Can't understand what "First arguments makes this function a method of mapping(int16 => uint256)." means here

Question

function nextInitializedTickWithinOneWord(
    mapping(int16 => uint256) storage self,
    int24 tick,
    int24 tickSpacing,
    bool lte
) internal view returns (int24 next, bool initialized) {
    int24 compressed = tick / tickSpacing;
    if (lte) {
    (int16 wordPos, uint8 bitPos) = position(compressed);
    uint256 mask = (1 << bitPos) - 1 + (1 << bitPos);
    uint256 masked = self[wordPos] & mask;

From here for the mapping parameter it is said First arguments makes this function a method of mapping(int16 => uint256). One thing to note is: when calling this function nothing is passed as agrument. I could not understand how it works.Help me to understand this.

One more thing i did not understand is how the masked value is calculated. Help me on this too.

Answer 1

This function is used as operator for the type mapping(int16 => uint256).

Basically in solidity you can attach functions to a type using a Using A for B syntax. The first argument of these function is special, and it's easier to understand looking at some examples.

So, in your case the code will have a library with some functions that all perform some operation on mapping(int16 => uint256). This is type B, and will appear as the first argument in the functions:

library LibraryName {
    function nextInitializedTickWithinOneWord(
        mapping(int16 => uint256) storage self,
        int24 tick,
        int24 tickSpacing,
        bool lte
    ) internal view returns (int24 next, bool initialized) {
        ...
    }
}

The main contract has a variable ticks of this type. Importing the library and using the syntax Using A for B, we can perform all the functions like this:

using LibraryName for mapping(int16 => uint256);
mapping(int16 => uint256) public ticks;

ticks.nextInitializedTickWithinOneWord(
    _tick,
    _tickSpacing,
    _lte
);

which is equivalent of doing:

LibraryName.nextInitializedTickWithinOneWord(
    ticks,
    _tick,
    _tickSpacing,
    _lte
);

Check the docs here for a other examples. A common one is Using SafeERC20 for IERC20, you have a function function safeTransfer(IERC20 token, address to, uint256 amount) that you call with token.safeTransfer(to, amount). So the first argument of the function is written "outside" kinda.

Hope it's clear. I can't help with the second question, maybe you're asking the meaning of << and &? If so, 1 << bitPos is basically 2**bitPos, and & is bitwise AND. In any case I agree it's better to ask it in a separate question.