[SCM] Fast arithmetic with dense matrices over F_{2^e} branch, upstream, updated. 9faf6ece9a183a703670566609063ab274b1c544
Martin Albrecht
martinralbrecht at googlemail.com
Mon Sep 10 12:24:23 UTC 2012
The following commit has been merged in the upstream branch:
commit c9207be954543e3a3f1c26bdb82ab982d7e2a4fc
Author: Martin Albrecht <martinralbrecht at googlemail.com>
Date: Thu Aug 9 21:30:15 2012 +0100
added gf2e_init(minpoly)
diff --git a/Makefile.am b/Makefile.am
index 8afbf8f..a7ff76c 100644
--- a/Makefile.am
+++ b/Makefile.am
@@ -46,34 +46,33 @@ TESTLIBADD = -lm4ri -lm4rie -lgivaro -lgmpxx -lgmp -lm -lstdc++
TESTLDADD = ${M4RIE_GIVARO_LDFLAGS}
TESTLDFLAGS =
-check_PROGRAMS=test_trsm test_elimination test_multiplication test_smallops test_ple
-test_elimination_SOURCES=tests/test_elimination.cc tests/testing.h
-test_elimination_LDADD= ${TESTLDADD} ${TESTLIBADD}
-test_elimination_LDFLAGS= ${TESTLDFLAGS}
-test_elimination_CXXFLAGS=${TESTCXXFLAGS}
-
-test_multiplication_SOURCES=tests/test_multiplication.cc tests/testing.h
-test_multiplication_LDADD=${TESTLDADD} ${TESTLIBADD}
-test_multiplication_LDFLAGS= ${TESTLDFLAGS}
-test_multiplication_CXXFLAGS=${TESTCXXFLAGS}
-
-test_smallops_SOURCES=tests/test_smallops.cc tests/testing.h
-test_smallops_LDADD=${TESTLDADD} ${TESTLIBADD}
-test_smallops_LDFLAGS= ${TESTLDFLAGS}
-test_smallops_CXXFLAGS=${TESTCXXFLAGS}
-
-test_trsm_SOURCES=tests/test_trsm.cc tests/testing.h
-test_trsm_LDADD=${TESTLDADD} ${TESTLIBADD}
-test_trsm_LDFLAGS= ${TESTLDFLAGS}
-test_trsm_CXXFLAGS=${TESTCXXFLAGS}
-
-test_ple_SOURCES=tests/test_ple.cc tests/testing.h
-test_ple_LDADD=${TESTLDADD} ${TESTLIBADD}
-test_ple_LDFLAGS= ${TESTLDFLAGS}
-test_ple_CXXFLAGS=${TESTCXXFLAGS}
-
-
-TESTS=test_trsm test_elimination test_multiplication test_smallops test_ple
+check_PROGRAMS = test_trsm test_elimination test_multiplication test_smallops test_ple test_gf2e
+test_elimination_SOURCES = tests/test_elimination.cc tests/testing.h
+test_elimination_LDADD = ${TESTLDADD} ${TESTLIBADD}
+test_elimination_LDFLAGS = ${TESTLDFLAGS}
+test_elimination_CXXFLAGS = ${TESTCXXFLAGS}
+
+test_multiplication_SOURCES = tests/test_multiplication.cc tests/testing.h
+test_multiplication_LDADD = ${TESTLDADD} ${TESTLIBADD}
+test_multiplication_LDFLAGS = ${TESTLDFLAGS}
+test_multiplication_CXXFLAGS = ${TESTCXXFLAGS}
+
+test_smallops_SOURCES = tests/test_smallops.cc tests/testing.h
+test_smallops_LDADD = ${TESTLDADD} ${TESTLIBADD}
+test_smallops_LDFLAGS = ${TESTLDFLAGS}
+test_smallops_CXXFLAGS = ${TESTCXXFLAGS}
+
+test_trsm_SOURCES = tests/test_trsm.cc tests/testing.h
+test_trsm_LDADD = ${TESTLDADD} ${TESTLIBADD}
+test_trsm_LDFLAGS = ${TESTLDFLAGS}
+test_trsm_CXXFLAGS = ${TESTCXXFLAGS}
+
+test_ple_SOURCES = tests/test_ple.cc tests/testing.h
+test_ple_LDADD = ${TESTLDADD} ${TESTLIBADD}
+test_ple_LDFLAGS = ${TESTLDFLAGS}
+test_ple_CXXFLAGS = ${TESTCXXFLAGS}
+
+TESTS = test_trsm test_elimination test_multiplication test_smallops test_ple
# benchmarketing
diff --git a/src/gf2e.c b/src/gf2e.c
index 6cd363b..a691726 100644
--- a/src/gf2e.c
+++ b/src/gf2e.c
@@ -1,8 +1,52 @@
#include <m4ri/m4ri.h>
#include "gf2e.h"
-void gf2e_free(gf2e *ff) {
+gf2e *gf2e_init(const word minpoly) {
+ gf2e *ff = (gf2e*)m4ri_mm_calloc(1, sizeof(gf2e));
+
+ for(int i=0; i<=M4RIE_MAX_DEGREE; i++)
+ if(1<<i & minpoly)
+ ff->degree = i;
+
+ ff->minpoly = minpoly;
+ gf2e_make_pow_gen(ff);
+
+ const size_t order = __M4RI_TWOPOW(ff->degree);
+
+ word *red = (word*)m4ri_mm_calloc(order, sizeof(word));
+
+ for(unsigned int i=1; i<order; i++) {
+ word tmp = 0;
+ for(unsigned int j=0; j<ff->degree; j++)
+ if (__M4RI_TWOPOW(j) & i)
+ tmp ^= minpoly<<j;
+ assert(red[tmp>>ff->degree] == 0);
+ red[tmp>>ff->degree] = tmp;
+ }
+
+ ff->mul = (word **)m4ri_mm_calloc(order, sizeof(word *));
+ ff->mul[0] = (word *)m4ri_mm_calloc(order, sizeof(word));
+ for(unsigned int i = 1; i<order; i++) {
+ ff->mul[i] = (word *)m4ri_mm_calloc(order, sizeof(word));
+ for(unsigned int j=1; j<order; j++) {
+ word res = gf2x_mul(i,j, ff->degree);
+ ff->mul[i][j] = res ^ red[res>>ff->degree];
+ }
+ }
+
+ ff->inv = (word *)m4ri_mm_calloc(order, sizeof(word));
+ ff->inv[0] = 1;
+ for(unsigned int i=1; i<order; i++) {
+ ff->inv[i] = gf2x_invmod(i, ff->minpoly, ff->degree);
+ }
+
+ m4ri_mm_free(red);
+
+ return ff;
+}
+
+void gf2e_free(gf2e *ff) {
for(size_t i=0; i<__M4RI_TWOPOW(ff->degree); i++) {
m4ri_mm_free(ff->mul[i]);
}
@@ -11,3 +55,28 @@ void gf2e_free(gf2e *ff) {
m4ri_mm_free(ff->pow_gen);
}
+const word _irreducible_polynomials_degree_02[ 2] = { 1, 0x00007 };
+const word _irreducible_polynomials_degree_03[ 3] = { 2, 0x0000b, 0x0000d };
+const word _irreducible_polynomials_degree_04[ 4] = { 3, 0x00013, 0x00019, 0x0001f };
+const word _irreducible_polynomials_degree_05[ 7] = { 6, 0x00025, 0x00029, 0x0002f, 0x00037, 0x0003b, 0x0003d };
+const word _irreducible_polynomials_degree_06[ 10] = { 9, 0x00043, 0x00049, 0x00057, 0x0005b, 0x00061, 0x00067, 0x0006d, 0x00073, 0x00075 };
+const word _irreducible_polynomials_degree_07[ 19] = { 18, 0x00083, 0x00089, 0x0008f, 0x00091, 0x0009d, 0x000a7, 0x000ab, 0x000b9, 0x000bf, 0x000c1, 0x000cb, 0x000d3, 0x000d5, 0x000e5, 0x000ef, 0x000f1, 0x000f7, 0x000fd };
+const word _irreducible_polynomials_degree_08[ 31] = { 30, 0x0011b, 0x0011d, 0x0012b, 0x0012d, 0x00139, 0x0013f, 0x0014d, 0x0015f, 0x00163, 0x00165, 0x00169, 0x00171, 0x00177, 0x0017b, 0x00187, 0x0018b, 0x0018d, 0x0019f, 0x001a3, 0x001a9, 0x001b1, 0x001bd, 0x001c3, 0x001cf, 0x001d7, 0x001dd, 0x001e7, 0x001f3, 0x001f5, 0x001f9 };
+const word _irreducible_polynomials_degree_09[ 57] = { 56, 0x00203, 0x00211, 0x00217, 0x0021b, 0x00221, 0x0022d, 0x00233, 0x0024b, 0x00259, 0x0025f, 0x00265, 0x00269, 0x0026f, 0x00277, 0x0027d, 0x00287, 0x00295, 0x00299, 0x002a3, 0x002a5, 0x002af, 0x002b7, 0x002bd, 0x002cf, 0x002d1, 0x002db, 0x002f5, 0x002f9, 0x00301, 0x00313, 0x00315, 0x0031f, 0x00323, 0x00331, 0x0033b, 0x00349, 0x0034f, 0x0035b, 0x00361, 0x0036b, 0x0036d, 0x00373, 0x0037f, 0x00385, 0x0038f, 0x003a1, 0x003b5, 0x003b9, 0x003c7, 0x003cb, 0x003cd, 0x003d5, 0x003d9, 0x003e3, 0x003e9, 0x003fb };
+const word _irreducible_polynomials_degree_10[ 100] = { 99, 0x00409, 0x0040f, 0x0041b, 0x0041d, 0x00427, 0x0042d, 0x00435, 0x00447, 0x00453, 0x00463, 0x00465, 0x0046f, 0x00481, 0x0048b, 0x00499, 0x004a9, 0x004af, 0x004c5, 0x004c9, 0x004d7, 0x004e7, 0x004ed, 0x004f3, 0x004ff, 0x0050b, 0x0050d, 0x00519, 0x0051f, 0x00523, 0x00531, 0x0053d, 0x00543, 0x00557, 0x00561, 0x00567, 0x0056b, 0x00585, 0x0058f, 0x00597, 0x0059b, 0x005a1, 0x005ab, 0x005b9, 0x005c1, 0x005c7, 0x005e5, 0x005f7, 0x005fb, 0x00613, 0x00615, 0x00623, 0x00625, 0x00631, 0x00637, 0x00643, 0x0064f, 0x00651, 0x0065b, 0x00679, 0x0067f, 0x00685, 0x00689, 0x006a7, 0x006ad, 0x006b5, 0x006bf, 0x006c1, 0x006cd, 0x006d3, 0x006df, 0x006f7, 0x006fd, 0x0070f, 0x00711, 0x00717, 0x0071d, 0x00721, 0x0072b, 0x00735, 0x00739, 0x00747, 0x0074d, 0x00755, 0x00759, 0x00763, 0x0077b, 0x0077d, 0x00781, 0x00787, 0x0078d, 0x00793, 0x007a9, 0x007b1, 0x007c5, 0x007db, 0x007eb, 0x007f3, 0x007f9, 0x007ff };
+const word _irreducible_polynomials_degree_11[ 187] = { 186, 0x00805, 0x00817, 0x0082b, 0x0082d, 0x00847, 0x00863, 0x00865, 0x00871, 0x0087b, 0x0088d, 0x00895, 0x0089f, 0x008a9, 0x008b1, 0x008c3, 0x008cf, 0x008d1, 0x008e1, 0x008e7, 0x008eb, 0x008f5, 0x0090d, 0x00913, 0x00925, 0x00929, 0x00937, 0x0093b, 0x0093d, 0x00945, 0x00949, 0x00951, 0x0095b, 0x00973, 0x00975, 0x0097f, 0x00983, 0x0098f, 0x009ab, 0x009ad, 0x009b9, 0x009c7, 0x009d9, 0x009e5, 0x009ef, 0x009f7, 0x00a01, 0x00a07, 0x00a13, 0x00a15, 0x00a29, 0x00a49, 0x00a61, 0x00a6d, 0x00a79, 0x00a7f, 0x00a85, 0x00a91, 0x00a9d, 0x00aa7, 0x00aab, 0x00ab3, 0x00ab5, 0x00ad5, 0x00adf, 0x00ae3, 0x00ae9, 0x00aef, 0x00af1, 0x00afb, 0x00b03, 0x00b09, 0x00b11, 0x00b33, 0x00b3f, 0x00b41, 0x00b4b, 0x00b59, 0x00b5f, 0x00b65, 0x00b6f, 0x00b7d, 0x00b87, 0x00b8b, 0x00b93, 0x00b95, 0x00baf, 0x00bb7, 0x00bbd, 0x00bc9, 0x00bdb, 0x00bdd, 0x00be7, 0x00bed, 0x00c0b, 0x00c0d, 0x00c19, 0x00c1f, 0x00c31, 0x00c57, 0x00c61, 0x00c6b, 0x00c73, 0x00c75, 0x00c85, 0x00c89, 0x00c97, 0x00c9b, 0x00c9d, 0x00cb3, 0x00cbf, 0x00cc7, 0x00ccd, 0x00cd3, 0x00cd5, 0x00ce3, 0x00ce9, 0x00cf7, 0x00d03, 0x00d0f, 0x00d1d, 0x00d27, 0x00d2d, 0x00d41, 0x00d47, 0x00d55, 0x00d59, 0x00d63, 0x00d6f, 0x00d71, 0x00d93, 0x00d9f, 0x00da9, 0x00dbb, 0x00dbd, 0x00dc9, 0x00dd7, 0x00ddb, 0x00de1, 0x00de7, 0x00df5, 0x00dff, 0x00e05, 0x00e1d, 0x00e21, 0x00e27, 0x00e2b, 0x00e33, 0x00e39, 0x00e47, 0x00e4b, 0x00e55, 0x00e5f, 0x00e71, 0x00e7b, 0x00e7d, 0x00e81, 0x00e93, 0x00e9f, 0x00ea3, 0x00ebb, 0x00ec9, 0x00ecf, 0x00edd, 0x00ef3, 0x00ef9, 0x00f0b, 0x00f19, 0x00f31, 0x00f37, 0x00f5d, 0x00f6b, 0x00f6d, 0x00f75, 0x00f79, 0x00f83, 0x00f91, 0x00f97, 0x00f9b, 0x00fa7, 0x00fad, 0x00fb5, 0x00fcd, 0x00fd3, 0x00fe5, 0x00fe9, 0x00ffb };
+const word _irreducible_polynomials_degree_12[ 336] = { 335, 0x01009, 0x01017, 0x01021, 0x01033, 0x01035, 0x0103f, 0x0104d, 0x01053, 0x01069, 0x01077, 0x0107b, 0x0107d, 0x01081, 0x0108b, 0x01099, 0x010a3, 0x010a5, 0x010cf, 0x010d1, 0x010eb, 0x010ed, 0x010ff, 0x01107, 0x0111f, 0x01123, 0x01131, 0x01137, 0x0113b, 0x0114f, 0x01157, 0x01161, 0x0116b, 0x0116d, 0x01179, 0x01183, 0x01185, 0x01191, 0x011ab, 0x011b3, 0x011d9, 0x011df, 0x011e3, 0x011ef, 0x011f1, 0x01201, 0x0120d, 0x01213, 0x01219, 0x01225, 0x01237, 0x0123b, 0x0123d, 0x01243, 0x01245, 0x01267, 0x0126d, 0x01273, 0x0127f, 0x012b5, 0x012b9, 0x012c1, 0x012cb, 0x01309, 0x0130f, 0x0131b, 0x0131d, 0x01321, 0x01333, 0x01339, 0x0133f, 0x0134d, 0x01365, 0x01371, 0x01399, 0x0139f, 0x013a3, 0x013a9, 0x013af, 0x013bb, 0x013c3, 0x013d1, 0x013d7, 0x013dd, 0x013f3, 0x013f5, 0x01407, 0x01413, 0x01431, 0x01437, 0x01449, 0x0144f, 0x0145b, 0x0145d, 0x01467, 0x0146b, 0x01475, 0x0147f, 0x01489, 0x014a1, 0x014a7, 0x014ad, 0x014b5, 0x014cd, 0x014d3, 0x014d9, 0x014df, 0x014e5, 0x0150f, 0x0151d, 0x0154b, 0x0154d, 0x01581, 0x01593, 0x015a5, 0x015a9, 0x015bb, 0x015c5, 0x015d7, 0x015dd, 0x015eb, 0x015f9, 0x01603, 0x01609, 0x0161b, 0x0163f, 0x01641, 0x01647, 0x0164b, 0x01655, 0x01659, 0x01663, 0x01665, 0x0166f, 0x01693, 0x016a5, 0x016bd, 0x016c3, 0x016c9, 0x016d1, 0x016e1, 0x016e7, 0x016f3, 0x016ff, 0x0170b, 0x01715, 0x01719, 0x0173d, 0x01743, 0x01745, 0x0174f, 0x01757, 0x0175d, 0x01773, 0x01775, 0x01779, 0x01789, 0x0178f, 0x01797, 0x0179d, 0x017ad, 0x017b3, 0x017bf, 0x017c1, 0x017df, 0x017fb, 0x01807, 0x0180d, 0x0181f, 0x01823, 0x01831, 0x01837, 0x01849, 0x01857, 0x0185d, 0x0186d, 0x01879, 0x0187f, 0x01883, 0x01891, 0x01897, 0x018a1, 0x018b9, 0x018cb, 0x018cd, 0x018ef, 0x018f1, 0x018fb, 0x01905, 0x01909, 0x0191b, 0x0192d, 0x01935, 0x01941, 0x0194b, 0x0195f, 0x01965, 0x0196f, 0x0197b, 0x01981, 0x0198b, 0x01999, 0x019b1, 0x019b7, 0x019bd, 0x019c9, 0x019cf, 0x019dd, 0x019e7, 0x019ed, 0x019f9, 0x01a1b, 0x01a1d, 0x01a21, 0x01a2b, 0x01a33, 0x01a4d, 0x01a53, 0x01a55, 0x01a5f, 0x01a63, 0x01a69, 0x01a7b, 0x01a8b, 0x01ab1, 0x01ac5, 0x01ad1, 0x01ae1, 0x01ae7, 0x01aeb, 0x01af5, 0x01b0b, 0x01b0d, 0x01b13, 0x01b19, 0x01b1f, 0x01b2f, 0x01b45, 0x01b57, 0x01b89, 0x01b8f, 0x01b91, 0x01ba7, 0x01bb5, 0x01bb9, 0x01bbf, 0x01bc1, 0x01bcb, 0x01bd3, 0x01be3, 0x01bfd, 0x01c03, 0x01c05, 0x01c0f, 0x01c11, 0x01c17, 0x01c27, 0x01c4d, 0x01c5f, 0x01c87, 0x01c9f, 0x01ca5, 0x01cb7, 0x01cbb, 0x01cc5, 0x01cc9, 0x01ccf, 0x01cd7, 0x01ceb, 0x01ced, 0x01cf3, 0x01d01, 0x01d07, 0x01d23, 0x01d2f, 0x01d3d, 0x01d43, 0x01d51, 0x01d5b, 0x01d5d, 0x01d67, 0x01d75, 0x01d79, 0x01d83, 0x01d85, 0x01d89, 0x01d91, 0x01da7, 0x01db3, 0x01dc1, 0x01def, 0x01e07, 0x01e15, 0x01e19, 0x01e2f, 0x01e3b, 0x01e3d, 0x01e45, 0x01e51, 0x01e5d, 0x01e61, 0x01e67, 0x01e73, 0x01e8f, 0x01e97, 0x01e9b, 0x01eb9, 0x01ebf, 0x01ecd, 0x01ed3, 0x01ee3, 0x01ef1, 0x01ef7, 0x01f03, 0x01f11, 0x01f1b, 0x01f27, 0x01f39, 0x01f47, 0x01f4b, 0x01f53, 0x01f65, 0x01f71, 0x01f7d, 0x01f81, 0x01f8d, 0x01f99, 0x01faf, 0x01fbb, 0x01fbd, 0x01fc3, 0x01fc5, 0x01fc9, 0x01fe1, 0x01fed, 0x01fff };
+const word _irreducible_polynomials_degree_13[ 631] = { 630, 0x0201b, 0x02027, 0x02035, 0x02053, 0x02065, 0x0206f, 0x0208b, 0x0208d, 0x0209f, 0x020a5, 0x020af, 0x020bb, 0x020bd, 0x020c3, 0x020c9, 0x020e1, 0x020f3, 0x0210d, 0x02115, 0x02129, 0x0212f, 0x0213b, 0x02143, 0x02167, 0x0216b, 0x02179, 0x02189, 0x02197, 0x0219d, 0x021bf, 0x021c1, 0x021c7, 0x021cd, 0x021df, 0x021e3, 0x021f1, 0x021fb, 0x02219, 0x02225, 0x02237, 0x0223d, 0x02243, 0x0225b, 0x0225d, 0x02279, 0x0227f, 0x02289, 0x02297, 0x0229b, 0x022b3, 0x022bf, 0x022cd, 0x022ef, 0x022f7, 0x022fb, 0x02305, 0x02327, 0x0232b, 0x02347, 0x02355, 0x02359, 0x0236f, 0x02371, 0x0237d, 0x02387, 0x0238d, 0x02395, 0x023a3, 0x023a9, 0x023b1, 0x023b7, 0x023bb, 0x023e1, 0x023ed, 0x023f9, 0x0240b, 0x02413, 0x0241f, 0x02425, 0x02429, 0x0243d, 0x02451, 0x02457, 0x02461, 0x0246d, 0x0247f, 0x02483, 0x0249b, 0x0249d, 0x024b5, 0x024bf, 0x024c1, 0x024c7, 0x024cb, 0x024e3, 0x02509, 0x02517, 0x0251d, 0x02521, 0x0252d, 0x02539, 0x02553, 0x02555, 0x02563, 0x02571, 0x02577, 0x02587, 0x0258b, 0x02595, 0x02599, 0x0259f, 0x025af, 0x025bd, 0x025c5, 0x025cf, 0x025d7, 0x025eb, 0x02603, 0x02605, 0x02611, 0x0262d, 0x0263f, 0x0264b, 0x02653, 0x02659, 0x02669, 0x02677, 0x0267b, 0x02687, 0x02693, 0x02699, 0x026b1, 0x026b7, 0x026bd, 0x026c3, 0x026eb, 0x026f5, 0x02713, 0x02729, 0x0273b, 0x0274f, 0x02757, 0x0275d, 0x0276b, 0x02773, 0x02779, 0x02783, 0x02791, 0x027a1, 0x027b9, 0x027c7, 0x027cb, 0x027df, 0x027ef, 0x027f1, 0x02807, 0x02819, 0x0281f, 0x02823, 0x02831, 0x0283b, 0x0283d, 0x02845, 0x02867, 0x02875, 0x02885, 0x028ab, 0x028ad, 0x028bf, 0x028cd, 0x028d5, 0x028df, 0x028e3, 0x028e9, 0x028fb, 0x02909, 0x0290f, 0x02911, 0x0291b, 0x0292b, 0x02935, 0x0293f, 0x02941, 0x0294b, 0x02955, 0x02977, 0x0297d, 0x02981, 0x02993, 0x0299f, 0x029af, 0x029b7, 0x029bd, 0x029c3, 0x029d7, 0x029f3, 0x029f5, 0x02a03, 0x02a0f, 0x02a1d, 0x02a21, 0x02a33, 0x02a35, 0x02a4d, 0x02a69, 0x02a6f, 0x02a71, 0x02a7b, 0x02a7d, 0x02aa5, 0x02aa9, 0x02ab1, 0x02ac5, 0x02ad7, 0x02adb, 0x02aeb, 0x02af3, 0x02b01, 0x02b15, 0x02b23, 0x02b25, 0x02b2f, 0x02b37, 0x02b43, 0x02b49, 0x02b6d, 0x02b7f, 0x02b85, 0x02b97, 0x02b9b, 0x02bad, 0x02bb3, 0x02bd9, 0x02be5, 0x02bfd, 0x02c0f, 0x02c21, 0x02c2b, 0x02c2d, 0x02c3f, 0x02c41, 0x02c4d, 0x02c71, 0x02c8b, 0x02c8d, 0x02c95, 0x02ca3, 0x02caf, 0x02cbd, 0x02cc5, 0x02cd1, 0x02cd7, 0x02ce1, 0x02ce7, 0x02ceb, 0x02d0d, 0x02d19, 0x02d29, 0x02d2f, 0x02d37, 0x02d3b, 0x02d45, 0x02d5b, 0x02d67, 0x02d75, 0x02d89, 0x02d8f, 0x02da7, 0x02dab, 0x02db5, 0x02de3, 0x02df1, 0x02dfd, 0x02e07, 0x02e13, 0x02e15, 0x02e29, 0x02e49, 0x02e4f, 0x02e5b, 0x02e5d, 0x02e61, 0x02e6b, 0x02e8f, 0x02e91, 0x02e97, 0x02e9d, 0x02eab, 0x02eb3, 0x02eb9, 0x02edf, 0x02efb, 0x02efd, 0x02f05, 0x02f09, 0x02f11, 0x02f17, 0x02f3f, 0x02f41, 0x02f4b, 0x02f4d, 0x02f59, 0x02f5f, 0x02f65, 0x02f69, 0x02f95, 0x02fa5, 0x02faf, 0x02fb1, 0x02fcf, 0x02fdd, 0x02fe7, 0x02fed, 0x02ff5, 0x02fff, 0x03007, 0x03015, 0x03019, 0x0302f, 0x03049, 0x0304f, 0x03067, 0x03079, 0x0307f, 0x03091, 0x030a1, 0x030b5, 0x030bf, 0x030c1, 0x030d3, 0x030d9, 0x030e5, 0x030ef, 0x03105, 0x0310f, 0x03135, 0x03147, 0x0314d, 0x0315f, 0x03163, 0x03171, 0x0317b, 0x031a3, 0x031a9, 0x031b7, 0x031c5, 0x031c9, 0x031db, 0x031e1, 0x031eb, 0x031ed, 0x031f3, 0x031ff, 0x03209, 0x0320f, 0x0321d, 0x03227, 0x03239, 0x0324b, 0x03253, 0x03259, 0x03265, 0x03281, 0x03293, 0x03299, 0x0329f, 0x032a9, 0x032b7, 0x032bb, 0x032c3, 0x032d7, 0x032db, 0x032e7, 0x03307, 0x03315, 0x0332f, 0x03351, 0x0335d, 0x03375, 0x03397, 0x0339b, 0x033ab, 0x033b9, 0x033c1, 0x033c7, 0x033d5, 0x033e3, 0x033e5, 0x033f7, 0x033fb, 0x03409, 0x0341b, 0x03427, 0x03441, 0x0344d, 0x0345f, 0x03469, 0x03477, 0x0347b, 0x03487, 0x03493, 0x03499, 0x034a5, 0x034bd, 0x034c9, 0x034db, 0x034e7, 0x034f9, 0x0350d, 0x0351f, 0x03525, 0x03531, 0x03537, 0x03545, 0x0354f, 0x0355d, 0x0356d, 0x03573, 0x0357f, 0x0359d, 0x035a1, 0x035b9, 0x035cd, 0x035d5, 0x035d9, 0x035e3, 0x035e9, 0x035ef, 0x03601, 0x0360b, 0x0361f, 0x03625, 0x0362f, 0x0363b, 0x03649, 0x03651, 0x0365b, 0x03673, 0x03675, 0x03691, 0x0369b, 0x0369d, 0x036ad, 0x036cb, 0x036d3, 0x036d5, 0x036e3, 0x036ef, 0x03705, 0x0370f, 0x0371b, 0x03721, 0x0372d, 0x03739, 0x03741, 0x03747, 0x03753, 0x03771, 0x03777, 0x0378b, 0x03795, 0x03799, 0x037a3, 0x037c5, 0x037cf, 0x037d1, 0x037d7, 0x037dd, 0x037e1, 0x037f3, 0x03803, 0x03805, 0x03817, 0x0381d, 0x03827, 0x03833, 0x0384b, 0x03859, 0x03869, 0x03871, 0x038a3, 0x038b1, 0x038bb, 0x038c9, 0x038cf, 0x038e1, 0x038f3, 0x038f9, 0x03901, 0x03907, 0x0390b, 0x03913, 0x03931, 0x0394f, 0x03967, 0x0396d, 0x03983, 0x03985, 0x03997, 0x039a1, 0x039a7, 0x039ad, 0x039cb, 0x039cd, 0x039d3, 0x039ef, 0x039f7, 0x039fd, 0x03a07, 0x03a29, 0x03a2f, 0x03a3d, 0x03a51, 0x03a5d, 0x03a61, 0x03a67, 0x03a73, 0x03a75, 0x03a89, 0x03ab9, 0x03abf, 0x03acd, 0x03ad3, 0x03ad5, 0x03adf, 0x03ae5, 0x03ae9, 0x03afb, 0x03b11, 0x03b2b, 0x03b2d, 0x03b35, 0x03b3f, 0x03b53, 0x03b59, 0x03b63, 0x03b65, 0x03b6f, 0x03b71, 0x03b77, 0x03b8b, 0x03b99, 0x03ba5, 0x03ba9, 0x03bb7, 0x03bbb, 0x03bd1, 0x03be7, 0x03bf3, 0x03bff, 0x03c0d, 0x03c13, 0x03c15, 0x03c1f, 0x03c23, 0x03c25, 0x03c3b, 0x03c4f, 0x03c5d, 0x03c6d, 0x03c83, 0x03c8f, 0x03c9d, 0x03ca7, 0x03cab, 0x03cb9, 0x03cc7, 0x03ce9, 0x03cfb, 0x03cfd, 0x03d03, 0x03d17, 0x03d1b, 0x03d21, 0x03d2d, 0x03d33, 0x03d35, 0x03d41, 0x03d4d, 0x03d65, 0x03d69, 0x03d7d, 0x03d81, 0x03d95, 0x03db1, 0x03db7, 0x03dc3, 0x03dd1, 0x03ddb, 0x03de7, 0x03deb, 0x03df9, 0x03e05, 0x03e09, 0x03e0f, 0x03e1b, 0x03e2b, 0x03e3f, 0x03e41, 0x03e53, 0x03e65, 0x03e69, 0x03e8b, 0x03ea3, 0x03ebd, 0x03ec5, 0x03ed7, 0x03edd, 0x03ee1, 0x03ef9, 0x03f0d, 0x03f19, 0x03f1f, 0x03f25, 0x03f37, 0x03f3d, 0x03f43, 0x03f45, 0x03f49, 0x03f51, 0x03f57, 0x03f61, 0x03f83, 0x03f89, 0x03f91, 0x03fab, 0x03fb5, 0x03fe3, 0x03ff7, 0x03ffd };
+const word _irreducible_polynomials_degree_14[1162] = { 1161, 0x04021, 0x0402b, 0x04033, 0x04039, 0x0403f, 0x04053, 0x0405f, 0x04065, 0x0407b, 0x04087, 0x040a9, 0x040af, 0x040bb, 0x040bd, 0x040cf, 0x040d7, 0x040eb, 0x040f3, 0x040f9, 0x0410b, 0x0410d, 0x04113, 0x0413b, 0x04143, 0x04149, 0x04157, 0x04167, 0x0416d, 0x04191, 0x0419b, 0x0419d, 0x041a7, 0x041ab, 0x041ad, 0x041b5, 0x041d5, 0x041d9, 0x041f1, 0x04201, 0x0420d, 0x04245, 0x04249, 0x04257, 0x04261, 0x04273, 0x04279, 0x0427f, 0x04283, 0x04285, 0x0429d, 0x042a1, 0x042c7, 0x042cb, 0x042cd, 0x042e3, 0x042e9, 0x042ef, 0x04303, 0x04309, 0x0431b, 0x04321, 0x04327, 0x0433f, 0x04369, 0x0437b, 0x0437d, 0x04387, 0x04395, 0x043af, 0x043c9, 0x043dd, 0x043eb, 0x043ed, 0x043ff, 0x0440b, 0x0440d, 0x04443, 0x0445d, 0x04473, 0x04489, 0x044c1, 0x044d3, 0x044d5, 0x044df, 0x044e3, 0x044f1, 0x044fb, 0x04503, 0x04509, 0x0450f, 0x0452b, 0x04539, 0x04559, 0x0456f, 0x04577, 0x0457d, 0x0458d, 0x04599, 0x0459f, 0x045a5, 0x045b7, 0x045c5, 0x045c9, 0x045d1, 0x045d7, 0x045e7, 0x045f3, 0x045ff, 0x0460f, 0x0461d, 0x04627, 0x04635, 0x04647, 0x04659, 0x04663, 0x04671, 0x0467b, 0x0468d, 0x04693, 0x04695, 0x046a3, 0x046a5, 0x046c5, 0x046cf, 0x046db, 0x046eb, 0x046ff, 0x04725, 0x04731, 0x04743, 0x0474f, 0x0477f, 0x04789, 0x04791, 0x0479b, 0x047a7, 0x047b5, 0x047c1, 0x047d3, 0x047d9, 0x047e5, 0x047e9, 0x047ef, 0x047fd, 0x04813, 0x04819, 0x0481f, 0x0483b, 0x04843, 0x04851, 0x0485b, 0x04861, 0x04867, 0x0487f, 0x04883, 0x04891, 0x048bf, 0x048c7, 0x048e3, 0x048f1, 0x048f7, 0x048fd, 0x0491d, 0x04921, 0x0492d, 0x04939, 0x04941, 0x04953, 0x0495f, 0x04965, 0x04969, 0x04977, 0x04987, 0x0498b, 0x049a9, 0x049cf, 0x049d1, 0x049dd, 0x049e1, 0x049e7, 0x04a17, 0x04a35, 0x04a59, 0x04a65, 0x04a7b, 0x04a81, 0x04a87, 0x04a8b, 0x04a93, 0x04aa3, 0x04aaf, 0x04abd, 0x04ac9, 0x04add, 0x04aed, 0x04af9, 0x04b1f, 0x04b37, 0x04b49, 0x04b5b, 0x04b61, 0x04b6b, 0x04b6d, 0x04b73, 0x04b79, 0x04b85, 0x04b8f, 0x04b97, 0x04ba1, 0x04bab, 0x04bb3, 0x04bb9, 0x04bcb, 0x04bcd, 0x04bd5, 0x04bdf, 0x04bf1, 0x04bfb, 0x04c09, 0x04c1b, 0x04c1d, 0x04c27, 0x04c2b, 0x04c3f, 0x04c47, 0x04c4b, 0x04c53, 0x04c55, 0x04c65, 0x04c7d, 0x04c8d, 0x04ca5, 0x04cbd, 0x04cc5, 0x04cd1, 0x04cd7, 0x04ced, 0x04cff, 0x04d15, 0x04d1f, 0x04d29, 0x04d31, 0x04d45, 0x04d4f, 0x04d51, 0x04d75, 0x04d85, 0x04d8f, 0x04dad, 0x04db3, 0x04dc1, 0x04dd3, 0x04df1, 0x04dfb, 0x04e01, 0x04e15, 0x04e23, 0x04e37, 0x04e43, 0x04e49, 0x04e51, 0x04e6b, 0x04e6d, 0x04e83, 0x04e9b, 0x04eb3, 0x04ed3, 0x04ee5, 0x04ee9, 0x04eef, 0x04f1d, 0x04f21, 0x04f4b, 0x04f55, 0x04f5f, 0x04f69, 0x04f6f, 0x04f81, 0x04f8d, 0x04f9f, 0x04fa5, 0x04fa9, 0x04fb7, 0x04fbb, 0x04fd7, 0x04feb, 0x04fed, 0x04ff9, 0x05007, 0x0501f, 0x05025, 0x0505b, 0x0505d, 0x050a1, 0x050cb, 0x050d5, 0x050d9, 0x050e3, 0x050e9, 0x050ef, 0x050fb, 0x0511b, 0x05121, 0x0512d, 0x0513f, 0x05153, 0x05159, 0x0515f, 0x0516f, 0x0517d, 0x0518b, 0x05199, 0x051a5, 0x051b1, 0x051b7, 0x051cf, 0x051d1, 0x051db, 0x051eb, 0x051ed, 0x051f5, 0x051ff, 0x05205, 0x0520f, 0x0522d, 0x05265, 0x05271, 0x0528b, 0x05299, 0x052a3, 0x052b1, 0x052bd, 0x052c3, 0x052c5, 0x052cf, 0x052d1, 0x052e7, 0x052eb, 0x052f9, 0x05301, 0x05319, 0x05325, 0x05329, 0x05337, 0x05349, 0x0535b, 0x05367, 0x05375, 0x0539b, 0x0539d, 0x053a7, 0x053b9, 0x053bf, 0x053c7, 0x053d3, 0x053e5, 0x053f1, 0x053fd, 0x05403, 0x0540f, 0x05417, 0x05435, 0x05439, 0x05447, 0x05459, 0x0545f, 0x0547b, 0x0548d, 0x05493, 0x05495, 0x0549f, 0x054b1, 0x054b7, 0x054bb, 0x054dd, 0x054e1, 0x054eb, 0x05513, 0x05519, 0x0552f, 0x05537, 0x05567, 0x0556b, 0x05575, 0x05579, 0x0557f, 0x05583, 0x05585, 0x05591, 0x05597, 0x055ad, 0x055c1, 0x055d3, 0x055df, 0x055e9, 0x055f7, 0x05607, 0x0560d, 0x05615, 0x05623, 0x05629, 0x0562f, 0x05631, 0x05657, 0x0565d, 0x0569b, 0x056ab, 0x056ad, 0x056b3, 0x056c1, 0x056c7, 0x056cd, 0x056f1, 0x056f7, 0x056fb, 0x0572b, 0x0572d, 0x0573f, 0x0574b, 0x05755, 0x05759, 0x05763, 0x05765, 0x0577d, 0x05793, 0x057af, 0x057bd, 0x057c3, 0x057c5, 0x057d7, 0x057e7, 0x057f3, 0x05803, 0x05811, 0x05821, 0x0582d, 0x05833, 0x05835, 0x0583f, 0x05841, 0x0587d, 0x05887, 0x0588b, 0x05895, 0x05899, 0x058a3, 0x058af, 0x058b1, 0x058d1, 0x058dd, 0x058e7, 0x058eb, 0x058f9, 0x058ff, 0x05913, 0x05923, 0x0593b, 0x0594f, 0x0597f, 0x0598f, 0x05997, 0x0599d, 0x059a1, 0x059a7, 0x059ab, 0x059b5, 0x059cb, 0x059df, 0x059e9, 0x059fd, 0x05a0d, 0x05a13, 0x05a1f, 0x05a25, 0x05a3b, 0x05a3d, 0x05a43, 0x05a45, 0x05a49, 0x05a75, 0x05a8f, 0x05aa7, 0x05ab5, 0x05ac1, 0x05ad3, 0x05ad5, 0x05ad9, 0x05af7, 0x05b0f, 0x05b17, 0x05b1d, 0x05b2b, 0x05b33, 0x05b39, 0x05b41, 0x05b63, 0x05b69, 0x05b77, 0x05b99, 0x05ba3, 0x05ba9, 0x05bc3, 0x05bc5, 0x05be1, 0x05beb, 0x05bf9, 0x05c07, 0x05c0b, 0x05c19, 0x05c31, 0x05c37, 0x05c49, 0x05c5d, 0x05c6d, 0x05c79, 0x05c83, 0x05ca1, 0x05cbf, 0x05cc1, 0x05ccb, 0x05ccd, 0x05ce5, 0x05d05, 0x05d11, 0x05d1d, 0x05d33, 0x05d35, 0x05d47, 0x05d6f, 0x05d87, 0x05d8d, 0x05d95, 0x05d9f, 0x05da3, 0x05da9, 0x05dbb, 0x05dc9, 0x05dcf, 0x05ddb, 0x05de1, 0x05e03, 0x05e0f, 0x05e1b, 0x05e2d, 0x05e47, 0x05e4b, 0x05e63, 0x05e7d, 0x05e81, 0x05e99, 0x05ea5, 0x05ea9, 0x05ed7, 0x05edb, 0x05ee7, 0x05ef5, 0x05f07, 0x05f0d, 0x05f19, 0x05f1f, 0x05f23, 0x05f3d, 0x05f43, 0x05f45, 0x05f51, 0x05f61, 0x05f6b, 0x05f75, 0x05f89, 0x05f97, 0x05fab, 0x05fcd, 0x05fdf, 0x05fe3, 0x05fe5, 0x05ff1, 0x0600b, 0x0600d, 0x06015, 0x0602f, 0x0603d, 0x0604f, 0x06051, 0x06061, 0x06067, 0x0606b, 0x06089, 0x06097, 0x0609d, 0x060a1, 0x060ab, 0x060b3, 0x060b9, 0x060d3, 0x060d5, 0x060f7, 0x06109, 0x06111, 0x0612d, 0x06139, 0x06141, 0x06153, 0x06171, 0x0617d, 0x0619f, 0x061a5, 0x061af, 0x061bb, 0x061db, 0x061ed, 0x061f5, 0x061ff, 0x0622b, 0x06233, 0x06235, 0x06239, 0x06247, 0x0624d, 0x06263, 0x0626f, 0x0627d, 0x0628d, 0x0629f, 0x062a5, 0x062a9, 0x062b1, 0x062b7, 0x062d7, 0x062db, 0x062dd, 0x062eb, 0x062ed, 0x062f3, 0x062ff, 0x06323, 0x06331, 0x06337, 0x0633d, 0x0635b, 0x0636d, 0x06375, 0x06385, 0x06389, 0x06391, 0x063a1, 0x063bf, 0x063ef, 0x063fd, 0x06409, 0x06417, 0x0642d, 0x06441, 0x06447, 0x0644d, 0x06455, 0x0648b, 0x06495, 0x0649f, 0x064a9, 0x064b1, 0x064e7, 0x064f5, 0x06501, 0x0650b, 0x06519, 0x06537, 0x0653b, 0x06543, 0x06545, 0x06549, 0x0655b, 0x06583, 0x06591, 0x065a7, 0x065ad, 0x065b9, 0x065bf, 0x065d3, 0x065d5, 0x065d9, 0x065e5, 0x065ef, 0x065f1, 0x065f7, 0x06601, 0x06607, 0x0660d, 0x06623, 0x0663b, 0x0664f, 0x0665d, 0x0666b, 0x0666d, 0x06673, 0x06683, 0x0668f, 0x06697, 0x066a7, 0x066ab, 0x066b5, 0x066b9, 0x066d9, 0x066df, 0x066e9, 0x06711, 0x0671b, 0x06721, 0x06733, 0x0674b, 0x0675f, 0x06769, 0x06777, 0x06781, 0x067a3, 0x067af, 0x067b7, 0x067d1, 0x067e7, 0x067eb, 0x067f5, 0x06803, 0x06811, 0x0681b, 0x0681d, 0x0682b, 0x06841, 0x06853, 0x0686f, 0x06877, 0x0688b, 0x0688d, 0x06893, 0x0689f, 0x068a5, 0x068a9, 0x068c5, 0x068c9, 0x068ff, 0x06907, 0x06919, 0x0692f, 0x0693d, 0x06957, 0x0696b, 0x06973, 0x06975, 0x06979, 0x06985, 0x0698f, 0x0699b, 0x0699d, 0x069a1, 0x069ab, 0x069c7, 0x069cd, 0x069e9, 0x06a01, 0x06a07, 0x06a0b, 0x06a19, 0x06a23, 0x06a2f, 0x06a51, 0x06a5b, 0x06a67, 0x06a6b, 0x06a6d, 0x06a75, 0x06a83, 0x06a97, 0x06ab3, 0x06ab5, 0x06abf, 0x06ac1, 0x06acb, 0x06acd, 0x06ae9, 0x06aef, 0x06afb, 0x06afd, 0x06b03, 0x06b17, 0x06b2b, 0x06b33, 0x06b39, 0x06b47, 0x06b4b, 0x06b55, 0x06b69, 0x06b7d, 0x06b81, 0x06b8d, 0x06b95, 0x06b9f, 0x06ba3, 0x06ba5, 0x06bb1, 0x06bb7, 0x06bc5, 0x06bd7, 0x06be1, 0x06bed, 0x06bf3, 0x06bf9, 0x06c0b, 0x06c19, 0x06c2f, 0x06c3d, 0x06c45, 0x06c57, 0x06c61, 0x06c73, 0x06cb5, 0x06cb9, 0x06cbf, 0x06cc1, 0x06cc7, 0x06ccb, 0x06ce5, 0x06cf1, 0x06d05, 0x06d09, 0x06d0f, 0x06d17, 0x06d2b, 0x06d53, 0x06d63, 0x06d65, 0x06d69, 0x06d7b, 0x06da3, 0x06db1, 0x06dbb, 0x06dbd, 0x06dc3, 0x06dc5, 0x06ddd, 0x06e09, 0x06e27, 0x06e2d, 0x06e33, 0x06e41, 0x06e4d, 0x06e53, 0x06e6f, 0x06e7b, 0x06e81, 0x06e87, 0x06e95, 0x06eaf, 0x06eb7, 0x06ec3, 0x06edb, 0x06edd, 0x06ef9, 0x06f01, 0x06f15, 0x06f29, 0x06f31, 0x06f3b, 0x06f4f, 0x06f57, 0x06f5b, 0x06f61, 0x06f85, 0x06f91, 0x06f97, 0x06fab, 0x06fb5, 0x06fc7, 0x06fd9, 0x06fdf, 0x06fe9, 0x07005, 0x0701d, 0x0702b, 0x07033, 0x07035, 0x0704b, 0x0707d, 0x07081, 0x0708d, 0x070a9, 0x070b7, 0x070bb, 0x070c9, 0x070cf, 0x070dd, 0x070e1, 0x07113, 0x07115, 0x07119, 0x07123, 0x07131, 0x07137, 0x0713d, 0x0715d, 0x0716b, 0x07189, 0x07197, 0x0719b, 0x071a1, 0x071b5, 0x071bf, 0x071cb, 0x071df, 0x071e5, 0x071f7, 0x071fb, 0x07219, 0x0721f, 0x0722f, 0x07231, 0x0723b, 0x0724f, 0x07261, 0x07267, 0x0728f, 0x072ad, 0x072b3, 0x072c1, 0x072cd, 0x072d3, 0x072df, 0x072e5, 0x072f1, 0x072f7, 0x07303, 0x07309, 0x07327, 0x0732b, 0x07341, 0x07355, 0x07365, 0x0736f, 0x0738d, 0x07393, 0x073a5, 0x073bd, 0x073c9, 0x073d1, 0x073e7, 0x073f3, 0x073f5, 0x073ff, 0x07413, 0x07415, 0x07429, 0x0744f, 0x07457, 0x0745b, 0x0746b, 0x0746d, 0x07483, 0x074ab, 0x074b3, 0x074c7, 0x074cd, 0x074d5, 0x074df, 0x074e9, 0x074fb, 0x074fd, 0x07517, 0x0751b, 0x07521, 0x07535, 0x07541, 0x0754b, 0x07577, 0x0757b, 0x07581, 0x07599, 0x075a3, 0x075bd, 0x075cf, 0x075d1, 0x075eb, 0x075f5, 0x075f9, 0x075ff, 0x0761d, 0x07639, 0x07647, 0x07653, 0x07655, 0x0765f, 0x07663, 0x07665, 0x07669, 0x07687, 0x07695, 0x0769f, 0x076a3, 0x076af, 0x076bb, 0x076c5, 0x076d1, 0x076eb, 0x076f3, 0x076f9, 0x0770b, 0x0772f, 0x07749, 0x07751, 0x07757, 0x0776d, 0x07773, 0x07783, 0x07789, 0x077a7, 0x077ad, 0x077b5, 0x077c7, 0x077d3, 0x077d5, 0x077ef, 0x07815, 0x07825, 0x07831, 0x0783d, 0x0784f, 0x07851, 0x0785b, 0x0786d, 0x078a7, 0x078ad, 0x078b3, 0x078bf, 0x078cb, 0x078cd, 0x078d9, 0x078df, 0x078e9, 0x078ef, 0x07903, 0x0790f, 0x07917, 0x07927, 0x07933, 0x0794d, 0x07959, 0x0796f, 0x07971, 0x0797b, 0x07981, 0x07987, 0x079a5, 0x079b1, 0x079c5, 0x079c9, 0x079d7, 0x079dd, 0x07a03, 0x07a1b, 0x07a27, 0x07a2b, 0x07a35, 0x07a3f, 0x07a4b, 0x07a55, 0x07a77, 0x07a81, 0x07a8d, 0x07aa9, 0x07ab7, 0x07abb, 0x07ac3, 0x07ae1, 0x07af3, 0x07af5, 0x07b0b, 0x07b23, 0x07b3b, 0x07b45, 0x07b4f, 0x07b51, 0x07b5d, 0x07b67, 0x07b79, 0x07b85, 0x07b8f, 0x07ba1, 0x07bab, 0x07bb9, 0x07bd3, 0x07be3, 0x07bf1, 0x07bf7, 0x07c05, 0x07c09, 0x07c27, 0x07c2d, 0x07c59, 0x07c69, 0x07c7d, 0x07c8b, 0x07c93, 0x07c95, 0x07ca3, 0x07cb7, 0x07cc3, 0x07cd1, 0x07cdd, 0x07ceb, 0x07cf9, 0x07cff, 0x07d01, 0x07d15, 0x07d37, 0x07d45, 0x07d49, 0x07d73, 0x07d79, 0x07d8f, 0x07d91, 0x07d97, 0x07da7, 0x07db3, 0x07dc7, 0x07dcd, 0x07dd5, 0x07de9, 0x07dfb, 0x07dfd, 0x07e01, 0x07e0d, 0x07e19, 0x07e2f, 0x07e45, 0x07e61, 0x07e75, 0x07e7f, 0x07e89, 0x07e8f, 0x07e9b, 0x07e9d, 0x07eab, 0x07ebf, 0x07ec7, 0x07ed3, 0x07ee3, 0x07ee5, 0x07f09, 0x07f21, 0x07f3f, 0x07f4d, 0x07f55, 0x07f71, 0x07f8b, 0x07f8d, 0x07f99, 0x07f9f, 0x07fa3, 0x07fb1, 0x07fc3, 0x07fc5, 0x07fd1, 0x07fd7, 0x07fe1, 0x07fe7 };
+const word _irreducible_polynomials_degree_15[2183] = { 2182, 0x08003, 0x08011, 0x08017, 0x0802d, 0x08035, 0x0805f, 0x0806f, 0x08077, 0x08081, 0x08087, 0x08093, 0x080a5, 0x080b1, 0x080bd, 0x080c3, 0x080cf, 0x080dd, 0x080e7, 0x080f5, 0x080ff, 0x08101, 0x08115, 0x08125, 0x08157, 0x0815d, 0x08161, 0x0816d, 0x08179, 0x08185, 0x081a1, 0x081a7, 0x081b9, 0x081cb, 0x081cd, 0x081d5, 0x081df, 0x081fd, 0x08213, 0x0823b, 0x08245, 0x0827f, 0x08289, 0x0828f, 0x0829b, 0x082cb, 0x082d9, 0x082e3, 0x082f1, 0x08317, 0x0831b, 0x0832b, 0x08333, 0x08347, 0x0834d, 0x0835f, 0x08363, 0x08369, 0x08371, 0x0838b, 0x08395, 0x08399, 0x083af, 0x083bb, 0x083bd, 0x083c5, 0x083d1, 0x083f5, 0x08419, 0x08423, 0x0842f, 0x08431, 0x08437, 0x08449, 0x08467, 0x0846d, 0x08479, 0x08483, 0x08485, 0x08497, 0x084a1, 0x084b5, 0x084df, 0x084ef, 0x084f7, 0x084fb, 0x084fd, 0x0851d, 0x08521, 0x08527, 0x08533, 0x08547, 0x0854b, 0x0855f, 0x08571, 0x0857b, 0x08581, 0x0858d, 0x085a3, 0x085b1, 0x085b7, 0x085c5, 0x085c9, 0x085db, 0x085ed, 0x085f3, 0x08609, 0x08611, 0x0861d, 0x0862b, 0x08655, 0x08659, 0x08665, 0x0867d, 0x08681, 0x08693, 0x086a9, 0x086af, 0x086b7, 0x086c3, 0x086db, 0x086f3, 0x086ff, 0x0870b, 0x0870d, 0x08715, 0x0871f, 0x08729, 0x08731, 0x0876b, 0x08785, 0x08789, 0x0878f, 0x0879d, 0x087ab, 0x087ad, 0x087b3, 0x087bf, 0x087df, 0x087e9, 0x087f1, 0x087f7, 0x08801, 0x08807, 0x08825, 0x08837, 0x0883b, 0x08849, 0x0885d, 0x08861, 0x08873, 0x08879, 0x08883, 0x0888f, 0x08891, 0x088b3, 0x088b5, 0x088c7, 0x088d9, 0x08903, 0x08905, 0x08909, 0x08911, 0x08917, 0x08927, 0x08965, 0x0897d, 0x08995, 0x08999, 0x089af, 0x089cf, 0x089d1, 0x089db, 0x089dd, 0x089ed, 0x089ff, 0x08a17, 0x08a39, 0x08a55, 0x08a63, 0x08a65, 0x08a71, 0x08a7b, 0x08a87, 0x08a8b, 0x08a9f, 0x08aaf, 0x08ab1, 0x08add, 0x08b0b, 0x08b0d, 0x08b3b, 0x08b3d, 0x08b43, 0x08b6d, 0x08b73, 0x08b91, 0x08b9d, 0x08bc1, 0x08bcb, 0x08bd5, 0x08bd9, 0x08be5, 0x08bf1, 0x08c21, 0x08c27, 0x08c47, 0x08c55, 0x08c59, 0x08c63, 0x08c69, 0x08c87, 0x08c93, 0x08ca3, 0x08ca9, 0x08cbb, 0x08cc9, 0x08ce1, 0x08ceb, 0x08d01, 0x08d07, 0x08d0b, 0x08d25, 0x08d2f, 0x08d43, 0x08d51, 0x08d5b, 0x08d6d, 0x08d7f, 0x08d85, 0x08d89, 0x08d9b, 0x08da1, 0x08dbf, 0x08dcb, 0x08dcd, 0x08de5, 0x08de9, 0x08def, 0x08df7, 0x08e0b, 0x08e1f, 0x08e3b, 0x08e51, 0x08e57, 0x08e73, 0x08e75, 0x08e8f, 0x08e97, 0x08e9b, 0x08ea1, 0x08ebf, 0x08ec1, 0x08ed3, 0x08edf, 0x08ee5, 0x08efb, 0x08f0f, 0x08f27, 0x08f2b, 0x08f39, 0x08f41, 0x08f53, 0x08f55, 0x08f65, 0x08f77, 0x08f7d, 0x08fa5, 0x08fb7, 0x08fbd, 0x08fc9, 0x08fd1, 0x08fe1, 0x08fe7, 0x0900b, 0x09019, 0x0901f, 0x09025, 0x09037, 0x0903d, 0x09043, 0x09057, 0x09061, 0x0906d, 0x09075, 0x09089, 0x09091, 0x0909b, 0x0909d, 0x090ad, 0x090e3, 0x09105, 0x09109, 0x0910f, 0x09117, 0x0911b, 0x0911d, 0x09141, 0x0914d, 0x09177, 0x0917b, 0x09199, 0x091a3, 0x091a9, 0x091b1, 0x091bd, 0x091cf, 0x091e1, 0x09203, 0x09211, 0x0921b, 0x09221, 0x09227, 0x09233, 0x0923f, 0x0924d, 0x09253, 0x0925f, 0x0927b, 0x09287, 0x09295, 0x092a3, 0x092b7, 0x092c9, 0x092dd, 0x092f5, 0x092f9, 0x09313, 0x09331, 0x09337, 0x09345, 0x09349, 0x09357, 0x09373, 0x0937f, 0x09383, 0x0939d, 0x093a1, 0x093b5, 0x093cb, 0x093df, 0x093ef, 0x093f1, 0x093fb, 0x0940f, 0x0942b, 0x0942d, 0x09435, 0x0944b, 0x09453, 0x09477, 0x0947d, 0x0948b, 0x09493, 0x09499, 0x094a5, 0x094a9, 0x094bb, 0x094c5, 0x094d7, 0x094db, 0x094e1, 0x094e7, 0x094f5, 0x094ff, 0x09507, 0x09515, 0x09529, 0x09531, 0x0953d, 0x09545, 0x09561, 0x0956b, 0x09589, 0x0959b, 0x095ad, 0x095cd, 0x095df, 0x095e3, 0x095e9, 0x09613, 0x09615, 0x0962f, 0x09631, 0x09637, 0x0963d, 0x09643, 0x0965d, 0x09667, 0x09679, 0x09697, 0x096ad, 0x096c1, 0x096cb, 0x096d3, 0x096df, 0x096ef, 0x096fb, 0x09705, 0x0972b, 0x09735, 0x09739, 0x0974d, 0x09763, 0x09795, 0x0979f, 0x097a3, 0x097a5, 0x097a9, 0x097b1, 0x097db, 0x097dd, 0x097e1, 0x097f3, 0x097ff, 0x09809, 0x09821, 0x0982d, 0x09847, 0x09895, 0x09899, 0x098af, 0x098bb, 0x098c3, 0x098c5, 0x098d7, 0x098dd, 0x098e7, 0x098f3, 0x098f9, 0x0990b, 0x09919, 0x09925, 0x09929, 0x0992f, 0x09937, 0x09943, 0x09945, 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0x0e14f, 0x0e151, 0x0e15d, 0x0e167, 0x0e16b, 0x0e17f, 0x0e1b3, 0x0e1d3, 0x0e1d9, 0x0e1ef, 0x0e207, 0x0e20b, 0x0e219, 0x0e223, 0x0e231, 0x0e245, 0x0e24f, 0x0e267, 0x0e279, 0x0e285, 0x0e28f, 0x0e29b, 0x0e29d, 0x0e2a1, 0x0e2ab, 0x0e2ad, 0x0e2bf, 0x0e2c1, 0x0e2d5, 0x0e30f, 0x0e311, 0x0e31b, 0x0e335, 0x0e339, 0x0e359, 0x0e363, 0x0e365, 0x0e377, 0x0e38d, 0x0e393, 0x0e39f, 0x0e3a5, 0x0e3af, 0x0e3b7, 0x0e3c3, 0x0e3db, 0x0e3f3, 0x0e3ff, 0x0e41f, 0x0e431, 0x0e449, 0x0e45b, 0x0e46b, 0x0e46d, 0x0e473, 0x0e479, 0x0e485, 0x0e491, 0x0e497, 0x0e49d, 0x0e4a1, 0x0e4ab, 0x0e4cb, 0x0e4cd, 0x0e4df, 0x0e4f1, 0x0e4fd, 0x0e503, 0x0e505, 0x0e517, 0x0e51b, 0x0e52d, 0x0e533, 0x0e581, 0x0e595, 0x0e5a5, 0x0e5af, 0x0e5e7, 0x0e605, 0x0e621, 0x0e639, 0x0e63f, 0x0e647, 0x0e653, 0x0e669, 0x0e687, 0x0e6bb, 0x0e6bd, 0x0e6d7, 0x0e6dd, 0x0e6eb, 0x0e6f5, 0x0e6f9, 0x0e701, 0x0e719, 0x0e729, 0x0e76d, 0x0e775, 0x0e783, 0x0e78f, 0x0e7a7, 0x0e7ab, 0x0e7ad, 0x0e7b5, 0x0e7cb, 0x0e7d3, 0x0e7d5, 0x0e7e5, 0x0e7f1, 0x0e7f7, 0x0e801, 0x0e82f, 0x0e843, 0x0e84f, 0x0e851, 0x0e85b, 0x0e86d, 0x0e879, 0x0e889, 0x0e891, 0x0e8a7, 0x0e8bf, 0x0e8c1, 0x0e8cb, 0x0e8cd, 0x0e8d3, 0x0e8fb, 0x0e8fd, 0x0e903, 0x0e90f, 0x0e921, 0x0e927, 0x0e92b, 0x0e935, 0x0e959, 0x0e95f, 0x0e963, 0x0e969, 0x0e971, 0x0e98d, 0x0e9b7, 0x0e9c5, 0x0e9cf, 0x0e9d7, 0x0e9ed, 0x0ea09, 0x0ea1b, 0x0ea2d, 0x0ea4b, 0x0ea59, 0x0ea71, 0x0ea7d, 0x0ea81, 0x0ea8d, 0x0eabb, 0x0eac3, 0x0eac9, 0x0ead7, 0x0eaed, 0x0eaff, 0x0eb07, 0x0eb0b, 0x0eb19, 0x0eb23, 0x0eb29, 0x0eb3b, 0x0eb45, 0x0eb57, 0x0eb5d, 0x0eb67, 0x0eb6b, 0x0eb73, 0x0eb75, 0x0eb97, 0x0eb9b, 0x0ebad, 0x0ebb3, 0x0ebcd, 0x0ebd3, 0x0ebd5, 0x0ebe3, 0x0ec09, 0x0ec11, 0x0ec21, 0x0ec35, 0x0ec4b, 0x0ec5f, 0x0ec65, 0x0ec69, 0x0ec7d, 0x0ec93, 0x0ec99, 0x0ecaf, 0x0ecb7, 0x0ecbd, 0x0ecc9, 0x0eccf, 0x0ecff, 0x0ed07, 0x0ed15, 0x0ed23, 0x0ed37, 0x0ed49, 0x0ed5d, 0x0ed61, 0x0ed6b, 0x0ed97, 0x0eda1, 0x0edab, 0x0edb3, 0x0edc7, 0x0edcd, 0x0edd9, 0x0eddf, 0x0edef, 0x0edf1, 0x0edfd, 0x0ee01, 0x0ee0b, 0x0ee0d, 0x0ee1f, 0x0ee29, 0x0ee75, 0x0ee83, 0x0ee89, 0x0ee9d, 0x0eead, 0x0eeb9, 0x0eec7, 0x0eecb, 0x0eed9, 0x0eee3, 0x0eef1, 0x0eef7, 0x0ef0f, 0x0ef21, 0x0ef2d, 0x0ef33, 0x0ef39, 0x0ef4d, 0x0ef77, 0x0ef95, 0x0ef9f, 0x0efb1, 0x0efbb, 0x0efe1, 0x0efe7, 0x0efeb, 0x0eff3, 0x0eff5, 0x0eff9, 0x0f007, 0x0f00d, 0x0f01f, 0x0f029, 0x0f02f, 0x0f045, 0x0f05d, 0x0f085, 0x0f089, 0x0f097, 0x0f0ab, 0x0f0bf, 0x0f0c7, 0x0f0d5, 0x0f0df, 0x0f0f1, 0x0f0f7, 0x0f111, 0x0f11b, 0x0f135, 0x0f141, 0x0f147, 0x0f14b, 0x0f153, 0x0f163, 0x0f171, 0x0f18d, 0x0f193, 0x0f1c5, 0x0f1e1, 0x0f1e7, 0x0f1f3, 0x0f1f5, 0x0f1ff, 0x0f217, 0x0f21d, 0x0f247, 0x0f24d, 0x0f255, 0x0f259, 0x0f26f, 0x0f27b, 0x0f287, 0x0f29f, 0x0f2a5, 0x0f2db, 0x0f2dd, 0x0f2f9, 0x0f2ff, 0x0f301, 0x0f30b, 0x0f315, 0x0f32f, 0x0f337, 0x0f343, 0x0f385, 0x0f389, 0x0f391, 0x0f397, 0x0f3b3, 0x0f3df, 0x0f3e5, 0x0f405, 0x0f40f, 0x0f417, 0x0f421, 0x0f439, 0x0f453, 0x0f455, 0x0f463, 0x0f465, 0x0f469, 0x0f47b, 0x0f48b, 0x0f499, 0x0f4a3, 0x0f4b1, 0x0f4bd, 0x0f4c3, 0x0f4cf, 0x0f4f3, 0x0f4f5, 0x0f4f9, 0x0f50d, 0x0f519, 0x0f525, 0x0f537, 0x0f53b, 0x0f551, 0x0f561, 0x0f56d, 0x0f591, 0x0f59d, 0x0f5a7, 0x0f5b5, 0x0f5bf, 0x0f5c1, 0x0f5c7, 0x0f601, 0x0f615, 0x0f61f, 0x0f623, 0x0f63b, 0x0f645, 0x0f64f, 0x0f65d, 0x0f66b, 0x0f673, 0x0f683, 0x0f685, 0x0f6b3, 0x0f6b5, 0x0f6d9, 0x0f6ef, 0x0f6fb, 0x0f721, 0x0f72d, 0x0f73f, 0x0f74d, 0x0f753, 0x0f769, 0x0f76f, 0x0f787, 0x0f78b, 0x0f795, 0x0f7a3, 0x0f7b1, 0x0f7b7, 0x0f7c3, 0x0f7c9, 0x0f7db, 0x0f7ff, 0x0f803, 0x0f809, 0x0f80f, 0x0f81d, 0x0f827, 0x0f82d, 0x0f839, 0x0f83f, 0x0f84b, 0x0f86f, 0x0f871, 0x0f877, 0x0f893, 0x0f8c5, 0x0f8db, 0x0f8e1, 0x0f8ed, 0x0f8f3, 0x0f8f5, 0x0f907, 0x0f915, 0x0f923, 0x0f93b, 0x0f93d, 0x0f94f, 0x0f951, 0x0f973, 0x0f979, 0x0f985, 0x0f99b, 0x0f9b3, 0x0f9b9, 0x0f9c7, 0x0f9e3, 0x0f9e9, 0x0f9f7, 0x0fa01, 0x0fa07, 0x0fa13, 0x0fa23, 0x0fa37, 0x0fa49, 0x0fa6b, 0x0fa75, 0x0fa79, 0x0fa7f, 0x0fa83, 0x0fa97, 0x0fa9b, 0x0faa1, 0x0fac1, 0x0facb, 0x0fad9, 0x0fadf, 0x0fae5, 0x0fb05, 0x0fb0f, 0x0fb21, 0x0fb27, 0x0fb35, 0x0fb4d, 0x0fb55, 0x0fb5f, 0x0fb69, 0x0fb71, 0x0fb81, 0x0fb8d, 0x0fba3, 0x0fba9, 0x0fbb7, 0x0fbc9, 0x0fbcf, 0x0fbdb, 0x0fbe1, 0x0fc0b, 0x0fc0d, 0x0fc1f, 0x0fc49, 0x0fc5b, 0x0fc67, 0x0fc75, 0x0fc83, 0x0fcad, 0x0fcd3, 0x0fcef, 0x0fd0f, 0x0fd17, 0x0fd1d, 0x0fd2b, 0x0fd2d, 0x0fd39, 0x0fd47, 0x0fd53, 0x0fd71, 0x0fd8b, 0x0fd95, 0x0fd99, 0x0fda3, 0x0fdaf, 0x0fdb1, 0x0fdc3, 0x0fddd, 0x0fde1, 0x0fdeb, 0x0fe05, 0x0fe2d, 0x0fe33, 0x0fe35, 0x0fe41, 0x0fe4d, 0x0fe59, 0x0fe5f, 0x0fe7d, 0x0fe87, 0x0fe93, 0x0fe99, 0x0feb1, 0x0febd, 0x0fec9, 0x0feeb, 0x0feff, 0x0ff01, 0x0ff07, 0x0ff13, 0x0ff23, 0x0ff29, 0x0ff37, 0x0ff4f, 0x0ff57, 0x0ff5d, 0x0ff61, 0x0ff73, 0x0ff7f, 0x0ff8f, 0x0ff91, 0x0ffb3, 0x0ffc7, 0x0ffd9, 0x0ffe9, 0x0ffef, 0x0fffd };
+const word _irreducible_polynomials_degree_16[4081] = { 4080, 0x1002b, 0x1002d, 0x10039, 0x1003f, 0x10047, 0x10053, 0x1008d, 0x100bd, 0x100d7, 0x100f5, 0x10129, 0x1012f, 0x1013b, 0x1013d, 0x1014f, 0x1015d, 0x10173, 0x10175, 0x1018f, 0x10197, 0x101a1, 0x101ad, 0x101bf, 0x101c7, 0x101cd, 0x101d5, 0x101e9, 0x101f7, 0x10215, 0x10219, 0x10225, 0x1022f, 0x1025b, 0x1025d, 0x1026b, 0x1026d, 0x10275, 0x10285, 0x10291, 0x102a1, 0x102b3, 0x102cd, 0x102d3, 0x102e5, 0x102f7, 0x102fb, 0x10317, 0x1031d, 0x10335, 0x10339, 0x1034b, 0x1034d, 0x10369, 0x1036f, 0x10371, 0x10387, 0x1038d, 0x1039f, 0x103a3, 0x103bb, 0x103cf, 0x103dd, 0x103ed, 0x103f9, 0x1040b, 0x10425, 0x10429, 0x10457, 0x10461, 0x10467, 0x1046d, 0x10483, 0x10489, 0x10491, 0x104a7, 0x104ad, 0x104b5, 0x104bf, 0x104c1, 0x104fd, 0x10509, 0x10533, 0x10539, 0x10547, 0x10563, 0x10565, 0x10569, 0x10587, 0x105af, 0x105c3, 0x105cf, 0x105d1, 0x105dd, 0x105eb, 0x105f5, 0x105f9, 0x10641, 0x1064b, 0x10653, 0x1065f, 0x1067b, 0x1067d, 0x10687, 0x1068b, 0x106a3, 0x106af, 0x106c3, 0x106c9, 0x106f5, 0x106ff, 0x1076b, 0x1076d, 0x10779, 0x1077f, 0x10783, 0x1078f, 0x10797, 0x107ef, 0x107f1, 0x107fb, 0x10807, 0x1080b, 0x1080d, 0x10815, 0x1083b, 0x10861, 0x10879, 0x10897, 0x1089d, 0x108ab, 0x108bf, 0x108d5, 0x108df, 0x108e3, 0x108e9, 0x108f1, 0x108fb, 0x10939, 0x10959, 0x10977, 0x1097d, 0x1098b, 0x109a5, 0x109af, 0x109c3, 0x109c5, 0x109e1, 0x109e7, 0x109ed, 0x109f3, 0x10a03, 0x10a11, 0x10a35, 0x10a39, 0x10a5f, 0x10a63, 0x10a71, 0x10a7d, 0x10a81, 0x10a9f, 0x10abb, 0x10ac5, 0x10acf, 0x10add, 0x10ae1, 0x10aff, 0x10b01, 0x10b13, 0x10b15, 0x10b51, 0x10b5d, 0x10b91, 0x10b97, 0x10bb3, 0x10bcd, 0x10bd3, 0x10be5, 0x10bef, 0x10bf7, 0x10bfd, 0x10c0f, 0x10c1d, 0x10c21, 0x10c2b, 0x10c41, 0x10c69, 0x10c71, 0x10c7b, 0x10c8d, 0x10c95, 0x10ca3, 0x10caf, 0x10cbd, 0x10cdd, 0x10ceb, 0x10cf3, 0x10d0d, 0x10d19, 0x10d1f, 0x10d43, 0x10d49, 0x10d83, 0x10d8f, 0x10d91, 0x10d9d, 0x10dad, 0x10db5, 0x10dd3, 0x10de3, 0x10de5, 0x10e23, 0x10e45, 0x10e73, 0x10e7f, 0x10e85, 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0x1e5e5, 0x1e5fb, 0x1e607, 0x1e60b, 0x1e62f, 0x1e631, 0x1e63d, 0x1e643, 0x1e64f, 0x1e66b, 0x1e685, 0x1e689, 0x1e697, 0x1e69d, 0x1e6a1, 0x1e6ad, 0x1e6b9, 0x1e6d5, 0x1e6e3, 0x1e6f1, 0x1e6f7, 0x1e709, 0x1e71b, 0x1e72d, 0x1e735, 0x1e73f, 0x1e741, 0x1e74b, 0x1e755, 0x1e763, 0x1e76f, 0x1e777, 0x1e781, 0x1e78b, 0x1e793, 0x1e79f, 0x1e7a5, 0x1e7af, 0x1e7bb, 0x1e7e1, 0x1e817, 0x1e833, 0x1e85f, 0x1e86f, 0x1e877, 0x1e87d, 0x1e881, 0x1e895, 0x1e899, 0x1e8a5, 0x1e8cf, 0x1e8d1, 0x1e8ed, 0x1e901, 0x1e923, 0x1e925, 0x1e929, 0x1e93b, 0x1e957, 0x1e96b, 0x1e973, 0x1e97f, 0x1e98f, 0x1e997, 0x1e9cd, 0x1e9e3, 0x1e9ef, 0x1e9f1, 0x1e9fb, 0x1e9fd, 0x1ea13, 0x1ea19, 0x1ea1f, 0x1ea29, 0x1ea43, 0x1ea51, 0x1ea61, 0x1ea89, 0x1ea91, 0x1ea9d, 0x1eaa7, 0x1eab9, 0x1eac1, 0x1eac7, 0x1ead5, 0x1eae5, 0x1eaef, 0x1eaf7, 0x1eafd, 0x1eb05, 0x1eb1b, 0x1eb21, 0x1eb2b, 0x1eb2d, 0x1eb41, 0x1eb55, 0x1eb7b, 0x1eb9f, 0x1eba9, 0x1ebb1, 0x1ebc3, 0x1ebc5, 0x1ebcf, 0x1ebeb, 0x1ec0b, 0x1ec2f, 0x1ec31, 0x1ec43, 0x1ec4f, 0x1ec5b, 0x1ec5d, 0x1ec67, 0x1ec6d, 0x1ec79, 0x1ec97, 0x1ecad, 0x1ecb3, 0x1ecb5, 0x1eccb, 0x1ecd9, 0x1ece5, 0x1ece9, 0x1ecfb, 0x1ed03, 0x1ed11, 0x1ed1d, 0x1ed27, 0x1ed39, 0x1ed5f, 0x1ed6f, 0x1ed81, 0x1ed95, 0x1ed9f, 0x1eda9, 0x1edbb, 0x1edcf, 0x1eddb, 0x1edf3, 0x1ee1b, 0x1ee27, 0x1ee2b, 0x1ee35, 0x1ee53, 0x1ee63, 0x1ee71, 0x1ee99, 0x1eeaf, 0x1eeb7, 0x1eebd, 0x1eedb, 0x1eee7, 0x1eeed, 0x1eef3, 0x1ef0d, 0x1ef23, 0x1ef2f, 0x1ef3d, 0x1ef57, 0x1ef67, 0x1ef73, 0x1ef79, 0x1ef85, 0x1ef97, 0x1efa1, 0x1efab, 0x1efad, 0x1efb3, 0x1efb9, 0x1efc1, 0x1efdf, 0x1efe3, 0x1eff7, 0x1f009, 0x1f02d, 0x1f039, 0x1f04d, 0x1f055, 0x1f05f, 0x1f065, 0x1f069, 0x1f087, 0x1f095, 0x1f0af, 0x1f0bd, 0x1f0d1, 0x1f0f9, 0x1f10b, 0x1f113, 0x1f137, 0x1f13b, 0x1f145, 0x1f157, 0x1f161, 0x1f175, 0x1f189, 0x1f18f, 0x1f1a7, 0x1f1ab, 0x1f1bf, 0x1f1cb, 0x1f1d3, 0x1f1e3, 0x1f207, 0x1f20d, 0x1f215, 0x1f229, 0x1f245, 0x1f249, 0x1f27f, 0x1f283, 0x1f297, 0x1f2a1, 0x1f2ab, 0x1f2b9, 0x1f2d5, 0x1f2df, 0x1f2f1, 0x1f317, 0x1f32d, 0x1f335, 0x1f359, 0x1f369, 0x1f36f, 0x1f381, 0x1f387, 0x1f393, 0x1f395, 0x1f399, 0x1f3a3, 0x1f3af, 0x1f3cf, 0x1f3f9, 0x1f41f, 0x1f423, 0x1f42f, 0x1f43b, 0x1f43d, 0x1f451, 0x1f457, 0x1f46b, 0x1f489, 0x1f48f, 0x1f49d, 0x1f4a1, 0x1f4c1, 0x1f4d3, 0x1f4e9, 0x1f4f1, 0x1f4fb, 0x1f511, 0x1f51b, 0x1f51d, 0x1f527, 0x1f539, 0x1f553, 0x1f565, 0x1f56f, 0x1f571, 0x1f58b, 0x1f5c5, 0x1f5d7, 0x1f5ff, 0x1f60f, 0x1f621, 0x1f627, 0x1f62b, 0x1f635, 0x1f639, 0x1f655, 0x1f687, 0x1f693, 0x1f69f, 0x1f6a5, 0x1f6c5, 0x1f6dd, 0x1f6eb, 0x1f6f3, 0x1f6f9, 0x1f707, 0x1f715, 0x1f725, 0x1f743, 0x1f74f, 0x1f751, 0x1f767, 0x1f76b, 0x1f775, 0x1f783, 0x1f791, 0x1f7b3, 0x1f7b5, 0x1f7bf, 0x1f7cd, 0x1f7e9, 0x1f7ef, 0x1f7fb, 0x1f801, 0x1f825, 0x1f83d, 0x1f849, 0x1f857, 0x1f873, 0x1f8ad, 0x1f8bf, 0x1f8cb, 0x1f8d9, 0x1f8e3, 0x1f8f1, 0x1f905, 0x1f939, 0x1f93f, 0x1f94d, 0x1f953, 0x1f971, 0x1f977, 0x1f97b, 0x1f9bb, 0x1f9cf, 0x1f9d1, 0x1f9dd, 0x1f9e7, 0x1f9f5, 0x1fa17, 0x1fa21, 0x1fa27, 0x1fa3f, 0x1fa41, 0x1fa4b, 0x1fa59, 0x1fa7d, 0x1fa8b, 0x1fa93, 0x1fa95, 0x1faa5, 0x1fab1, 0x1fadb, 0x1fae7, 0x1faeb, 0x1fb01, 0x1fb1f, 0x1fb49, 0x1fb4f, 0x1fb57, 0x1fb5b, 0x1fb6d, 0x1fb7f, 0x1fb83, 0x1fb85, 0x1fb97, 0x1fb9d, 0x1fba7, 0x1fbab, 0x1fbc7, 0x1fbcb, 0x1fbcd, 0x1fbdf, 0x1fbe9, 0x1fbf1, 0x1fc0f, 0x1fc11, 0x1fc1b, 0x1fc2d, 0x1fc47, 0x1fc55, 0x1fc59, 0x1fc63, 0x1fc71, 0x1fc77, 0x1fc7d, 0x1fc8d, 0x1fc9f, 0x1fca9, 0x1fcbd, 0x1fcc9, 0x1fcdb, 0x1fce1, 0x1fce7, 0x1fced, 0x1fd07, 0x1fd0d, 0x1fd23, 0x1fd29, 0x1fd2f, 0x1fd3d, 0x1fd43, 0x1fd4f, 0x1fd57, 0x1fd73, 0x1fd75, 0x1fd85, 0x1fd97, 0x1fd9b, 0x1fdb3, 0x1fdbf, 0x1fdc1, 0x1fdd3, 0x1fde9, 0x1fdfb, 0x1fe15, 0x1fe25, 0x1fe31, 0x1fe37, 0x1fe49, 0x1fe67, 0x1fe79, 0x1fe83, 0x1fe91, 0x1fea1, 0x1fec1, 0x1fee5, 0x1fee9, 0x1fefb, 0x1fefd, 0x1ff05, 0x1ff33, 0x1ff35, 0x1ff39, 0x1ff5f, 0x1ff71, 0x1ff93, 0x1ffa5, 0x1ffb1, 0x1ffeb, 0x1ffed };
+
+const word* irreducible_polynomials[17] = {NULL, NULL,
+ _irreducible_polynomials_degree_02, _irreducible_polynomials_degree_03,
+ _irreducible_polynomials_degree_04, _irreducible_polynomials_degree_05,
+ _irreducible_polynomials_degree_06, _irreducible_polynomials_degree_07,
+ _irreducible_polynomials_degree_08, _irreducible_polynomials_degree_09,
+ _irreducible_polynomials_degree_10, _irreducible_polynomials_degree_11,
+ _irreducible_polynomials_degree_12, _irreducible_polynomials_degree_13,
+ _irreducible_polynomials_degree_14, _irreducible_polynomials_degree_15,
+ _irreducible_polynomials_degree_16};
diff --git a/src/gf2e.h b/src/gf2e.h
index f3c0dec..2906b31 100644
--- a/src/gf2e.h
+++ b/src/gf2e.h
@@ -11,6 +11,104 @@
#include <m4ri/m4ri.h>
+#define M4RIE_MAX_DEGREE 10
+
+/**
+ * \brief Multiplication in GF(2)[x] where a,b have a degree smaller than d <= 16.
+ */
+
+static inline word gf2x_mul(const word a, const word b, unsigned int d) {
+ /* double check that integer multiplication is indeed not horribly slow here */
+ word res = 0;
+
+ switch(d) {
+ case 16: res ^= ((a&(1<<15))>>15) * (b<<15);
+ case 15: res ^= ((a&(1<<14))>>14) * (b<<14);
+ case 14: res ^= ((a&(1<<13))>>13) * (b<<13);
+ case 13: res ^= ((a&(1<<12))>>12) * (b<<12);
+ case 12: res ^= ((a&(1<<11))>>11) * (b<<11);
+ case 11: res ^= ((a&(1<<10))>>10) * (b<<10);
+ case 10: res ^= ((a&(1<< 9))>> 9) * (b<< 9);
+ case 9: res ^= ((a&(1<< 8))>> 8) * (b<< 8);
+ case 8: res ^= ((a&(1<< 7))>> 7) * (b<< 7);
+ case 7: res ^= ((a&(1<< 6))>> 6) * (b<< 6);
+ case 6: res ^= ((a&(1<< 5))>> 5) * (b<< 5);
+ case 5: res ^= ((a&(1<< 4))>> 4) * (b<< 4);
+ case 4: res ^= ((a&(1<< 3))>> 3) * (b<< 3);
+ case 3: res ^= ((a&(1<< 2))>> 2) * (b<< 2);
+ case 2: res ^= ((a&(1<< 1))>> 1) * (b<< 1);
+ case 1: res ^= ((a&(1<< 0))>> 0) * (b<< 0);
+ break;
+ default:
+ m4ri_die("degree %d not supported.",d);
+ }
+ return res;
+}
+
+/**
+ * \brief Degree of elements in GF(2)[x].
+ */
+
+static inline unsigned int gf2x_deg(word a) {
+ unsigned int 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 Division in GF(2)[x].
+ */
+
+static inline word gf2x_div(word a, word b) {
+ word res = 0;
+ while(a >= b) {
+ unsigned int diff = gf2x_deg(a) - gf2x_deg(b);
+ res |= __M4RI_TWOPOW(diff);
+ a ^= b<<diff;
+ }
+ return res;
+}
+
+/**
+ * \brief Remainders in GF(2)[x].
+ */
+
+static inline word gf2x_mod(word a, word b) {
+ word res = 0;
+ while(a >= b) {
+ unsigned int diff = gf2x_deg(a) - gf2x_deg(b);
+ res |= __M4RI_TWOPOW(diff);
+ a ^= b<<diff;
+ }
+ return a;
+}
+
+/**
+ * \brief a^(-1) % b.
+ */
+
+static inline word gf2x_invmod(word a, word b, unsigned int d) {
+ word x = 0;
+ word lastx = 1;
+ word y = 1;
+ word lasty = 0;
+
+ word tmp = 0;
+
+ while (b != 0) {
+ word quotient = gf2x_div(a,b);
+ tmp = b; b = gf2x_mod(a, b); a = tmp;
+ tmp = x; x = lastx ^ gf2x_mul(quotient, x, d); lastx = tmp;
+ tmp = y; y = lasty ^ gf2x_mul(quotient, y, d); lasty = tmp;
+ }
+ return lastx;
+}
+
/**
* \brief \GF2E
*/
@@ -18,14 +116,24 @@
typedef struct {
unsigned int degree; /**< The degree \e. */
word minpoly; /**< Irreducible polynomial of degree \e. */
+
+ word *inv; /**< inv[a] holds \f$a^{-1}\f$. */
+ word *pow_gen; /**< pow_gen[i] holds \f$a^i / <f>\f$ for \f$a\f$ a generator of this field. */
+
word **mul; /**<
* mul[a][b] holds \f$ a \cdot b\f$.
* \warning this entry will disappear in future releases. */
- word *inv; /**< inv[a] holds \f$a^{-1}\f$. */
- word *pow_gen; /**< pow_gen[i] holds \f$a^i / <f>\f$ for \f$a\f$ a generator of this field. */
} 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.
@@ -67,6 +175,26 @@ static inline size_t gf2e_degree_to_w(const gf2e *ff) {
}
/**
+ * Generate gf2e::pow_gen.
+ *
+ * \param ff Finite field.
+ */
+
+static inline void gf2e_make_pow_gen(gf2e *ff) {
+ unsigned int n = 2*ff->degree-1;
+ word *m = (word*)m4ri_mm_malloc( n * sizeof(word));
+ for(unsigned int i=0; i<n; i++) {
+ m[i] = 1<<i;
+ for(unsigned int j=i; j>=ff->degree; j--) {
+ if (m[i] & 1<<j)
+ m[i] ^= ff->minpoly<<(j - ff->degree);
+ }
+ }
+ ff->pow_gen = m;
+}
+
+
+/**
* Compute all multiples by a of vectors fitting into 16 bits.
*
* \param ff Finite field.
@@ -113,23 +241,6 @@ static inline void gf2e_t16_free(word *mul) {
m4ri_mm_free(mul);
}
-/**
- * Generate gf2e::pow_gen.
- *
- * \param ff Finite field.
- */
-
-static inline void gf2e_make_pow_gen(gf2e *ff) {
- unsigned int n = 2*ff->degree-1;
- word *m = (word*)m4ri_mm_malloc( n * sizeof(word));
- for(unsigned int i=0; i<n; i++) {
- m[i] = 1<<i;
- for(unsigned int j=i; j>=ff->degree; j--) {
- if (m[i] & 1<<j)
- m[i] ^= ff->minpoly<<(j - ff->degree);
- }
- }
- ff->pow_gen = m;
-}
+extern const word* irreducible_polynomials[17];
#endif //M4RIE_GF2E_H
diff --git a/src/mzd_slice.c b/src/mzd_slice.c
index 3e0b698..1602758 100644
--- a/src/mzd_slice.c
+++ b/src/mzd_slice.c
@@ -23,7 +23,7 @@
/**
* \brief Add A to coefficient of X^t but perform modular reductions on the fly.
*
- * B[0] += (A*X^t % minpoly)[0] , ..., B[degree-1] += (A*X^t % minpoly)[degree-1]
+ * (A + X^t % minpoly)
*
* \param ff Finite field
* \param A Matrix
diff --git a/tests/testing.h b/tests/testing.h
index b2a6001..ea2669d 100644
--- a/tests/testing.h
+++ b/tests/testing.h
@@ -92,7 +92,7 @@ static inline int mzed_interval_clean(mzed_t *A) {
return 0;
}
return 1;
-};
+}
static inline void mzd_slice_set_canary(mzd_slice_t *A) {
const word mask_begin = __M4RI_RIGHT_BITMASK(m4ri_radix - A->x[0]->offset);
@@ -144,7 +144,7 @@ static inline int mzd_slice_canary_is_alive(mzd_slice_t *A) {
}
return 1;
}
-};
+}
static inline mzed_t *random_mzed_t(gf2e *ff, int m, int n) {
mzed_t *A = mzed_init(ff,m,n);
--
Fast arithmetic with dense matrices over F_{2^e}
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