CODEWITHSUNDEEP
c++mathcompression
zxi
zxi

Reputation: 195

How to convert a double to its' binary form in Arithmetic Coding?

I am doing Arithmetic Coding now, and I have got the final start position and distance, then I add them. How can I convert the result to binary mode?

For example, how can I convert 0.125 decimal to 0.001 binary in C++?

void CArithmeticCoding::Encode()
{
    if ( 0 == m_input )
        return;
    printf("The input is [%s].\n", this->m_input);

    while (*m_input)
    {
        if ( *m_input == m_MPS )
        {
            DOMPS();
        }
        else
        {
            DOLPS();
        }
        ++m_input;
    }
    double ret = m_start + m_dis;

    return;
}

Upvotes: 2

Views: 660

Answers (3)

Mark Adler
Mark Adler

Reputation: 112394

Arithmetic coding is done with integer data types for efficiency and predicability. There are no advantages and only disadvantages to using floating point types. You can simply consider the integer of n bits to be an n-bit fraction. As you take bits off the top, you renormalize the fraction to use those bits.

See Practical Implementations of Arithmetic Coding, and Introduction to Arithmetic Coding - Theory and Practice.

Upvotes: 3

jxh
jxh

Reputation: 70422

Converting anything to binary means finding out how many of each kind of power of 2 is involved. In the case of a decimal number, the powers involved are negative.

For .125, the sequence is like this:

.125 x 2 =  .250 (< 1)
.250 x 2 =  .500 (< 1)
.500 x 2 = 1.000 (>= 1)
.000     = 0     done

So, the binary representation is 0x2^-1 + 0x2^-2 + 1x2^-3 = .001 binary. As an exercise, contrast this technique with converting a normal integer into binary representation.

Just as regular decimals can have non-terminating patterns (like 1/3 or pi/4), the same can happen for the binary representations. In those cases, you have to stop the calculation when you reach your desired precision.

Upvotes: 2

Mare Infinitus
Mare Infinitus

Reputation: 8182

You should investigate IEEE 754

This is the standard for binary representation of floating point formats, both single and double precision

Upvotes: 1

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