1 /*
2 * Copyright (c) 2008-2020 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 LIBMPDEC_BASEARITH_H_
30 #define LIBMPDEC_BASEARITH_H_
31
32
33 #include "mpdecimal.h"
34 #include "typearith.h"
35
36
37 /* Internal header file: all symbols have local scope in the DSO */
38 MPD_PRAGMA(MPD_HIDE_SYMBOLS_START)
39
40
41 mpd_uint_t _mpd_baseadd(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
42 mpd_size_t m, mpd_size_t n);
43 void _mpd_baseaddto(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n);
44 mpd_uint_t _mpd_shortadd(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v);
45 mpd_uint_t _mpd_shortadd_b(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v,
46 mpd_uint_t b);
47 mpd_uint_t _mpd_baseincr(mpd_uint_t *u, mpd_size_t n);
48 void _mpd_basesub(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
49 mpd_size_t m, mpd_size_t n);
50 void _mpd_basesubfrom(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n);
51 void _mpd_basemul(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
52 mpd_size_t m, mpd_size_t n);
53 void _mpd_shortmul(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
54 mpd_uint_t v);
55 mpd_uint_t _mpd_shortmul_c(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
56 mpd_uint_t v);
57 mpd_uint_t _mpd_shortmul_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
58 mpd_uint_t v, mpd_uint_t b);
59 mpd_uint_t _mpd_shortdiv(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
60 mpd_uint_t v);
61 mpd_uint_t _mpd_shortdiv_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
62 mpd_uint_t v, mpd_uint_t b);
63 int _mpd_basedivmod(mpd_uint_t *q, mpd_uint_t *r, const mpd_uint_t *uconst,
64 const mpd_uint_t *vconst, mpd_size_t nplusm, mpd_size_t n);
65 void _mpd_baseshiftl(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t n,
66 mpd_size_t m, mpd_size_t shift);
67 mpd_uint_t _mpd_baseshiftr(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t slen,
68 mpd_size_t shift);
69
70
71
72 #ifdef CONFIG_64
73 extern const mpd_uint_t mprime_rdx;
74
75 /*
76 * Algorithm from: Division by Invariant Integers using Multiplication,
77 * T. Granlund and P. L. Montgomery, Proceedings of the SIGPLAN '94
78 * Conference on Programming Language Design and Implementation.
79 *
80 * http://gmplib.org/~tege/divcnst-pldi94.pdf
81 *
82 * Variables from the paper and their translations (See section 8):
83 *
84 * N := 64
85 * d := MPD_RADIX
86 * l := 64
87 * m' := floor((2**(64+64) - 1)/MPD_RADIX) - 2**64
88 *
89 * Since N-l == 0:
90 *
91 * dnorm := d
92 * n2 := hi
93 * n10 := lo
94 *
95 * ACL2 proof: mpd-div-words-r-correct
96 */
97 static inline void
98 _mpd_div_words_r(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo)
99 {
100 mpd_uint_t n_adj, h, l, t;
101 mpd_uint_t n1_neg;
102
103 /* n1_neg = if lo >= 2**63 then MPD_UINT_MAX else 0 */
104 n1_neg = (lo & (1ULL<<63)) ? MPD_UINT_MAX : 0;
105 /* n_adj = if lo >= 2**63 then lo+MPD_RADIX else lo */
106 n_adj = lo + (n1_neg & MPD_RADIX);
107
108 /* (h, l) = if lo >= 2**63 then m'*(hi+1) else m'*hi */
109 _mpd_mul_words(&h, &l, mprime_rdx, hi-n1_neg);
110 l = l + n_adj;
111 if (l < n_adj) h++;
112 t = h + hi;
113 /* At this point t == qest, with q == qest or q == qest+1:
114 * 1) 0 <= 2**64*hi + lo - qest*MPD_RADIX < 2*MPD_RADIX
115 */
116
117 /* t = 2**64-1 - qest = 2**64 - (qest+1) */
118 t = MPD_UINT_MAX - t;
119
120 /* (h, l) = 2**64*MPD_RADIX - (qest+1)*MPD_RADIX */
121 _mpd_mul_words(&h, &l, t, MPD_RADIX);
122 l = l + lo;
123 if (l < lo) h++;
124 h += hi;
125 h -= MPD_RADIX;
126 /* (h, l) = 2**64*hi + lo - (qest+1)*MPD_RADIX (mod 2**128)
127 * Case q == qest+1:
128 * a) h == 0, l == r
129 * b) q := h - t == qest+1
130 * c) r := l
131 * Case q == qest:
132 * a) h == MPD_UINT_MAX, l == 2**64-(MPD_RADIX-r)
133 * b) q := h - t == qest
134 * c) r := l + MPD_RADIX = r
135 */
136
137 *q = (h - t);
138 *r = l + (MPD_RADIX & h);
139 }
140 #else
141 static inline void
142 _mpd_div_words_r(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo)
143 {
144 _mpd_div_words(q, r, hi, lo, MPD_RADIX);
145 }
146 #endif
147
148
149 /* Multiply two single base MPD_RADIX words, store result in array w[2]. */
150 static inline void
151 _mpd_singlemul(mpd_uint_t w[2], mpd_uint_t u, mpd_uint_t v)
152 {
153 mpd_uint_t hi, lo;
154
155 _mpd_mul_words(&hi, &lo, u, v);
156 _mpd_div_words_r(&w[1], &w[0], hi, lo);
157 }
158
159 /* Multiply u (len 2) and v (len m, 1 <= m <= 2). */
160 static inline void
161 _mpd_mul_2_le2(mpd_uint_t w[4], mpd_uint_t u[2], mpd_uint_t v[2], mpd_ssize_t m)
162 {
163 mpd_uint_t hi, lo;
164
165 _mpd_mul_words(&hi, &lo, u[0], v[0]);
166 _mpd_div_words_r(&w[1], &w[0], hi, lo);
167
168 _mpd_mul_words(&hi, &lo, u[1], v[0]);
169 lo = w[1] + lo;
170 if (lo < w[1]) hi++;
171 _mpd_div_words_r(&w[2], &w[1], hi, lo);
172 if (m == 1) return;
173
174 _mpd_mul_words(&hi, &lo, u[0], v[1]);
175 lo = w[1] + lo;
176 if (lo < w[1]) hi++;
177 _mpd_div_words_r(&w[3], &w[1], hi, lo);
178
179 _mpd_mul_words(&hi, &lo, u[1], v[1]);
180 lo = w[2] + lo;
181 if (lo < w[2]) hi++;
182 lo = w[3] + lo;
183 if (lo < w[3]) hi++;
184 _mpd_div_words_r(&w[3], &w[2], hi, lo);
185 }
186
187
188 /*
189 * Test if all words from data[len-1] to data[0] are zero. If len is 0, nothing
190 * is tested and the coefficient is regarded as "all zero".
191 */
192 static inline int
193 _mpd_isallzero(const mpd_uint_t *data, mpd_ssize_t len)
194 {
195 while (--len >= 0) {
196 if (data[len] != 0) return 0;
197 }
198 return 1;
199 }
200
201 /*
202 * Test if all full words from data[len-1] to data[0] are MPD_RADIX-1
203 * (all nines). Return true if len == 0.
204 */
205 static inline int
206 _mpd_isallnine(const mpd_uint_t *data, mpd_ssize_t len)
207 {
208 while (--len >= 0) {
209 if (data[len] != MPD_RADIX-1) return 0;
210 }
211 return 1;
212 }
213
214
215 MPD_PRAGMA(MPD_HIDE_SYMBOLS_END) /* restore previous scope rules */
216
217
218 #endif /* LIBMPDEC_BASEARITH_H_ */