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fecpp.cpp
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/*
* Forward error correction based on Vandermonde matrices
*
* (C) 1997-1998 Luigi Rizzo ([email protected])
* (C) 2009-2010 Jack Lloyd ([email protected])
* (C) 2011 Billy Brumley ([email protected])
*
* Distributed under the terms given in license.txt
*/
#include "fecpp.h"
#include <stdexcept>
#include <vector>
#include <cstring>
#define FECPP_USE_SSSE3
//#define FECPP_USE_SSE2
#if defined (FECPP_USE_SSE2)
#include <emmintrin.h>
#include <stdint.h>
#elif defined (FECPP_USE_SSSE3)
#include <tmmintrin.h>
#include <stdint.h>
#endif
namespace fecpp {
namespace {
/* Tables for arithetic in GF(2^8) using 1+x^2+x^3+x^4+x^8
*
* See Lin & Costello, Appendix A, and Lee & Messerschmitt, p. 453.
*
* Generate GF(2**m) from the irreducible polynomial p(X) in p[0]..p[m]
* Lookup tables:
* index->polynomial form gf_exp[] contains j= \alpha^i;
* polynomial form -> index form gf_log[ j = \alpha^i ] = i
* \alpha=x is the primitive element of GF(2^m)
*
* For efficiency, gf_exp[] has size 2*GF_SIZE, so that a simple
* multiplication of two numbers can be resolved without calling mod
*/
const byte GF_EXP[510] = {
0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80, 0x1D, 0x3A, 0x74,
0xE8, 0xCD, 0x87, 0x13, 0x26, 0x4C, 0x98, 0x2D, 0x5A, 0xB4, 0x75,
0xEA, 0xC9, 0x8F, 0x03, 0x06, 0x0C, 0x18, 0x30, 0x60, 0xC0, 0x9D,
0x27, 0x4E, 0x9C, 0x25, 0x4A, 0x94, 0x35, 0x6A, 0xD4, 0xB5, 0x77,
0xEE, 0xC1, 0x9F, 0x23, 0x46, 0x8C, 0x05, 0x0A, 0x14, 0x28, 0x50,
0xA0, 0x5D, 0xBA, 0x69, 0xD2, 0xB9, 0x6F, 0xDE, 0xA1, 0x5F, 0xBE,
0x61, 0xC2, 0x99, 0x2F, 0x5E, 0xBC, 0x65, 0xCA, 0x89, 0x0F, 0x1E,
0x3C, 0x78, 0xF0, 0xFD, 0xE7, 0xD3, 0xBB, 0x6B, 0xD6, 0xB1, 0x7F,
0xFE, 0xE1, 0xDF, 0xA3, 0x5B, 0xB6, 0x71, 0xE2, 0xD9, 0xAF, 0x43,
0x86, 0x11, 0x22, 0x44, 0x88, 0x0D, 0x1A, 0x34, 0x68, 0xD0, 0xBD,
0x67, 0xCE, 0x81, 0x1F, 0x3E, 0x7C, 0xF8, 0xED, 0xC7, 0x93, 0x3B,
0x76, 0xEC, 0xC5, 0x97, 0x33, 0x66, 0xCC, 0x85, 0x17, 0x2E, 0x5C,
0xB8, 0x6D, 0xDA, 0xA9, 0x4F, 0x9E, 0x21, 0x42, 0x84, 0x15, 0x2A,
0x54, 0xA8, 0x4D, 0x9A, 0x29, 0x52, 0xA4, 0x55, 0xAA, 0x49, 0x92,
0x39, 0x72, 0xE4, 0xD5, 0xB7, 0x73, 0xE6, 0xD1, 0xBF, 0x63, 0xC6,
0x91, 0x3F, 0x7E, 0xFC, 0xE5, 0xD7, 0xB3, 0x7B, 0xF6, 0xF1, 0xFF,
0xE3, 0xDB, 0xAB, 0x4B, 0x96, 0x31, 0x62, 0xC4, 0x95, 0x37, 0x6E,
0xDC, 0xA5, 0x57, 0xAE, 0x41, 0x82, 0x19, 0x32, 0x64, 0xC8, 0x8D,
0x07, 0x0E, 0x1C, 0x38, 0x70, 0xE0, 0xDD, 0xA7, 0x53, 0xA6, 0x51,
0xA2, 0x59, 0xB2, 0x79, 0xF2, 0xF9, 0xEF, 0xC3, 0x9B, 0x2B, 0x56,
0xAC, 0x45, 0x8A, 0x09, 0x12, 0x24, 0x48, 0x90, 0x3D, 0x7A, 0xF4,
0xF5, 0xF7, 0xF3, 0xFB, 0xEB, 0xCB, 0x8B, 0x0B, 0x16, 0x2C, 0x58,
0xB0, 0x7D, 0xFA, 0xE9, 0xCF, 0x83, 0x1B, 0x36, 0x6C, 0xD8, 0xAD,
0x47, 0x8E,
0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80, 0x1D, 0x3A, 0x74,
0xE8, 0xCD, 0x87, 0x13, 0x26, 0x4C, 0x98, 0x2D, 0x5A, 0xB4, 0x75,
0xEA, 0xC9, 0x8F, 0x03, 0x06, 0x0C, 0x18, 0x30, 0x60, 0xC0, 0x9D,
0x27, 0x4E, 0x9C, 0x25, 0x4A, 0x94, 0x35, 0x6A, 0xD4, 0xB5, 0x77,
0xEE, 0xC1, 0x9F, 0x23, 0x46, 0x8C, 0x05, 0x0A, 0x14, 0x28, 0x50,
0xA0, 0x5D, 0xBA, 0x69, 0xD2, 0xB9, 0x6F, 0xDE, 0xA1, 0x5F, 0xBE,
0x61, 0xC2, 0x99, 0x2F, 0x5E, 0xBC, 0x65, 0xCA, 0x89, 0x0F, 0x1E,
0x3C, 0x78, 0xF0, 0xFD, 0xE7, 0xD3, 0xBB, 0x6B, 0xD6, 0xB1, 0x7F,
0xFE, 0xE1, 0xDF, 0xA3, 0x5B, 0xB6, 0x71, 0xE2, 0xD9, 0xAF, 0x43,
0x86, 0x11, 0x22, 0x44, 0x88, 0x0D, 0x1A, 0x34, 0x68, 0xD0, 0xBD,
0x67, 0xCE, 0x81, 0x1F, 0x3E, 0x7C, 0xF8, 0xED, 0xC7, 0x93, 0x3B,
0x76, 0xEC, 0xC5, 0x97, 0x33, 0x66, 0xCC, 0x85, 0x17, 0x2E, 0x5C,
0xB8, 0x6D, 0xDA, 0xA9, 0x4F, 0x9E, 0x21, 0x42, 0x84, 0x15, 0x2A,
0x54, 0xA8, 0x4D, 0x9A, 0x29, 0x52, 0xA4, 0x55, 0xAA, 0x49, 0x92,
0x39, 0x72, 0xE4, 0xD5, 0xB7, 0x73, 0xE6, 0xD1, 0xBF, 0x63, 0xC6,
0x91, 0x3F, 0x7E, 0xFC, 0xE5, 0xD7, 0xB3, 0x7B, 0xF6, 0xF1, 0xFF,
0xE3, 0xDB, 0xAB, 0x4B, 0x96, 0x31, 0x62, 0xC4, 0x95, 0x37, 0x6E,
0xDC, 0xA5, 0x57, 0xAE, 0x41, 0x82, 0x19, 0x32, 0x64, 0xC8, 0x8D,
0x07, 0x0E, 0x1C, 0x38, 0x70, 0xE0, 0xDD, 0xA7, 0x53, 0xA6, 0x51,
0xA2, 0x59, 0xB2, 0x79, 0xF2, 0xF9, 0xEF, 0xC3, 0x9B, 0x2B, 0x56,
0xAC, 0x45, 0x8A, 0x09, 0x12, 0x24, 0x48, 0x90, 0x3D, 0x7A, 0xF4,
0xF5, 0xF7, 0xF3, 0xFB, 0xEB, 0xCB, 0x8B, 0x0B, 0x16, 0x2C, 0x58,
0xB0, 0x7D, 0xFA, 0xE9, 0xCF, 0x83, 0x1B, 0x36, 0x6C, 0xD8, 0xAD,
0x47, 0x8E };
const byte GF_LOG[256] = {
0xFF, 0x00, 0x01, 0x19, 0x02, 0x32, 0x1A, 0xC6, 0x03, 0xDF, 0x33,
0xEE, 0x1B, 0x68, 0xC7, 0x4B, 0x04, 0x64, 0xE0, 0x0E, 0x34, 0x8D,
0xEF, 0x81, 0x1C, 0xC1, 0x69, 0xF8, 0xC8, 0x08, 0x4C, 0x71, 0x05,
0x8A, 0x65, 0x2F, 0xE1, 0x24, 0x0F, 0x21, 0x35, 0x93, 0x8E, 0xDA,
0xF0, 0x12, 0x82, 0x45, 0x1D, 0xB5, 0xC2, 0x7D, 0x6A, 0x27, 0xF9,
0xB9, 0xC9, 0x9A, 0x09, 0x78, 0x4D, 0xE4, 0x72, 0xA6, 0x06, 0xBF,
0x8B, 0x62, 0x66, 0xDD, 0x30, 0xFD, 0xE2, 0x98, 0x25, 0xB3, 0x10,
0x91, 0x22, 0x88, 0x36, 0xD0, 0x94, 0xCE, 0x8F, 0x96, 0xDB, 0xBD,
0xF1, 0xD2, 0x13, 0x5C, 0x83, 0x38, 0x46, 0x40, 0x1E, 0x42, 0xB6,
0xA3, 0xC3, 0x48, 0x7E, 0x6E, 0x6B, 0x3A, 0x28, 0x54, 0xFA, 0x85,
0xBA, 0x3D, 0xCA, 0x5E, 0x9B, 0x9F, 0x0A, 0x15, 0x79, 0x2B, 0x4E,
0xD4, 0xE5, 0xAC, 0x73, 0xF3, 0xA7, 0x57, 0x07, 0x70, 0xC0, 0xF7,
0x8C, 0x80, 0x63, 0x0D, 0x67, 0x4A, 0xDE, 0xED, 0x31, 0xC5, 0xFE,
0x18, 0xE3, 0xA5, 0x99, 0x77, 0x26, 0xB8, 0xB4, 0x7C, 0x11, 0x44,
0x92, 0xD9, 0x23, 0x20, 0x89, 0x2E, 0x37, 0x3F, 0xD1, 0x5B, 0x95,
0xBC, 0xCF, 0xCD, 0x90, 0x87, 0x97, 0xB2, 0xDC, 0xFC, 0xBE, 0x61,
0xF2, 0x56, 0xD3, 0xAB, 0x14, 0x2A, 0x5D, 0x9E, 0x84, 0x3C, 0x39,
0x53, 0x47, 0x6D, 0x41, 0xA2, 0x1F, 0x2D, 0x43, 0xD8, 0xB7, 0x7B,
0xA4, 0x76, 0xC4, 0x17, 0x49, 0xEC, 0x7F, 0x0C, 0x6F, 0xF6, 0x6C,
0xA1, 0x3B, 0x52, 0x29, 0x9D, 0x55, 0xAA, 0xFB, 0x60, 0x86, 0xB1,
0xBB, 0xCC, 0x3E, 0x5A, 0xCB, 0x59, 0x5F, 0xB0, 0x9C, 0xA9, 0xA0,
0x51, 0x0B, 0xF5, 0x16, 0xEB, 0x7A, 0x75, 0x2C, 0xD7, 0x4F, 0xAE,
0xD5, 0xE9, 0xE6, 0xE7, 0xAD, 0xE8, 0x74, 0xD6, 0xF4, 0xEA, 0xA8,
0x50, 0x58, 0xAF };
const byte GF_INVERSE[256] = {
0x00, 0x01, 0x8E, 0xF4, 0x47, 0xA7, 0x7A, 0xBA, 0xAD, 0x9D, 0xDD,
0x98, 0x3D, 0xAA, 0x5D, 0x96, 0xD8, 0x72, 0xC0, 0x58, 0xE0, 0x3E,
0x4C, 0x66, 0x90, 0xDE, 0x55, 0x80, 0xA0, 0x83, 0x4B, 0x2A, 0x6C,
0xED, 0x39, 0x51, 0x60, 0x56, 0x2C, 0x8A, 0x70, 0xD0, 0x1F, 0x4A,
0x26, 0x8B, 0x33, 0x6E, 0x48, 0x89, 0x6F, 0x2E, 0xA4, 0xC3, 0x40,
0x5E, 0x50, 0x22, 0xCF, 0xA9, 0xAB, 0x0C, 0x15, 0xE1, 0x36, 0x5F,
0xF8, 0xD5, 0x92, 0x4E, 0xA6, 0x04, 0x30, 0x88, 0x2B, 0x1E, 0x16,
0x67, 0x45, 0x93, 0x38, 0x23, 0x68, 0x8C, 0x81, 0x1A, 0x25, 0x61,
0x13, 0xC1, 0xCB, 0x63, 0x97, 0x0E, 0x37, 0x41, 0x24, 0x57, 0xCA,
0x5B, 0xB9, 0xC4, 0x17, 0x4D, 0x52, 0x8D, 0xEF, 0xB3, 0x20, 0xEC,
0x2F, 0x32, 0x28, 0xD1, 0x11, 0xD9, 0xE9, 0xFB, 0xDA, 0x79, 0xDB,
0x77, 0x06, 0xBB, 0x84, 0xCD, 0xFE, 0xFC, 0x1B, 0x54, 0xA1, 0x1D,
0x7C, 0xCC, 0xE4, 0xB0, 0x49, 0x31, 0x27, 0x2D, 0x53, 0x69, 0x02,
0xF5, 0x18, 0xDF, 0x44, 0x4F, 0x9B, 0xBC, 0x0F, 0x5C, 0x0B, 0xDC,
0xBD, 0x94, 0xAC, 0x09, 0xC7, 0xA2, 0x1C, 0x82, 0x9F, 0xC6, 0x34,
0xC2, 0x46, 0x05, 0xCE, 0x3B, 0x0D, 0x3C, 0x9C, 0x08, 0xBE, 0xB7,
0x87, 0xE5, 0xEE, 0x6B, 0xEB, 0xF2, 0xBF, 0xAF, 0xC5, 0x64, 0x07,
0x7B, 0x95, 0x9A, 0xAE, 0xB6, 0x12, 0x59, 0xA5, 0x35, 0x65, 0xB8,
0xA3, 0x9E, 0xD2, 0xF7, 0x62, 0x5A, 0x85, 0x7D, 0xA8, 0x3A, 0x29,
0x71, 0xC8, 0xF6, 0xF9, 0x43, 0xD7, 0xD6, 0x10, 0x73, 0x76, 0x78,
0x99, 0x0A, 0x19, 0x91, 0x14, 0x3F, 0xE6, 0xF0, 0x86, 0xB1, 0xE2,
0xF1, 0xFA, 0x74, 0xF3, 0xB4, 0x6D, 0x21, 0xB2, 0x6A, 0xE3, 0xE7,
0xB5, 0xEA, 0x03, 0x8F, 0xD3, 0xC9, 0x42, 0xD4, 0xE8, 0x75, 0x7F,
0xFF, 0x7E, 0xFD };
static byte GF_MUL_TABLE[256][256];
#if defined (FECPP_USE_SSSE3)
/*
* these tables are for the linear map bx^4 + a -> y(bx^4 + a)
* implemented as two maps:
* a -> y(a)
* b -> y(bx^4)
* and the final output is the sum of these two outputs.
*/
const byte GFTBL[] __attribute__((aligned(16))) = {
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,
0x00, 0x10, 0x20, 0x30, 0x40, 0x50, 0x60, 0x70, 0x80, 0x90, 0xa0, 0xb0, 0xc0, 0xd0, 0xe0, 0xf0,
0x00, 0x02, 0x04, 0x06, 0x08, 0x0a, 0x0c, 0x0e, 0x10, 0x12, 0x14, 0x16, 0x18, 0x1a, 0x1c, 0x1e,
0x00, 0x20, 0x40, 0x60, 0x80, 0xa0, 0xc0, 0xe0, 0x1d, 0x3d, 0x5d, 0x7d, 0x9d, 0xbd, 0xdd, 0xfd,
0x00, 0x03, 0x06, 0x05, 0x0c, 0x0f, 0x0a, 0x09, 0x18, 0x1b, 0x1e, 0x1d, 0x14, 0x17, 0x12, 0x11,
0x00, 0x30, 0x60, 0x50, 0xc0, 0xf0, 0xa0, 0x90, 0x9d, 0xad, 0xfd, 0xcd, 0x5d, 0x6d, 0x3d, 0x0d,
0x00, 0x04, 0x08, 0x0c, 0x10, 0x14, 0x18, 0x1c, 0x20, 0x24, 0x28, 0x2c, 0x30, 0x34, 0x38, 0x3c,
0x00, 0x40, 0x80, 0xc0, 0x1d, 0x5d, 0x9d, 0xdd, 0x3a, 0x7a, 0xba, 0xfa, 0x27, 0x67, 0xa7, 0xe7,
0x00, 0x05, 0x0a, 0x0f, 0x14, 0x11, 0x1e, 0x1b, 0x28, 0x2d, 0x22, 0x27, 0x3c, 0x39, 0x36, 0x33,
0x00, 0x50, 0xa0, 0xf0, 0x5d, 0x0d, 0xfd, 0xad, 0xba, 0xea, 0x1a, 0x4a, 0xe7, 0xb7, 0x47, 0x17,
0x00, 0x06, 0x0c, 0x0a, 0x18, 0x1e, 0x14, 0x12, 0x30, 0x36, 0x3c, 0x3a, 0x28, 0x2e, 0x24, 0x22,
0x00, 0x60, 0xc0, 0xa0, 0x9d, 0xfd, 0x5d, 0x3d, 0x27, 0x47, 0xe7, 0x87, 0xba, 0xda, 0x7a, 0x1a,
0x00, 0x07, 0x0e, 0x09, 0x1c, 0x1b, 0x12, 0x15, 0x38, 0x3f, 0x36, 0x31, 0x24, 0x23, 0x2a, 0x2d,
0x00, 0x70, 0xe0, 0x90, 0xdd, 0xad, 0x3d, 0x4d, 0xa7, 0xd7, 0x47, 0x37, 0x7a, 0x0a, 0x9a, 0xea,
0x00, 0x08, 0x10, 0x18, 0x20, 0x28, 0x30, 0x38, 0x40, 0x48, 0x50, 0x58, 0x60, 0x68, 0x70, 0x78,
0x00, 0x80, 0x1d, 0x9d, 0x3a, 0xba, 0x27, 0xa7, 0x74, 0xf4, 0x69, 0xe9, 0x4e, 0xce, 0x53, 0xd3,
0x00, 0x09, 0x12, 0x1b, 0x24, 0x2d, 0x36, 0x3f, 0x48, 0x41, 0x5a, 0x53, 0x6c, 0x65, 0x7e, 0x77,
0x00, 0x90, 0x3d, 0xad, 0x7a, 0xea, 0x47, 0xd7, 0xf4, 0x64, 0xc9, 0x59, 0x8e, 0x1e, 0xb3, 0x23,
0x00, 0x0a, 0x14, 0x1e, 0x28, 0x22, 0x3c, 0x36, 0x50, 0x5a, 0x44, 0x4e, 0x78, 0x72, 0x6c, 0x66,
0x00, 0xa0, 0x5d, 0xfd, 0xba, 0x1a, 0xe7, 0x47, 0x69, 0xc9, 0x34, 0x94, 0xd3, 0x73, 0x8e, 0x2e,
0x00, 0x0b, 0x16, 0x1d, 0x2c, 0x27, 0x3a, 0x31, 0x58, 0x53, 0x4e, 0x45, 0x74, 0x7f, 0x62, 0x69,
0x00, 0xb0, 0x7d, 0xcd, 0xfa, 0x4a, 0x87, 0x37, 0xe9, 0x59, 0x94, 0x24, 0x13, 0xa3, 0x6e, 0xde,
0x00, 0x0c, 0x18, 0x14, 0x30, 0x3c, 0x28, 0x24, 0x60, 0x6c, 0x78, 0x74, 0x50, 0x5c, 0x48, 0x44,
0x00, 0xc0, 0x9d, 0x5d, 0x27, 0xe7, 0xba, 0x7a, 0x4e, 0x8e, 0xd3, 0x13, 0x69, 0xa9, 0xf4, 0x34,
0x00, 0x0d, 0x1a, 0x17, 0x34, 0x39, 0x2e, 0x23, 0x68, 0x65, 0x72, 0x7f, 0x5c, 0x51, 0x46, 0x4b,
0x00, 0xd0, 0xbd, 0x6d, 0x67, 0xb7, 0xda, 0x0a, 0xce, 0x1e, 0x73, 0xa3, 0xa9, 0x79, 0x14, 0xc4,
0x00, 0x0e, 0x1c, 0x12, 0x38, 0x36, 0x24, 0x2a, 0x70, 0x7e, 0x6c, 0x62, 0x48, 0x46, 0x54, 0x5a,
0x00, 0xe0, 0xdd, 0x3d, 0xa7, 0x47, 0x7a, 0x9a, 0x53, 0xb3, 0x8e, 0x6e, 0xf4, 0x14, 0x29, 0xc9,
0x00, 0x0f, 0x1e, 0x11, 0x3c, 0x33, 0x22, 0x2d, 0x78, 0x77, 0x66, 0x69, 0x44, 0x4b, 0x5a, 0x55,
0x00, 0xf0, 0xfd, 0x0d, 0xe7, 0x17, 0x1a, 0xea, 0xd3, 0x23, 0x2e, 0xde, 0x34, 0xc4, 0xc9, 0x39,
0x00, 0x10, 0x20, 0x30, 0x40, 0x50, 0x60, 0x70, 0x80, 0x90, 0xa0, 0xb0, 0xc0, 0xd0, 0xe0, 0xf0,
0x00, 0x1d, 0x3a, 0x27, 0x74, 0x69, 0x4e, 0x53, 0xe8, 0xf5, 0xd2, 0xcf, 0x9c, 0x81, 0xa6, 0xbb,
0x00, 0x11, 0x22, 0x33, 0x44, 0x55, 0x66, 0x77, 0x88, 0x99, 0xaa, 0xbb, 0xcc, 0xdd, 0xee, 0xff,
0x00, 0x0d, 0x1a, 0x17, 0x34, 0x39, 0x2e, 0x23, 0x68, 0x65, 0x72, 0x7f, 0x5c, 0x51, 0x46, 0x4b,
0x00, 0x12, 0x24, 0x36, 0x48, 0x5a, 0x6c, 0x7e, 0x90, 0x82, 0xb4, 0xa6, 0xd8, 0xca, 0xfc, 0xee,
0x00, 0x3d, 0x7a, 0x47, 0xf4, 0xc9, 0x8e, 0xb3, 0xf5, 0xc8, 0x8f, 0xb2, 0x01, 0x3c, 0x7b, 0x46,
0x00, 0x13, 0x26, 0x35, 0x4c, 0x5f, 0x6a, 0x79, 0x98, 0x8b, 0xbe, 0xad, 0xd4, 0xc7, 0xf2, 0xe1,
0x00, 0x2d, 0x5a, 0x77, 0xb4, 0x99, 0xee, 0xc3, 0x75, 0x58, 0x2f, 0x02, 0xc1, 0xec, 0x9b, 0xb6,
0x00, 0x14, 0x28, 0x3c, 0x50, 0x44, 0x78, 0x6c, 0xa0, 0xb4, 0x88, 0x9c, 0xf0, 0xe4, 0xd8, 0xcc,
0x00, 0x5d, 0xba, 0xe7, 0x69, 0x34, 0xd3, 0x8e, 0xd2, 0x8f, 0x68, 0x35, 0xbb, 0xe6, 0x01, 0x5c,
0x00, 0x15, 0x2a, 0x3f, 0x54, 0x41, 0x7e, 0x6b, 0xa8, 0xbd, 0x82, 0x97, 0xfc, 0xe9, 0xd6, 0xc3,
0x00, 0x4d, 0x9a, 0xd7, 0x29, 0x64, 0xb3, 0xfe, 0x52, 0x1f, 0xc8, 0x85, 0x7b, 0x36, 0xe1, 0xac,
0x00, 0x16, 0x2c, 0x3a, 0x58, 0x4e, 0x74, 0x62, 0xb0, 0xa6, 0x9c, 0x8a, 0xe8, 0xfe, 0xc4, 0xd2,
0x00, 0x7d, 0xfa, 0x87, 0xe9, 0x94, 0x13, 0x6e, 0xcf, 0xb2, 0x35, 0x48, 0x26, 0x5b, 0xdc, 0xa1,
0x00, 0x17, 0x2e, 0x39, 0x5c, 0x4b, 0x72, 0x65, 0xb8, 0xaf, 0x96, 0x81, 0xe4, 0xf3, 0xca, 0xdd,
0x00, 0x6d, 0xda, 0xb7, 0xa9, 0xc4, 0x73, 0x1e, 0x4f, 0x22, 0x95, 0xf8, 0xe6, 0x8b, 0x3c, 0x51,
0x00, 0x18, 0x30, 0x28, 0x60, 0x78, 0x50, 0x48, 0xc0, 0xd8, 0xf0, 0xe8, 0xa0, 0xb8, 0x90, 0x88,
0x00, 0x9d, 0x27, 0xba, 0x4e, 0xd3, 0x69, 0xf4, 0x9c, 0x01, 0xbb, 0x26, 0xd2, 0x4f, 0xf5, 0x68,
0x00, 0x19, 0x32, 0x2b, 0x64, 0x7d, 0x56, 0x4f, 0xc8, 0xd1, 0xfa, 0xe3, 0xac, 0xb5, 0x9e, 0x87,
0x00, 0x8d, 0x07, 0x8a, 0x0e, 0x83, 0x09, 0x84, 0x1c, 0x91, 0x1b, 0x96, 0x12, 0x9f, 0x15, 0x98,
0x00, 0x1a, 0x34, 0x2e, 0x68, 0x72, 0x5c, 0x46, 0xd0, 0xca, 0xe4, 0xfe, 0xb8, 0xa2, 0x8c, 0x96,
0x00, 0xbd, 0x67, 0xda, 0xce, 0x73, 0xa9, 0x14, 0x81, 0x3c, 0xe6, 0x5b, 0x4f, 0xf2, 0x28, 0x95,
0x00, 0x1b, 0x36, 0x2d, 0x6c, 0x77, 0x5a, 0x41, 0xd8, 0xc3, 0xee, 0xf5, 0xb4, 0xaf, 0x82, 0x99,
0x00, 0xad, 0x47, 0xea, 0x8e, 0x23, 0xc9, 0x64, 0x01, 0xac, 0x46, 0xeb, 0x8f, 0x22, 0xc8, 0x65,
0x00, 0x1c, 0x38, 0x24, 0x70, 0x6c, 0x48, 0x54, 0xe0, 0xfc, 0xd8, 0xc4, 0x90, 0x8c, 0xa8, 0xb4,
0x00, 0xdd, 0xa7, 0x7a, 0x53, 0x8e, 0xf4, 0x29, 0xa6, 0x7b, 0x01, 0xdc, 0xf5, 0x28, 0x52, 0x8f,
0x00, 0x1d, 0x3a, 0x27, 0x74, 0x69, 0x4e, 0x53, 0xe8, 0xf5, 0xd2, 0xcf, 0x9c, 0x81, 0xa6, 0xbb,
0x00, 0xcd, 0x87, 0x4a, 0x13, 0xde, 0x94, 0x59, 0x26, 0xeb, 0xa1, 0x6c, 0x35, 0xf8, 0xb2, 0x7f,
0x00, 0x1e, 0x3c, 0x22, 0x78, 0x66, 0x44, 0x5a, 0xf0, 0xee, 0xcc, 0xd2, 0x88, 0x96, 0xb4, 0xaa,
0x00, 0xfd, 0xe7, 0x1a, 0xd3, 0x2e, 0x34, 0xc9, 0xbb, 0x46, 0x5c, 0xa1, 0x68, 0x95, 0x8f, 0x72,
0x00, 0x1f, 0x3e, 0x21, 0x7c, 0x63, 0x42, 0x5d, 0xf8, 0xe7, 0xc6, 0xd9, 0x84, 0x9b, 0xba, 0xa5,
0x00, 0xed, 0xc7, 0x2a, 0x93, 0x7e, 0x54, 0xb9, 0x3b, 0xd6, 0xfc, 0x11, 0xa8, 0x45, 0x6f, 0x82,
0x00, 0x20, 0x40, 0x60, 0x80, 0xa0, 0xc0, 0xe0, 0x1d, 0x3d, 0x5d, 0x7d, 0x9d, 0xbd, 0xdd, 0xfd,
0x00, 0x3a, 0x74, 0x4e, 0xe8, 0xd2, 0x9c, 0xa6, 0xcd, 0xf7, 0xb9, 0x83, 0x25, 0x1f, 0x51, 0x6b,
0x00, 0x21, 0x42, 0x63, 0x84, 0xa5, 0xc6, 0xe7, 0x15, 0x34, 0x57, 0x76, 0x91, 0xb0, 0xd3, 0xf2,
0x00, 0x2a, 0x54, 0x7e, 0xa8, 0x82, 0xfc, 0xd6, 0x4d, 0x67, 0x19, 0x33, 0xe5, 0xcf, 0xb1, 0x9b,
0x00, 0x22, 0x44, 0x66, 0x88, 0xaa, 0xcc, 0xee, 0x0d, 0x2f, 0x49, 0x6b, 0x85, 0xa7, 0xc1, 0xe3,
0x00, 0x1a, 0x34, 0x2e, 0x68, 0x72, 0x5c, 0x46, 0xd0, 0xca, 0xe4, 0xfe, 0xb8, 0xa2, 0x8c, 0x96,
0x00, 0x23, 0x46, 0x65, 0x8c, 0xaf, 0xca, 0xe9, 0x05, 0x26, 0x43, 0x60, 0x89, 0xaa, 0xcf, 0xec,
0x00, 0x0a, 0x14, 0x1e, 0x28, 0x22, 0x3c, 0x36, 0x50, 0x5a, 0x44, 0x4e, 0x78, 0x72, 0x6c, 0x66,
0x00, 0x24, 0x48, 0x6c, 0x90, 0xb4, 0xd8, 0xfc, 0x3d, 0x19, 0x75, 0x51, 0xad, 0x89, 0xe5, 0xc1,
0x00, 0x7a, 0xf4, 0x8e, 0xf5, 0x8f, 0x01, 0x7b, 0xf7, 0x8d, 0x03, 0x79, 0x02, 0x78, 0xf6, 0x8c,
0x00, 0x25, 0x4a, 0x6f, 0x94, 0xb1, 0xde, 0xfb, 0x35, 0x10, 0x7f, 0x5a, 0xa1, 0x84, 0xeb, 0xce,
0x00, 0x6a, 0xd4, 0xbe, 0xb5, 0xdf, 0x61, 0x0b, 0x77, 0x1d, 0xa3, 0xc9, 0xc2, 0xa8, 0x16, 0x7c,
0x00, 0x26, 0x4c, 0x6a, 0x98, 0xbe, 0xd4, 0xf2, 0x2d, 0x0b, 0x61, 0x47, 0xb5, 0x93, 0xf9, 0xdf,
0x00, 0x5a, 0xb4, 0xee, 0x75, 0x2f, 0xc1, 0x9b, 0xea, 0xb0, 0x5e, 0x04, 0x9f, 0xc5, 0x2b, 0x71,
0x00, 0x27, 0x4e, 0x69, 0x9c, 0xbb, 0xd2, 0xf5, 0x25, 0x02, 0x6b, 0x4c, 0xb9, 0x9e, 0xf7, 0xd0,
0x00, 0x4a, 0x94, 0xde, 0x35, 0x7f, 0xa1, 0xeb, 0x6a, 0x20, 0xfe, 0xb4, 0x5f, 0x15, 0xcb, 0x81,
0x00, 0x28, 0x50, 0x78, 0xa0, 0x88, 0xf0, 0xd8, 0x5d, 0x75, 0x0d, 0x25, 0xfd, 0xd5, 0xad, 0x85,
0x00, 0xba, 0x69, 0xd3, 0xd2, 0x68, 0xbb, 0x01, 0xb9, 0x03, 0xd0, 0x6a, 0x6b, 0xd1, 0x02, 0xb8,
0x00, 0x29, 0x52, 0x7b, 0xa4, 0x8d, 0xf6, 0xdf, 0x55, 0x7c, 0x07, 0x2e, 0xf1, 0xd8, 0xa3, 0x8a,
0x00, 0xaa, 0x49, 0xe3, 0x92, 0x38, 0xdb, 0x71, 0x39, 0x93, 0x70, 0xda, 0xab, 0x01, 0xe2, 0x48,
0x00, 0x2a, 0x54, 0x7e, 0xa8, 0x82, 0xfc, 0xd6, 0x4d, 0x67, 0x19, 0x33, 0xe5, 0xcf, 0xb1, 0x9b,
0x00, 0x9a, 0x29, 0xb3, 0x52, 0xc8, 0x7b, 0xe1, 0xa4, 0x3e, 0x8d, 0x17, 0xf6, 0x6c, 0xdf, 0x45,
0x00, 0x2b, 0x56, 0x7d, 0xac, 0x87, 0xfa, 0xd1, 0x45, 0x6e, 0x13, 0x38, 0xe9, 0xc2, 0xbf, 0x94,
0x00, 0x8a, 0x09, 0x83, 0x12, 0x98, 0x1b, 0x91, 0x24, 0xae, 0x2d, 0xa7, 0x36, 0xbc, 0x3f, 0xb5,
0x00, 0x2c, 0x58, 0x74, 0xb0, 0x9c, 0xe8, 0xc4, 0x7d, 0x51, 0x25, 0x09, 0xcd, 0xe1, 0x95, 0xb9,
0x00, 0xfa, 0xe9, 0x13, 0xcf, 0x35, 0x26, 0xdc, 0x83, 0x79, 0x6a, 0x90, 0x4c, 0xb6, 0xa5, 0x5f,
0x00, 0x2d, 0x5a, 0x77, 0xb4, 0x99, 0xee, 0xc3, 0x75, 0x58, 0x2f, 0x02, 0xc1, 0xec, 0x9b, 0xb6,
0x00, 0xea, 0xc9, 0x23, 0x8f, 0x65, 0x46, 0xac, 0x03, 0xe9, 0xca, 0x20, 0x8c, 0x66, 0x45, 0xaf,
0x00, 0x2e, 0x5c, 0x72, 0xb8, 0x96, 0xe4, 0xca, 0x6d, 0x43, 0x31, 0x1f, 0xd5, 0xfb, 0x89, 0xa7,
0x00, 0xda, 0xa9, 0x73, 0x4f, 0x95, 0xe6, 0x3c, 0x9e, 0x44, 0x37, 0xed, 0xd1, 0x0b, 0x78, 0xa2,
0x00, 0x2f, 0x5e, 0x71, 0xbc, 0x93, 0xe2, 0xcd, 0x65, 0x4a, 0x3b, 0x14, 0xd9, 0xf6, 0x87, 0xa8,
0x00, 0xca, 0x89, 0x43, 0x0f, 0xc5, 0x86, 0x4c, 0x1e, 0xd4, 0x97, 0x5d, 0x11, 0xdb, 0x98, 0x52,
0x00, 0x30, 0x60, 0x50, 0xc0, 0xf0, 0xa0, 0x90, 0x9d, 0xad, 0xfd, 0xcd, 0x5d, 0x6d, 0x3d, 0x0d,
0x00, 0x27, 0x4e, 0x69, 0x9c, 0xbb, 0xd2, 0xf5, 0x25, 0x02, 0x6b, 0x4c, 0xb9, 0x9e, 0xf7, 0xd0,
0x00, 0x31, 0x62, 0x53, 0xc4, 0xf5, 0xa6, 0x97, 0x95, 0xa4, 0xf7, 0xc6, 0x51, 0x60, 0x33, 0x02,
0x00, 0x37, 0x6e, 0x59, 0xdc, 0xeb, 0xb2, 0x85, 0xa5, 0x92, 0xcb, 0xfc, 0x79, 0x4e, 0x17, 0x20,
0x00, 0x32, 0x64, 0x56, 0xc8, 0xfa, 0xac, 0x9e, 0x8d, 0xbf, 0xe9, 0xdb, 0x45, 0x77, 0x21, 0x13,
0x00, 0x07, 0x0e, 0x09, 0x1c, 0x1b, 0x12, 0x15, 0x38, 0x3f, 0x36, 0x31, 0x24, 0x23, 0x2a, 0x2d,
0x00, 0x33, 0x66, 0x55, 0xcc, 0xff, 0xaa, 0x99, 0x85, 0xb6, 0xe3, 0xd0, 0x49, 0x7a, 0x2f, 0x1c,
0x00, 0x17, 0x2e, 0x39, 0x5c, 0x4b, 0x72, 0x65, 0xb8, 0xaf, 0x96, 0x81, 0xe4, 0xf3, 0xca, 0xdd,
0x00, 0x34, 0x68, 0x5c, 0xd0, 0xe4, 0xb8, 0x8c, 0xbd, 0x89, 0xd5, 0xe1, 0x6d, 0x59, 0x05, 0x31,
0x00, 0x67, 0xce, 0xa9, 0x81, 0xe6, 0x4f, 0x28, 0x1f, 0x78, 0xd1, 0xb6, 0x9e, 0xf9, 0x50, 0x37,
0x00, 0x35, 0x6a, 0x5f, 0xd4, 0xe1, 0xbe, 0x8b, 0xb5, 0x80, 0xdf, 0xea, 0x61, 0x54, 0x0b, 0x3e,
0x00, 0x77, 0xee, 0x99, 0xc1, 0xb6, 0x2f, 0x58, 0x9f, 0xe8, 0x71, 0x06, 0x5e, 0x29, 0xb0, 0xc7,
0x00, 0x36, 0x6c, 0x5a, 0xd8, 0xee, 0xb4, 0x82, 0xad, 0x9b, 0xc1, 0xf7, 0x75, 0x43, 0x19, 0x2f,
0x00, 0x47, 0x8e, 0xc9, 0x01, 0x46, 0x8f, 0xc8, 0x02, 0x45, 0x8c, 0xcb, 0x03, 0x44, 0x8d, 0xca,
0x00, 0x37, 0x6e, 0x59, 0xdc, 0xeb, 0xb2, 0x85, 0xa5, 0x92, 0xcb, 0xfc, 0x79, 0x4e, 0x17, 0x20,
0x00, 0x57, 0xae, 0xf9, 0x41, 0x16, 0xef, 0xb8, 0x82, 0xd5, 0x2c, 0x7b, 0xc3, 0x94, 0x6d, 0x3a,
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0x00, 0xe7, 0xd3, 0x34, 0xbb, 0x5c, 0x68, 0x8f, 0x6b, 0x8c, 0xb8, 0x5f, 0xd0, 0x37, 0x03, 0xe4,
0x00, 0xd6, 0xb1, 0x67, 0x7f, 0xa9, 0xce, 0x18, 0xfe, 0x28, 0x4f, 0x99, 0x81, 0x57, 0x30, 0xe6,
0x00, 0xe8, 0xcd, 0x25, 0x87, 0x6f, 0x4a, 0xa2, 0x13, 0xfb, 0xde, 0x36, 0x94, 0x7c, 0x59, 0xb1,
0x00, 0x26, 0x4c, 0x6a, 0x98, 0xbe, 0xd4, 0xf2, 0x2d, 0x0b, 0x61, 0x47, 0xb5, 0x93, 0xf9, 0xdf,
0x00, 0xe9, 0xcf, 0x26, 0x83, 0x6a, 0x4c, 0xa5, 0x1b, 0xf2, 0xd4, 0x3d, 0x98, 0x71, 0x57, 0xbe,
0x00, 0x36, 0x6c, 0x5a, 0xd8, 0xee, 0xb4, 0x82, 0xad, 0x9b, 0xc1, 0xf7, 0x75, 0x43, 0x19, 0x2f,
0x00, 0xea, 0xc9, 0x23, 0x8f, 0x65, 0x46, 0xac, 0x03, 0xe9, 0xca, 0x20, 0x8c, 0x66, 0x45, 0xaf,
0x00, 0x06, 0x0c, 0x0a, 0x18, 0x1e, 0x14, 0x12, 0x30, 0x36, 0x3c, 0x3a, 0x28, 0x2e, 0x24, 0x22,
0x00, 0xeb, 0xcb, 0x20, 0x8b, 0x60, 0x40, 0xab, 0x0b, 0xe0, 0xc0, 0x2b, 0x80, 0x6b, 0x4b, 0xa0,
0x00, 0x16, 0x2c, 0x3a, 0x58, 0x4e, 0x74, 0x62, 0xb0, 0xa6, 0x9c, 0x8a, 0xe8, 0xfe, 0xc4, 0xd2,
0x00, 0xec, 0xc5, 0x29, 0x97, 0x7b, 0x52, 0xbe, 0x33, 0xdf, 0xf6, 0x1a, 0xa4, 0x48, 0x61, 0x8d,
0x00, 0x66, 0xcc, 0xaa, 0x85, 0xe3, 0x49, 0x2f, 0x17, 0x71, 0xdb, 0xbd, 0x92, 0xf4, 0x5e, 0x38,
0x00, 0xed, 0xc7, 0x2a, 0x93, 0x7e, 0x54, 0xb9, 0x3b, 0xd6, 0xfc, 0x11, 0xa8, 0x45, 0x6f, 0x82,
0x00, 0x76, 0xec, 0x9a, 0xc5, 0xb3, 0x29, 0x5f, 0x97, 0xe1, 0x7b, 0x0d, 0x52, 0x24, 0xbe, 0xc8,
0x00, 0xee, 0xc1, 0x2f, 0x9f, 0x71, 0x5e, 0xb0, 0x23, 0xcd, 0xe2, 0x0c, 0xbc, 0x52, 0x7d, 0x93,
0x00, 0x46, 0x8c, 0xca, 0x05, 0x43, 0x89, 0xcf, 0x0a, 0x4c, 0x86, 0xc0, 0x0f, 0x49, 0x83, 0xc5,
0x00, 0xef, 0xc3, 0x2c, 0x9b, 0x74, 0x58, 0xb7, 0x2b, 0xc4, 0xe8, 0x07, 0xb0, 0x5f, 0x73, 0x9c,
0x00, 0x56, 0xac, 0xfa, 0x45, 0x13, 0xe9, 0xbf, 0x8a, 0xdc, 0x26, 0x70, 0xcf, 0x99, 0x63, 0x35,
0x00, 0xf0, 0xfd, 0x0d, 0xe7, 0x17, 0x1a, 0xea, 0xd3, 0x23, 0x2e, 0xde, 0x34, 0xc4, 0xc9, 0x39,
0x00, 0xbb, 0x6b, 0xd0, 0xd6, 0x6d, 0xbd, 0x06, 0xb1, 0x0a, 0xda, 0x61, 0x67, 0xdc, 0x0c, 0xb7,
0x00, 0xf1, 0xff, 0x0e, 0xe3, 0x12, 0x1c, 0xed, 0xdb, 0x2a, 0x24, 0xd5, 0x38, 0xc9, 0xc7, 0x36,
0x00, 0xab, 0x4b, 0xe0, 0x96, 0x3d, 0xdd, 0x76, 0x31, 0x9a, 0x7a, 0xd1, 0xa7, 0x0c, 0xec, 0x47,
0x00, 0xf2, 0xf9, 0x0b, 0xef, 0x1d, 0x16, 0xe4, 0xc3, 0x31, 0x3a, 0xc8, 0x2c, 0xde, 0xd5, 0x27,
0x00, 0x9b, 0x2b, 0xb0, 0x56, 0xcd, 0x7d, 0xe6, 0xac, 0x37, 0x87, 0x1c, 0xfa, 0x61, 0xd1, 0x4a,
0x00, 0xf3, 0xfb, 0x08, 0xeb, 0x18, 0x10, 0xe3, 0xcb, 0x38, 0x30, 0xc3, 0x20, 0xd3, 0xdb, 0x28,
0x00, 0x8b, 0x0b, 0x80, 0x16, 0x9d, 0x1d, 0x96, 0x2c, 0xa7, 0x27, 0xac, 0x3a, 0xb1, 0x31, 0xba,
0x00, 0xf4, 0xf5, 0x01, 0xf7, 0x03, 0x02, 0xf6, 0xf3, 0x07, 0x06, 0xf2, 0x04, 0xf0, 0xf1, 0x05,
0x00, 0xfb, 0xeb, 0x10, 0xcb, 0x30, 0x20, 0xdb, 0x8b, 0x70, 0x60, 0x9b, 0x40, 0xbb, 0xab, 0x50,
0x00, 0xf5, 0xf7, 0x02, 0xf3, 0x06, 0x04, 0xf1, 0xfb, 0x0e, 0x0c, 0xf9, 0x08, 0xfd, 0xff, 0x0a,
0x00, 0xeb, 0xcb, 0x20, 0x8b, 0x60, 0x40, 0xab, 0x0b, 0xe0, 0xc0, 0x2b, 0x80, 0x6b, 0x4b, 0xa0,
0x00, 0xf6, 0xf1, 0x07, 0xff, 0x09, 0x0e, 0xf8, 0xe3, 0x15, 0x12, 0xe4, 0x1c, 0xea, 0xed, 0x1b,
0x00, 0xdb, 0xab, 0x70, 0x4b, 0x90, 0xe0, 0x3b, 0x96, 0x4d, 0x3d, 0xe6, 0xdd, 0x06, 0x76, 0xad,
0x00, 0xf7, 0xf3, 0x04, 0xfb, 0x0c, 0x08, 0xff, 0xeb, 0x1c, 0x18, 0xef, 0x10, 0xe7, 0xe3, 0x14,
0x00, 0xcb, 0x8b, 0x40, 0x0b, 0xc0, 0x80, 0x4b, 0x16, 0xdd, 0x9d, 0x56, 0x1d, 0xd6, 0x96, 0x5d,
0x00, 0xf8, 0xed, 0x15, 0xc7, 0x3f, 0x2a, 0xd2, 0x93, 0x6b, 0x7e, 0x86, 0x54, 0xac, 0xb9, 0x41,
0x00, 0x3b, 0x76, 0x4d, 0xec, 0xd7, 0x9a, 0xa1, 0xc5, 0xfe, 0xb3, 0x88, 0x29, 0x12, 0x5f, 0x64,
0x00, 0xf9, 0xef, 0x16, 0xc3, 0x3a, 0x2c, 0xd5, 0x9b, 0x62, 0x74, 0x8d, 0x58, 0xa1, 0xb7, 0x4e,
0x00, 0x2b, 0x56, 0x7d, 0xac, 0x87, 0xfa, 0xd1, 0x45, 0x6e, 0x13, 0x38, 0xe9, 0xc2, 0xbf, 0x94,
0x00, 0xfa, 0xe9, 0x13, 0xcf, 0x35, 0x26, 0xdc, 0x83, 0x79, 0x6a, 0x90, 0x4c, 0xb6, 0xa5, 0x5f,
0x00, 0x1b, 0x36, 0x2d, 0x6c, 0x77, 0x5a, 0x41, 0xd8, 0xc3, 0xee, 0xf5, 0xb4, 0xaf, 0x82, 0x99,
0x00, 0xfb, 0xeb, 0x10, 0xcb, 0x30, 0x20, 0xdb, 0x8b, 0x70, 0x60, 0x9b, 0x40, 0xbb, 0xab, 0x50,
0x00, 0x0b, 0x16, 0x1d, 0x2c, 0x27, 0x3a, 0x31, 0x58, 0x53, 0x4e, 0x45, 0x74, 0x7f, 0x62, 0x69,
0x00, 0xfc, 0xe5, 0x19, 0xd7, 0x2b, 0x32, 0xce, 0xb3, 0x4f, 0x56, 0xaa, 0x64, 0x98, 0x81, 0x7d,
0x00, 0x7b, 0xf6, 0x8d, 0xf1, 0x8a, 0x07, 0x7c, 0xff, 0x84, 0x09, 0x72, 0x0e, 0x75, 0xf8, 0x83,
0x00, 0xfd, 0xe7, 0x1a, 0xd3, 0x2e, 0x34, 0xc9, 0xbb, 0x46, 0x5c, 0xa1, 0x68, 0x95, 0x8f, 0x72,
0x00, 0x6b, 0xd6, 0xbd, 0xb1, 0xda, 0x67, 0x0c, 0x7f, 0x14, 0xa9, 0xc2, 0xce, 0xa5, 0x18, 0x73,
0x00, 0xfe, 0xe1, 0x1f, 0xdf, 0x21, 0x3e, 0xc0, 0xa3, 0x5d, 0x42, 0xbc, 0x7c, 0x82, 0x9d, 0x63,
0x00, 0x5b, 0xb6, 0xed, 0x71, 0x2a, 0xc7, 0x9c, 0xe2, 0xb9, 0x54, 0x0f, 0x93, 0xc8, 0x25, 0x7e,
0x00, 0xff, 0xe3, 0x1c, 0xdb, 0x24, 0x38, 0xc7, 0xab, 0x54, 0x48, 0xb7, 0x70, 0x8f, 0x93, 0x6c,
0x00, 0x4b, 0x96, 0xdd, 0x31, 0x7a, 0xa7, 0xec, 0x62, 0x29, 0xf4, 0xbf, 0x53, 0x18, 0xc5, 0x8e };
#endif
void init_fec()
{
static bool fec_initialized = false;
if(!fec_initialized)
{
fec_initialized = true;
for(size_t i = 0; i != 256; ++i)
for(size_t j = 0; j != 256; ++j)
GF_MUL_TABLE[i][j] = GF_EXP[(GF_LOG[i] + GF_LOG[j]) % 255];
for(size_t i = 0; i != 256; ++i)
GF_MUL_TABLE[0][i] = GF_MUL_TABLE[i][0] = 0;
}
}
/*
* addmul() computes z[] = z[] + x[] * y
*/
void addmul(byte z[], const byte x[], byte y, size_t size)
{
if(y == 0)
return;
const byte* GF_MUL_Y = GF_MUL_TABLE[y];
#if defined(FECPP_USE_SSE2) || defined(FECPP_USE_SSSE3)
while(size && (uintptr_t)z % 16) // first align z to 16 bytes
{
z[0] ^= GF_MUL_Y[x[0]];
++z;
++x;
size--;
}
#endif
#if defined(FECPP_USE_SSE2)
const __m128i polynomial = _mm_set1_epi8(0x1D);
const size_t y_bits = 32 - __builtin_clz(y);
// unrolled out to cache line size
while(size >= 64)
{
__m128i x_1 = _mm_loadu_si128((const __m128i*)(x));
__m128i x_2 = _mm_loadu_si128((const __m128i*)(x + 16));
__m128i x_3 = _mm_loadu_si128((const __m128i*)(x + 32));
__m128i x_4 = _mm_loadu_si128((const __m128i*)(x + 48));
__m128i z_1 = _mm_load_si128((const __m128i*)(z));
__m128i z_2 = _mm_load_si128((const __m128i*)(z + 16));
__m128i z_3 = _mm_load_si128((const __m128i*)(z + 32));
__m128i z_4 = _mm_load_si128((const __m128i*)(z + 48));
// prefetch next two x and z blocks
_mm_prefetch(x + 64, _MM_HINT_T0);
_mm_prefetch(z + 64, _MM_HINT_T0);
_mm_prefetch(x + 128, _MM_HINT_T1);
_mm_prefetch(z + 128, _MM_HINT_T1);
if(y & 0x01)
{
z_1 = _mm_xor_si128(z_1, x_1);
z_2 = _mm_xor_si128(z_2, x_2);
z_3 = _mm_xor_si128(z_3, x_3);
z_4 = _mm_xor_si128(z_4, x_4);
}
for(size_t j = 1; j != y_bits; ++j)
{
/*
* Each byte of each mask is either 0 or the polynomial 0x1D,
* depending on if the high bit of x_i is set or not.
*/
__m128i mask_1 = _mm_setzero_si128();
__m128i mask_2 = _mm_setzero_si128();
__m128i mask_3 = _mm_setzero_si128();
__m128i mask_4 = _mm_setzero_si128();
// flip operation?
mask_1 = _mm_cmpgt_epi8(mask_1, x_1);
mask_2 = _mm_cmpgt_epi8(mask_2, x_2);
mask_3 = _mm_cmpgt_epi8(mask_3, x_3);
mask_4 = _mm_cmpgt_epi8(mask_4, x_4);
x_1 = _mm_add_epi8(x_1, x_1);
x_2 = _mm_add_epi8(x_2, x_2);
x_3 = _mm_add_epi8(x_3, x_3);
x_4 = _mm_add_epi8(x_4, x_4);
mask_1 = _mm_and_si128(mask_1, polynomial);
mask_2 = _mm_and_si128(mask_2, polynomial);
mask_3 = _mm_and_si128(mask_3, polynomial);
mask_4 = _mm_and_si128(mask_4, polynomial);
x_1 = _mm_xor_si128(x_1, mask_1);
x_2 = _mm_xor_si128(x_2, mask_2);
x_3 = _mm_xor_si128(x_3, mask_3);
x_4 = _mm_xor_si128(x_4, mask_4);
if((y >> j) & 1)
{
z_1 = _mm_xor_si128(z_1, x_1);
z_2 = _mm_xor_si128(z_2, x_2);
z_3 = _mm_xor_si128(z_3, x_3);
z_4 = _mm_xor_si128(z_4, x_4);
}
}
_mm_store_si128((__m128i*)(z ), z_1);
_mm_store_si128((__m128i*)(z + 16), z_2);
_mm_store_si128((__m128i*)(z + 32), z_3);
_mm_store_si128((__m128i*)(z + 48), z_4);
x += 64;
z += 64;
size -= 64;
}
#elif defined(FECPP_USE_SSSE3)
while(size && (uintptr_t)z % 16) // first align z to 16 bytes
{
z[0] ^= GF_MUL_Y[x[0]];
++z;
++x;
size--;
}
__m128i mask = _mm_set1_epi8(0x0f);
// fetch the lookup tables for the given y
__m128i t_lo = _mm_load_si128((const __m128i*)(GFTBL + 32*y));
__m128i t_hi = _mm_load_si128((const __m128i*)(GFTBL + 32*y + 16));
while(size >= 16)
{
__m128i x_1 = _mm_loadu_si128((const __m128i*)(x));
__m128i z_1 = _mm_load_si128((const __m128i*)(z));
// mask to get LO nibble for LO LUT input
__m128i x_lo = _mm_and_si128(x_1, mask);
// mask to get HI nibble for HI LUT input
__m128i x_hi = _mm_and_si128(_mm_srli_epi64(x_1, 4), mask);
// 16x parallel lookups
__m128i r_lo = _mm_shuffle_epi8(t_lo, x_lo);
__m128i r_hi = _mm_shuffle_epi8(t_hi, x_hi);
// sum the outputs.
z_1 = _mm_xor_si128(z_1, r_lo);
z_1 = _mm_xor_si128(z_1, r_hi);
_mm_store_si128((__m128i*)(z), z_1);
x += 16;
z += 16;
size -= 16;
}
#endif
while(size >= 16)
{
z[0] ^= GF_MUL_Y[x[0]];
z[1] ^= GF_MUL_Y[x[1]];
z[2] ^= GF_MUL_Y[x[2]];
z[3] ^= GF_MUL_Y[x[3]];
z[4] ^= GF_MUL_Y[x[4]];
z[5] ^= GF_MUL_Y[x[5]];
z[6] ^= GF_MUL_Y[x[6]];
z[7] ^= GF_MUL_Y[x[7]];
z[8] ^= GF_MUL_Y[x[8]];
z[9] ^= GF_MUL_Y[x[9]];
z[10] ^= GF_MUL_Y[x[10]];
z[11] ^= GF_MUL_Y[x[11]];
z[12] ^= GF_MUL_Y[x[12]];
z[13] ^= GF_MUL_Y[x[13]];
z[14] ^= GF_MUL_Y[x[14]];
z[15] ^= GF_MUL_Y[x[15]];
x += 16;
z += 16;
size -= 16;
}
// Clean up the trailing pieces
for(size_t i = 0; i != size; ++i)
z[i] ^= GF_MUL_Y[x[i]];
}
/*
* invert_matrix() takes a K*K matrix and produces its inverse
* (Gauss-Jordan algorithm, adapted from Numerical Recipes in C)
*/
void invert_matrix(byte matrix[], size_t K)
{
class pivot_searcher
{
public:
pivot_searcher(size_t K) : ipiv(K) {}
std::pair<size_t, size_t> operator()(size_t col, const byte* matrix)
{
const size_t K = ipiv.size();
if(ipiv[col] == false && matrix[col*K + col] != 0)
{
ipiv[col] = true;
return std::make_pair(col, col);
}
for(size_t row = 0; row != K; ++row)
{
if(ipiv[row])
continue;
for(size_t i = 0; i != K; ++i)
{
if(ipiv[i] == false && matrix[row*K + i] != 0)
{
ipiv[i] = true;
return std::make_pair(row, i);
}
}
}
throw std::invalid_argument("pivot not found in invert_matrix");
}
private:
// Marks elements already used as pivots
std::vector<bool> ipiv;
};
pivot_searcher pivot_search(K);
std::vector<size_t> indxc(K);
std::vector<size_t> indxr(K);
std::vector<byte> id_row(K);
for(size_t col = 0; col != K; ++col)
{
/*
* Zeroing column 'col', look for a non-zero element.
* First try on the diagonal, if it fails, look elsewhere.
*/
std::pair<size_t, size_t> icolrow = pivot_search(col, matrix);
size_t icol = icolrow.first;
size_t irow = icolrow.second;
/*
* swap rows irow and icol, so afterwards the diagonal
* element will be correct. Rarely done, not worth
* optimizing.
*/
if(irow != icol)
{
for(size_t i = 0; i != K; ++i)
std::swap(matrix[irow*K + i], matrix[icol*K + i]);
}
indxr[col] = irow;
indxc[col] = icol;
byte* pivot_row = &matrix[icol*K];
byte c = pivot_row[icol];
if(c == 0)
throw std::invalid_argument("singlar matrix");
if(c != 1)
{ /* otherwhise this is a NOP */
/*
* this is done often, but optimizing is not so
* fruitful, at least in the obvious ways (unrolling)
*/
c = GF_INVERSE[c];
pivot_row[icol] = 1;
const byte* mul_c = GF_MUL_TABLE[c];
for(size_t i = 0; i != K; ++i)
pivot_row[i] = mul_c[pivot_row[i]];
}
/*
* from all rows, remove multiples of the selected row
* to zero the relevant entry (in fact, the entry is not zero
* because we know it must be zero).
* (Here, if we know that the pivot_row is the identity,
* we can optimize the addmul).
*/
id_row[icol] = 1;
if(memcmp(pivot_row, &id_row[0], K) != 0)
{
byte* p = matrix;
for(size_t i = 0; i != K; ++i)
{
if(i != icol)
{
c = p[icol];
p[icol] = 0;
addmul(p, pivot_row, c, K);
}
p += K;
}
}
id_row[icol] = 0;
} /* done all columns */
for(size_t i = 0; i != K; ++i)
{
if(indxr[i] != indxc[i])
{
for(size_t row = 0; row != K; ++row)
std::swap(matrix[row*K + indxr[i]], matrix[row*K + indxc[i]]);
}
}
}
/*
* Generate and invert a Vandermonde matrix.
*