2019-01-27 03:16:07 +00:00
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use std::ops::Add;
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use std::ops::Mul;
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use std::ops::Div;
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use std::ops::Sub;
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2019-01-29 07:08:22 +00:00
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use std::ops::AddAssign;
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2019-01-27 03:16:07 +00:00
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// As defined in section 5.7.3
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const OCT_EXP: [u8; 510] = [
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1, 2, 4, 8, 16, 32, 64, 128, 29, 58, 116, 232, 205, 135, 19, 38, 76,
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152, 45, 90, 180, 117, 234, 201, 143, 3, 6, 12, 24, 48, 96, 192, 157,
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39, 78, 156, 37, 74, 148, 53, 106, 212, 181, 119, 238, 193, 159, 35,
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70, 140, 5, 10, 20, 40, 80, 160, 93, 186, 105, 210, 185, 111, 222,
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161, 95, 190, 97, 194, 153, 47, 94, 188, 101, 202, 137, 15, 30, 60,
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120, 240, 253, 231, 211, 187, 107, 214, 177, 127, 254, 225, 223, 163,
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91, 182, 113, 226, 217, 175, 67, 134, 17, 34, 68, 136, 13, 26, 52,
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104, 208, 189, 103, 206, 129, 31, 62, 124, 248, 237, 199, 147, 59,
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118, 236, 197, 151, 51, 102, 204, 133, 23, 46, 92, 184, 109, 218,
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169, 79, 158, 33, 66, 132, 21, 42, 84, 168, 77, 154, 41, 82, 164, 85,
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170, 73, 146, 57, 114, 228, 213, 183, 115, 230, 209, 191, 99, 198,
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145, 63, 126, 252, 229, 215, 179, 123, 246, 241, 255, 227, 219, 171,
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75, 150, 49, 98, 196, 149, 55, 110, 220, 165, 87, 174, 65, 130, 25,
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50, 100, 200, 141, 7, 14, 28, 56, 112, 224, 221, 167, 83, 166, 81,
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162, 89, 178, 121, 242, 249, 239, 195, 155, 43, 86, 172, 69, 138, 9,
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18, 36, 72, 144, 61, 122, 244, 245, 247, 243, 251, 235, 203, 139, 11,
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22, 44, 88, 176, 125, 250, 233, 207, 131, 27, 54, 108, 216, 173, 71,
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142, 1, 2, 4, 8, 16, 32, 64, 128, 29, 58, 116, 232, 205, 135, 19, 38,
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76, 152, 45, 90, 180, 117, 234, 201, 143, 3, 6, 12, 24, 48, 96, 192,
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157, 39, 78, 156, 37, 74, 148, 53, 106, 212, 181, 119, 238, 193, 159,
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35, 70, 140, 5, 10, 20, 40, 80, 160, 93, 186, 105, 210, 185, 111,
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222, 161, 95, 190, 97, 194, 153, 47, 94, 188, 101, 202, 137, 15, 30,
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60, 120, 240, 253, 231, 211, 187, 107, 214, 177, 127, 254, 225, 223,
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163, 91, 182, 113, 226, 217, 175, 67, 134, 17, 34, 68, 136, 13, 26,
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52, 104, 208, 189, 103, 206, 129, 31, 62, 124, 248, 237, 199, 147,
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59, 118, 236, 197, 151, 51, 102, 204, 133, 23, 46, 92, 184, 109, 218,
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169, 79, 158, 33, 66, 132, 21, 42, 84, 168, 77, 154, 41, 82, 164, 85,
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170, 73, 146, 57, 114, 228, 213, 183, 115, 230, 209, 191, 99, 198,
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145, 63, 126, 252, 229, 215, 179, 123, 246, 241, 255, 227, 219, 171,
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75, 150, 49, 98, 196, 149, 55, 110, 220, 165, 87, 174, 65, 130, 25,
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50, 100, 200, 141, 7, 14, 28, 56, 112, 224, 221, 167, 83, 166, 81,
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162, 89, 178, 121, 242, 249, 239, 195, 155, 43, 86, 172, 69, 138, 9,
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18, 36, 72, 144, 61, 122, 244, 245, 247, 243, 251, 235, 203, 139, 11,
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22, 44, 88, 176, 125, 250, 233, 207, 131, 27, 54, 108, 216, 173, 71,
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142];
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// As defined in section 5.7.4, but with a prepended zero to make this zero indexed
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const OCT_LOG: [u8; 256] = [
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0, 0, 1, 25, 2, 50, 26, 198, 3, 223, 51, 238, 27, 104, 199, 75, 4, 100,
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224, 14, 52, 141, 239, 129, 28, 193, 105, 248, 200, 8, 76, 113, 5,
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138, 101, 47, 225, 36, 15, 33, 53, 147, 142, 218, 240, 18, 130, 69,
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29, 181, 194, 125, 106, 39, 249, 185, 201, 154, 9, 120, 77, 228, 114,
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166, 6, 191, 139, 98, 102, 221, 48, 253, 226, 152, 37, 179, 16, 145,
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34, 136, 54, 208, 148, 206, 143, 150, 219, 189, 241, 210, 19, 92,
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131, 56, 70, 64, 30, 66, 182, 163, 195, 72, 126, 110, 107, 58, 40,
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84, 250, 133, 186, 61, 202, 94, 155, 159, 10, 21, 121, 43, 78, 212,
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229, 172, 115, 243, 167, 87, 7, 112, 192, 247, 140, 128, 99, 13, 103,
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74, 222, 237, 49, 197, 254, 24, 227, 165, 153, 119, 38, 184, 180,
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124, 17, 68, 146, 217, 35, 32, 137, 46, 55, 63, 209, 91, 149, 188,
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207, 205, 144, 135, 151, 178, 220, 252, 190, 97, 242, 86, 211, 171,
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20, 42, 93, 158, 132, 60, 57, 83, 71, 109, 65, 162, 31, 45, 67, 216,
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183, 123, 164, 118, 196, 23, 73, 236, 127, 12, 111, 246, 108, 161,
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59, 82, 41, 157, 85, 170, 251, 96, 134, 177, 187, 204, 62, 90, 203,
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89, 95, 176, 156, 169, 160, 81, 11, 245, 22, 235, 122, 117, 44, 215,
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79, 174, 213, 233, 230, 231, 173, 232, 116, 214, 244, 234, 168, 80,
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88, 175];
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2019-02-05 06:44:38 +00:00
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pub static mut OCTET_MUL: [u8; 256*256] = [0; 256*256];
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2019-02-07 06:39:19 +00:00
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// See "Screaming Fast Galois Field Arithmetic Using Intel SIMD Instructions" by Plank et al.
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// Further adapted to AVX2
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pub static mut OCTET_MUL_HI_BITS: [[u8; 32]; 256] = [[0; 32]; 256];
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pub static mut OCTET_MUL_LOW_BITS: [[u8; 32]; 256] = [[0; 32]; 256];
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2019-01-27 03:16:07 +00:00
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#[derive(Clone, Debug, PartialEq)]
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pub struct Octet {
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value: u8
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}
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impl Octet {
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2019-02-08 03:01:22 +00:00
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pub fn new(value: u8) -> Octet {
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Octet {
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value
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}
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}
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2019-01-27 03:16:07 +00:00
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pub fn zero() -> Octet {
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Octet {
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value: 0
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}
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}
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2019-01-27 05:35:43 +00:00
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2019-01-31 22:45:21 +00:00
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pub fn one() -> Octet {
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Octet {
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2019-02-03 20:38:26 +00:00
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value: 1
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2019-01-31 22:45:21 +00:00
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}
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}
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2019-01-27 05:35:43 +00:00
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pub fn alpha(i: u8) -> Octet {
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Octet {
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value: OCT_EXP[i as usize]
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}
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}
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2019-01-30 03:07:16 +00:00
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2019-02-05 06:44:38 +00:00
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// TODO: rather awful hack. This should be replaced with something more user friendly
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pub fn static_init() {
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for x in 0..256 {
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for y in 0..256 {
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if x == 0 || y == 0 {
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continue;
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}
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else {
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let log_u = OCT_LOG[x as usize] as usize;
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let log_v = OCT_LOG[y as usize] as usize;
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unsafe {
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OCTET_MUL[x << 8 | y] = OCT_EXP[log_u + log_v];
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}
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}
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}
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2019-02-07 06:39:19 +00:00
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for y in 0..16 {
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if x == 0 || y == 0 {
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continue;
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}
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else {
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let log_u = OCT_LOG[x as usize] as usize;
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let log_hi_bits = OCT_LOG[(y << 4) as usize] as usize;
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let log_low_bits = OCT_LOG[y as usize] as usize;
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unsafe {
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OCTET_MUL_HI_BITS[x as usize][y as usize] = OCT_EXP[log_u + log_hi_bits];
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OCTET_MUL_LOW_BITS[x as usize][y as usize] = OCT_EXP[log_u + log_low_bits];
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OCTET_MUL_HI_BITS[x as usize][(y + 16) as usize] = OCT_EXP[log_u + log_hi_bits];
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OCTET_MUL_LOW_BITS[x as usize][(y + 16) as usize] = OCT_EXP[log_u + log_low_bits];
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}
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}
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}
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2019-02-05 06:44:38 +00:00
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}
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}
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pub fn byte(&self) -> u8 {
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self.value
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}
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2019-01-30 03:07:16 +00:00
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pub fn fma(&mut self, other1: &Octet, other2: &Octet) {
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if other1.value != 0 && other2.value != 0 {
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unsafe {
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// This is safe because value is a u8, and OCT_LOG is 256 elements long
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let log_u = *OCT_LOG.get_unchecked(other1.value as usize) as usize;
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let log_v = *OCT_LOG.get_unchecked(other2.value as usize) as usize;
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// This is safe because the sum of two values in OCT_LOG cannot exceed 509
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self.value ^= *OCT_EXP.get_unchecked(log_u + log_v)
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}
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}
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}
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2019-01-27 03:16:07 +00:00
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}
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impl Add for Octet {
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type Output = Octet;
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fn add(self, other: Octet) -> Octet {
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Octet {
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// As defined in section 5.7.2, addition on octets is implemented as bitxor
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2019-02-04 06:37:30 +00:00
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value: self.value ^ other.value
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}
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}
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}
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impl<'a, 'b> Add<&'b Octet> for &'a Octet {
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type Output = Octet;
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fn add(self, other: &'b Octet) -> Octet {
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Octet {
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// As defined in section 5.7.2, addition on octets is implemented as bitxor
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2019-01-27 03:16:07 +00:00
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value: self.value ^ other.value
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}
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}
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}
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2019-01-29 07:08:22 +00:00
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impl AddAssign for Octet {
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fn add_assign(&mut self, other: Octet) {
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self.value ^= other.value;
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}
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}
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2019-02-04 03:28:32 +00:00
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impl<'a> AddAssign<&'a Octet> for Octet {
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fn add_assign(&mut self, other: &'a Octet) {
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self.value ^= other.value;
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}
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}
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2019-01-27 03:16:07 +00:00
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impl Sub for Octet {
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type Output = Octet;
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fn sub(self, rhs: Octet) -> Octet {
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Octet {
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// As defined in section 5.7.2, subtraction on octets is implemented as bitxor
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value: self.value ^ rhs.value
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}
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}
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}
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impl Mul for Octet {
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type Output = Octet;
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fn mul(self, other: Octet) -> Octet {
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2019-01-30 02:20:36 +00:00
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&self * &other
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}
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}
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impl<'a, 'b> Mul<&'b Octet> for &'a Octet {
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type Output = Octet;
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fn mul(self, other: &'b Octet) -> Octet {
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2019-01-27 03:16:07 +00:00
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// As defined in section 5.7.2, multiplication is implemented via the tables above
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if self.value == 0 || other.value == 0 {
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Octet {
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value: 0
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}
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}
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else {
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2019-01-30 02:32:57 +00:00
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unsafe {
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// This is safe because value is a u8, and OCT_LOG is 256 elements long
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let log_u = *OCT_LOG.get_unchecked(self.value as usize) as usize;
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let log_v = *OCT_LOG.get_unchecked(other.value as usize) as usize;
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// This is safe because the sum of two values in OCT_LOG cannot exceed 509
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Octet {
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value: *OCT_EXP.get_unchecked(log_u + log_v)
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}
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2019-01-27 03:16:07 +00:00
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}
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}
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}
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}
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impl Div for Octet {
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type Output = Octet;
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fn div(self, rhs: Octet) -> Octet {
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2019-02-03 03:22:39 +00:00
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&self / &rhs
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}
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}
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impl<'a, 'b> Div<&'b Octet> for &'a Octet {
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type Output = Octet;
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fn div(self, rhs: &'b Octet) -> Octet {
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2019-01-27 03:16:07 +00:00
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assert_ne!(0, rhs.value);
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// As defined in section 5.7.2, division is implemented via the tables above
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if self.value == 0 {
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Octet {
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value: 0
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}
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}
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else {
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let log_u = OCT_LOG[self.value as usize] as usize;
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let log_v = OCT_LOG[rhs.value as usize] as usize;
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Octet {
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value: OCT_EXP[255 + log_u - log_v]
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}
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}
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}
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}
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#[cfg(test)]
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mod tests {
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extern crate rand;
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use octet::tests::rand::Rng;
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use octet::Octet;
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2019-01-30 02:32:57 +00:00
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use octet::OCT_LOG;
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use octet::OCT_EXP;
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2019-02-09 19:17:08 +00:00
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use octet::OCTET_MUL_LOW_BITS;
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use octet::OCTET_MUL_HI_BITS;
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#[test]
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fn multiplication_tables() {
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Octet::static_init();
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for i in 0..=255 {
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for j in 0..=255 {
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let expected = Octet::new(i) * Octet::new(j);
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let low;
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let hi;
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unsafe {
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low = OCTET_MUL_LOW_BITS[i as usize][(j & 0x0F) as usize];
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hi = OCTET_MUL_HI_BITS[i as usize][((j & 0xF0) >> 4) as usize];
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}
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assert_eq!(low ^ hi, expected.byte());
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}
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}
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}
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2019-01-27 03:16:07 +00:00
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#[test]
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fn addition() {
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let octet = Octet {
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value: rand::thread_rng().gen()
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};
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let octet2 = octet.clone();
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let zero = Octet {
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value: 0
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};
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// See section 5.7.2. u is its own additive inverse
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assert_eq!(zero, octet + octet2);
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}
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#[test]
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fn multiplication_identity() {
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let octet = Octet {
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value: rand::thread_rng().gen()
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};
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let one = Octet {
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value: 1
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};
|
|
|
|
assert_eq!(octet, octet.clone() * one);
|
|
|
|
}
|
|
|
|
|
|
|
|
#[test]
|
|
|
|
fn multiplicative_inverse() {
|
|
|
|
let octet = Octet {
|
|
|
|
value: rand::thread_rng().gen_range(1, 255)
|
|
|
|
};
|
|
|
|
let one = Octet {
|
|
|
|
value: 1
|
|
|
|
};
|
|
|
|
assert_eq!(one.clone(), octet.clone() * (one.clone() / octet.clone()));
|
|
|
|
}
|
|
|
|
|
|
|
|
#[test]
|
|
|
|
fn division() {
|
|
|
|
let octet = Octet {
|
|
|
|
value: rand::thread_rng().gen_range(1, 255)
|
|
|
|
};
|
|
|
|
let octet2 = octet.clone();
|
|
|
|
let one = Octet {
|
|
|
|
value: 1
|
|
|
|
};
|
|
|
|
assert_eq!(one, octet / octet2);
|
|
|
|
}
|
2019-01-30 02:32:57 +00:00
|
|
|
|
|
|
|
#[test]
|
|
|
|
fn unsafe_mul_gaurantees() {
|
|
|
|
let max_value = *OCT_LOG.iter().max().unwrap() as usize;
|
|
|
|
assert!(2*max_value < OCT_EXP.len());
|
|
|
|
}
|
2019-01-30 03:07:16 +00:00
|
|
|
|
|
|
|
#[test]
|
|
|
|
fn fma() {
|
|
|
|
let mut result = Octet::zero();
|
|
|
|
let mut fma_result = Octet::zero();
|
|
|
|
for i in 0..255 {
|
|
|
|
for j in 0..255 {
|
2019-02-08 03:06:08 +00:00
|
|
|
result += Octet::new(i) * Octet::new(j);
|
|
|
|
fma_result.fma(&Octet::new(i), &Octet::new(j));
|
2019-01-30 03:07:16 +00:00
|
|
|
assert_eq!(result, fma_result);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
2019-01-27 03:16:07 +00:00
|
|
|
}
|