b928942e | 47 | mp_limb_t divisor_limb) |
28f540f4 | 48 | #else |
6b628d36 | 49 | mpn_divmod_1 (quot_ptr, dividend_ptr, dividend_size, divisor_limb) |
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50 | mp_ptr quot_ptr; |
51 | mp_srcptr dividend_ptr; | |
52 | mp_size_t dividend_size; | |
b928942e | 53 | mp_limb_t divisor_limb; |
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54 | #endif |
55 | { | |
56 | mp_size_t i; | |
b928942e | 57 | mp_limb_t n1, n0, r; |
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58 | int dummy; |
59 | ||
60 | /* ??? Should this be handled at all? Rely on callers? */ | |
61 | if (dividend_size == 0) | |
62 | return 0; | |
63 | ||
64 | /* If multiplication is much faster than division, and the | |
65 | dividend is large, pre-invert the divisor, and use | |
66 | only multiplications in the inner loop. */ | |
67 | ||
68 | /* This test should be read: | |
69 | Does it ever help to use udiv_qrnnd_preinv? | |
70 | && Does what we save compensate for the inversion overhead? */ | |
71 | if (UDIV_TIME > (2 * UMUL_TIME + 6) | |
72 | && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) | |
73 | { | |
74 | int normalization_steps; | |
75 | ||
76 | count_leading_zeros (normalization_steps, divisor_limb); | |
77 | if (normalization_steps != 0) | |
78 | { | |
b928942e | 79 | mp_limb_t divisor_limb_inverted; |
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80 | |
81 | divisor_limb <<= normalization_steps; | |
82 | ||
83 | /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The | |
84 | result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the | |
85 | most significant bit (with weight 2**N) implicit. */ | |
86 | ||
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87 | /* Special case for DIVISOR_LIMB == 100...000. */ |
88 | if (divisor_limb << 1 == 0) | |
b928942e | 89 | divisor_limb_inverted = ~(mp_limb_t) 0; |
28f540f4 | 90 | else |
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91 | udiv_qrnnd (divisor_limb_inverted, dummy, |
92 | -divisor_limb, 0, divisor_limb); | |
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93 | |
94 | n1 = dividend_ptr[dividend_size - 1]; | |
95 | r = n1 >> (BITS_PER_MP_LIMB - normalization_steps); | |
96 | ||
97 | /* Possible optimization: | |
98 | if (r == 0 | |
99 | && divisor_limb > ((n1 << normalization_steps) | |
100 | | (dividend_ptr[dividend_size - 2] >> ...))) | |
101 | ...one division less... */ | |
102 | ||
103 | for (i = dividend_size - 2; i >= 0; i--) | |
104 | { | |
105 | n0 = dividend_ptr[i]; | |
106 | udiv_qrnnd_preinv (quot_ptr[i + 1], r, r, | |
107 | ((n1 << normalization_steps) | |
108 | | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))), | |
109 | divisor_limb, divisor_limb_inverted); | |
110 | n1 = n0; | |
111 | } | |
112 | udiv_qrnnd_preinv (quot_ptr[0], r, r, | |
113 | n1 << normalization_steps, | |
114 | divisor_limb, divisor_limb_inverted); | |
115 | return r >> normalization_steps; | |
116 | } | |
117 | else | |
118 | { | |
b928942e | 119 | mp_limb_t divisor_limb_inverted; |
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120 | |
121 | /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The | |
122 | result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the | |
123 | most significant bit (with weight 2**N) implicit. */ | |
124 | ||
125 | /* Special case for DIVISOR_LIMB == 100...000. */ | |
126 | if (divisor_limb << 1 == 0) | |
b928942e | 127 | divisor_limb_inverted = ~(mp_limb_t) 0; |
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128 | else |
129 | udiv_qrnnd (divisor_limb_inverted, dummy, | |
130 | -divisor_limb, 0, divisor_limb); | |
131 | ||
132 | i = dividend_size - 1; | |
133 | r = dividend_ptr[i]; | |
134 | ||
135 | if (r >= divisor_limb) | |
136 | r = 0; | |
137 | else | |
138 | { | |
139 | quot_ptr[i] = 0; | |
140 | i--; | |
141 | } | |
142 | ||
143 | for (; i >= 0; i--) | |
144 | { | |
145 | n0 = dividend_ptr[i]; | |
146 | udiv_qrnnd_preinv (quot_ptr[i], r, r, | |
147 | n0, divisor_limb, divisor_limb_inverted); | |
148 | } | |
149 | return r; | |
150 | } | |
151 | } | |
152 | else | |
153 | { | |
154 | if (UDIV_NEEDS_NORMALIZATION) | |
155 | { | |
156 | int normalization_steps; | |
157 | ||
158 | count_leading_zeros (normalization_steps, divisor_limb); | |
159 | if (normalization_steps != 0) | |
160 | { | |
161 | divisor_limb <<= normalization_steps; | |
162 | ||
163 | n1 = dividend_ptr[dividend_size - 1]; | |
164 | r = n1 >> (BITS_PER_MP_LIMB - normalization_steps); | |
165 | ||
166 | /* Possible optimization: | |
167 | if (r == 0 | |
168 | && divisor_limb > ((n1 << normalization_steps) | |
169 | | (dividend_ptr[dividend_size - 2] >> ...))) | |
170 | ...one division less... */ | |
171 | ||
172 | for (i = dividend_size - 2; i >= 0; i--) | |
173 | { | |
174 | n0 = dividend_ptr[i]; | |
175 | udiv_qrnnd (quot_ptr[i + 1], r, r, | |
176 | ((n1 << normalization_steps) | |
177 | | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))), | |
178 | divisor_limb); | |
179 | n1 = n0; | |
180 | } | |
181 | udiv_qrnnd (quot_ptr[0], r, r, | |
182 | n1 << normalization_steps, | |
183 | divisor_limb); | |
184 | return r >> normalization_steps; | |
185 | } | |
186 | } | |
187 | /* No normalization needed, either because udiv_qrnnd doesn't require | |
188 | it, or because DIVISOR_LIMB is already normalized. */ | |
189 | ||
190 | i = dividend_size - 1; | |
191 | r = dividend_ptr[i]; | |
192 | ||
193 | if (r >= divisor_limb) | |
194 | r = 0; | |
195 | else | |
196 | { | |
197 | quot_ptr[i] = 0; | |
198 | i--; | |
199 | } | |
200 | ||
201 | for (; i >= 0; i--) | |
202 | { | |
203 | n0 = dividend_ptr[i]; | |
204 | udiv_qrnnd (quot_ptr[i], r, r, n0, divisor_limb); | |
205 | } | |
206 | return r; | |
207 | } | |
208 | } |