mirror of
https://github.com/ggerganov/wave-share.git
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240 lines
9.5 KiB
C++
240 lines
9.5 KiB
C++
/* Author: Mike Lubinets (aka mersinvald)
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* Date: 29.12.15
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*
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* See LICENSE */
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#ifndef GF_H
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#define GF_H
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#include <stdint.h>
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#include <string.h>
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#include "poly.hpp"
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#if !defined DEBUG && !defined __CC_ARM
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#include <assert.h>
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#else
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#define assert(dummy)
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#endif
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namespace RS {
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namespace gf {
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/* GF tables pre-calculated for 0x11d primitive polynomial */
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const uint8_t exp[512] = {
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0x1, 0x2, 0x4, 0x8, 0x10, 0x20, 0x40, 0x80, 0x1d, 0x3a, 0x74, 0xe8, 0xcd, 0x87, 0x13, 0x26, 0x4c,
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0x98, 0x2d, 0x5a, 0xb4, 0x75, 0xea, 0xc9, 0x8f, 0x3, 0x6, 0xc, 0x18, 0x30, 0x60, 0xc0, 0x9d,
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0x27, 0x4e, 0x9c, 0x25, 0x4a, 0x94, 0x35, 0x6a, 0xd4, 0xb5, 0x77, 0xee, 0xc1, 0x9f, 0x23, 0x46,
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0x8c, 0x5, 0xa, 0x14, 0x28, 0x50, 0xa0, 0x5d, 0xba, 0x69, 0xd2, 0xb9, 0x6f, 0xde, 0xa1, 0x5f,
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0xbe, 0x61, 0xc2, 0x99, 0x2f, 0x5e, 0xbc, 0x65, 0xca, 0x89, 0xf, 0x1e, 0x3c, 0x78, 0xf0, 0xfd,
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0xe7, 0xd3, 0xbb, 0x6b, 0xd6, 0xb1, 0x7f, 0xfe, 0xe1, 0xdf, 0xa3, 0x5b, 0xb6, 0x71, 0xe2, 0xd9,
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0xaf, 0x43, 0x86, 0x11, 0x22, 0x44, 0x88, 0xd, 0x1a, 0x34, 0x68, 0xd0, 0xbd, 0x67, 0xce, 0x81,
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0x1f, 0x3e, 0x7c, 0xf8, 0xed, 0xc7, 0x93, 0x3b, 0x76, 0xec, 0xc5, 0x97, 0x33, 0x66, 0xcc, 0x85,
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0x17, 0x2e, 0x5c, 0xb8, 0x6d, 0xda, 0xa9, 0x4f, 0x9e, 0x21, 0x42, 0x84, 0x15, 0x2a, 0x54, 0xa8,
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0x4d, 0x9a, 0x29, 0x52, 0xa4, 0x55, 0xaa, 0x49, 0x92, 0x39, 0x72, 0xe4, 0xd5, 0xb7, 0x73, 0xe6,
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0xd1, 0xbf, 0x63, 0xc6, 0x91, 0x3f, 0x7e, 0xfc, 0xe5, 0xd7, 0xb3, 0x7b, 0xf6, 0xf1, 0xff, 0xe3,
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0xdb, 0xab, 0x4b, 0x96, 0x31, 0x62, 0xc4, 0x95, 0x37, 0x6e, 0xdc, 0xa5, 0x57, 0xae, 0x41, 0x82,
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0x19, 0x32, 0x64, 0xc8, 0x8d, 0x7, 0xe, 0x1c, 0x38, 0x70, 0xe0, 0xdd, 0xa7, 0x53, 0xa6, 0x51,
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0xa2, 0x59, 0xb2, 0x79, 0xf2, 0xf9, 0xef, 0xc3, 0x9b, 0x2b, 0x56, 0xac, 0x45, 0x8a, 0x9, 0x12,
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0x24, 0x48, 0x90, 0x3d, 0x7a, 0xf4, 0xf5, 0xf7, 0xf3, 0xfb, 0xeb, 0xcb, 0x8b, 0xb, 0x16, 0x2c,
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0x58, 0xb0, 0x7d, 0xfa, 0xe9, 0xcf, 0x83, 0x1b, 0x36, 0x6c, 0xd8, 0xad, 0x47, 0x8e, 0x1, 0x2,
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0x4, 0x8, 0x10, 0x20, 0x40, 0x80, 0x1d, 0x3a, 0x74, 0xe8, 0xcd, 0x87, 0x13, 0x26, 0x4c, 0x98,
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0x2d, 0x5a, 0xb4, 0x75, 0xea, 0xc9, 0x8f, 0x3, 0x6, 0xc, 0x18, 0x30, 0x60, 0xc0, 0x9d, 0x27,
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0x4e, 0x9c, 0x25, 0x4a, 0x94, 0x35, 0x6a, 0xd4, 0xb5, 0x77, 0xee, 0xc1, 0x9f, 0x23, 0x46, 0x8c,
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0x5, 0xa, 0x14, 0x28, 0x50, 0xa0, 0x5d, 0xba, 0x69, 0xd2, 0xb9, 0x6f, 0xde, 0xa1, 0x5f, 0xbe,
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0x61, 0xc2, 0x99, 0x2f, 0x5e, 0xbc, 0x65, 0xca, 0x89, 0xf, 0x1e, 0x3c, 0x78, 0xf0, 0xfd, 0xe7,
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0xd3, 0xbb, 0x6b, 0xd6, 0xb1, 0x7f, 0xfe, 0xe1, 0xdf, 0xa3, 0x5b, 0xb6, 0x71, 0xe2, 0xd9, 0xaf,
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0x43, 0x86, 0x11, 0x22, 0x44, 0x88, 0xd, 0x1a, 0x34, 0x68, 0xd0, 0xbd, 0x67, 0xce, 0x81, 0x1f,
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0x3e, 0x7c, 0xf8, 0xed, 0xc7, 0x93, 0x3b, 0x76, 0xec, 0xc5, 0x97, 0x33, 0x66, 0xcc, 0x85, 0x17,
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0x2e, 0x5c, 0xb8, 0x6d, 0xda, 0xa9, 0x4f, 0x9e, 0x21, 0x42, 0x84, 0x15, 0x2a, 0x54, 0xa8, 0x4d,
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0x9a, 0x29, 0x52, 0xa4, 0x55, 0xaa, 0x49, 0x92, 0x39, 0x72, 0xe4, 0xd5, 0xb7, 0x73, 0xe6, 0xd1,
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0xbf, 0x63, 0xc6, 0x91, 0x3f, 0x7e, 0xfc, 0xe5, 0xd7, 0xb3, 0x7b, 0xf6, 0xf1, 0xff, 0xe3, 0xdb,
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0xab, 0x4b, 0x96, 0x31, 0x62, 0xc4, 0x95, 0x37, 0x6e, 0xdc, 0xa5, 0x57, 0xae, 0x41, 0x82, 0x19,
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0x32, 0x64, 0xc8, 0x8d, 0x7, 0xe, 0x1c, 0x38, 0x70, 0xe0, 0xdd, 0xa7, 0x53, 0xa6, 0x51, 0xa2,
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0x59, 0xb2, 0x79, 0xf2, 0xf9, 0xef, 0xc3, 0x9b, 0x2b, 0x56, 0xac, 0x45, 0x8a, 0x9, 0x12, 0x24,
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0x48, 0x90, 0x3d, 0x7a, 0xf4, 0xf5, 0xf7, 0xf3, 0xfb, 0xeb, 0xcb, 0x8b, 0xb, 0x16, 0x2c, 0x58,
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0xb0, 0x7d, 0xfa, 0xe9, 0xcf, 0x83, 0x1b, 0x36, 0x6c, 0xd8, 0xad, 0x47, 0x8e, 0x1, 0x2
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};
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const uint8_t log[256] = {
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0x0, 0x0, 0x1, 0x19, 0x2, 0x32, 0x1a, 0xc6, 0x3, 0xdf, 0x33, 0xee, 0x1b, 0x68, 0xc7, 0x4b, 0x4,
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0x64, 0xe0, 0xe, 0x34, 0x8d, 0xef, 0x81, 0x1c, 0xc1, 0x69, 0xf8, 0xc8, 0x8, 0x4c, 0x71, 0x5,
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0x8a, 0x65, 0x2f, 0xe1, 0x24, 0xf, 0x21, 0x35, 0x93, 0x8e, 0xda, 0xf0, 0x12, 0x82, 0x45, 0x1d,
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0xb5, 0xc2, 0x7d, 0x6a, 0x27, 0xf9, 0xb9, 0xc9, 0x9a, 0x9, 0x78, 0x4d, 0xe4, 0x72, 0xa6, 0x6,
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0xbf, 0x8b, 0x62, 0x66, 0xdd, 0x30, 0xfd, 0xe2, 0x98, 0x25, 0xb3, 0x10, 0x91, 0x22, 0x88, 0x36,
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0xd0, 0x94, 0xce, 0x8f, 0x96, 0xdb, 0xbd, 0xf1, 0xd2, 0x13, 0x5c, 0x83, 0x38, 0x46, 0x40, 0x1e,
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0x42, 0xb6, 0xa3, 0xc3, 0x48, 0x7e, 0x6e, 0x6b, 0x3a, 0x28, 0x54, 0xfa, 0x85, 0xba, 0x3d, 0xca,
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0x5e, 0x9b, 0x9f, 0xa, 0x15, 0x79, 0x2b, 0x4e, 0xd4, 0xe5, 0xac, 0x73, 0xf3, 0xa7, 0x57, 0x7,
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0x70, 0xc0, 0xf7, 0x8c, 0x80, 0x63, 0xd, 0x67, 0x4a, 0xde, 0xed, 0x31, 0xc5, 0xfe, 0x18, 0xe3,
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0xa5, 0x99, 0x77, 0x26, 0xb8, 0xb4, 0x7c, 0x11, 0x44, 0x92, 0xd9, 0x23, 0x20, 0x89, 0x2e, 0x37,
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0x3f, 0xd1, 0x5b, 0x95, 0xbc, 0xcf, 0xcd, 0x90, 0x87, 0x97, 0xb2, 0xdc, 0xfc, 0xbe, 0x61, 0xf2,
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0x56, 0xd3, 0xab, 0x14, 0x2a, 0x5d, 0x9e, 0x84, 0x3c, 0x39, 0x53, 0x47, 0x6d, 0x41, 0xa2, 0x1f,
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0x2d, 0x43, 0xd8, 0xb7, 0x7b, 0xa4, 0x76, 0xc4, 0x17, 0x49, 0xec, 0x7f, 0xc, 0x6f, 0xf6, 0x6c,
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0xa1, 0x3b, 0x52, 0x29, 0x9d, 0x55, 0xaa, 0xfb, 0x60, 0x86, 0xb1, 0xbb, 0xcc, 0x3e, 0x5a, 0xcb,
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0x59, 0x5f, 0xb0, 0x9c, 0xa9, 0xa0, 0x51, 0xb, 0xf5, 0x16, 0xeb, 0x7a, 0x75, 0x2c, 0xd7, 0x4f,
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0xae, 0xd5, 0xe9, 0xe6, 0xe7, 0xad, 0xe8, 0x74, 0xd6, 0xf4, 0xea, 0xa8, 0x50, 0x58, 0xaf
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};
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/* ################################
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* # OPERATIONS OVER GALUA FIELDS #
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* ################################ */
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/* @brief Addition in Galua Fields
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* @param x - left operand
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* @param y - right operand
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* @return x + y */
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inline uint8_t add(uint8_t x, uint8_t y) {
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return x^y;
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}
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/* ##### GF substraction ###### */
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/* @brief Substraction in Galua Fields
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* @param x - left operand
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* @param y - right operand
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* @return x - y */
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inline uint8_t sub(uint8_t x, uint8_t y) {
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return x^y;
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}
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/* @brief Multiplication in Galua Fields
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* @param x - left operand
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* @param y - rifht operand
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* @return x * y */
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inline uint8_t mul(uint16_t x, uint16_t y){
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if (x == 0 || y == 0)
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return 0;
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return exp[log[x] + log[y]];
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}
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/* @brief Division in Galua Fields
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* @param x - dividend
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* @param y - divisor
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* @return x / y */
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inline uint8_t div(uint8_t x, uint8_t y){
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assert(y != 0);
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if(x == 0) return 0;
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return exp[(log[x] + 255 - log[y]) % 255];
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}
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/* @brief X in power Y w
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* @param x - operand
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* @param power - power
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* @return x^power */
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inline uint8_t pow(uint8_t x, intmax_t power){
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intmax_t i = log[x];
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i *= power;
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i %= 255;
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if(i < 0) i = i + 255;
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return exp[i];
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}
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/* @brief Inversion in Galua Fields
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* @param x - number
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* @return inversion of x */
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inline uint8_t inverse(uint8_t x){
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return exp[255 - log[x]]; /* == div(1, x); */
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}
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/* ##########################
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* # POLYNOMIALS OPERATIONS #
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* ########################## */
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/* @brief Multiplication polynomial by scalar
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* @param &p - source polynomial
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* @param &newp - destination polynomial
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* @param x - scalar */
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inline void
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poly_scale(const Poly *p, Poly *newp, uint16_t x) {
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newp->length = p->length;
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for(uint16_t i = 0; i < p->length; i++){
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newp->at(i) = mul(p->at(i), x);
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}
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}
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/* @brief Addition of two polynomials
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* @param &p - right operand polynomial
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* @param &q - left operand polynomial
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* @param &newp - destination polynomial */
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inline void
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poly_add(const Poly *p, const Poly *q, Poly *newp) {
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newp->length = poly_max(p->length, q->length);
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memset(newp->ptr(), 0, newp->length * sizeof(uint8_t));
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for(uint8_t i = 0; i < p->length; i++){
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newp->at(i + newp->length - p->length) = p->at(i);
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}
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for(uint8_t i = 0; i < q->length; i++){
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newp->at(i + newp->length - q->length) ^= q->at(i);
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}
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}
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/* @brief Multiplication of two polynomials
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* @param &p - right operand polynomial
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* @param &q - left operand polynomial
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* @param &newp - destination polynomial */
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inline void
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poly_mul(const Poly *p, const Poly *q, Poly *newp) {
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newp->length = p->length + q->length - 1;
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memset(newp->ptr(), 0, newp->length * sizeof(uint8_t));
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/* Compute the polynomial multiplication (just like the outer product of two vectors,
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* we multiply each coefficients of p with all coefficients of q) */
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for(uint8_t j = 0; j < q->length; j++){
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for(uint8_t i = 0; i < p->length; i++){
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newp->at(i+j) ^= mul(p->at(i), q->at(j)); /* == r[i + j] = gf_add(r[i+j], gf_mul(p[i], q[j])) */
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}
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}
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}
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/* @brief Division of two polynomials
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* @param &p - right operand polynomial
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* @param &q - left operand polynomial
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* @param &newp - destination polynomial */
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inline void
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poly_div(const Poly *p, const Poly *q, Poly *newp) {
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if(p->ptr() != newp->ptr()) {
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memcpy(newp->ptr(), p->ptr(), p->length*sizeof(uint8_t));
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}
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newp->length = p->length;
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uint8_t coef;
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for(int i = 0; i < (p->length-(q->length-1)); i++){
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coef = newp->at(i);
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if(coef != 0){
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for(uint8_t j = 1; j < q->length; j++){
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if(q->at(j) != 0)
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newp->at(i+j) ^= mul(q->at(j), coef);
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}
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}
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}
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size_t sep = p->length-(q->length-1);
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memmove(newp->ptr(), newp->ptr()+sep, (newp->length-sep) * sizeof(uint8_t));
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newp->length = newp->length-sep;
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}
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/* @brief Evaluation of polynomial in x
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* @param &p - polynomial to evaluate
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* @param x - evaluation point */
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inline int8_t
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poly_eval(const Poly *p, uint16_t x) {
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uint8_t y = p->at(0);
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for(uint8_t i = 1; i < p->length; i++){
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y = mul(y, x) ^ p->at(i);
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}
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return y;
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}
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} /* end of gf namespace */
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}
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#endif // GF_H
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