trimmed modes to free some bits in first symbol

This commit is contained in:
Ahmet Inan 2025-07-13 08:23:34 +02:00
commit 34abccdf6e
7 changed files with 32 additions and 224 deletions

2
Makefile vendored
View file

@ -15,7 +15,7 @@ CXX = clang++ -stdlib=libc++ -march=native
all: encode decode
test: encode decode
$(QEMU) ./encode audio.wav 8000 8 1 1500 17 /dev/urandom
$(QEMU) ./encode audio.wav 8000 8 1 1500 5 /dev/urandom
$(QEMU) ./decode audio.wav /dev/null
encode: encode.cc common.hh

44
README.md vendored
View file

@ -3,16 +3,16 @@
Quick start:
Create file ```uncoded.dat``` with ```2048``` bits of random data:
Create file ```uncoded.dat``` with ```8192``` bits of random data:
```
dd if=/dev/urandom of=uncoded.dat bs=1 count=256
dd if=/dev/urandom of=uncoded.dat bs=1 count=1024
```
Encode file ```uncoded.dat``` to ```encoded.wav``` [WAV](https://en.wikipedia.org/wiki/WAV) audio file with 8000 Hz sample rate, 16 bits and only 1 (real) channel:
```
./encode encoded.wav 8000 16 1 1500 17 uncoded.dat
./encode encoded.wav 8000 16 1 1500 5 uncoded.dat
```
Start recording to ```recorded.wav``` audio file and stop after 5 seconds:
@ -44,36 +44,16 @@ diff -s uncoded.dat decoded.dat
All modes need a bandwidth of 2000 Hz and use a 1/2-rate forward error correction code
These use a differential modulation scheme:
* Mode 0: DBPSK, 1.70 seconds and 128 bytes
* Mode 1: DBPSK, 3.06 seconds and 256 bytes
* Mode 2: DBPSK, 5.78 seconds and 512 bytes
* Mode 3: DQPSK, 1.02 seconds and 128 bytes
* Mode 4: DQPSK, 1.70 seconds and 256 bytes
* Mode 5: DQPSK, 3.06 seconds and 512 bytes
* Mode 6: DQPSK, 5.78 seconds and 1024 bytes
* Mode 7: D8PSK, 2.21 seconds and 512 bytes
* Mode 8: D8PSK, 4.08 seconds and 1024 bytes
* Mode 9: D8PSK, 7.82 seconds and 2048 bytes
* Mode 0: DBPSK, 3.06 seconds and 256 bytes
* Mode 1: DQPSK, 3.06 seconds and 512 bytes
* Mode 2: D8PSK, 4.08 seconds and 1024 bytes
And these a coherent modulation scheme:
* Mode 10: BPSK, 1.70 seconds and 128 bytes
* Mode 11: BPSK, 3.06 seconds and 256 bytes
* Mode 12: BPSK, 5.78 seconds and 512 bytes
* Mode 13: QPSK, 1.02 seconds and 128 bytes
* Mode 14: QPSK, 1.70 seconds and 256 bytes
* Mode 15: QPSK, 3.06 seconds and 512 bytes
* Mode 16: QPSK, 5.78 seconds and 1024 bytes
* Mode 17: QAM16, 1.02 seconds and 256 bytes
* Mode 18: QAM16, 1.70 seconds and 512 bytes
* Mode 19: QAM16, 3.06 seconds and 1024 bytes
* Mode 20: QAM16, 5.78 seconds and 2048 bytes
* Mode 21: QAM64, 2.21 seconds and 1024 bytes
* Mode 22: QAM64, 4.08 seconds and 2048 bytes
* Mode 23: QAM64, 7.82 seconds and 4096 bytes
* Mode 24: QAM256, 1.02 seconds and 512 bytes
* Mode 25: QAM256, 1.70 seconds and 1024 bytes
* Mode 26: QAM256, 3.06 seconds and 2048 bytes
* Mode 27: QAM256, 5.78 seconds and 4096 bytes
* Mode 3: BPSK, 3.06 seconds and 256 bytes
* Mode 4: QPSK, 3.06 seconds and 512 bytes
* Mode 5: QAM16, 3.06 seconds and 1024 bytes
* Mode 6: QAM64, 4.08 seconds and 2048 bytes
* Mode 7: QAM256, 5.78 seconds and 4096 bytes
### Simulating
@ -82,7 +62,7 @@ Prerequisite: [disorders](https://github.com/aicodix/disorders)
Encode ```uncoded.dat``` to [analytic](https://en.wikipedia.org/wiki/Analytic_signal) audio signal, add [multipath](https://en.wikipedia.org/wiki/Multipath_propagation), [CFO, SFO](https://en.wikipedia.org/wiki/Carrier_frequency_offset), [AWGN](https://en.wikipedia.org/wiki/Additive_white_Gaussian_noise), decode and compare:
```
./encode - 8000 16 2 1500 17 uncoded.dat | ../disorders/multipath - - ../disorders/multipath.txt 10 | ../disorders/cfo - - 234.567 | ../disorders/sfo - - 147 | ../disorders/awgn - - -20 | ./decode - - | diff -q -s uncoded.dat -
./encode - 8000 16 2 1500 5 uncoded.dat | ../disorders/multipath - - ../disorders/multipath.txt 10 | ../disorders/cfo - - 234.567 | ../disorders/sfo - - 147 | ../disorders/awgn - - -20 | ./decode - - | diff -q -s uncoded.dat -
```
### Reading

228
common.hh
View file

@ -16,7 +16,7 @@ struct Common
static const int code_max = 16;
static const int bits_max = 1 << code_max;
static const int data_max = 4096;
static const int symbols_max = 44;
static const int symbols_max = 32;
static const int mls0_poly = 0x331;
static const int mls0_seed = 214;
static const int mls1_poly = 0x43;
@ -55,14 +55,6 @@ struct Common
{
switch (mode) {
case 0:
mod_bits = 1;
symbol_count = 8;
differential = true;
code_order = 11;
data_bits = 1024;
frozen_bits = frozen_2048_1056;
break;
case 1:
mod_bits = 1;
symbol_count = 16;
differential = true;
@ -70,207 +62,55 @@ struct Common
data_bits = 2048;
frozen_bits = frozen_4096_2080;
break;
case 2:
mod_bits = 1;
symbol_count = 32;
case 1:
mod_bits = 2;
symbol_count = 16;
differential = true;
code_order = 13;
data_bits = 4096;
frozen_bits = frozen_8192_4128;
break;
case 3:
mod_bits = 2;
symbol_count = 4;
case 2:
mod_bits = 3;
symbol_count = 22;
differential = true;
code_order = 11;
data_bits = 1024;
frozen_bits = frozen_2048_1056;
code_order = 14;
data_bits = 8192;
frozen_bits = frozen_16384_8224;
break;
case 3:
mod_bits = 1;
symbol_count = 16;
differential = false;
code_order = 12;
data_bits = 2048;
frozen_bits = frozen_4096_2080;
break;
case 4:
mod_bits = 2;
symbol_count = 8;
differential = true;
code_order = 12;
data_bits = 2048;
frozen_bits = frozen_4096_2080;
symbol_count = 16;
differential = false;
code_order = 13;
data_bits = 4096;
frozen_bits = frozen_8192_4128;
break;
case 5:
mod_bits = 2;
mod_bits = 4;
symbol_count = 16;
differential = true;
code_order = 13;
data_bits = 4096;
frozen_bits = frozen_8192_4128;
differential = false;
code_order = 14;
data_bits = 8192;
frozen_bits = frozen_16384_8224;
break;
case 6:
mod_bits = 2;
symbol_count = 32;
differential = true;
code_order = 14;
data_bits = 8192;
frozen_bits = frozen_16384_8224;
mod_bits = 6;
symbol_count = 22;
differential = false;
code_order = 15;
data_bits = 16384;
frozen_bits = frozen_32768_16416;
break;
case 7:
mod_bits = 3;
symbol_count = 11;
differential = true;
code_order = 13;
data_bits = 4096;
frozen_bits = frozen_8192_4128;
break;
case 8:
mod_bits = 3;
symbol_count = 22;
differential = true;
code_order = 14;
data_bits = 8192;
frozen_bits = frozen_16384_8224;
break;
case 9:
mod_bits = 3;
symbol_count = 44;
differential = true;
code_order = 15;
data_bits = 16384;
frozen_bits = frozen_32768_16416;
break;
case 10:
mod_bits = 1;
symbol_count = 8;
differential = false;
code_order = 11;
data_bits = 1024;
frozen_bits = frozen_2048_1056;
break;
case 11:
mod_bits = 1;
symbol_count = 16;
differential = false;
code_order = 12;
data_bits = 2048;
frozen_bits = frozen_4096_2080;
break;
case 12:
mod_bits = 1;
symbol_count = 32;
differential = false;
code_order = 13;
data_bits = 4096;
frozen_bits = frozen_8192_4128;
break;
case 13:
mod_bits = 2;
symbol_count = 4;
differential = false;
code_order = 11;
data_bits = 1024;
frozen_bits = frozen_2048_1056;
break;
case 14:
mod_bits = 2;
symbol_count = 8;
differential = false;
code_order = 12;
data_bits = 2048;
frozen_bits = frozen_4096_2080;
break;
case 15:
mod_bits = 2;
symbol_count = 16;
differential = false;
code_order = 13;
data_bits = 4096;
frozen_bits = frozen_8192_4128;
break;
case 16:
mod_bits = 2;
symbol_count = 32;
differential = false;
code_order = 14;
data_bits = 8192;
frozen_bits = frozen_16384_8224;
break;
case 17:
mod_bits = 4;
symbol_count = 4;
differential = false;
code_order = 12;
data_bits = 2048;
frozen_bits = frozen_4096_2080;
break;
case 18:
mod_bits = 4;
symbol_count = 8;
differential = false;
code_order = 13;
data_bits = 4096;
frozen_bits = frozen_8192_4128;
break;
case 19:
mod_bits = 4;
symbol_count = 16;
differential = false;
code_order = 14;
data_bits = 8192;
frozen_bits = frozen_16384_8224;
break;
case 20:
mod_bits = 4;
symbol_count = 32;
differential = false;
code_order = 15;
data_bits = 16384;
frozen_bits = frozen_32768_16416;
break;
case 21:
mod_bits = 6;
symbol_count = 11;
differential = false;
code_order = 14;
data_bits = 8192;
frozen_bits = frozen_16384_8224;
break;
case 22:
mod_bits = 6;
symbol_count = 22;
differential = false;
code_order = 15;
data_bits = 16384;
frozen_bits = frozen_32768_16416;
break;
case 23:
mod_bits = 6;
symbol_count = 44;
differential = false;
code_order = 16;
data_bits = 32768;
frozen_bits = frozen_65536_32800;
break;
case 24:
mod_bits = 8;
symbol_count = 4;
differential = false;
code_order = 13;
data_bits = 4096;
frozen_bits = frozen_8192_4128;
break;
case 25:
mod_bits = 8;
symbol_count = 8;
differential = false;
code_order = 14;
data_bits = 8192;
frozen_bits = frozen_16384_8224;
break;
case 26:
mod_bits = 8;
symbol_count = 16;
differential = false;
code_order = 15;
data_bits = 16384;
frozen_bits = frozen_32768_16416;
break;
case 27:
mod_bits = 8;
symbol_count = 32;
differential = false;

View file

@ -140,12 +140,7 @@ struct Decoder : Common
}
void shuffle(code_type *dest, const code_type *src)
{
if (code_order == 11) {
CODE::XorShiftMask<int, 11, 1, 3, 4, 1> seq;
dest[0] = src[0];
for (int i = 1; i < 2048; ++i)
dest[seq()] = src[i];
} else if (code_order == 12) {
if (code_order == 12) {
CODE::XorShiftMask<int, 12, 1, 1, 4, 1> seq;
dest[0] = src[0];
for (int i = 1; i < 4096; ++i)
@ -238,13 +233,13 @@ struct Decoder : Common
seq1();
}
int mode = hadamard_decoder(meta);
if (mode < 0 || mode > 27) {
if (mode < 0 || mode > 7) {
std::cerr << "operation mode " << mode << " unsupported." << std::endl;
continue;
}
setup(mode);
std::cerr << "oper mode: " << oper_mode << std::endl;
if (oper_mode >= 10) {
if (oper_mode >= 3) {
for (int i = 0; i < tone_count; ++i)
tone[i] *= DSP::polar<value>(1, tse(i+tone_off));
for (int i = 0; i < tone_count; ++i)
@ -339,9 +334,9 @@ struct Decoder : Common
cmplx hard(1, 0);
if (i % block_length != meta_off && i % block_length != seed_off) {
int bits = mod_bits;
if (oper_mode >= 7 && oper_mode <= 9 && l % 32 == 30)
if (oper_mode == 2 && l % 32 == 30)
bits = 2;
if (oper_mode >= 21 && oper_mode <= 23 && l % 64 == 60)
if (oper_mode == 6 && l % 64 == 60)
bits = 4;
demap_hard(perm+l, demod[i], bits);
hard = map_bits(perm+l, bits);
@ -357,9 +352,9 @@ struct Decoder : Common
for (int i = 0; i < tone_count; ++i) {
if (i % block_length != meta_off && i % block_length != seed_off) {
int bits = mod_bits;
if (oper_mode >= 7 && oper_mode <= 9 && k % 32 == 30)
if (oper_mode == 2 && k % 32 == 30)
bits = 2;
if (oper_mode >= 21 && oper_mode <= 23 && k % 64 == 60)
if (oper_mode == 6 && k % 64 == 60)
bits = 4;
demap_soft(perm+k, demod[i], precision, bits);
k += bits;

View file

@ -207,12 +207,7 @@ struct Encoder : public Common
}
void shuffle(code_type *dest, const code_type *src)
{
if (code_order == 11) {
CODE::XorShiftMask<int, 11, 1, 3, 4, 1> seq;
dest[0] = src[0];
for (int i = 1; i < 2048; ++i)
dest[i] = src[seq()];
} else if (code_order == 12) {
if (code_order == 12) {
CODE::XorShiftMask<int, 12, 1, 1, 4, 1> seq;
dest[0] = src[0];
for (int i = 1; i < 4096; ++i)
@ -290,9 +285,9 @@ struct Encoder : public Common
tone[i] = nrz(seq1());
} else {
int bits = mod_bits;
if (oper_mode >= 7 && oper_mode <= 9 && k % 32 == 30)
if (oper_mode == 2 && k % 32 == 30)
bits = 2;
if (oper_mode >= 21 && oper_mode <= 23 && k % 64 == 60)
if (oper_mode == 6 && k % 64 == 60)
bits = 4;
tone[i] = map_bits(perm+k, bits);
k += bits;
@ -328,7 +323,7 @@ int main(int argc, char **argv)
}
int input_count = argc - 7;
int oper_mode = std::atoi(argv[6]);
if (oper_mode < 0 || oper_mode > 27) {
if (oper_mode < 0 || oper_mode > 7) {
std::cerr << "Unsupported operation mode." << std::endl;
return 1;
}

View file

@ -32,6 +32,5 @@ int main()
code<14>(16384, 8192+32, 0.39);
code<13>(8192, 4096+32, 0.38);
code<12>(4096, 2048+32, 0.37);
code<11>(2048, 1024+32, 0.34);
return 0;
}

View file

@ -3,4 +3,3 @@ static const uint32_t frozen_32768_16416[1024] = { 0xffffffff, 0xffffffff, 0xfff
static const uint32_t frozen_16384_8224[512] = { 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x177f7fff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0x7fffffff, 0x1171fff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0x17ffffff, 0x177fffff, 0x3177f, 0xffffffff, 0xffffffff, 0xffffffff, 0x177fffff, 0x7fffffff, 0x77f7fff, 0x11f7fff, 0x10117, 0x7fffffff, 0x1171fff, 0x117177f, 0x117, 0x17177f, 0x3, 0x1, 0x0, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x17ffffff, 0xffffffff, 0x177f7fff, 0x37f7fff, 0x1011f, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x177fffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0x37f7fff, 0x7fffffff, 0x1171fff, 0x117177f, 0x117, 0xffffffff, 0x7fffffff, 0x1fffffff, 0x117177f, 0x177fffff, 0x7177f, 0x1017f, 0x1, 0x37f7fff, 0x1011f, 0x10117, 0x1, 0x10117, 0x1, 0x1, 0x0, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0x7fffffff, 0x11717ff, 0xffffffff, 0x1fffffff, 0x177fffff, 0x7177f, 0x77f7fff, 0x1013f, 0x10117, 0x1, 0xffffffff, 0x177f7fff, 0x13f7fff, 0x10117, 0x1171fff, 0x10117, 0x10117, 0x0, 0x117177f, 0x17, 0x3, 0x0, 0x1, 0x0, 0x0, 0x0, 0x7fffffff, 0x1171fff, 0x117177f, 0x117, 0x17177f, 0x3, 0x1, 0x0, 0x1037f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1011f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x177fffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0x11f7fff, 0xffffffff, 0x7fffffff, 0x1fffffff, 0x117177f, 0x177f7fff, 0x3177f, 0x1013f, 0x1, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0x1fffffff, 0x177fffff, 0x17177f, 0xffffffff, 0x177f7fff, 0x37f7fff, 0x1011f, 0x1171fff, 0x10117, 0x10117, 0x1, 0x7fffffff, 0x11f7fff, 0x11717ff, 0x10117, 0x117177f, 0x7, 0x1, 0x0, 0x3177f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0xffffffff, 0xffffffff, 0xffffffff, 0x177f7fff, 0x7fffffff, 0x17f7fff, 0x1171fff, 0x10117, 0x3fffffff, 0x11717ff, 0x117177f, 0x7, 0x3177f, 0x1, 0x1, 0x0, 0x177fffff, 0x7177f, 0x1017f, 0x1, 0x10117, 0x1, 0x1, 0x0, 0x10117, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x37f7fff, 0x1011f, 0x10117, 0x1, 0x10117, 0x1, 0x1, 0x0, 0x10117, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x17, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0xffffffff, 0x7fffffff, 0x3fffffff, 0x11717ff, 0x177fffff, 0x17177f, 0x1037f, 0x1, 0x77f7fff, 0x1013f, 0x10117, 0x1, 0x10117, 0x1, 0x1, 0x0, 0x1173fff, 0x10117, 0x10117, 0x1, 0x117, 0x0, 0x0, 0x0, 0x7, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x117177f, 0x10117, 0x17, 0x0, 0x3, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x17177f, 0x3, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, };
static const uint32_t frozen_8192_4128[256] = { 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x1fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x177f7fff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0x7fffffff, 0x1171fff, 0xffffffff, 0x3fffffff, 0x177fffff, 0x17177f, 0x177f7fff, 0x1017f, 0x10117, 0x1, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0x7fffffff, 0x1fffffff, 0x117177f, 0xffffffff, 0xffffffff, 0xffffffff, 0x3fffffff, 0xffffffff, 0x177fffff, 0x77f7fff, 0x1013f, 0x7fffffff, 0x17f7fff, 0x1171fff, 0x10117, 0x117177f, 0x17, 0x3, 0x0, 0xffffffff, 0xffffffff, 0xffffffff, 0x77f7fff, 0x7fffffff, 0x1173fff, 0x117177f, 0x117, 0x17ffffff, 0x117177f, 0x3177f, 0x1, 0x1013f, 0x1, 0x1, 0x0, 0x177f7fff, 0x1017f, 0x10117, 0x1, 0x10117, 0x1, 0x1, 0x0, 0x10117, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x1fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x177f7fff, 0x7fffffff, 0x13f7fff, 0x1171fff, 0x10117, 0xffffffff, 0x7fffffff, 0x7fffffff, 0x1173fff, 0x17ffffff, 0x117177f, 0x7177f, 0x1, 0x177f7fff, 0x1077f, 0x1011f, 0x1, 0x10117, 0x1, 0x1, 0x0, 0xffffffff, 0x1fffffff, 0x177fffff, 0x3177f, 0x37f7fff, 0x1011f, 0x10117, 0x1, 0x1173fff, 0x10117, 0x10117, 0x0, 0x17, 0x0, 0x0, 0x0, 0x117177f, 0x17, 0x3, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x7fffffff, 0x37f7fff, 0x1177fff, 0x10117, 0x11717ff, 0x117, 0x7, 0x0, 0x17177f, 0x3, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1037f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1011f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, };
static const uint32_t frozen_4096_2080[128] = { 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x17ffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x77f7fff, 0x7fffffff, 0x1173fff, 0x11717ff, 0x117, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0x13f7fff, 0xffffffff, 0x7fffffff, 0x1fffffff, 0x117177f, 0x177fffff, 0x3077f, 0x1013f, 0x1, 0xffffffff, 0x177fffff, 0x177f7fff, 0x1017f, 0x11f7fff, 0x10117, 0x10117, 0x0, 0x11717ff, 0x117, 0x7, 0x0, 0x1, 0x0, 0x0, 0x0, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0x17ffffff, 0x177fffff, 0x1077f, 0xffffffff, 0x177f7fff, 0x13f7fff, 0x10117, 0x11717ff, 0x10117, 0x17, 0x0, 0x7fffffff, 0x1171fff, 0x117177f, 0x17, 0x3177f, 0x1, 0x1, 0x0, 0x1013f, 0x1, 0x1, 0x0, 0x1, 0x0, 0x0, 0x0, 0x177fffff, 0x7177f, 0x1037f, 0x1, 0x1011f, 0x1, 0x1, 0x0, 0x10117, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x117, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, };
static const uint32_t frozen_2048_1056[64] = { 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, 0xffffffff, 0x177fffff, 0x177f7fff, 0x1013f, 0xffffffff, 0xffffffff, 0xffffffff, 0x177f7fff, 0x7fffffff, 0x13f7fff, 0x1171fff, 0x10117, 0x1fffffff, 0x11717ff, 0x7177f, 0x1, 0x1037f, 0x1, 0x1, 0x0, 0xffffffff, 0x7fffffff, 0x7fffffff, 0x11717ff, 0x17ffffff, 0x7177f, 0x1037f, 0x1, 0x77f7fff, 0x1013f, 0x10117, 0x1, 0x10117, 0x1, 0x0, 0x0, 0x1173fff, 0x10117, 0x117, 0x0, 0x7, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, };