/usr/include/m4rie/gf2e.h is in libm4rie-dev 20150908-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 | /**
* \file gf2e.h
*
* \brief \GF2E
*
* \author Martin Albrecht <martinralbrecht@googlemail.com>
*/
#ifndef M4RIE_GF2E_H
#define M4RIE_GF2E_H
/******************************************************************************
*
* M4RIE: Linear Algebra over GF(2^e)
*
* Copyright (C) 2010,2011 Martin Albrecht <martinralbrecht@googlemail.com>
*
* Distributed under the terms of the GNU General Public License (GPL)
* version 2 or higher.
*
* This code is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* The full text of the GPL is available at:
*
* http://www.gnu.org/licenses/
******************************************************************************/
#include <m4ri/m4ri.h>
#include <m4rie/gf2x.h>
/**
* \brief maximal supported degree
*/
#define M4RIE_MAX_DEGREE 16
/**
* \brief \GF2E
*/
typedef struct gf2e_struct gf2e;
/**
* \brief \GF2E
*/
struct gf2e_struct {
deg_t degree; /**< The degree \e. */
word minpoly; /**< Irreducible polynomial of degree \e. */
word *pow_gen; /**< pow_gen[i] holds \f$a^i / \langle f\rangle\f$ for \f$a\f$ a generator of this field.*/
word *red; /**< red[i] holds precomputed reductors for the minpoly.*/
word **_mul; /**< mul[a][b] holds \f$ a \cdot b\f$ for small fields.*/
word (*inv)(const gf2e *ff, const word a); /**< implements \f$a^{-1}\f$ for a in \GF2E*/
word (*mul)(const gf2e *ff, const word a, const word b); /**< implements \f$a \cdot b\f$ for a in \GF2E.*/
};
/**
* Create finite field from minimal polynomial
*
* \param minpoly Polynomial represented as series of bits.
*/
gf2e *gf2e_init(const word minpoly);
/**
* Free ff
*
* \param ff Finite field.
*/
void gf2e_free(gf2e *ff);
/**
* \brief a^(-1) % minpoly
*/
static inline word gf2e_inv(const gf2e *ff, word a) {
return gf2x_invmod(a, ff->minpoly, ff->degree);
}
/**
* \brief a*b in \GF2E using a table lookups.
*/
static inline word _gf2e_mul_table(const gf2e *ff, const word a, const word b) {
return ff->_mul[a][b];
}
/**
* \brief a*b in \GF2E using a gf2x_mul() lookups.
*/
static inline word _gf2e_mul_arith(const gf2e *ff, const word a, const word b) {
const word res = gf2x_mul(a, b, ff->degree);
return res ^ ff->red[res>>ff->degree];
}
/**
* \brief a*b in \GF2E.
*/
static inline word gf2e_mul(const gf2e *ff, const word a, const word b) {
if( ff->_mul != NULL )
return _gf2e_mul_table(ff, a, b);
else
return _gf2e_mul_arith(ff, a, b);
}
/**
* Return the width used for storing elements of ff
*
* \param ff Finite field.
*/
static inline size_t gf2e_degree_to_w(const gf2e *ff) {
switch(ff->degree) {
case 2:
return 2;
case 3:
case 4:
return 4;
case 5:
case 6:
case 7:
case 8:
return 8;
case 9:
case 10:
case 11:
case 12:
case 13:
case 14:
case 15:
case 16:
return 16;
default:
m4ri_die("degree %d not supported.\n",ff->degree);
}
return 0;
}
/**
* Compute all multiples by a of vectors fitting into 16 bits.
*
* \param ff Finite field.
* \param a Finite field element.
*/
static inline word *gf2e_t16_init(const gf2e *ff, const word a) {
word *mul = (word*)m4ri_mm_calloc(1<<16, sizeof(word));
const deg_t w = gf2e_degree_to_w(ff);
const word mask_w = (1<<w)-1;
/**
* @todo: this is a bit of overkill, we could do better
*/
for(word i=0; i<1<<16; i++) {
switch(w) {
case 2:
mul[i] = gf2e_mul(ff, a, ((i>>0)&mask_w))<<0 | gf2e_mul(ff, a, ((i>> 2)&mask_w))<< 2 | gf2e_mul(ff, a, ((i>> 4)&mask_w))<< 4 | gf2e_mul(ff, a, ((i>> 6)&mask_w))<< 6;
mul[i] |= gf2e_mul(ff, a, ((i>>8)&mask_w))<<8 | gf2e_mul(ff, a, ((i>>10)&mask_w))<<10 | gf2e_mul(ff, a, ((i>>12)&mask_w))<<12 | gf2e_mul(ff, a, ((i>>14)&mask_w))<<14;
break;
case 4:
mul[i] = gf2e_mul(ff, a, (i&mask_w)) | gf2e_mul(ff, a, ((i>>4)&mask_w))<<4 | gf2e_mul(ff, a, ((i>>8)&mask_w))<<8 | gf2e_mul(ff, a, ((i>>12)&mask_w))<<12;
break;
case 8:
mul[i] = gf2e_mul(ff, a, (i&mask_w)) | gf2e_mul(ff, a, ((i>>8)&mask_w))<<8;
break;
case 16:
mul[i] = gf2e_mul(ff, a, (i&mask_w));
break;
};
}
return mul;
}
/**
* \brief Free multiplication table.
*
* \param mul Multiplication table
*/
static inline void gf2e_t16_free(word *mul) {
m4ri_mm_free(mul);
}
/**
* \brief all Irreducible polynomials over GF(2) up to degree 16.
*/
extern const word* irreducible_polynomials[17];
#endif //M4RIE_GF2E_H
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