/**
* Licensed to the Apache Software Foundation (ASF) under one
* or more contributor license agreements. See the NOTICE file
* distributed with this work for additional information
* regarding copyright ownership. The ASF licenses this file
* to you under the Apache License, Version 2.0 (the
* "License"); you may not use this file except in compliance
* with the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.hadoop.io.erasurecode.rawcoder.util;
import org.apache.hadoop.classification.InterfaceAudience;
/**
* A GaloisField utility class only caring of 256 fields for efficiency. Some
* of the codes are borrowed from ISA-L implementation (C or ASM codes).
*/
@InterfaceAudience.Private
public final class GF256 {
private GF256() { }
public static byte[] gfBase() {
return GF_BASE;
}
private static final byte[] GF_BASE = new byte[] {
(byte) 0x01, (byte) 0x02, (byte) 0x04, (byte) 0x08, (byte) 0x10,
(byte) 0x20, (byte) 0x40, (byte) 0x80, (byte) 0x1d, (byte) 0x3a,
(byte) 0x74, (byte) 0xe8, (byte) 0xcd, (byte) 0x87, (byte) 0x13,
(byte) 0x26, (byte) 0x4c, (byte) 0x98, (byte) 0x2d, (byte) 0x5a,
(byte) 0xb4, (byte) 0x75, (byte) 0xea, (byte) 0xc9, (byte) 0x8f,
(byte) 0x03, (byte) 0x06, (byte) 0x0c, (byte) 0x18, (byte) 0x30,
(byte) 0x60, (byte) 0xc0, (byte) 0x9d, (byte) 0x27, (byte) 0x4e,
(byte) 0x9c, (byte) 0x25, (byte) 0x4a, (byte) 0x94, (byte) 0x35,
(byte) 0x6a, (byte) 0xd4, (byte) 0xb5, (byte) 0x77, (byte) 0xee,
(byte) 0xc1, (byte) 0x9f, (byte) 0x23, (byte) 0x46, (byte) 0x8c,
(byte) 0x05, (byte) 0x0a, (byte) 0x14, (byte) 0x28, (byte) 0x50,
(byte) 0xa0, (byte) 0x5d, (byte) 0xba, (byte) 0x69, (byte) 0xd2,
(byte) 0xb9, (byte) 0x6f, (byte) 0xde, (byte) 0xa1, (byte) 0x5f,
(byte) 0xbe, (byte) 0x61, (byte) 0xc2, (byte) 0x99, (byte) 0x2f,
(byte) 0x5e, (byte) 0xbc, (byte) 0x65, (byte) 0xca, (byte) 0x89,
(byte) 0x0f, (byte) 0x1e, (byte) 0x3c, (byte) 0x78, (byte) 0xf0,
(byte) 0xfd, (byte) 0xe7, (byte) 0xd3, (byte) 0xbb, (byte) 0x6b,
(byte) 0xd6, (byte) 0xb1, (byte) 0x7f, (byte) 0xfe, (byte) 0xe1,
(byte) 0xdf, (byte) 0xa3, (byte) 0x5b, (byte) 0xb6, (byte) 0x71,
(byte) 0xe2, (byte) 0xd9, (byte) 0xaf, (byte) 0x43, (byte) 0x86,
(byte) 0x11, (byte) 0x22, (byte) 0x44, (byte) 0x88, (byte) 0x0d,
(byte) 0x1a, (byte) 0x34, (byte) 0x68, (byte) 0xd0, (byte) 0xbd,
(byte) 0x67, (byte) 0xce, (byte) 0x81, (byte) 0x1f, (byte) 0x3e,
(byte) 0x7c, (byte) 0xf8, (byte) 0xed, (byte) 0xc7, (byte) 0x93,
(byte) 0x3b, (byte) 0x76, (byte) 0xec, (byte) 0xc5, (byte) 0x97,
(byte) 0x33, (byte) 0x66, (byte) 0xcc, (byte) 0x85, (byte) 0x17,
(byte) 0x2e, (byte) 0x5c, (byte) 0xb8, (byte) 0x6d, (byte) 0xda,
(byte) 0xa9, (byte) 0x4f, (byte) 0x9e, (byte) 0x21, (byte) 0x42,
(byte) 0x84, (byte) 0x15, (byte) 0x2a, (byte) 0x54, (byte) 0xa8,
(byte) 0x4d, (byte) 0x9a, (byte) 0x29, (byte) 0x52, (byte) 0xa4,
(byte) 0x55, (byte) 0xaa, (byte) 0x49, (byte) 0x92, (byte) 0x39,
(byte) 0x72, (byte) 0xe4, (byte) 0xd5, (byte) 0xb7, (byte) 0x73,
(byte) 0xe6, (byte) 0xd1, (byte) 0xbf, (byte) 0x63, (byte) 0xc6,
(byte) 0x91, (byte) 0x3f, (byte) 0x7e, (byte) 0xfc, (byte) 0xe5,
(byte) 0xd7, (byte) 0xb3, (byte) 0x7b, (byte) 0xf6, (byte) 0xf1,
(byte) 0xff, (byte) 0xe3, (byte) 0xdb, (byte) 0xab, (byte) 0x4b,
(byte) 0x96, (byte) 0x31, (byte) 0x62, (byte) 0xc4, (byte) 0x95,
(byte) 0x37, (byte) 0x6e, (byte) 0xdc, (byte) 0xa5, (byte) 0x57,
(byte) 0xae, (byte) 0x41, (byte) 0x82, (byte) 0x19, (byte) 0x32,
(byte) 0x64, (byte) 0xc8, (byte) 0x8d, (byte) 0x07, (byte) 0x0e,
(byte) 0x1c, (byte) 0x38, (byte) 0x70, (byte) 0xe0, (byte) 0xdd,
(byte) 0xa7, (byte) 0x53, (byte) 0xa6, (byte) 0x51, (byte) 0xa2,
(byte) 0x59, (byte) 0xb2, (byte) 0x79, (byte) 0xf2, (byte) 0xf9,
(byte) 0xef, (byte) 0xc3, (byte) 0x9b, (byte) 0x2b, (byte) 0x56,
(byte) 0xac, (byte) 0x45, (byte) 0x8a, (byte) 0x09, (byte) 0x12,
(byte) 0x24, (byte) 0x48, (byte) 0x90, (byte) 0x3d, (byte) 0x7a,
(byte) 0xf4, (byte) 0xf5, (byte) 0xf7, (byte) 0xf3, (byte) 0xfb,
(byte) 0xeb, (byte) 0xcb, (byte) 0x8b, (byte) 0x0b, (byte) 0x16,
(byte) 0x2c, (byte) 0x58, (byte) 0xb0, (byte) 0x7d, (byte) 0xfa,
(byte) 0xe9, (byte) 0xcf, (byte) 0x83, (byte) 0x1b, (byte) 0x36,
(byte) 0x6c, (byte) 0xd8, (byte) 0xad, (byte) 0x47, (byte) 0x8e,
(byte) 0x01
};
public static byte[] gfLogBase() {
return GF_LOG_BASE;
}
private static final byte[] GF_LOG_BASE = new byte[] {
(byte) 0x00, (byte) 0xff, (byte) 0x01, (byte) 0x19, (byte) 0x02,
(byte) 0x32, (byte) 0x1a, (byte) 0xc6, (byte) 0x03, (byte) 0xdf,
(byte) 0x33, (byte) 0xee, (byte) 0x1b, (byte) 0x68, (byte) 0xc7,
(byte) 0x4b, (byte) 0x04, (byte) 0x64, (byte) 0xe0, (byte) 0x0e,
(byte) 0x34, (byte) 0x8d, (byte) 0xef, (byte) 0x81, (byte) 0x1c,
(byte) 0xc1, (byte) 0x69, (byte) 0xf8, (byte) 0xc8, (byte) 0x08,
(byte) 0x4c, (byte) 0x71, (byte) 0x05, (byte) 0x8a, (byte) 0x65,
(byte) 0x2f, (byte) 0xe1, (byte) 0x24, (byte) 0x0f, (byte) 0x21,
(byte) 0x35, (byte) 0x93, (byte) 0x8e, (byte) 0xda, (byte) 0xf0,
(byte) 0x12, (byte) 0x82, (byte) 0x45, (byte) 0x1d, (byte) 0xb5,
(byte) 0xc2, (byte) 0x7d, (byte) 0x6a, (byte) 0x27, (byte) 0xf9,
(byte) 0xb9, (byte) 0xc9, (byte) 0x9a, (byte) 0x09, (byte) 0x78,
(byte) 0x4d, (byte) 0xe4, (byte) 0x72, (byte) 0xa6, (byte) 0x06,
(byte) 0xbf, (byte) 0x8b, (byte) 0x62, (byte) 0x66, (byte) 0xdd,
(byte) 0x30, (byte) 0xfd, (byte) 0xe2, (byte) 0x98, (byte) 0x25,
(byte) 0xb3, (byte) 0x10, (byte) 0x91, (byte) 0x22, (byte) 0x88,
(byte) 0x36, (byte) 0xd0, (byte) 0x94, (byte) 0xce, (byte) 0x8f,
(byte) 0x96, (byte) 0xdb, (byte) 0xbd, (byte) 0xf1, (byte) 0xd2,
(byte) 0x13, (byte) 0x5c, (byte) 0x83, (byte) 0x38, (byte) 0x46,
(byte) 0x40, (byte) 0x1e, (byte) 0x42, (byte) 0xb6, (byte) 0xa3,
(byte) 0xc3, (byte) 0x48, (byte) 0x7e, (byte) 0x6e, (byte) 0x6b,
(byte) 0x3a, (byte) 0x28, (byte) 0x54, (byte) 0xfa, (byte) 0x85,
(byte) 0xba, (byte) 0x3d, (byte) 0xca, (byte) 0x5e, (byte) 0x9b,
(byte) 0x9f, (byte) 0x0a, (byte) 0x15, (byte) 0x79, (byte) 0x2b,
(byte) 0x4e, (byte) 0xd4, (byte) 0xe5, (byte) 0xac, (byte) 0x73,
(byte) 0xf3, (byte) 0xa7, (byte) 0x57, (byte) 0x07, (byte) 0x70,
(byte) 0xc0, (byte) 0xf7, (byte) 0x8c, (byte) 0x80, (byte) 0x63,
(byte) 0x0d, (byte) 0x67, (byte) 0x4a, (byte) 0xde, (byte) 0xed,
(byte) 0x31, (byte) 0xc5, (byte) 0xfe, (byte) 0x18, (byte) 0xe3,
(byte) 0xa5, (byte) 0x99, (byte) 0x77, (byte) 0x26, (byte) 0xb8,
(byte) 0xb4, (byte) 0x7c, (byte) 0x11, (byte) 0x44, (byte) 0x92,
(byte) 0xd9, (byte) 0x23, (byte) 0x20, (byte) 0x89, (byte) 0x2e,
(byte) 0x37, (byte) 0x3f, (byte) 0xd1, (byte) 0x5b, (byte) 0x95,
(byte) 0xbc, (byte) 0xcf, (byte) 0xcd, (byte) 0x90, (byte) 0x87,
(byte) 0x97, (byte) 0xb2, (byte) 0xdc, (byte) 0xfc, (byte) 0xbe,
(byte) 0x61, (byte) 0xf2, (byte) 0x56, (byte) 0xd3, (byte) 0xab,
(byte) 0x14, (byte) 0x2a, (byte) 0x5d, (byte) 0x9e, (byte) 0x84,
(byte) 0x3c, (byte) 0x39, (byte) 0x53, (byte) 0x47, (byte) 0x6d,
(byte) 0x41, (byte) 0xa2, (byte) 0x1f, (byte) 0x2d, (byte) 0x43,
(byte) 0xd8, (byte) 0xb7, (byte) 0x7b, (byte) 0xa4, (byte) 0x76,
(byte) 0xc4, (byte) 0x17, (byte) 0x49, (byte) 0xec, (byte) 0x7f,
(byte) 0x0c, (byte) 0x6f, (byte) 0xf6, (byte) 0x6c, (byte) 0xa1,
(byte) 0x3b, (byte) 0x52, (byte) 0x29, (byte) 0x9d, (byte) 0x55,
(byte) 0xaa, (byte) 0xfb, (byte) 0x60, (byte) 0x86, (byte) 0xb1,
(byte) 0xbb, (byte) 0xcc, (byte) 0x3e, (byte) 0x5a, (byte) 0xcb,
(byte) 0x59, (byte) 0x5f, (byte) 0xb0, (byte) 0x9c, (byte) 0xa9,
(byte) 0xa0, (byte) 0x51, (byte) 0x0b, (byte) 0xf5, (byte) 0x16,
(byte) 0xeb, (byte) 0x7a, (byte) 0x75, (byte) 0x2c, (byte) 0xd7,
(byte) 0x4f, (byte) 0xae, (byte) 0xd5, (byte) 0xe9, (byte) 0xe6,
(byte) 0xe7, (byte) 0xad, (byte) 0xe8, (byte) 0x74, (byte) 0xd6,
(byte) 0xf4, (byte) 0xea, (byte) 0xa8, (byte) 0x50, (byte) 0x58,
(byte) 0xaf
};
private static byte[][] theGfMulTab; // multiply result table in GF 256 space
/**
* Initialize the GF multiply table for performance. Just compute once, and
* avoid repeatedly doing the multiply during encoding/decoding.
*/
static {
theGfMulTab = new byte[256][256];
for (int i = 0; i < 256; i++) {
for (int j = 0; j < 256; j++) {
theGfMulTab[i][j] = gfMul((byte) i, (byte) j);
}
}
}
/**
* Get the big GF multiply table so utilize it efficiently.
* @return the big GF multiply table
*/
public static byte[][] gfMulTab() {
return theGfMulTab;
}
public static byte gfMul(byte a, byte b) {
if ((a == 0) || (b == 0)) {
return 0;
}
int tmp = (GF_LOG_BASE[a & 0xff] & 0xff) +
(GF_LOG_BASE[b & 0xff] & 0xff);
if (tmp > 254) {
tmp -= 255;
}
return GF_BASE[tmp];
}
public static byte gfInv(byte a) {
if (a == 0) {
return 0;
}
return GF_BASE[255 - GF_LOG_BASE[a & 0xff] & 0xff];
}
/**
* Invert a matrix assuming it's invertible.
*
* Ported from Intel ISA-L library.
*/
public static void gfInvertMatrix(byte[] inMatrix, byte[] outMatrix, int n) {
byte temp;
// Set outMatrix[] to the identity matrix
for (int i = 0; i < n * n; i++) {
// memset(outMatrix, 0, n*n)
outMatrix[i] = 0;
}
for (int i = 0; i < n; i++) {
outMatrix[i * n + i] = 1;
}
// Inverse
for (int j, i = 0; i < n; i++) {
// Check for 0 in pivot element
if (inMatrix[i * n + i] == 0) {
// Find a row with non-zero in current column and swap
for (j = i + 1; j < n; j++) {
if (inMatrix[j * n + i] != 0) {
break;
}
}
if (j == n) {
// Couldn't find means it's singular
throw new RuntimeException("Not invertble");
}
for (int k = 0; k < n; k++) {
// Swap rows i,j
temp = inMatrix[i * n + k];
inMatrix[i * n + k] = inMatrix[j * n + k];
inMatrix[j * n + k] = temp;
temp = outMatrix[i * n + k];
outMatrix[i * n + k] = outMatrix[j * n + k];
outMatrix[j * n + k] = temp;
}
}
temp = gfInv(inMatrix[i * n + i]); // 1/pivot
for (j = 0; j < n; j++) {
// Scale row i by 1/pivot
inMatrix[i * n + j] = gfMul(inMatrix[i * n + j], temp);
outMatrix[i * n + j] = gfMul(outMatrix[i * n + j], temp);
}
for (j = 0; j < n; j++) {
if (j == i) {
continue;
}
temp = inMatrix[j * n + i];
for (int k = 0; k < n; k++) {
outMatrix[j * n + k] ^= gfMul(temp, outMatrix[i * n + k]);
inMatrix[j * n + k] ^= gfMul(temp, inMatrix[i * n + k]);
}
}
}
}
/**
* Ported from Intel ISA-L library.
*
* Calculates const table gftbl in GF(2^8) from single input A
* gftbl(A) = {A{00}, A{01}, A{02}, ... , A{0f} }, {A{00}, A{10}, A{20},
* ... , A{f0} } -- from ISA-L implementation
*/
public static void gfVectMulInit(byte c, byte[] tbl, int offset) {
byte c2 = (byte) ((c << 1) ^ ((c & 0x80) != 0 ? 0x1d : 0));
byte c4 = (byte) ((c2 << 1) ^ ((c2 & 0x80) != 0 ? 0x1d : 0));
byte c8 = (byte) ((c4 << 1) ^ ((c4 & 0x80) != 0 ? 0x1d : 0));
byte c3, c5, c6, c7, c9, c10, c11, c12, c13, c14, c15;
byte c17, c18, c19, c20, c21, c22, c23, c24, c25, c26,
c27, c28, c29, c30, c31;
c3 = (byte) (c2 ^ c);
c5 = (byte) (c4 ^ c);
c6 = (byte) (c4 ^ c2);
c7 = (byte) (c4 ^ c3);
c9 = (byte) (c8 ^ c);
c10 = (byte) (c8 ^ c2);
c11 = (byte) (c8 ^ c3);
c12 = (byte) (c8 ^ c4);
c13 = (byte) (c8 ^ c5);
c14 = (byte) (c8 ^ c6);
c15 = (byte) (c8 ^ c7);
tbl[offset + 0] = 0;
tbl[offset + 1] = c;
tbl[offset + 2] = c2;
tbl[offset + 3] = c3;
tbl[offset + 4] = c4;
tbl[offset + 5] = c5;
tbl[offset + 6] = c6;
tbl[offset + 7] = c7;
tbl[offset + 8] = c8;
tbl[offset + 9] = c9;
tbl[offset + 10] = c10;
tbl[offset + 11] = c11;
tbl[offset + 12] = c12;
tbl[offset + 13] = c13;
tbl[offset + 14] = c14;
tbl[offset + 15] = c15;
c17 = (byte) ((c8 << 1) ^ ((c8 & 0x80) != 0 ? 0x1d : 0));
c18 = (byte) ((c17 << 1) ^ ((c17 & 0x80) != 0 ? 0x1d : 0));
c19 = (byte) (c18 ^ c17);
c20 = (byte) ((c18 << 1) ^ ((c18 & 0x80) != 0 ? 0x1d : 0));
c21 = (byte) (c20 ^ c17);
c22 = (byte) (c20 ^ c18);
c23 = (byte) (c20 ^ c19);
c24 = (byte) ((c20 << 1) ^ ((c20 & 0x80) != 0 ? 0x1d : 0));
c25 = (byte) (c24 ^ c17);
c26 = (byte) (c24 ^ c18);
c27 = (byte) (c24 ^ c19);
c28 = (byte) (c24 ^ c20);
c29 = (byte) (c24 ^ c21);
c30 = (byte) (c24 ^ c22);
c31 = (byte) (c24 ^ c23);
tbl[offset + 16] = 0;
tbl[offset + 17] = c17;
tbl[offset + 18] = c18;
tbl[offset + 19] = c19;
tbl[offset + 20] = c20;
tbl[offset + 21] = c21;
tbl[offset + 22] = c22;
tbl[offset + 23] = c23;
tbl[offset + 24] = c24;
tbl[offset + 25] = c25;
tbl[offset + 26] = c26;
tbl[offset + 27] = c27;
tbl[offset + 28] = c28;
tbl[offset + 29] = c29;
tbl[offset + 30] = c30;
tbl[offset + 31] = c31;
}
}