1 /* mpn_mod_1(dividend_ptr, dividend_size, divisor_limb) --
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
6 Copyright 1991, 1993, 1994, 1999, 2000, 2002, 2007-2009, 2012, 2020
7 Free Software Foundation, Inc.
8
9 This file is part of the GNU MP Library.
10
11 The GNU MP Library is free software; you can redistribute it and/or modify
12 it under the terms of either:
13
14 * the GNU Lesser General Public License as published by the Free
15 Software Foundation; either version 3 of the License, or (at your
16 option) any later version.
17
18 or
19
20 * the GNU General Public License as published by the Free Software
21 Foundation; either version 2 of the License, or (at your option) any
22 later version.
23
24 or both in parallel, as here.
25
26 The GNU MP Library is distributed in the hope that it will be useful, but
27 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
28 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
29 for more details.
30
31 You should have received copies of the GNU General Public License and the
32 GNU Lesser General Public License along with the GNU MP Library. If not,
33 see https://www.gnu.org/licenses/. */
34
35 #include "gmp-impl.h"
36 #include "longlong.h"
37
38
39 /* The size where udiv_qrnnd_preinv should be used rather than udiv_qrnnd,
40 meaning the quotient size where that should happen, the quotient size
41 being how many udiv divisions will be done.
42
43 The default is to use preinv always, CPUs where this doesn't suit have
44 tuned thresholds. Note in particular that preinv should certainly be
45 used if that's the only division available (USE_PREINV_ALWAYS). */
46
47 #ifndef MOD_1_NORM_THRESHOLD
48 #define MOD_1_NORM_THRESHOLD 0
49 #endif
50
51 #ifndef MOD_1_UNNORM_THRESHOLD
52 #define MOD_1_UNNORM_THRESHOLD 0
53 #endif
54
55 #ifndef MOD_1U_TO_MOD_1_1_THRESHOLD
56 #define MOD_1U_TO_MOD_1_1_THRESHOLD MP_SIZE_T_MAX /* default is not to use mpn_mod_1s */
57 #endif
58
59 #ifndef MOD_1N_TO_MOD_1_1_THRESHOLD
60 #define MOD_1N_TO_MOD_1_1_THRESHOLD MP_SIZE_T_MAX /* default is not to use mpn_mod_1s */
61 #endif
62
63 #ifndef MOD_1_1_TO_MOD_1_2_THRESHOLD
64 #define MOD_1_1_TO_MOD_1_2_THRESHOLD 10
65 #endif
66
67 #ifndef MOD_1_2_TO_MOD_1_4_THRESHOLD
68 #define MOD_1_2_TO_MOD_1_4_THRESHOLD 20
69 #endif
70
71 #if TUNE_PROGRAM_BUILD && !HAVE_NATIVE_mpn_mod_1_1p
72 /* Duplicates declarations in tune/speed.h */
73 mp_limb_t mpn_mod_1_1p_1 (mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t [4]);
74 mp_limb_t mpn_mod_1_1p_2 (mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t [4]);
75
76 void mpn_mod_1_1p_cps_1 (mp_limb_t [4], mp_limb_t);
77 void mpn_mod_1_1p_cps_2 (mp_limb_t [4], mp_limb_t);
78
79 #undef mpn_mod_1_1p
80 #define mpn_mod_1_1p(ap, n, b, pre) \
81 (mod_1_1p_method == 1 ? mpn_mod_1_1p_1 (ap, n, b, pre) \
82 : (mod_1_1p_method == 2 ? mpn_mod_1_1p_2 (ap, n, b, pre) \
83 : __gmpn_mod_1_1p (ap, n, b, pre)))
84
85 #undef mpn_mod_1_1p_cps
86 #define mpn_mod_1_1p_cps(pre, b) \
87 (mod_1_1p_method == 1 ? mpn_mod_1_1p_cps_1 (pre, b) \
88 : (mod_1_1p_method == 2 ? mpn_mod_1_1p_cps_2 (pre, b) \
89 : __gmpn_mod_1_1p_cps (pre, b)))
90 #endif /* TUNE_PROGRAM_BUILD && !HAVE_NATIVE_mpn_mod_1_1p */
91
92
93 /* The comments in mpn/generic/divrem_1.c apply here too.
94
95 As noted in the algorithms section of the manual, the shifts in the loop
96 for the unnorm case can be avoided by calculating r = a%(d*2^n), followed
97 by a final (r*2^n)%(d*2^n). In fact if it happens that a%(d*2^n) can
98 skip a division where (a*2^n)%(d*2^n) can't then there's the same number
99 of divide steps, though how often that happens depends on the assumed
100 distributions of dividend and divisor. In any case this idea is left to
101 CPU specific implementations to consider. */
102
103 static mp_limb_t
104 mpn_mod_1_unnorm (mp_srcptr up, mp_size_t un, mp_limb_t d)
105 {
106 mp_size_t i;
107 mp_limb_t n1, n0, r;
108 mp_limb_t dummy;
109 int cnt;
110
111 ASSERT (un > 0);
112 ASSERT (d != 0);
113
114 /* Skip a division if high < divisor. Having the test here before
115 normalizing will still skip as often as possible. */
116 r = up[un - 1];
117 if (r < d)
118 {
119 if (--un == 0)
120 return r;
121 }
122 else
123 r = 0;
124
125 d <<= GMP_NAIL_BITS;
126
127 /* If udiv_qrnnd doesn't need a normalized divisor, can use the simple
128 code above. */
129 if (! UDIV_NEEDS_NORMALIZATION
130 && BELOW_THRESHOLD (un, MOD_1_UNNORM_THRESHOLD))
131 {
132 for (i = un - 1; i >= 0; i--)
133 {
134 n0 = up[i] << GMP_NAIL_BITS;
135 udiv_qrnnd (dummy, r, r, n0, d);
136 r >>= GMP_NAIL_BITS;
137 }
138 return r;
139 }
140
141 count_leading_zeros (cnt, d);
142 d <<= cnt;
143
144 n1 = up[un - 1] << GMP_NAIL_BITS;
145 r = (r << cnt) | (n1 >> (GMP_LIMB_BITS - cnt));
146
147 if (UDIV_NEEDS_NORMALIZATION
148 && BELOW_THRESHOLD (un, MOD_1_UNNORM_THRESHOLD))
149 {
150 mp_limb_t nshift;
151 for (i = un - 2; i >= 0; i--)
152 {
153 n0 = up[i] << GMP_NAIL_BITS;
154 nshift = (n1 << cnt) | (n0 >> (GMP_NUMB_BITS - cnt));
155 udiv_qrnnd (dummy, r, r, nshift, d);
156 r >>= GMP_NAIL_BITS;
157 n1 = n0;
158 }
159 udiv_qrnnd (dummy, r, r, n1 << cnt, d);
160 r >>= GMP_NAIL_BITS;
161 return r >> cnt;
162 }
163 else
164 {
165 mp_limb_t inv, nshift;
166 invert_limb (inv, d);
167
168 for (i = un - 2; i >= 0; i--)
169 {
170 n0 = up[i] << GMP_NAIL_BITS;
171 nshift = (n1 << cnt) | (n0 >> (GMP_NUMB_BITS - cnt));
172 udiv_rnnd_preinv (r, r, nshift, d, inv);
173 r >>= GMP_NAIL_BITS;
174 n1 = n0;
175 }
176 udiv_rnnd_preinv (r, r, n1 << cnt, d, inv);
177 r >>= GMP_NAIL_BITS;
178 return r >> cnt;
179 }
180 }
181
182 static mp_limb_t
183 mpn_mod_1_norm (mp_srcptr up, mp_size_t un, mp_limb_t d)
184 {
185 mp_size_t i;
186 mp_limb_t n0, r;
187 mp_limb_t dummy;
188
189 ASSERT (un > 0);
190
191 d <<= GMP_NAIL_BITS;
192
193 ASSERT (d & GMP_LIMB_HIGHBIT);
194
195 /* High limb is initial remainder, possibly with one subtract of
196 d to get r<d. */
197 r = up[un - 1] << GMP_NAIL_BITS;
198 if (r >= d)
199 r -= d;
200 r >>= GMP_NAIL_BITS;
201 un--;
202 if (un == 0)
203 return r;
204
205 if (BELOW_THRESHOLD (un, MOD_1_NORM_THRESHOLD))
206 {
207 for (i = un - 1; i >= 0; i--)
208 {
209 n0 = up[i] << GMP_NAIL_BITS;
210 udiv_qrnnd (dummy, r, r, n0, d);
211 r >>= GMP_NAIL_BITS;
212 }
213 return r;
214 }
215 else
216 {
217 mp_limb_t inv;
218 invert_limb (inv, d);
219 for (i = un - 1; i >= 0; i--)
220 {
221 n0 = up[i] << GMP_NAIL_BITS;
222 udiv_rnnd_preinv (r, r, n0, d, inv);
223 r >>= GMP_NAIL_BITS;
224 }
225 return r;
226 }
227 }
228
229 mp_limb_t
230 mpn_mod_1 (mp_srcptr ap, mp_size_t n, mp_limb_t b)
231 {
232 ASSERT (n >= 0);
233 ASSERT (b != 0);
234
235 /* Should this be handled at all? Rely on callers? Note un==0 is currently
236 required by mpz/fdiv_r_ui.c and possibly other places. */
237 if (n == 0)
238 return 0;
239
240 if (UNLIKELY ((b & GMP_NUMB_HIGHBIT) != 0))
241 {
242 if (BELOW_THRESHOLD (n, MOD_1N_TO_MOD_1_1_THRESHOLD))
243 {
244 return mpn_mod_1_norm (ap, n, b);
245 }
246 else
247 {
248 mp_limb_t pre[4];
249 mpn_mod_1_1p_cps (pre, b);
250 return mpn_mod_1_1p (ap, n, b, pre);
251 }
252 }
253 else
254 {
255 if (BELOW_THRESHOLD (n, MOD_1U_TO_MOD_1_1_THRESHOLD))
256 {
257 return mpn_mod_1_unnorm (ap, n, b);
258 }
259 else if (BELOW_THRESHOLD (n, MOD_1_1_TO_MOD_1_2_THRESHOLD))
260 {
261 mp_limb_t pre[4];
262 mpn_mod_1_1p_cps (pre, b);
263 return mpn_mod_1_1p (ap, n, b << pre[1], pre);
264 }
265 else if (BELOW_THRESHOLD (n, MOD_1_2_TO_MOD_1_4_THRESHOLD) || UNLIKELY (b > GMP_NUMB_MASK / 4))
266 {
267 mp_limb_t pre[5];
268 mpn_mod_1s_2p_cps (pre, b);
269 return mpn_mod_1s_2p (ap, n, b << pre[1], pre);
270 }
271 else
272 {
273 mp_limb_t pre[7];
274 mpn_mod_1s_4p_cps (pre, b);
275 return mpn_mod_1s_4p (ap, n, b << pre[1], pre);
276 }
277 }
278 }