zig/lib/std/compress/flate/huffman_encoder.zig
Igor Anić d645114f7e add deflate implemented from first principles
Zig deflate compression/decompression implementation. It supports compression and decompression of gzip, zlib and raw deflate format.

Fixes #18062.

This PR replaces current compress/gzip and compress/zlib packages. Deflate package is renamed to flate. Flate is common name for deflate/inflate where deflate is compression and inflate decompression.

There are breaking change. Methods signatures are changed because of removal of the allocator, and I also unified API for all three namespaces (flate, gzip, zlib).

Currently I put old packages under v1 namespace they are still available as compress/v1/gzip, compress/v1/zlib, compress/v1/deflate. Idea is to give users of the current API little time to postpone analyzing what they had to change. Although that rises question when it is safe to remove that v1 namespace.

Here is current API in the compress package:

```Zig
// deflate
    fn compressor(allocator, writer, options) !Compressor(@TypeOf(writer))
    fn Compressor(comptime WriterType) type

    fn decompressor(allocator, reader, null) !Decompressor(@TypeOf(reader))
    fn Decompressor(comptime ReaderType: type) type

// gzip
    fn compress(allocator, writer, options) !Compress(@TypeOf(writer))
    fn Compress(comptime WriterType: type) type

    fn decompress(allocator, reader) !Decompress(@TypeOf(reader))
    fn Decompress(comptime ReaderType: type) type

// zlib
    fn compressStream(allocator, writer, options) !CompressStream(@TypeOf(writer))
    fn CompressStream(comptime WriterType: type) type

    fn decompressStream(allocator, reader) !DecompressStream(@TypeOf(reader))
    fn DecompressStream(comptime ReaderType: type) type

// xz
   fn decompress(allocator: Allocator, reader: anytype) !Decompress(@TypeOf(reader))
   fn Decompress(comptime ReaderType: type) type

// lzma
    fn decompress(allocator, reader) !Decompress(@TypeOf(reader))
    fn Decompress(comptime ReaderType: type) type

// lzma2
    fn decompress(allocator, reader, writer !void

// zstandard:
    fn DecompressStream(ReaderType, options) type
    fn decompressStream(allocator, reader) DecompressStream(@TypeOf(reader), .{})
    struct decompress
```

The proposed naming convention:
 - Compressor/Decompressor for functions which return type, like Reader/Writer/GeneralPurposeAllocator
 - compressor/compressor for functions which are initializers for that type, like reader/writer/allocator
 - compress/decompress for one shot operations, accepts reader/writer pair, like read/write/alloc

```Zig
/// Compress from reader and write compressed data to the writer.
fn compress(reader: anytype, writer: anytype, options: Options) !void

/// Create Compressor which outputs the writer.
fn compressor(writer: anytype, options: Options) !Compressor(@TypeOf(writer))

/// Compressor type
fn Compressor(comptime WriterType: type) type

/// Decompress from reader and write plain data to the writer.
fn decompress(reader: anytype, writer: anytype) !void

/// Create Decompressor which reads from reader.
fn decompressor(reader: anytype) Decompressor(@TypeOf(reader)

/// Decompressor type
fn Decompressor(comptime ReaderType: type) type

```

Comparing this implementation with the one we currently have in Zig's standard library (std).
Std is roughly 1.2-1.4 times slower in decompression, and 1.1-1.2 times slower in compression. Compressed sizes are pretty much same in both cases.
More resutls in [this](https://github.com/ianic/flate) repo.

This library uses static allocations for all structures, doesn't require allocator. That makes sense especially for deflate where all structures, internal buffers are allocated to the full size. Little less for inflate where we std version uses less memory by not preallocating to theoretical max size array which are usually not fully used.

For deflate this library allocates 395K while std 779K.
For inflate this library allocates 74.5K while std around 36K.

Inflate difference is because we here use 64K history instead of 32K in std.

If merged existing usage of compress gzip/zlib/deflate need some changes. Here is example with necessary changes in comments:

```Zig

const std = @import("std");

// To get this file:
// wget -nc -O war_and_peace.txt https://www.gutenberg.org/ebooks/2600.txt.utf-8
const data = @embedFile("war_and_peace.txt");

pub fn main() !void {
    var gpa = std.heap.GeneralPurposeAllocator(.{}){};
    defer std.debug.assert(gpa.deinit() == .ok);
    const allocator = gpa.allocator();

    try oldDeflate(allocator);
    try new(std.compress.flate, allocator);

    try oldZlib(allocator);
    try new(std.compress.zlib, allocator);

    try oldGzip(allocator);
    try new(std.compress.gzip, allocator);
}

pub fn new(comptime pkg: type, allocator: std.mem.Allocator) !void {
    var buf = std.ArrayList(u8).init(allocator);
    defer buf.deinit();

    // Compressor
    var cmp = try pkg.compressor(buf.writer(), .{});
    _ = try cmp.write(data);
    try cmp.finish();

    var fbs = std.io.fixedBufferStream(buf.items);
    // Decompressor
    var dcp = pkg.decompressor(fbs.reader());

    const plain = try dcp.reader().readAllAlloc(allocator, std.math.maxInt(usize));
    defer allocator.free(plain);
    try std.testing.expectEqualSlices(u8, data, plain);
}

pub fn oldDeflate(allocator: std.mem.Allocator) !void {
    const deflate = std.compress.v1.deflate;

    // Compressor
    var buf = std.ArrayList(u8).init(allocator);
    defer buf.deinit();
    // Remove allocator
    // Rename deflate -> flate
    var cmp = try deflate.compressor(allocator, buf.writer(), .{});
    _ = try cmp.write(data);
    try cmp.close(); // Rename to finish
    cmp.deinit(); // Remove

    // Decompressor
    var fbs = std.io.fixedBufferStream(buf.items);
    // Remove allocator and last param
    // Rename deflate -> flate
    // Remove try
    var dcp = try deflate.decompressor(allocator, fbs.reader(), null);
    defer dcp.deinit(); // Remove

    const plain = try dcp.reader().readAllAlloc(allocator, std.math.maxInt(usize));
    defer allocator.free(plain);
    try std.testing.expectEqualSlices(u8, data, plain);
}

pub fn oldZlib(allocator: std.mem.Allocator) !void {
    const zlib = std.compress.v1.zlib;

    var buf = std.ArrayList(u8).init(allocator);
    defer buf.deinit();

    // Compressor
    // Rename compressStream => compressor
    // Remove allocator
    var cmp = try zlib.compressStream(allocator, buf.writer(), .{});
    _ = try cmp.write(data);
    try cmp.finish();
    cmp.deinit(); // Remove

    var fbs = std.io.fixedBufferStream(buf.items);
    // Decompressor
    // decompressStream => decompressor
    // Remove allocator
    // Remove try
    var dcp = try zlib.decompressStream(allocator, fbs.reader());
    defer dcp.deinit(); // Remove

    const plain = try dcp.reader().readAllAlloc(allocator, std.math.maxInt(usize));
    defer allocator.free(plain);
    try std.testing.expectEqualSlices(u8, data, plain);
}

pub fn oldGzip(allocator: std.mem.Allocator) !void {
    const gzip = std.compress.v1.gzip;

    var buf = std.ArrayList(u8).init(allocator);
    defer buf.deinit();

    // Compressor
    // Rename compress => compressor
    // Remove allocator
    var cmp = try gzip.compress(allocator, buf.writer(), .{});
    _ = try cmp.write(data);
    try cmp.close(); // Rename to finisho
    cmp.deinit(); // Remove

    var fbs = std.io.fixedBufferStream(buf.items);
    // Decompressor
    // Rename decompress => decompressor
    // Remove allocator
    // Remove try
    var dcp = try gzip.decompress(allocator, fbs.reader());
    defer dcp.deinit(); // Remove

    const plain = try dcp.reader().readAllAlloc(allocator, std.math.maxInt(usize));
    defer allocator.free(plain);
    try std.testing.expectEqualSlices(u8, data, plain);
}

```
2024-02-14 18:28:20 +01:00

536 lines
22 KiB
Zig

const std = @import("std");
const assert = std.debug.assert;
const math = std.math;
const mem = std.mem;
const sort = std.sort;
const testing = std.testing;
const consts = @import("consts.zig").huffman;
const LiteralNode = struct {
literal: u16,
freq: u16,
};
// Describes the state of the constructed tree for a given depth.
const LevelInfo = struct {
// Our level. for better printing
level: u32,
// The frequency of the last node at this level
last_freq: u32,
// The frequency of the next character to add to this level
next_char_freq: u32,
// The frequency of the next pair (from level below) to add to this level.
// Only valid if the "needed" value of the next lower level is 0.
next_pair_freq: u32,
// The number of chains remaining to generate for this level before moving
// up to the next level
needed: u32,
};
// hcode is a huffman code with a bit code and bit length.
pub const HuffCode = struct {
code: u16 = 0,
len: u16 = 0,
// set sets the code and length of an hcode.
fn set(self: *HuffCode, code: u16, length: u16) void {
self.len = length;
self.code = code;
}
};
pub fn HuffmanEncoder(comptime size: usize) type {
return struct {
codes: [size]HuffCode = undefined,
// Reusable buffer with the longest possible frequency table.
freq_cache: [consts.max_num_frequencies + 1]LiteralNode = undefined,
bit_count: [17]u32 = undefined,
lns: []LiteralNode = undefined, // sorted by literal, stored to avoid repeated allocation in generate
lfs: []LiteralNode = undefined, // sorted by frequency, stored to avoid repeated allocation in generate
const Self = @This();
// Update this Huffman Code object to be the minimum code for the specified frequency count.
//
// freq An array of frequencies, in which frequency[i] gives the frequency of literal i.
// max_bits The maximum number of bits to use for any literal.
pub fn generate(self: *Self, freq: []u16, max_bits: u32) void {
var list = self.freq_cache[0 .. freq.len + 1];
// Number of non-zero literals
var count: u32 = 0;
// Set list to be the set of all non-zero literals and their frequencies
for (freq, 0..) |f, i| {
if (f != 0) {
list[count] = LiteralNode{ .literal = @as(u16, @intCast(i)), .freq = f };
count += 1;
} else {
list[count] = LiteralNode{ .literal = 0x00, .freq = 0 };
self.codes[i].len = 0;
}
}
list[freq.len] = LiteralNode{ .literal = 0x00, .freq = 0 };
list = list[0..count];
if (count <= 2) {
// Handle the small cases here, because they are awkward for the general case code. With
// two or fewer literals, everything has bit length 1.
for (list, 0..) |node, i| {
// "list" is in order of increasing literal value.
self.codes[node.literal].set(@as(u16, @intCast(i)), 1);
}
return;
}
self.lfs = list;
mem.sort(LiteralNode, self.lfs, {}, byFreq);
// Get the number of literals for each bit count
const bit_count = self.bitCounts(list, max_bits);
// And do the assignment
self.assignEncodingAndSize(bit_count, list);
}
pub fn bitLength(self: *Self, freq: []u16) u32 {
var total: u32 = 0;
for (freq, 0..) |f, i| {
if (f != 0) {
total += @as(u32, @intCast(f)) * @as(u32, @intCast(self.codes[i].len));
}
}
return total;
}
// Return the number of literals assigned to each bit size in the Huffman encoding
//
// This method is only called when list.len >= 3
// The cases of 0, 1, and 2 literals are handled by special case code.
//
// list: An array of the literals with non-zero frequencies
// and their associated frequencies. The array is in order of increasing
// frequency, and has as its last element a special element with frequency
// std.math.maxInt(i32)
//
// max_bits: The maximum number of bits that should be used to encode any literal.
// Must be less than 16.
//
// Returns an integer array in which array[i] indicates the number of literals
// that should be encoded in i bits.
fn bitCounts(self: *Self, list: []LiteralNode, max_bits_to_use: usize) []u32 {
var max_bits = max_bits_to_use;
const n = list.len;
const max_bits_limit = 16;
assert(max_bits < max_bits_limit);
// The tree can't have greater depth than n - 1, no matter what. This
// saves a little bit of work in some small cases
max_bits = @min(max_bits, n - 1);
// Create information about each of the levels.
// A bogus "Level 0" whose sole purpose is so that
// level1.prev.needed == 0. This makes level1.next_pair_freq
// be a legitimate value that never gets chosen.
var levels: [max_bits_limit]LevelInfo = mem.zeroes([max_bits_limit]LevelInfo);
// leaf_counts[i] counts the number of literals at the left
// of ancestors of the rightmost node at level i.
// leaf_counts[i][j] is the number of literals at the left
// of the level j ancestor.
var leaf_counts: [max_bits_limit][max_bits_limit]u32 = mem.zeroes([max_bits_limit][max_bits_limit]u32);
{
var level = @as(u32, 1);
while (level <= max_bits) : (level += 1) {
// For every level, the first two items are the first two characters.
// We initialize the levels as if we had already figured this out.
levels[level] = LevelInfo{
.level = level,
.last_freq = list[1].freq,
.next_char_freq = list[2].freq,
.next_pair_freq = list[0].freq + list[1].freq,
.needed = 0,
};
leaf_counts[level][level] = 2;
if (level == 1) {
levels[level].next_pair_freq = math.maxInt(i32);
}
}
}
// We need a total of 2*n - 2 items at top level and have already generated 2.
levels[max_bits].needed = 2 * @as(u32, @intCast(n)) - 4;
{
var level = max_bits;
while (true) {
var l = &levels[level];
if (l.next_pair_freq == math.maxInt(i32) and l.next_char_freq == math.maxInt(i32)) {
// We've run out of both leafs and pairs.
// End all calculations for this level.
// To make sure we never come back to this level or any lower level,
// set next_pair_freq impossibly large.
l.needed = 0;
levels[level + 1].next_pair_freq = math.maxInt(i32);
level += 1;
continue;
}
const prev_freq = l.last_freq;
if (l.next_char_freq < l.next_pair_freq) {
// The next item on this row is a leaf node.
const next = leaf_counts[level][level] + 1;
l.last_freq = l.next_char_freq;
// Lower leaf_counts are the same of the previous node.
leaf_counts[level][level] = next;
if (next >= list.len) {
l.next_char_freq = maxNode().freq;
} else {
l.next_char_freq = list[next].freq;
}
} else {
// The next item on this row is a pair from the previous row.
// next_pair_freq isn't valid until we generate two
// more values in the level below
l.last_freq = l.next_pair_freq;
// Take leaf counts from the lower level, except counts[level] remains the same.
@memcpy(leaf_counts[level][0..level], leaf_counts[level - 1][0..level]);
levels[l.level - 1].needed = 2;
}
l.needed -= 1;
if (l.needed == 0) {
// We've done everything we need to do for this level.
// Continue calculating one level up. Fill in next_pair_freq
// of that level with the sum of the two nodes we've just calculated on
// this level.
if (l.level == max_bits) {
// All done!
break;
}
levels[l.level + 1].next_pair_freq = prev_freq + l.last_freq;
level += 1;
} else {
// If we stole from below, move down temporarily to replenish it.
while (levels[level - 1].needed > 0) {
level -= 1;
if (level == 0) {
break;
}
}
}
}
}
// Somethings is wrong if at the end, the top level is null or hasn't used
// all of the leaves.
assert(leaf_counts[max_bits][max_bits] == n);
var bit_count = self.bit_count[0 .. max_bits + 1];
var bits: u32 = 1;
const counts = &leaf_counts[max_bits];
{
var level = max_bits;
while (level > 0) : (level -= 1) {
// counts[level] gives the number of literals requiring at least "bits"
// bits to encode.
bit_count[bits] = counts[level] - counts[level - 1];
bits += 1;
if (level == 0) {
break;
}
}
}
return bit_count;
}
// Look at the leaves and assign them a bit count and an encoding as specified
// in RFC 1951 3.2.2
fn assignEncodingAndSize(self: *Self, bit_count: []u32, list_arg: []LiteralNode) void {
var code = @as(u16, 0);
var list = list_arg;
for (bit_count, 0..) |bits, n| {
code <<= 1;
if (n == 0 or bits == 0) {
continue;
}
// The literals list[list.len-bits] .. list[list.len-bits]
// are encoded using "bits" bits, and get the values
// code, code + 1, .... The code values are
// assigned in literal order (not frequency order).
const chunk = list[list.len - @as(u32, @intCast(bits)) ..];
self.lns = chunk;
mem.sort(LiteralNode, self.lns, {}, byLiteral);
for (chunk) |node| {
self.codes[node.literal] = HuffCode{
.code = bitReverse(u16, code, @as(u5, @intCast(n))),
.len = @as(u16, @intCast(n)),
};
code += 1;
}
list = list[0 .. list.len - @as(u32, @intCast(bits))];
}
}
};
}
fn maxNode() LiteralNode {
return LiteralNode{
.literal = math.maxInt(u16),
.freq = math.maxInt(u16),
};
}
pub fn huffmanEncoder(comptime size: u32) HuffmanEncoder(size) {
return .{};
}
pub const LiteralEncoder = HuffmanEncoder(consts.max_num_frequencies);
pub const DistanceEncoder = HuffmanEncoder(consts.distance_code_count);
pub const CodegenEncoder = HuffmanEncoder(19);
// Generates a HuffmanCode corresponding to the fixed literal table
pub fn fixedLiteralEncoder() LiteralEncoder {
var h: LiteralEncoder = undefined;
var ch: u16 = 0;
while (ch < consts.max_num_frequencies) : (ch += 1) {
var bits: u16 = undefined;
var size: u16 = undefined;
switch (ch) {
0...143 => {
// size 8, 000110000 .. 10111111
bits = ch + 48;
size = 8;
},
144...255 => {
// size 9, 110010000 .. 111111111
bits = ch + 400 - 144;
size = 9;
},
256...279 => {
// size 7, 0000000 .. 0010111
bits = ch - 256;
size = 7;
},
else => {
// size 8, 11000000 .. 11000111
bits = ch + 192 - 280;
size = 8;
},
}
h.codes[ch] = HuffCode{ .code = bitReverse(u16, bits, @as(u5, @intCast(size))), .len = size };
}
return h;
}
pub fn fixedDistanceEncoder() DistanceEncoder {
var h: DistanceEncoder = undefined;
for (h.codes, 0..) |_, ch| {
h.codes[ch] = HuffCode{ .code = bitReverse(u16, @as(u16, @intCast(ch)), 5), .len = 5 };
}
return h;
}
pub fn huffmanDistanceEncoder() DistanceEncoder {
var distance_freq = [1]u16{0} ** consts.distance_code_count;
distance_freq[0] = 1;
// huff_distance is a static distance encoder used for huffman only encoding.
// It can be reused since we will not be encoding distance values.
var h: DistanceEncoder = .{};
h.generate(distance_freq[0..], 15);
return h;
}
fn byLiteral(context: void, a: LiteralNode, b: LiteralNode) bool {
_ = context;
return a.literal < b.literal;
}
fn byFreq(context: void, a: LiteralNode, b: LiteralNode) bool {
_ = context;
if (a.freq == b.freq) {
return a.literal < b.literal;
}
return a.freq < b.freq;
}
test "flate.HuffmanEncoder generate a Huffman code from an array of frequencies" {
var freqs: [19]u16 = [_]u16{
8, // 0
1, // 1
1, // 2
2, // 3
5, // 4
10, // 5
9, // 6
1, // 7
0, // 8
0, // 9
0, // 10
0, // 11
0, // 12
0, // 13
0, // 14
0, // 15
1, // 16
3, // 17
5, // 18
};
var enc = huffmanEncoder(19);
enc.generate(freqs[0..], 7);
try testing.expectEqual(@as(u32, 141), enc.bitLength(freqs[0..]));
try testing.expectEqual(@as(usize, 3), enc.codes[0].len);
try testing.expectEqual(@as(usize, 6), enc.codes[1].len);
try testing.expectEqual(@as(usize, 6), enc.codes[2].len);
try testing.expectEqual(@as(usize, 5), enc.codes[3].len);
try testing.expectEqual(@as(usize, 3), enc.codes[4].len);
try testing.expectEqual(@as(usize, 2), enc.codes[5].len);
try testing.expectEqual(@as(usize, 2), enc.codes[6].len);
try testing.expectEqual(@as(usize, 6), enc.codes[7].len);
try testing.expectEqual(@as(usize, 0), enc.codes[8].len);
try testing.expectEqual(@as(usize, 0), enc.codes[9].len);
try testing.expectEqual(@as(usize, 0), enc.codes[10].len);
try testing.expectEqual(@as(usize, 0), enc.codes[11].len);
try testing.expectEqual(@as(usize, 0), enc.codes[12].len);
try testing.expectEqual(@as(usize, 0), enc.codes[13].len);
try testing.expectEqual(@as(usize, 0), enc.codes[14].len);
try testing.expectEqual(@as(usize, 0), enc.codes[15].len);
try testing.expectEqual(@as(usize, 6), enc.codes[16].len);
try testing.expectEqual(@as(usize, 5), enc.codes[17].len);
try testing.expectEqual(@as(usize, 3), enc.codes[18].len);
try testing.expectEqual(@as(u16, 0x0), enc.codes[5].code);
try testing.expectEqual(@as(u16, 0x2), enc.codes[6].code);
try testing.expectEqual(@as(u16, 0x1), enc.codes[0].code);
try testing.expectEqual(@as(u16, 0x5), enc.codes[4].code);
try testing.expectEqual(@as(u16, 0x3), enc.codes[18].code);
try testing.expectEqual(@as(u16, 0x7), enc.codes[3].code);
try testing.expectEqual(@as(u16, 0x17), enc.codes[17].code);
try testing.expectEqual(@as(u16, 0x0f), enc.codes[1].code);
try testing.expectEqual(@as(u16, 0x2f), enc.codes[2].code);
try testing.expectEqual(@as(u16, 0x1f), enc.codes[7].code);
try testing.expectEqual(@as(u16, 0x3f), enc.codes[16].code);
}
test "flate.HuffmanEncoder generate a Huffman code for the fixed literal table specific to Deflate" {
const enc = fixedLiteralEncoder();
for (enc.codes) |c| {
switch (c.len) {
7 => {
const v = @bitReverse(@as(u7, @intCast(c.code)));
try testing.expect(v <= 0b0010111);
},
8 => {
const v = @bitReverse(@as(u8, @intCast(c.code)));
try testing.expect((v >= 0b000110000 and v <= 0b10111111) or
(v >= 0b11000000 and v <= 11000111));
},
9 => {
const v = @bitReverse(@as(u9, @intCast(c.code)));
try testing.expect(v >= 0b110010000 and v <= 0b111111111);
},
else => unreachable,
}
}
}
test "flate.HuffmanEncoder generate a Huffman code for the 30 possible relative distances (LZ77 distances) of Deflate" {
const enc = fixedDistanceEncoder();
for (enc.codes) |c| {
const v = @bitReverse(@as(u5, @intCast(c.code)));
try testing.expect(v <= 29);
try testing.expect(c.len == 5);
}
}
// Reverse bit-by-bit a N-bit code.
fn bitReverse(comptime T: type, value: T, n: usize) T {
const r = @bitReverse(value);
return r >> @as(math.Log2Int(T), @intCast(@typeInfo(T).Int.bits - n));
}
test "flate bitReverse" {
const ReverseBitsTest = struct {
in: u16,
bit_count: u5,
out: u16,
};
const reverse_bits_tests = [_]ReverseBitsTest{
.{ .in = 1, .bit_count = 1, .out = 1 },
.{ .in = 1, .bit_count = 2, .out = 2 },
.{ .in = 1, .bit_count = 3, .out = 4 },
.{ .in = 1, .bit_count = 4, .out = 8 },
.{ .in = 1, .bit_count = 5, .out = 16 },
.{ .in = 17, .bit_count = 5, .out = 17 },
.{ .in = 257, .bit_count = 9, .out = 257 },
.{ .in = 29, .bit_count = 5, .out = 23 },
};
for (reverse_bits_tests) |h| {
const v = bitReverse(u16, h.in, h.bit_count);
try std.testing.expectEqual(h.out, v);
}
}
test "flate.HuffmanEncoder fixedLiteralEncoder codes" {
var al = std.ArrayList(u8).init(testing.allocator);
defer al.deinit();
var bw = std.io.bitWriter(.little, al.writer());
const f = fixedLiteralEncoder();
for (f.codes) |c| {
try bw.writeBits(c.code, c.len);
}
try testing.expectEqualSlices(u8, &fixed_codes, al.items);
}
pub const fixed_codes = [_]u8{
0b00001100, 0b10001100, 0b01001100, 0b11001100, 0b00101100, 0b10101100, 0b01101100, 0b11101100,
0b00011100, 0b10011100, 0b01011100, 0b11011100, 0b00111100, 0b10111100, 0b01111100, 0b11111100,
0b00000010, 0b10000010, 0b01000010, 0b11000010, 0b00100010, 0b10100010, 0b01100010, 0b11100010,
0b00010010, 0b10010010, 0b01010010, 0b11010010, 0b00110010, 0b10110010, 0b01110010, 0b11110010,
0b00001010, 0b10001010, 0b01001010, 0b11001010, 0b00101010, 0b10101010, 0b01101010, 0b11101010,
0b00011010, 0b10011010, 0b01011010, 0b11011010, 0b00111010, 0b10111010, 0b01111010, 0b11111010,
0b00000110, 0b10000110, 0b01000110, 0b11000110, 0b00100110, 0b10100110, 0b01100110, 0b11100110,
0b00010110, 0b10010110, 0b01010110, 0b11010110, 0b00110110, 0b10110110, 0b01110110, 0b11110110,
0b00001110, 0b10001110, 0b01001110, 0b11001110, 0b00101110, 0b10101110, 0b01101110, 0b11101110,
0b00011110, 0b10011110, 0b01011110, 0b11011110, 0b00111110, 0b10111110, 0b01111110, 0b11111110,
0b00000001, 0b10000001, 0b01000001, 0b11000001, 0b00100001, 0b10100001, 0b01100001, 0b11100001,
0b00010001, 0b10010001, 0b01010001, 0b11010001, 0b00110001, 0b10110001, 0b01110001, 0b11110001,
0b00001001, 0b10001001, 0b01001001, 0b11001001, 0b00101001, 0b10101001, 0b01101001, 0b11101001,
0b00011001, 0b10011001, 0b01011001, 0b11011001, 0b00111001, 0b10111001, 0b01111001, 0b11111001,
0b00000101, 0b10000101, 0b01000101, 0b11000101, 0b00100101, 0b10100101, 0b01100101, 0b11100101,
0b00010101, 0b10010101, 0b01010101, 0b11010101, 0b00110101, 0b10110101, 0b01110101, 0b11110101,
0b00001101, 0b10001101, 0b01001101, 0b11001101, 0b00101101, 0b10101101, 0b01101101, 0b11101101,
0b00011101, 0b10011101, 0b01011101, 0b11011101, 0b00111101, 0b10111101, 0b01111101, 0b11111101,
0b00010011, 0b00100110, 0b01001110, 0b10011010, 0b00111100, 0b01100101, 0b11101010, 0b10110100,
0b11101001, 0b00110011, 0b01100110, 0b11001110, 0b10011010, 0b00111101, 0b01100111, 0b11101110,
0b10111100, 0b11111001, 0b00001011, 0b00010110, 0b00101110, 0b01011010, 0b10111100, 0b01100100,
0b11101001, 0b10110010, 0b11100101, 0b00101011, 0b01010110, 0b10101110, 0b01011010, 0b10111101,
0b01100110, 0b11101101, 0b10111010, 0b11110101, 0b00011011, 0b00110110, 0b01101110, 0b11011010,
0b10111100, 0b01100101, 0b11101011, 0b10110110, 0b11101101, 0b00111011, 0b01110110, 0b11101110,
0b11011010, 0b10111101, 0b01100111, 0b11101111, 0b10111110, 0b11111101, 0b00000111, 0b00001110,
0b00011110, 0b00111010, 0b01111100, 0b11100100, 0b11101000, 0b10110001, 0b11100011, 0b00100111,
0b01001110, 0b10011110, 0b00111010, 0b01111101, 0b11100110, 0b11101100, 0b10111001, 0b11110011,
0b00010111, 0b00101110, 0b01011110, 0b10111010, 0b01111100, 0b11100101, 0b11101010, 0b10110101,
0b11101011, 0b00110111, 0b01101110, 0b11011110, 0b10111010, 0b01111101, 0b11100111, 0b11101110,
0b10111101, 0b11111011, 0b00001111, 0b00011110, 0b00111110, 0b01111010, 0b11111100, 0b11100100,
0b11101001, 0b10110011, 0b11100111, 0b00101111, 0b01011110, 0b10111110, 0b01111010, 0b11111101,
0b11100110, 0b11101101, 0b10111011, 0b11110111, 0b00011111, 0b00111110, 0b01111110, 0b11111010,
0b11111100, 0b11100101, 0b11101011, 0b10110111, 0b11101111, 0b00111111, 0b01111110, 0b11111110,
0b11111010, 0b11111101, 0b11100111, 0b11101111, 0b10111111, 0b11111111, 0b00000000, 0b00100000,
0b00001000, 0b00001100, 0b10000001, 0b11000010, 0b11100000, 0b00001000, 0b00100100, 0b00001010,
0b10001101, 0b11000001, 0b11100010, 0b11110000, 0b00000100, 0b00100010, 0b10001001, 0b01001100,
0b10100001, 0b11010010, 0b11101000, 0b00000011, 0b10000011, 0b01000011, 0b11000011, 0b00100011,
0b10100011,
};