Galois256.cpp

/*
	Copyright (c) 2013-2014 Christopher A. Taylor.  All rights reserved.

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#include "Galois256.hpp"
#include "MemXOR.hpp"
using namespace cat;

#include <stdlib.h> // malloc


//// Bootstrap tables

const u16 cat::GF256_LOG_TABLE[256] = {
	512, 255, 1, 122, 2, 244, 123, 181, 3, 48, 245, 224, 124, 84, 182, 111,
	4, 233, 49, 19, 246, 107, 225, 206, 125, 56, 85, 170, 183, 91, 112, 250,
	5, 117, 234, 10, 50, 156, 20, 213, 247, 203, 108, 178, 226, 37, 207, 210,
	126, 150, 57, 100, 86, 141, 171, 40, 184, 73, 92, 164, 113, 146, 251, 229,
	6, 96, 118, 15, 235, 193, 11, 13, 51, 68, 157, 195, 21, 31, 214, 237,
	248, 168, 204, 17, 109, 222, 179, 120, 227, 162, 38, 98, 208, 176, 211, 8,
	127, 188, 151, 239, 58, 132, 101, 216, 87, 80, 142, 33, 172, 27, 41, 23,
	185, 77, 74, 197, 93, 65, 165, 159, 114, 200, 147, 70, 252, 45, 230, 53,
	7, 175, 97, 161, 119, 221, 16, 167, 236, 30, 194, 67, 12, 192, 14, 95,
	52, 44, 69, 199, 158, 64, 196, 76, 22, 26, 32, 79, 215, 131, 238, 187,
	249, 90, 169, 55, 205, 106, 18, 232, 110, 83, 223, 47, 180, 243, 121, 254,
	228, 145, 163, 72, 39, 140, 99, 149, 209, 36, 177, 202, 212, 155, 9, 116,
	128, 61, 189, 218, 152, 137, 240, 103, 59, 135, 133, 134, 102, 136, 217, 60,
	88, 104, 81, 241, 143, 138, 34, 153, 173, 219, 28, 190, 42, 62, 24, 129,
	186, 130, 78, 25, 75, 63, 198, 43, 94, 191, 66, 29, 166, 220, 160, 174,
	115, 154, 201, 35, 148, 139, 71, 144, 253, 242, 46, 82, 231, 105, 54, 89
};

const u8 cat::GF256_EXP_TABLE[512*2+1] = {
	1, 2, 4, 8, 16, 32, 64, 128, 95, 190, 35, 70, 140, 71, 142, 67,
	134, 83, 166, 19, 38, 76, 152, 111, 222, 227, 153, 109, 218, 235, 137, 77,
	154, 107, 214, 243, 185, 45, 90, 180, 55, 110, 220, 231, 145, 125, 250, 171,
	9, 18, 36, 72, 144, 127, 254, 163, 25, 50, 100, 200, 207, 193, 221, 229,
	149, 117, 234, 139, 73, 146, 123, 246, 179, 57, 114, 228, 151, 113, 226, 155,
	105, 210, 251, 169, 13, 26, 52, 104, 208, 255, 161, 29, 58, 116, 232, 143,
	65, 130, 91, 182, 51, 102, 204, 199, 209, 253, 165, 21, 42, 84, 168, 15,
	30, 60, 120, 240, 191, 33, 66, 132, 87, 174, 3, 6, 12, 24, 48, 96,
	192, 223, 225, 157, 101, 202, 203, 201, 205, 197, 213, 245, 181, 53, 106, 212,
	247, 177, 61, 122, 244, 183, 49, 98, 196, 215, 241, 189, 37, 74, 148, 119,
	238, 131, 89, 178, 59, 118, 236, 135, 81, 162, 27, 54, 108, 216, 239, 129,
	93, 186, 43, 86, 172, 7, 14, 28, 56, 112, 224, 159, 97, 194, 219, 233,
	141, 69, 138, 75, 150, 115, 230, 147, 121, 242, 187, 41, 82, 164, 23, 46,
	92, 184, 47, 94, 188, 39, 78, 156, 103, 206, 195, 217, 237, 133, 85, 170,
	11, 22, 44, 88, 176, 63, 126, 252, 167, 17, 34, 68, 136, 79, 158, 99,
	198, 211, 249, 173, 5, 10, 20, 40, 80, 160, 31, 62, 124, 248, 175, 1,
	2, 4, 8, 16, 32, 64, 128, 95, 190, 35, 70, 140, 71, 142, 67, 134,
	83, 166, 19, 38, 76, 152, 111, 222, 227, 153, 109, 218, 235, 137, 77, 154,
	107, 214, 243, 185, 45, 90, 180, 55, 110, 220, 231, 145, 125, 250, 171, 9,
	18, 36, 72, 144, 127, 254, 163, 25, 50, 100, 200, 207, 193, 221, 229, 149,
	117, 234, 139, 73, 146, 123, 246, 179, 57, 114, 228, 151, 113, 226, 155, 105,
	210, 251, 169, 13, 26, 52, 104, 208, 255, 161, 29, 58, 116, 232, 143, 65,
	130, 91, 182, 51, 102, 204, 199, 209, 253, 165, 21, 42, 84, 168, 15, 30,
	60, 120, 240, 191, 33, 66, 132, 87, 174, 3, 6, 12, 24, 48, 96, 192,
	223, 225, 157, 101, 202, 203, 201, 205, 197, 213, 245, 181, 53, 106, 212, 247,
	177, 61, 122, 244, 183, 49, 98, 196, 215, 241, 189, 37, 74, 148, 119, 238,
	131, 89, 178, 59, 118, 236, 135, 81, 162, 27, 54, 108, 216, 239, 129, 93,
	186, 43, 86, 172, 7, 14, 28, 56, 112, 224, 159, 97, 194, 219, 233, 141,
	69, 138, 75, 150, 115, 230, 147, 121, 242, 187, 41, 82, 164, 23, 46, 92,
	184, 47, 94, 188, 39, 78, 156, 103, 206, 195, 217, 237, 133, 85, 170, 11,
	22, 44, 88, 176, 63, 126, 252, 167, 17, 34, 68, 136, 79, 158, 99, 198,
	211, 249, 173, 5, 10, 20, 40, 80, 160, 31, 62, 124, 248, 175, 1, 0,
};

const u8 cat::GF256_INV_TABLE[256] = {
	0, 1, 175, 202, 248, 70, 101, 114, 124, 46, 35, 77, 157, 54, 57, 247,
	62, 152, 23, 136, 190, 244, 137, 18, 225, 147, 27, 26, 179, 59, 212, 32,
	31, 213, 76, 10, 164, 182, 68, 220, 95, 144, 122, 113, 235, 195, 9, 125,
	223, 253, 230, 189, 162, 120, 13, 156, 246, 14, 178, 29, 106, 84, 16, 153,
	160, 119, 197, 198, 38, 221, 5, 249, 82, 159, 91, 207, 34, 11, 110, 166,
	128, 104, 72, 158, 61, 107, 151, 201, 218, 116, 206, 74, 171, 155, 145, 40,
	192, 139, 209, 134, 115, 6, 241, 180, 81, 129, 60, 85, 169, 176, 78, 167,
	123, 43, 7, 100, 89, 219, 161, 65, 53, 163, 42, 112, 8, 47, 227, 187,
	80, 105, 148, 232, 205, 214, 99, 208, 19, 22, 193, 97, 173, 229, 211, 238,
	41, 94, 224, 25, 130, 233, 200, 86, 17, 63, 170, 93, 55, 12, 83, 73,
	64, 118, 52, 121, 36, 183, 79, 111, 177, 108, 154, 92, 228, 140, 203, 2,
	109, 168, 58, 28, 103, 240, 37, 165, 250, 217, 226, 127, 231, 51, 20, 245,
	96, 138, 234, 45, 199, 66, 67, 196, 150, 87, 3, 174, 215, 132, 90, 75,
	135, 98, 239, 142, 30, 33, 133, 204, 251, 185, 88, 117, 39, 69, 252, 48,
	146, 24, 186, 126, 172, 141, 50, 188, 131, 149, 194, 44, 255, 243, 143, 210,
	181, 102, 254, 237, 21, 191, 56, 15, 4, 71, 184, 216, 222, 49, 242, 236
};


//// Mul/Div tables

u8 * CAT_RESTRICT cat::GF256_MUL_TABLE = 0;
u8 * CAT_RESTRICT cat::GF256_DIV_TABLE = 0;


// Unpack 256x256 multiplication tables
void cat::GF256Init() {
	// If initialized already,
	if (GF256_MUL_TABLE) {
		return;
	}

	// Allocate table memory 65KB x 2
	GF256_MUL_TABLE = (u8 *)malloc(256 * 256 * 2);
	GF256_DIV_TABLE = GF256_MUL_TABLE + 256 * 256;
	u8 *m = GF256_MUL_TABLE, *d = GF256_DIV_TABLE;

	// Unroll y = 0 subtable
	for (int x = 0; x < 256; ++x) {
		m[x] = d[x] = 0;
	}

	// For each other y value,
	for (int y = 1; y < 256; ++y) {
		// Calculate log(y) for mult and 255 - log(y) for div
		const u8 log_y = (u8)GF256_LOG_TABLE[y];
		const u8 log_yn = 255 - log_y;

		// Next subtable
		m += 256;
		d += 256;

		// Unroll x = 0
		m[0] = 0;
		d[0] = 0;

		// Calculate x * y, x / y
		for (int x = 1; x < 256; ++x) {
			int log_x = GF256_LOG_TABLE[x];

			m[x] = GF256_EXP_TABLE[log_x + log_y];
			d[x] = GF256_EXP_TABLE[log_x + log_yn];
		}
	}
}

// Performs "dest[] += src[] * x" operation in GF(256)
void cat::GF256MemMulAdd(void * CAT_RESTRICT vdest, u8 x, const void * CAT_RESTRICT vsrc, int bytes) {
	if (x == 0) {
		return;
	}

	if (x == 1) {
		memxor(vdest, vsrc, bytes);
		return;
	}

	u8 * CAT_RESTRICT dest = reinterpret_cast<u8*>( vdest );
	const u8 * CAT_RESTRICT src = reinterpret_cast<const u8*>( vsrc );
	const u8 * CAT_RESTRICT table = GF256_MUL_TABLE + ((u32)x << 8);

	// For each block of 8 bytes,
	while (bytes >= 8) {
#ifdef CAT_ENDIAN_LITTLE
		// This optimization works because it reduces the number of memory
		// accesses on desktops by almost half.
		u64 x = table[src[0]];
		x |= (u64)table[src[1]] << 8;
		x |= (u64)table[src[2]] << 16;
		x |= (u64)table[src[3]] << 24;
		x |= (u64)table[src[4]] << 32;
		x |= (u64)table[src[5]] << 40;
		x |= (u64)table[src[6]] << 48;
		x |= (u64)table[src[7]] << 56;
		*(u64*)dest ^= x;
#else
		dest[0] ^= table[src[0]];
		dest[1] ^= table[src[1]];
		dest[2] ^= table[src[2]];
		dest[3] ^= table[src[3]];
		dest[4] ^= table[src[4]];
		dest[5] ^= table[src[5]];
		dest[6] ^= table[src[6]];
		dest[7] ^= table[src[7]];
#endif // CAT_ENDIAN_LITTLE

		src += 8;
		dest += 8;
		bytes -= 8;
	}

	// For each byte,
	while (bytes-- > 0) {
		// Multiply source byte by x and add it to destination byte
		*dest++ ^= table[*src++];
	}
}

// Performs "dest[] /= x" operation in GF(256)
void cat::GF256MemDivide(void * CAT_RESTRICT vdest, u8 x, int bytes) {
	u8 * CAT_RESTRICT dest = reinterpret_cast<u8*>( vdest );
	const u8 * CAT_RESTRICT table = GF256_DIV_TABLE + ((u32)x << 8);

	// For each block of 8 bytes,
	while (bytes >= 8) {
#ifdef CAT_ENDIAN_LITTLE
		// This optimization works because it reduces the number of memory
		// accesses on desktops by almost half.
		u64 x = table[dest[0]];
		x |= (u64)table[dest[1]] << 8;
		x |= (u64)table[dest[2]] << 16;
		x |= (u64)table[dest[3]] << 24;
		x |= (u64)table[dest[4]] << 32;
		x |= (u64)table[dest[5]] << 40;
		x |= (u64)table[dest[6]] << 48;
		x |= (u64)table[dest[7]] << 56;
		*(u64*)dest = x;
#else
		dest[0] = table[dest[0]];
		dest[1] = table[dest[1]];
		dest[2] = table[dest[2]];
		dest[3] = table[dest[3]];
		dest[4] = table[dest[4]];
		dest[5] = table[dest[5]];
		dest[6] = table[dest[6]];
		dest[7] = table[dest[7]];
#endif // CAT_ENDIAN_LITTLE

		dest += 8;
		bytes -= 8;
	}

	// For each byte,
	while (bytes-- > 0) {
		// Multiply source byte by x and add it to destination byte
		*dest = table[*dest];
		++dest;
	}
}