1 /*
2 * Copyright (c) 2008-2016 Stefan Krah. All rights reserved.
3 *
4 * Redistribution and use in source and binary forms, with or without
5 * modification, are permitted provided that the following conditions
6 * are met:
7 *
8 * 1. Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
10 *
11 * 2. Redistributions in binary form must reproduce the above copyright
12 * notice, this list of conditions and the following disclaimer in the
13 * documentation and/or other materials provided with the distribution.
14 *
15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
16 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
17 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
18 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
19 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
20 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
21 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
22 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
23 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
24 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
25 * SUCH DAMAGE.
26 */
27
28
29 #ifndef BASEARITH_H
30 #define BASEARITH_H
31
32
33 #include "mpdecimal.h"
34 #include <stdio.h>
35 #include "typearith.h"
36
37
38 /* Internal header file: all symbols have local scope in the DSO */
39 MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
40
41
42 mpd_uint_t _mpd_baseadd(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
43 mpd_size_t m, mpd_size_t n);
44 void _mpd_baseaddto(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n);
45 mpd_uint_t _mpd_shortadd(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v);
46 mpd_uint_t _mpd_shortadd_b(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v,
47 mpd_uint_t b);
48 mpd_uint_t _mpd_baseincr(mpd_uint_t *u, mpd_size_t n);
49 void _mpd_basesub(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
50 mpd_size_t m, mpd_size_t n);
51 void _mpd_basesubfrom(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n);
52 void _mpd_basemul(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
53 mpd_size_t m, mpd_size_t n);
54 void _mpd_shortmul(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
55 mpd_uint_t v);
56 mpd_uint_t _mpd_shortmul_c(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
57 mpd_uint_t v);
58 mpd_uint_t _mpd_shortmul_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
59 mpd_uint_t v, mpd_uint_t b);
60 mpd_uint_t _mpd_shortdiv(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
61 mpd_uint_t v);
62 mpd_uint_t _mpd_shortdiv_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
63 mpd_uint_t v, mpd_uint_t b);
64 int _mpd_basedivmod(mpd_uint_t *q, mpd_uint_t *r, const mpd_uint_t *uconst,
65 const mpd_uint_t *vconst, mpd_size_t nplusm, mpd_size_t n);
66 void _mpd_baseshiftl(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t n,
67 mpd_size_t m, mpd_size_t shift);
68 mpd_uint_t _mpd_baseshiftr(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t slen,
69 mpd_size_t shift);
70
71
72
73 #ifdef CONFIG_64
74 extern const mpd_uint_t mprime_rdx;
75
76 /*
77 * Algorithm from: Division by Invariant Integers using Multiplication,
78 * T. Granlund and P. L. Montgomery, Proceedings of the SIGPLAN '94
79 * Conference on Programming Language Design and Implementation.
80 *
81 * http://gmplib.org/~tege/divcnst-pldi94.pdf
82 *
83 * Variables from the paper and their translations (See section 8):
84 *
85 * N := 64
86 * d := MPD_RADIX
87 * l := 64
88 * m' := floor((2**(64+64) - 1)/MPD_RADIX) - 2**64
89 *
90 * Since N-l == 0:
91 *
92 * dnorm := d
93 * n2 := hi
94 * n10 := lo
95 *
96 * ACL2 proof: mpd-div-words-r-correct
97 */
98 static inline void
_mpd_div_words_r(mpd_uint_t * q,mpd_uint_t * r,mpd_uint_t hi,mpd_uint_t lo)99 _mpd_div_words_r(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo)
100 {
101 mpd_uint_t n_adj, h, l, t;
102 mpd_uint_t n1_neg;
103
104 /* n1_neg = if lo >= 2**63 then MPD_UINT_MAX else 0 */
105 n1_neg = (lo & (1ULL<<63)) ? MPD_UINT_MAX : 0;
106 /* n_adj = if lo >= 2**63 then lo+MPD_RADIX else lo */
107 n_adj = lo + (n1_neg & MPD_RADIX);
108
109 /* (h, l) = if lo >= 2**63 then m'*(hi+1) else m'*hi */
110 _mpd_mul_words(&h, &l, mprime_rdx, hi-n1_neg);
111 l = l + n_adj;
112 if (l < n_adj) h++;
113 t = h + hi;
114 /* At this point t == qest, with q == qest or q == qest+1:
115 * 1) 0 <= 2**64*hi + lo - qest*MPD_RADIX < 2*MPD_RADIX
116 */
117
118 /* t = 2**64-1 - qest = 2**64 - (qest+1) */
119 t = MPD_UINT_MAX - t;
120
121 /* (h, l) = 2**64*MPD_RADIX - (qest+1)*MPD_RADIX */
122 _mpd_mul_words(&h, &l, t, MPD_RADIX);
123 l = l + lo;
124 if (l < lo) h++;
125 h += hi;
126 h -= MPD_RADIX;
127 /* (h, l) = 2**64*hi + lo - (qest+1)*MPD_RADIX (mod 2**128)
128 * Case q == qest+1:
129 * a) h == 0, l == r
130 * b) q := h - t == qest+1
131 * c) r := l
132 * Case q == qest:
133 * a) h == MPD_UINT_MAX, l == 2**64-(MPD_RADIX-r)
134 * b) q := h - t == qest
135 * c) r := l + MPD_RADIX = r
136 */
137
138 *q = (h - t);
139 *r = l + (MPD_RADIX & h);
140 }
141 #else
142 static inline void
_mpd_div_words_r(mpd_uint_t * q,mpd_uint_t * r,mpd_uint_t hi,mpd_uint_t lo)143 _mpd_div_words_r(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo)
144 {
145 _mpd_div_words(q, r, hi, lo, MPD_RADIX);
146 }
147 #endif
148
149
150 /* Multiply two single base MPD_RADIX words, store result in array w[2]. */
151 static inline void
_mpd_singlemul(mpd_uint_t w[2],mpd_uint_t u,mpd_uint_t v)152 _mpd_singlemul(mpd_uint_t w[2], mpd_uint_t u, mpd_uint_t v)
153 {
154 mpd_uint_t hi, lo;
155
156 _mpd_mul_words(&hi, &lo, u, v);
157 _mpd_div_words_r(&w[1], &w[0], hi, lo);
158 }
159
160 /* Multiply u (len 2) and v (len m, 1 <= m <= 2). */
161 static inline void
_mpd_mul_2_le2(mpd_uint_t w[4],mpd_uint_t u[2],mpd_uint_t v[2],mpd_ssize_t m)162 _mpd_mul_2_le2(mpd_uint_t w[4], mpd_uint_t u[2], mpd_uint_t v[2], mpd_ssize_t m)
163 {
164 mpd_uint_t hi, lo;
165
166 _mpd_mul_words(&hi, &lo, u[0], v[0]);
167 _mpd_div_words_r(&w[1], &w[0], hi, lo);
168
169 _mpd_mul_words(&hi, &lo, u[1], v[0]);
170 lo = w[1] + lo;
171 if (lo < w[1]) hi++;
172 _mpd_div_words_r(&w[2], &w[1], hi, lo);
173 if (m == 1) return;
174
175 _mpd_mul_words(&hi, &lo, u[0], v[1]);
176 lo = w[1] + lo;
177 if (lo < w[1]) hi++;
178 _mpd_div_words_r(&w[3], &w[1], hi, lo);
179
180 _mpd_mul_words(&hi, &lo, u[1], v[1]);
181 lo = w[2] + lo;
182 if (lo < w[2]) hi++;
183 lo = w[3] + lo;
184 if (lo < w[3]) hi++;
185 _mpd_div_words_r(&w[3], &w[2], hi, lo);
186 }
187
188
189 /*
190 * Test if all words from data[len-1] to data[0] are zero. If len is 0, nothing
191 * is tested and the coefficient is regarded as "all zero".
192 */
193 static inline int
_mpd_isallzero(const mpd_uint_t * data,mpd_ssize_t len)194 _mpd_isallzero(const mpd_uint_t *data, mpd_ssize_t len)
195 {
196 while (--len >= 0) {
197 if (data[len] != 0) return 0;
198 }
199 return 1;
200 }
201
202 /*
203 * Test if all full words from data[len-1] to data[0] are MPD_RADIX-1
204 * (all nines). Return true if len == 0.
205 */
206 static inline int
_mpd_isallnine(const mpd_uint_t * data,mpd_ssize_t len)207 _mpd_isallnine(const mpd_uint_t *data, mpd_ssize_t len)
208 {
209 while (--len >= 0) {
210 if (data[len] != MPD_RADIX-1) return 0;
211 }
212 return 1;
213 }
214
215
216 MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
217
218
219 #endif /* BASEARITH_H */
220
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