# XYHASH

The XYXYX smart contract has a built-in hash function called XYHASH, which provides uniqueness to each token output. 

Unlike traditional hash functions that output a string of numbers and characters (e.g., SHA256), XYHASH generates outputs in the form of Hex color codes, utilizing the `tokenId` of each XYXYX as the input variable. 

For each combination of numbers that represents a `tokenId` — which is always unique for each token —, a unique combination of two Hex colors is produced as hashed output by the XYXYX smart contract.

```solidity
function getColorComponentRed(uint256 value)    
    internal
    pure
    returns (uint16)
{
    return uint16((value >> 8) & 0xf);
}

function getColorComponentGreen(uint256 value)
    internal
    pure
    returns (uint16)
{
    return uint16((value >> 4) & 0xf);
}

function getColorComponentBlue(uint256 value)
    internal
    pure
    returns (uint16)
{
    return uint16(value & 0xf);
}

bytes16 private constant _HEX_SYMBOLS = "0123456789abcdef";

function getColorHexCode(uint256 value)
    internal
    pure
    returns (string memory)
{
    uint16 red = getColorComponentRed(value);
    uint16 green = getColorComponentGreen(value);
    uint16 blue = getColorComponentBlue(value);

    bytes memory buffer = new bytes(7);

    buffer[0] = "#";
    buffer[1] = _HEX_SYMBOLS[red];
    buffer[2] = _HEX_SYMBOLS[red];
    buffer[3] = _HEX_SYMBOLS[green];
    buffer[4] = _HEX_SYMBOLS[green];
    buffer[5] = _HEX_SYMBOLS[blue];
    buffer[6] = _HEX_SYMBOLS[blue];

    return string(buffer);
}

function xyHash(string memory prefix, uint256 tokenId)
    private
    pure
    returns (uint256)
{
    return uint256(keccak256(abi.encodePacked(prefix, tokenId))) % 4096;
}

function getColor1(uint256 tokenId) public pure returns (uint256) {
    return xyHash("1", tokenId);
}

function getColor2(uint256 tokenId) public pure returns (uint256) {
    return xyHash("2", tokenId);
}
```

1. **getColorComponentRed, getColorComponentGreen, getColorComponentBlue**: These three functions extract the red, green, and blue components of a color from a `uint256` value. This is achieved by bit-shifting the value to the right (`>>`) and applying a bitwise, and operation (`&`) with `0xf` (hexadecimal for 15) to isolate the last four bits. The bit-shifting distances (8 for red, 4 for green, and 0 for blue) position the bits of interest in the rightmost position to apply the mask (`0xf`). The result is cast to `uint16` and represents the color component value in the range of 0 to 15.
   * **Red Component**: Extracted by shifting the value 8 bits to the right and isolating the last four bits.
   * **Green Component**: Extracted by shifting the value 4 bits to the right and isolating the last four bits.
   * **Blue Component**: Extracted by directly isolating the last four bits of the value.
2. **\_HEX\_SYMBOLS**: A private constant byte array containing the hexadecimal symbols '0' to 'f'. This is used to map the numeric color component values (0-15) to their hexadecimal character representations.
3. **getColorHexCode**: This function uses the three color component functions to obtain the red, green, and blue values of a color, maps these values to their hexadecimal characters using the `_HEX_SYMBOLS` array, and constructs a hexadecimal color code string. The color code string starts with a "#" followed by two characters for each color component, doubling each character for simplicity (e.g., if the red component is `0xf`, it will be represented as "ff" in the string).
4. **xyHash**: A function that generates a hash value based on a given string prefix and a `uint256` `tokenId`. It uses the `keccak256` hash function on the concatenated string and `tokenId`, then takes the result modulo 4096 *(refers to the mathematical operation known as the "modulo" operation, which finds the remainder when one number is divided by another. In this context, after computing the hash function (likely producing a large integer as a result), the modulo operation is applied with 4096 as the divisor.).* This ensures a fixed range of possible outcomes, which is useful for generating predictable yet unique values for color determination.
5. **getColor1 and getColor2**: These public functions generate color values by calling `xyHash` with different string prefixes ("1" and "2", respectively), and the given `tokenId`. The resultant hash values can then be used to determine unique colors for each, potentially for use in generating or coloring tokens.

<div data-full-width="false"><figure><img src="/files/au7EHb3oz9dSReBf0Edi" alt=""><figcaption><p>A sequence diagram illustrating the process from receiving a token ID to generating a color Hex code executed by XYHASH</p></figcaption></figure></div>


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