/usr/include/m4rie/gf2x.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 | /**
* \file gf2x.h
*
* \brief \GF2X for degrees < 64
*
* \author Martin Albrecht <martinralbrecht@googlemail.com>
*
* \warning Do not rely on these functions for high performance, they are not fully optimised.
*/
#ifndef M4RIE_GF2X_H
#define M4RIE_GF2X_H
/******************************************************************************
*
* M4RIE: Linear Algebra over GF(2^e)
*
* Copyright (C) 2012 Martin Albrecht <martinralbrecht@googlemail.com>
*
* Distributed under the terms of the GNU General Public License (GEL)
* 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>
#define __M4RIE_1tF(X) ~((X)-1) /**< Maps 1 to word with all ones and 0 to 0. */
typedef int deg_t; /**< degree type **/
/**
* \brief a*b in \GF2X with deg(a) and deg(b) < d.
*/
static inline word gf2x_mul(const word a, const word b, deg_t d) {
word res = 0;
switch(d) {
case 32: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(31)) >>31) & (b<<31);
case 31: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(30)) >>30) & (b<<30);
case 30: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(29)) >>29) & (b<<29);
case 29: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(28)) >>28) & (b<<28);
case 28: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(27)) >>27) & (b<<27);
case 27: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(26)) >>26) & (b<<26);
case 26: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(25)) >>25) & (b<<25);
case 25: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(24)) >>24) & (b<<24);
case 24: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(23)) >>23) & (b<<23);
case 23: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(22)) >>22) & (b<<22);
case 22: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(21)) >>21) & (b<<21);
case 21: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(20)) >>20) & (b<<20);
case 20: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(19)) >>19) & (b<<19);
case 19: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(18)) >>18) & (b<<18);
case 18: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(17)) >>17) & (b<<17);
case 17: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(16)) >>16) & (b<<16);
case 16: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(15)) >>15) & (b<<15);
case 15: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(14)) >>14) & (b<<14);
case 14: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(13)) >>13) & (b<<13);
case 13: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(12)) >>12) & (b<<12);
case 12: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(11)) >>11) & (b<<11);
case 11: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW(10)) >>10) & (b<<10);
case 10: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW( 9)) >> 9) & (b<< 9);
case 9: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW( 8)) >> 8) & (b<< 8);
case 8: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW( 7)) >> 7) & (b<< 7);
case 7: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW( 6)) >> 6) & (b<< 6);
case 6: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW( 5)) >> 5) & (b<< 5);
case 5: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW( 4)) >> 4) & (b<< 4);
case 4: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW( 3)) >> 3) & (b<< 3);
case 3: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW( 2)) >> 2) & (b<< 2);
case 2: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW( 1)) >> 1) & (b<< 1);
case 1: res ^= __M4RIE_1tF((a & __M4RI_TWOPOW( 0)) >> 0) & (b<< 0);
break;
default:
m4ri_die("degree %d too big.\n",d);
}
return res;
}
/**
* \brief deg(a) in \GF2X.
*
* \param a Polynomial of degree <= 64.
*/
static inline deg_t gf2x_deg(word a) {
deg_t degree = 0;
if( (a & 0xffffffff00000000ULL) != 0) { degree += 32; a>>=32; }
if( (a & 0xffff0000ULL) != 0) { degree += 16; a>>=16; }
if( (a & 0xff00ULL) != 0) { degree += 8; a>>= 8; }
if( (a & 0xf0ULL) != 0) { degree += 4; a>>= 4; }
if( (a & 0xcULL) != 0) { degree += 2; a>>= 2; }
if( (a & 0x2ULL) != 0) { degree += 1; a>>= 1; }
return degree;
}
/**
* \brief a / b in \GF2X.
*/
static inline word gf2x_div(word a, word b) {
word res = 0;
word mask = 0;
const deg_t deg_b = gf2x_deg(b);
for(deg_t deg_a = gf2x_deg(a); deg_a >= deg_b; deg_a--) {
mask = __M4RIE_1tF(a>>deg_a);
res |= mask & __M4RI_TWOPOW(deg_a - deg_b);
a ^= mask & b<<(deg_a - deg_b);
}
return res;
}
/**
* \brief a mod b in \GF2X.
*/
static inline word gf2x_mod(word a, word b) {
const deg_t deg_b = gf2x_deg(b);
for(deg_t deg_a=gf2x_deg(a); deg_a>=deg_b; deg_a--) {
a ^= __M4RIE_1tF(a>>deg_a) & b<<(deg_a - deg_b);
}
return a;
}
/**
* \brief a / b and a mod b in \GF2X.
*/
static inline word gf2x_divmod(word a, word b, word *rem) {
word res = 0;
word mask = 0;
const deg_t deg_b = gf2x_deg(b);
for(deg_t deg_a=gf2x_deg(a); deg_a>=deg_b; deg_a--) {
mask = __M4RIE_1tF(a>>deg_a);
res |= mask & __M4RI_TWOPOW(deg_a - deg_b);
a ^= mask & b<<(deg_a - deg_b);
}
*rem = a;
return res;
}
/**
* \brief a^(-1) % b with deg(a), deg(b) <= d.
*/
static inline word gf2x_invmod(word a, word b, const deg_t d) {
word x = 0;
word lastx = 1;
word y = 1;
word lasty = 0;
word rem;
word quo;
word tmp = 0;
while (b != 0) {
quo = gf2x_divmod(a,b, &rem);
a = b; b = rem;
tmp = x; x = lastx ^ gf2x_mul(quo, x, d); lastx = tmp;
tmp = y; y = lasty ^ gf2x_mul(quo, y, d); lasty = tmp;
}
return lastx;
}
#endif //M4RIE_GF2X_H
|