1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
/// input data
/// output parity data
pub fn encode(data: [u8; 8]) -> u8 {
let data = u64::from_le_bytes(data);
let mut ret = 0u8;
for (i, mask) in generated::PARITY_BITS_MASK.iter().enumerate() {
let parity_bit = ((data & mask).count_ones() & 1) as u8;
ret |= parity_bit << i;
}
ret |= ((data.count_ones() & 1) as u8) << 7;
ret
}
/// correct input data if there is one bit error,
/// return Err(()) if double bit error was detected
pub fn decode(src_data: &mut [u8; 8], exp_parity: u8) -> Result<(), ()> {
let mut data = u64::from_le_bytes(*src_data);
let mut index_of_error = 0;
debug_assert_eq!(7, generated::PARITY_BITS_MASK.len());
for (i, mask) in generated::PARITY_BITS_MASK.iter().enumerate() {
let parity = ((data & mask).count_ones() & 1) as u8;
let expected = (exp_parity >> i) & 1;
if parity != expected {
index_of_error |= 1u8 << i;
}
}
let overall_parity = (data.count_ones() & 1) as u8;
let overall_expected = (exp_parity >> 7) & 1;
let overall_correct = overall_expected == overall_parity;
match (index_of_error, overall_correct) {
(0, true) => Ok(()),
(0, false) => Err(()),
(_, true) => Err(()),
(_, false) => {
let skip = if !index_of_error.is_power_of_two() {
8 - (index_of_error.leading_zeros() as u8) + 1
} else {
8 - (index_of_error.leading_zeros() as u8)
};
index_of_error -= skip;
data ^= 1u64 << index_of_error;
*src_data = data.to_le_bytes();
Ok(())
}
}
}
mod generated {
/*
Generated with:
```python
from math import floor, ceil, log2
def is_power_of_two(n: int) -> bool:
return log2(n).is_integer()
def next_power_of_two(n: int) -> int:
if is_power_of_two(n):
return n << 1
else:
return 2 ** ceil(log2(n))
def data_bits_covered_by_parity(parity: int, lim: int):
assert is_power_of_two(parity), "parity bits should be powert of two"
# use 1-based indexing for simpler computational logic
data_index = 1 # bit we're currently at in the DATA bitstring
total_index = 3 # bit we're currently at in the OVERALL bitstring
while data_index <= lim:
curr_bit_is_data = not is_power_of_two(total_index)
if curr_bit_is_data and (total_index % (parity << 1)) >= parity:
yield data_index - 1 # adjust output to be zero indexed
data_index += curr_bit_is_data
total_index += 1
return None
def parity_bits_needed(data_len):
n = next_power_of_two(data_len)
lower_bin = floor(log2(n))
upper_bin = lower_bin + 1
data_bit_boundary = n - lower_bin - 1
return lower_bin if data_len <= data_bit_boundary else upper_bin
def calc_parity_bit_mask(parity: int, data_len: int):
mask = 0
for data_index in data_bits_covered_by_parity(parity, data_len):
mask = mask | (1 << data_index)
return mask
data_len = 64
n_parity_bits = parity_bits_needed(data_len)
print("[")
i = 0
power = 1
while i < n_parity_bits:
print("0x%x," % calc_parity_bit_mask(power, data_len))
power <<= 1
i += 1
print("]")
```
*/
pub const PARITY_BITS_MASK: [u64; 7] = [
0xab55555556aaad5b,
0xcd9999999b33366d,
0xf1e1e1e1e3c3c78e,
0x1fe01fe03fc07f0,
0x1fffe0003fff800,
0x1fffffffc000000,
0xfe00000000000000,
];
}
#[cfg(test)]
mod tests {
use super::*;
use quickcheck::{QuickCheck, TestResult};
#[test]
fn somke_test() {
for data in &[[0xff; 8], [0; 8], *b"ABCDEFGH"] {
assert!(enc_dec(*data, IntroduceError::None,));
for i in 0..=63 {
println!("ERROR for {}", i);
assert!(enc_dec(*data, IntroduceError::Single(i),));
}
for i in 0..=63 {
for j in 0..=63 {
if i != j {
assert!(enc_dec(*data, IntroduceError::Double(i, j),));
}
}
}
}
}
#[test]
fn random_data_with_opt_single_error() {
fn prop(data: u64, pos: Option<u8>) -> TestResult {
let err = if let Some(pos) = pos {
if pos >= 64 {
return TestResult::discard();
}
IntroduceError::Single(pos)
} else {
IntroduceError::None
};
TestResult::from_bool(enc_dec(data.to_le_bytes(), err))
}
QuickCheck::new()
.tests(10_000_000_000u64)
.quickcheck(prop as fn(data: u64, pos: Option<u8>) -> TestResult);
}
#[test]
fn random_data_with_opt_double_error() {
fn prop(data: u64, pos1: Option<u8>, pos2: Option<u8>) -> TestResult {
let err = match (pos1, pos2) {
(Some(pos1), Some(pos2)) => {
if pos1 >= 64 || pos2 >= 64 {
return TestResult::discard();
}
if pos1 == pos2 {
IntroduceError::Single(pos1)
} else {
IntroduceError::Double(pos1, pos2)
}
}
(Some(pos), None) | (None, Some(pos)) => {
if pos >= 64 {
return TestResult::discard();
}
IntroduceError::Single(pos)
}
(None, None) => IntroduceError::None,
};
TestResult::from_bool(enc_dec(data.to_le_bytes(), err))
}
QuickCheck::new()
.tests(10_000_000_000u64)
.quickcheck(prop as fn(data: u64, pos1: Option<u8>, pos2: Option<u8>) -> TestResult);
}
enum IntroduceError {
None,
Single(u8),
Double(u8, u8),
}
fn enc_dec(data: [u8; 8], intr_err: IntroduceError) -> bool {
let parity = encode(data);
let mut enc_data = data;
match intr_err {
IntroduceError::None => {
let is_err = decode(&mut enc_data, parity).is_err() || data != enc_data;
if is_err {
eprintln!(
"Error (without error) enc_data {:x?}, parity {:x}",
enc_data, parity
);
false
} else {
true
}
}
IntroduceError::Single(single_err_pos) => {
let mut word = u64::from_le_bytes(enc_data);
word ^= 1u64 << single_err_pos;
enc_data = word.to_le_bytes();
let is_err = decode(&mut enc_data, parity).is_err() || data != enc_data;
if is_err {
println!("introduce error: {:x?} => {:x?}", data, enc_data);
eprintln!(
"Error (with 1 error) enc_data {:x?}, parity {:x}",
enc_data, parity
);
false
} else {
true
}
}
IntroduceError::Double(err_pos1, err_pos2) => {
let mut word = u64::from_le_bytes(enc_data);
word ^= 1u64 << err_pos1;
word ^= 1u64 << err_pos2;
enc_data = word.to_le_bytes();
if decode(&mut enc_data, parity).is_ok() {
println!("introduce error: {:x?} => {:x?}", data, enc_data);
eprintln!(
"Error (with 2 errors) enc_data {:x?}, parity {:x}",
enc_data, parity
);
false
} else {
true
}
}
}
}
}