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'''Elias delta code''' is a [[Universal code (data compression)|universal code]] encoding the positive integers developed by [[Peter Elias]]<ref name="Elias">{{cite journal | first = Peter | last = Elias | title = Universal codeword sets and representations of the integers | journal = [[IEEE Transactions on Information Theory]] | volume = 21 | issue = 2 | pages = 194–203 |date=March 1975 | url = http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1055349}}</ref>{{rp|200}}. To code a number:
#Write it in binary.
#Count the bits and write down that number of bits in binary (X).
#Use the binary representation written in step 1 again, remove the leading bit and write down the remaining bits (Y).
#Append the second binary representation (Y) to the first binary representation (X).
#Count the bits written in step 2 (X), subtract 1 from that number and prepend that many zeros.


An equivalent way to express the same process:
#Separate the integer into the highest power of 2 it contains (2<sup>''N' ''</sup>) and the remaining ''N''' binary digits of the integer.
#Encode ''N = N' + 1'' with [[Elias gamma coding]].
#Append the remaining ''N''' binary digits to this representation of ''N''.


To represent a number <math>x</math>, Elias delta uses <math>\lfloor \log_2(x) \rfloor  + 2 \lfloor \log_2 (\lfloor \log_2(x) \rfloor +1) \rfloor + 1</math> bits<ref name="Elias"/>{{rp|200}}.
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The code begins, using <math>\gamma'</math> instead of <math>\gamma</math>:
 
{| class="wikitable"
! Number !! N' !! N !! Encoding !! Implied probability
|-
|  1 = 2<sup>0</sup>         || 0 || 1 || 1            || 1/2
|-
|  2 = 2<sup>1</sup> + ''0'' || 1 || 2 || 010''0''      || 1/16
|-
|  3 = 2<sup>1</sup> + ''1'' || 1 || 2 || 010''1''      || "
|-
|  4 = 2<sup>2</sup> + ''0'' || 2 || 3 || 011''00''    || 1/32
|-
|  5 = 2<sup>2</sup> + ''1'' || 2 || 3 || 011''01''    || "
|-
|  6 = 2<sup>2</sup> + ''2'' || 2 || 3 || 011''10''    || "
|-
|  7 = 2<sup>2</sup> + ''3'' || 2 || 3 || 011''11''    || "
|-
|  8 = 2<sup>3</sup> + ''0'' || 3 || 4 || 00100''000''  || 1/256
|-
|  9 = 2<sup>3</sup> + ''1'' || 3 || 4 || 00100''001''  || "
|-
| 10 = 2<sup>3</sup> + ''2'' || 3 || 4 || 00100''010''  || "
|-
| 11 = 2<sup>3</sup> + ''3'' || 3 || 4 || 00100''011''  || "
|-
| 12 = 2<sup>3</sup> + ''4'' || 3 || 4 || 00100''100''  || "
|-
| 13 = 2<sup>3</sup> + ''5'' || 3 || 4 || 00100''101''  || "
|-
| 14 = 2<sup>3</sup> + ''6'' || 3 || 4 || 00100''110''  || "
|-
| 15 = 2<sup>3</sup> + ''7'' || 3 || 4 || 00100''111''  || "
|-
| 16 = 2<sup>4</sup> + ''0'' || 4 || 5 || 00101''0000'' || 1/512
|-
| 17 = 2<sup>4</sup> + ''1'' || 4 || 5 || 00101''0001'' || "
|}
 
To decode an Elias delta-coded integer:
#Read and count zeroes from the stream until you reach the first one. Call this count of zeroes ''L''.
#Considering the one that was reached to be the first digit of an integer, with a value of 2<sup>''L''</sup>, read the remaining ''L'' digits of the integer. Call this integer ''N''.
#Put a one in the first place of our final output, representing the value 2<sup>''N-1''</sup>. Read and append the following ''N-1'' digits.
 
Example:
001010001
1. 2 leading zeros in 001
2. read 2 more bits i.e. 00101
3. decode N = 00101 = 5
4. get N' = 5 - 1 = 4 remaining bits for the complete code i.e. '0001'
5. encoded number = 2<sup>4</sup> + 1 = 17
 
This code can be generalized to zero or negative integers in the same ways described in [[Elias gamma coding#Generalizations|Elias gamma coding]].
 
== Example code ==
=== Encoding ===
<source lang="cpp">
void eliasDeltaEncode(char* source, char* dest)
{
    IntReader intreader(source);
    BitWriter bitwriter(dest);
    while (intreader.hasLeft())
    {
        int num = intreader.getInt();
        int len = 0;
        int lengthOfLen = 0;
        for (int temp = num; temp > 0; temp >>= 1)  // calculate 1+floor(log2(num))
            len++;
        for (int temp = len; temp > 1; temp >>= 1) // calculate floor(log2(len))
            lengthOfLen++;
        for (int i = lengthOfLen; i > 0; --i)
            bitwriter.outputBit(0);
        for (int i = lengthOfLen; i >= 0; --i)
            bitwriter.outputBit((len >> i) & 1);
        for (int i = len-2; i >= 0; i--)
            bitwriter.outputBit((num >> i) & 1);
    }
    bitwriter.close();
    intreader.close();
}
</source>
 
=== Decoding ===
<source lang="cpp">
void eliasDeltaDecode(char* source, char* dest)
{
    BitReader bitreader(source);
    IntWriter intwriter(dest);
    while (bitreader.hasLeft())
    {
        int num = 1;
        int len = 1;
        int lengthOfLen = 0;
        while (!bitreader.inputBit())    // potentially dangerous with malformed files.
            lengthOfLen++;
        for (int i = 0; i < lengthOfLen; i++)
        {
            len <<= 1;
            if (bitreader.inputBit())
                len |= 1;
        }
        for (int i = 0; i < len-1; i++)
        {
            num <<= 1;
            if (bitreader.inputBit())
                num |= 1;
        }
        intwriter.putInt(num);            // write out the value
    }
    bitreader.close();
    intwriter.close();
}
</source>
 
== Generalizations ==<!-- This section is linked from [[Elias gamma coding]] -->
Elias delta coding does not code zero or negative integers.
One way to code all non negative integers is to add 1 before coding and then subtract 1 after decoding.
One way to code all integers is to set up a [[bijection]], mapping integers all integers (0, 1, -1, 2, -2, 3, -3, ...) to strictly positive integers (1, 2, 3, 4, 5, 6, 7, ...) before coding.
 
== References ==
 
<references/>
{{Compression Methods}}
 
== See also ==
 
*[[Elias gamma coding]]
*[[Elias omega coding]]
 
[[Category:Numeral systems]]
[[Category:Lossless compression algorithms]]

Revision as of 02:59, 10 February 2014


Pizza Is Adore Shared. Get In Touch With In For Dominos Pizza Today.

Want to generate an influence when targeting "new movers" in your local spot? Insert shade to your mailing. The large bulk of envelopes that get there in the mailbox are white, so a dash of shade (or a whole lot if you're daring!) will truly get seen. If you want to let newly arrived homeowners know about your Italy pride neighborhood pizza cafe, there genuinely is no greater way.

There had been two critical variables that assisted the Pizza acquire far more reputation amid the American men and women soon after Entire world War II. Firstly the American troops who had been stationed in Italy pride took their obtained taste back again home to The us, in addition, the hundreds of thousands of Italian immigrants who were called to assist restore the economic system introduced their delicacies above to the US and the relaxation of Europe.

Pizzas right now have flourished a wonderful deal in America as the arts and creative imagination have inspired self-expression even in your foodstuff. Simply because of this, you can really put anything at all you want on a pizza. It could have every little thing from the a lot more first toppings to items like spicy buffalo chicken with a blue cheese sauce.

Next, you would fill out the necessary shipping and delivery, billing, and secure credit score card data. You could also include a specific touch by typing in a personalized concept as well. The complete process of likely to the web, purchasing about, and finishing the process may possibly only get 10 to fifteen minutes. How's that for performance?

Okay ample about pizza background. Allow's go to toppings. Toppings range drastically reflecting various tastes and choices. Nevertheless, when it comes to position, pepperoni often can make it to the prime even though anchovies are always on the very last italy flag .

The 1st pies in New York had been easy affairs: the crust, mozzarella cheese, tomato, and new basil. These have been also the italy flag. One particular idea even states that the word "pie" comes from the Magpie, a blackbird that gathers tiny objects and drops them into his nest, just like you would scatter toppings on best of the pizza. One issue is for particular however, we enjoy the things Italy pride . The typical American consumes about twenty five pounds of pizza per yr.

Rametta Attire- Don't enable the title fool you. This isn't just an apparel shop. You will find a large selection of Italian Christmas ornaments for beneath $10.00 italian flag bracelet below. Most of the ornaments basically have distinct sayings on them. If you are Italian or know someone who is, this is the perfect website to pay a visit to to point out heritage loud and clear.

Pasta will help create healthy italian food since it cuts down on the volume of excess fat in the meal. If the food is largely pasta, you will have no problem staying under the thirty%25 of calories coming from unwanted fat. Of program this assumes that you are remaining away from product and cheese primarily based sauces like Alfredo, and sticking to tomato sauce. Even most meat sauces are Ok to eat. This is also accurate for saturated fat, once more assuming that you continue to be away from the cream and cheese primarily based sauces. So ordering an purchase of spaghetti with tomato sauce is much healthier than other alternatives.

A few years in the past Cincinnati hosted an show of historical Vatican artwork treasures. No doubt several men and women imagined those parts must be offered to aid the very poor. Or far better nevertheless, they ought to by no means have been created since the cash ought to have gone to the poor Italy pride in the first place. If it experienced, we'd nonetheless have just as numerous poor people, and no art.

And there you have it, a Margherita pizza just the like Queen of Italy had in 1889. You can perform around with this fundamental recipe to make several types of pizzas, including toppings to suit the taste buds of the complete loved ones.

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