pcsx-redux/third_party/iec-60908b/tables.c

/*

MIT License

Copyright (c) 2022 Nicolas "Pixel" Noble

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

*/

#include <stdint.h>

#include "tables.h"

/* This isn't your standard CRC32 table, because the yellow book specifies the following polynomial:
   P(x) = (x¹⁶ + x¹⁵ + x² + 1)·(x¹⁶ + x² + x + 1), expanded to Gallois field's polynomial
   x³² + x³¹ + x¹⁶ + x¹⁵ + x⁴ + x³ + x + 1, which encodes to 0x8001801b */

const uint32_t yellow_book_crctable[256] = {
    0x00000000, 0x90910101, 0x91210201, 0x01b00300, 0x92410401, 0x02d00500, 0x03600600, 0x93f10701,  // 00
    0x94810801, 0x04100900, 0x05a00a00, 0x95310b01, 0x06c00c00, 0x96510d01, 0x97e10e01, 0x07700f00,  // 08
    0x99011001, 0x09901100, 0x08201200, 0x98b11301, 0x0b401400, 0x9bd11501, 0x9a611601, 0x0af01700,  // 10
    0x0d801800, 0x9d111901, 0x9ca11a01, 0x0c301b00, 0x9fc11c01, 0x0f501d00, 0x0ee01e00, 0x9e711f01,  // 18
    0x82012001, 0x12902100, 0x13202200, 0x83b12301, 0x10402400, 0x80d12501, 0x81612601, 0x11f02700,  // 20
    0x16802800, 0x86112901, 0x87a12a01, 0x17302b00, 0x84c12c01, 0x14502d00, 0x15e02e00, 0x85712f01,  // 28
    0x1b003000, 0x8b913101, 0x8a213201, 0x1ab03300, 0x89413401, 0x19d03500, 0x18603600, 0x88f13701,  // 30
    0x8f813801, 0x1f103900, 0x1ea03a00, 0x8e313b01, 0x1dc03c00, 0x8d513d01, 0x8ce13e01, 0x1c703f00,  // 38
    0xb4014001, 0x24904100, 0x25204200, 0xb5b14301, 0x26404400, 0xb6d14501, 0xb7614601, 0x27f04700,  // 40
    0x20804800, 0xb0114901, 0xb1a14a01, 0x21304b00, 0xb2c14c01, 0x22504d00, 0x23e04e00, 0xb3714f01,  // 48
    0x2d005000, 0xbd915101, 0xbc215201, 0x2cb05300, 0xbf415401, 0x2fd05500, 0x2e605600, 0xbef15701,  // 50
    0xb9815801, 0x29105900, 0x28a05a00, 0xb8315b01, 0x2bc05c00, 0xbb515d01, 0xbae15e01, 0x2a705f00,  // 58
    0x36006000, 0xa6916101, 0xa7216201, 0x37b06300, 0xa4416401, 0x34d06500, 0x35606600, 0xa5f16701,  // 60
    0xa2816801, 0x32106900, 0x33a06a00, 0xa3316b01, 0x30c06c00, 0xa0516d01, 0xa1e16e01, 0x31706f00,  // 68
    0xaf017001, 0x3f907100, 0x3e207200, 0xaeb17301, 0x3d407400, 0xadd17501, 0xac617601, 0x3cf07700,  // 70
    0x3b807800, 0xab117901, 0xaaa17a01, 0x3a307b00, 0xa9c17c01, 0x39507d00, 0x38e07e00, 0xa8717f01,  // 78
    0xd8018001, 0x48908100, 0x49208200, 0xd9b18301, 0x4a408400, 0xdad18501, 0xdb618601, 0x4bf08700,  // 80
    0x4c808800, 0xdc118901, 0xdda18a01, 0x4d308b00, 0xdec18c01, 0x4e508d00, 0x4fe08e00, 0xdf718f01,  // 88
    0x41009000, 0xd1919101, 0xd0219201, 0x40b09300, 0xd3419401, 0x43d09500, 0x42609600, 0xd2f19701,  // 90
    0xd5819801, 0x45109900, 0x44a09a00, 0xd4319b01, 0x47c09c00, 0xd7519d01, 0xd6e19e01, 0x46709f00,  // 98
    0x5a00a000, 0xca91a101, 0xcb21a201, 0x5bb0a300, 0xc841a401, 0x58d0a500, 0x5960a600, 0xc9f1a701,  // a0
    0xce81a801, 0x5e10a900, 0x5fa0aa00, 0xcf31ab01, 0x5cc0ac00, 0xcc51ad01, 0xcde1ae01, 0x5d70af00,  // a8
    0xc301b001, 0x5390b100, 0x5220b200, 0xc2b1b301, 0x5140b400, 0xc1d1b501, 0xc061b601, 0x50f0b700,  // b0
    0x5780b800, 0xc711b901, 0xc6a1ba01, 0x5630bb00, 0xc5c1bc01, 0x5550bd00, 0x54e0be00, 0xc471bf01,  // b8
    0x6c00c000, 0xfc91c101, 0xfd21c201, 0x6db0c300, 0xfe41c401, 0x6ed0c500, 0x6f60c600, 0xfff1c701,  // c0
    0xf881c801, 0x6810c900, 0x69a0ca00, 0xf931cb01, 0x6ac0cc00, 0xfa51cd01, 0xfbe1ce01, 0x6b70cf00,  // c8
    0xf501d001, 0x6590d100, 0x6420d200, 0xf4b1d301, 0x6740d400, 0xf7d1d501, 0xf661d601, 0x66f0d700,  // d0
    0x6180d800, 0xf111d901, 0xf0a1da01, 0x6030db00, 0xf3c1dc01, 0x6350dd00, 0x62e0de00, 0xf271df01,  // d8
    0xee01e001, 0x7e90e100, 0x7f20e200, 0xefb1e301, 0x7c40e400, 0xecd1e501, 0xed61e601, 0x7df0e700,  // e0
    0x7a80e800, 0xea11e901, 0xeba1ea01, 0x7b30eb00, 0xe8c1ec01, 0x7850ed00, 0x79e0ee00, 0xe971ef01,  // e8
    0x7700f000, 0xe791f101, 0xe621f201, 0x76b0f300, 0xe541f401, 0x75d0f500, 0x7460f600, 0xe4f1f701,  // f0
    0xe381f801, 0x7310f900, 0x72a0fa00, 0xe231fb01, 0x71c0fc00, 0xe151fd01, 0xe0e1fe01, 0x7070ff00,  // f8
};

/*
Table above generated using the following code:
*/

#if 0
#include <stdint.h>
#include <stdio.h>

static uint32_t reverse(uint32_t value) {
    value = ((value >> 1) & 0x55555555) | ((value & 0x55555555) << 1);
    value = ((value >> 2) & 0x33333333) | ((value & 0x33333333) << 2);
    value = ((value >> 4) & 0x0F0F0F0F) | ((value & 0x0F0F0F0F) << 4);
    value = ((value >> 8) & 0x00FF00FF) | ((value & 0x00FF00FF) << 8);
    return (value >> 16) | (value << 16);
}

static void make_crc_table(uint32_t table[], const uint32_t poly_in, int reversed) {
    const uint32_t poly = reversed ? reverse(poly_in) : poly_in;
    for (unsigned d = 0; d < 256; d++) {
        uint32_t r = d;
        for (unsigned i = 0; i < 8; i++) {
            uint32_t flip = r & 1 ? poly : 0;
            r >>= 1;
            r ^= flip;
        }
        table[d] = r;
    }
}

int main() {
    uint32_t crc[256];

    // this call can also be used to generate the table at runtime
    make_crc_table(crc, 0x8001801b, 1);

    for (int i = 0; i < 256; i++) {
        if ((i & 7) == 0) printf("    ");
        printf("0x%08x, ", crc[i]);
        if ((i & 7) == 7) {
            printf("  // %02x\n", i - 7);
        }
    }
}
#endif

/* These tables are to help with galois field lookups. The yellow book is
   using the typical galois field primitive of x⁸ + x⁴ + x³ + x² + 1,
   so these tables shouldn't be anything surprising from other galois field
   algorithms. The generator code is still available at the end. The exponent
   table is doubled in order to perform the multiplication operation without
   using modulo 255, which can be slow on some platforms. This is a tradeoff
   between computational speed and memory usage. It is possible to further
   reduce the table size by going only at the maximum of the polynomial used
   for Reed-Solomon, but this would be really small savings, and some
   dangerous and obscure optimizations to make. Also for the case of doing
   reed-solomon over two symbols, pre-generating lookup tables for
   multiplying by 2 and dividing by 3 are going to be very useful in terms
   of speeding up computation of our ECC, so we're going to add them too. */

const uint8_t gf_exp_table[512] = {
    0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80, 0x1d, 0x3a, 0x74, 0xe8, 0xcd, 0x87, 0x13, 0x26,   // 000
    0x4c, 0x98, 0x2d, 0x5a, 0xb4, 0x75, 0xea, 0xc9, 0x8f, 0x03, 0x06, 0x0c, 0x18, 0x30, 0x60, 0xc0,   // 010
    0x9d, 0x27, 0x4e, 0x9c, 0x25, 0x4a, 0x94, 0x35, 0x6a, 0xd4, 0xb5, 0x77, 0xee, 0xc1, 0x9f, 0x23,   // 020
    0x46, 0x8c, 0x05, 0x0a, 0x14, 0x28, 0x50, 0xa0, 0x5d, 0xba, 0x69, 0xd2, 0xb9, 0x6f, 0xde, 0xa1,   // 030
    0x5f, 0xbe, 0x61, 0xc2, 0x99, 0x2f, 0x5e, 0xbc, 0x65, 0xca, 0x89, 0x0f, 0x1e, 0x3c, 0x78, 0xf0,   // 040
    0xfd, 0xe7, 0xd3, 0xbb, 0x6b, 0xd6, 0xb1, 0x7f, 0xfe, 0xe1, 0xdf, 0xa3, 0x5b, 0xb6, 0x71, 0xe2,   // 050
    0xd9, 0xaf, 0x43, 0x86, 0x11, 0x22, 0x44, 0x88, 0x0d, 0x1a, 0x34, 0x68, 0xd0, 0xbd, 0x67, 0xce,   // 060
    0x81, 0x1f, 0x3e, 0x7c, 0xf8, 0xed, 0xc7, 0x93, 0x3b, 0x76, 0xec, 0xc5, 0x97, 0x33, 0x66, 0xcc,   // 070
    0x85, 0x17, 0x2e, 0x5c, 0xb8, 0x6d, 0xda, 0xa9, 0x4f, 0x9e, 0x21, 0x42, 0x84, 0x15, 0x2a, 0x54,   // 080
    0xa8, 0x4d, 0x9a, 0x29, 0x52, 0xa4, 0x55, 0xaa, 0x49, 0x92, 0x39, 0x72, 0xe4, 0xd5, 0xb7, 0x73,   // 090
    0xe6, 0xd1, 0xbf, 0x63, 0xc6, 0x91, 0x3f, 0x7e, 0xfc, 0xe5, 0xd7, 0xb3, 0x7b, 0xf6, 0xf1, 0xff,   // 0a0
    0xe3, 0xdb, 0xab, 0x4b, 0x96, 0x31, 0x62, 0xc4, 0x95, 0x37, 0x6e, 0xdc, 0xa5, 0x57, 0xae, 0x41,   // 0b0
    0x82, 0x19, 0x32, 0x64, 0xc8, 0x8d, 0x07, 0x0e, 0x1c, 0x38, 0x70, 0xe0, 0xdd, 0xa7, 0x53, 0xa6,   // 0c0
    0x51, 0xa2, 0x59, 0xb2, 0x79, 0xf2, 0xf9, 0xef, 0xc3, 0x9b, 0x2b, 0x56, 0xac, 0x45, 0x8a, 0x09,   // 0d0
    0x12, 0x24, 0x48, 0x90, 0x3d, 0x7a, 0xf4, 0xf5, 0xf7, 0xf3, 0xfb, 0xeb, 0xcb, 0x8b, 0x0b, 0x16,   // 0e0
    0x2c, 0x58, 0xb0, 0x7d, 0xfa, 0xe9, 0xcf, 0x83, 0x1b, 0x36, 0x6c, 0xd8, 0xad, 0x47, 0x8e, 0x01,   // 0f0
    0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80, 0x1d, 0x3a, 0x74, 0xe8, 0xcd, 0x87, 0x13, 0x26, 0x4c,   // 100
    0x98, 0x2d, 0x5a, 0xb4, 0x75, 0xea, 0xc9, 0x8f, 0x03, 0x06, 0x0c, 0x18, 0x30, 0x60, 0xc0, 0x9d,   // 110
    0x27, 0x4e, 0x9c, 0x25, 0x4a, 0x94, 0x35, 0x6a, 0xd4, 0xb5, 0x77, 0xee, 0xc1, 0x9f, 0x23, 0x46,   // 120
    0x8c, 0x05, 0x0a, 0x14, 0x28, 0x50, 0xa0, 0x5d, 0xba, 0x69, 0xd2, 0xb9, 0x6f, 0xde, 0xa1, 0x5f,   // 130
    0xbe, 0x61, 0xc2, 0x99, 0x2f, 0x5e, 0xbc, 0x65, 0xca, 0x89, 0x0f, 0x1e, 0x3c, 0x78, 0xf0, 0xfd,   // 140
    0xe7, 0xd3, 0xbb, 0x6b, 0xd6, 0xb1, 0x7f, 0xfe, 0xe1, 0xdf, 0xa3, 0x5b, 0xb6, 0x71, 0xe2, 0xd9,   // 150
    0xaf, 0x43, 0x86, 0x11, 0x22, 0x44, 0x88, 0x0d, 0x1a, 0x34, 0x68, 0xd0, 0xbd, 0x67, 0xce, 0x81,   // 160
    0x1f, 0x3e, 0x7c, 0xf8, 0xed, 0xc7, 0x93, 0x3b, 0x76, 0xec, 0xc5, 0x97, 0x33, 0x66, 0xcc, 0x85,   // 170
    0x17, 0x2e, 0x5c, 0xb8, 0x6d, 0xda, 0xa9, 0x4f, 0x9e, 0x21, 0x42, 0x84, 0x15, 0x2a, 0x54, 0xa8,   // 180
    0x4d, 0x9a, 0x29, 0x52, 0xa4, 0x55, 0xaa, 0x49, 0x92, 0x39, 0x72, 0xe4, 0xd5, 0xb7, 0x73, 0xe6,   // 190
    0xd1, 0xbf, 0x63, 0xc6, 0x91, 0x3f, 0x7e, 0xfc, 0xe5, 0xd7, 0xb3, 0x7b, 0xf6, 0xf1, 0xff, 0xe3,   // 1a0
    0xdb, 0xab, 0x4b, 0x96, 0x31, 0x62, 0xc4, 0x95, 0x37, 0x6e, 0xdc, 0xa5, 0x57, 0xae, 0x41, 0x82,   // 1b0
    0x19, 0x32, 0x64, 0xc8, 0x8d, 0x07, 0x0e, 0x1c, 0x38, 0x70, 0xe0, 0xdd, 0xa7, 0x53, 0xa6, 0x51,   // 1c0
    0xa2, 0x59, 0xb2, 0x79, 0xf2, 0xf9, 0xef, 0xc3, 0x9b, 0x2b, 0x56, 0xac, 0x45, 0x8a, 0x09, 0x12,   // 1d0
    0x24, 0x48, 0x90, 0x3d, 0x7a, 0xf4, 0xf5, 0xf7, 0xf3, 0xfb, 0xeb, 0xcb, 0x8b, 0x0b, 0x16, 0x2c,   // 1e0
    0x58, 0xb0, 0x7d, 0xfa, 0xe9, 0xcf, 0x83, 0x1b, 0x36, 0x6c, 0xd8, 0xad, 0x47, 0x8e, 0x01, 0x02,   // 1f0
};

const uint8_t gf_log_table[256] = {
    0x00, 0x00, 0x01, 0x19, 0x02, 0x32, 0x1a, 0xc6, 0x03, 0xdf, 0x33, 0xee, 0x1b, 0x68, 0xc7, 0x4b,   // 00
    0x04, 0x64, 0xe0, 0x0e, 0x34, 0x8d, 0xef, 0x81, 0x1c, 0xc1, 0x69, 0xf8, 0xc8, 0x08, 0x4c, 0x71,   // 10
    0x05, 0x8a, 0x65, 0x2f, 0xe1, 0x24, 0x0f, 0x21, 0x35, 0x93, 0x8e, 0xda, 0xf0, 0x12, 0x82, 0x45,   // 20
    0x1d, 0xb5, 0xc2, 0x7d, 0x6a, 0x27, 0xf9, 0xb9, 0xc9, 0x9a, 0x09, 0x78, 0x4d, 0xe4, 0x72, 0xa6,   // 30
    0x06, 0xbf, 0x8b, 0x62, 0x66, 0xdd, 0x30, 0xfd, 0xe2, 0x98, 0x25, 0xb3, 0x10, 0x91, 0x22, 0x88,   // 40
    0x36, 0xd0, 0x94, 0xce, 0x8f, 0x96, 0xdb, 0xbd, 0xf1, 0xd2, 0x13, 0x5c, 0x83, 0x38, 0x46, 0x40,   // 50
    0x1e, 0x42, 0xb6, 0xa3, 0xc3, 0x48, 0x7e, 0x6e, 0x6b, 0x3a, 0x28, 0x54, 0xfa, 0x85, 0xba, 0x3d,   // 60
    0xca, 0x5e, 0x9b, 0x9f, 0x0a, 0x15, 0x79, 0x2b, 0x4e, 0xd4, 0xe5, 0xac, 0x73, 0xf3, 0xa7, 0x57,   // 70
    0x07, 0x70, 0xc0, 0xf7, 0x8c, 0x80, 0x63, 0x0d, 0x67, 0x4a, 0xde, 0xed, 0x31, 0xc5, 0xfe, 0x18,   // 80
    0xe3, 0xa5, 0x99, 0x77, 0x26, 0xb8, 0xb4, 0x7c, 0x11, 0x44, 0x92, 0xd9, 0x23, 0x20, 0x89, 0x2e,   // 90
    0x37, 0x3f, 0xd1, 0x5b, 0x95, 0xbc, 0xcf, 0xcd, 0x90, 0x87, 0x97, 0xb2, 0xdc, 0xfc, 0xbe, 0x61,   // a0
    0xf2, 0x56, 0xd3, 0xab, 0x14, 0x2a, 0x5d, 0x9e, 0x84, 0x3c, 0x39, 0x53, 0x47, 0x6d, 0x41, 0xa2,   // b0
    0x1f, 0x2d, 0x43, 0xd8, 0xb7, 0x7b, 0xa4, 0x76, 0xc4, 0x17, 0x49, 0xec, 0x7f, 0x0c, 0x6f, 0xf6,   // c0
    0x6c, 0xa1, 0x3b, 0x52, 0x29, 0x9d, 0x55, 0xaa, 0xfb, 0x60, 0x86, 0xb1, 0xbb, 0xcc, 0x3e, 0x5a,   // d0
    0xcb, 0x59, 0x5f, 0xb0, 0x9c, 0xa9, 0xa0, 0x51, 0x0b, 0xf5, 0x16, 0xeb, 0x7a, 0x75, 0x2c, 0xd7,   // e0
    0x4f, 0xae, 0xd5, 0xe9, 0xe6, 0xe7, 0xad, 0xe8, 0x74, 0xd6, 0xf4, 0xea, 0xa8, 0x50, 0x58, 0xaf,   // f0
};

const uint8_t gf_mul2_table[256] = {
    0x00, 0x02, 0x04, 0x06, 0x08, 0x0a, 0x0c, 0x0e, 0x10, 0x12, 0x14, 0x16, 0x18, 0x1a, 0x1c, 0x1e,   // 00
    0x20, 0x22, 0x24, 0x26, 0x28, 0x2a, 0x2c, 0x2e, 0x30, 0x32, 0x34, 0x36, 0x38, 0x3a, 0x3c, 0x3e,   // 10
    0x40, 0x42, 0x44, 0x46, 0x48, 0x4a, 0x4c, 0x4e, 0x50, 0x52, 0x54, 0x56, 0x58, 0x5a, 0x5c, 0x5e,   // 20
    0x60, 0x62, 0x64, 0x66, 0x68, 0x6a, 0x6c, 0x6e, 0x70, 0x72, 0x74, 0x76, 0x78, 0x7a, 0x7c, 0x7e,   // 30
    0x80, 0x82, 0x84, 0x86, 0x88, 0x8a, 0x8c, 0x8e, 0x90, 0x92, 0x94, 0x96, 0x98, 0x9a, 0x9c, 0x9e,   // 40
    0xa0, 0xa2, 0xa4, 0xa6, 0xa8, 0xaa, 0xac, 0xae, 0xb0, 0xb2, 0xb4, 0xb6, 0xb8, 0xba, 0xbc, 0xbe,   // 50
    0xc0, 0xc2, 0xc4, 0xc6, 0xc8, 0xca, 0xcc, 0xce, 0xd0, 0xd2, 0xd4, 0xd6, 0xd8, 0xda, 0xdc, 0xde,   // 60
    0xe0, 0xe2, 0xe4, 0xe6, 0xe8, 0xea, 0xec, 0xee, 0xf0, 0xf2, 0xf4, 0xf6, 0xf8, 0xfa, 0xfc, 0xfe,   // 70
    0x1d, 0x1f, 0x19, 0x1b, 0x15, 0x17, 0x11, 0x13, 0x0d, 0x0f, 0x09, 0x0b, 0x05, 0x07, 0x01, 0x03,   // 80
    0x3d, 0x3f, 0x39, 0x3b, 0x35, 0x37, 0x31, 0x33, 0x2d, 0x2f, 0x29, 0x2b, 0x25, 0x27, 0x21, 0x23,   // 90
    0x5d, 0x5f, 0x59, 0x5b, 0x55, 0x57, 0x51, 0x53, 0x4d, 0x4f, 0x49, 0x4b, 0x45, 0x47, 0x41, 0x43,   // a0
    0x7d, 0x7f, 0x79, 0x7b, 0x75, 0x77, 0x71, 0x73, 0x6d, 0x6f, 0x69, 0x6b, 0x65, 0x67, 0x61, 0x63,   // b0
    0x9d, 0x9f, 0x99, 0x9b, 0x95, 0x97, 0x91, 0x93, 0x8d, 0x8f, 0x89, 0x8b, 0x85, 0x87, 0x81, 0x83,   // c0
    0xbd, 0xbf, 0xb9, 0xbb, 0xb5, 0xb7, 0xb1, 0xb3, 0xad, 0xaf, 0xa9, 0xab, 0xa5, 0xa7, 0xa1, 0xa3,   // d0
    0xdd, 0xdf, 0xd9, 0xdb, 0xd5, 0xd7, 0xd1, 0xd3, 0xcd, 0xcf, 0xc9, 0xcb, 0xc5, 0xc7, 0xc1, 0xc3,   // e0
    0xfd, 0xff, 0xf9, 0xfb, 0xf5, 0xf7, 0xf1, 0xf3, 0xed, 0xef, 0xe9, 0xeb, 0xe5, 0xe7, 0xe1, 0xe3,   // f0
};

const uint8_t gf_div3_table[256] = {
    0x00, 0xf4, 0xf5, 0x01, 0xf7, 0x03, 0x02, 0xf6, 0xf3, 0x07, 0x06, 0xf2, 0x04, 0xf0, 0xf1, 0x05,  // 00
    0xfb, 0x0f, 0x0e, 0xfa, 0x0c, 0xf8, 0xf9, 0x0d, 0x08, 0xfc, 0xfd, 0x09, 0xff, 0x0b, 0x0a, 0xfe,  // 10
    0xeb, 0x1f, 0x1e, 0xea, 0x1c, 0xe8, 0xe9, 0x1d, 0x18, 0xec, 0xed, 0x19, 0xef, 0x1b, 0x1a, 0xee,  // 20
    0x10, 0xe4, 0xe5, 0x11, 0xe7, 0x13, 0x12, 0xe6, 0xe3, 0x17, 0x16, 0xe2, 0x14, 0xe0, 0xe1, 0x15,  // 30
    0xcb, 0x3f, 0x3e, 0xca, 0x3c, 0xc8, 0xc9, 0x3d, 0x38, 0xcc, 0xcd, 0x39, 0xcf, 0x3b, 0x3a, 0xce,  // 40
    0x30, 0xc4, 0xc5, 0x31, 0xc7, 0x33, 0x32, 0xc6, 0xc3, 0x37, 0x36, 0xc2, 0x34, 0xc0, 0xc1, 0x35,  // 50
    0x20, 0xd4, 0xd5, 0x21, 0xd7, 0x23, 0x22, 0xd6, 0xd3, 0x27, 0x26, 0xd2, 0x24, 0xd0, 0xd1, 0x25,  // 60
    0xdb, 0x2f, 0x2e, 0xda, 0x2c, 0xd8, 0xd9, 0x2d, 0x28, 0xdc, 0xdd, 0x29, 0xdf, 0x2b, 0x2a, 0xde,  // 70
    0x8b, 0x7f, 0x7e, 0x8a, 0x7c, 0x88, 0x89, 0x7d, 0x78, 0x8c, 0x8d, 0x79, 0x8f, 0x7b, 0x7a, 0x8e,  // 80
    0x70, 0x84, 0x85, 0x71, 0x87, 0x73, 0x72, 0x86, 0x83, 0x77, 0x76, 0x82, 0x74, 0x80, 0x81, 0x75,  // 90
    0x60, 0x94, 0x95, 0x61, 0x97, 0x63, 0x62, 0x96, 0x93, 0x67, 0x66, 0x92, 0x64, 0x90, 0x91, 0x65,  // a0
    0x9b, 0x6f, 0x6e, 0x9a, 0x6c, 0x98, 0x99, 0x6d, 0x68, 0x9c, 0x9d, 0x69, 0x9f, 0x6b, 0x6a, 0x9e,  // b0
    0x40, 0xb4, 0xb5, 0x41, 0xb7, 0x43, 0x42, 0xb6, 0xb3, 0x47, 0x46, 0xb2, 0x44, 0xb0, 0xb1, 0x45,  // c0
    0xbb, 0x4f, 0x4e, 0xba, 0x4c, 0xb8, 0xb9, 0x4d, 0x48, 0xbc, 0xbd, 0x49, 0xbf, 0x4b, 0x4a, 0xbe,  // d0
    0xab, 0x5f, 0x5e, 0xaa, 0x5c, 0xa8, 0xa9, 0x5d, 0x58, 0xac, 0xad, 0x59, 0xaf, 0x5b, 0x5a, 0xae,  // e0
    0x50, 0xa4, 0xa5, 0x51, 0xa7, 0x53, 0x52, 0xa6, 0xa3, 0x57, 0x56, 0xa2, 0x54, 0xa0, 0xa1, 0x55,  // f0
};

#if 0
#include <stdint.h>
#include <stdio.h>

static void create_exponent_table(uint8_t table[], const uint32_t PRIM) {
    uint32_t x = 1;
    for (unsigned i = 0; i < 512; i++) {
        table[i] = x;
        x <<= 1;
        x ^= (x >= 256) ? PRIM : 0;
    }
}

static void create_logarithm_table(uint8_t table[], const uint8_t exp_table[]) {
    for (unsigned i = 0; i < 256; i++) {
        table[i] = 0;
    }
    for (unsigned i = 0; i < 255; i++) {
        table[exp_table[i]] = i;
    }
}

static void create_mul2_table(uint8_t table[], const uint8_t exp_table[], const uint8_t log_table[]) {
    table[0] = 0;
    for (unsigned i = 1; i < 256; i++) {
        table[i] = exp_table[log_table[i] + log_table[2]];
    }
}

static void create_div3_table(uint8_t table[], const uint8_t mul2_table[]) {
    for (unsigned i = 0; i < 256; i++) {
        table[mul2_table[i] ^ i] = i;
    }
}

int main() {
    uint8_t exp_table[512];
    uint8_t log_table[256];
    uint8_t mul2_table[256];
    uint8_t div3_table[256];

    // these calls can also be used to generate the tables at runtime
    create_exponent_table(exp_table, 0x11d);
    create_logarithm_table(log_table, exp_table);
    create_mul2_table(mul2_table, exp_table, log_table);
    create_div3_table(div3_table, mul2_table);

    for (int i = 0; i < 512; i++) {
        if ((i & 15) == 0) printf("    ");
        printf("0x%02x, ", exp_table[i]);
        if ((i & 15) == 15) {
            printf("  // %03x\n", i - 15);
        }
    }
    for (int i = 0; i < 256; i++) {
        if ((i & 15) == 0) printf("    ");
        printf("0x%02x, ", log_table[i]);
        if ((i & 15) == 15) {
            printf("  // %02x\n", i - 15);
        }
    }
    for (int i = 0; i < 256; i++) {
        if ((i & 15) == 0) printf("    ");
        printf("0x%02x, ", mul2_table[i]);
        if ((i & 15) == 15) {
            printf("  // %02x\n", i - 15);
        }
    }
    for (int i = 0; i < 256; i++) {
        if ((i & 15) == 0) printf("    ");
        printf("0x%02x, ", div3_table[i]);
        if ((i & 15) == 15) {
            printf("  // %02x\n", i - 15);
        }
    }
}
#endif