DoubleEndedQueue

*A sequence of items with the ability to efficiently push and pop items (i.e. insert and remove) on both ends of the sequence (called front and back). Among other access patterns, it can be used to implement efficient LIFO and FIFO queues. Storage use is optimized, and all operations are O(1) constant time. This includes clear, given that the existing queue contents are left in storage. The struct is called Bytes32Deque. Other types can be cast to and from bytes32. This data structure can only be used in storage, and not in memory.

DoubleEndedQueue.Bytes32Deque queue;
```*


## Functions
### pushBack

*Inserts an item at the end of the queue.
Reverts with {Panic-RESOURCE_ERROR} if the queue is full.*


```solidity
function pushBack(Bytes32Deque storage deque, bytes32 value) internal;

popBack

Removes the item at the end of the queue and returns it. Reverts with {Panic-EMPTY_ARRAY_POP} if the queue is empty.

function popBack(Bytes32Deque storage deque) internal returns (bytes32 value);

pushFront

Inserts an item at the beginning of the queue. Reverts with {Panic-RESOURCE_ERROR} if the queue is full.

function pushFront(Bytes32Deque storage deque, bytes32 value) internal;

popFront

Removes the item at the beginning of the queue and returns it. Reverts with {Panic-EMPTY_ARRAY_POP} if the queue is empty.

function popFront(Bytes32Deque storage deque) internal returns (bytes32 value);

front

Returns the item at the beginning of the queue. Reverts with {Panic-ARRAY_OUT_OF_BOUNDS} if the queue is empty.

function front(Bytes32Deque storage deque) internal view returns (bytes32 value);

back

Returns the item at the end of the queue. Reverts with {Panic-ARRAY_OUT_OF_BOUNDS} if the queue is empty.

function back(Bytes32Deque storage deque) internal view returns (bytes32 value);

at

Return the item at a position in the queue given by index, with the first item at 0 and last item at length(deque) - 1. Reverts with {Panic-ARRAY_OUT_OF_BOUNDS} if the index is out of bounds.

function at(Bytes32Deque storage deque, uint256 index) internal view returns (bytes32 value);

clear

Resets the queue back to being empty. NOTE: The current items are left behind in storage. This does not affect the functioning of the queue, but misses out on potential gas refunds.

function clear(Bytes32Deque storage deque) internal;

length

Returns the number of items in the queue.

function length(Bytes32Deque storage deque) internal view returns (uint256);

empty

Returns true if the queue is empty.

function empty(Bytes32Deque storage deque) internal view returns (bool);

Structs

Bytes32Deque

Indices are 128 bits so begin and end are packed in a single storage slot for efficient access. Struct members have an underscore prefix indicating that they are "private" and should not be read or written to directly. Use the functions provided below instead. Modifying the struct manually may violate assumptions and lead to unexpected behavior. The first item is at data[begin] and the last item is at data[end - 1]. This range can wrap around.

struct Bytes32Deque {
    uint128 _begin;
    uint128 _end;
    mapping(uint128 index => bytes32) _data;
}

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