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Bugfix + added M17 decoder to the linux CI

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AlexandreRouma
2021-10-02 17:01:23 +02:00
parent 26fa23c8f5
commit b4213ea049
86 changed files with 6601 additions and 20 deletions
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2
core/libcorrect/src/CMakeLists.txt Normal file
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add_subdirectory(convolutional)
add_subdirectory(reed-solomon)

5
core/libcorrect/src/convolutional/CMakeLists.txt Normal file
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set(SRCFILES bit.c metric.c history_buffer.c error_buffer.c lookup.c convolutional.c encode.c decode.c)
add_library(correct-convolutional OBJECT ${SRCFILES})
if(HAVE_SSE)
add_subdirectory(sse)
endif()

232
core/libcorrect/src/convolutional/bit.c Normal file
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#include "correct/convolutional/bit.h"
bit_writer_t *bit_writer_create(uint8_t *bytes, size_t len) {
bit_writer_t *w = calloc(1, sizeof(bit_writer_t));
if (bytes) {
bit_writer_reconfigure(w, bytes, len);
}
return w;
}
void bit_writer_reconfigure(bit_writer_t *w, uint8_t *bytes, size_t len) {
w->bytes = bytes;
w->len = len;
w->current_byte = 0;
w->current_byte_len = 0;
w->byte_index = 0;
}
void bit_writer_destroy(bit_writer_t *w) {
free(w);
}
void bit_writer_write(bit_writer_t *w, uint8_t val, unsigned int n) {
for (size_t j = 0; j < n; j++) {
bit_writer_write_1(w, val);
val >>= 1;
}
}
void bit_writer_write_1(bit_writer_t *w, uint8_t val) {
w->current_byte |= val & 1;
w->current_byte_len++;
if (w->current_byte_len == 8) {
// 8 bits in a byte -- move to the next byte
w->bytes[w->byte_index] = w->current_byte;
w->byte_index++;
w->current_byte_len = 0;
w->current_byte = 0;
} else {
w->current_byte <<= 1;
}
}
void bit_writer_write_bitlist(bit_writer_t *w, uint8_t *l, size_t len) {
// first close the current byte
// we might have been given too few elements to do that. be careful.
size_t close_len = 8 - w->current_byte_len;
close_len = (close_len < len) ? close_len : len;
uint16_t b = w->current_byte;
for (ptrdiff_t i = 0; i < close_len; i++) {
b |= l[i];
b <<= 1;
}
l += close_len;
len -= close_len;
uint8_t *bytes = w->bytes;
size_t byte_index = w->byte_index;
if (w->current_byte_len + close_len == 8) {
b >>= 1;
bytes[byte_index] = b;
byte_index++;
} else {
w->current_byte = b;
w->current_byte_len += close_len;
return;
}
size_t full_bytes = len/8;
for (size_t i = 0; i < full_bytes; i++) {
bytes[byte_index] = l[0] << 7 | l[1] << 6 | l[2] << 5 |
l[3] << 4 | l[4] << 3 | l[5] << 2 |
l[6] << 1 | l[7];
byte_index += 1;
l += 8;
}
len -= 8*full_bytes;
b = 0;
for (ptrdiff_t i = 0; i < len; i++) {
b |= l[i];
b <<= 1;
}
w->current_byte = b;
w->byte_index = byte_index;
w->current_byte_len = len;
}
void bit_writer_write_bitlist_reversed(bit_writer_t *w, uint8_t *l, size_t len) {
l = l + len - 1;
uint8_t *bytes = w->bytes;
size_t byte_index = w->byte_index;
uint16_t b;
if (w->current_byte_len != 0) {
size_t close_len = 8 - w->current_byte_len;
close_len = (close_len < len) ? close_len : len;
b = w->current_byte;
for (ptrdiff_t i = 0; i < close_len; i++) {
b |= *l;
b <<= 1;
l--;
}
len -= close_len;
if (w->current_byte_len + close_len == 8) {
b >>= 1;
bytes[byte_index] = b;
byte_index++;
} else {
w->current_byte = b;
w->current_byte_len += close_len;
return;
}
}
size_t full_bytes = len/8;
for (size_t i = 0; i < full_bytes; i++) {
bytes[byte_index] = l[0] << 7 | l[-1] << 6 | l[-2] << 5 |
l[-3] << 4 | l[-4] << 3 | l[-5] << 2 |
l[-6] << 1 | l[-7];
byte_index += 1;
l -= 8;
}
len -= 8*full_bytes;
b = 0;
for (ptrdiff_t i = 0; i < len; i++) {
b |= *l;
b <<= 1;
l--;
}
w->current_byte = (uint8_t)b;
w->byte_index = byte_index;
w->current_byte_len = len;
}
void bit_writer_flush_byte(bit_writer_t *w) {
if (w->current_byte_len != 0) {
w->current_byte <<= (8 - w->current_byte_len);
w->bytes[w->byte_index] = w->current_byte;
w->byte_index++;
w->current_byte_len = 0;
}
}
size_t bit_writer_length(bit_writer_t *w) {
return w->byte_index;
}
uint8_t reverse_byte(uint8_t b) {
return (b & 0x80) >> 7 | (b & 0x40) >> 5 | (b & 0x20) >> 3 |
(b & 0x10) >> 1 | (b & 0x08) << 1 | (b & 0x04) << 3 |
(b & 0x02) << 5 | (b & 0x01) << 7;
}
static uint8_t reverse_table[256];
void create_reverse_table() {
for (uint16_t i = 0; i < 256; i++) {
reverse_table[i] = reverse_byte(i);
}
}
bit_reader_t *bit_reader_create(const uint8_t *bytes, size_t len) {
bit_reader_t *r = calloc(1, sizeof(bit_reader_t));
static bool reverse_table_created = false;
if (!reverse_table_created) {
create_reverse_table();
reverse_table_created = true;
}
if (bytes) {
bit_reader_reconfigure(r, bytes, len);
}
return r;
}
void bit_reader_reconfigure(bit_reader_t *r, const uint8_t *bytes, size_t len) {
r->bytes = bytes;
r->len = len;
r->current_byte_len = 8;
r->current_byte = bytes[0];
r->byte_index = 0;
}
void bit_reader_destroy(bit_reader_t *r) {
free(r);
}
uint8_t bit_reader_read(bit_reader_t *r, unsigned int n) {
unsigned int read = 0;
unsigned int n_copy = n;
if (r->current_byte_len < n) {
read = r->current_byte & ((1 << r->current_byte_len) - 1);
r->byte_index++;
r->current_byte = r->bytes[r->byte_index];
n -= r->current_byte_len;
r->current_byte_len = 8;
read <<= n;
}
uint8_t copy_mask = (1 << n) - 1;
copy_mask <<= (r->current_byte_len - n);
read |= (r->current_byte & copy_mask) >> (r->current_byte_len - n);
r->current_byte_len -= n;
return reverse_table[read] >> (8 - n_copy);
}

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core/libcorrect/src/convolutional/convolutional.c Normal file
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#include "correct/convolutional/convolutional.h"
// https://www.youtube.com/watch?v=b3_lVSrPB6w
correct_convolutional *_correct_convolutional_init(correct_convolutional *conv,
size_t rate, size_t order,
const polynomial_t *poly) {
if (order > 8 * sizeof(shift_register_t)) {
// XXX turn this into an error code
// printf("order must be smaller than 8 * sizeof(shift_register_t)\n");
return NULL;
}
if (rate < 2) {
// XXX turn this into an error code
// printf("rate must be 2 or greater\n");
return NULL;
}
conv->order = order;
conv->rate = rate;
conv->numstates = 1 << order;
unsigned int *table = malloc(sizeof(unsigned int) * (1 << order));
fill_table(conv->rate, conv->order, poly, table);
*(unsigned int **)&conv->table = table;
conv->bit_writer = bit_writer_create(NULL, 0);
conv->bit_reader = bit_reader_create(NULL, 0);
conv->has_init_decode = false;
return conv;
}
correct_convolutional *correct_convolutional_create(size_t rate, size_t order,
const polynomial_t *poly) {
correct_convolutional *conv = malloc(sizeof(correct_convolutional));
correct_convolutional *init_conv = _correct_convolutional_init(conv, rate, order, poly);
if (!init_conv) {
free(conv);
}
return init_conv;
}
void _correct_convolutional_teardown(correct_convolutional *conv) {
free(*(unsigned int **)&conv->table);
bit_writer_destroy(conv->bit_writer);
bit_reader_destroy(conv->bit_reader);
if (conv->has_init_decode) {
pair_lookup_destroy(conv->pair_lookup);
history_buffer_destroy(conv->history_buffer);
error_buffer_destroy(conv->errors);
free(conv->distances);
}
}
void correct_convolutional_destroy(correct_convolutional *conv) {
_correct_convolutional_teardown(conv);
free(conv);
}

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core/libcorrect/src/convolutional/decode.c Normal file
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#include "correct/convolutional/convolutional.h"
void conv_decode_print_iter(correct_convolutional *conv, unsigned int iter,
unsigned int winner_index) {
if (iter < 2220) {
return;
}
printf("iteration: %d\n", iter);
distance_t *errors = conv->errors->write_errors;
printf("errors:\n");
for (shift_register_t i = 0; i < conv->numstates / 2; i++) {
printf("%2d: %d\n", i, errors[i]);
}
printf("\n");
printf("history:\n");
for (shift_register_t i = 0; i < conv->numstates / 2; i++) {
printf("%2d: ", i);
for (unsigned int j = 0; j <= winner_index; j++) {
printf("%d", conv->history_buffer->history[j][i] ? 1 : 0);
}
printf("\n");
}
printf("\n");
}
void convolutional_decode_warmup(correct_convolutional *conv, unsigned int sets,
const uint8_t *soft) {
// first phase: load shiftregister up from 0 (order goes from 1 to conv->order)
// we are building up error metrics for the first order bits
for (unsigned int i = 0; i < conv->order - 1 && i < sets; i++) {
// peel off rate bits from encoded to recover the same `out` as in the encoding process
// the difference being that this `out` will have the channel noise/errors applied
unsigned int out;
if (!soft) {
out = bit_reader_read(conv->bit_reader, conv->rate);
}
const distance_t *read_errors = conv->errors->read_errors;
distance_t *write_errors = conv->errors->write_errors;
// walk all of the state we have so far
for (size_t j = 0; j < (1 << (i + 1)); j += 1) {
unsigned int last = j >> 1;
distance_t dist;
if (soft) {
if (conv->soft_measurement == CORRECT_SOFT_LINEAR) {
dist = metric_soft_distance_linear(conv->table[j], soft + i * conv->rate,
conv->rate);
} else {
dist = metric_soft_distance_quadratic(conv->table[j], soft + i * conv->rate,
conv->rate);
}
} else {
dist = metric_distance(conv->table[j], out);
}
write_errors[j] = dist + read_errors[last];
}
error_buffer_swap(conv->errors);
}
}
void convolutional_decode_inner(correct_convolutional *conv, unsigned int sets,
const uint8_t *soft) {
shift_register_t highbit = 1 << (conv->order - 1);
for (unsigned int i = conv->order - 1; i < (sets - conv->order + 1); i++) {
distance_t *distances = conv->distances;
// lasterrors are the aggregate bit errors for the states of shiftregister for the previous
// time slice
if (soft) {
if (conv->soft_measurement == CORRECT_SOFT_LINEAR) {
for (unsigned int j = 0; j < 1 << (conv->rate); j++) {
distances[j] =
metric_soft_distance_linear(j, soft + i * conv->rate, conv->rate);
}
} else {
for (unsigned int j = 0; j < 1 << (conv->rate); j++) {
distances[j] =
metric_soft_distance_quadratic(j, soft + i * conv->rate, conv->rate);
}
}
} else {
unsigned int out = bit_reader_read(conv->bit_reader, conv->rate);
for (unsigned int i = 0; i < 1 << (conv->rate); i++) {
distances[i] = metric_distance(i, out);
}
}
pair_lookup_t pair_lookup = conv->pair_lookup;
pair_lookup_fill_distance(pair_lookup, distances);
// a mask to get the high order bit from the shift register
unsigned int num_iter = highbit << 1;
const distance_t *read_errors = conv->errors->read_errors;
// aggregate bit errors for this time slice
distance_t *write_errors = conv->errors->write_errors;
uint8_t *history = history_buffer_get_slice(conv->history_buffer);
// walk through all states, ignoring oldest bit
// we will track a best register state (path) and the number of bit errors at that path at
// this time slice
// this loop considers two paths per iteration (high order bit set, clear)
// so, it only runs numstates/2 iterations
// we'll update the history for every state and find the path with the least aggregated bit
// errors
// now run the main loop
// we calculate 2 sets of 2 register states here (4 states per iter)
// this creates 2 sets which share a predecessor, and 2 sets which share a successor
//
// the first set definition is the two states that are the same except for the least order
// bit
// these two share a predecessor because their high n - 1 bits are the same (differ only by
// newest bit)
//
// the second set definition is the two states that are the same except for the high order
// bit
// these two share a successor because the oldest high order bit will be shifted out, and
// the other bits will be present in the successor
//
shift_register_t highbase = highbit >> 1;
for (shift_register_t low = 0, high = highbit, base = 0; high < num_iter;
low += 8, high += 8, base += 4) {
// shifted-right ancestors
// low and low_plus_one share low_past_error
// note that they are the same when shifted right by 1
// same goes for high and high_plus_one
for (shift_register_t offset = 0, base_offset = 0; base_offset < 4;
offset += 2, base_offset += 1) {
distance_pair_key_t low_key = pair_lookup.keys[base + base_offset];
distance_pair_key_t high_key = pair_lookup.keys[highbase + base + base_offset];
distance_pair_t low_concat_dist = pair_lookup.distances[low_key];
distance_pair_t high_concat_dist = pair_lookup.distances[high_key];
distance_t low_past_error = read_errors[base + base_offset];
distance_t high_past_error = read_errors[highbase + base + base_offset];
distance_t low_error = (low_concat_dist & 0xffff) + low_past_error;
distance_t high_error = (high_concat_dist & 0xffff) + high_past_error;
shift_register_t successor = low + offset;
distance_t error;
uint8_t history_mask;
if (low_error <= high_error) {
error = low_error;
history_mask = 0;
} else {
error = high_error;
history_mask = 1;
}
write_errors[successor] = error;
history[successor] = history_mask;
shift_register_t low_plus_one = low + offset + 1;
distance_t low_plus_one_error = (low_concat_dist >> 16) + low_past_error;
distance_t high_plus_one_error = (high_concat_dist >> 16) + high_past_error;
shift_register_t plus_one_successor = low_plus_one;
distance_t plus_one_error;
uint8_t plus_one_history_mask;
if (low_plus_one_error <= high_plus_one_error) {
plus_one_error = low_plus_one_error;
plus_one_history_mask = 0;
} else {
plus_one_error = high_plus_one_error;
plus_one_history_mask = 1;
}
write_errors[plus_one_successor] = plus_one_error;
history[plus_one_successor] = plus_one_history_mask;
}
}
history_buffer_process(conv->history_buffer, write_errors, conv->bit_writer);
error_buffer_swap(conv->errors);
}
}
void convolutional_decode_tail(correct_convolutional *conv, unsigned int sets,
const uint8_t *soft) {
// flush state registers
// now we only shift in 0s, skipping 1-successors
shift_register_t highbit = 1 << (conv->order - 1);
for (unsigned int i = sets - conv->order + 1; i < sets; i++) {
// lasterrors are the aggregate bit errors for the states of shiftregister for the previous
// time slice
const distance_t *read_errors = conv->errors->read_errors;
// aggregate bit errors for this time slice
distance_t *write_errors = conv->errors->write_errors;
uint8_t *history = history_buffer_get_slice(conv->history_buffer);
// calculate the distance from all output states to our sliced bits
distance_t *distances = conv->distances;
if (soft) {
if (conv->soft_measurement == CORRECT_SOFT_LINEAR) {
for (unsigned int j = 0; j < 1 << (conv->rate); j++) {
distances[j] =
metric_soft_distance_linear(j, soft + i * conv->rate, conv->rate);
}
} else {
for (unsigned int j = 0; j < 1 << (conv->rate); j++) {
distances[j] =
metric_soft_distance_quadratic(j, soft + i * conv->rate, conv->rate);
}
}
} else {
unsigned int out = bit_reader_read(conv->bit_reader, conv->rate);
for (unsigned int i = 0; i < 1 << (conv->rate); i++) {
distances[i] = metric_distance(i, out);
}
}
const unsigned int *table = conv->table;
// a mask to get the high order bit from the shift register
unsigned int num_iter = highbit << 1;
unsigned int skip = 1 << (conv->order - (sets - i));
unsigned int base_skip = skip >> 1;
shift_register_t highbase = highbit >> 1;
for (shift_register_t low = 0, high = highbit, base = 0; high < num_iter;
low += skip, high += skip, base += base_skip) {
unsigned int low_output = table[low];
unsigned int high_output = table[high];
distance_t low_dist = distances[low_output];
distance_t high_dist = distances[high_output];
distance_t low_past_error = read_errors[base];
distance_t high_past_error = read_errors[highbase + base];
distance_t low_error = low_dist + low_past_error;
distance_t high_error = high_dist + high_past_error;
shift_register_t successor = low;
distance_t error;
uint8_t history_mask;
if (low_error < high_error) {
error = low_error;
history_mask = 0;
} else {
error = high_error;
history_mask = 1;
}
write_errors[successor] = error;
history[successor] = history_mask;
}
history_buffer_process_skip(conv->history_buffer, write_errors, conv->bit_writer, skip);
error_buffer_swap(conv->errors);
}
}
void _convolutional_decode_init(correct_convolutional *conv, unsigned int min_traceback,
unsigned int traceback_length, unsigned int renormalize_interval) {
conv->has_init_decode = true;
conv->distances = calloc(1 << (conv->rate), sizeof(distance_t));
conv->pair_lookup = pair_lookup_create(conv->rate, conv->order, conv->table);
conv->soft_measurement = CORRECT_SOFT_LINEAR;
// we limit history to go back as far as 5 * the order of our polynomial
conv->history_buffer = history_buffer_create(min_traceback, traceback_length, renormalize_interval,
conv->numstates / 2, 1 << (conv->order - 1));
conv->errors = error_buffer_create(conv->numstates);
}
static ssize_t _convolutional_decode(correct_convolutional *conv, size_t num_encoded_bits,
size_t num_encoded_bytes, uint8_t *msg,
const soft_t *soft_encoded) {
if (!conv->has_init_decode) {
uint64_t max_error_per_input = conv->rate * soft_max;
unsigned int renormalize_interval = distance_max / max_error_per_input;
_convolutional_decode_init(conv, 5 * conv->order, 15 * conv->order, renormalize_interval);
}
size_t sets = num_encoded_bits / conv->rate;
// XXX fix this vvvvvv
size_t decoded_len_bytes = num_encoded_bytes;
bit_writer_reconfigure(conv->bit_writer, msg, decoded_len_bytes);
error_buffer_reset(conv->errors);
history_buffer_reset(conv->history_buffer);
// no outputs are generated during warmup
convolutional_decode_warmup(conv, sets, soft_encoded);
convolutional_decode_inner(conv, sets, soft_encoded);
convolutional_decode_tail(conv, sets, soft_encoded);
history_buffer_flush(conv->history_buffer, conv->bit_writer);
return bit_writer_length(conv->bit_writer);
}
// perform viterbi decoding
// hard decoder
ssize_t correct_convolutional_decode(correct_convolutional *conv, const uint8_t *encoded,
size_t num_encoded_bits, uint8_t *msg) {
if (num_encoded_bits % conv->rate) {
// XXX turn this into an error code
// printf("encoded length of message must be a multiple of rate\n");
return -1;
}
size_t num_encoded_bytes =
(num_encoded_bits % 8) ? (num_encoded_bits / 8 + 1) : (num_encoded_bits / 8);
bit_reader_reconfigure(conv->bit_reader, encoded, num_encoded_bytes);
return _convolutional_decode(conv, num_encoded_bits, num_encoded_bytes, msg, NULL);
}
ssize_t correct_convolutional_decode_soft(correct_convolutional *conv, const soft_t *encoded,
size_t num_encoded_bits, uint8_t *msg) {
if (num_encoded_bits % conv->rate) {
// XXX turn this into an error code
// printf("encoded length of message must be a multiple of rate\n");
return -1;
}
size_t num_encoded_bytes =
(num_encoded_bits % 8) ? (num_encoded_bits / 8 + 1) : (num_encoded_bits / 8);
return _convolutional_decode(conv, num_encoded_bits, num_encoded_bytes, msg, encoded);
}

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core/libcorrect/src/convolutional/encode.c Normal file
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#include "correct/convolutional/convolutional.h"
size_t correct_convolutional_encode_len(correct_convolutional *conv, size_t msg_len) {
size_t msgbits = 8 * msg_len;
size_t encodedbits = conv->rate * (msgbits + conv->order + 1);
return encodedbits;
}
// shift in most significant bit every time, one byte at a time
// shift register takes most recent bit on right, shifts left
// poly is written in same order, just & mask message w/ poly
// assume that encoded length is long enough?
size_t correct_convolutional_encode(correct_convolutional *conv,
const uint8_t *msg,
size_t msg_len,
uint8_t *encoded) {
// convolutional code convolves filter coefficients, given by
// the polynomial, with some history from our message.
// the history is stored as single subsequent bits in shiftregister
shift_register_t shiftregister = 0;
// shiftmask is the shiftregister bit mask that removes bits
// that extend beyond order
// e.g. if order is 7, then remove the 8th bit and beyond
unsigned int shiftmask = (1 << conv->order) - 1;
size_t encoded_len_bits = correct_convolutional_encode_len(conv, msg_len);
size_t encoded_len = (encoded_len_bits % 8) ? (encoded_len_bits / 8 + 1) : (encoded_len_bits / 8);
bit_writer_reconfigure(conv->bit_writer, encoded, encoded_len);
bit_reader_reconfigure(conv->bit_reader, msg, msg_len);
for (size_t i = 0; i < 8 * msg_len; i++) {
// shiftregister has oldest bits on left, newest on right
shiftregister <<= 1;
shiftregister |= bit_reader_read(conv->bit_reader, 1);
shiftregister &= shiftmask;
// shift most significant bit from byte and move down one bit at a time
// we do direct lookup of our convolutional output here
// all of the bits from this convolution are stored in this row
unsigned int out = conv->table[shiftregister];
bit_writer_write(conv->bit_writer, out, conv->rate);
}
// now flush the shiftregister
// this is simply running the loop as above but without any new inputs
// or rather, the new input string is all 0s
for (size_t i = 0; i < conv->order + 1; i++) {
shiftregister <<= 1;
shiftregister &= shiftmask;
unsigned int out = conv->table[shiftregister];
bit_writer_write(conv->bit_writer, out, conv->rate);
}
// 0-fill any remaining bits on our final byte
bit_writer_flush_byte(conv->bit_writer);
return encoded_len_bits;
}

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core/libcorrect/src/convolutional/error_buffer.c Normal file
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#include "correct/convolutional/error_buffer.h"
error_buffer_t *error_buffer_create(unsigned int num_states) {
error_buffer_t *buf = calloc(1, sizeof(error_buffer_t));
// how large are the error buffers?
buf->num_states = num_states;
// save two error metrics, one for last round and one for this
// (double buffer)
// the error metric is the aggregated number of bit errors found
// at a given path which terminates at a particular shift register state
buf->errors[0] = calloc(sizeof(distance_t), num_states);
buf->errors[1] = calloc(sizeof(distance_t), num_states);
// which buffer are we using, 0 or 1?
buf->index = 0;
buf->read_errors = buf->errors[0];
buf->write_errors = buf->errors[1];
return buf;
}
void error_buffer_destroy(error_buffer_t *buf) {
free(buf->errors[0]);
free(buf->errors[1]);
free(buf);
}
void error_buffer_reset(error_buffer_t *buf) {
memset(buf->errors[0], 0, buf->num_states * sizeof(distance_t));
memset(buf->errors[1], 0, buf->num_states * sizeof(distance_t));
buf->index = 0;
buf->read_errors = buf->errors[0];
buf->write_errors = buf->errors[1];
}
void error_buffer_swap(error_buffer_t *buf) {
buf->read_errors = buf->errors[buf->index];
buf->index = (buf->index + 1) % 2;
buf->write_errors = buf->errors[buf->index];
}

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#include "correct/convolutional/history_buffer.h"
history_buffer *history_buffer_create(unsigned int min_traceback_length,
unsigned int traceback_group_length,
unsigned int renormalize_interval, unsigned int num_states,
shift_register_t highbit) {
history_buffer *buf = calloc(1, sizeof(history_buffer));
*(unsigned int *)&buf->min_traceback_length = min_traceback_length;
*(unsigned int *)&buf->traceback_group_length = traceback_group_length;
*(unsigned int *)&buf->cap = min_traceback_length + traceback_group_length;
*(unsigned int *)&buf->num_states = num_states;
*(shift_register_t *)&buf->highbit = highbit;
buf->history = malloc(buf->cap * sizeof(uint8_t *));
for (unsigned int i = 0; i < buf->cap; i++) {
buf->history[i] = calloc(num_states, sizeof(uint8_t));
}
buf->fetched = malloc(buf->cap * sizeof(uint8_t));
buf->index = 0;
buf->len = 0;
buf->renormalize_counter = 0;
buf->renormalize_interval = renormalize_interval;
return buf;
}
void history_buffer_destroy(history_buffer *buf) {
for (unsigned int i = 0; i < buf->cap; i++) {
free(buf->history[i]);
}
free(buf->history);
free(buf->fetched);
free(buf);
}
void history_buffer_reset(history_buffer *buf) {
buf->len = 0;
buf->index = 0;
}
uint8_t *history_buffer_get_slice(history_buffer *buf) { return buf->history[buf->index]; }
shift_register_t history_buffer_search(history_buffer *buf, const distance_t *distances,
unsigned int search_every) {
shift_register_t bestpath;
distance_t leasterror = USHRT_MAX;
// search for a state with the least error
for (shift_register_t state = 0; state < buf->num_states; state += search_every) {
if (distances[state] < leasterror) {
leasterror = distances[state];
bestpath = state;
}
}
return bestpath;
}
void history_buffer_renormalize(history_buffer *buf, distance_t *distances,
shift_register_t min_register) {
distance_t min_distance = distances[min_register];
for (shift_register_t i = 0; i < buf->num_states; i++) {
distances[i] -= min_distance;
}
}
void history_buffer_traceback(history_buffer *buf, shift_register_t bestpath,
unsigned int min_traceback_length, bit_writer_t *output) {
unsigned int fetched_index = 0;
shift_register_t highbit = buf->highbit;
unsigned int index = buf->index;
unsigned int cap = buf->cap;
for (unsigned int j = 0; j < min_traceback_length; j++) {
if (index == 0) {
index = cap - 1;
} else {
index--;
}
// we're walking backwards from what the work we did before
// so, we'll shift high order bits in
// the path will cross multiple different shift register states, and we determine
// which state by going backwards one time slice at a time
uint8_t history = buf->history[index][bestpath];
shift_register_t pathbit = history ? highbit : 0;
bestpath |= pathbit;
bestpath >>= 1;
}
unsigned int prefetch_index = index;
if (prefetch_index == 0) {
prefetch_index = cap - 1;
} else {
prefetch_index--;
}
unsigned int len = buf->len;
for (unsigned int j = min_traceback_length; j < len; j++) {
index = prefetch_index;
if (prefetch_index == 0) {
prefetch_index = cap - 1;
} else {
prefetch_index--;
}
prefetch(buf->history[prefetch_index]);
// we're walking backwards from what the work we did before
// so, we'll shift high order bits in
// the path will cross multiple different shift register states, and we determine
// which state by going backwards one time slice at a time
uint8_t history = buf->history[index][bestpath];
shift_register_t pathbit = history ? highbit : 0;
bestpath |= pathbit;
bestpath >>= 1;
buf->fetched[fetched_index] = (pathbit ? 1 : 0);
fetched_index++;
}
bit_writer_write_bitlist_reversed(output, buf->fetched, fetched_index);
buf->len -= fetched_index;
}
void history_buffer_process_skip(history_buffer *buf, distance_t *distances, bit_writer_t *output,
unsigned int skip) {
buf->index++;
if (buf->index == buf->cap) {
buf->index = 0;
}
buf->renormalize_counter++;
buf->len++;
// there are four ways these branches can resolve
// a) we are neither renormalizing nor doing a traceback
// b) we are renormalizing but not doing a traceback
// c) we are renormalizing and doing a traceback
// d) we are not renormalizing but we are doing a traceback
// in case c, we want to save the effort of finding the bestpath
// since that's expensive
// so we have to check for that case after we renormalize
if (buf->renormalize_counter == buf->renormalize_interval) {
buf->renormalize_counter = 0;
shift_register_t bestpath = history_buffer_search(buf, distances, skip);
history_buffer_renormalize(buf, distances, bestpath);
if (buf->len == buf->cap) {
// reuse the bestpath found for renormalizing
history_buffer_traceback(buf, bestpath, buf->min_traceback_length, output);
}
} else if (buf->len == buf->cap) {
// not renormalizing, find the bestpath here
shift_register_t bestpath = history_buffer_search(buf, distances, skip);
history_buffer_traceback(buf, bestpath, buf->min_traceback_length, output);
}
}
void history_buffer_process(history_buffer *buf, distance_t *distances, bit_writer_t *output) {
history_buffer_process_skip(buf, distances, output, 1);
}
void history_buffer_flush(history_buffer *buf, bit_writer_t *output) {
history_buffer_traceback(buf, 0, 0, output);
}

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#include "correct/convolutional/lookup.h"
// table has numstates rows
// each row contains all of the polynomial output bits concatenated together
// e.g. for rate 2, we have 2 bits in each row
// the first poly gets the LEAST significant bit, last poly gets most significant
void fill_table(unsigned int rate,
unsigned int order,
const polynomial_t *poly,
unsigned int *table) {
for (shift_register_t i = 0; i < 1 << order; i++) {
unsigned int out = 0;
unsigned int mask = 1;
for (size_t j = 0; j < rate; j++) {
out |= (popcount(i & poly[j]) % 2) ? mask : 0;
mask <<= 1;
}
table[i] = out;
}
}
pair_lookup_t pair_lookup_create(unsigned int rate,
unsigned int order,
const unsigned int *table) {
pair_lookup_t pairs;
pairs.keys = malloc(sizeof(unsigned int) * (1 << (order - 1)));
pairs.outputs = calloc((1 << (rate * 2)), sizeof(unsigned int));
unsigned int *inv_outputs = calloc((1 << (rate * 2)), sizeof(unsigned int));
unsigned int output_counter = 1;
// for every (even-numbered) shift register state, find the concatenated output of the state
// and the subsequent state that follows it (low bit set). then, check to see if this
// concatenated output has a unique key assigned to it already. if not, give it a key.
// if it does, retrieve the key. assign this key to the shift register state.
for (unsigned int i = 0; i < (1 << (order - 1)); i++) {
// first get the concatenated pair of outputs
unsigned int out = table[i * 2 + 1];
out <<= rate;
out |= table[i * 2];
// does this concatenated output exist in the outputs table yet?
if (!inv_outputs[out]) {
// doesn't exist, allocate a new key
inv_outputs[out] = output_counter;
pairs.outputs[output_counter] = out;
output_counter++;
}
// set the opaque key for the ith shift register state to the concatenated output entry
pairs.keys[i] = inv_outputs[out];
}
pairs.outputs_len = output_counter;
pairs.output_mask = (1 << (rate)) - 1;
pairs.output_width = rate;
pairs.distances = calloc(pairs.outputs_len, sizeof(distance_pair_t));
free(inv_outputs);
return pairs;
}
void pair_lookup_destroy(pair_lookup_t pairs) {
free(pairs.keys);
free(pairs.outputs);
free(pairs.distances);
}
void pair_lookup_fill_distance(pair_lookup_t pairs, distance_t *distances) {
for (unsigned int i = 1; i < pairs.outputs_len; i += 1) {
output_pair_t concat_out = pairs.outputs[i];
unsigned int i_0 = concat_out & pairs.output_mask;
concat_out >>= pairs.output_width;
unsigned int i_1 = concat_out;
pairs.distances[i] = (distances[i_1] << 16) | distances[i_0];
}
}

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#include "correct/convolutional/metric.h"
// measure the square of the euclidean distance between x and y
// since euclidean dist is sqrt(a^2 + b^2 + ... + n^2), the square is just
// a^2 + b^2 + ... + n^2
distance_t metric_soft_distance_quadratic(unsigned int hard_x, const uint8_t *soft_y, size_t len) {
distance_t dist = 0;
for (unsigned int i = 0; i < len; i++) {
// first, convert hard_x to a soft measurement (0 -> 0, 1 - > 255)
unsigned int soft_x = (hard_x & 1) ? 255 : 0;
hard_x >>= 1;
int d = soft_y[i] - soft_x;
dist += d*d;
}
return dist >> 3;
}

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set(SRCFILES lookup.c convolutional.c encode.c decode.c)
add_library(correct-convolutional-sse OBJECT ${SRCFILES})

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#include "correct/convolutional/sse/convolutional.h"
correct_convolutional_sse *correct_convolutional_sse_create(size_t rate,
size_t order,
const polynomial_t *poly) {
correct_convolutional_sse *conv = malloc(sizeof(correct_convolutional_sse));
correct_convolutional *init_conv = _correct_convolutional_init(&conv->base_conv, rate, order, poly);
if (!init_conv) {
free(conv);
conv = NULL;
}
return conv;
}
void correct_convolutional_sse_destroy(correct_convolutional_sse *conv) {
if (conv->base_conv.has_init_decode) {
oct_lookup_destroy(conv->oct_lookup);
}
_correct_convolutional_teardown(&conv->base_conv);
free(conv);
}

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#include "correct/convolutional/sse/convolutional.h"
static void convolutional_sse_decode_inner(correct_convolutional_sse *sse_conv, unsigned int sets,
const uint8_t *soft) {
correct_convolutional *conv = &sse_conv->base_conv;
shift_register_t highbit = 1 << (conv->order - 1);
unsigned int hist_buf_index = conv->history_buffer->index;
unsigned int hist_buf_cap = conv->history_buffer->cap;
unsigned int hist_buf_len = conv->history_buffer->len;
unsigned int hist_buf_rn_int = conv->history_buffer->renormalize_interval;
unsigned int hist_buf_rn_cnt = conv->history_buffer->renormalize_counter;
for (unsigned int i = conv->order - 1; i < (sets - conv->order + 1); i++) {
distance_t *distances = conv->distances;
// lasterrors are the aggregate bit errors for the states of
// shiftregister for the previous time slice
if (soft) {
if (conv->soft_measurement == CORRECT_SOFT_LINEAR) {
for (unsigned int j = 0; j < 1 << (conv->rate); j++) {
distances[j] =
metric_soft_distance_linear(j, soft + i * conv->rate, conv->rate);
}
} else {
for (unsigned int j = 0; j < 1 << (conv->rate); j++) {
distances[j] =
metric_soft_distance_quadratic(j, soft + i * conv->rate, conv->rate);
}
}
} else {
unsigned int out = bit_reader_read(conv->bit_reader, conv->rate);
for (unsigned int i = 0; i < 1 << (conv->rate); i++) {
distances[i] = metric_distance(i, out);
}
}
oct_lookup_t oct_lookup = sse_conv->oct_lookup;
oct_lookup_fill_distance(oct_lookup, distances);
// a mask to get the high order bit from the shift register
unsigned int num_iter = highbit << 1;
const distance_t *read_errors = conv->errors->read_errors;
// aggregate bit errors for this time slice
distance_t *write_errors = conv->errors->write_errors;
uint8_t *history = conv->history_buffer->history[hist_buf_index];
;
// walk through all states, ignoring oldest bit
// we will track a best register state (path) and the number of bit
// errors at that path at this time slice
// this loop considers two paths per iteration (high order bit set,
// clear)
// so, it only runs numstates/2 iterations
// we'll update the history for every state and find the path with the
// least aggregated bit errors
// now run the main loop
// we calculate 2 sets of 2 register states here (4 states per iter)
// this creates 2 sets which share a predecessor, and 2 sets which share
// a successor
//
// the first set definition is the two states that are the same except
// for the least order bit
// these two share a predecessor because their high n - 1 bits are the
// same (differ only by newest bit)
//
// the second set definition is the two states that are the same except
// for the high order bit
// these two share a successor because the oldest high order bit will be
// shifted out, and the other bits will be present in the successor
//
shift_register_t highbase = highbit >> 1;
shift_register_t oct_highbase = highbase >> 2;
for (shift_register_t low = 0, high = highbit, base = 0, oct = 0; high < num_iter;
low += 32, high += 32, base += 16, oct += 4) {
// shifted-right ancestors
// low and low_plus_one share low_past_error
// note that they are the same when shifted right by 1
// same goes for high and high_plus_one
__m128i past_shuffle_mask =
_mm_set_epi32(0x07060706, 0x05040504, 0x03020302, 0x01000100);
__m128i hist_mask =
_mm_set_epi32(0x80808080, 0x80808080, 0x0e0c0a09, 0x07050301);
// the loop below calculates 64 register states per loop iteration
// it does this by packing the 128-bit xmm registers with 8, 16-bit
// distances
// 4 of these registers hold distances for convolutional shift
// register states with the high bit cleared
// and 4 hold distances for the corresponding shift register
// states with the high bit set
// since each xmm register holds 8 distances, this adds up to a
// total of 8 * 8 = 64 shift register states
for (shift_register_t offset = 0, base_offset = 0; base_offset < 16;
offset += 32, base_offset += 16) {
// load the past error for the register states with the high
// order bit cleared
__m128i low_past_error =
_mm_loadl_epi64((const __m128i *)(read_errors + base + base_offset));
__m128i low_past_error0 =
_mm_loadl_epi64((const __m128i *)(read_errors + base + base_offset + 4));
__m128i low_past_error1 =
_mm_loadl_epi64((const __m128i *)(read_errors + base + base_offset + 8));
__m128i low_past_error2 =
_mm_loadl_epi64((const __m128i *)(read_errors + base + base_offset + 12));
// shuffle the low past error
// register states that differ only by their low order bit share
// a past error
low_past_error = _mm_shuffle_epi8(low_past_error, past_shuffle_mask);
low_past_error0 = _mm_shuffle_epi8(low_past_error0, past_shuffle_mask);
low_past_error1 = _mm_shuffle_epi8(low_past_error1, past_shuffle_mask);
low_past_error2 = _mm_shuffle_epi8(low_past_error2, past_shuffle_mask);
// repeat past error lookup for register states with high order
// bit set
__m128i high_past_error =
_mm_loadl_epi64((const __m128i *)(read_errors + highbase + base + base_offset));
__m128i high_past_error0 = _mm_loadl_epi64(
(const __m128i *)(read_errors + highbase + base + base_offset + 4));
__m128i high_past_error1 = _mm_loadl_epi64(
(const __m128i *)(read_errors + highbase + base + base_offset + 8));
__m128i high_past_error2 = _mm_loadl_epi64(
(const __m128i *)(read_errors + highbase + base + base_offset + 12));
high_past_error = _mm_shuffle_epi8(high_past_error, past_shuffle_mask);
high_past_error0 = _mm_shuffle_epi8(high_past_error0, past_shuffle_mask);
high_past_error1 = _mm_shuffle_epi8(high_past_error1, past_shuffle_mask);
high_past_error2 = _mm_shuffle_epi8(high_past_error2, past_shuffle_mask);
// __m128i this_shuffle_mask = (__m128i){0x80800100, 0x80800302,
// 0x80800504, 0x80800706};
// load the opaque oct distance table keys from out loop index
distance_oct_key_t low_key = oct_lookup.keys[oct + (base_offset / 4)];
distance_oct_key_t low_key0 = oct_lookup.keys[oct + (base_offset / 4) + 1];
distance_oct_key_t low_key1 = oct_lookup.keys[oct + (base_offset / 4) + 2];
distance_oct_key_t low_key2 = oct_lookup.keys[oct + (base_offset / 4) + 3];
// load the distances for the register states with high order
// bit cleared
__m128i low_this_error =
_mm_load_si128((const __m128i *)(oct_lookup.distances + low_key));
__m128i low_this_error0 =
_mm_load_si128((const __m128i *)(oct_lookup.distances + low_key0));
__m128i low_this_error1 =
_mm_load_si128((const __m128i *)(oct_lookup.distances + low_key1));
__m128i low_this_error2 =
_mm_load_si128((const __m128i *)(oct_lookup.distances + low_key2));
// add the distance for this time slice to the past distances
__m128i low_error = _mm_add_epi16(low_past_error, low_this_error);
__m128i low_error0 = _mm_add_epi16(low_past_error0, low_this_error0);
__m128i low_error1 = _mm_add_epi16(low_past_error1, low_this_error1);
__m128i low_error2 = _mm_add_epi16(low_past_error2, low_this_error2);
// repeat oct distance table lookup for registers with high
// order bit set
distance_oct_key_t high_key =
oct_lookup.keys[oct_highbase + oct + (base_offset / 4)];
distance_oct_key_t high_key0 =
oct_lookup.keys[oct_highbase + oct + (base_offset / 4) + 1];
distance_oct_key_t high_key1 =
oct_lookup.keys[oct_highbase + oct + (base_offset / 4) + 2];
distance_oct_key_t high_key2 =
oct_lookup.keys[oct_highbase + oct + (base_offset / 4) + 3];
__m128i high_this_error =
_mm_load_si128((const __m128i *)(oct_lookup.distances + high_key));
__m128i high_this_error0 =
_mm_load_si128((const __m128i *)(oct_lookup.distances + high_key0));
__m128i high_this_error1 =
_mm_load_si128((const __m128i *)(oct_lookup.distances + high_key1));
__m128i high_this_error2 =
_mm_load_si128((const __m128i *)(oct_lookup.distances + high_key2));
__m128i high_error = _mm_add_epi16(high_past_error, high_this_error);
__m128i high_error0 = _mm_add_epi16(high_past_error0, high_this_error0);
__m128i high_error1 = _mm_add_epi16(high_past_error1, high_this_error1);
__m128i high_error2 = _mm_add_epi16(high_past_error2, high_this_error2);
// distances for this time slice calculated
// find the least error between registers who differ only in
// their high order bit
__m128i min_error = _mm_min_epu16(low_error, high_error);
__m128i min_error0 = _mm_min_epu16(low_error0, high_error0);
__m128i min_error1 = _mm_min_epu16(low_error1, high_error1);
__m128i min_error2 = _mm_min_epu16(low_error2, high_error2);
_mm_store_si128((__m128i *)(write_errors + low + offset), min_error);
_mm_store_si128((__m128i *)(write_errors + low + offset + 8), min_error0);
_mm_store_si128((__m128i *)(write_errors + low + offset + 16), min_error1);
_mm_store_si128((__m128i *)(write_errors + low + offset + 24), min_error2);
// generate history bits as (low_error > least_error)
// this operation fills each element with all 1s if true and 0s
// if false
// in other words, we set the history bit to 1 if
// the register state with high order bit set was the least
// error
__m128i hist = _mm_cmpgt_epi16(low_error, min_error);
// pack the bits down from 16-bit wide to 8-bit wide to
// accomodate history table
hist = _mm_shuffle_epi8(hist, hist_mask);
__m128i hist0 = _mm_cmpgt_epi16(low_error0, min_error0);
hist0 = _mm_shuffle_epi8(hist0, hist_mask);
__m128i hist1 = _mm_cmpgt_epi16(low_error1, min_error1);
hist1 = _mm_shuffle_epi8(hist1, hist_mask);
__m128i hist2 = _mm_cmpgt_epi16(low_error2, min_error2);
hist2 = _mm_shuffle_epi8(hist2, hist_mask);
// write the least error so that the next time slice sees it as
// the past error
// store the history bits set by cmp and shuffle operations
_mm_storel_epi64((__m128i *)(history + low + offset), hist);
_mm_storel_epi64((__m128i *)(history + low + offset + 8), hist0);
_mm_storel_epi64((__m128i *)(history + low + offset + 16), hist1);
_mm_storel_epi64((__m128i *)(history + low + offset + 24), hist2);
}
}
// bypass the call to history buffer
// we should really make that function inline and remove this below
if (hist_buf_len == hist_buf_cap - 1 || hist_buf_rn_cnt == hist_buf_rn_int - 1) {
// restore hist buffer state and invoke it
conv->history_buffer->len = hist_buf_len;
conv->history_buffer->index = hist_buf_index;
conv->history_buffer->renormalize_counter = hist_buf_rn_cnt;
history_buffer_process(conv->history_buffer, write_errors, conv->bit_writer);
// restore our local values
hist_buf_len = conv->history_buffer->len;
hist_buf_index = conv->history_buffer->index;
hist_buf_cap = conv->history_buffer->cap;
hist_buf_rn_cnt = conv->history_buffer->renormalize_counter;
} else {
hist_buf_len++;
hist_buf_index++;
if (hist_buf_index == hist_buf_cap) {
hist_buf_index = 0;
}
hist_buf_rn_cnt++;
}
error_buffer_swap(conv->errors);
}
conv->history_buffer->len = hist_buf_len;
conv->history_buffer->index = hist_buf_index;
conv->history_buffer->renormalize_counter = hist_buf_rn_cnt;
}
static void _convolutional_sse_decode_init(correct_convolutional_sse *conv,
unsigned int min_traceback,
unsigned int traceback_length,
unsigned int renormalize_interval) {
_convolutional_decode_init(&conv->base_conv, min_traceback, traceback_length,
renormalize_interval);
conv->oct_lookup =
oct_lookup_create(conv->base_conv.rate, conv->base_conv.order, conv->base_conv.table);
}
static ssize_t _convolutional_sse_decode(correct_convolutional_sse *sse_conv,
size_t num_encoded_bits, size_t num_encoded_bytes,
uint8_t *msg, const soft_t *soft_encoded) {
correct_convolutional *conv = &sse_conv->base_conv;
if (!conv->has_init_decode) {
uint64_t max_error_per_input = conv->rate * soft_max;
// sse implementation unfortunately uses signed math on our unsigned values
// reduces usable distance by /2
unsigned int renormalize_interval = (distance_max / 2) / max_error_per_input;
_convolutional_sse_decode_init(sse_conv, 5 * conv->order, 100 * conv->order,
renormalize_interval);
}
size_t sets = num_encoded_bits / conv->rate;
// XXX fix this vvvvvv
size_t decoded_len_bytes = num_encoded_bytes;
bit_writer_reconfigure(conv->bit_writer, msg, decoded_len_bytes);
error_buffer_reset(conv->errors);
history_buffer_reset(conv->history_buffer);
// no outputs are generated during warmup
convolutional_decode_warmup(conv, sets, soft_encoded);
convolutional_sse_decode_inner(sse_conv, sets, soft_encoded);
convolutional_decode_tail(conv, sets, soft_encoded);
history_buffer_flush(conv->history_buffer, conv->bit_writer);
return bit_writer_length(conv->bit_writer);
}
ssize_t correct_convolutional_sse_decode(correct_convolutional_sse *conv, const uint8_t *encoded,
size_t num_encoded_bits, uint8_t *msg) {
if (num_encoded_bits % conv->base_conv.rate) {
// XXX turn this into an error code
// printf("encoded length of message must be a multiple of rate\n");
return -1;
}
size_t num_encoded_bytes =
(num_encoded_bits % 8) ? (num_encoded_bits / 8 + 1) : (num_encoded_bits / 8);
bit_reader_reconfigure(conv->base_conv.bit_reader, encoded, num_encoded_bytes);
return _convolutional_sse_decode(conv, num_encoded_bits, num_encoded_bytes, msg, NULL);
}
ssize_t correct_convolutional_sse_decode_soft(correct_convolutional_sse *conv, const soft_t *encoded,
size_t num_encoded_bits, uint8_t *msg) {
if (num_encoded_bits % conv->base_conv.rate) {
// XXX turn this into an error code
// printf("encoded length of message must be a multiple of rate\n");
return -1;
}
size_t num_encoded_bytes =
(num_encoded_bits % 8) ? (num_encoded_bits / 8 + 1) : (num_encoded_bits / 8);
return _convolutional_sse_decode(conv, num_encoded_bits, num_encoded_bytes, msg, encoded);
}

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#include "correct/convolutional/sse/convolutional.h"
size_t correct_convolutional_sse_encode_len(correct_convolutional_sse *conv, size_t msg_len) {
return correct_convolutional_encode_len(&conv->base_conv, msg_len);
}
size_t correct_convolutional_sse_encode(correct_convolutional_sse *conv, const uint8_t *msg, size_t msg_len, uint8_t *encoded) {
return correct_convolutional_encode(&conv->base_conv, msg, msg_len, encoded);
}

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#include "correct/convolutional/sse/lookup.h"
quad_lookup_t quad_lookup_create(unsigned int rate,
unsigned int order,
const unsigned int *table) {
quad_lookup_t quads;
quads.keys = malloc(sizeof(unsigned int) * (1 << (order - 2)));
quads.outputs = calloc((1 << (rate * 4)), sizeof(unsigned int));
unsigned int *inv_outputs = calloc((1 << (rate * 4)), sizeof(unsigned int));
unsigned int output_counter = 1;
// for every (even-numbered) shift register state, find the concatenated output of the state
// and the subsequent state that follows it (low bit set). then, check to see if this
// concatenated output has a unique key assigned to it already. if not, give it a key.
// if it does, retrieve the key. assign this key to the shift register state.
for (unsigned int i = 0; i < (1 << (order - 2)); i++) {
// first get the concatenated quad of outputs
unsigned int out = table[i * 4 + 3];
out <<= rate;
out |= table[i * 4 + 2];
out <<= rate;
out |= table[i * 4 + 1];
out <<= rate;
out |= table[i * 4];
// does this concatenated output exist in the outputs table yet?
if (!inv_outputs[out]) {
// doesn't exist, allocate a new key
inv_outputs[out] = output_counter;
quads.outputs[output_counter] = out;
output_counter++;
}
// set the opaque key for the ith shift register state to the concatenated output entry
quads.keys[i] = inv_outputs[out];
}
quads.outputs_len = output_counter;
quads.output_mask = (1 << (rate)) - 1;
quads.output_width = rate;
quads.distances = calloc(quads.outputs_len, sizeof(distance_quad_t));
free(inv_outputs);
return quads;
}
void quad_lookup_destroy(quad_lookup_t quads) {
free(quads.keys);
free(quads.outputs);
free(quads.distances);
}
void quad_lookup_fill_distance(quad_lookup_t quads, distance_t *distances) {
for (unsigned int i = 1; i < quads.outputs_len; i += 1) {
output_quad_t concat_out = quads.outputs[i];
unsigned int i_0 = concat_out & quads.output_mask;
concat_out >>= quads.output_width;
unsigned int i_1 = concat_out & quads.output_mask;
concat_out >>= quads.output_width;
unsigned int i_2 = concat_out & quads.output_mask;
concat_out >>= quads.output_width;
unsigned int i_3 = concat_out;
quads.distances[i] = ((uint64_t)distances[i_3] << 48) | ((uint64_t)distances[i_2] << 32) | (distances[i_1] << 16) | distances[i_0];
}
}
distance_oct_key_t oct_lookup_find_key(output_oct_t *outputs, output_oct_t out, size_t num_keys) {
for (size_t i = 1; i < num_keys; i++) {
if (outputs[i] == out) {
return i;
}
}
return 0;
}
oct_lookup_t oct_lookup_create(unsigned int rate,
unsigned int order,
const unsigned int *table) {
oct_lookup_t octs;
octs.keys = malloc((1 << (order - 3)) * sizeof(distance_oct_key_t));
octs.outputs = malloc(((output_oct_t)2 << rate) * sizeof(uint64_t));
output_oct_t *short_outs = calloc(((output_oct_t)2 << rate), sizeof(output_oct_t));
size_t outputs_len = 2 << rate;
unsigned int output_counter = 1;
// for every (even-numbered) shift register state, find the concatenated output of the state
// and the subsequent state that follows it (low bit set). then, check to see if this
// concatenated output has a unique key assigned to it already. if not, give it a key.
// if it does, retrieve the key. assign this key to the shift register state.
for (shift_register_t i = 0; i < (1 << (order - 3)); i++) {
// first get the concatenated oct of outputs
output_oct_t out = table[i * 8 + 7];
out <<= rate;
out |= table[i * 8 + 6];
out <<= rate;
out |= table[i * 8 + 5];
out <<= rate;
out |= table[i * 8 + 4];
out <<= rate;
out |= table[i * 8 + 3];
out <<= rate;
out |= table[i * 8 + 2];
out <<= rate;
out |= table[i * 8 + 1];
out <<= rate;
out |= table[i * 8];
distance_oct_key_t key = oct_lookup_find_key(short_outs, out, output_counter);
// does this concatenated output exist in the outputs table yet?
if (!key) {
// doesn't exist, allocate a new key
// now build it in expanded form
output_oct_t expanded_out = table[i * 8 + 7];
expanded_out <<= 8;
expanded_out |= table[i * 8 + 6];
expanded_out <<= 8;
expanded_out |= table[i * 8 + 5];
expanded_out <<= 8;
expanded_out |= table[i * 8 + 4];
expanded_out <<= 8;
expanded_out |= table[i * 8 + 3];
expanded_out <<= 8;
expanded_out |= table[i * 8 + 2];
expanded_out <<= 8;
expanded_out |= table[i * 8 + 1];
expanded_out <<= 8;
expanded_out |= table[i * 8];
if (output_counter == outputs_len) {
octs.outputs = realloc(octs.outputs, outputs_len * 2 * sizeof(output_oct_t));
short_outs = realloc(short_outs, outputs_len * 2 * sizeof(output_oct_t));
outputs_len *= 2;
}
short_outs[output_counter] = out;
octs.outputs[output_counter] = expanded_out;
key = output_counter;
output_counter++;
}
// set the opaque key for the ith shift register state to the concatenated output entry
// we multiply the key by 2 since the distances are strided by 2
octs.keys[i] = key * 2;
}
free(short_outs);
octs.outputs_len = output_counter;
octs.output_mask = (1 << (rate)) - 1;
octs.output_width = rate;
octs.distances = malloc(octs.outputs_len * 2 * sizeof(uint64_t));
return octs;
}
void oct_lookup_destroy(oct_lookup_t octs) {
free(octs.keys);
free(octs.outputs);
free(octs.distances);
}
// WIP: sse approach to filling the distance table
/*
void oct_lookup_fill_distance_sse(oct_lookup_t octs, distance_t *distances) {
distance_pair_t *distance_pair = (distance_pair_t*)octs.distances;
__v4si index_shuffle_mask = (__v4si){0xffffff00, 0xffffff01, 0xffffff02, 0xffffff03};
__m256i dist_shuffle_mask = (__m256i){0x01000504, 0x09080d0c, 0xffffffff, 0xffffffff,
0x01000504, 0x09080d0c, 0xffffffff, 0xffffffff};
const int dist_permute_mask = 0x0c;
for (unsigned int i = 1; i < octs.outputs_len; i += 2) {
// big heaping todo vvv
// a) we want 16 bit distances GATHERed, not 32 bit
// b) we need to load 8 of those distances, not 4
__v4si short_concat_index = _mm_loadl_epi64(octs.outputs + 2*i);
__v4si short_concat_index0 = _mm_loadl_epi64(octs.outputs + 2*i + 1);
__m256i concat_index = _mm256_cvtepu8_epi32(short_concat_index);
__m256i concat_index0 = _mm256_cvtepu8_epi32(short_concat_index0);
__m256i dist = _mm256_i32gather_epi32(distances, concat_index, sizeof(distance_t));
__m256i dist0 = _mm256_i32gather_epi32(distances, concat_index0, sizeof(distance_t));
dist = _mm256_shuffle_epi8(dist, dist_shuffle_mask);
dist0 = _mm256_shuffle_epi8(dist0, dist_shuffle_mask);
dist = __builtin_shufflevector(dist, dist, 0, 5, 0, 0);
dist0 = __builtin_shufflevector(dist0, dist0, 0, 5, 0, 0);
__v4si packed_dist = _mm256_castsi256_si128(dist);
_mm_store_si128(distance_pair + 8 * i, packed_dist);
__v4si packed_dist0 = _mm256_castsi256_si128(dist0);
_mm_store_si128(distance_pair + 8 * i + 4, packed_dist0);
}
}
*/

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#include <stdlib.h>
#include <string.h>
#include "fec_shim.h"
typedef struct {
correct_reed_solomon *rs;
unsigned int msg_length;
unsigned int block_length;
unsigned int num_roots;
uint8_t *msg_out;
unsigned int pad;
uint8_t *erasures;
} reed_solomon_shim;
void *init_rs_char(int symbol_size, int primitive_polynomial,
int first_consecutive_root, int root_gap, int number_roots,
unsigned int pad) {
if (symbol_size != 8) {
return NULL;
}
reed_solomon_shim *shim = malloc(sizeof(reed_solomon_shim));
shim->pad = pad;
shim->block_length = 255 - pad;
shim->num_roots = number_roots;
shim->msg_length = shim->block_length - number_roots;
shim->rs = correct_reed_solomon_create(primitive_polynomial,
first_consecutive_root, root_gap, number_roots);
shim->msg_out = malloc(shim->block_length);
shim->erasures = malloc(number_roots);
return shim;
}
void free_rs_char(void *rs) {
reed_solomon_shim *shim = (reed_solomon_shim *)rs;
correct_reed_solomon_destroy(shim->rs);
free(shim->msg_out);
free(shim->erasures);
free(shim);
}
void encode_rs_char(void *rs, const unsigned char *msg, unsigned char *parity) {
reed_solomon_shim *shim = (reed_solomon_shim *)rs;
correct_reed_solomon_encode(shim->rs, msg, shim->msg_length, shim->msg_out);
memcpy(parity, shim->msg_out + shim->msg_length, shim->num_roots);
}
void decode_rs_char(void *rs, unsigned char *block, int *erasure_locations,
int num_erasures) {
reed_solomon_shim *shim = (reed_solomon_shim *)rs;
for (int i = 0; i < num_erasures; i++) {
shim->erasures[i] = (uint8_t)(erasure_locations[i]) - shim->pad;
}
correct_reed_solomon_decode_with_erasures(shim->rs, block, shim->block_length,
shim->erasures, num_erasures,
block);
}
typedef struct {
correct_convolutional *conv;
unsigned int rate;
unsigned int order;
uint8_t *buf;
size_t buf_len;
uint8_t *read_iter;
uint8_t *write_iter;
} convolutional_shim;
static correct_convolutional_polynomial_t r12k7[] = {V27POLYA, V27POLYB};
static correct_convolutional_polynomial_t r12k9[] = {V29POLYA, V29POLYB};
static correct_convolutional_polynomial_t r13k9[] = {V39POLYA, V39POLYB,
V39POLYC};
static correct_convolutional_polynomial_t r16k15[] = {
V615POLYA, V615POLYB, V615POLYC, V615POLYD, V615POLYE, V615POLYF};
/* Common methods */
static void *create_viterbi(unsigned int num_decoded_bits, unsigned int rate,
unsigned int order,
correct_convolutional_polynomial_t *poly) {
convolutional_shim *shim = malloc(sizeof(convolutional_shim));
size_t num_decoded_bytes = (num_decoded_bits % 8)
? (num_decoded_bits / 8 + 1)
: num_decoded_bits / 8;
shim->rate = rate;
shim->order = order;
shim->buf = malloc(num_decoded_bytes);
shim->buf_len = num_decoded_bytes;
shim->conv = correct_convolutional_create(rate, order, poly);
shim->read_iter = shim->buf;
shim->write_iter = shim->buf;
return shim;
}
static void delete_viterbi(void *vit) {
convolutional_shim *shim = (convolutional_shim *)vit;
free(shim->buf);
correct_convolutional_destroy(shim->conv);
free(shim);
}
static void init_viterbi(void *vit) {
convolutional_shim *shim = (convolutional_shim *)vit;
shim->read_iter = shim->buf;
shim->write_iter = shim->buf;
}
static void update_viterbi_blk(void *vit, const unsigned char *encoded_soft,
unsigned int num_encoded_groups) {
convolutional_shim *shim = (convolutional_shim *)vit;
// don't overwrite our buffer
size_t rem = (shim->buf + shim->buf_len) - shim->write_iter;
size_t rem_bits = 8 * rem;
// this math isn't very clear
// here we sort of do the opposite of what liquid-dsp does
size_t n_write_bits = num_encoded_groups - (shim->order - 1);
if (n_write_bits > rem_bits) {
size_t reduction = n_write_bits - rem_bits;
num_encoded_groups -= reduction;
n_write_bits -= reduction;
}
// what if n_write_bits isn't a multiple of 8?
// libcorrect can't start and stop at arbitrary indices...
correct_convolutional_decode_soft(
shim->conv, encoded_soft, num_encoded_groups * shim->rate, shim->write_iter);
shim->write_iter += n_write_bits / 8;
}
static void chainback_viterbi(void *vit, unsigned char *decoded,
unsigned int num_decoded_bits) {
convolutional_shim *shim = (convolutional_shim *)vit;
// num_decoded_bits not a multiple of 8?
// this is a similar problem to update_viterbi_blk
// although here we could actually resolve a non-multiple of 8
size_t rem = shim->write_iter - shim->read_iter;
size_t rem_bits = 8 * rem;
if (num_decoded_bits > rem_bits) {
num_decoded_bits = rem_bits;
}
size_t num_decoded_bytes = (num_decoded_bits % 8)
? (num_decoded_bits / 8 + 1)
: num_decoded_bits / 8;
memcpy(decoded, shim->read_iter, num_decoded_bytes);
shim->read_iter += num_decoded_bytes;
}
/* Rate 1/2, k = 7 */
void *create_viterbi27(int num_decoded_bits) {
return create_viterbi(num_decoded_bits, 2, 7, r12k7);
}
void delete_viterbi27(void *vit) { delete_viterbi(vit); }
int init_viterbi27(void *vit, int _) {
init_viterbi(vit);
return 0;
}
int update_viterbi27_blk(void *vit, unsigned char *encoded_soft,
int num_encoded_groups) {
update_viterbi_blk(vit, encoded_soft, num_encoded_groups);
return 0;
}
int chainback_viterbi27(void *vit, unsigned char *decoded,
unsigned int num_decoded_bits, unsigned int _) {
chainback_viterbi(vit, decoded, num_decoded_bits);
return 0;
}
/* Rate 1/2, k = 9 */
void *create_viterbi29(int num_decoded_bits) {
return create_viterbi(num_decoded_bits, 2, 9, r12k9);
}
void delete_viterbi29(void *vit) { delete_viterbi(vit); }
int init_viterbi29(void *vit, int _) {
init_viterbi(vit);
return 0;
}
int update_viterbi29_blk(void *vit, unsigned char *encoded_soft,
int num_encoded_groups) {
update_viterbi_blk(vit, encoded_soft, num_encoded_groups);
return 0;
}
int chainback_viterbi29(void *vit, unsigned char *decoded,
unsigned int num_decoded_bits, unsigned int _) {
chainback_viterbi(vit, decoded, num_decoded_bits);
return 0;
}
/* Rate 1/3, k = 9 */
void *create_viterbi39(int num_decoded_bits) {
return create_viterbi(num_decoded_bits, 3, 9, r13k9);
}
void delete_viterbi39(void *vit) { delete_viterbi(vit); }
int init_viterbi39(void *vit, int _) {
init_viterbi(vit);
return 0;
}
int update_viterbi39_blk(void *vit, unsigned char *encoded_soft,
int num_encoded_groups) {
update_viterbi_blk(vit, encoded_soft, num_encoded_groups);
return 0;
}
int chainback_viterbi39(void *vit, unsigned char *decoded,
unsigned int num_decoded_bits, unsigned int _) {
chainback_viterbi(vit, decoded, num_decoded_bits);
return 0;
}
/* Rate 1/6, k = 15 */
void *create_viterbi615(int num_decoded_bits) {
return create_viterbi(num_decoded_bits, 6, 15, r16k15);
}
void delete_viterbi615(void *vit) { delete_viterbi(vit); }
int init_viterbi615(void *vit, int _) {
init_viterbi(vit);
return 0;
}
int update_viterbi615_blk(void *vit, unsigned char *encoded_soft,
int num_encoded_groups) {
update_viterbi_blk(vit, encoded_soft, num_encoded_groups);
return 0;
}
int chainback_viterbi615(void *vit, unsigned char *decoded,
unsigned int num_decoded_bits, unsigned int _) {
chainback_viterbi(vit, decoded, num_decoded_bits);
return 0;
}

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set(SRCFILES polynomial.c reed-solomon.c encode.c decode.c)
add_library(correct-reed-solomon OBJECT ${SRCFILES})

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#include "correct/reed-solomon/encode.h"
// calculate all syndromes of the received polynomial at the roots of the generator
// because we're evaluating at the roots of the generator, and because the transmitted
// polynomial was made to be a product of the generator, we know that the transmitted
// polynomial is 0 at these roots
// any nonzero syndromes we find here are the values of the error polynomial evaluated
// at these roots, so these values give us a window into the error polynomial. if
// these syndromes are all zero, then we can conclude the error polynomial is also
// zero. if they're nonzero, then we know our message received an error in transit.
// returns true if syndromes are all zero
static bool reed_solomon_find_syndromes(field_t field, polynomial_t msgpoly, field_logarithm_t **generator_root_exp,
field_element_t *syndromes, size_t min_distance) {
bool all_zero = true;
memset(syndromes, 0, min_distance * sizeof(field_element_t));
for (unsigned int i = 0; i < min_distance; i++) {
// profiling reveals that this function takes about 50% of the cpu time of
// decoding. so, in order to speed it up a little, we precompute and save
// the successive powers of the roots of the generator, which are
// located in generator_root_exp
field_element_t eval = polynomial_eval_lut(field, msgpoly, generator_root_exp[i]);
if (eval) {
all_zero = false;
}
syndromes[i] = eval;
}
return all_zero;
}
// Berlekamp-Massey algorithm to find LFSR that describes syndromes
// returns number of errors and writes the error locator polynomial to rs->error_locator
static unsigned int reed_solomon_find_error_locator(correct_reed_solomon *rs, size_t num_erasures) {
unsigned int numerrors = 0;
memset(rs->error_locator.coeff, 0, (rs->min_distance + 1) * sizeof(field_element_t));
// initialize to f(x) = 1
rs->error_locator.coeff[0] = 1;
rs->error_locator.order = 0;
memcpy(rs->last_error_locator.coeff, rs->error_locator.coeff, (rs->min_distance + 1) * sizeof(field_element_t));
rs->last_error_locator.order = rs->error_locator.order;
field_element_t discrepancy;
field_element_t last_discrepancy = 1;
unsigned int delay_length = 1;
for (unsigned int i = rs->error_locator.order; i < rs->min_distance - num_erasures; i++) {
discrepancy = rs->syndromes[i];
for (unsigned int j = 1; j <= numerrors; j++) {
discrepancy = field_add(rs->field, discrepancy,
field_mul(rs->field, rs->error_locator.coeff[j], rs->syndromes[i - j]));
}
if (!discrepancy) {
// our existing LFSR describes the new syndrome as well
// leave it as-is but update the number of delay elements
// so that if a discrepancy occurs later we can eliminate it
delay_length++;
continue;
}
if (2 * numerrors <= i) {
// there's a discrepancy, but we still have room for more taps
// lengthen LFSR by one tap and set weight to eliminate discrepancy
// shift the last locator by the delay length, multiply by discrepancy,
// and divide by the last discrepancy
// we move down because we're shifting up, and this prevents overwriting
for (int j = rs->last_error_locator.order; j >= 0; j--) {
// the bounds here will be ok since we have a headroom of numerrors
rs->last_error_locator.coeff[j + delay_length] = field_div(
rs->field, field_mul(rs->field, rs->last_error_locator.coeff[j], discrepancy), last_discrepancy);
}
for (int j = delay_length - 1; j >= 0; j--) {
rs->last_error_locator.coeff[j] = 0;
}
// locator = locator - last_locator
// we will also update last_locator to be locator before this loop takes place
field_element_t temp;
for (int j = 0; j <= (rs->last_error_locator.order + delay_length); j++) {
temp = rs->error_locator.coeff[j];
rs->error_locator.coeff[j] =
field_add(rs->field, rs->error_locator.coeff[j], rs->last_error_locator.coeff[j]);
rs->last_error_locator.coeff[j] = temp;
}
unsigned int temp_order = rs->error_locator.order;
rs->error_locator.order = rs->last_error_locator.order + delay_length;
rs->last_error_locator.order = temp_order;
// now last_locator is locator before we started,
// and locator is (locator - (discrepancy/last_discrepancy) * x^(delay_length) * last_locator)
numerrors = i + 1 - numerrors;
last_discrepancy = discrepancy;
delay_length = 1;
continue;
}
// no more taps
// unlike the previous case, we are preserving last locator,
// but we'll update locator as before
// we're basically flattening the two loops from the previous case because
// we no longer need to update last_locator
for (int j = rs->last_error_locator.order; j >= 0; j--) {
rs->error_locator.coeff[j + delay_length] =
field_add(rs->field, rs->error_locator.coeff[j + delay_length],
field_div(rs->field, field_mul(rs->field, rs->last_error_locator.coeff[j], discrepancy),
last_discrepancy));
}
rs->error_locator.order = (rs->last_error_locator.order + delay_length > rs->error_locator.order)
? rs->last_error_locator.order + delay_length
: rs->error_locator.order;
delay_length++;
}
return rs->error_locator.order;
}
// find the roots of the error locator polynomial
// Chien search
bool reed_solomon_factorize_error_locator(field_t field, unsigned int num_skip, polynomial_t locator_log, field_element_t *roots,
field_logarithm_t **element_exp) {
// normally it'd be tricky to find all the roots
// but, the finite field is awfully finite...
// just brute force search across every field element
unsigned int root = num_skip;
memset(roots + num_skip, 0, (locator_log.order) * sizeof(field_element_t));
for (field_operation_t i = 0; i < 256; i++) {
// we make two optimizations here to help this search go faster
// a) we have precomputed the first successive powers of every single element
// in the field. we need at most n powers, where n is the largest possible
// degree of the error locator
// b) we have precomputed the error locator polynomial in log form, which
// helps reduce some lookups that would be done here
if (!polynomial_eval_log_lut(field, locator_log, element_exp[i])) {
roots[root] = (field_element_t)i;
root++;
}
}
// this is where we find out if we are have too many errors to recover from
// berlekamp-massey may have built an error locator that has 0 discrepancy
// on the syndromes but doesn't have enough roots
return root == locator_log.order + num_skip;
}
// use error locator and syndromes to find the error evaluator polynomial
void reed_solomon_find_error_evaluator(field_t field, polynomial_t locator, polynomial_t syndromes,
polynomial_t error_evaluator) {
// the error evaluator, omega(x), is S(x)*Lamba(x) mod x^(2t)
// where S(x) is a polynomial constructed from the syndromes
// S(1) + S(2)*x + ... + S(2t)*x(2t - 1)
// and Lambda(x) is the error locator
// the modulo is implicit here -- we have limited the max length of error_evaluator,
// which polynomial_mul will interpret to mean that it should not compute
// powers larger than that, which is the same as performing mod x^(2t)
polynomial_mul(field, locator, syndromes, error_evaluator);
}
// use error locator, error roots and syndromes to find the error values
// that is, the elements in the finite field which can be added to the received
// polynomial at the locations of the error roots in order to produce the
// transmitted polynomial
// forney algorithm
void reed_solomon_find_error_values(correct_reed_solomon *rs) {
// error value e(j) = -(X(j)^(1-c) * omega(X(j)^-1))/(lambda'(X(j)^-1))
// where X(j)^-1 is a root of the error locator, omega(X) is the error evaluator,
// lambda'(X) is the first formal derivative of the error locator,
// and c is the first consecutive root of the generator used in encoding
// first find omega(X), the error evaluator
// we generate S(x), the polynomial constructed from the roots of the syndromes
// this is *not* the polynomial constructed by expanding the products of roots
// S(x) = S(1) + S(2)*x + ... + S(2t)*x(2t - 1)
polynomial_t syndrome_poly;
syndrome_poly.order = rs->min_distance - 1;
syndrome_poly.coeff = rs->syndromes;
memset(rs->error_evaluator.coeff, 0, (rs->error_evaluator.order + 1) * sizeof(field_element_t));
reed_solomon_find_error_evaluator(rs->field, rs->error_locator, syndrome_poly, rs->error_evaluator);
// now find lambda'(X)
rs->error_locator_derivative.order = rs->error_locator.order - 1;
polynomial_formal_derivative(rs->field, rs->error_locator, rs->error_locator_derivative);
// calculate each e(j)
for (unsigned int i = 0; i < rs->error_locator.order; i++) {
if (rs->error_roots[i] == 0) {
continue;
}
rs->error_vals[i] = field_mul(
rs->field, field_pow(rs->field, rs->error_roots[i], rs->first_consecutive_root - 1),
field_div(
rs->field, polynomial_eval_lut(rs->field, rs->error_evaluator, rs->element_exp[rs->error_roots[i]]),
polynomial_eval_lut(rs->field, rs->error_locator_derivative, rs->element_exp[rs->error_roots[i]])));
}
}
void reed_solomon_find_error_locations(field_t field, field_logarithm_t generator_root_gap,
field_element_t *error_roots, field_logarithm_t *error_locations,
unsigned int num_errors, unsigned int num_skip) {
for (unsigned int i = 0; i < num_errors; i++) {
// the error roots are the reciprocals of the error locations, so div 1 by them
// we do mod 255 here because the log table aliases at index 1
// the log of 1 is both 0 and 255 (alpha^255 = alpha^0 = 1)
// for most uses it makes sense to have log(1) = 255, but in this case
// we're interested in a byte index, and the 255th index is not even valid
// just wrap it back to 0
if (error_roots[i] == 0) {
continue;
}
field_operation_t loc = field_div(field, 1, error_roots[i]);
for (field_operation_t j = 0; j < 256; j++) {
if (field_pow(field, j, generator_root_gap) == loc) {
error_locations[i] = field.log[j];
break;
}
}
}
}
// erasure method -- take given locations and convert to roots
// this is the inverse of reed_solomon_find_error_locations
static void reed_solomon_find_error_roots_from_locations(field_t field, field_logarithm_t generator_root_gap,
const field_logarithm_t *error_locations,
field_element_t *error_roots, unsigned int num_errors) {
for (unsigned int i = 0; i < num_errors; i++) {
field_element_t loc = field_pow(field, field.exp[error_locations[i]], generator_root_gap);
// field_element_t loc = field.exp[error_locations[i]];
error_roots[i] = field_div(field, 1, loc);
// error_roots[i] = loc;
}
}
// erasure method -- given the roots of the error locator, create the polynomial
static polynomial_t reed_solomon_find_error_locator_from_roots(field_t field, unsigned int num_errors,
field_element_t *error_roots,
polynomial_t error_locator,
polynomial_t *scratch) {
// multiply out roots to build the error locator polynomial
return polynomial_init_from_roots(field, num_errors, error_roots, error_locator, scratch);
}
// erasure method
static void reed_solomon_find_modified_syndromes(correct_reed_solomon *rs, field_element_t *syndromes, polynomial_t error_locator, field_element_t *modified_syndromes) {
polynomial_t syndrome_poly;
syndrome_poly.order = rs->min_distance - 1;
syndrome_poly.coeff = syndromes;
polynomial_t modified_syndrome_poly;
modified_syndrome_poly.order = rs->min_distance - 1;
modified_syndrome_poly.coeff = modified_syndromes;
polynomial_mul(rs->field, error_locator, syndrome_poly, modified_syndrome_poly);
}
void correct_reed_solomon_decoder_create(correct_reed_solomon *rs) {
rs->has_init_decode = true;
rs->syndromes = calloc(rs->min_distance, sizeof(field_element_t));
rs->modified_syndromes = calloc(2 * rs->min_distance, sizeof(field_element_t));
rs->received_polynomial = polynomial_create(rs->block_length - 1);
rs->error_locator = polynomial_create(rs->min_distance);
rs->error_locator_log = polynomial_create(rs->min_distance);
rs->erasure_locator = polynomial_create(rs->min_distance);
rs->error_roots = calloc(2 * rs->min_distance, sizeof(field_element_t));
rs->error_vals = malloc(rs->min_distance * sizeof(field_element_t));
rs->error_locations = malloc(rs->min_distance * sizeof(field_logarithm_t));
rs->last_error_locator = polynomial_create(rs->min_distance);
rs->error_evaluator = polynomial_create(rs->min_distance - 1);
rs->error_locator_derivative = polynomial_create(rs->min_distance - 1);
// calculate and store the first block_length powers of every generator root
// we would have to do this work in order to calculate the syndromes
// if we save it, we can prevent the need to recalculate it on subsequent calls
// total memory usage is min_distance * block_length bytes e.g. 32 * 255 ~= 8k
rs->generator_root_exp = malloc(rs->min_distance * sizeof(field_logarithm_t *));
for (unsigned int i = 0; i < rs->min_distance; i++) {
rs->generator_root_exp[i] = malloc(rs->block_length * sizeof(field_logarithm_t));
polynomial_build_exp_lut(rs->field, rs->generator_roots[i], rs->block_length - 1, rs->generator_root_exp[i]);
}
// calculate and store the first min_distance powers of every element in the field
// we would have to do this for chien search anyway, and its size is only 256 * min_distance bytes
// for min_distance = 32 this is 8k of memory, a pittance for the speedup we receive in exchange
// we also get to reuse this work during error value calculation
rs->element_exp = malloc(256 * sizeof(field_logarithm_t *));
for (field_operation_t i = 0; i < 256; i++) {
rs->element_exp[i] = malloc(rs->min_distance * sizeof(field_logarithm_t));
polynomial_build_exp_lut(rs->field, i, rs->min_distance - 1, rs->element_exp[i]);
}
rs->init_from_roots_scratch[0] = polynomial_create(rs->min_distance);
rs->init_from_roots_scratch[1] = polynomial_create(rs->min_distance);
}
ssize_t correct_reed_solomon_decode(correct_reed_solomon *rs, const uint8_t *encoded, size_t encoded_length,
uint8_t *msg) {
if (encoded_length > rs->block_length) {
return -1;
}
// the message is the non-remainder part
size_t msg_length = encoded_length - rs->min_distance;
// if they handed us a nonfull block, we'll write in 0s
size_t pad_length = rs->block_length - encoded_length;
if (!rs->has_init_decode) {
// initialize rs for decoding
correct_reed_solomon_decoder_create(rs);
}
// we need to copy to our local buffer
// the buffer we're given has the coordinates in the wrong direction
// e.g. byte 0 corresponds to the 254th order coefficient
// so we're going to flip and then write padding
// the final copied buffer will look like
// | rem (rs->min_distance) | msg (msg_length) | pad (pad_length) |
for (unsigned int i = 0; i < encoded_length; i++) {
rs->received_polynomial.coeff[i] = encoded[encoded_length - (i + 1)];
}
// fill the pad_length with 0s
for (unsigned int i = 0; i < pad_length; i++) {
rs->received_polynomial.coeff[i + encoded_length] = 0;
}
bool all_zero = reed_solomon_find_syndromes(rs->field, rs->received_polynomial, rs->generator_root_exp,
rs->syndromes, rs->min_distance);
if (all_zero) {
// syndromes were all zero, so there was no error in the message
// copy to msg and we are done
for (unsigned int i = 0; i < msg_length; i++) {
msg[i] = rs->received_polynomial.coeff[encoded_length - (i + 1)];
}
return msg_length;
}
unsigned int order = reed_solomon_find_error_locator(rs, 0);
// XXX fix this vvvv
rs->error_locator.order = order;
for (unsigned int i = 0; i <= rs->error_locator.order; i++) {
// this is a little strange since the coeffs are logs, not elements
// also, we'll be storing log(0) = 0 for any 0 coeffs in the error locator
// that would seem bad but we'll just be using this in chien search, and we'll skip all 0 coeffs
// (you might point out that log(1) also = 0, which would seem to alias. however, that's ok,
// because log(1) = 255 as well, and in fact that's how it's represented in our log table)
rs->error_locator_log.coeff[i] = rs->field.log[rs->error_locator.coeff[i]];
}
rs->error_locator_log.order = rs->error_locator.order;
if (!reed_solomon_factorize_error_locator(rs->field, 0, rs->error_locator_log, rs->error_roots, rs->element_exp)) {
// roots couldn't be found, so there were too many errors to deal with
// RS has failed for this message
return -1;
}
reed_solomon_find_error_locations(rs->field, rs->generator_root_gap, rs->error_roots, rs->error_locations,
rs->error_locator.order, 0);
reed_solomon_find_error_values(rs);
for (unsigned int i = 0; i < rs->error_locator.order; i++) {
rs->received_polynomial.coeff[rs->error_locations[i]] =
field_sub(rs->field, rs->received_polynomial.coeff[rs->error_locations[i]], rs->error_vals[i]);
}
for (unsigned int i = 0; i < msg_length; i++) {
msg[i] = rs->received_polynomial.coeff[encoded_length - (i + 1)];
}
return msg_length;
}
ssize_t correct_reed_solomon_decode_with_erasures(correct_reed_solomon *rs, const uint8_t *encoded,
size_t encoded_length, const uint8_t *erasure_locations,
size_t erasure_length, uint8_t *msg) {
if (!erasure_length) {
return correct_reed_solomon_decode(rs, encoded, encoded_length, msg);
}
if (encoded_length > rs->block_length) {
return -1;
}
if (erasure_length > rs->min_distance) {
return -1;
}
// the message is the non-remainder part
size_t msg_length = encoded_length - rs->min_distance;
// if they handed us a nonfull block, we'll write in 0s
size_t pad_length = rs->block_length - encoded_length;
if (!rs->has_init_decode) {
// initialize rs for decoding
correct_reed_solomon_decoder_create(rs);
}
// we need to copy to our local buffer
// the buffer we're given has the coordinates in the wrong direction
// e.g. byte 0 corresponds to the 254th order coefficient
// so we're going to flip and then write padding
// the final copied buffer will look like
// | rem (rs->min_distance) | msg (msg_length) | pad (pad_length) |
for (unsigned int i = 0; i < encoded_length; i++) {
rs->received_polynomial.coeff[i] = encoded[encoded_length - (i + 1)];
}
// fill the pad_length with 0s
for (unsigned int i = 0; i < pad_length; i++) {
rs->received_polynomial.coeff[i + encoded_length] = 0;
}
for (unsigned int i = 0; i < erasure_length; i++) {
// remap the coordinates of the erasures
rs->error_locations[i] = rs->block_length - (erasure_locations[i] + pad_length + 1);
}
reed_solomon_find_error_roots_from_locations(rs->field, rs->generator_root_gap, rs->error_locations,
rs->error_roots, erasure_length);
rs->erasure_locator =
reed_solomon_find_error_locator_from_roots(rs->field, erasure_length, rs->error_roots, rs->erasure_locator, rs->init_from_roots_scratch);
bool all_zero = reed_solomon_find_syndromes(rs->field, rs->received_polynomial, rs->generator_root_exp,
rs->syndromes, rs->min_distance);
if (all_zero) {
// syndromes were all zero, so there was no error in the message
// copy to msg and we are done
for (unsigned int i = 0; i < msg_length; i++) {
msg[i] = rs->received_polynomial.coeff[encoded_length - (i + 1)];
}
return msg_length;
}
reed_solomon_find_modified_syndromes(rs, rs->syndromes, rs->erasure_locator, rs->modified_syndromes);
field_element_t *syndrome_copy = malloc(rs->min_distance * sizeof(field_element_t));
memcpy(syndrome_copy, rs->syndromes, rs->min_distance * sizeof(field_element_t));
for (unsigned int i = erasure_length; i < rs->min_distance; i++) {
rs->syndromes[i - erasure_length] = rs->modified_syndromes[i];
}
unsigned int order = reed_solomon_find_error_locator(rs, erasure_length);
// XXX fix this vvvv
rs->error_locator.order = order;
for (unsigned int i = 0; i <= rs->error_locator.order; i++) {
// this is a little strange since the coeffs are logs, not elements
// also, we'll be storing log(0) = 0 for any 0 coeffs in the error locator
// that would seem bad but we'll just be using this in chien search, and we'll skip all 0 coeffs
// (you might point out that log(1) also = 0, which would seem to alias. however, that's ok,
// because log(1) = 255 as well, and in fact that's how it's represented in our log table)
rs->error_locator_log.coeff[i] = rs->field.log[rs->error_locator.coeff[i]];
}
rs->error_locator_log.order = rs->error_locator.order;
/*
for (unsigned int i = 0; i < erasure_length; i++) {
rs->error_roots[i] = field_div(rs->field, 1, rs->error_roots[i]);
}
*/
if (!reed_solomon_factorize_error_locator(rs->field, erasure_length, rs->error_locator_log, rs->error_roots, rs->element_exp)) {
// roots couldn't be found, so there were too many errors to deal with
// RS has failed for this message
free(syndrome_copy);
return -1;
}
polynomial_t temp_poly = polynomial_create(rs->error_locator.order + erasure_length);
polynomial_mul(rs->field, rs->erasure_locator, rs->error_locator, temp_poly);
polynomial_t placeholder_poly = rs->error_locator;
rs->error_locator = temp_poly;
reed_solomon_find_error_locations(rs->field, rs->generator_root_gap, rs->error_roots, rs->error_locations,
rs->error_locator.order, erasure_length);
memcpy(rs->syndromes, syndrome_copy, rs->min_distance * sizeof(field_element_t));
reed_solomon_find_error_values(rs);
for (unsigned int i = 0; i < rs->error_locator.order; i++) {
rs->received_polynomial.coeff[rs->error_locations[i]] =
field_sub(rs->field, rs->received_polynomial.coeff[rs->error_locations[i]], rs->error_vals[i]);
}
rs->error_locator = placeholder_poly;
for (unsigned int i = 0; i < msg_length; i++) {
msg[i] = rs->received_polynomial.coeff[encoded_length - (i + 1)];
}
polynomial_destroy(temp_poly);
free(syndrome_copy);
return msg_length;
}

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core/libcorrect/src/reed-solomon/encode.c Normal file
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#include "correct/reed-solomon/encode.h"
ssize_t correct_reed_solomon_encode(correct_reed_solomon *rs, const uint8_t *msg, size_t msg_length, uint8_t *encoded) {
if (msg_length > rs->message_length) {
return -1;
}
size_t pad_length = rs->message_length - msg_length;
for (unsigned int i = 0; i < msg_length; i++) {
// message goes from high order to low order but libcorrect polynomials go low to high
// so we reverse on the way in and on the way out
// we'd have to do a copy anyway so this reversal should be free
rs->encoded_polynomial.coeff[rs->encoded_polynomial.order - (i + pad_length)] = msg[i];
}
// 0-fill the rest of the coefficients -- this length will always be > 0
// because the order of this poly is block_length and the msg_length <= message_length
// e.g. 255 and 223
memset(rs->encoded_polynomial.coeff + (rs->encoded_polynomial.order + 1 - pad_length), 0, pad_length);
memset(rs->encoded_polynomial.coeff, 0, (rs->encoded_polynomial.order + 1 - rs->message_length));
polynomial_mod(rs->field, rs->encoded_polynomial, rs->generator, rs->encoded_remainder);
// now return byte order to highest order to lowest order
for (unsigned int i = 0; i < msg_length; i++) {
encoded[i] = rs->encoded_polynomial.coeff[rs->encoded_polynomial.order - (i + pad_length)];
}
for (unsigned int i = 0; i < rs->min_distance; i++) {
encoded[msg_length + i] = rs->encoded_remainder.coeff[rs->min_distance - (i + 1)];
}
return rs->block_length;
}

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core/libcorrect/src/reed-solomon/polynomial.c Normal file
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#include "correct/reed-solomon/polynomial.h"
polynomial_t polynomial_create(unsigned int order) {
polynomial_t polynomial;
polynomial.coeff = malloc(sizeof(field_element_t) * (order + 1));
polynomial.order = order;
return polynomial;
}
void polynomial_destroy(polynomial_t polynomial) {
free(polynomial.coeff);
}
// if you want a full multiplication, then make res.order = l.order + r.order
// but if you just care about a lower order, e.g. mul mod x^i, then you can select
// fewer coefficients
void polynomial_mul(field_t field, polynomial_t l, polynomial_t r, polynomial_t res) {
// perform an element-wise multiplication of two polynomials
memset(res.coeff, 0, sizeof(field_element_t) * (res.order + 1));
for (unsigned int i = 0; i <= l.order; i++) {
if (i > res.order) {
continue;
}
unsigned int j_limit = (r.order > res.order - i) ? res.order - i : r.order;
for (unsigned int j = 0; j <= j_limit; j++) {
// e.g. alpha^5*x * alpha^37*x^2 --> alpha^42*x^3
res.coeff[i + j] = field_add(field, res.coeff[i + j], field_mul(field, l.coeff[i], r.coeff[j]));
}
}
}
void polynomial_mod(field_t field, polynomial_t dividend, polynomial_t divisor, polynomial_t mod) {
// find the polynomial remainder of dividend mod divisor
// do long division and return just the remainder (written to mod)
if (mod.order < dividend.order) {
// mod.order must be >= dividend.order (scratch space needed)
// this is an error -- catch it in debug?
return;
}
// initialize remainder as dividend
memcpy(mod.coeff, dividend.coeff, sizeof(field_element_t) * (dividend.order + 1));
// XXX make sure divisor[divisor_order] is nonzero
field_logarithm_t divisor_leading = field.log[divisor.coeff[divisor.order]];
// long division steps along one order at a time, starting at the highest order
for (unsigned int i = dividend.order; i > 0; i--) {
// look at the leading coefficient of dividend and divisor
// if leading coefficient of dividend / leading coefficient of divisor is q
// then the next row of subtraction will be q * divisor
// if order of q < 0 then what we have is the remainder and we are done
if (i < divisor.order) {
break;
}
if (mod.coeff[i] == 0) {
continue;
}
unsigned int q_order = i - divisor.order;
field_logarithm_t q_coeff = field_div_log(field, field.log[mod.coeff[i]], divisor_leading);
// now that we've chosen q, multiply the divisor by q and subtract from
// our remainder. subtracting in GF(2^8) is XOR, just like addition
for (unsigned int j = 0; j <= divisor.order; j++) {
if (divisor.coeff[j] == 0) {
continue;
}
// all of the multiplication is shifted up by q_order places
mod.coeff[j + q_order] = field_add(field, mod.coeff[j + q_order],
field_mul_log_element(field, field.log[divisor.coeff[j]], q_coeff));
}
}
}
void polynomial_formal_derivative(field_t field, polynomial_t poly, polynomial_t der) {
// if f(x) = a(n)*x^n + ... + a(1)*x + a(0)
// then f'(x) = n*a(n)*x^(n-1) + ... + 2*a(2)*x + a(1)
// where n*a(n) = sum(k=1, n, a(n)) e.g. the nth sum of a(n) in GF(2^8)
// assumes der.order = poly.order - 1
memset(der.coeff, 0, sizeof(field_element_t) * (der.order + 1));
for (unsigned int i = 0; i <= der.order; i++) {
// we're filling in the ith power of der, so we look ahead one power in poly
// f(x) = a(i + 1)*x^(i + 1) -> f'(x) = (i + 1)*a(i + 1)*x^i
// where (i + 1)*a(i + 1) is the sum of a(i + 1) (i + 1) times, not the product
der.coeff[i] = field_sum(field, poly.coeff[i + 1], i + 1);
}
}
field_element_t polynomial_eval(field_t field, polynomial_t poly, field_element_t val) {
// evaluate the polynomial poly at a particular element val
if (val == 0) {
return poly.coeff[0];
}
field_element_t res = 0;
// we're going to start at 0th order and multiply by val each time
field_logarithm_t val_exponentiated = field.log[1];
field_logarithm_t val_log = field.log[val];
for (unsigned int i = 0; i <= poly.order; i++) {
if (poly.coeff[i] != 0) {
// multiply-accumulate by the next coeff times the next power of val
res = field_add(field, res,
field_mul_log_element(field, field.log[poly.coeff[i]], val_exponentiated));
}
// now advance to the next power
val_exponentiated = field_mul_log(field, val_exponentiated, val_log);
}
return res;
}
field_element_t polynomial_eval_lut(field_t field, polynomial_t poly, const field_logarithm_t *val_exp) {
// evaluate the polynomial poly at a particular element val
// in this case, all of the logarithms of the successive powers of val have been precalculated
// this removes the extra work we'd have to do to calculate val_exponentiated each time
// if this function is to be called on the same val multiple times
if (val_exp[0] == 0) {
return poly.coeff[0];
}
field_element_t res = 0;
for (unsigned int i = 0; i <= poly.order; i++) {
if (poly.coeff[i] != 0) {
// multiply-accumulate by the next coeff times the next power of val
res = field_add(field, res,
field_mul_log_element(field, field.log[poly.coeff[i]], val_exp[i]));
}
}
return res;
}
field_element_t polynomial_eval_log_lut(field_t field, polynomial_t poly_log, const field_logarithm_t *val_exp) {
// evaluate the log_polynomial poly at a particular element val
// like polynomial_eval_lut, the logarithms of the successive powers of val have been
// precomputed
if (val_exp[0] == 0) {
if (poly_log.coeff[0] == 0) {
// special case for the non-existant log case
return 0;
}
return field.exp[poly_log.coeff[0]];
}
field_element_t res = 0;
for (unsigned int i = 0; i <= poly_log.order; i++) {
// using 0 as a sentinel value in log -- log(0) is really -inf
if (poly_log.coeff[i] != 0) {
// multiply-accumulate by the next coeff times the next power of val
res = field_add(field, res,
field_mul_log_element(field, poly_log.coeff[i], val_exp[i]));
}
}
return res;
}
void polynomial_build_exp_lut(field_t field, field_element_t val, unsigned int order, field_logarithm_t *val_exp) {
// create the lookup table of successive powers of val used by polynomial_eval_lut
field_logarithm_t val_exponentiated = field.log[1];
field_logarithm_t val_log = field.log[val];
for (unsigned int i = 0; i <= order; i++) {
if (val == 0) {
val_exp[i] = 0;
} else {
val_exp[i] = val_exponentiated;
val_exponentiated = field_mul_log(field, val_exponentiated, val_log);
}
}
}
polynomial_t polynomial_init_from_roots(field_t field, unsigned int nroots, field_element_t *roots, polynomial_t poly, polynomial_t *scratch) {
unsigned int order = nroots;
polynomial_t l;
field_element_t l_coeff[2];
l.order = 1;
l.coeff = l_coeff;
// we'll keep two temporary stores of rightside polynomial
// each time through the loop, we take the previous result and use it as new rightside
// swap back and forth (prevents the need for a copy)
polynomial_t r[2];
r[0] = scratch[0];
r[1] = scratch[1];
unsigned int rcoeffres = 0;
// initialize the result with x + roots[0]
r[rcoeffres].coeff[1] = 1;
r[rcoeffres].coeff[0] = roots[0];
r[rcoeffres].order = 1;
// initialize lcoeff[1] with x
// we'll fill in the 0th order term in each loop iter
l.coeff[1] = 1;
// loop through, using previous run's result as the new right hand side
// this allows us to multiply one group at a time
for (unsigned int i = 1; i < nroots; i++) {
l.coeff[0] = roots[i];
unsigned int nextrcoeff = rcoeffres;
rcoeffres = (rcoeffres + 1) % 2;
r[rcoeffres].order = i + 1;
polynomial_mul(field, l, r[nextrcoeff], r[rcoeffres]);
}
memcpy(poly.coeff, r[rcoeffres].coeff, (order + 1) * sizeof(field_element_t));
poly.order = order;
return poly;
}
polynomial_t polynomial_create_from_roots(field_t field, unsigned int nroots, field_element_t *roots) {
polynomial_t poly = polynomial_create(nroots);
unsigned int order = nroots;
polynomial_t l;
l.order = 1;
l.coeff = calloc(2, sizeof(field_element_t));
polynomial_t r[2];
// we'll keep two temporary stores of rightside polynomial
// each time through the loop, we take the previous result and use it as new rightside
// swap back and forth (prevents the need for a copy)
r[0].coeff = calloc(order + 1, sizeof(field_element_t));
r[1].coeff = calloc(order + 1, sizeof(field_element_t));
unsigned int rcoeffres = 0;
// initialize the result with x + roots[0]
r[rcoeffres].coeff[0] = roots[0];
r[rcoeffres].coeff[1] = 1;
r[rcoeffres].order = 1;
// initialize lcoeff[1] with x
// we'll fill in the 0th order term in each loop iter
l.coeff[1] = 1;
// loop through, using previous run's result as the new right hand side
// this allows us to multiply one group at a time
for (unsigned int i = 1; i < nroots; i++) {
l.coeff[0] = roots[i];
unsigned int nextrcoeff = rcoeffres;
rcoeffres = (rcoeffres + 1) % 2;
r[rcoeffres].order = i + 1;
polynomial_mul(field, l, r[nextrcoeff], r[rcoeffres]);
}
memcpy(poly.coeff, r[rcoeffres].coeff, (order + 1) * sizeof(field_element_t));
poly.order = order;
free(l.coeff);
free(r[0].coeff);
free(r[1].coeff);
return poly;
}

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core/libcorrect/src/reed-solomon/reed-solomon.c Normal file
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#include "correct/reed-solomon/reed-solomon.h"
// coeff must be of size nroots + 1
// e.g. 2 roots (x + alpha)(x + alpha^2) yields a poly with 3 terms x^2 + g0*x + g1
static polynomial_t reed_solomon_build_generator(field_t field, unsigned int nroots, field_element_t first_consecutive_root, unsigned int root_gap, polynomial_t generator, field_element_t *roots) {
// generator has order 2*t
// of form (x + alpha^1)(x + alpha^2)...(x - alpha^2*t)
for (unsigned int i = 0; i < nroots; i++) {
roots[i] = field.exp[(root_gap * (i + first_consecutive_root)) % 255];
}
return polynomial_create_from_roots(field, nroots, roots);
}
correct_reed_solomon *correct_reed_solomon_create(field_operation_t primitive_polynomial, field_logarithm_t first_consecutive_root, field_logarithm_t generator_root_gap, size_t num_roots) {
correct_reed_solomon *rs = calloc(1, sizeof(correct_reed_solomon));
rs->field = field_create(primitive_polynomial);
rs->block_length = 255;
rs->min_distance = num_roots;
rs->message_length = rs->block_length - rs->min_distance;
rs->first_consecutive_root = first_consecutive_root;
rs->generator_root_gap = generator_root_gap;
rs->generator_roots = malloc(rs->min_distance * sizeof(field_element_t));
rs->generator = reed_solomon_build_generator(rs->field, rs->min_distance, rs->first_consecutive_root, rs->generator_root_gap, rs->generator, rs->generator_roots);
rs->encoded_polynomial = polynomial_create(rs->block_length - 1);
rs->encoded_remainder = polynomial_create(rs->block_length - 1);
rs->has_init_decode = false;
return rs;
}
void correct_reed_solomon_destroy(correct_reed_solomon *rs) {
field_destroy(rs->field);
polynomial_destroy(rs->generator);
free(rs->generator_roots);
polynomial_destroy(rs->encoded_polynomial);
polynomial_destroy(rs->encoded_remainder);
if (rs->has_init_decode) {
free(rs->syndromes);
free(rs->modified_syndromes);
polynomial_destroy(rs->received_polynomial);
polynomial_destroy(rs->error_locator);
polynomial_destroy(rs->error_locator_log);
polynomial_destroy(rs->erasure_locator);
free(rs->error_roots);
free(rs->error_vals);
free(rs->error_locations);
polynomial_destroy(rs->last_error_locator);
polynomial_destroy(rs->error_evaluator);
polynomial_destroy(rs->error_locator_derivative);
for (unsigned int i = 0; i < rs->min_distance; i++) {
free(rs->generator_root_exp[i]);
}
free(rs->generator_root_exp);
for (field_operation_t i = 0; i < 256; i++) {
free(rs->element_exp[i]);
}
free(rs->element_exp);
polynomial_destroy(rs->init_from_roots_scratch[0]);
polynomial_destroy(rs->init_from_roots_scratch[1]);
}
free(rs);
}
void correct_reed_solomon_debug_print(correct_reed_solomon *rs) {
for (unsigned int i = 0; i < 256; i++) {
printf("%3d %3d %3d %3d\n", i, rs->field.exp[i], i, rs->field.log[i]);
}
printf("\n");
printf("roots: ");
for (unsigned int i = 0; i < rs->min_distance; i++) {
printf("%d", rs->generator_roots[i]);
if (i < rs->min_distance - 1) {
printf(", ");
}
}
printf("\n\n");
printf("generator: ");
for (unsigned int i = 0; i < rs->generator.order + 1; i++) {
printf("%d*x^%d", rs->generator.coeff[i], i);
if (i < rs->generator.order) {
printf(" + ");
}
}
printf("\n\n");
printf("generator (alpha format): ");
for (unsigned int i = rs->generator.order + 1; i > 0; i--) {
printf("alpha^%d*x^%d", rs->field.log[rs->generator.coeff[i - 1]], i - 1);
if (i > 1) {
printf(" + ");
}
}
printf("\n\n");
printf("remainder: ");
bool has_printed = false;
for (unsigned int i = 0; i < rs->encoded_remainder.order + 1; i++) {
if (!rs->encoded_remainder.coeff[i]) {
continue;
}
if (has_printed) {
printf(" + ");
}
has_printed = true;
printf("%d*x^%d", rs->encoded_remainder.coeff[i], i);
}
printf("\n\n");
printf("syndromes: ");
for (unsigned int i = 0; i < rs->min_distance; i++) {
printf("%d", rs->syndromes[i]);
if (i < rs->min_distance - 1) {
printf(", ");
}
}
printf("\n\n");
printf("numerrors: %d\n\n", rs->error_locator.order);
printf("error locator: ");
has_printed = false;
for (unsigned int i = 0; i < rs->error_locator.order + 1; i++) {
if (!rs->error_locator.coeff[i]) {
continue;
}
if (has_printed) {
printf(" + ");
}
has_printed = true;
printf("%d*x^%d", rs->error_locator.coeff[i], i);
}
printf("\n\n");
printf("error roots: ");
for (unsigned int i = 0; i < rs->error_locator.order; i++) {
printf("%d@%d", polynomial_eval(rs->field, rs->error_locator, rs->error_roots[i]), rs->error_roots[i]);
if (i < rs->error_locator.order - 1) {
printf(", ");
}
}
printf("\n\n");
printf("error evaluator: ");
has_printed = false;
for (unsigned int i = 0; i < rs->error_evaluator.order; i++) {
if (!rs->error_evaluator.coeff[i]) {
continue;
}
if (has_printed) {
printf(" + ");
}
has_printed = true;
printf("%d*x^%d", rs->error_evaluator.coeff[i], i);
}
printf("\n\n");
printf("error locator derivative: ");
has_printed = false;
for (unsigned int i = 0; i < rs->error_locator_derivative.order; i++) {
if (!rs->error_locator_derivative.coeff[i]) {
continue;
}
if (has_printed) {
printf(" + ");
}
has_printed = true;
printf("%d*x^%d", rs->error_locator_derivative.coeff[i], i);
}
printf("\n\n");
printf("error locator: ");
for (unsigned int i = 0; i < rs->error_locator.order; i++) {
printf("%d@%d", rs->error_vals[i], rs->error_locations[i]);
if (i < rs->error_locator.order - 1) {
printf(", ");
}
}
printf("\n\n");
}