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1 | /* -*-c-*- |
2 | * | |
3 | * Utilities for quick field arithmetic | |
4 | * | |
5 | * (c) 2017 Straylight/Edgeware | |
6 | */ | |
7 | ||
8 | /*----- Licensing notice --------------------------------------------------* | |
9 | * | |
10 | * This file is part of Catacomb. | |
11 | * | |
12 | * Catacomb is free software; you can redistribute it and/or modify | |
13 | * it under the terms of the GNU Library General Public License as | |
14 | * published by the Free Software Foundation; either version 2 of the | |
15 | * License, or (at your option) any later version. | |
16 | * | |
17 | * Catacomb is distributed in the hope that it will be useful, | |
18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
20 | * GNU Library General Public License for more details. | |
21 | * | |
22 | * You should have received a copy of the GNU Library General Public | |
23 | * License along with Catacomb; if not, write to the Free | |
24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, | |
25 | * MA 02111-1307, USA. | |
26 | */ | |
27 | ||
28 | #ifndef CATACOMB_QFARITH_H | |
29 | #define CATACOMB_QFARITH_H | |
30 | ||
31 | #ifdef __cplusplus | |
32 | extern "C" { | |
33 | #endif | |
34 | ||
35 | /*----- Header files ------------------------------------------------------*/ | |
36 | ||
37 | #include <limits.h> | |
38 | ||
39 | #include <mLib/bits.h> | |
40 | ||
41 | /*----- Signed integer types ----------------------------------------------*/ | |
42 | ||
43 | /* See if we can find a suitable 64-bit or wider type. Don't bother if we | |
44 | * don't have a corresponding unsigned type, because we really need both. | |
45 | */ | |
46 | #ifdef HAVE_UINT64 | |
47 | # if INT_MAX >> 31 == 0xffffffff | |
48 | # define HAVE_INT64 | |
49 | typedef int int64; | |
50 | # elif LONG_MAX >> 31 == 0xffffffff | |
51 | # define HAVE_INT64 | |
52 | typedef long int64; | |
53 | # elif defined(LLONG_MAX) | |
54 | # define HAVE_INT64 | |
55 | MLIB_BITS_EXTENSION typedef long long int64; | |
56 | # endif | |
57 | #endif | |
58 | ||
59 | /* Choose suitable 32- and 16-bit types. */ | |
60 | #if INT_MAX >= 0x7fffffff | |
61 | typedef int int32; | |
62 | #else | |
63 | typedef long int32; | |
64 | #endif | |
65 | ||
66 | typedef short int16; | |
67 | ||
68 | /*----- General bit-hacking utilities -------------------------------------*/ | |
69 | ||
70 | /* Individual bits, and masks for low bits. */ | |
71 | #define BIT(n) (1ul << (n)) | |
72 | #define MASK(n) (BIT(n) - 1) | |
73 | ||
74 | /* Arithmetic right shift. If X is a value of type TY, and N is a | |
75 | * nonnegative integer, then return the value of X shifted right by N bits; | |
76 | * alternatively, this is floor(X/2^N). | |
77 | * | |
78 | * GCC manages to compile this into a simple shift operation if one is | |
79 | * available, but it's correct for all C targets. | |
80 | */ | |
81 | #define ASR(ty, x, n) (((x) - (ty)((u##ty)(x)&MASK(n)))/(ty)BIT(n)) | |
82 | ||
83 | /*----- Constant-time utilities -------------------------------------------*/ | |
84 | ||
85 | /* The following have better implementations on a two's complement target. */ | |
86 | #ifdef NEG_TWOC | |
87 | ||
88 | /* If we have two's complement arithmetic then masks are signed; this | |
89 | * avoids a switch to unsigned representation, with the consequent problem | |
90 | * of overflow when we convert back. | |
91 | */ | |
92 | typedef int32 mask32; | |
93 | ||
94 | /* Convert an unsigned mask M into a `mask32'. This is a hairy-looking | |
95 | * no-op on many targets, but, given that we have two's complement | |
96 | * integers, it is free of arithmetic overflow. | |
97 | */ | |
98 | # define FIX_MASK32(m) \ | |
99 | ((mask32)((m)&0x7fffffffu) + (-(mask32)0x7fffffff - 1)*(((m) >> 31)&1u)) | |
100 | ||
101 | /* If Z is zero and M has its low 32 bits set, then copy (at least) the low | |
102 | * 32 bits of X to Z; if M is zero, do nothing. Otherwise, scramble Z | |
103 | * unhelpfully. | |
104 | */ | |
105 | # define CONDPICK(z, x, m) do { (z) |= (x)&(m); } while (0) | |
106 | ||
107 | /* If M has its low 32 bits set, then return (at least) the low 32 bits of | |
108 | * X in Z; if M is zero, then return (at least) the low 32 bits of Y in Z. | |
109 | * Otherwise, return an unhelful result. | |
110 | */ | |
111 | # define PICK2(x, y, m) (((x)&(m)) | ((y)&~(m))) | |
112 | ||
113 | /* If M has its low 32 bits set then swap (at least) the low 32 bits of X | |
114 | * and Y; if M is zero, then do nothing. Otherwise, scramble X and Y | |
115 | * unhelpfully. | |
116 | */ | |
117 | # define CONDSWAP(x, y, m) \ | |
118 | do { mask32 t_ = ((x) ^ (y))&(m); (x) ^= t_; (y) ^= t_; } while (0) | |
119 | #else | |
120 | ||
121 | /* We don't have two's complement arithmetic. We can't use bithacking at | |
122 | * all: if we try to hack on the bits of signed numbers we'll come unstuck | |
123 | * when we hit the other representation of zero; and if we switch to | |
124 | * unsigned arithmetic then we'll have overflow when we try to convert a | |
125 | * negative number back. So fall back to simple arithmetic. | |
126 | */ | |
127 | typedef uint32 mask32; | |
128 | ||
129 | /* Convert an unsigned mask M into a `mask32'. Our masks are unsigned, so | |
130 | * this does nothing. | |
131 | */ | |
132 | # define FIX_MASK32(m) ((mask32)(m)) | |
133 | ||
134 | /* If Z is zero and M has its low 32 bits set, then copy (at least) the low | |
135 | * 32 bits of X to Z; if M is zero, do nothing. Otherwise, scramble Z | |
136 | * unhelpfully. | |
137 | */ | |
138 | # define CONDPICK(z, x, m) \ | |
139 | do { (z) += (x)*(int)((unsigned)(m)&1u); } while (0) | |
140 | ||
141 | /* If M has its low 32 bits set, then return (at least) the low 32 bits of | |
142 | * X in Z; if M is zero, then return (at least) the low 32 bits of Y in Z. | |
143 | * Otherwise, return an unhelful result. | |
144 | */ | |
145 | # define PICK2(x, y, m) \ | |
146 | ((x)*(int)((unsigned)(m)&1u) + (y)*(int)(1 - ((unsigned)(m)&1u))) | |
147 | ||
148 | /* If M has its low 32 bits set then swap (at least) the low 32 bits of X | |
149 | * and Y; if M is zero, then do nothing. Otherwise, scramble X and Y | |
150 | * unhelpfully. | |
151 | */ | |
152 | # define CONDSWAP(x, y, m) do { \ | |
153 | int32 x_ = PICK2((y), (x), (m)), y_ = PICK2((x), (y), (m)); \ | |
154 | (x) = x_; (y) = y_; \ | |
155 | } while (0) | |
156 | #endif | |
157 | ||
158 | /* Return zero if bit 31 of X is clear, or a mask with (at least) the low 32 | |
159 | * bits set if bit 31 of X is set. | |
160 | */ | |
161 | #define SIGN(x) (-(mask32)(((uint32)(x) >> 31)&1)) | |
162 | ||
163 | /* Return zero if X is zero, or a mask with (at least) the low 32 bits set if | |
164 | * X is nonzero. | |
165 | */ | |
166 | #define NONZEROP(x) SIGN((U32(x) >> 1) - U32(x)) | |
167 | ||
168 | /*----- Debugging utilities -----------------------------------------------*/ | |
169 | ||
170 | /* Define a debugging function DUMPFN, which will dump an integer represented | |
171 | * modulo M. The integer is represented as a vector of NPIECE pieces of type | |
172 | * PIECETY. The pieces are assembled at possibly irregular offsets: piece i | |
173 | * logically has width PIECEWD(i), but may overhang the next piece. The | |
174 | * pieces may be signed. GETMOD is an expression which calculates and | |
175 | * returns the value of M, as an `mp *'. | |
176 | * | |
177 | * The generated function writes the value of such an integer X to the stream | |
178 | * FP, labelled with the string WHAT. | |
179 | * | |
180 | * The definition assumes that <stdio.h>, <catacomb/mp.h>, and | |
181 | * <catacomb/mptext.h> have been included. | |
182 | */ | |
183 | #define DEF_FDUMP(dumpfn, piecety, piecewd, npiece, noctet, getmod) \ | |
184 | static void dumpfn(FILE *fp, const char *what, const piecety *x) \ | |
185 | { \ | |
186 | mpw w; \ | |
187 | mp m, *y = MP_ZERO, *t = MP_NEW, *p; \ | |
188 | octet b[noctet]; \ | |
189 | unsigned i, o; \ | |
190 | \ | |
191 | p = getmod; \ | |
192 | mp_build(&m, &w, &w + 1); \ | |
193 | for (i = o = 0; i < npiece; i++) { \ | |
194 | if (x[i] >= 0) { w = x[i]; m.f &= ~MP_NEG; } \ | |
195 | else { w = -x[i]; m.f |= MP_NEG; } \ | |
196 | t = mp_lsl(t, &m, o); \ | |
197 | y = mp_add(y, y, t); \ | |
198 | o += piecewd(i); \ | |
199 | } \ | |
200 | \ | |
201 | fprintf(fp, "%s = <", what); \ | |
202 | for (i = 0; i < npiece; i++) { \ | |
203 | if (i) fputs(", ", fp); \ | |
204 | fprintf(fp, "%ld", (long)x[i]); \ | |
205 | } \ | |
206 | fputs(">\n\t= ", fp); \ | |
207 | mp_writefile(y, fp, 10); \ | |
208 | fputs("\n\t== ", fp); \ | |
209 | mp_div(0, &y, y, p); \ | |
210 | mp_writefile(y, fp, 10); \ | |
211 | fputs("\n\t= 0x", fp); \ | |
212 | mp_writefile(y, fp, 16); \ | |
213 | fputs(" (mod 2^255 - 19)\n\t= [", fp); \ | |
214 | mp_storel(y, b, sizeof(b)); \ | |
215 | for (i = 0; i < 32; i++) { \ | |
216 | if (i && !(i%4)) fputc(':', fp); \ | |
217 | fprintf(fp, "%02x", b[i]); \ | |
218 | } \ | |
219 | fputs("]\n", fp); \ | |
220 | mp_drop(y); mp_drop(p); mp_drop(t); \ | |
221 | } | |
222 | ||
223 | /*----- That's all, folks -------------------------------------------------*/ | |
224 | ||
225 | #ifdef __cplusplus | |
226 | } | |
227 | #endif | |
228 | ||
229 | #endif |