/// <summary>
/// Even-Rodeh code
///
/// Encode a non-negative integer N :
/// 1. If N is less than 4 then output N in 3 bits and stop.
/// 2. If N is less than 8 then prepend the coded value with 3 bits containing the value of N and stop.
/// 3. Prepend the coded value with the binary representation of N.
/// 4. Store the number of bits prepended in step 3 as the new value of N.
/// 5. Go back to step 2
/// 6. Output a single 0 bit.
///
/// </summary>
/// <returns></returns>
public static void Encode(Bitstream bitstream, uint value)
{
if (value < 4)
{
bitstream.Write(value, 3);
return;
}
var stack = new Stack <uint>();
uint n = value;
while (true)
{
if (n < 8)
{
stack.Push(n);
break;
}
stack.Push(n);
n = CodecBase.BitsRequired(n);
}
while (stack.Any())
{
uint val = stack.Pop();
if (val < 8)
{
bitstream.Write(val, 3);
}
else
{
bitstream.Write(val);
}
}
bitstream.Write(0, 1);
}
/// <summary>
/// Compress stream of numbers:
/// Store length+1 using EliasDelta (to avoid 0 case)
/// First number x0 requires b0 bits. Write b0 in EliasDelta. Write x0 in b0 bits.
/// Each subsequent number xi requires bi bits. If bi leq b(i-1) then
/// write a 0 bit, then xi in b(i-1) bits. Else write (bi-b(i-1)) 1 bits, then a 0,
/// then the least sig bi - 1 bits of xi (the leading 1 in xi is implied, xi>0).
/// TODO - alternatives - allow the bi to change slowly, removes some hiccups for odd data points, set b to avg of some prev values
/// </summary>
/// <param name="bitstream"></param>
/// <param name="data"></param>
/// <param name="universalCoder">How to encode/decode a data length and first bitlength items. Elias.EncodeDelta is useful</param>
public static void BinaryAdaptiveSequentialEncode(Bitstream bitstream, Datastream data, Action <Bitstream, uint> universalCoder)
{
universalCoder(bitstream, (uint)data.Count + 1);
if (data.Count == 0)
{
return;
}
uint b1 = CodecBase.BitsRequired(data[0]);
universalCoder(bitstream, b1);
bitstream.Write(data[0]);
for (var i = 1; i < data.Count; ++i)
{
uint d = data[i];
uint b2 = CodecBase.BitsRequired(d);
if (b2 <= b1)
{ // b1 is enough bits
bitstream.Write(0);
bitstream.Write(d, b1);
}
else
{ // b2 requires more bits, tell how many
Trace.Assert(d > 0);
for (var ik = 0; ik < b2 - b1; ++ik)
{
bitstream.Write(1);
}
bitstream.Write(0, 1); // end of bit count
bitstream.Write(d, b2 - 1); // strip off leading '1'
}
b1 = CodecBase.BitsRequired(d); // for next pass
}
}
/// <summary>
/// Encode integer N via Sk(N) 0 B(N,floor(log_2 N)+1)
///
/// Recursively define: for fixed integer k > 1
/// Sk(n) = B(n,l) if n in [0,2^k-1], else = Sk(Floor[Log_2 n]-k) B(n,Floor[Log_2 n]+1)
/// where B(n,l) writes n in k bits
/// Note the final B value is 0 prefixed, which lets the decoder know this is the last block.
/// </summary>
public static void Encode(Bitstream bitstream, uint value, uint k)
{
uint bitLength = CodecBase.BitsRequired(value);
Recurse(bitstream, bitLength, k);
bitstream.Write(0);
bitstream.Write(value);
}
/// <summary>
/// L = bits needed to store value
/// Write L-1 zero bits, then the value in binary (which necessarily starts with one)
/// </summary>
/// <param name="bitstream"></param>
/// <param name="value32"></param>
public static void EncodeGamma(Bitstream bitstream, uint value32)
{
Trace.Assert(value32 >= 1);
uint n = CodecBase.BitsRequired(value32);
for (var i = 0; i < n - 1; ++i)
{
bitstream.Write(0);
}
bitstream.Write(value32, n);
}
/// <summary>
/// Write the value to the bitstream in the minimum number of bits.
/// Writes 0 using 1 bit.
/// </summary>
/// <param name="value"></param>
public void Write(uint value)
{
if (value != 0)
{
Write(value, CodecBase.BitsRequired(value));
}
else
{
Write(0, 1);
}
}
/// <summary>
/// Encode a 32 bit value into the bitstream using Lomont method 3
/// </summary>
/// <param name="bitstream"></param>
/// <param name="value32"></param>
public static void EncodeLomont3(Bitstream bitstream, uint value32)
{
Trace.Assert(value32 > 0);
uint n = CodecBase.BitsRequired(value32);
for (var i = 0; i < n - 1; ++i)
{
bitstream.Write(0, 1); // n-1 of these
}
bitstream.Write(1, 1); // end of n count
bitstream.Write(value32, n - 1); // remove leading 1
}
/// <summary>
/// Encode a 32 bit value into the bitstream using Elias Delta coding
/// To encode a number X greater than 0:
/// 1. N = number of bits needed to store X. N >=1
/// 2. L = number of bits needed to store N. L >= 1
/// 3. Write L-1 zeroes.
/// 4. Write the L bit representation of N (which starts with a 1)
/// 5. Write all but the leading 1 bit of X (i.e., the last N-1 bits)
/// </summary>
/// <param name="bitstream"></param>
/// <param name="value32"></param>
public static void EncodeDelta(Bitstream bitstream, uint value32)
{
Trace.Assert(value32 >= 1);
uint n = CodecBase.BitsRequired(value32);
uint l = CodecBase.BitsRequired(n);
for (var i = 1; i <= l - 1; ++i)
{
bitstream.Write(0, 1);
}
bitstream.Write(n, l);
bitstream.Write(value32, n - 1);
}
/// <summary>
/// Decodes truncated code item
/// </summary>
/// <param name="bitstream"></param>
/// <param name="n"></param>
/// <returns></returns>
public static uint Decode(Bitstream bitstream, uint n)
{
uint k = CodecBase.BitsRequired(n);
uint u = (1U << (int)k) - n; // u = number of unused codewords
uint x = bitstream.Read(k - 1);
if (x >= u)
{ // need another bit
x = 2 * x + bitstream.Read(1);
x -= u;
}
return(x);
}
/// <summary>
/// Write a universal compression header
/// </summary>
/// <param name="bitstream"></param>
/// <param name="data"></param>
/// <param name="headerFlags"></param>
public static void WriteUniversalHeader(Bitstream bitstream, Datastream data, HeaderFlags headerFlags)
{
if (headerFlags.HasFlag(HeaderFlags.SymbolCount))
{
UniversalCodec.Lomont.EncodeLomont1(bitstream, (uint)data.Count, 6, 0);
}
if (headerFlags.HasFlag(HeaderFlags.BitsPerSymbol))
{
var max = data.Any() ? data.Max() : 0;
var bitsPerSymbol = CodecBase.BitsRequired(max);
UniversalCodec.Lomont.EncodeLomont1(bitstream, bitsPerSymbol - 1, 3, 0);
}
}
static void Recurse(Bitstream bitstream, uint n, uint k)
{
Trace.Assert(k > 1);
if (n < (1U << (int)k))
{
bitstream.Write(n, k);
}
else
{
uint m = CodecBase.FloorLog2(n);
Recurse(bitstream, m - k, k);
bitstream.Write(n, m + 1);
}
}
/// <summary>
/// Exponential Golumb code for x geq 0
/// 1. Write (x+1) in binary in n bits
/// 2. Prepend n-1 zero bits
///
/// Order k > 0, do above to Floor[x/2^k]
/// Then x mod 2^k in binary
/// </summary>
/// <param name="bitstream"></param>
/// <param name="value"></param>
/// <param name="k"></param>
public static void EncodeExp(Bitstream bitstream, uint value, uint k)
{
if (k > 0)
{
EncodeExp(bitstream, value >> (int)k, 0);
uint mask = (1U << (int)k) - 1;
bitstream.Write(value & mask, k);
}
else
{
uint n = CodecBase.BitsRequired(value + 1);
bitstream.Write(0, n - 1);
bitstream.Write(value + 1, n);
}
}
/// <summary>
/// Useful for encoding a value in [0,N).
/// k = bit length N, k > 0
/// If N is a power of 2, uses k bits.
/// If N is not a power of two, encodes some choices in k-1 bits, others in k bits
/// </summary>
public static void Encode(Bitstream bitstream, uint value, uint n)
{
Trace.Assert(value < n);
uint k = CodecBase.BitsRequired(n);
uint u = (1U << (int)k) - n; // u = number of unused codewords
if (value < u)
{
bitstream.Write(value, k - 1);
}
else
{
bitstream.Write(value + u, k);
}
}
public static void EncodeOmega(Bitstream bitstream, uint value32)
{
Trace.Assert(value32 >= 1);
var stack = new Stack <uint>();
while (value32 != 1)
{
stack.Push(value32);
value32 = CodecBase.BitsRequired(value32) - 1;
}
while (stack.Any())
{
bitstream.Write(stack.Pop());
}
bitstream.Write(0);
}
/// <summary>
///
/// </summary>
/// <param name="bitstream"></param>
/// <param name="universalDecoder">The same encoder/decoder pair used to encode this</param>
/// <returns></returns>
public static List <uint> BinaryAdaptiveSequentialDecode(Bitstream bitstream, Func <Bitstream, uint> universalDecoder)
{
var list = new List <uint>();
uint length = universalDecoder(bitstream) - 1;
if (length == 0)
{
return(list);
}
uint b1 = universalDecoder(bitstream);
uint xi = bitstream.Read(b1);
list.Add(xi);
while (list.Count < length)
{
var decision = bitstream.Read(1);
if (decision == 0)
{ // bi is <= b(i-1), so enough bits
xi = bitstream.Read(b1);
}
else
{ // bi is bigger than b(i-1), must increase it
uint delta = 0;
do
{
decision = bitstream.Read(1);
delta++;
} while (decision != 0);
b1 += delta;
xi = bitstream.Read(b1 - 1); // xi has implied leading 1
xi |= 1U << (int)(b1 - 1);
}
list.Add(xi);
b1 = CodecBase.BitsRequired(xi);
}
return(list);
}