| 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 |