openzeppelin-contracts/docs/modules/api/pages/utils.adoc

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:IERC165: pass:normal[xref:utils.adoc#IERC165[`IERC165`]]
:IERC1820Implementer: pass:normal[xref:utils.adoc#IERC1820Implementer[`IERC1820Implementer`]]
:IERC1820Implementer-canImplementInterfaceForAddress: pass:normal[xref:utils.adoc#IERC1820Implementer-canImplementInterfaceForAddress-bytes32-address-[`IERC1820Implementer.canImplementInterfaceForAddress`]]
:IERC165: pass:normal[xref:utils.adoc#IERC165[`IERC165`]]
:IERC1820Registry: pass:normal[xref:utils.adoc#IERC1820Registry[`IERC1820Registry`]]
:xref-IERC1820Implementer-canImplementInterfaceForAddress-bytes32-address-: xref:utils.adoc#IERC1820Implementer-canImplementInterfaceForAddress-bytes32-address-
:IERC1820Registry-setInterfaceImplementer: pass:normal[xref:utils.adoc#IERC1820Registry-setInterfaceImplementer-address-bytes32-address-[`IERC1820Registry.setInterfaceImplementer`]]
:IERC1820Implementer: pass:normal[xref:utils.adoc#IERC1820Implementer[`IERC1820Implementer`]]
:IERC1820Registry-setInterfaceImplementer: pass:normal[xref:utils.adoc#IERC1820Registry-setInterfaceImplementer-address-bytes32-address-[`IERC1820Registry.setInterfaceImplementer`]]
:xref-ERC1820Implementer-canImplementInterfaceForAddress-bytes32-address-: xref:utils.adoc#ERC1820Implementer-canImplementInterfaceForAddress-bytes32-address-
:xref-ERC1820Implementer-_registerInterfaceForAddress-bytes32-address-: xref:utils.adoc#ERC1820Implementer-_registerInterfaceForAddress-bytes32-address-
:IERC1820Implementer-canImplementInterfaceForAddress: pass:normal[xref:utils.adoc#IERC1820Implementer-canImplementInterfaceForAddress-bytes32-address-[`IERC1820Implementer.canImplementInterfaceForAddress`]]
:IERC1820Registry-setInterfaceImplementer: pass:normal[xref:utils.adoc#IERC1820Registry-setInterfaceImplementer-address-bytes32-address-[`IERC1820Registry.setInterfaceImplementer`]]
:IERC1820Registry-interfaceHash: pass:normal[xref:utils.adoc#IERC1820Registry-interfaceHash-string-[`IERC1820Registry.interfaceHash`]]
:xref-BitMaps-get-struct-BitMaps-BitMap-uint256-: xref:utils.adoc#BitMaps-get-struct-BitMaps-BitMap-uint256-
:xref-BitMaps-setTo-struct-BitMaps-BitMap-uint256-bool-: xref:utils.adoc#BitMaps-setTo-struct-BitMaps-BitMap-uint256-bool-
:xref-BitMaps-set-struct-BitMaps-BitMap-uint256-: xref:utils.adoc#BitMaps-set-struct-BitMaps-BitMap-uint256-
:xref-BitMaps-unset-struct-BitMaps-BitMap-uint256-: xref:utils.adoc#BitMaps-unset-struct-BitMaps-BitMap-uint256-
:xref-EnumerableMap-set-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-bytes32-: xref:utils.adoc#EnumerableMap-set-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-bytes32-
:xref-EnumerableMap-remove-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-: xref:utils.adoc#EnumerableMap-remove-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-
:xref-EnumerableMap-contains-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-: xref:utils.adoc#EnumerableMap-contains-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-
:xref-EnumerableMap-length-struct-EnumerableMap-Bytes32ToBytes32Map-: xref:utils.adoc#EnumerableMap-length-struct-EnumerableMap-Bytes32ToBytes32Map-
:xref-EnumerableMap-at-struct-EnumerableMap-Bytes32ToBytes32Map-uint256-: xref:utils.adoc#EnumerableMap-at-struct-EnumerableMap-Bytes32ToBytes32Map-uint256-
:xref-EnumerableMap-tryGet-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-: xref:utils.adoc#EnumerableMap-tryGet-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-
:xref-EnumerableMap-get-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-: xref:utils.adoc#EnumerableMap-get-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-
:xref-EnumerableMap-get-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-string-: xref:utils.adoc#EnumerableMap-get-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-string-
:xref-EnumerableMap-set-struct-EnumerableMap-UintToUintMap-uint256-uint256-: xref:utils.adoc#EnumerableMap-set-struct-EnumerableMap-UintToUintMap-uint256-uint256-
:xref-EnumerableMap-remove-struct-EnumerableMap-UintToUintMap-uint256-: xref:utils.adoc#EnumerableMap-remove-struct-EnumerableMap-UintToUintMap-uint256-
:xref-EnumerableMap-contains-struct-EnumerableMap-UintToUintMap-uint256-: xref:utils.adoc#EnumerableMap-contains-struct-EnumerableMap-UintToUintMap-uint256-
:xref-EnumerableMap-length-struct-EnumerableMap-UintToUintMap-: xref:utils.adoc#EnumerableMap-length-struct-EnumerableMap-UintToUintMap-
:xref-EnumerableMap-at-struct-EnumerableMap-UintToUintMap-uint256-: xref:utils.adoc#EnumerableMap-at-struct-EnumerableMap-UintToUintMap-uint256-
:xref-EnumerableMap-tryGet-struct-EnumerableMap-UintToUintMap-uint256-: xref:utils.adoc#EnumerableMap-tryGet-struct-EnumerableMap-UintToUintMap-uint256-
:xref-EnumerableMap-get-struct-EnumerableMap-UintToUintMap-uint256-: xref:utils.adoc#EnumerableMap-get-struct-EnumerableMap-UintToUintMap-uint256-
:xref-EnumerableMap-get-struct-EnumerableMap-UintToUintMap-uint256-string-: xref:utils.adoc#EnumerableMap-get-struct-EnumerableMap-UintToUintMap-uint256-string-
:xref-EnumerableMap-set-struct-EnumerableMap-UintToAddressMap-uint256-address-: xref:utils.adoc#EnumerableMap-set-struct-EnumerableMap-UintToAddressMap-uint256-address-
:xref-EnumerableMap-remove-struct-EnumerableMap-UintToAddressMap-uint256-: xref:utils.adoc#EnumerableMap-remove-struct-EnumerableMap-UintToAddressMap-uint256-
:xref-EnumerableMap-contains-struct-EnumerableMap-UintToAddressMap-uint256-: xref:utils.adoc#EnumerableMap-contains-struct-EnumerableMap-UintToAddressMap-uint256-
:xref-EnumerableMap-length-struct-EnumerableMap-UintToAddressMap-: xref:utils.adoc#EnumerableMap-length-struct-EnumerableMap-UintToAddressMap-
:xref-EnumerableMap-at-struct-EnumerableMap-UintToAddressMap-uint256-: xref:utils.adoc#EnumerableMap-at-struct-EnumerableMap-UintToAddressMap-uint256-
:xref-EnumerableMap-tryGet-struct-EnumerableMap-UintToAddressMap-uint256-: xref:utils.adoc#EnumerableMap-tryGet-struct-EnumerableMap-UintToAddressMap-uint256-
:xref-EnumerableMap-get-struct-EnumerableMap-UintToAddressMap-uint256-: xref:utils.adoc#EnumerableMap-get-struct-EnumerableMap-UintToAddressMap-uint256-
:xref-EnumerableMap-get-struct-EnumerableMap-UintToAddressMap-uint256-string-: xref:utils.adoc#EnumerableMap-get-struct-EnumerableMap-UintToAddressMap-uint256-string-
:xref-EnumerableMap-set-struct-EnumerableMap-AddressToUintMap-address-uint256-: xref:utils.adoc#EnumerableMap-set-struct-EnumerableMap-AddressToUintMap-address-uint256-
:xref-EnumerableMap-remove-struct-EnumerableMap-AddressToUintMap-address-: xref:utils.adoc#EnumerableMap-remove-struct-EnumerableMap-AddressToUintMap-address-
:xref-EnumerableMap-contains-struct-EnumerableMap-AddressToUintMap-address-: xref:utils.adoc#EnumerableMap-contains-struct-EnumerableMap-AddressToUintMap-address-
:xref-EnumerableMap-length-struct-EnumerableMap-AddressToUintMap-: xref:utils.adoc#EnumerableMap-length-struct-EnumerableMap-AddressToUintMap-
:xref-EnumerableMap-at-struct-EnumerableMap-AddressToUintMap-uint256-: xref:utils.adoc#EnumerableMap-at-struct-EnumerableMap-AddressToUintMap-uint256-
:xref-EnumerableMap-tryGet-struct-EnumerableMap-AddressToUintMap-address-: xref:utils.adoc#EnumerableMap-tryGet-struct-EnumerableMap-AddressToUintMap-address-
:xref-EnumerableMap-get-struct-EnumerableMap-AddressToUintMap-address-: xref:utils.adoc#EnumerableMap-get-struct-EnumerableMap-AddressToUintMap-address-
:xref-EnumerableMap-get-struct-EnumerableMap-AddressToUintMap-address-string-: xref:utils.adoc#EnumerableMap-get-struct-EnumerableMap-AddressToUintMap-address-string-
:xref-EnumerableMap-set-struct-EnumerableMap-Bytes32ToUintMap-bytes32-uint256-: xref:utils.adoc#EnumerableMap-set-struct-EnumerableMap-Bytes32ToUintMap-bytes32-uint256-
:xref-EnumerableMap-remove-struct-EnumerableMap-Bytes32ToUintMap-bytes32-: xref:utils.adoc#EnumerableMap-remove-struct-EnumerableMap-Bytes32ToUintMap-bytes32-
:xref-EnumerableMap-contains-struct-EnumerableMap-Bytes32ToUintMap-bytes32-: xref:utils.adoc#EnumerableMap-contains-struct-EnumerableMap-Bytes32ToUintMap-bytes32-
:xref-EnumerableMap-length-struct-EnumerableMap-Bytes32ToUintMap-: xref:utils.adoc#EnumerableMap-length-struct-EnumerableMap-Bytes32ToUintMap-
:xref-EnumerableMap-at-struct-EnumerableMap-Bytes32ToUintMap-uint256-: xref:utils.adoc#EnumerableMap-at-struct-EnumerableMap-Bytes32ToUintMap-uint256-
:xref-EnumerableMap-tryGet-struct-EnumerableMap-Bytes32ToUintMap-bytes32-: xref:utils.adoc#EnumerableMap-tryGet-struct-EnumerableMap-Bytes32ToUintMap-bytes32-
:xref-EnumerableMap-get-struct-EnumerableMap-Bytes32ToUintMap-bytes32-: xref:utils.adoc#EnumerableMap-get-struct-EnumerableMap-Bytes32ToUintMap-bytes32-
:xref-EnumerableMap-get-struct-EnumerableMap-Bytes32ToUintMap-bytes32-string-: xref:utils.adoc#EnumerableMap-get-struct-EnumerableMap-Bytes32ToUintMap-bytes32-string-
:xref-EnumerableSet-add-struct-EnumerableSet-Bytes32Set-bytes32-: xref:utils.adoc#EnumerableSet-add-struct-EnumerableSet-Bytes32Set-bytes32-
:xref-EnumerableSet-remove-struct-EnumerableSet-Bytes32Set-bytes32-: xref:utils.adoc#EnumerableSet-remove-struct-EnumerableSet-Bytes32Set-bytes32-
:xref-EnumerableSet-contains-struct-EnumerableSet-Bytes32Set-bytes32-: xref:utils.adoc#EnumerableSet-contains-struct-EnumerableSet-Bytes32Set-bytes32-
:xref-EnumerableSet-length-struct-EnumerableSet-Bytes32Set-: xref:utils.adoc#EnumerableSet-length-struct-EnumerableSet-Bytes32Set-
:xref-EnumerableSet-at-struct-EnumerableSet-Bytes32Set-uint256-: xref:utils.adoc#EnumerableSet-at-struct-EnumerableSet-Bytes32Set-uint256-
:xref-EnumerableSet-values-struct-EnumerableSet-Bytes32Set-: xref:utils.adoc#EnumerableSet-values-struct-EnumerableSet-Bytes32Set-
:xref-EnumerableSet-add-struct-EnumerableSet-AddressSet-address-: xref:utils.adoc#EnumerableSet-add-struct-EnumerableSet-AddressSet-address-
:xref-EnumerableSet-remove-struct-EnumerableSet-AddressSet-address-: xref:utils.adoc#EnumerableSet-remove-struct-EnumerableSet-AddressSet-address-
:xref-EnumerableSet-contains-struct-EnumerableSet-AddressSet-address-: xref:utils.adoc#EnumerableSet-contains-struct-EnumerableSet-AddressSet-address-
:xref-EnumerableSet-length-struct-EnumerableSet-AddressSet-: xref:utils.adoc#EnumerableSet-length-struct-EnumerableSet-AddressSet-
:xref-EnumerableSet-at-struct-EnumerableSet-AddressSet-uint256-: xref:utils.adoc#EnumerableSet-at-struct-EnumerableSet-AddressSet-uint256-
:xref-EnumerableSet-values-struct-EnumerableSet-AddressSet-: xref:utils.adoc#EnumerableSet-values-struct-EnumerableSet-AddressSet-
:xref-EnumerableSet-add-struct-EnumerableSet-UintSet-uint256-: xref:utils.adoc#EnumerableSet-add-struct-EnumerableSet-UintSet-uint256-
:xref-EnumerableSet-remove-struct-EnumerableSet-UintSet-uint256-: xref:utils.adoc#EnumerableSet-remove-struct-EnumerableSet-UintSet-uint256-
:xref-EnumerableSet-contains-struct-EnumerableSet-UintSet-uint256-: xref:utils.adoc#EnumerableSet-contains-struct-EnumerableSet-UintSet-uint256-
:xref-EnumerableSet-length-struct-EnumerableSet-UintSet-: xref:utils.adoc#EnumerableSet-length-struct-EnumerableSet-UintSet-
:xref-EnumerableSet-at-struct-EnumerableSet-UintSet-uint256-: xref:utils.adoc#EnumerableSet-at-struct-EnumerableSet-UintSet-uint256-
:xref-EnumerableSet-values-struct-EnumerableSet-UintSet-: xref:utils.adoc#EnumerableSet-values-struct-EnumerableSet-UintSet-
:xref-DoubleEndedQueue-pushBack-struct-DoubleEndedQueue-Bytes32Deque-bytes32-: xref:utils.adoc#DoubleEndedQueue-pushBack-struct-DoubleEndedQueue-Bytes32Deque-bytes32-
:xref-DoubleEndedQueue-popBack-struct-DoubleEndedQueue-Bytes32Deque-: xref:utils.adoc#DoubleEndedQueue-popBack-struct-DoubleEndedQueue-Bytes32Deque-
:xref-DoubleEndedQueue-pushFront-struct-DoubleEndedQueue-Bytes32Deque-bytes32-: xref:utils.adoc#DoubleEndedQueue-pushFront-struct-DoubleEndedQueue-Bytes32Deque-bytes32-
:xref-DoubleEndedQueue-popFront-struct-DoubleEndedQueue-Bytes32Deque-: xref:utils.adoc#DoubleEndedQueue-popFront-struct-DoubleEndedQueue-Bytes32Deque-
:xref-DoubleEndedQueue-front-struct-DoubleEndedQueue-Bytes32Deque-: xref:utils.adoc#DoubleEndedQueue-front-struct-DoubleEndedQueue-Bytes32Deque-
:xref-DoubleEndedQueue-back-struct-DoubleEndedQueue-Bytes32Deque-: xref:utils.adoc#DoubleEndedQueue-back-struct-DoubleEndedQueue-Bytes32Deque-
:xref-DoubleEndedQueue-at-struct-DoubleEndedQueue-Bytes32Deque-uint256-: xref:utils.adoc#DoubleEndedQueue-at-struct-DoubleEndedQueue-Bytes32Deque-uint256-
:xref-DoubleEndedQueue-clear-struct-DoubleEndedQueue-Bytes32Deque-: xref:utils.adoc#DoubleEndedQueue-clear-struct-DoubleEndedQueue-Bytes32Deque-
:xref-DoubleEndedQueue-length-struct-DoubleEndedQueue-Bytes32Deque-: xref:utils.adoc#DoubleEndedQueue-length-struct-DoubleEndedQueue-Bytes32Deque-
:xref-DoubleEndedQueue-empty-struct-DoubleEndedQueue-Bytes32Deque-: xref:utils.adoc#DoubleEndedQueue-empty-struct-DoubleEndedQueue-Bytes32Deque-
:Votes: pass:normal[xref:governance.adoc#Votes[`Votes`]]
:xref-Checkpoints-getAtBlock-struct-Checkpoints-History-uint256-: xref:utils.adoc#Checkpoints-getAtBlock-struct-Checkpoints-History-uint256-
:xref-Checkpoints-getAtProbablyRecentBlock-struct-Checkpoints-History-uint256-: xref:utils.adoc#Checkpoints-getAtProbablyRecentBlock-struct-Checkpoints-History-uint256-
:xref-Checkpoints-push-struct-Checkpoints-History-uint256-: xref:utils.adoc#Checkpoints-push-struct-Checkpoints-History-uint256-
:xref-Checkpoints-push-struct-Checkpoints-History-function--uint256-uint256--view-returns--uint256--uint256-: xref:utils.adoc#Checkpoints-push-struct-Checkpoints-History-function--uint256-uint256--view-returns--uint256--uint256-
:xref-Checkpoints-latest-struct-Checkpoints-History-: xref:utils.adoc#Checkpoints-latest-struct-Checkpoints-History-
:xref-Checkpoints-latestCheckpoint-struct-Checkpoints-History-: xref:utils.adoc#Checkpoints-latestCheckpoint-struct-Checkpoints-History-
:xref-Checkpoints-length-struct-Checkpoints-History-: xref:utils.adoc#Checkpoints-length-struct-Checkpoints-History-
:xref-Checkpoints-push-struct-Checkpoints-Trace224-uint32-uint224-: xref:utils.adoc#Checkpoints-push-struct-Checkpoints-Trace224-uint32-uint224-
:xref-Checkpoints-lowerLookup-struct-Checkpoints-Trace224-uint32-: xref:utils.adoc#Checkpoints-lowerLookup-struct-Checkpoints-Trace224-uint32-
:xref-Checkpoints-upperLookup-struct-Checkpoints-Trace224-uint32-: xref:utils.adoc#Checkpoints-upperLookup-struct-Checkpoints-Trace224-uint32-
:xref-Checkpoints-latest-struct-Checkpoints-Trace224-: xref:utils.adoc#Checkpoints-latest-struct-Checkpoints-Trace224-
:xref-Checkpoints-latestCheckpoint-struct-Checkpoints-Trace224-: xref:utils.adoc#Checkpoints-latestCheckpoint-struct-Checkpoints-Trace224-
:xref-Checkpoints-length-struct-Checkpoints-Trace224-: xref:utils.adoc#Checkpoints-length-struct-Checkpoints-Trace224-
:xref-Checkpoints-push-struct-Checkpoints-Trace160-uint96-uint160-: xref:utils.adoc#Checkpoints-push-struct-Checkpoints-Trace160-uint96-uint160-
:xref-Checkpoints-lowerLookup-struct-Checkpoints-Trace160-uint96-: xref:utils.adoc#Checkpoints-lowerLookup-struct-Checkpoints-Trace160-uint96-
:xref-Checkpoints-upperLookup-struct-Checkpoints-Trace160-uint96-: xref:utils.adoc#Checkpoints-upperLookup-struct-Checkpoints-Trace160-uint96-
:xref-Checkpoints-latest-struct-Checkpoints-Trace160-: xref:utils.adoc#Checkpoints-latest-struct-Checkpoints-Trace160-
:xref-Checkpoints-latestCheckpoint-struct-Checkpoints-Trace160-: xref:utils.adoc#Checkpoints-latestCheckpoint-struct-Checkpoints-Trace160-
:xref-Checkpoints-length-struct-Checkpoints-Trace160-: xref:utils.adoc#Checkpoints-length-struct-Checkpoints-Trace160-
:xref-Create2-deploy-uint256-bytes32-bytes-: xref:utils.adoc#Create2-deploy-uint256-bytes32-bytes-
:xref-Create2-computeAddress-bytes32-bytes32-: xref:utils.adoc#Create2-computeAddress-bytes32-bytes32-
:xref-Create2-computeAddress-bytes32-bytes32-address-: xref:utils.adoc#Create2-computeAddress-bytes32-bytes32-address-
:xref-Address-isContract-address-: xref:utils.adoc#Address-isContract-address-
:xref-Address-sendValue-address-payable-uint256-: xref:utils.adoc#Address-sendValue-address-payable-uint256-
:xref-Address-functionCall-address-bytes-: xref:utils.adoc#Address-functionCall-address-bytes-
:xref-Address-functionCall-address-bytes-string-: xref:utils.adoc#Address-functionCall-address-bytes-string-
:xref-Address-functionCallWithValue-address-bytes-uint256-: xref:utils.adoc#Address-functionCallWithValue-address-bytes-uint256-
:xref-Address-functionCallWithValue-address-bytes-uint256-string-: xref:utils.adoc#Address-functionCallWithValue-address-bytes-uint256-string-
:xref-Address-functionStaticCall-address-bytes-: xref:utils.adoc#Address-functionStaticCall-address-bytes-
:xref-Address-functionStaticCall-address-bytes-string-: xref:utils.adoc#Address-functionStaticCall-address-bytes-string-
:xref-Address-functionDelegateCall-address-bytes-: xref:utils.adoc#Address-functionDelegateCall-address-bytes-
:xref-Address-functionDelegateCall-address-bytes-string-: xref:utils.adoc#Address-functionDelegateCall-address-bytes-string-
:xref-Address-verifyCallResultFromTarget-address-bool-bytes-string-: xref:utils.adoc#Address-verifyCallResultFromTarget-address-bool-bytes-string-
:xref-Address-verifyCallResult-bool-bytes-string-: xref:utils.adoc#Address-verifyCallResult-bool-bytes-string-
:ReentrancyGuard: pass:normal[xref:security.adoc#ReentrancyGuard[`ReentrancyGuard`]]
:xref-Address-functionCall-address-bytes-: xref:utils.adoc#Address-functionCall-address-bytes-
:xref-Address-functionCall-address-bytes-: xref:utils.adoc#Address-functionCall-address-bytes-
:xref-Address-functionCallWithValue-address-bytes-uint256-: xref:utils.adoc#Address-functionCallWithValue-address-bytes-uint256-
:xref-Address-functionCall-address-bytes-: xref:utils.adoc#Address-functionCall-address-bytes-
:xref-Address-functionCall-address-bytes-string-: xref:utils.adoc#Address-functionCall-address-bytes-string-
:xref-Address-functionCall-address-bytes-: xref:utils.adoc#Address-functionCall-address-bytes-
:xref-Address-functionCall-address-bytes-string-: xref:utils.adoc#Address-functionCall-address-bytes-string-
:xref-Arrays-findUpperBound-uint256---uint256-: xref:utils.adoc#Arrays-findUpperBound-uint256---uint256-
:xref-Arrays-unsafeAccess-address---uint256-: xref:utils.adoc#Arrays-unsafeAccess-address---uint256-
:xref-Arrays-unsafeAccess-bytes32---uint256-: xref:utils.adoc#Arrays-unsafeAccess-bytes32---uint256-
:xref-Arrays-unsafeAccess-uint256---uint256-: xref:utils.adoc#Arrays-unsafeAccess-uint256---uint256-
:xref-Base64-encode-bytes-: xref:utils.adoc#Base64-encode-bytes-
:xref-Counters-current-struct-Counters-Counter-: xref:utils.adoc#Counters-current-struct-Counters-Counter-
:xref-Counters-increment-struct-Counters-Counter-: xref:utils.adoc#Counters-increment-struct-Counters-Counter-
:xref-Counters-decrement-struct-Counters-Counter-: xref:utils.adoc#Counters-decrement-struct-Counters-Counter-
:xref-Counters-reset-struct-Counters-Counter-: xref:utils.adoc#Counters-reset-struct-Counters-Counter-
:xref-Strings-toString-uint256-: xref:utils.adoc#Strings-toString-uint256-
:xref-Strings-toHexString-uint256-: xref:utils.adoc#Strings-toHexString-uint256-
:xref-Strings-toHexString-uint256-uint256-: xref:utils.adoc#Strings-toHexString-uint256-uint256-
:xref-Strings-toHexString-address-: xref:utils.adoc#Strings-toHexString-address-
:xref-StorageSlot-getAddressSlot-bytes32-: xref:utils.adoc#StorageSlot-getAddressSlot-bytes32-
:xref-StorageSlot-getBooleanSlot-bytes32-: xref:utils.adoc#StorageSlot-getBooleanSlot-bytes32-
:xref-StorageSlot-getBytes32Slot-bytes32-: xref:utils.adoc#StorageSlot-getBytes32Slot-bytes32-
:xref-StorageSlot-getUint256Slot-bytes32-: xref:utils.adoc#StorageSlot-getUint256Slot-bytes32-
:xref-Multicall-multicall-bytes---: xref:utils.adoc#Multicall-multicall-bytes---
= Utilities

[.readme-notice]
NOTE: This document is better viewed at https://docs.openzeppelin.com/contracts/api/utils

Miscellaneous contracts and libraries containing utility functions you can use to improve security, work with new data types, or safely use low-level primitives.

The {Address}, {Arrays}, {Base64} and {Strings} libraries provide more operations related to these native data types, while {SafeCast} adds ways to safely convert between the different signed and unsigned numeric types.
{Multicall} provides a function to batch together multiple calls in a single external call.

For new data types:

 * {Counters}: a simple way to get a counter that can only be incremented, decremented or reset. Very useful for ID generation, counting contract activity, among others.
 * {EnumerableMap}: like Solidity's https://solidity.readthedocs.io/en/latest/types.html#mapping-types[`mapping`] type, but with key-value _enumeration_: this will let you know how many entries a mapping has, and iterate over them (which is not possible with `mapping`).
 * {EnumerableSet}: like {EnumerableMap}, but for https://en.wikipedia.org/wiki/Set_(abstract_data_type)[sets]. Can be used to store privileged accounts, issued IDs, etc.

[NOTE]
====
Because Solidity does not support generic types, {EnumerableMap} and {EnumerableSet} are specialized to a limited number of key-value types.

As of v3.0, {EnumerableMap} supports `uint256 -> address` (`UintToAddressMap`), and {EnumerableSet} supports `address` and `uint256` (`AddressSet` and `UintSet`).
====

Finally, {Create2} contains all necessary utilities to safely use the https://blog.openzeppelin.com/getting-the-most-out-of-create2/[`CREATE2` EVM opcode], without having to deal with low-level assembly.

== Math

:Rounding: pass:normal[xref:#Math-Rounding[`++Rounding++`]]
:max: pass:normal[xref:#Math-max-uint256-uint256-[`++max++`]]
:min: pass:normal[xref:#Math-min-uint256-uint256-[`++min++`]]
:average: pass:normal[xref:#Math-average-uint256-uint256-[`++average++`]]
:ceilDiv: pass:normal[xref:#Math-ceilDiv-uint256-uint256-[`++ceilDiv++`]]
:mulDiv: pass:normal[xref:#Math-mulDiv-uint256-uint256-uint256-[`++mulDiv++`]]
:mulDiv: pass:normal[xref:#Math-mulDiv-uint256-uint256-uint256-enum-Math-Rounding-[`++mulDiv++`]]
:sqrt: pass:normal[xref:#Math-sqrt-uint256-[`++sqrt++`]]
:sqrt: pass:normal[xref:#Math-sqrt-uint256-enum-Math-Rounding-[`++sqrt++`]]
:log2: pass:normal[xref:#Math-log2-uint256-[`++log2++`]]
:log2: pass:normal[xref:#Math-log2-uint256-enum-Math-Rounding-[`++log2++`]]
:log10: pass:normal[xref:#Math-log10-uint256-[`++log10++`]]
:log10: pass:normal[xref:#Math-log10-uint256-enum-Math-Rounding-[`++log10++`]]
:log256: pass:normal[xref:#Math-log256-uint256-[`++log256++`]]
:log256: pass:normal[xref:#Math-log256-uint256-enum-Math-Rounding-[`++log256++`]]

[.contract]
[[Math]]
=== `++Math++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/math/Math.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/math/Math.sol";
```

Standard math utilities missing in the Solidity language.

[.contract-index]
.Functions
--
* {xref-Math-max-uint256-uint256-}[`++max(a, b)++`]
* {xref-Math-min-uint256-uint256-}[`++min(a, b)++`]
* {xref-Math-average-uint256-uint256-}[`++average(a, b)++`]
* {xref-Math-ceilDiv-uint256-uint256-}[`++ceilDiv(a, b)++`]
* {xref-Math-mulDiv-uint256-uint256-uint256-}[`++mulDiv(x, y, denominator)++`]
* {xref-Math-mulDiv-uint256-uint256-uint256-enum-Math-Rounding-}[`++mulDiv(x, y, denominator, rounding)++`]
* {xref-Math-sqrt-uint256-}[`++sqrt(a)++`]
* {xref-Math-sqrt-uint256-enum-Math-Rounding-}[`++sqrt(a, rounding)++`]
* {xref-Math-log2-uint256-}[`++log2(value)++`]
* {xref-Math-log2-uint256-enum-Math-Rounding-}[`++log2(value, rounding)++`]
* {xref-Math-log10-uint256-}[`++log10(value)++`]
* {xref-Math-log10-uint256-enum-Math-Rounding-}[`++log10(value, rounding)++`]
* {xref-Math-log256-uint256-}[`++log256(value)++`]
* {xref-Math-log256-uint256-enum-Math-Rounding-}[`++log256(value, rounding)++`]

--

[.contract-item]
[[Math-max-uint256-uint256-]]
==== `[.contract-item-name]#++max++#++(uint256 a, uint256 b) → uint256++` [.item-kind]#internal#

Returns the largest of two numbers.

[.contract-item]
[[Math-min-uint256-uint256-]]
==== `[.contract-item-name]#++min++#++(uint256 a, uint256 b) → uint256++` [.item-kind]#internal#

Returns the smallest of two numbers.

[.contract-item]
[[Math-average-uint256-uint256-]]
==== `[.contract-item-name]#++average++#++(uint256 a, uint256 b) → uint256++` [.item-kind]#internal#

Returns the average of two numbers. The result is rounded towards
zero.

[.contract-item]
[[Math-ceilDiv-uint256-uint256-]]
==== `[.contract-item-name]#++ceilDiv++#++(uint256 a, uint256 b) → uint256++` [.item-kind]#internal#

Returns the ceiling of the division of two numbers.

This differs from standard division with `/` in that it rounds up instead
of rounding down.

[.contract-item]
[[Math-mulDiv-uint256-uint256-uint256-]]
==== `[.contract-item-name]#++mulDiv++#++(uint256 x, uint256 y, uint256 denominator) → uint256 result++` [.item-kind]#internal#

Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)
with further edits by Uniswap Labs also under MIT license.

[.contract-item]
[[Math-mulDiv-uint256-uint256-uint256-enum-Math-Rounding-]]
==== `[.contract-item-name]#++mulDiv++#++(uint256 x, uint256 y, uint256 denominator, enum Math.Rounding rounding) → uint256++` [.item-kind]#internal#

[.contract-item]
[[Math-sqrt-uint256-]]
==== `[.contract-item-name]#++sqrt++#++(uint256 a) → uint256++` [.item-kind]#internal#

Returns the square root of a number. If the number is not a perfect square, the value is rounded down.

Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).

[.contract-item]
[[Math-sqrt-uint256-enum-Math-Rounding-]]
==== `[.contract-item-name]#++sqrt++#++(uint256 a, enum Math.Rounding rounding) → uint256++` [.item-kind]#internal#

[.contract-item]
[[Math-log2-uint256-]]
==== `[.contract-item-name]#++log2++#++(uint256 value) → uint256++` [.item-kind]#internal#

Return the log in base 2, rounded down, of a positive value.
Returns 0 if given 0.

[.contract-item]
[[Math-log2-uint256-enum-Math-Rounding-]]
==== `[.contract-item-name]#++log2++#++(uint256 value, enum Math.Rounding rounding) → uint256++` [.item-kind]#internal#

Return the log in base 2, following the selected rounding direction, of a positive value.
Returns 0 if given 0.

[.contract-item]
[[Math-log10-uint256-]]
==== `[.contract-item-name]#++log10++#++(uint256 value) → uint256++` [.item-kind]#internal#

Return the log in base 10, rounded down, of a positive value.
Returns 0 if given 0.

[.contract-item]
[[Math-log10-uint256-enum-Math-Rounding-]]
==== `[.contract-item-name]#++log10++#++(uint256 value, enum Math.Rounding rounding) → uint256++` [.item-kind]#internal#

Return the log in base 10, following the selected rounding direction, of a positive value.
Returns 0 if given 0.

[.contract-item]
[[Math-log256-uint256-]]
==== `[.contract-item-name]#++log256++#++(uint256 value) → uint256++` [.item-kind]#internal#

Return the log in base 256, rounded down, of a positive value.
Returns 0 if given 0.

Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.

[.contract-item]
[[Math-log256-uint256-enum-Math-Rounding-]]
==== `[.contract-item-name]#++log256++#++(uint256 value, enum Math.Rounding rounding) → uint256++` [.item-kind]#internal#

Return the log in base 10, following the selected rounding direction, of a positive value.
Returns 0 if given 0.

:max: pass:normal[xref:#SignedMath-max-int256-int256-[`++max++`]]
:min: pass:normal[xref:#SignedMath-min-int256-int256-[`++min++`]]
:average: pass:normal[xref:#SignedMath-average-int256-int256-[`++average++`]]
:abs: pass:normal[xref:#SignedMath-abs-int256-[`++abs++`]]

[.contract]
[[SignedMath]]
=== `++SignedMath++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/math/SignedMath.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/math/SignedMath.sol";
```

Standard signed math utilities missing in the Solidity language.

[.contract-index]
.Functions
--
* {xref-SignedMath-max-int256-int256-}[`++max(a, b)++`]
* {xref-SignedMath-min-int256-int256-}[`++min(a, b)++`]
* {xref-SignedMath-average-int256-int256-}[`++average(a, b)++`]
* {xref-SignedMath-abs-int256-}[`++abs(n)++`]

--

[.contract-item]
[[SignedMath-max-int256-int256-]]
==== `[.contract-item-name]#++max++#++(int256 a, int256 b) → int256++` [.item-kind]#internal#

Returns the largest of two signed numbers.

[.contract-item]
[[SignedMath-min-int256-int256-]]
==== `[.contract-item-name]#++min++#++(int256 a, int256 b) → int256++` [.item-kind]#internal#

Returns the smallest of two signed numbers.

[.contract-item]
[[SignedMath-average-int256-int256-]]
==== `[.contract-item-name]#++average++#++(int256 a, int256 b) → int256++` [.item-kind]#internal#

Returns the average of two signed numbers without overflow.
The result is rounded towards zero.

[.contract-item]
[[SignedMath-abs-int256-]]
==== `[.contract-item-name]#++abs++#++(int256 n) → uint256++` [.item-kind]#internal#

Returns the absolute unsigned value of a signed value.

:toUint248: pass:normal[xref:#SafeCast-toUint248-uint256-[`++toUint248++`]]
:toUint240: pass:normal[xref:#SafeCast-toUint240-uint256-[`++toUint240++`]]
:toUint232: pass:normal[xref:#SafeCast-toUint232-uint256-[`++toUint232++`]]
:toUint224: pass:normal[xref:#SafeCast-toUint224-uint256-[`++toUint224++`]]
:toUint216: pass:normal[xref:#SafeCast-toUint216-uint256-[`++toUint216++`]]
:toUint208: pass:normal[xref:#SafeCast-toUint208-uint256-[`++toUint208++`]]
:toUint200: pass:normal[xref:#SafeCast-toUint200-uint256-[`++toUint200++`]]
:toUint192: pass:normal[xref:#SafeCast-toUint192-uint256-[`++toUint192++`]]
:toUint184: pass:normal[xref:#SafeCast-toUint184-uint256-[`++toUint184++`]]
:toUint176: pass:normal[xref:#SafeCast-toUint176-uint256-[`++toUint176++`]]
:toUint168: pass:normal[xref:#SafeCast-toUint168-uint256-[`++toUint168++`]]
:toUint160: pass:normal[xref:#SafeCast-toUint160-uint256-[`++toUint160++`]]
:toUint152: pass:normal[xref:#SafeCast-toUint152-uint256-[`++toUint152++`]]
:toUint144: pass:normal[xref:#SafeCast-toUint144-uint256-[`++toUint144++`]]
:toUint136: pass:normal[xref:#SafeCast-toUint136-uint256-[`++toUint136++`]]
:toUint128: pass:normal[xref:#SafeCast-toUint128-uint256-[`++toUint128++`]]
:toUint120: pass:normal[xref:#SafeCast-toUint120-uint256-[`++toUint120++`]]
:toUint112: pass:normal[xref:#SafeCast-toUint112-uint256-[`++toUint112++`]]
:toUint104: pass:normal[xref:#SafeCast-toUint104-uint256-[`++toUint104++`]]
:toUint96: pass:normal[xref:#SafeCast-toUint96-uint256-[`++toUint96++`]]
:toUint88: pass:normal[xref:#SafeCast-toUint88-uint256-[`++toUint88++`]]
:toUint80: pass:normal[xref:#SafeCast-toUint80-uint256-[`++toUint80++`]]
:toUint72: pass:normal[xref:#SafeCast-toUint72-uint256-[`++toUint72++`]]
:toUint64: pass:normal[xref:#SafeCast-toUint64-uint256-[`++toUint64++`]]
:toUint56: pass:normal[xref:#SafeCast-toUint56-uint256-[`++toUint56++`]]
:toUint48: pass:normal[xref:#SafeCast-toUint48-uint256-[`++toUint48++`]]
:toUint40: pass:normal[xref:#SafeCast-toUint40-uint256-[`++toUint40++`]]
:toUint32: pass:normal[xref:#SafeCast-toUint32-uint256-[`++toUint32++`]]
:toUint24: pass:normal[xref:#SafeCast-toUint24-uint256-[`++toUint24++`]]
:toUint16: pass:normal[xref:#SafeCast-toUint16-uint256-[`++toUint16++`]]
:toUint8: pass:normal[xref:#SafeCast-toUint8-uint256-[`++toUint8++`]]
:toUint256: pass:normal[xref:#SafeCast-toUint256-int256-[`++toUint256++`]]
:toInt248: pass:normal[xref:#SafeCast-toInt248-int256-[`++toInt248++`]]
:toInt240: pass:normal[xref:#SafeCast-toInt240-int256-[`++toInt240++`]]
:toInt232: pass:normal[xref:#SafeCast-toInt232-int256-[`++toInt232++`]]
:toInt224: pass:normal[xref:#SafeCast-toInt224-int256-[`++toInt224++`]]
:toInt216: pass:normal[xref:#SafeCast-toInt216-int256-[`++toInt216++`]]
:toInt208: pass:normal[xref:#SafeCast-toInt208-int256-[`++toInt208++`]]
:toInt200: pass:normal[xref:#SafeCast-toInt200-int256-[`++toInt200++`]]
:toInt192: pass:normal[xref:#SafeCast-toInt192-int256-[`++toInt192++`]]
:toInt184: pass:normal[xref:#SafeCast-toInt184-int256-[`++toInt184++`]]
:toInt176: pass:normal[xref:#SafeCast-toInt176-int256-[`++toInt176++`]]
:toInt168: pass:normal[xref:#SafeCast-toInt168-int256-[`++toInt168++`]]
:toInt160: pass:normal[xref:#SafeCast-toInt160-int256-[`++toInt160++`]]
:toInt152: pass:normal[xref:#SafeCast-toInt152-int256-[`++toInt152++`]]
:toInt144: pass:normal[xref:#SafeCast-toInt144-int256-[`++toInt144++`]]
:toInt136: pass:normal[xref:#SafeCast-toInt136-int256-[`++toInt136++`]]
:toInt128: pass:normal[xref:#SafeCast-toInt128-int256-[`++toInt128++`]]
:toInt120: pass:normal[xref:#SafeCast-toInt120-int256-[`++toInt120++`]]
:toInt112: pass:normal[xref:#SafeCast-toInt112-int256-[`++toInt112++`]]
:toInt104: pass:normal[xref:#SafeCast-toInt104-int256-[`++toInt104++`]]
:toInt96: pass:normal[xref:#SafeCast-toInt96-int256-[`++toInt96++`]]
:toInt88: pass:normal[xref:#SafeCast-toInt88-int256-[`++toInt88++`]]
:toInt80: pass:normal[xref:#SafeCast-toInt80-int256-[`++toInt80++`]]
:toInt72: pass:normal[xref:#SafeCast-toInt72-int256-[`++toInt72++`]]
:toInt64: pass:normal[xref:#SafeCast-toInt64-int256-[`++toInt64++`]]
:toInt56: pass:normal[xref:#SafeCast-toInt56-int256-[`++toInt56++`]]
:toInt48: pass:normal[xref:#SafeCast-toInt48-int256-[`++toInt48++`]]
:toInt40: pass:normal[xref:#SafeCast-toInt40-int256-[`++toInt40++`]]
:toInt32: pass:normal[xref:#SafeCast-toInt32-int256-[`++toInt32++`]]
:toInt24: pass:normal[xref:#SafeCast-toInt24-int256-[`++toInt24++`]]
:toInt16: pass:normal[xref:#SafeCast-toInt16-int256-[`++toInt16++`]]
:toInt8: pass:normal[xref:#SafeCast-toInt8-int256-[`++toInt8++`]]
:toInt256: pass:normal[xref:#SafeCast-toInt256-uint256-[`++toInt256++`]]

[.contract]
[[SafeCast]]
=== `++SafeCast++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/math/SafeCast.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/math/SafeCast.sol";
```

Wrappers over Solidity's uintXX/intXX casting operators with added overflow
checks.

Downcasting from uint256/int256 in Solidity does not revert on overflow. This can
easily result in undesired exploitation or bugs, since developers usually
assume that overflows raise errors. `SafeCast` restores this intuition by
reverting the transaction when such an operation overflows.

Using this library instead of the unchecked operations eliminates an entire
class of bugs, so it's recommended to use it always.

Can be combined with {SafeMath} and {SignedSafeMath} to extend it to smaller types, by performing
all math on `uint256` and `int256` and then downcasting.

[.contract-index]
.Functions
--
* {xref-SafeCast-toUint248-uint256-}[`++toUint248(value)++`]
* {xref-SafeCast-toUint240-uint256-}[`++toUint240(value)++`]
* {xref-SafeCast-toUint232-uint256-}[`++toUint232(value)++`]
* {xref-SafeCast-toUint224-uint256-}[`++toUint224(value)++`]
* {xref-SafeCast-toUint216-uint256-}[`++toUint216(value)++`]
* {xref-SafeCast-toUint208-uint256-}[`++toUint208(value)++`]
* {xref-SafeCast-toUint200-uint256-}[`++toUint200(value)++`]
* {xref-SafeCast-toUint192-uint256-}[`++toUint192(value)++`]
* {xref-SafeCast-toUint184-uint256-}[`++toUint184(value)++`]
* {xref-SafeCast-toUint176-uint256-}[`++toUint176(value)++`]
* {xref-SafeCast-toUint168-uint256-}[`++toUint168(value)++`]
* {xref-SafeCast-toUint160-uint256-}[`++toUint160(value)++`]
* {xref-SafeCast-toUint152-uint256-}[`++toUint152(value)++`]
* {xref-SafeCast-toUint144-uint256-}[`++toUint144(value)++`]
* {xref-SafeCast-toUint136-uint256-}[`++toUint136(value)++`]
* {xref-SafeCast-toUint128-uint256-}[`++toUint128(value)++`]
* {xref-SafeCast-toUint120-uint256-}[`++toUint120(value)++`]
* {xref-SafeCast-toUint112-uint256-}[`++toUint112(value)++`]
* {xref-SafeCast-toUint104-uint256-}[`++toUint104(value)++`]
* {xref-SafeCast-toUint96-uint256-}[`++toUint96(value)++`]
* {xref-SafeCast-toUint88-uint256-}[`++toUint88(value)++`]
* {xref-SafeCast-toUint80-uint256-}[`++toUint80(value)++`]
* {xref-SafeCast-toUint72-uint256-}[`++toUint72(value)++`]
* {xref-SafeCast-toUint64-uint256-}[`++toUint64(value)++`]
* {xref-SafeCast-toUint56-uint256-}[`++toUint56(value)++`]
* {xref-SafeCast-toUint48-uint256-}[`++toUint48(value)++`]
* {xref-SafeCast-toUint40-uint256-}[`++toUint40(value)++`]
* {xref-SafeCast-toUint32-uint256-}[`++toUint32(value)++`]
* {xref-SafeCast-toUint24-uint256-}[`++toUint24(value)++`]
* {xref-SafeCast-toUint16-uint256-}[`++toUint16(value)++`]
* {xref-SafeCast-toUint8-uint256-}[`++toUint8(value)++`]
* {xref-SafeCast-toUint256-int256-}[`++toUint256(value)++`]
* {xref-SafeCast-toInt248-int256-}[`++toInt248(value)++`]
* {xref-SafeCast-toInt240-int256-}[`++toInt240(value)++`]
* {xref-SafeCast-toInt232-int256-}[`++toInt232(value)++`]
* {xref-SafeCast-toInt224-int256-}[`++toInt224(value)++`]
* {xref-SafeCast-toInt216-int256-}[`++toInt216(value)++`]
* {xref-SafeCast-toInt208-int256-}[`++toInt208(value)++`]
* {xref-SafeCast-toInt200-int256-}[`++toInt200(value)++`]
* {xref-SafeCast-toInt192-int256-}[`++toInt192(value)++`]
* {xref-SafeCast-toInt184-int256-}[`++toInt184(value)++`]
* {xref-SafeCast-toInt176-int256-}[`++toInt176(value)++`]
* {xref-SafeCast-toInt168-int256-}[`++toInt168(value)++`]
* {xref-SafeCast-toInt160-int256-}[`++toInt160(value)++`]
* {xref-SafeCast-toInt152-int256-}[`++toInt152(value)++`]
* {xref-SafeCast-toInt144-int256-}[`++toInt144(value)++`]
* {xref-SafeCast-toInt136-int256-}[`++toInt136(value)++`]
* {xref-SafeCast-toInt128-int256-}[`++toInt128(value)++`]
* {xref-SafeCast-toInt120-int256-}[`++toInt120(value)++`]
* {xref-SafeCast-toInt112-int256-}[`++toInt112(value)++`]
* {xref-SafeCast-toInt104-int256-}[`++toInt104(value)++`]
* {xref-SafeCast-toInt96-int256-}[`++toInt96(value)++`]
* {xref-SafeCast-toInt88-int256-}[`++toInt88(value)++`]
* {xref-SafeCast-toInt80-int256-}[`++toInt80(value)++`]
* {xref-SafeCast-toInt72-int256-}[`++toInt72(value)++`]
* {xref-SafeCast-toInt64-int256-}[`++toInt64(value)++`]
* {xref-SafeCast-toInt56-int256-}[`++toInt56(value)++`]
* {xref-SafeCast-toInt48-int256-}[`++toInt48(value)++`]
* {xref-SafeCast-toInt40-int256-}[`++toInt40(value)++`]
* {xref-SafeCast-toInt32-int256-}[`++toInt32(value)++`]
* {xref-SafeCast-toInt24-int256-}[`++toInt24(value)++`]
* {xref-SafeCast-toInt16-int256-}[`++toInt16(value)++`]
* {xref-SafeCast-toInt8-int256-}[`++toInt8(value)++`]
* {xref-SafeCast-toInt256-uint256-}[`++toInt256(value)++`]

--

[.contract-item]
[[SafeCast-toUint248-uint256-]]
==== `[.contract-item-name]#++toUint248++#++(uint256 value) → uint248++` [.item-kind]#internal#

Returns the downcasted uint248 from uint256, reverting on
overflow (when the input is greater than largest uint248).

Counterpart to Solidity's `uint248` operator.

Requirements:

- input must fit into 248 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint240-uint256-]]
==== `[.contract-item-name]#++toUint240++#++(uint256 value) → uint240++` [.item-kind]#internal#

Returns the downcasted uint240 from uint256, reverting on
overflow (when the input is greater than largest uint240).

Counterpart to Solidity's `uint240` operator.

Requirements:

- input must fit into 240 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint232-uint256-]]
==== `[.contract-item-name]#++toUint232++#++(uint256 value) → uint232++` [.item-kind]#internal#

Returns the downcasted uint232 from uint256, reverting on
overflow (when the input is greater than largest uint232).

Counterpart to Solidity's `uint232` operator.

Requirements:

- input must fit into 232 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint224-uint256-]]
==== `[.contract-item-name]#++toUint224++#++(uint256 value) → uint224++` [.item-kind]#internal#

Returns the downcasted uint224 from uint256, reverting on
overflow (when the input is greater than largest uint224).

Counterpart to Solidity's `uint224` operator.

Requirements:

- input must fit into 224 bits

_Available since v4.2._

[.contract-item]
[[SafeCast-toUint216-uint256-]]
==== `[.contract-item-name]#++toUint216++#++(uint256 value) → uint216++` [.item-kind]#internal#

Returns the downcasted uint216 from uint256, reverting on
overflow (when the input is greater than largest uint216).

Counterpart to Solidity's `uint216` operator.

Requirements:

- input must fit into 216 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint208-uint256-]]
==== `[.contract-item-name]#++toUint208++#++(uint256 value) → uint208++` [.item-kind]#internal#

Returns the downcasted uint208 from uint256, reverting on
overflow (when the input is greater than largest uint208).

Counterpart to Solidity's `uint208` operator.

Requirements:

- input must fit into 208 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint200-uint256-]]
==== `[.contract-item-name]#++toUint200++#++(uint256 value) → uint200++` [.item-kind]#internal#

Returns the downcasted uint200 from uint256, reverting on
overflow (when the input is greater than largest uint200).

Counterpart to Solidity's `uint200` operator.

Requirements:

- input must fit into 200 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint192-uint256-]]
==== `[.contract-item-name]#++toUint192++#++(uint256 value) → uint192++` [.item-kind]#internal#

Returns the downcasted uint192 from uint256, reverting on
overflow (when the input is greater than largest uint192).

Counterpart to Solidity's `uint192` operator.

Requirements:

- input must fit into 192 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint184-uint256-]]
==== `[.contract-item-name]#++toUint184++#++(uint256 value) → uint184++` [.item-kind]#internal#

Returns the downcasted uint184 from uint256, reverting on
overflow (when the input is greater than largest uint184).

Counterpart to Solidity's `uint184` operator.

Requirements:

- input must fit into 184 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint176-uint256-]]
==== `[.contract-item-name]#++toUint176++#++(uint256 value) → uint176++` [.item-kind]#internal#

Returns the downcasted uint176 from uint256, reverting on
overflow (when the input is greater than largest uint176).

Counterpart to Solidity's `uint176` operator.

Requirements:

- input must fit into 176 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint168-uint256-]]
==== `[.contract-item-name]#++toUint168++#++(uint256 value) → uint168++` [.item-kind]#internal#

Returns the downcasted uint168 from uint256, reverting on
overflow (when the input is greater than largest uint168).

Counterpart to Solidity's `uint168` operator.

Requirements:

- input must fit into 168 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint160-uint256-]]
==== `[.contract-item-name]#++toUint160++#++(uint256 value) → uint160++` [.item-kind]#internal#

Returns the downcasted uint160 from uint256, reverting on
overflow (when the input is greater than largest uint160).

Counterpart to Solidity's `uint160` operator.

Requirements:

- input must fit into 160 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint152-uint256-]]
==== `[.contract-item-name]#++toUint152++#++(uint256 value) → uint152++` [.item-kind]#internal#

Returns the downcasted uint152 from uint256, reverting on
overflow (when the input is greater than largest uint152).

Counterpart to Solidity's `uint152` operator.

Requirements:

- input must fit into 152 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint144-uint256-]]
==== `[.contract-item-name]#++toUint144++#++(uint256 value) → uint144++` [.item-kind]#internal#

Returns the downcasted uint144 from uint256, reverting on
overflow (when the input is greater than largest uint144).

Counterpart to Solidity's `uint144` operator.

Requirements:

- input must fit into 144 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint136-uint256-]]
==== `[.contract-item-name]#++toUint136++#++(uint256 value) → uint136++` [.item-kind]#internal#

Returns the downcasted uint136 from uint256, reverting on
overflow (when the input is greater than largest uint136).

Counterpart to Solidity's `uint136` operator.

Requirements:

- input must fit into 136 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint128-uint256-]]
==== `[.contract-item-name]#++toUint128++#++(uint256 value) → uint128++` [.item-kind]#internal#

Returns the downcasted uint128 from uint256, reverting on
overflow (when the input is greater than largest uint128).

Counterpart to Solidity's `uint128` operator.

Requirements:

- input must fit into 128 bits

_Available since v2.5._

[.contract-item]
[[SafeCast-toUint120-uint256-]]
==== `[.contract-item-name]#++toUint120++#++(uint256 value) → uint120++` [.item-kind]#internal#

Returns the downcasted uint120 from uint256, reverting on
overflow (when the input is greater than largest uint120).

Counterpart to Solidity's `uint120` operator.

Requirements:

- input must fit into 120 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint112-uint256-]]
==== `[.contract-item-name]#++toUint112++#++(uint256 value) → uint112++` [.item-kind]#internal#

Returns the downcasted uint112 from uint256, reverting on
overflow (when the input is greater than largest uint112).

Counterpart to Solidity's `uint112` operator.

Requirements:

- input must fit into 112 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint104-uint256-]]
==== `[.contract-item-name]#++toUint104++#++(uint256 value) → uint104++` [.item-kind]#internal#

Returns the downcasted uint104 from uint256, reverting on
overflow (when the input is greater than largest uint104).

Counterpart to Solidity's `uint104` operator.

Requirements:

- input must fit into 104 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint96-uint256-]]
==== `[.contract-item-name]#++toUint96++#++(uint256 value) → uint96++` [.item-kind]#internal#

Returns the downcasted uint96 from uint256, reverting on
overflow (when the input is greater than largest uint96).

Counterpart to Solidity's `uint96` operator.

Requirements:

- input must fit into 96 bits

_Available since v4.2._

[.contract-item]
[[SafeCast-toUint88-uint256-]]
==== `[.contract-item-name]#++toUint88++#++(uint256 value) → uint88++` [.item-kind]#internal#

Returns the downcasted uint88 from uint256, reverting on
overflow (when the input is greater than largest uint88).

Counterpart to Solidity's `uint88` operator.

Requirements:

- input must fit into 88 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint80-uint256-]]
==== `[.contract-item-name]#++toUint80++#++(uint256 value) → uint80++` [.item-kind]#internal#

Returns the downcasted uint80 from uint256, reverting on
overflow (when the input is greater than largest uint80).

Counterpart to Solidity's `uint80` operator.

Requirements:

- input must fit into 80 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint72-uint256-]]
==== `[.contract-item-name]#++toUint72++#++(uint256 value) → uint72++` [.item-kind]#internal#

Returns the downcasted uint72 from uint256, reverting on
overflow (when the input is greater than largest uint72).

Counterpart to Solidity's `uint72` operator.

Requirements:

- input must fit into 72 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint64-uint256-]]
==== `[.contract-item-name]#++toUint64++#++(uint256 value) → uint64++` [.item-kind]#internal#

Returns the downcasted uint64 from uint256, reverting on
overflow (when the input is greater than largest uint64).

Counterpart to Solidity's `uint64` operator.

Requirements:

- input must fit into 64 bits

_Available since v2.5._

[.contract-item]
[[SafeCast-toUint56-uint256-]]
==== `[.contract-item-name]#++toUint56++#++(uint256 value) → uint56++` [.item-kind]#internal#

Returns the downcasted uint56 from uint256, reverting on
overflow (when the input is greater than largest uint56).

Counterpart to Solidity's `uint56` operator.

Requirements:

- input must fit into 56 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint48-uint256-]]
==== `[.contract-item-name]#++toUint48++#++(uint256 value) → uint48++` [.item-kind]#internal#

Returns the downcasted uint48 from uint256, reverting on
overflow (when the input is greater than largest uint48).

Counterpart to Solidity's `uint48` operator.

Requirements:

- input must fit into 48 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint40-uint256-]]
==== `[.contract-item-name]#++toUint40++#++(uint256 value) → uint40++` [.item-kind]#internal#

Returns the downcasted uint40 from uint256, reverting on
overflow (when the input is greater than largest uint40).

Counterpart to Solidity's `uint40` operator.

Requirements:

- input must fit into 40 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint32-uint256-]]
==== `[.contract-item-name]#++toUint32++#++(uint256 value) → uint32++` [.item-kind]#internal#

Returns the downcasted uint32 from uint256, reverting on
overflow (when the input is greater than largest uint32).

Counterpart to Solidity's `uint32` operator.

Requirements:

- input must fit into 32 bits

_Available since v2.5._

[.contract-item]
[[SafeCast-toUint24-uint256-]]
==== `[.contract-item-name]#++toUint24++#++(uint256 value) → uint24++` [.item-kind]#internal#

Returns the downcasted uint24 from uint256, reverting on
overflow (when the input is greater than largest uint24).

Counterpart to Solidity's `uint24` operator.

Requirements:

- input must fit into 24 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toUint16-uint256-]]
==== `[.contract-item-name]#++toUint16++#++(uint256 value) → uint16++` [.item-kind]#internal#

Returns the downcasted uint16 from uint256, reverting on
overflow (when the input is greater than largest uint16).

Counterpart to Solidity's `uint16` operator.

Requirements:

- input must fit into 16 bits

_Available since v2.5._

[.contract-item]
[[SafeCast-toUint8-uint256-]]
==== `[.contract-item-name]#++toUint8++#++(uint256 value) → uint8++` [.item-kind]#internal#

Returns the downcasted uint8 from uint256, reverting on
overflow (when the input is greater than largest uint8).

Counterpart to Solidity's `uint8` operator.

Requirements:

- input must fit into 8 bits

_Available since v2.5._

[.contract-item]
[[SafeCast-toUint256-int256-]]
==== `[.contract-item-name]#++toUint256++#++(int256 value) → uint256++` [.item-kind]#internal#

Converts a signed int256 into an unsigned uint256.

Requirements:

- input must be greater than or equal to 0.

_Available since v3.0._

[.contract-item]
[[SafeCast-toInt248-int256-]]
==== `[.contract-item-name]#++toInt248++#++(int256 value) → int248 downcasted++` [.item-kind]#internal#

Returns the downcasted int248 from int256, reverting on
overflow (when the input is less than smallest int248 or
greater than largest int248).

Counterpart to Solidity's `int248` operator.

Requirements:

- input must fit into 248 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt240-int256-]]
==== `[.contract-item-name]#++toInt240++#++(int256 value) → int240 downcasted++` [.item-kind]#internal#

Returns the downcasted int240 from int256, reverting on
overflow (when the input is less than smallest int240 or
greater than largest int240).

Counterpart to Solidity's `int240` operator.

Requirements:

- input must fit into 240 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt232-int256-]]
==== `[.contract-item-name]#++toInt232++#++(int256 value) → int232 downcasted++` [.item-kind]#internal#

Returns the downcasted int232 from int256, reverting on
overflow (when the input is less than smallest int232 or
greater than largest int232).

Counterpart to Solidity's `int232` operator.

Requirements:

- input must fit into 232 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt224-int256-]]
==== `[.contract-item-name]#++toInt224++#++(int256 value) → int224 downcasted++` [.item-kind]#internal#

Returns the downcasted int224 from int256, reverting on
overflow (when the input is less than smallest int224 or
greater than largest int224).

Counterpart to Solidity's `int224` operator.

Requirements:

- input must fit into 224 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt216-int256-]]
==== `[.contract-item-name]#++toInt216++#++(int256 value) → int216 downcasted++` [.item-kind]#internal#

Returns the downcasted int216 from int256, reverting on
overflow (when the input is less than smallest int216 or
greater than largest int216).

Counterpart to Solidity's `int216` operator.

Requirements:

- input must fit into 216 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt208-int256-]]
==== `[.contract-item-name]#++toInt208++#++(int256 value) → int208 downcasted++` [.item-kind]#internal#

Returns the downcasted int208 from int256, reverting on
overflow (when the input is less than smallest int208 or
greater than largest int208).

Counterpart to Solidity's `int208` operator.

Requirements:

- input must fit into 208 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt200-int256-]]
==== `[.contract-item-name]#++toInt200++#++(int256 value) → int200 downcasted++` [.item-kind]#internal#

Returns the downcasted int200 from int256, reverting on
overflow (when the input is less than smallest int200 or
greater than largest int200).

Counterpart to Solidity's `int200` operator.

Requirements:

- input must fit into 200 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt192-int256-]]
==== `[.contract-item-name]#++toInt192++#++(int256 value) → int192 downcasted++` [.item-kind]#internal#

Returns the downcasted int192 from int256, reverting on
overflow (when the input is less than smallest int192 or
greater than largest int192).

Counterpart to Solidity's `int192` operator.

Requirements:

- input must fit into 192 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt184-int256-]]
==== `[.contract-item-name]#++toInt184++#++(int256 value) → int184 downcasted++` [.item-kind]#internal#

Returns the downcasted int184 from int256, reverting on
overflow (when the input is less than smallest int184 or
greater than largest int184).

Counterpart to Solidity's `int184` operator.

Requirements:

- input must fit into 184 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt176-int256-]]
==== `[.contract-item-name]#++toInt176++#++(int256 value) → int176 downcasted++` [.item-kind]#internal#

Returns the downcasted int176 from int256, reverting on
overflow (when the input is less than smallest int176 or
greater than largest int176).

Counterpart to Solidity's `int176` operator.

Requirements:

- input must fit into 176 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt168-int256-]]
==== `[.contract-item-name]#++toInt168++#++(int256 value) → int168 downcasted++` [.item-kind]#internal#

Returns the downcasted int168 from int256, reverting on
overflow (when the input is less than smallest int168 or
greater than largest int168).

Counterpart to Solidity's `int168` operator.

Requirements:

- input must fit into 168 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt160-int256-]]
==== `[.contract-item-name]#++toInt160++#++(int256 value) → int160 downcasted++` [.item-kind]#internal#

Returns the downcasted int160 from int256, reverting on
overflow (when the input is less than smallest int160 or
greater than largest int160).

Counterpart to Solidity's `int160` operator.

Requirements:

- input must fit into 160 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt152-int256-]]
==== `[.contract-item-name]#++toInt152++#++(int256 value) → int152 downcasted++` [.item-kind]#internal#

Returns the downcasted int152 from int256, reverting on
overflow (when the input is less than smallest int152 or
greater than largest int152).

Counterpart to Solidity's `int152` operator.

Requirements:

- input must fit into 152 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt144-int256-]]
==== `[.contract-item-name]#++toInt144++#++(int256 value) → int144 downcasted++` [.item-kind]#internal#

Returns the downcasted int144 from int256, reverting on
overflow (when the input is less than smallest int144 or
greater than largest int144).

Counterpart to Solidity's `int144` operator.

Requirements:

- input must fit into 144 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt136-int256-]]
==== `[.contract-item-name]#++toInt136++#++(int256 value) → int136 downcasted++` [.item-kind]#internal#

Returns the downcasted int136 from int256, reverting on
overflow (when the input is less than smallest int136 or
greater than largest int136).

Counterpart to Solidity's `int136` operator.

Requirements:

- input must fit into 136 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt128-int256-]]
==== `[.contract-item-name]#++toInt128++#++(int256 value) → int128 downcasted++` [.item-kind]#internal#

Returns the downcasted int128 from int256, reverting on
overflow (when the input is less than smallest int128 or
greater than largest int128).

Counterpart to Solidity's `int128` operator.

Requirements:

- input must fit into 128 bits

_Available since v3.1._

[.contract-item]
[[SafeCast-toInt120-int256-]]
==== `[.contract-item-name]#++toInt120++#++(int256 value) → int120 downcasted++` [.item-kind]#internal#

Returns the downcasted int120 from int256, reverting on
overflow (when the input is less than smallest int120 or
greater than largest int120).

Counterpart to Solidity's `int120` operator.

Requirements:

- input must fit into 120 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt112-int256-]]
==== `[.contract-item-name]#++toInt112++#++(int256 value) → int112 downcasted++` [.item-kind]#internal#

Returns the downcasted int112 from int256, reverting on
overflow (when the input is less than smallest int112 or
greater than largest int112).

Counterpart to Solidity's `int112` operator.

Requirements:

- input must fit into 112 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt104-int256-]]
==== `[.contract-item-name]#++toInt104++#++(int256 value) → int104 downcasted++` [.item-kind]#internal#

Returns the downcasted int104 from int256, reverting on
overflow (when the input is less than smallest int104 or
greater than largest int104).

Counterpart to Solidity's `int104` operator.

Requirements:

- input must fit into 104 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt96-int256-]]
==== `[.contract-item-name]#++toInt96++#++(int256 value) → int96 downcasted++` [.item-kind]#internal#

Returns the downcasted int96 from int256, reverting on
overflow (when the input is less than smallest int96 or
greater than largest int96).

Counterpart to Solidity's `int96` operator.

Requirements:

- input must fit into 96 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt88-int256-]]
==== `[.contract-item-name]#++toInt88++#++(int256 value) → int88 downcasted++` [.item-kind]#internal#

Returns the downcasted int88 from int256, reverting on
overflow (when the input is less than smallest int88 or
greater than largest int88).

Counterpart to Solidity's `int88` operator.

Requirements:

- input must fit into 88 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt80-int256-]]
==== `[.contract-item-name]#++toInt80++#++(int256 value) → int80 downcasted++` [.item-kind]#internal#

Returns the downcasted int80 from int256, reverting on
overflow (when the input is less than smallest int80 or
greater than largest int80).

Counterpart to Solidity's `int80` operator.

Requirements:

- input must fit into 80 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt72-int256-]]
==== `[.contract-item-name]#++toInt72++#++(int256 value) → int72 downcasted++` [.item-kind]#internal#

Returns the downcasted int72 from int256, reverting on
overflow (when the input is less than smallest int72 or
greater than largest int72).

Counterpart to Solidity's `int72` operator.

Requirements:

- input must fit into 72 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt64-int256-]]
==== `[.contract-item-name]#++toInt64++#++(int256 value) → int64 downcasted++` [.item-kind]#internal#

Returns the downcasted int64 from int256, reverting on
overflow (when the input is less than smallest int64 or
greater than largest int64).

Counterpart to Solidity's `int64` operator.

Requirements:

- input must fit into 64 bits

_Available since v3.1._

[.contract-item]
[[SafeCast-toInt56-int256-]]
==== `[.contract-item-name]#++toInt56++#++(int256 value) → int56 downcasted++` [.item-kind]#internal#

Returns the downcasted int56 from int256, reverting on
overflow (when the input is less than smallest int56 or
greater than largest int56).

Counterpart to Solidity's `int56` operator.

Requirements:

- input must fit into 56 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt48-int256-]]
==== `[.contract-item-name]#++toInt48++#++(int256 value) → int48 downcasted++` [.item-kind]#internal#

Returns the downcasted int48 from int256, reverting on
overflow (when the input is less than smallest int48 or
greater than largest int48).

Counterpart to Solidity's `int48` operator.

Requirements:

- input must fit into 48 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt40-int256-]]
==== `[.contract-item-name]#++toInt40++#++(int256 value) → int40 downcasted++` [.item-kind]#internal#

Returns the downcasted int40 from int256, reverting on
overflow (when the input is less than smallest int40 or
greater than largest int40).

Counterpart to Solidity's `int40` operator.

Requirements:

- input must fit into 40 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt32-int256-]]
==== `[.contract-item-name]#++toInt32++#++(int256 value) → int32 downcasted++` [.item-kind]#internal#

Returns the downcasted int32 from int256, reverting on
overflow (when the input is less than smallest int32 or
greater than largest int32).

Counterpart to Solidity's `int32` operator.

Requirements:

- input must fit into 32 bits

_Available since v3.1._

[.contract-item]
[[SafeCast-toInt24-int256-]]
==== `[.contract-item-name]#++toInt24++#++(int256 value) → int24 downcasted++` [.item-kind]#internal#

Returns the downcasted int24 from int256, reverting on
overflow (when the input is less than smallest int24 or
greater than largest int24).

Counterpart to Solidity's `int24` operator.

Requirements:

- input must fit into 24 bits

_Available since v4.7._

[.contract-item]
[[SafeCast-toInt16-int256-]]
==== `[.contract-item-name]#++toInt16++#++(int256 value) → int16 downcasted++` [.item-kind]#internal#

Returns the downcasted int16 from int256, reverting on
overflow (when the input is less than smallest int16 or
greater than largest int16).

Counterpart to Solidity's `int16` operator.

Requirements:

- input must fit into 16 bits

_Available since v3.1._

[.contract-item]
[[SafeCast-toInt8-int256-]]
==== `[.contract-item-name]#++toInt8++#++(int256 value) → int8 downcasted++` [.item-kind]#internal#

Returns the downcasted int8 from int256, reverting on
overflow (when the input is less than smallest int8 or
greater than largest int8).

Counterpart to Solidity's `int8` operator.

Requirements:

- input must fit into 8 bits

_Available since v3.1._

[.contract-item]
[[SafeCast-toInt256-uint256-]]
==== `[.contract-item-name]#++toInt256++#++(uint256 value) → int256++` [.item-kind]#internal#

Converts an unsigned uint256 into a signed int256.

Requirements:

- input must be less than or equal to maxInt256.

_Available since v3.0._

:tryAdd: pass:normal[xref:#SafeMath-tryAdd-uint256-uint256-[`++tryAdd++`]]
:trySub: pass:normal[xref:#SafeMath-trySub-uint256-uint256-[`++trySub++`]]
:tryMul: pass:normal[xref:#SafeMath-tryMul-uint256-uint256-[`++tryMul++`]]
:tryDiv: pass:normal[xref:#SafeMath-tryDiv-uint256-uint256-[`++tryDiv++`]]
:tryMod: pass:normal[xref:#SafeMath-tryMod-uint256-uint256-[`++tryMod++`]]
:add: pass:normal[xref:#SafeMath-add-uint256-uint256-[`++add++`]]
:sub: pass:normal[xref:#SafeMath-sub-uint256-uint256-[`++sub++`]]
:mul: pass:normal[xref:#SafeMath-mul-uint256-uint256-[`++mul++`]]
:div: pass:normal[xref:#SafeMath-div-uint256-uint256-[`++div++`]]
:mod: pass:normal[xref:#SafeMath-mod-uint256-uint256-[`++mod++`]]
:sub: pass:normal[xref:#SafeMath-sub-uint256-uint256-string-[`++sub++`]]
:div: pass:normal[xref:#SafeMath-div-uint256-uint256-string-[`++div++`]]
:mod: pass:normal[xref:#SafeMath-mod-uint256-uint256-string-[`++mod++`]]

[.contract]
[[SafeMath]]
=== `++SafeMath++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/math/SafeMath.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/math/SafeMath.sol";
```

Wrappers over Solidity's arithmetic operations.

NOTE: `SafeMath` is generally not needed starting with Solidity 0.8, since the compiler
now has built in overflow checking.

[.contract-index]
.Functions
--
* {xref-SafeMath-tryAdd-uint256-uint256-}[`++tryAdd(a, b)++`]
* {xref-SafeMath-trySub-uint256-uint256-}[`++trySub(a, b)++`]
* {xref-SafeMath-tryMul-uint256-uint256-}[`++tryMul(a, b)++`]
* {xref-SafeMath-tryDiv-uint256-uint256-}[`++tryDiv(a, b)++`]
* {xref-SafeMath-tryMod-uint256-uint256-}[`++tryMod(a, b)++`]
* {xref-SafeMath-add-uint256-uint256-}[`++add(a, b)++`]
* {xref-SafeMath-sub-uint256-uint256-}[`++sub(a, b)++`]
* {xref-SafeMath-mul-uint256-uint256-}[`++mul(a, b)++`]
* {xref-SafeMath-div-uint256-uint256-}[`++div(a, b)++`]
* {xref-SafeMath-mod-uint256-uint256-}[`++mod(a, b)++`]
* {xref-SafeMath-sub-uint256-uint256-string-}[`++sub(a, b, errorMessage)++`]
* {xref-SafeMath-div-uint256-uint256-string-}[`++div(a, b, errorMessage)++`]
* {xref-SafeMath-mod-uint256-uint256-string-}[`++mod(a, b, errorMessage)++`]

--

[.contract-item]
[[SafeMath-tryAdd-uint256-uint256-]]
==== `[.contract-item-name]#++tryAdd++#++(uint256 a, uint256 b) → bool, uint256++` [.item-kind]#internal#

Returns the addition of two unsigned integers, with an overflow flag.

_Available since v3.4._

[.contract-item]
[[SafeMath-trySub-uint256-uint256-]]
==== `[.contract-item-name]#++trySub++#++(uint256 a, uint256 b) → bool, uint256++` [.item-kind]#internal#

Returns the subtraction of two unsigned integers, with an overflow flag.

_Available since v3.4._

[.contract-item]
[[SafeMath-tryMul-uint256-uint256-]]
==== `[.contract-item-name]#++tryMul++#++(uint256 a, uint256 b) → bool, uint256++` [.item-kind]#internal#

Returns the multiplication of two unsigned integers, with an overflow flag.

_Available since v3.4._

[.contract-item]
[[SafeMath-tryDiv-uint256-uint256-]]
==== `[.contract-item-name]#++tryDiv++#++(uint256 a, uint256 b) → bool, uint256++` [.item-kind]#internal#

Returns the division of two unsigned integers, with a division by zero flag.

_Available since v3.4._

[.contract-item]
[[SafeMath-tryMod-uint256-uint256-]]
==== `[.contract-item-name]#++tryMod++#++(uint256 a, uint256 b) → bool, uint256++` [.item-kind]#internal#

Returns the remainder of dividing two unsigned integers, with a division by zero flag.

_Available since v3.4._

[.contract-item]
[[SafeMath-add-uint256-uint256-]]
==== `[.contract-item-name]#++add++#++(uint256 a, uint256 b) → uint256++` [.item-kind]#internal#

Returns the addition of two unsigned integers, reverting on
overflow.

Counterpart to Solidity's `+` operator.

Requirements:

- Addition cannot overflow.

[.contract-item]
[[SafeMath-sub-uint256-uint256-]]
==== `[.contract-item-name]#++sub++#++(uint256 a, uint256 b) → uint256++` [.item-kind]#internal#

Returns the subtraction of two unsigned integers, reverting on
overflow (when the result is negative).

Counterpart to Solidity's `-` operator.

Requirements:

- Subtraction cannot overflow.

[.contract-item]
[[SafeMath-mul-uint256-uint256-]]
==== `[.contract-item-name]#++mul++#++(uint256 a, uint256 b) → uint256++` [.item-kind]#internal#

Returns the multiplication of two unsigned integers, reverting on
overflow.

Counterpart to Solidity's `*` operator.

Requirements:

- Multiplication cannot overflow.

[.contract-item]
[[SafeMath-div-uint256-uint256-]]
==== `[.contract-item-name]#++div++#++(uint256 a, uint256 b) → uint256++` [.item-kind]#internal#

Returns the integer division of two unsigned integers, reverting on
division by zero. The result is rounded towards zero.

Counterpart to Solidity's `/` operator.

Requirements:

- The divisor cannot be zero.

[.contract-item]
[[SafeMath-mod-uint256-uint256-]]
==== `[.contract-item-name]#++mod++#++(uint256 a, uint256 b) → uint256++` [.item-kind]#internal#

Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
reverting when dividing by zero.

Counterpart to Solidity's `%` operator. This function uses a `revert`
opcode (which leaves remaining gas untouched) while Solidity uses an
invalid opcode to revert (consuming all remaining gas).

Requirements:

- The divisor cannot be zero.

[.contract-item]
[[SafeMath-sub-uint256-uint256-string-]]
==== `[.contract-item-name]#++sub++#++(uint256 a, uint256 b, string errorMessage) → uint256++` [.item-kind]#internal#

Returns the subtraction of two unsigned integers, reverting with custom message on
overflow (when the result is negative).

CAUTION: This function is deprecated because it requires allocating memory for the error
message unnecessarily. For custom revert reasons use {trySub}.

Counterpart to Solidity's `-` operator.

Requirements:

- Subtraction cannot overflow.

[.contract-item]
[[SafeMath-div-uint256-uint256-string-]]
==== `[.contract-item-name]#++div++#++(uint256 a, uint256 b, string errorMessage) → uint256++` [.item-kind]#internal#

Returns the integer division of two unsigned integers, reverting with custom message on
division by zero. The result is rounded towards zero.

Counterpart to Solidity's `/` operator. Note: this function uses a
`revert` opcode (which leaves remaining gas untouched) while Solidity
uses an invalid opcode to revert (consuming all remaining gas).

Requirements:

- The divisor cannot be zero.

[.contract-item]
[[SafeMath-mod-uint256-uint256-string-]]
==== `[.contract-item-name]#++mod++#++(uint256 a, uint256 b, string errorMessage) → uint256++` [.item-kind]#internal#

Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
reverting with custom message when dividing by zero.

CAUTION: This function is deprecated because it requires allocating memory for the error
message unnecessarily. For custom revert reasons use {tryMod}.

Counterpart to Solidity's `%` operator. This function uses a `revert`
opcode (which leaves remaining gas untouched) while Solidity uses an
invalid opcode to revert (consuming all remaining gas).

Requirements:

- The divisor cannot be zero.

:mul: pass:normal[xref:#SignedSafeMath-mul-int256-int256-[`++mul++`]]
:div: pass:normal[xref:#SignedSafeMath-div-int256-int256-[`++div++`]]
:sub: pass:normal[xref:#SignedSafeMath-sub-int256-int256-[`++sub++`]]
:add: pass:normal[xref:#SignedSafeMath-add-int256-int256-[`++add++`]]

[.contract]
[[SignedSafeMath]]
=== `++SignedSafeMath++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/math/SignedSafeMath.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/math/SignedSafeMath.sol";
```

Wrappers over Solidity's arithmetic operations.

NOTE: `SignedSafeMath` is no longer needed starting with Solidity 0.8. The compiler
now has built in overflow checking.

[.contract-index]
.Functions
--
* {xref-SignedSafeMath-mul-int256-int256-}[`++mul(a, b)++`]
* {xref-SignedSafeMath-div-int256-int256-}[`++div(a, b)++`]
* {xref-SignedSafeMath-sub-int256-int256-}[`++sub(a, b)++`]
* {xref-SignedSafeMath-add-int256-int256-}[`++add(a, b)++`]

--

[.contract-item]
[[SignedSafeMath-mul-int256-int256-]]
==== `[.contract-item-name]#++mul++#++(int256 a, int256 b) → int256++` [.item-kind]#internal#

Returns the multiplication of two signed integers, reverting on
overflow.

Counterpart to Solidity's `*` operator.

Requirements:

- Multiplication cannot overflow.

[.contract-item]
[[SignedSafeMath-div-int256-int256-]]
==== `[.contract-item-name]#++div++#++(int256 a, int256 b) → int256++` [.item-kind]#internal#

Returns the integer division of two signed integers. Reverts on
division by zero. The result is rounded towards zero.

Counterpart to Solidity's `/` operator.

Requirements:

- The divisor cannot be zero.

[.contract-item]
[[SignedSafeMath-sub-int256-int256-]]
==== `[.contract-item-name]#++sub++#++(int256 a, int256 b) → int256++` [.item-kind]#internal#

Returns the subtraction of two signed integers, reverting on
overflow.

Counterpart to Solidity's `-` operator.

Requirements:

- Subtraction cannot overflow.

[.contract-item]
[[SignedSafeMath-add-int256-int256-]]
==== `[.contract-item-name]#++add++#++(int256 a, int256 b) → int256++` [.item-kind]#internal#

Returns the addition of two signed integers, reverting on
overflow.

Counterpart to Solidity's `+` operator.

Requirements:

- Addition cannot overflow.

== Cryptography

:RecoverError: pass:normal[xref:#ECDSA-RecoverError[`++RecoverError++`]]
:_throwError: pass:normal[xref:#ECDSA-_throwError-enum-ECDSA-RecoverError-[`++_throwError++`]]
:tryRecover: pass:normal[xref:#ECDSA-tryRecover-bytes32-bytes-[`++tryRecover++`]]
:recover: pass:normal[xref:#ECDSA-recover-bytes32-bytes-[`++recover++`]]
:tryRecover: pass:normal[xref:#ECDSA-tryRecover-bytes32-bytes32-bytes32-[`++tryRecover++`]]
:recover: pass:normal[xref:#ECDSA-recover-bytes32-bytes32-bytes32-[`++recover++`]]
:tryRecover: pass:normal[xref:#ECDSA-tryRecover-bytes32-uint8-bytes32-bytes32-[`++tryRecover++`]]
:recover: pass:normal[xref:#ECDSA-recover-bytes32-uint8-bytes32-bytes32-[`++recover++`]]
:toEthSignedMessageHash: pass:normal[xref:#ECDSA-toEthSignedMessageHash-bytes32-[`++toEthSignedMessageHash++`]]
:toEthSignedMessageHash: pass:normal[xref:#ECDSA-toEthSignedMessageHash-bytes-[`++toEthSignedMessageHash++`]]
:toTypedDataHash: pass:normal[xref:#ECDSA-toTypedDataHash-bytes32-bytes32-[`++toTypedDataHash++`]]

[.contract]
[[ECDSA]]
=== `++ECDSA++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/cryptography/ECDSA.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/cryptography/ECDSA.sol";
```

Elliptic Curve Digital Signature Algorithm (ECDSA) operations.

These functions can be used to verify that a message was signed by the holder
of the private keys of a given address.

[.contract-index]
.Functions
--
* {xref-ECDSA-tryRecover-bytes32-bytes-}[`++tryRecover(hash, signature)++`]
* {xref-ECDSA-recover-bytes32-bytes-}[`++recover(hash, signature)++`]
* {xref-ECDSA-tryRecover-bytes32-bytes32-bytes32-}[`++tryRecover(hash, r, vs)++`]
* {xref-ECDSA-recover-bytes32-bytes32-bytes32-}[`++recover(hash, r, vs)++`]
* {xref-ECDSA-tryRecover-bytes32-uint8-bytes32-bytes32-}[`++tryRecover(hash, v, r, s)++`]
* {xref-ECDSA-recover-bytes32-uint8-bytes32-bytes32-}[`++recover(hash, v, r, s)++`]
* {xref-ECDSA-toEthSignedMessageHash-bytes32-}[`++toEthSignedMessageHash(hash)++`]
* {xref-ECDSA-toEthSignedMessageHash-bytes-}[`++toEthSignedMessageHash(s)++`]
* {xref-ECDSA-toTypedDataHash-bytes32-bytes32-}[`++toTypedDataHash(domainSeparator, structHash)++`]

--

[.contract-item]
[[ECDSA-tryRecover-bytes32-bytes-]]
==== `[.contract-item-name]#++tryRecover++#++(bytes32 hash, bytes signature) → address, enum ECDSA.RecoverError++` [.item-kind]#internal#

Returns the address that signed a hashed message (`hash`) with
`signature` or error string. This address can then be used for verification purposes.

The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
this function rejects them by requiring the `s` value to be in the lower
half order, and the `v` value to be either 27 or 28.

IMPORTANT: `hash` _must_ be the result of a hash operation for the
verification to be secure: it is possible to craft signatures that
recover to arbitrary addresses for non-hashed data. A safe way to ensure
this is by receiving a hash of the original message (which may otherwise
be too long), and then calling {toEthSignedMessageHash} on it.

Documentation for signature generation:
- with https://web3js.readthedocs.io/en/v1.3.4/web3-eth-accounts.html#sign[Web3.js]
- with https://docs.ethers.io/v5/api/signer/#Signer-signMessage[ethers]

_Available since v4.3._

[.contract-item]
[[ECDSA-recover-bytes32-bytes-]]
==== `[.contract-item-name]#++recover++#++(bytes32 hash, bytes signature) → address++` [.item-kind]#internal#

Returns the address that signed a hashed message (`hash`) with
`signature`. This address can then be used for verification purposes.

The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
this function rejects them by requiring the `s` value to be in the lower
half order, and the `v` value to be either 27 or 28.

IMPORTANT: `hash` _must_ be the result of a hash operation for the
verification to be secure: it is possible to craft signatures that
recover to arbitrary addresses for non-hashed data. A safe way to ensure
this is by receiving a hash of the original message (which may otherwise
be too long), and then calling {toEthSignedMessageHash} on it.

[.contract-item]
[[ECDSA-tryRecover-bytes32-bytes32-bytes32-]]
==== `[.contract-item-name]#++tryRecover++#++(bytes32 hash, bytes32 r, bytes32 vs) → address, enum ECDSA.RecoverError++` [.item-kind]#internal#

Overload of {ECDSA-tryRecover} that receives the `r` and `vs` short-signature fields separately.

See https://eips.ethereum.org/EIPS/eip-2098[EIP-2098 short signatures]

_Available since v4.3._

[.contract-item]
[[ECDSA-recover-bytes32-bytes32-bytes32-]]
==== `[.contract-item-name]#++recover++#++(bytes32 hash, bytes32 r, bytes32 vs) → address++` [.item-kind]#internal#

Overload of {ECDSA-recover} that receives the `r and `vs` short-signature fields separately.

_Available since v4.2._

[.contract-item]
[[ECDSA-tryRecover-bytes32-uint8-bytes32-bytes32-]]
==== `[.contract-item-name]#++tryRecover++#++(bytes32 hash, uint8 v, bytes32 r, bytes32 s) → address, enum ECDSA.RecoverError++` [.item-kind]#internal#

Overload of {ECDSA-tryRecover} that receives the `v`,
`r` and `s` signature fields separately.

_Available since v4.3._

[.contract-item]
[[ECDSA-recover-bytes32-uint8-bytes32-bytes32-]]
==== `[.contract-item-name]#++recover++#++(bytes32 hash, uint8 v, bytes32 r, bytes32 s) → address++` [.item-kind]#internal#

Overload of {ECDSA-recover} that receives the `v`,
`r` and `s` signature fields separately.

[.contract-item]
[[ECDSA-toEthSignedMessageHash-bytes32-]]
==== `[.contract-item-name]#++toEthSignedMessageHash++#++(bytes32 hash) → bytes32++` [.item-kind]#internal#

Returns an Ethereum Signed Message, created from a `hash`. This
produces hash corresponding to the one signed with the
https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
JSON-RPC method as part of EIP-191.

See {recover}.

[.contract-item]
[[ECDSA-toEthSignedMessageHash-bytes-]]
==== `[.contract-item-name]#++toEthSignedMessageHash++#++(bytes s) → bytes32++` [.item-kind]#internal#

Returns an Ethereum Signed Message, created from `s`. This
produces hash corresponding to the one signed with the
https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
JSON-RPC method as part of EIP-191.

See {recover}.

[.contract-item]
[[ECDSA-toTypedDataHash-bytes32-bytes32-]]
==== `[.contract-item-name]#++toTypedDataHash++#++(bytes32 domainSeparator, bytes32 structHash) → bytes32++` [.item-kind]#internal#

Returns an Ethereum Signed Typed Data, created from a
`domainSeparator` and a `structHash`. This produces hash corresponding
to the one signed with the
https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`]
JSON-RPC method as part of EIP-712.

See {recover}.

:isValidSignatureNow: pass:normal[xref:#SignatureChecker-isValidSignatureNow-address-bytes32-bytes-[`++isValidSignatureNow++`]]

[.contract]
[[SignatureChecker]]
=== `++SignatureChecker++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/cryptography/SignatureChecker.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/cryptography/SignatureChecker.sol";
```

Signature verification helper that can be used instead of `ECDSA.recover` to seamlessly support both ECDSA
signatures from externally owned accounts (EOAs) as well as ERC1271 signatures from smart contract wallets like
Argent and Gnosis Safe.

_Available since v4.1._

[.contract-index]
.Functions
--
* {xref-SignatureChecker-isValidSignatureNow-address-bytes32-bytes-}[`++isValidSignatureNow(signer, hash, signature)++`]

--

[.contract-item]
[[SignatureChecker-isValidSignatureNow-address-bytes32-bytes-]]
==== `[.contract-item-name]#++isValidSignatureNow++#++(address signer, bytes32 hash, bytes signature) → bool++` [.item-kind]#internal#

Checks if a signature is valid for a given signer and data hash. If the signer is a smart contract, the
signature is validated against that smart contract using ERC1271, otherwise it's validated using `ECDSA.recover`.

NOTE: Unlike ECDSA signatures, contract signatures are revocable, and the outcome of this function can thus
change through time. It could return true at block N and false at block N+1 (or the opposite).

:verify: pass:normal[xref:#MerkleProof-verify-bytes32---bytes32-bytes32-[`++verify++`]]
:verifyCalldata: pass:normal[xref:#MerkleProof-verifyCalldata-bytes32---bytes32-bytes32-[`++verifyCalldata++`]]
:processProof: pass:normal[xref:#MerkleProof-processProof-bytes32---bytes32-[`++processProof++`]]
:processProofCalldata: pass:normal[xref:#MerkleProof-processProofCalldata-bytes32---bytes32-[`++processProofCalldata++`]]
:multiProofVerify: pass:normal[xref:#MerkleProof-multiProofVerify-bytes32---bool---bytes32-bytes32---[`++multiProofVerify++`]]
:multiProofVerifyCalldata: pass:normal[xref:#MerkleProof-multiProofVerifyCalldata-bytes32---bool---bytes32-bytes32---[`++multiProofVerifyCalldata++`]]
:processMultiProof: pass:normal[xref:#MerkleProof-processMultiProof-bytes32---bool---bytes32---[`++processMultiProof++`]]
:processMultiProofCalldata: pass:normal[xref:#MerkleProof-processMultiProofCalldata-bytes32---bool---bytes32---[`++processMultiProofCalldata++`]]
:_hashPair: pass:normal[xref:#MerkleProof-_hashPair-bytes32-bytes32-[`++_hashPair++`]]
:_efficientHash: pass:normal[xref:#MerkleProof-_efficientHash-bytes32-bytes32-[`++_efficientHash++`]]

[.contract]
[[MerkleProof]]
=== `++MerkleProof++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/cryptography/MerkleProof.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/cryptography/MerkleProof.sol";
```

These functions deal with verification of Merkle Tree proofs.

The tree and the proofs can be generated using our
https://github.com/OpenZeppelin/merkle-tree[JavaScript library].
You will find a quickstart guide in the readme.

WARNING: You should avoid using leaf values that are 64 bytes long prior to
hashing, or use a hash function other than keccak256 for hashing leaves.
This is because the concatenation of a sorted pair of internal nodes in
the merkle tree could be reinterpreted as a leaf value.
OpenZeppelin's JavaScript library generates merkle trees that are safe
against this attack out of the box.

[.contract-index]
.Functions
--
* {xref-MerkleProof-verify-bytes32---bytes32-bytes32-}[`++verify(proof, root, leaf)++`]
* {xref-MerkleProof-verifyCalldata-bytes32---bytes32-bytes32-}[`++verifyCalldata(proof, root, leaf)++`]
* {xref-MerkleProof-processProof-bytes32---bytes32-}[`++processProof(proof, leaf)++`]
* {xref-MerkleProof-processProofCalldata-bytes32---bytes32-}[`++processProofCalldata(proof, leaf)++`]
* {xref-MerkleProof-multiProofVerify-bytes32---bool---bytes32-bytes32---}[`++multiProofVerify(proof, proofFlags, root, leaves)++`]
* {xref-MerkleProof-multiProofVerifyCalldata-bytes32---bool---bytes32-bytes32---}[`++multiProofVerifyCalldata(proof, proofFlags, root, leaves)++`]
* {xref-MerkleProof-processMultiProof-bytes32---bool---bytes32---}[`++processMultiProof(proof, proofFlags, leaves)++`]
* {xref-MerkleProof-processMultiProofCalldata-bytes32---bool---bytes32---}[`++processMultiProofCalldata(proof, proofFlags, leaves)++`]

--

[.contract-item]
[[MerkleProof-verify-bytes32---bytes32-bytes32-]]
==== `[.contract-item-name]#++verify++#++(bytes32[] proof, bytes32 root, bytes32 leaf) → bool++` [.item-kind]#internal#

Returns true if a `leaf` can be proved to be a part of a Merkle tree
defined by `root`. For this, a `proof` must be provided, containing
sibling hashes on the branch from the leaf to the root of the tree. Each
pair of leaves and each pair of pre-images are assumed to be sorted.

[.contract-item]
[[MerkleProof-verifyCalldata-bytes32---bytes32-bytes32-]]
==== `[.contract-item-name]#++verifyCalldata++#++(bytes32[] proof, bytes32 root, bytes32 leaf) → bool++` [.item-kind]#internal#

Calldata version of {verify}

_Available since v4.7._

[.contract-item]
[[MerkleProof-processProof-bytes32---bytes32-]]
==== `[.contract-item-name]#++processProof++#++(bytes32[] proof, bytes32 leaf) → bytes32++` [.item-kind]#internal#

Returns the rebuilt hash obtained by traversing a Merkle tree up
from `leaf` using `proof`. A `proof` is valid if and only if the rebuilt
hash matches the root of the tree. When processing the proof, the pairs
of leafs & pre-images are assumed to be sorted.

_Available since v4.4._

[.contract-item]
[[MerkleProof-processProofCalldata-bytes32---bytes32-]]
==== `[.contract-item-name]#++processProofCalldata++#++(bytes32[] proof, bytes32 leaf) → bytes32++` [.item-kind]#internal#

Calldata version of {processProof}

_Available since v4.7._

[.contract-item]
[[MerkleProof-multiProofVerify-bytes32---bool---bytes32-bytes32---]]
==== `[.contract-item-name]#++multiProofVerify++#++(bytes32[] proof, bool[] proofFlags, bytes32 root, bytes32[] leaves) → bool++` [.item-kind]#internal#

Returns true if the `leaves` can be simultaneously proven to be a part of a merkle tree defined by
`root`, according to `proof` and `proofFlags` as described in {processMultiProof}.

CAUTION: Not all merkle trees admit multiproofs. See {processMultiProof} for details.

_Available since v4.7._

[.contract-item]
[[MerkleProof-multiProofVerifyCalldata-bytes32---bool---bytes32-bytes32---]]
==== `[.contract-item-name]#++multiProofVerifyCalldata++#++(bytes32[] proof, bool[] proofFlags, bytes32 root, bytes32[] leaves) → bool++` [.item-kind]#internal#

Calldata version of {multiProofVerify}

CAUTION: Not all merkle trees admit multiproofs. See {processMultiProof} for details.

_Available since v4.7._

[.contract-item]
[[MerkleProof-processMultiProof-bytes32---bool---bytes32---]]
==== `[.contract-item-name]#++processMultiProof++#++(bytes32[] proof, bool[] proofFlags, bytes32[] leaves) → bytes32 merkleRoot++` [.item-kind]#internal#

Returns the root of a tree reconstructed from `leaves` and sibling nodes in `proof`. The reconstruction
proceeds by incrementally reconstructing all inner nodes by combining a leaf/inner node with either another
leaf/inner node or a proof sibling node, depending on whether each `proofFlags` item is true or false
respectively.

CAUTION: Not all merkle trees admit multiproofs. To use multiproofs, it is sufficient to ensure that: 1) the tree
is complete (but not necessarily perfect), 2) the leaves to be proven are in the opposite order they are in the
tree (i.e., as seen from right to left starting at the deepest layer and continuing at the next layer).

_Available since v4.7._

[.contract-item]
[[MerkleProof-processMultiProofCalldata-bytes32---bool---bytes32---]]
==== `[.contract-item-name]#++processMultiProofCalldata++#++(bytes32[] proof, bool[] proofFlags, bytes32[] leaves) → bytes32 merkleRoot++` [.item-kind]#internal#

Calldata version of {processMultiProof}.

CAUTION: Not all merkle trees admit multiproofs. See {processMultiProof} for details.

_Available since v4.7._

:_CACHED_DOMAIN_SEPARATOR: pass:normal[xref:#EIP712-_CACHED_DOMAIN_SEPARATOR-bytes32[`++_CACHED_DOMAIN_SEPARATOR++`]]
:_CACHED_CHAIN_ID: pass:normal[xref:#EIP712-_CACHED_CHAIN_ID-uint256[`++_CACHED_CHAIN_ID++`]]
:_CACHED_THIS: pass:normal[xref:#EIP712-_CACHED_THIS-address[`++_CACHED_THIS++`]]
:_HASHED_NAME: pass:normal[xref:#EIP712-_HASHED_NAME-bytes32[`++_HASHED_NAME++`]]
:_HASHED_VERSION: pass:normal[xref:#EIP712-_HASHED_VERSION-bytes32[`++_HASHED_VERSION++`]]
:_TYPE_HASH: pass:normal[xref:#EIP712-_TYPE_HASH-bytes32[`++_TYPE_HASH++`]]
:constructor: pass:normal[xref:#EIP712-constructor-string-string-[`++constructor++`]]
:_domainSeparatorV4: pass:normal[xref:#EIP712-_domainSeparatorV4--[`++_domainSeparatorV4++`]]
:_buildDomainSeparator: pass:normal[xref:#EIP712-_buildDomainSeparator-bytes32-bytes32-bytes32-[`++_buildDomainSeparator++`]]
:_hashTypedDataV4: pass:normal[xref:#EIP712-_hashTypedDataV4-bytes32-[`++_hashTypedDataV4++`]]

[.contract]
[[EIP712]]
=== `++EIP712++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/cryptography/EIP712.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/cryptography/EIP712.sol";
```

https://eips.ethereum.org/EIPS/eip-712[EIP 712] is a standard for hashing and signing of typed structured data.

The encoding specified in the EIP is very generic, and such a generic implementation in Solidity is not feasible,
thus this contract does not implement the encoding itself. Protocols need to implement the type-specific encoding
they need in their contracts using a combination of `abi.encode` and `keccak256`.

This contract implements the EIP 712 domain separator ({_domainSeparatorV4}) that is used as part of the encoding
scheme, and the final step of the encoding to obtain the message digest that is then signed via ECDSA
({_hashTypedDataV4}).

The implementation of the domain separator was designed to be as efficient as possible while still properly updating
the chain id to protect against replay attacks on an eventual fork of the chain.

NOTE: This contract implements the version of the encoding known as "v4", as implemented by the JSON RPC method
https://docs.metamask.io/guide/signing-data.html[`eth_signTypedDataV4` in MetaMask].

_Available since v3.4._

[.contract-index]
.Functions
--
* {xref-EIP712-constructor-string-string-}[`++constructor(name, version)++`]
* {xref-EIP712-_domainSeparatorV4--}[`++_domainSeparatorV4()++`]
* {xref-EIP712-_hashTypedDataV4-bytes32-}[`++_hashTypedDataV4(structHash)++`]

--

[.contract-item]
[[EIP712-constructor-string-string-]]
==== `[.contract-item-name]#++constructor++#++(string name, string version)++` [.item-kind]#internal#

Initializes the domain separator and parameter caches.

The meaning of `name` and `version` is specified in
https://eips.ethereum.org/EIPS/eip-712#definition-of-domainseparator[EIP 712]:

- `name`: the user readable name of the signing domain, i.e. the name of the DApp or the protocol.
- `version`: the current major version of the signing domain.

NOTE: These parameters cannot be changed except through a xref:learn::upgrading-smart-contracts.adoc[smart
contract upgrade].

[.contract-item]
[[EIP712-_domainSeparatorV4--]]
==== `[.contract-item-name]#++_domainSeparatorV4++#++() → bytes32++` [.item-kind]#internal#

Returns the domain separator for the current chain.

[.contract-item]
[[EIP712-_hashTypedDataV4-bytes32-]]
==== `[.contract-item-name]#++_hashTypedDataV4++#++(bytes32 structHash) → bytes32++` [.item-kind]#internal#

Given an already https://eips.ethereum.org/EIPS/eip-712#definition-of-hashstruct[hashed struct], this
function returns the hash of the fully encoded EIP712 message for this domain.

This hash can be used together with {ECDSA-recover} to obtain the signer of a message. For example:

```solidity
bytes32 digest = _hashTypedDataV4(keccak256(abi.encode(
    keccak256("Mail(address to,string contents)"),
    mailTo,
    keccak256(bytes(mailContents))
)));
address signer = ECDSA.recover(digest, signature);
```

== Escrow

:withdrawalAllowed: pass:normal[xref:#ConditionalEscrow-withdrawalAllowed-address-[`++withdrawalAllowed++`]]
:withdraw: pass:normal[xref:#ConditionalEscrow-withdraw-address-payable-[`++withdraw++`]]

[.contract]
[[ConditionalEscrow]]
=== `++ConditionalEscrow++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/escrow/ConditionalEscrow.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/escrow/ConditionalEscrow.sol";
```

Base abstract escrow to only allow withdrawal if a condition is met.
Intended usage: See {Escrow}. Same usage guidelines apply here.

[.contract-index]
.Functions
--
* {xref-ConditionalEscrow-withdrawalAllowed-address-}[`++withdrawalAllowed(payee)++`]
* {xref-ConditionalEscrow-withdraw-address-payable-}[`++withdraw(payee)++`]

[.contract-subindex-inherited]
.Escrow
* {xref-Escrow-depositsOf-address-}[`++depositsOf(payee)++`]
* {xref-Escrow-deposit-address-}[`++deposit(payee)++`]

[.contract-subindex-inherited]
.Ownable
* {xref-Ownable-owner--}[`++owner()++`]
* {xref-Ownable-_checkOwner--}[`++_checkOwner()++`]
* {xref-Ownable-renounceOwnership--}[`++renounceOwnership()++`]
* {xref-Ownable-transferOwnership-address-}[`++transferOwnership(newOwner)++`]
* {xref-Ownable-_transferOwnership-address-}[`++_transferOwnership(newOwner)++`]

--

[.contract-index]
.Events
--

[.contract-subindex-inherited]
.Escrow
* {xref-Escrow-Deposited-address-uint256-}[`++Deposited(payee, weiAmount)++`]
* {xref-Escrow-Withdrawn-address-uint256-}[`++Withdrawn(payee, weiAmount)++`]

[.contract-subindex-inherited]
.Ownable
* {xref-Ownable-OwnershipTransferred-address-address-}[`++OwnershipTransferred(previousOwner, newOwner)++`]

--

[.contract-item]
[[ConditionalEscrow-withdrawalAllowed-address-]]
==== `[.contract-item-name]#++withdrawalAllowed++#++(address payee) → bool++` [.item-kind]#public#

Returns whether an address is allowed to withdraw their funds. To be
implemented by derived contracts.

[.contract-item]
[[ConditionalEscrow-withdraw-address-payable-]]
==== `[.contract-item-name]#++withdraw++#++(address payable payee)++` [.item-kind]#public#

Withdraw accumulated balance for a payee, forwarding all gas to the
recipient.

WARNING: Forwarding all gas opens the door to reentrancy vulnerabilities.
Make sure you trust the recipient, or are either following the
checks-effects-interactions pattern or using {ReentrancyGuard}.

:Deposited: pass:normal[xref:#Escrow-Deposited-address-uint256-[`++Deposited++`]]
:Withdrawn: pass:normal[xref:#Escrow-Withdrawn-address-uint256-[`++Withdrawn++`]]
:_deposits: pass:normal[xref:#Escrow-_deposits-mapping-address----uint256-[`++_deposits++`]]
:depositsOf: pass:normal[xref:#Escrow-depositsOf-address-[`++depositsOf++`]]
:deposit: pass:normal[xref:#Escrow-deposit-address-[`++deposit++`]]
:withdraw: pass:normal[xref:#Escrow-withdraw-address-payable-[`++withdraw++`]]

[.contract]
[[Escrow]]
=== `++Escrow++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/escrow/Escrow.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/escrow/Escrow.sol";
```

Base escrow contract, holds funds designated for a payee until they
withdraw them.

Intended usage: This contract (and derived escrow contracts) should be a
standalone contract, that only interacts with the contract that instantiated
it. That way, it is guaranteed that all Ether will be handled according to
the `Escrow` rules, and there is no need to check for payable functions or
transfers in the inheritance tree. The contract that uses the escrow as its
payment method should be its owner, and provide public methods redirecting
to the escrow's deposit and withdraw.

[.contract-index]
.Functions
--
* {xref-Escrow-depositsOf-address-}[`++depositsOf(payee)++`]
* {xref-Escrow-deposit-address-}[`++deposit(payee)++`]
* {xref-Escrow-withdraw-address-payable-}[`++withdraw(payee)++`]

[.contract-subindex-inherited]
.Ownable
* {xref-Ownable-owner--}[`++owner()++`]
* {xref-Ownable-_checkOwner--}[`++_checkOwner()++`]
* {xref-Ownable-renounceOwnership--}[`++renounceOwnership()++`]
* {xref-Ownable-transferOwnership-address-}[`++transferOwnership(newOwner)++`]
* {xref-Ownable-_transferOwnership-address-}[`++_transferOwnership(newOwner)++`]

--

[.contract-index]
.Events
--
* {xref-Escrow-Deposited-address-uint256-}[`++Deposited(payee, weiAmount)++`]
* {xref-Escrow-Withdrawn-address-uint256-}[`++Withdrawn(payee, weiAmount)++`]

[.contract-subindex-inherited]
.Ownable
* {xref-Ownable-OwnershipTransferred-address-address-}[`++OwnershipTransferred(previousOwner, newOwner)++`]

--

[.contract-item]
[[Escrow-depositsOf-address-]]
==== `[.contract-item-name]#++depositsOf++#++(address payee) → uint256++` [.item-kind]#public#

[.contract-item]
[[Escrow-deposit-address-]]
==== `[.contract-item-name]#++deposit++#++(address payee)++` [.item-kind]#public#

Stores the sent amount as credit to be withdrawn.

[.contract-item]
[[Escrow-withdraw-address-payable-]]
==== `[.contract-item-name]#++withdraw++#++(address payable payee)++` [.item-kind]#public#

Withdraw accumulated balance for a payee, forwarding all gas to the
recipient.

WARNING: Forwarding all gas opens the door to reentrancy vulnerabilities.
Make sure you trust the recipient, or are either following the
checks-effects-interactions pattern or using {ReentrancyGuard}.

[.contract-item]
[[Escrow-Deposited-address-uint256-]]
==== `[.contract-item-name]#++Deposited++#++(address payee, uint256 weiAmount)++` [.item-kind]#event#

[.contract-item]
[[Escrow-Withdrawn-address-uint256-]]
==== `[.contract-item-name]#++Withdrawn++#++(address payee, uint256 weiAmount)++` [.item-kind]#event#

:State: pass:normal[xref:#RefundEscrow-State[`++State++`]]
:RefundsClosed: pass:normal[xref:#RefundEscrow-RefundsClosed--[`++RefundsClosed++`]]
:RefundsEnabled: pass:normal[xref:#RefundEscrow-RefundsEnabled--[`++RefundsEnabled++`]]
:_state: pass:normal[xref:#RefundEscrow-_state-enum-RefundEscrow-State[`++_state++`]]
:_beneficiary: pass:normal[xref:#RefundEscrow-_beneficiary-address-payable[`++_beneficiary++`]]
:constructor: pass:normal[xref:#RefundEscrow-constructor-address-payable-[`++constructor++`]]
:state: pass:normal[xref:#RefundEscrow-state--[`++state++`]]
:beneficiary: pass:normal[xref:#RefundEscrow-beneficiary--[`++beneficiary++`]]
:deposit: pass:normal[xref:#RefundEscrow-deposit-address-[`++deposit++`]]
:close: pass:normal[xref:#RefundEscrow-close--[`++close++`]]
:enableRefunds: pass:normal[xref:#RefundEscrow-enableRefunds--[`++enableRefunds++`]]
:beneficiaryWithdraw: pass:normal[xref:#RefundEscrow-beneficiaryWithdraw--[`++beneficiaryWithdraw++`]]
:withdrawalAllowed: pass:normal[xref:#RefundEscrow-withdrawalAllowed-address-[`++withdrawalAllowed++`]]

[.contract]
[[RefundEscrow]]
=== `++RefundEscrow++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/escrow/RefundEscrow.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/escrow/RefundEscrow.sol";
```

Escrow that holds funds for a beneficiary, deposited from multiple
parties.
Intended usage: See {Escrow}. Same usage guidelines apply here.
The owner account (that is, the contract that instantiates this
contract) may deposit, close the deposit period, and allow for either
withdrawal by the beneficiary, or refunds to the depositors. All interactions
with `RefundEscrow` will be made through the owner contract.

[.contract-index]
.Functions
--
* {xref-RefundEscrow-constructor-address-payable-}[`++constructor(beneficiary_)++`]
* {xref-RefundEscrow-state--}[`++state()++`]
* {xref-RefundEscrow-beneficiary--}[`++beneficiary()++`]
* {xref-RefundEscrow-deposit-address-}[`++deposit(refundee)++`]
* {xref-RefundEscrow-close--}[`++close()++`]
* {xref-RefundEscrow-enableRefunds--}[`++enableRefunds()++`]
* {xref-RefundEscrow-beneficiaryWithdraw--}[`++beneficiaryWithdraw()++`]
* {xref-RefundEscrow-withdrawalAllowed-address-}[`++withdrawalAllowed()++`]

[.contract-subindex-inherited]
.ConditionalEscrow
* {xref-ConditionalEscrow-withdraw-address-payable-}[`++withdraw(payee)++`]

[.contract-subindex-inherited]
.Escrow
* {xref-Escrow-depositsOf-address-}[`++depositsOf(payee)++`]

[.contract-subindex-inherited]
.Ownable
* {xref-Ownable-owner--}[`++owner()++`]
* {xref-Ownable-_checkOwner--}[`++_checkOwner()++`]
* {xref-Ownable-renounceOwnership--}[`++renounceOwnership()++`]
* {xref-Ownable-transferOwnership-address-}[`++transferOwnership(newOwner)++`]
* {xref-Ownable-_transferOwnership-address-}[`++_transferOwnership(newOwner)++`]

--

[.contract-index]
.Events
--
* {xref-RefundEscrow-RefundsClosed--}[`++RefundsClosed()++`]
* {xref-RefundEscrow-RefundsEnabled--}[`++RefundsEnabled()++`]

[.contract-subindex-inherited]
.ConditionalEscrow

[.contract-subindex-inherited]
.Escrow
* {xref-Escrow-Deposited-address-uint256-}[`++Deposited(payee, weiAmount)++`]
* {xref-Escrow-Withdrawn-address-uint256-}[`++Withdrawn(payee, weiAmount)++`]

[.contract-subindex-inherited]
.Ownable
* {xref-Ownable-OwnershipTransferred-address-address-}[`++OwnershipTransferred(previousOwner, newOwner)++`]

--

[.contract-item]
[[RefundEscrow-constructor-address-payable-]]
==== `[.contract-item-name]#++constructor++#++(address payable beneficiary_)++` [.item-kind]#public#

Constructor.

[.contract-item]
[[RefundEscrow-state--]]
==== `[.contract-item-name]#++state++#++() → enum RefundEscrow.State++` [.item-kind]#public#

[.contract-item]
[[RefundEscrow-beneficiary--]]
==== `[.contract-item-name]#++beneficiary++#++() → address payable++` [.item-kind]#public#

[.contract-item]
[[RefundEscrow-deposit-address-]]
==== `[.contract-item-name]#++deposit++#++(address refundee)++` [.item-kind]#public#

Stores funds that may later be refunded.

[.contract-item]
[[RefundEscrow-close--]]
==== `[.contract-item-name]#++close++#++()++` [.item-kind]#public#

Allows for the beneficiary to withdraw their funds, rejecting
further deposits.

[.contract-item]
[[RefundEscrow-enableRefunds--]]
==== `[.contract-item-name]#++enableRefunds++#++()++` [.item-kind]#public#

Allows for refunds to take place, rejecting further deposits.

[.contract-item]
[[RefundEscrow-beneficiaryWithdraw--]]
==== `[.contract-item-name]#++beneficiaryWithdraw++#++()++` [.item-kind]#public#

Withdraws the beneficiary's funds.

[.contract-item]
[[RefundEscrow-withdrawalAllowed-address-]]
==== `[.contract-item-name]#++withdrawalAllowed++#++(address) → bool++` [.item-kind]#public#

Returns whether refundees can withdraw their deposits (be refunded). The overridden function receives a
'payee' argument, but we ignore it here since the condition is global, not per-payee.

[.contract-item]
[[RefundEscrow-RefundsClosed--]]
==== `[.contract-item-name]#++RefundsClosed++#++()++` [.item-kind]#event#

[.contract-item]
[[RefundEscrow-RefundsEnabled--]]
==== `[.contract-item-name]#++RefundsEnabled++#++()++` [.item-kind]#event#

== Introspection

This set of interfaces and contracts deal with https://en.wikipedia.org/wiki/Type_introspection[type introspection] of contracts, that is, examining which functions can be called on them. This is usually referred to as a contract's _interface_.

Ethereum contracts have no native concept of an interface, so applications must usually simply trust they are not making an incorrect call. For trusted setups this is a non-issue, but often unknown and untrusted third-party addresses need to be interacted with. There may even not be any direct calls to them! (e.g. `ERC20` tokens may be sent to a contract that lacks a way to transfer them out of it, locking them forever). In these cases, a contract _declaring_ its interface can be very helpful in preventing errors.

There are two main ways to approach this.

* Locally, where a contract implements `IERC165` and declares an interface, and a second one queries it directly via `ERC165Checker`.
* Globally, where a global and unique registry (`IERC1820Registry`) is used to register implementers of a certain interface (`IERC1820Implementer`). It is then the registry that is queried, which allows for more complex setups, like contracts implementing interfaces for externally-owned accounts.

Note that, in all cases, accounts simply _declare_ their interfaces, but they are not required to actually implement them. This mechanism can therefore be used to both prevent errors and allow for complex interactions (see `ERC777`), but it must not be relied on for security.

:supportsInterface: pass:normal[xref:#IERC165-supportsInterface-bytes4-[`++supportsInterface++`]]

[.contract]
[[IERC165]]
=== `++IERC165++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/introspection/IERC165.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/introspection/IERC165.sol";
```

Interface of the ERC165 standard, as defined in the
https://eips.ethereum.org/EIPS/eip-165[EIP].

Implementers can declare support of contract interfaces, which can then be
queried by others ({ERC165Checker}).

For an implementation, see {ERC165}.

[.contract-index]
.Functions
--
* {xref-IERC165-supportsInterface-bytes4-}[`++supportsInterface(interfaceId)++`]

--

[.contract-item]
[[IERC165-supportsInterface-bytes4-]]
==== `[.contract-item-name]#++supportsInterface++#++(bytes4 interfaceId) → bool++` [.item-kind]#external#

Returns true if this contract implements the interface defined by
`interfaceId`. See the corresponding
https://eips.ethereum.org/EIPS/eip-165#how-interfaces-are-identified[EIP section]
to learn more about how these ids are created.

This function call must use less than 30 000 gas.

:supportsInterface: pass:normal[xref:#ERC165-supportsInterface-bytes4-[`++supportsInterface++`]]

[.contract]
[[ERC165]]
=== `++ERC165++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/introspection/ERC165.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/introspection/ERC165.sol";
```

Implementation of the {IERC165} interface.

Contracts that want to implement ERC165 should inherit from this contract and override {supportsInterface} to check
for the additional interface id that will be supported. For example:

```solidity
function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
    return interfaceId == type(MyInterface).interfaceId || super.supportsInterface(interfaceId);
}
```

Alternatively, {ERC165Storage} provides an easier to use but more expensive implementation.

[.contract-index]
.Functions
--
* {xref-ERC165-supportsInterface-bytes4-}[`++supportsInterface(interfaceId)++`]

[.contract-subindex-inherited]
.IERC165

--

[.contract-item]
[[ERC165-supportsInterface-bytes4-]]
==== `[.contract-item-name]#++supportsInterface++#++(bytes4 interfaceId) → bool++` [.item-kind]#public#

See {IERC165-supportsInterface}.

:_supportedInterfaces: pass:normal[xref:#ERC165Storage-_supportedInterfaces-mapping-bytes4----bool-[`++_supportedInterfaces++`]]
:supportsInterface: pass:normal[xref:#ERC165Storage-supportsInterface-bytes4-[`++supportsInterface++`]]
:_registerInterface: pass:normal[xref:#ERC165Storage-_registerInterface-bytes4-[`++_registerInterface++`]]

[.contract]
[[ERC165Storage]]
=== `++ERC165Storage++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/introspection/ERC165Storage.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/introspection/ERC165Storage.sol";
```

Storage based implementation of the {IERC165} interface.

Contracts may inherit from this and call {_registerInterface} to declare
their support of an interface.

[.contract-index]
.Functions
--
* {xref-ERC165Storage-supportsInterface-bytes4-}[`++supportsInterface(interfaceId)++`]
* {xref-ERC165Storage-_registerInterface-bytes4-}[`++_registerInterface(interfaceId)++`]

[.contract-subindex-inherited]
.ERC165

[.contract-subindex-inherited]
.IERC165

--

[.contract-item]
[[ERC165Storage-supportsInterface-bytes4-]]
==== `[.contract-item-name]#++supportsInterface++#++(bytes4 interfaceId) → bool++` [.item-kind]#public#

See {IERC165-supportsInterface}.

[.contract-item]
[[ERC165Storage-_registerInterface-bytes4-]]
==== `[.contract-item-name]#++_registerInterface++#++(bytes4 interfaceId)++` [.item-kind]#internal#

Registers the contract as an implementer of the interface defined by
`interfaceId`. Support of the actual ERC165 interface is automatic and
registering its interface id is not required.

See {IERC165-supportsInterface}.

Requirements:

- `interfaceId` cannot be the ERC165 invalid interface (`0xffffffff`).

:_INTERFACE_ID_INVALID: pass:normal[xref:#ERC165Checker-_INTERFACE_ID_INVALID-bytes4[`++_INTERFACE_ID_INVALID++`]]
:supportsERC165: pass:normal[xref:#ERC165Checker-supportsERC165-address-[`++supportsERC165++`]]
:supportsInterface: pass:normal[xref:#ERC165Checker-supportsInterface-address-bytes4-[`++supportsInterface++`]]
:getSupportedInterfaces: pass:normal[xref:#ERC165Checker-getSupportedInterfaces-address-bytes4---[`++getSupportedInterfaces++`]]
:supportsAllInterfaces: pass:normal[xref:#ERC165Checker-supportsAllInterfaces-address-bytes4---[`++supportsAllInterfaces++`]]
:supportsERC165InterfaceUnchecked: pass:normal[xref:#ERC165Checker-supportsERC165InterfaceUnchecked-address-bytes4-[`++supportsERC165InterfaceUnchecked++`]]

[.contract]
[[ERC165Checker]]
=== `++ERC165Checker++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/introspection/ERC165Checker.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/introspection/ERC165Checker.sol";
```

Library used to query support of an interface declared via {IERC165}.

Note that these functions return the actual result of the query: they do not
`revert` if an interface is not supported. It is up to the caller to decide
what to do in these cases.

[.contract-index]
.Functions
--
* {xref-ERC165Checker-supportsERC165-address-}[`++supportsERC165(account)++`]
* {xref-ERC165Checker-supportsInterface-address-bytes4-}[`++supportsInterface(account, interfaceId)++`]
* {xref-ERC165Checker-getSupportedInterfaces-address-bytes4---}[`++getSupportedInterfaces(account, interfaceIds)++`]
* {xref-ERC165Checker-supportsAllInterfaces-address-bytes4---}[`++supportsAllInterfaces(account, interfaceIds)++`]
* {xref-ERC165Checker-supportsERC165InterfaceUnchecked-address-bytes4-}[`++supportsERC165InterfaceUnchecked(account, interfaceId)++`]

--

[.contract-item]
[[ERC165Checker-supportsERC165-address-]]
==== `[.contract-item-name]#++supportsERC165++#++(address account) → bool++` [.item-kind]#internal#

Returns true if `account` supports the {IERC165} interface.

[.contract-item]
[[ERC165Checker-supportsInterface-address-bytes4-]]
==== `[.contract-item-name]#++supportsInterface++#++(address account, bytes4 interfaceId) → bool++` [.item-kind]#internal#

Returns true if `account` supports the interface defined by
`interfaceId`. Support for {IERC165} itself is queried automatically.

See {IERC165-supportsInterface}.

[.contract-item]
[[ERC165Checker-getSupportedInterfaces-address-bytes4---]]
==== `[.contract-item-name]#++getSupportedInterfaces++#++(address account, bytes4[] interfaceIds) → bool[]++` [.item-kind]#internal#

Returns a boolean array where each value corresponds to the
interfaces passed in and whether they're supported or not. This allows
you to batch check interfaces for a contract where your expectation
is that some interfaces may not be supported.

See {IERC165-supportsInterface}.

_Available since v3.4._

[.contract-item]
[[ERC165Checker-supportsAllInterfaces-address-bytes4---]]
==== `[.contract-item-name]#++supportsAllInterfaces++#++(address account, bytes4[] interfaceIds) → bool++` [.item-kind]#internal#

Returns true if `account` supports all the interfaces defined in
`interfaceIds`. Support for {IERC165} itself is queried automatically.

Batch-querying can lead to gas savings by skipping repeated checks for
{IERC165} support.

See {IERC165-supportsInterface}.

[.contract-item]
[[ERC165Checker-supportsERC165InterfaceUnchecked-address-bytes4-]]
==== `[.contract-item-name]#++supportsERC165InterfaceUnchecked++#++(address account, bytes4 interfaceId) → bool++` [.item-kind]#internal#

Assumes that account contains a contract that supports ERC165, otherwise
the behavior of this method is undefined. This precondition can be checked
with {supportsERC165}.
Interface identification is specified in ERC-165.

:InterfaceImplementerSet: pass:normal[xref:#IERC1820Registry-InterfaceImplementerSet-address-bytes32-address-[`++InterfaceImplementerSet++`]]
:ManagerChanged: pass:normal[xref:#IERC1820Registry-ManagerChanged-address-address-[`++ManagerChanged++`]]
:setManager: pass:normal[xref:#IERC1820Registry-setManager-address-address-[`++setManager++`]]
:getManager: pass:normal[xref:#IERC1820Registry-getManager-address-[`++getManager++`]]
:setInterfaceImplementer: pass:normal[xref:#IERC1820Registry-setInterfaceImplementer-address-bytes32-address-[`++setInterfaceImplementer++`]]
:getInterfaceImplementer: pass:normal[xref:#IERC1820Registry-getInterfaceImplementer-address-bytes32-[`++getInterfaceImplementer++`]]
:interfaceHash: pass:normal[xref:#IERC1820Registry-interfaceHash-string-[`++interfaceHash++`]]
:updateERC165Cache: pass:normal[xref:#IERC1820Registry-updateERC165Cache-address-bytes4-[`++updateERC165Cache++`]]
:implementsERC165Interface: pass:normal[xref:#IERC1820Registry-implementsERC165Interface-address-bytes4-[`++implementsERC165Interface++`]]
:implementsERC165InterfaceNoCache: pass:normal[xref:#IERC1820Registry-implementsERC165InterfaceNoCache-address-bytes4-[`++implementsERC165InterfaceNoCache++`]]

[.contract]
[[IERC1820Registry]]
=== `++IERC1820Registry++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/introspection/IERC1820Registry.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/introspection/IERC1820Registry.sol";
```

Interface of the global ERC1820 Registry, as defined in the
https://eips.ethereum.org/EIPS/eip-1820[EIP]. Accounts may register
implementers for interfaces in this registry, as well as query support.

Implementers may be shared by multiple accounts, and can also implement more
than a single interface for each account. Contracts can implement interfaces
for themselves, but externally-owned accounts (EOA) must delegate this to a
contract.

{IERC165} interfaces can also be queried via the registry.

For an in-depth explanation and source code analysis, see the EIP text.

[.contract-index]
.Functions
--
* {xref-IERC1820Registry-setManager-address-address-}[`++setManager(account, newManager)++`]
* {xref-IERC1820Registry-getManager-address-}[`++getManager(account)++`]
* {xref-IERC1820Registry-setInterfaceImplementer-address-bytes32-address-}[`++setInterfaceImplementer(account, _interfaceHash, implementer)++`]
* {xref-IERC1820Registry-getInterfaceImplementer-address-bytes32-}[`++getInterfaceImplementer(account, _interfaceHash)++`]
* {xref-IERC1820Registry-interfaceHash-string-}[`++interfaceHash(interfaceName)++`]
* {xref-IERC1820Registry-updateERC165Cache-address-bytes4-}[`++updateERC165Cache(account, interfaceId)++`]
* {xref-IERC1820Registry-implementsERC165Interface-address-bytes4-}[`++implementsERC165Interface(account, interfaceId)++`]
* {xref-IERC1820Registry-implementsERC165InterfaceNoCache-address-bytes4-}[`++implementsERC165InterfaceNoCache(account, interfaceId)++`]

--

[.contract-index]
.Events
--
* {xref-IERC1820Registry-InterfaceImplementerSet-address-bytes32-address-}[`++InterfaceImplementerSet(account, interfaceHash, implementer)++`]
* {xref-IERC1820Registry-ManagerChanged-address-address-}[`++ManagerChanged(account, newManager)++`]

--

[.contract-item]
[[IERC1820Registry-setManager-address-address-]]
==== `[.contract-item-name]#++setManager++#++(address account, address newManager)++` [.item-kind]#external#

Sets `newManager` as the manager for `account`. A manager of an
account is able to set interface implementers for it.

By default, each account is its own manager. Passing a value of `0x0` in
`newManager` will reset the manager to this initial state.

Emits a {ManagerChanged} event.

Requirements:

- the caller must be the current manager for `account`.

[.contract-item]
[[IERC1820Registry-getManager-address-]]
==== `[.contract-item-name]#++getManager++#++(address account) → address++` [.item-kind]#external#

Returns the manager for `account`.

See {setManager}.

[.contract-item]
[[IERC1820Registry-setInterfaceImplementer-address-bytes32-address-]]
==== `[.contract-item-name]#++setInterfaceImplementer++#++(address account, bytes32 _interfaceHash, address implementer)++` [.item-kind]#external#

Sets the `implementer` contract as ``account``'s implementer for
`interfaceHash`.

`account` being the zero address is an alias for the caller's address.
The zero address can also be used in `implementer` to remove an old one.

See {interfaceHash} to learn how these are created.

Emits an {InterfaceImplementerSet} event.

Requirements:

- the caller must be the current manager for `account`.
- `interfaceHash` must not be an {IERC165} interface id (i.e. it must not
end in 28 zeroes).
- `implementer` must implement {IERC1820Implementer} and return true when
queried for support, unless `implementer` is the caller. See
{IERC1820Implementer-canImplementInterfaceForAddress}.

[.contract-item]
[[IERC1820Registry-getInterfaceImplementer-address-bytes32-]]
==== `[.contract-item-name]#++getInterfaceImplementer++#++(address account, bytes32 _interfaceHash) → address++` [.item-kind]#external#

Returns the implementer of `interfaceHash` for `account`. If no such
implementer is registered, returns the zero address.

If `interfaceHash` is an {IERC165} interface id (i.e. it ends with 28
zeroes), `account` will be queried for support of it.

`account` being the zero address is an alias for the caller's address.

[.contract-item]
[[IERC1820Registry-interfaceHash-string-]]
==== `[.contract-item-name]#++interfaceHash++#++(string interfaceName) → bytes32++` [.item-kind]#external#

Returns the interface hash for an `interfaceName`, as defined in the
corresponding
https://eips.ethereum.org/EIPS/eip-1820#interface-name[section of the EIP].

[.contract-item]
[[IERC1820Registry-updateERC165Cache-address-bytes4-]]
==== `[.contract-item-name]#++updateERC165Cache++#++(address account, bytes4 interfaceId)++` [.item-kind]#external#

[.contract-item]
[[IERC1820Registry-implementsERC165Interface-address-bytes4-]]
==== `[.contract-item-name]#++implementsERC165Interface++#++(address account, bytes4 interfaceId) → bool++` [.item-kind]#external#

[.contract-item]
[[IERC1820Registry-implementsERC165InterfaceNoCache-address-bytes4-]]
==== `[.contract-item-name]#++implementsERC165InterfaceNoCache++#++(address account, bytes4 interfaceId) → bool++` [.item-kind]#external#

[.contract-item]
[[IERC1820Registry-InterfaceImplementerSet-address-bytes32-address-]]
==== `[.contract-item-name]#++InterfaceImplementerSet++#++(address account, bytes32 interfaceHash, address implementer)++` [.item-kind]#event#

[.contract-item]
[[IERC1820Registry-ManagerChanged-address-address-]]
==== `[.contract-item-name]#++ManagerChanged++#++(address account, address newManager)++` [.item-kind]#event#

:canImplementInterfaceForAddress: pass:normal[xref:#IERC1820Implementer-canImplementInterfaceForAddress-bytes32-address-[`++canImplementInterfaceForAddress++`]]

[.contract]
[[IERC1820Implementer]]
=== `++IERC1820Implementer++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/introspection/IERC1820Implementer.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/introspection/IERC1820Implementer.sol";
```

Interface for an ERC1820 implementer, as defined in the
https://eips.ethereum.org/EIPS/eip-1820#interface-implementation-erc1820implementerinterface[EIP].
Used by contracts that will be registered as implementers in the
{IERC1820Registry}.

[.contract-index]
.Functions
--
* {xref-IERC1820Implementer-canImplementInterfaceForAddress-bytes32-address-}[`++canImplementInterfaceForAddress(interfaceHash, account)++`]

--

[.contract-item]
[[IERC1820Implementer-canImplementInterfaceForAddress-bytes32-address-]]
==== `[.contract-item-name]#++canImplementInterfaceForAddress++#++(bytes32 interfaceHash, address account) → bytes32++` [.item-kind]#external#

Returns a special value (`ERC1820_ACCEPT_MAGIC`) if this contract
implements `interfaceHash` for `account`.

See {IERC1820Registry-setInterfaceImplementer}.

:_ERC1820_ACCEPT_MAGIC: pass:normal[xref:#ERC1820Implementer-_ERC1820_ACCEPT_MAGIC-bytes32[`++_ERC1820_ACCEPT_MAGIC++`]]
:_supportedInterfaces: pass:normal[xref:#ERC1820Implementer-_supportedInterfaces-mapping-bytes32----mapping-address----bool--[`++_supportedInterfaces++`]]
:canImplementInterfaceForAddress: pass:normal[xref:#ERC1820Implementer-canImplementInterfaceForAddress-bytes32-address-[`++canImplementInterfaceForAddress++`]]
:_registerInterfaceForAddress: pass:normal[xref:#ERC1820Implementer-_registerInterfaceForAddress-bytes32-address-[`++_registerInterfaceForAddress++`]]

[.contract]
[[ERC1820Implementer]]
=== `++ERC1820Implementer++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/introspection/ERC1820Implementer.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/introspection/ERC1820Implementer.sol";
```

Implementation of the {IERC1820Implementer} interface.

Contracts may inherit from this and call {_registerInterfaceForAddress} to
declare their willingness to be implementers.
{IERC1820Registry-setInterfaceImplementer} should then be called for the
registration to be complete.

[.contract-index]
.Functions
--
* {xref-ERC1820Implementer-canImplementInterfaceForAddress-bytes32-address-}[`++canImplementInterfaceForAddress(interfaceHash, account)++`]
* {xref-ERC1820Implementer-_registerInterfaceForAddress-bytes32-address-}[`++_registerInterfaceForAddress(interfaceHash, account)++`]

[.contract-subindex-inherited]
.IERC1820Implementer

--

[.contract-item]
[[ERC1820Implementer-canImplementInterfaceForAddress-bytes32-address-]]
==== `[.contract-item-name]#++canImplementInterfaceForAddress++#++(bytes32 interfaceHash, address account) → bytes32++` [.item-kind]#public#

See {IERC1820Implementer-canImplementInterfaceForAddress}.

[.contract-item]
[[ERC1820Implementer-_registerInterfaceForAddress-bytes32-address-]]
==== `[.contract-item-name]#++_registerInterfaceForAddress++#++(bytes32 interfaceHash, address account)++` [.item-kind]#internal#

Declares the contract as willing to be an implementer of
`interfaceHash` for `account`.

See {IERC1820Registry-setInterfaceImplementer} and
{IERC1820Registry-interfaceHash}.

== Data Structures

:BitMap: pass:normal[xref:#BitMaps-BitMap[`++BitMap++`]]
:get: pass:normal[xref:#BitMaps-get-struct-BitMaps-BitMap-uint256-[`++get++`]]
:setTo: pass:normal[xref:#BitMaps-setTo-struct-BitMaps-BitMap-uint256-bool-[`++setTo++`]]
:set: pass:normal[xref:#BitMaps-set-struct-BitMaps-BitMap-uint256-[`++set++`]]
:unset: pass:normal[xref:#BitMaps-unset-struct-BitMaps-BitMap-uint256-[`++unset++`]]

[.contract]
[[BitMaps]]
=== `++BitMaps++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/structs/BitMaps.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/structs/BitMaps.sol";
```

Library for managing uint256 to bool mapping in a compact and efficient way, providing the keys are sequential.
Largely inspired by Uniswap's https://github.com/Uniswap/merkle-distributor/blob/master/contracts/MerkleDistributor.sol[merkle-distributor].

[.contract-index]
.Functions
--
* {xref-BitMaps-get-struct-BitMaps-BitMap-uint256-}[`++get(bitmap, index)++`]
* {xref-BitMaps-setTo-struct-BitMaps-BitMap-uint256-bool-}[`++setTo(bitmap, index, value)++`]
* {xref-BitMaps-set-struct-BitMaps-BitMap-uint256-}[`++set(bitmap, index)++`]
* {xref-BitMaps-unset-struct-BitMaps-BitMap-uint256-}[`++unset(bitmap, index)++`]

--

[.contract-item]
[[BitMaps-get-struct-BitMaps-BitMap-uint256-]]
==== `[.contract-item-name]#++get++#++(struct BitMaps.BitMap bitmap, uint256 index) → bool++` [.item-kind]#internal#

Returns whether the bit at `index` is set.

[.contract-item]
[[BitMaps-setTo-struct-BitMaps-BitMap-uint256-bool-]]
==== `[.contract-item-name]#++setTo++#++(struct BitMaps.BitMap bitmap, uint256 index, bool value)++` [.item-kind]#internal#

Sets the bit at `index` to the boolean `value`.

[.contract-item]
[[BitMaps-set-struct-BitMaps-BitMap-uint256-]]
==== `[.contract-item-name]#++set++#++(struct BitMaps.BitMap bitmap, uint256 index)++` [.item-kind]#internal#

Sets the bit at `index`.

[.contract-item]
[[BitMaps-unset-struct-BitMaps-BitMap-uint256-]]
==== `[.contract-item-name]#++unset++#++(struct BitMaps.BitMap bitmap, uint256 index)++` [.item-kind]#internal#

Unsets the bit at `index`.

:Bytes32ToBytes32Map: pass:normal[xref:#EnumerableMap-Bytes32ToBytes32Map[`++Bytes32ToBytes32Map++`]]
:set: pass:normal[xref:#EnumerableMap-set-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-bytes32-[`++set++`]]
:remove: pass:normal[xref:#EnumerableMap-remove-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-[`++remove++`]]
:contains: pass:normal[xref:#EnumerableMap-contains-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-[`++contains++`]]
:length: pass:normal[xref:#EnumerableMap-length-struct-EnumerableMap-Bytes32ToBytes32Map-[`++length++`]]
:at: pass:normal[xref:#EnumerableMap-at-struct-EnumerableMap-Bytes32ToBytes32Map-uint256-[`++at++`]]
:tryGet: pass:normal[xref:#EnumerableMap-tryGet-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-[`++tryGet++`]]
:get: pass:normal[xref:#EnumerableMap-get-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-[`++get++`]]
:get: pass:normal[xref:#EnumerableMap-get-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-string-[`++get++`]]
:UintToUintMap: pass:normal[xref:#EnumerableMap-UintToUintMap[`++UintToUintMap++`]]
:set: pass:normal[xref:#EnumerableMap-set-struct-EnumerableMap-UintToUintMap-uint256-uint256-[`++set++`]]
:remove: pass:normal[xref:#EnumerableMap-remove-struct-EnumerableMap-UintToUintMap-uint256-[`++remove++`]]
:contains: pass:normal[xref:#EnumerableMap-contains-struct-EnumerableMap-UintToUintMap-uint256-[`++contains++`]]
:length: pass:normal[xref:#EnumerableMap-length-struct-EnumerableMap-UintToUintMap-[`++length++`]]
:at: pass:normal[xref:#EnumerableMap-at-struct-EnumerableMap-UintToUintMap-uint256-[`++at++`]]
:tryGet: pass:normal[xref:#EnumerableMap-tryGet-struct-EnumerableMap-UintToUintMap-uint256-[`++tryGet++`]]
:get: pass:normal[xref:#EnumerableMap-get-struct-EnumerableMap-UintToUintMap-uint256-[`++get++`]]
:get: pass:normal[xref:#EnumerableMap-get-struct-EnumerableMap-UintToUintMap-uint256-string-[`++get++`]]
:UintToAddressMap: pass:normal[xref:#EnumerableMap-UintToAddressMap[`++UintToAddressMap++`]]
:set: pass:normal[xref:#EnumerableMap-set-struct-EnumerableMap-UintToAddressMap-uint256-address-[`++set++`]]
:remove: pass:normal[xref:#EnumerableMap-remove-struct-EnumerableMap-UintToAddressMap-uint256-[`++remove++`]]
:contains: pass:normal[xref:#EnumerableMap-contains-struct-EnumerableMap-UintToAddressMap-uint256-[`++contains++`]]
:length: pass:normal[xref:#EnumerableMap-length-struct-EnumerableMap-UintToAddressMap-[`++length++`]]
:at: pass:normal[xref:#EnumerableMap-at-struct-EnumerableMap-UintToAddressMap-uint256-[`++at++`]]
:tryGet: pass:normal[xref:#EnumerableMap-tryGet-struct-EnumerableMap-UintToAddressMap-uint256-[`++tryGet++`]]
:get: pass:normal[xref:#EnumerableMap-get-struct-EnumerableMap-UintToAddressMap-uint256-[`++get++`]]
:get: pass:normal[xref:#EnumerableMap-get-struct-EnumerableMap-UintToAddressMap-uint256-string-[`++get++`]]
:AddressToUintMap: pass:normal[xref:#EnumerableMap-AddressToUintMap[`++AddressToUintMap++`]]
:set: pass:normal[xref:#EnumerableMap-set-struct-EnumerableMap-AddressToUintMap-address-uint256-[`++set++`]]
:remove: pass:normal[xref:#EnumerableMap-remove-struct-EnumerableMap-AddressToUintMap-address-[`++remove++`]]
:contains: pass:normal[xref:#EnumerableMap-contains-struct-EnumerableMap-AddressToUintMap-address-[`++contains++`]]
:length: pass:normal[xref:#EnumerableMap-length-struct-EnumerableMap-AddressToUintMap-[`++length++`]]
:at: pass:normal[xref:#EnumerableMap-at-struct-EnumerableMap-AddressToUintMap-uint256-[`++at++`]]
:tryGet: pass:normal[xref:#EnumerableMap-tryGet-struct-EnumerableMap-AddressToUintMap-address-[`++tryGet++`]]
:get: pass:normal[xref:#EnumerableMap-get-struct-EnumerableMap-AddressToUintMap-address-[`++get++`]]
:get: pass:normal[xref:#EnumerableMap-get-struct-EnumerableMap-AddressToUintMap-address-string-[`++get++`]]
:Bytes32ToUintMap: pass:normal[xref:#EnumerableMap-Bytes32ToUintMap[`++Bytes32ToUintMap++`]]
:set: pass:normal[xref:#EnumerableMap-set-struct-EnumerableMap-Bytes32ToUintMap-bytes32-uint256-[`++set++`]]
:remove: pass:normal[xref:#EnumerableMap-remove-struct-EnumerableMap-Bytes32ToUintMap-bytes32-[`++remove++`]]
:contains: pass:normal[xref:#EnumerableMap-contains-struct-EnumerableMap-Bytes32ToUintMap-bytes32-[`++contains++`]]
:length: pass:normal[xref:#EnumerableMap-length-struct-EnumerableMap-Bytes32ToUintMap-[`++length++`]]
:at: pass:normal[xref:#EnumerableMap-at-struct-EnumerableMap-Bytes32ToUintMap-uint256-[`++at++`]]
:tryGet: pass:normal[xref:#EnumerableMap-tryGet-struct-EnumerableMap-Bytes32ToUintMap-bytes32-[`++tryGet++`]]
:get: pass:normal[xref:#EnumerableMap-get-struct-EnumerableMap-Bytes32ToUintMap-bytes32-[`++get++`]]
:get: pass:normal[xref:#EnumerableMap-get-struct-EnumerableMap-Bytes32ToUintMap-bytes32-string-[`++get++`]]

[.contract]
[[EnumerableMap]]
=== `++EnumerableMap++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/structs/EnumerableMap.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/structs/EnumerableMap.sol";
```

Library for managing an enumerable variant of Solidity's
https://solidity.readthedocs.io/en/latest/types.html#mapping-types[`mapping`]
type.

Maps have the following properties:

- Entries are added, removed, and checked for existence in constant time
(O(1)).
- Entries are enumerated in O(n). No guarantees are made on the ordering.

```
contract Example {
    // Add the library methods
    using EnumerableMap for EnumerableMap.UintToAddressMap;

    // Declare a set state variable
    EnumerableMap.UintToAddressMap private myMap;
}
```

The following map types are supported:

- `uint256 -> address` (`UintToAddressMap`) since v3.0.0
- `address -> uint256` (`AddressToUintMap`) since v4.6.0
- `bytes32 -> bytes32` (`Bytes32ToBytes32Map`) since v4.6.0
- `uint256 -> uint256` (`UintToUintMap`) since v4.7.0
- `bytes32 -> uint256` (`Bytes32ToUintMap`) since v4.7.0

[WARNING]
====
Trying to delete such a structure from storage will likely result in data corruption, rendering the structure
unusable.
See https://github.com/ethereum/solidity/pull/11843[ethereum/solidity#11843] for more info.

In order to clean an EnumerableMap, you can either remove all elements one by one or create a fresh instance using an
array of EnumerableMap.
====

[.contract-index]
.Functions
--
* {xref-EnumerableMap-set-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-bytes32-}[`++set(map, key, value)++`]
* {xref-EnumerableMap-remove-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-}[`++remove(map, key)++`]
* {xref-EnumerableMap-contains-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-}[`++contains(map, key)++`]
* {xref-EnumerableMap-length-struct-EnumerableMap-Bytes32ToBytes32Map-}[`++length(map)++`]
* {xref-EnumerableMap-at-struct-EnumerableMap-Bytes32ToBytes32Map-uint256-}[`++at(map, index)++`]
* {xref-EnumerableMap-tryGet-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-}[`++tryGet(map, key)++`]
* {xref-EnumerableMap-get-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-}[`++get(map, key)++`]
* {xref-EnumerableMap-get-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-string-}[`++get(map, key, errorMessage)++`]
* {xref-EnumerableMap-set-struct-EnumerableMap-UintToUintMap-uint256-uint256-}[`++set(map, key, value)++`]
* {xref-EnumerableMap-remove-struct-EnumerableMap-UintToUintMap-uint256-}[`++remove(map, key)++`]
* {xref-EnumerableMap-contains-struct-EnumerableMap-UintToUintMap-uint256-}[`++contains(map, key)++`]
* {xref-EnumerableMap-length-struct-EnumerableMap-UintToUintMap-}[`++length(map)++`]
* {xref-EnumerableMap-at-struct-EnumerableMap-UintToUintMap-uint256-}[`++at(map, index)++`]
* {xref-EnumerableMap-tryGet-struct-EnumerableMap-UintToUintMap-uint256-}[`++tryGet(map, key)++`]
* {xref-EnumerableMap-get-struct-EnumerableMap-UintToUintMap-uint256-}[`++get(map, key)++`]
* {xref-EnumerableMap-get-struct-EnumerableMap-UintToUintMap-uint256-string-}[`++get(map, key, errorMessage)++`]
* {xref-EnumerableMap-set-struct-EnumerableMap-UintToAddressMap-uint256-address-}[`++set(map, key, value)++`]
* {xref-EnumerableMap-remove-struct-EnumerableMap-UintToAddressMap-uint256-}[`++remove(map, key)++`]
* {xref-EnumerableMap-contains-struct-EnumerableMap-UintToAddressMap-uint256-}[`++contains(map, key)++`]
* {xref-EnumerableMap-length-struct-EnumerableMap-UintToAddressMap-}[`++length(map)++`]
* {xref-EnumerableMap-at-struct-EnumerableMap-UintToAddressMap-uint256-}[`++at(map, index)++`]
* {xref-EnumerableMap-tryGet-struct-EnumerableMap-UintToAddressMap-uint256-}[`++tryGet(map, key)++`]
* {xref-EnumerableMap-get-struct-EnumerableMap-UintToAddressMap-uint256-}[`++get(map, key)++`]
* {xref-EnumerableMap-get-struct-EnumerableMap-UintToAddressMap-uint256-string-}[`++get(map, key, errorMessage)++`]
* {xref-EnumerableMap-set-struct-EnumerableMap-AddressToUintMap-address-uint256-}[`++set(map, key, value)++`]
* {xref-EnumerableMap-remove-struct-EnumerableMap-AddressToUintMap-address-}[`++remove(map, key)++`]
* {xref-EnumerableMap-contains-struct-EnumerableMap-AddressToUintMap-address-}[`++contains(map, key)++`]
* {xref-EnumerableMap-length-struct-EnumerableMap-AddressToUintMap-}[`++length(map)++`]
* {xref-EnumerableMap-at-struct-EnumerableMap-AddressToUintMap-uint256-}[`++at(map, index)++`]
* {xref-EnumerableMap-tryGet-struct-EnumerableMap-AddressToUintMap-address-}[`++tryGet(map, key)++`]
* {xref-EnumerableMap-get-struct-EnumerableMap-AddressToUintMap-address-}[`++get(map, key)++`]
* {xref-EnumerableMap-get-struct-EnumerableMap-AddressToUintMap-address-string-}[`++get(map, key, errorMessage)++`]
* {xref-EnumerableMap-set-struct-EnumerableMap-Bytes32ToUintMap-bytes32-uint256-}[`++set(map, key, value)++`]
* {xref-EnumerableMap-remove-struct-EnumerableMap-Bytes32ToUintMap-bytes32-}[`++remove(map, key)++`]
* {xref-EnumerableMap-contains-struct-EnumerableMap-Bytes32ToUintMap-bytes32-}[`++contains(map, key)++`]
* {xref-EnumerableMap-length-struct-EnumerableMap-Bytes32ToUintMap-}[`++length(map)++`]
* {xref-EnumerableMap-at-struct-EnumerableMap-Bytes32ToUintMap-uint256-}[`++at(map, index)++`]
* {xref-EnumerableMap-tryGet-struct-EnumerableMap-Bytes32ToUintMap-bytes32-}[`++tryGet(map, key)++`]
* {xref-EnumerableMap-get-struct-EnumerableMap-Bytes32ToUintMap-bytes32-}[`++get(map, key)++`]
* {xref-EnumerableMap-get-struct-EnumerableMap-Bytes32ToUintMap-bytes32-string-}[`++get(map, key, errorMessage)++`]

--

[.contract-item]
[[EnumerableMap-set-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-bytes32-]]
==== `[.contract-item-name]#++set++#++(struct EnumerableMap.Bytes32ToBytes32Map map, bytes32 key, bytes32 value) → bool++` [.item-kind]#internal#

Adds a key-value pair to a map, or updates the value for an existing
key. O(1).

Returns true if the key was added to the map, that is if it was not
already present.

[.contract-item]
[[EnumerableMap-remove-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-]]
==== `[.contract-item-name]#++remove++#++(struct EnumerableMap.Bytes32ToBytes32Map map, bytes32 key) → bool++` [.item-kind]#internal#

Removes a key-value pair from a map. O(1).

Returns true if the key was removed from the map, that is if it was present.

[.contract-item]
[[EnumerableMap-contains-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-]]
==== `[.contract-item-name]#++contains++#++(struct EnumerableMap.Bytes32ToBytes32Map map, bytes32 key) → bool++` [.item-kind]#internal#

Returns true if the key is in the map. O(1).

[.contract-item]
[[EnumerableMap-length-struct-EnumerableMap-Bytes32ToBytes32Map-]]
==== `[.contract-item-name]#++length++#++(struct EnumerableMap.Bytes32ToBytes32Map map) → uint256++` [.item-kind]#internal#

Returns the number of key-value pairs in the map. O(1).

[.contract-item]
[[EnumerableMap-at-struct-EnumerableMap-Bytes32ToBytes32Map-uint256-]]
==== `[.contract-item-name]#++at++#++(struct EnumerableMap.Bytes32ToBytes32Map map, uint256 index) → bytes32, bytes32++` [.item-kind]#internal#

Returns the key-value pair stored at position `index` in the map. O(1).

Note that there are no guarantees on the ordering of entries inside the
array, and it may change when more entries are added or removed.

Requirements:

- `index` must be strictly less than {length}.

[.contract-item]
[[EnumerableMap-tryGet-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-]]
==== `[.contract-item-name]#++tryGet++#++(struct EnumerableMap.Bytes32ToBytes32Map map, bytes32 key) → bool, bytes32++` [.item-kind]#internal#

Tries to returns the value associated with `key`. O(1).
Does not revert if `key` is not in the map.

[.contract-item]
[[EnumerableMap-get-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-]]
==== `[.contract-item-name]#++get++#++(struct EnumerableMap.Bytes32ToBytes32Map map, bytes32 key) → bytes32++` [.item-kind]#internal#

Returns the value associated with `key`. O(1).

Requirements:

- `key` must be in the map.

[.contract-item]
[[EnumerableMap-get-struct-EnumerableMap-Bytes32ToBytes32Map-bytes32-string-]]
==== `[.contract-item-name]#++get++#++(struct EnumerableMap.Bytes32ToBytes32Map map, bytes32 key, string errorMessage) → bytes32++` [.item-kind]#internal#

Same as {get}, with a custom error message when `key` is not in the map.

CAUTION: This function is deprecated because it requires allocating memory for the error
message unnecessarily. For custom revert reasons use {tryGet}.

[.contract-item]
[[EnumerableMap-set-struct-EnumerableMap-UintToUintMap-uint256-uint256-]]
==== `[.contract-item-name]#++set++#++(struct EnumerableMap.UintToUintMap map, uint256 key, uint256 value) → bool++` [.item-kind]#internal#

Adds a key-value pair to a map, or updates the value for an existing
key. O(1).

Returns true if the key was added to the map, that is if it was not
already present.

[.contract-item]
[[EnumerableMap-remove-struct-EnumerableMap-UintToUintMap-uint256-]]
==== `[.contract-item-name]#++remove++#++(struct EnumerableMap.UintToUintMap map, uint256 key) → bool++` [.item-kind]#internal#

Removes a value from a set. O(1).

Returns true if the key was removed from the map, that is if it was present.

[.contract-item]
[[EnumerableMap-contains-struct-EnumerableMap-UintToUintMap-uint256-]]
==== `[.contract-item-name]#++contains++#++(struct EnumerableMap.UintToUintMap map, uint256 key) → bool++` [.item-kind]#internal#

Returns true if the key is in the map. O(1).

[.contract-item]
[[EnumerableMap-length-struct-EnumerableMap-UintToUintMap-]]
==== `[.contract-item-name]#++length++#++(struct EnumerableMap.UintToUintMap map) → uint256++` [.item-kind]#internal#

Returns the number of elements in the map. O(1).

[.contract-item]
[[EnumerableMap-at-struct-EnumerableMap-UintToUintMap-uint256-]]
==== `[.contract-item-name]#++at++#++(struct EnumerableMap.UintToUintMap map, uint256 index) → uint256, uint256++` [.item-kind]#internal#

Returns the element stored at position `index` in the set. O(1).
Note that there are no guarantees on the ordering of values inside the
array, and it may change when more values are added or removed.

Requirements:

- `index` must be strictly less than {length}.

[.contract-item]
[[EnumerableMap-tryGet-struct-EnumerableMap-UintToUintMap-uint256-]]
==== `[.contract-item-name]#++tryGet++#++(struct EnumerableMap.UintToUintMap map, uint256 key) → bool, uint256++` [.item-kind]#internal#

Tries to returns the value associated with `key`. O(1).
Does not revert if `key` is not in the map.

[.contract-item]
[[EnumerableMap-get-struct-EnumerableMap-UintToUintMap-uint256-]]
==== `[.contract-item-name]#++get++#++(struct EnumerableMap.UintToUintMap map, uint256 key) → uint256++` [.item-kind]#internal#

Returns the value associated with `key`. O(1).

Requirements:

- `key` must be in the map.

[.contract-item]
[[EnumerableMap-get-struct-EnumerableMap-UintToUintMap-uint256-string-]]
==== `[.contract-item-name]#++get++#++(struct EnumerableMap.UintToUintMap map, uint256 key, string errorMessage) → uint256++` [.item-kind]#internal#

Same as {get}, with a custom error message when `key` is not in the map.

CAUTION: This function is deprecated because it requires allocating memory for the error
message unnecessarily. For custom revert reasons use {tryGet}.

[.contract-item]
[[EnumerableMap-set-struct-EnumerableMap-UintToAddressMap-uint256-address-]]
==== `[.contract-item-name]#++set++#++(struct EnumerableMap.UintToAddressMap map, uint256 key, address value) → bool++` [.item-kind]#internal#

Adds a key-value pair to a map, or updates the value for an existing
key. O(1).

Returns true if the key was added to the map, that is if it was not
already present.

[.contract-item]
[[EnumerableMap-remove-struct-EnumerableMap-UintToAddressMap-uint256-]]
==== `[.contract-item-name]#++remove++#++(struct EnumerableMap.UintToAddressMap map, uint256 key) → bool++` [.item-kind]#internal#

Removes a value from a set. O(1).

Returns true if the key was removed from the map, that is if it was present.

[.contract-item]
[[EnumerableMap-contains-struct-EnumerableMap-UintToAddressMap-uint256-]]
==== `[.contract-item-name]#++contains++#++(struct EnumerableMap.UintToAddressMap map, uint256 key) → bool++` [.item-kind]#internal#

Returns true if the key is in the map. O(1).

[.contract-item]
[[EnumerableMap-length-struct-EnumerableMap-UintToAddressMap-]]
==== `[.contract-item-name]#++length++#++(struct EnumerableMap.UintToAddressMap map) → uint256++` [.item-kind]#internal#

Returns the number of elements in the map. O(1).

[.contract-item]
[[EnumerableMap-at-struct-EnumerableMap-UintToAddressMap-uint256-]]
==== `[.contract-item-name]#++at++#++(struct EnumerableMap.UintToAddressMap map, uint256 index) → uint256, address++` [.item-kind]#internal#

Returns the element stored at position `index` in the set. O(1).
Note that there are no guarantees on the ordering of values inside the
array, and it may change when more values are added or removed.

Requirements:

- `index` must be strictly less than {length}.

[.contract-item]
[[EnumerableMap-tryGet-struct-EnumerableMap-UintToAddressMap-uint256-]]
==== `[.contract-item-name]#++tryGet++#++(struct EnumerableMap.UintToAddressMap map, uint256 key) → bool, address++` [.item-kind]#internal#

Tries to returns the value associated with `key`. O(1).
Does not revert if `key` is not in the map.

[.contract-item]
[[EnumerableMap-get-struct-EnumerableMap-UintToAddressMap-uint256-]]
==== `[.contract-item-name]#++get++#++(struct EnumerableMap.UintToAddressMap map, uint256 key) → address++` [.item-kind]#internal#

Returns the value associated with `key`. O(1).

Requirements:

- `key` must be in the map.

[.contract-item]
[[EnumerableMap-get-struct-EnumerableMap-UintToAddressMap-uint256-string-]]
==== `[.contract-item-name]#++get++#++(struct EnumerableMap.UintToAddressMap map, uint256 key, string errorMessage) → address++` [.item-kind]#internal#

Same as {get}, with a custom error message when `key` is not in the map.

CAUTION: This function is deprecated because it requires allocating memory for the error
message unnecessarily. For custom revert reasons use {tryGet}.

[.contract-item]
[[EnumerableMap-set-struct-EnumerableMap-AddressToUintMap-address-uint256-]]
==== `[.contract-item-name]#++set++#++(struct EnumerableMap.AddressToUintMap map, address key, uint256 value) → bool++` [.item-kind]#internal#

Adds a key-value pair to a map, or updates the value for an existing
key. O(1).

Returns true if the key was added to the map, that is if it was not
already present.

[.contract-item]
[[EnumerableMap-remove-struct-EnumerableMap-AddressToUintMap-address-]]
==== `[.contract-item-name]#++remove++#++(struct EnumerableMap.AddressToUintMap map, address key) → bool++` [.item-kind]#internal#

Removes a value from a set. O(1).

Returns true if the key was removed from the map, that is if it was present.

[.contract-item]
[[EnumerableMap-contains-struct-EnumerableMap-AddressToUintMap-address-]]
==== `[.contract-item-name]#++contains++#++(struct EnumerableMap.AddressToUintMap map, address key) → bool++` [.item-kind]#internal#

Returns true if the key is in the map. O(1).

[.contract-item]
[[EnumerableMap-length-struct-EnumerableMap-AddressToUintMap-]]
==== `[.contract-item-name]#++length++#++(struct EnumerableMap.AddressToUintMap map) → uint256++` [.item-kind]#internal#

Returns the number of elements in the map. O(1).

[.contract-item]
[[EnumerableMap-at-struct-EnumerableMap-AddressToUintMap-uint256-]]
==== `[.contract-item-name]#++at++#++(struct EnumerableMap.AddressToUintMap map, uint256 index) → address, uint256++` [.item-kind]#internal#

Returns the element stored at position `index` in the set. O(1).
Note that there are no guarantees on the ordering of values inside the
array, and it may change when more values are added or removed.

Requirements:

- `index` must be strictly less than {length}.

[.contract-item]
[[EnumerableMap-tryGet-struct-EnumerableMap-AddressToUintMap-address-]]
==== `[.contract-item-name]#++tryGet++#++(struct EnumerableMap.AddressToUintMap map, address key) → bool, uint256++` [.item-kind]#internal#

Tries to returns the value associated with `key`. O(1).
Does not revert if `key` is not in the map.

[.contract-item]
[[EnumerableMap-get-struct-EnumerableMap-AddressToUintMap-address-]]
==== `[.contract-item-name]#++get++#++(struct EnumerableMap.AddressToUintMap map, address key) → uint256++` [.item-kind]#internal#

Returns the value associated with `key`. O(1).

Requirements:

- `key` must be in the map.

[.contract-item]
[[EnumerableMap-get-struct-EnumerableMap-AddressToUintMap-address-string-]]
==== `[.contract-item-name]#++get++#++(struct EnumerableMap.AddressToUintMap map, address key, string errorMessage) → uint256++` [.item-kind]#internal#

Same as {get}, with a custom error message when `key` is not in the map.

CAUTION: This function is deprecated because it requires allocating memory for the error
message unnecessarily. For custom revert reasons use {tryGet}.

[.contract-item]
[[EnumerableMap-set-struct-EnumerableMap-Bytes32ToUintMap-bytes32-uint256-]]
==== `[.contract-item-name]#++set++#++(struct EnumerableMap.Bytes32ToUintMap map, bytes32 key, uint256 value) → bool++` [.item-kind]#internal#

Adds a key-value pair to a map, or updates the value for an existing
key. O(1).

Returns true if the key was added to the map, that is if it was not
already present.

[.contract-item]
[[EnumerableMap-remove-struct-EnumerableMap-Bytes32ToUintMap-bytes32-]]
==== `[.contract-item-name]#++remove++#++(struct EnumerableMap.Bytes32ToUintMap map, bytes32 key) → bool++` [.item-kind]#internal#

Removes a value from a set. O(1).

Returns true if the key was removed from the map, that is if it was present.

[.contract-item]
[[EnumerableMap-contains-struct-EnumerableMap-Bytes32ToUintMap-bytes32-]]
==== `[.contract-item-name]#++contains++#++(struct EnumerableMap.Bytes32ToUintMap map, bytes32 key) → bool++` [.item-kind]#internal#

Returns true if the key is in the map. O(1).

[.contract-item]
[[EnumerableMap-length-struct-EnumerableMap-Bytes32ToUintMap-]]
==== `[.contract-item-name]#++length++#++(struct EnumerableMap.Bytes32ToUintMap map) → uint256++` [.item-kind]#internal#

Returns the number of elements in the map. O(1).

[.contract-item]
[[EnumerableMap-at-struct-EnumerableMap-Bytes32ToUintMap-uint256-]]
==== `[.contract-item-name]#++at++#++(struct EnumerableMap.Bytes32ToUintMap map, uint256 index) → bytes32, uint256++` [.item-kind]#internal#

Returns the element stored at position `index` in the set. O(1).
Note that there are no guarantees on the ordering of values inside the
array, and it may change when more values are added or removed.

Requirements:

- `index` must be strictly less than {length}.

[.contract-item]
[[EnumerableMap-tryGet-struct-EnumerableMap-Bytes32ToUintMap-bytes32-]]
==== `[.contract-item-name]#++tryGet++#++(struct EnumerableMap.Bytes32ToUintMap map, bytes32 key) → bool, uint256++` [.item-kind]#internal#

Tries to returns the value associated with `key`. O(1).
Does not revert if `key` is not in the map.

[.contract-item]
[[EnumerableMap-get-struct-EnumerableMap-Bytes32ToUintMap-bytes32-]]
==== `[.contract-item-name]#++get++#++(struct EnumerableMap.Bytes32ToUintMap map, bytes32 key) → uint256++` [.item-kind]#internal#

Returns the value associated with `key`. O(1).

Requirements:

- `key` must be in the map.

[.contract-item]
[[EnumerableMap-get-struct-EnumerableMap-Bytes32ToUintMap-bytes32-string-]]
==== `[.contract-item-name]#++get++#++(struct EnumerableMap.Bytes32ToUintMap map, bytes32 key, string errorMessage) → uint256++` [.item-kind]#internal#

Same as {get}, with a custom error message when `key` is not in the map.

CAUTION: This function is deprecated because it requires allocating memory for the error
message unnecessarily. For custom revert reasons use {tryGet}.

:Set: pass:normal[xref:#EnumerableSet-Set[`++Set++`]]
:_add: pass:normal[xref:#EnumerableSet-_add-struct-EnumerableSet-Set-bytes32-[`++_add++`]]
:_remove: pass:normal[xref:#EnumerableSet-_remove-struct-EnumerableSet-Set-bytes32-[`++_remove++`]]
:_contains: pass:normal[xref:#EnumerableSet-_contains-struct-EnumerableSet-Set-bytes32-[`++_contains++`]]
:_length: pass:normal[xref:#EnumerableSet-_length-struct-EnumerableSet-Set-[`++_length++`]]
:_at: pass:normal[xref:#EnumerableSet-_at-struct-EnumerableSet-Set-uint256-[`++_at++`]]
:_values: pass:normal[xref:#EnumerableSet-_values-struct-EnumerableSet-Set-[`++_values++`]]
:Bytes32Set: pass:normal[xref:#EnumerableSet-Bytes32Set[`++Bytes32Set++`]]
:add: pass:normal[xref:#EnumerableSet-add-struct-EnumerableSet-Bytes32Set-bytes32-[`++add++`]]
:remove: pass:normal[xref:#EnumerableSet-remove-struct-EnumerableSet-Bytes32Set-bytes32-[`++remove++`]]
:contains: pass:normal[xref:#EnumerableSet-contains-struct-EnumerableSet-Bytes32Set-bytes32-[`++contains++`]]
:length: pass:normal[xref:#EnumerableSet-length-struct-EnumerableSet-Bytes32Set-[`++length++`]]
:at: pass:normal[xref:#EnumerableSet-at-struct-EnumerableSet-Bytes32Set-uint256-[`++at++`]]
:values: pass:normal[xref:#EnumerableSet-values-struct-EnumerableSet-Bytes32Set-[`++values++`]]
:AddressSet: pass:normal[xref:#EnumerableSet-AddressSet[`++AddressSet++`]]
:add: pass:normal[xref:#EnumerableSet-add-struct-EnumerableSet-AddressSet-address-[`++add++`]]
:remove: pass:normal[xref:#EnumerableSet-remove-struct-EnumerableSet-AddressSet-address-[`++remove++`]]
:contains: pass:normal[xref:#EnumerableSet-contains-struct-EnumerableSet-AddressSet-address-[`++contains++`]]
:length: pass:normal[xref:#EnumerableSet-length-struct-EnumerableSet-AddressSet-[`++length++`]]
:at: pass:normal[xref:#EnumerableSet-at-struct-EnumerableSet-AddressSet-uint256-[`++at++`]]
:values: pass:normal[xref:#EnumerableSet-values-struct-EnumerableSet-AddressSet-[`++values++`]]
:UintSet: pass:normal[xref:#EnumerableSet-UintSet[`++UintSet++`]]
:add: pass:normal[xref:#EnumerableSet-add-struct-EnumerableSet-UintSet-uint256-[`++add++`]]
:remove: pass:normal[xref:#EnumerableSet-remove-struct-EnumerableSet-UintSet-uint256-[`++remove++`]]
:contains: pass:normal[xref:#EnumerableSet-contains-struct-EnumerableSet-UintSet-uint256-[`++contains++`]]
:length: pass:normal[xref:#EnumerableSet-length-struct-EnumerableSet-UintSet-[`++length++`]]
:at: pass:normal[xref:#EnumerableSet-at-struct-EnumerableSet-UintSet-uint256-[`++at++`]]
:values: pass:normal[xref:#EnumerableSet-values-struct-EnumerableSet-UintSet-[`++values++`]]

[.contract]
[[EnumerableSet]]
=== `++EnumerableSet++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/structs/EnumerableSet.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/structs/EnumerableSet.sol";
```

Library for managing
https://en.wikipedia.org/wiki/Set_(abstract_data_type)[sets] of primitive
types.

Sets have the following properties:

- Elements are added, removed, and checked for existence in constant time
(O(1)).
- Elements are enumerated in O(n). No guarantees are made on the ordering.

```
contract Example {
    // Add the library methods
    using EnumerableSet for EnumerableSet.AddressSet;

    // Declare a set state variable
    EnumerableSet.AddressSet private mySet;
}
```

As of v3.3.0, sets of type `bytes32` (`Bytes32Set`), `address` (`AddressSet`)
and `uint256` (`UintSet`) are supported.

[WARNING]
====
Trying to delete such a structure from storage will likely result in data corruption, rendering the structure
unusable.
See https://github.com/ethereum/solidity/pull/11843[ethereum/solidity#11843] for more info.

In order to clean an EnumerableSet, you can either remove all elements one by one or create a fresh instance using an
array of EnumerableSet.
====

[.contract-index]
.Functions
--
* {xref-EnumerableSet-add-struct-EnumerableSet-Bytes32Set-bytes32-}[`++add(set, value)++`]
* {xref-EnumerableSet-remove-struct-EnumerableSet-Bytes32Set-bytes32-}[`++remove(set, value)++`]
* {xref-EnumerableSet-contains-struct-EnumerableSet-Bytes32Set-bytes32-}[`++contains(set, value)++`]
* {xref-EnumerableSet-length-struct-EnumerableSet-Bytes32Set-}[`++length(set)++`]
* {xref-EnumerableSet-at-struct-EnumerableSet-Bytes32Set-uint256-}[`++at(set, index)++`]
* {xref-EnumerableSet-values-struct-EnumerableSet-Bytes32Set-}[`++values(set)++`]
* {xref-EnumerableSet-add-struct-EnumerableSet-AddressSet-address-}[`++add(set, value)++`]
* {xref-EnumerableSet-remove-struct-EnumerableSet-AddressSet-address-}[`++remove(set, value)++`]
* {xref-EnumerableSet-contains-struct-EnumerableSet-AddressSet-address-}[`++contains(set, value)++`]
* {xref-EnumerableSet-length-struct-EnumerableSet-AddressSet-}[`++length(set)++`]
* {xref-EnumerableSet-at-struct-EnumerableSet-AddressSet-uint256-}[`++at(set, index)++`]
* {xref-EnumerableSet-values-struct-EnumerableSet-AddressSet-}[`++values(set)++`]
* {xref-EnumerableSet-add-struct-EnumerableSet-UintSet-uint256-}[`++add(set, value)++`]
* {xref-EnumerableSet-remove-struct-EnumerableSet-UintSet-uint256-}[`++remove(set, value)++`]
* {xref-EnumerableSet-contains-struct-EnumerableSet-UintSet-uint256-}[`++contains(set, value)++`]
* {xref-EnumerableSet-length-struct-EnumerableSet-UintSet-}[`++length(set)++`]
* {xref-EnumerableSet-at-struct-EnumerableSet-UintSet-uint256-}[`++at(set, index)++`]
* {xref-EnumerableSet-values-struct-EnumerableSet-UintSet-}[`++values(set)++`]

--

[.contract-item]
[[EnumerableSet-add-struct-EnumerableSet-Bytes32Set-bytes32-]]
==== `[.contract-item-name]#++add++#++(struct EnumerableSet.Bytes32Set set, bytes32 value) → bool++` [.item-kind]#internal#

Add a value to a set. O(1).

Returns true if the value was added to the set, that is if it was not
already present.

[.contract-item]
[[EnumerableSet-remove-struct-EnumerableSet-Bytes32Set-bytes32-]]
==== `[.contract-item-name]#++remove++#++(struct EnumerableSet.Bytes32Set set, bytes32 value) → bool++` [.item-kind]#internal#

Removes a value from a set. O(1).

Returns true if the value was removed from the set, that is if it was
present.

[.contract-item]
[[EnumerableSet-contains-struct-EnumerableSet-Bytes32Set-bytes32-]]
==== `[.contract-item-name]#++contains++#++(struct EnumerableSet.Bytes32Set set, bytes32 value) → bool++` [.item-kind]#internal#

Returns true if the value is in the set. O(1).

[.contract-item]
[[EnumerableSet-length-struct-EnumerableSet-Bytes32Set-]]
==== `[.contract-item-name]#++length++#++(struct EnumerableSet.Bytes32Set set) → uint256++` [.item-kind]#internal#

Returns the number of values in the set. O(1).

[.contract-item]
[[EnumerableSet-at-struct-EnumerableSet-Bytes32Set-uint256-]]
==== `[.contract-item-name]#++at++#++(struct EnumerableSet.Bytes32Set set, uint256 index) → bytes32++` [.item-kind]#internal#

Returns the value stored at position `index` in the set. O(1).

Note that there are no guarantees on the ordering of values inside the
array, and it may change when more values are added or removed.

Requirements:

- `index` must be strictly less than {length}.

[.contract-item]
[[EnumerableSet-values-struct-EnumerableSet-Bytes32Set-]]
==== `[.contract-item-name]#++values++#++(struct EnumerableSet.Bytes32Set set) → bytes32[]++` [.item-kind]#internal#

Return the entire set in an array

WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
this function has an unbounded cost, and using it as part of a state-changing function may render the function
uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.

[.contract-item]
[[EnumerableSet-add-struct-EnumerableSet-AddressSet-address-]]
==== `[.contract-item-name]#++add++#++(struct EnumerableSet.AddressSet set, address value) → bool++` [.item-kind]#internal#

Add a value to a set. O(1).

Returns true if the value was added to the set, that is if it was not
already present.

[.contract-item]
[[EnumerableSet-remove-struct-EnumerableSet-AddressSet-address-]]
==== `[.contract-item-name]#++remove++#++(struct EnumerableSet.AddressSet set, address value) → bool++` [.item-kind]#internal#

Removes a value from a set. O(1).

Returns true if the value was removed from the set, that is if it was
present.

[.contract-item]
[[EnumerableSet-contains-struct-EnumerableSet-AddressSet-address-]]
==== `[.contract-item-name]#++contains++#++(struct EnumerableSet.AddressSet set, address value) → bool++` [.item-kind]#internal#

Returns true if the value is in the set. O(1).

[.contract-item]
[[EnumerableSet-length-struct-EnumerableSet-AddressSet-]]
==== `[.contract-item-name]#++length++#++(struct EnumerableSet.AddressSet set) → uint256++` [.item-kind]#internal#

Returns the number of values in the set. O(1).

[.contract-item]
[[EnumerableSet-at-struct-EnumerableSet-AddressSet-uint256-]]
==== `[.contract-item-name]#++at++#++(struct EnumerableSet.AddressSet set, uint256 index) → address++` [.item-kind]#internal#

Returns the value stored at position `index` in the set. O(1).

Note that there are no guarantees on the ordering of values inside the
array, and it may change when more values are added or removed.

Requirements:

- `index` must be strictly less than {length}.

[.contract-item]
[[EnumerableSet-values-struct-EnumerableSet-AddressSet-]]
==== `[.contract-item-name]#++values++#++(struct EnumerableSet.AddressSet set) → address[]++` [.item-kind]#internal#

Return the entire set in an array

WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
this function has an unbounded cost, and using it as part of a state-changing function may render the function
uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.

[.contract-item]
[[EnumerableSet-add-struct-EnumerableSet-UintSet-uint256-]]
==== `[.contract-item-name]#++add++#++(struct EnumerableSet.UintSet set, uint256 value) → bool++` [.item-kind]#internal#

Add a value to a set. O(1).

Returns true if the value was added to the set, that is if it was not
already present.

[.contract-item]
[[EnumerableSet-remove-struct-EnumerableSet-UintSet-uint256-]]
==== `[.contract-item-name]#++remove++#++(struct EnumerableSet.UintSet set, uint256 value) → bool++` [.item-kind]#internal#

Removes a value from a set. O(1).

Returns true if the value was removed from the set, that is if it was
present.

[.contract-item]
[[EnumerableSet-contains-struct-EnumerableSet-UintSet-uint256-]]
==== `[.contract-item-name]#++contains++#++(struct EnumerableSet.UintSet set, uint256 value) → bool++` [.item-kind]#internal#

Returns true if the value is in the set. O(1).

[.contract-item]
[[EnumerableSet-length-struct-EnumerableSet-UintSet-]]
==== `[.contract-item-name]#++length++#++(struct EnumerableSet.UintSet set) → uint256++` [.item-kind]#internal#

Returns the number of values in the set. O(1).

[.contract-item]
[[EnumerableSet-at-struct-EnumerableSet-UintSet-uint256-]]
==== `[.contract-item-name]#++at++#++(struct EnumerableSet.UintSet set, uint256 index) → uint256++` [.item-kind]#internal#

Returns the value stored at position `index` in the set. O(1).

Note that there are no guarantees on the ordering of values inside the
array, and it may change when more values are added or removed.

Requirements:

- `index` must be strictly less than {length}.

[.contract-item]
[[EnumerableSet-values-struct-EnumerableSet-UintSet-]]
==== `[.contract-item-name]#++values++#++(struct EnumerableSet.UintSet set) → uint256[]++` [.item-kind]#internal#

Return the entire set in an array

WARNING: This operation will copy the entire storage to memory, which can be quite expensive. This is designed
to mostly be used by view accessors that are queried without any gas fees. Developers should keep in mind that
this function has an unbounded cost, and using it as part of a state-changing function may render the function
uncallable if the set grows to a point where copying to memory consumes too much gas to fit in a block.

:Empty: pass:normal[xref:#DoubleEndedQueue-Empty--[`++Empty++`]]
:OutOfBounds: pass:normal[xref:#DoubleEndedQueue-OutOfBounds--[`++OutOfBounds++`]]
:Bytes32Deque: pass:normal[xref:#DoubleEndedQueue-Bytes32Deque[`++Bytes32Deque++`]]
:pushBack: pass:normal[xref:#DoubleEndedQueue-pushBack-struct-DoubleEndedQueue-Bytes32Deque-bytes32-[`++pushBack++`]]
:popBack: pass:normal[xref:#DoubleEndedQueue-popBack-struct-DoubleEndedQueue-Bytes32Deque-[`++popBack++`]]
:pushFront: pass:normal[xref:#DoubleEndedQueue-pushFront-struct-DoubleEndedQueue-Bytes32Deque-bytes32-[`++pushFront++`]]
:popFront: pass:normal[xref:#DoubleEndedQueue-popFront-struct-DoubleEndedQueue-Bytes32Deque-[`++popFront++`]]
:front: pass:normal[xref:#DoubleEndedQueue-front-struct-DoubleEndedQueue-Bytes32Deque-[`++front++`]]
:back: pass:normal[xref:#DoubleEndedQueue-back-struct-DoubleEndedQueue-Bytes32Deque-[`++back++`]]
:at: pass:normal[xref:#DoubleEndedQueue-at-struct-DoubleEndedQueue-Bytes32Deque-uint256-[`++at++`]]
:clear: pass:normal[xref:#DoubleEndedQueue-clear-struct-DoubleEndedQueue-Bytes32Deque-[`++clear++`]]
:length: pass:normal[xref:#DoubleEndedQueue-length-struct-DoubleEndedQueue-Bytes32Deque-[`++length++`]]
:empty: pass:normal[xref:#DoubleEndedQueue-empty-struct-DoubleEndedQueue-Bytes32Deque-[`++empty++`]]

[.contract]
[[DoubleEndedQueue]]
=== `++DoubleEndedQueue++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/structs/DoubleEndedQueue.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/structs/DoubleEndedQueue.sol";
```

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;
```

_Available since v4.6._

[.contract-index]
.Functions
--
* {xref-DoubleEndedQueue-pushBack-struct-DoubleEndedQueue-Bytes32Deque-bytes32-}[`++pushBack(deque, value)++`]
* {xref-DoubleEndedQueue-popBack-struct-DoubleEndedQueue-Bytes32Deque-}[`++popBack(deque)++`]
* {xref-DoubleEndedQueue-pushFront-struct-DoubleEndedQueue-Bytes32Deque-bytes32-}[`++pushFront(deque, value)++`]
* {xref-DoubleEndedQueue-popFront-struct-DoubleEndedQueue-Bytes32Deque-}[`++popFront(deque)++`]
* {xref-DoubleEndedQueue-front-struct-DoubleEndedQueue-Bytes32Deque-}[`++front(deque)++`]
* {xref-DoubleEndedQueue-back-struct-DoubleEndedQueue-Bytes32Deque-}[`++back(deque)++`]
* {xref-DoubleEndedQueue-at-struct-DoubleEndedQueue-Bytes32Deque-uint256-}[`++at(deque, index)++`]
* {xref-DoubleEndedQueue-clear-struct-DoubleEndedQueue-Bytes32Deque-}[`++clear(deque)++`]
* {xref-DoubleEndedQueue-length-struct-DoubleEndedQueue-Bytes32Deque-}[`++length(deque)++`]
* {xref-DoubleEndedQueue-empty-struct-DoubleEndedQueue-Bytes32Deque-}[`++empty(deque)++`]

--

[.contract-item]
[[DoubleEndedQueue-pushBack-struct-DoubleEndedQueue-Bytes32Deque-bytes32-]]
==== `[.contract-item-name]#++pushBack++#++(struct DoubleEndedQueue.Bytes32Deque deque, bytes32 value)++` [.item-kind]#internal#

Inserts an item at the end of the queue.

[.contract-item]
[[DoubleEndedQueue-popBack-struct-DoubleEndedQueue-Bytes32Deque-]]
==== `[.contract-item-name]#++popBack++#++(struct DoubleEndedQueue.Bytes32Deque deque) → bytes32 value++` [.item-kind]#internal#

Removes the item at the end of the queue and returns it.

Reverts with `Empty` if the queue is empty.

[.contract-item]
[[DoubleEndedQueue-pushFront-struct-DoubleEndedQueue-Bytes32Deque-bytes32-]]
==== `[.contract-item-name]#++pushFront++#++(struct DoubleEndedQueue.Bytes32Deque deque, bytes32 value)++` [.item-kind]#internal#

Inserts an item at the beginning of the queue.

[.contract-item]
[[DoubleEndedQueue-popFront-struct-DoubleEndedQueue-Bytes32Deque-]]
==== `[.contract-item-name]#++popFront++#++(struct DoubleEndedQueue.Bytes32Deque deque) → bytes32 value++` [.item-kind]#internal#

Removes the item at the beginning of the queue and returns it.

Reverts with `Empty` if the queue is empty.

[.contract-item]
[[DoubleEndedQueue-front-struct-DoubleEndedQueue-Bytes32Deque-]]
==== `[.contract-item-name]#++front++#++(struct DoubleEndedQueue.Bytes32Deque deque) → bytes32 value++` [.item-kind]#internal#

Returns the item at the beginning of the queue.

Reverts with `Empty` if the queue is empty.

[.contract-item]
[[DoubleEndedQueue-back-struct-DoubleEndedQueue-Bytes32Deque-]]
==== `[.contract-item-name]#++back++#++(struct DoubleEndedQueue.Bytes32Deque deque) → bytes32 value++` [.item-kind]#internal#

Returns the item at the end of the queue.

Reverts with `Empty` if the queue is empty.

[.contract-item]
[[DoubleEndedQueue-at-struct-DoubleEndedQueue-Bytes32Deque-uint256-]]
==== `[.contract-item-name]#++at++#++(struct DoubleEndedQueue.Bytes32Deque deque, uint256 index) → bytes32 value++` [.item-kind]#internal#

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 `OutOfBounds` if the index is out of bounds.

[.contract-item]
[[DoubleEndedQueue-clear-struct-DoubleEndedQueue-Bytes32Deque-]]
==== `[.contract-item-name]#++clear++#++(struct DoubleEndedQueue.Bytes32Deque deque)++` [.item-kind]#internal#

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.

[.contract-item]
[[DoubleEndedQueue-length-struct-DoubleEndedQueue-Bytes32Deque-]]
==== `[.contract-item-name]#++length++#++(struct DoubleEndedQueue.Bytes32Deque deque) → uint256++` [.item-kind]#internal#

Returns the number of items in the queue.

[.contract-item]
[[DoubleEndedQueue-empty-struct-DoubleEndedQueue-Bytes32Deque-]]
==== `[.contract-item-name]#++empty++#++(struct DoubleEndedQueue.Bytes32Deque deque) → bool++` [.item-kind]#internal#

Returns true if the queue is empty.

:History: pass:normal[xref:#Checkpoints-History[`++History++`]]
:Checkpoint: pass:normal[xref:#Checkpoints-Checkpoint[`++Checkpoint++`]]
:getAtBlock: pass:normal[xref:#Checkpoints-getAtBlock-struct-Checkpoints-History-uint256-[`++getAtBlock++`]]
:getAtProbablyRecentBlock: pass:normal[xref:#Checkpoints-getAtProbablyRecentBlock-struct-Checkpoints-History-uint256-[`++getAtProbablyRecentBlock++`]]
:push: pass:normal[xref:#Checkpoints-push-struct-Checkpoints-History-uint256-[`++push++`]]
:push: pass:normal[xref:#Checkpoints-push-struct-Checkpoints-History-function--uint256-uint256--view-returns--uint256--uint256-[`++push++`]]
:latest: pass:normal[xref:#Checkpoints-latest-struct-Checkpoints-History-[`++latest++`]]
:latestCheckpoint: pass:normal[xref:#Checkpoints-latestCheckpoint-struct-Checkpoints-History-[`++latestCheckpoint++`]]
:length: pass:normal[xref:#Checkpoints-length-struct-Checkpoints-History-[`++length++`]]
:_insert: pass:normal[xref:#Checkpoints-_insert-struct-Checkpoints-Checkpoint---uint32-uint224-[`++_insert++`]]
:_upperBinaryLookup: pass:normal[xref:#Checkpoints-_upperBinaryLookup-struct-Checkpoints-Checkpoint---uint32-uint256-uint256-[`++_upperBinaryLookup++`]]
:_lowerBinaryLookup: pass:normal[xref:#Checkpoints-_lowerBinaryLookup-struct-Checkpoints-Checkpoint---uint32-uint256-uint256-[`++_lowerBinaryLookup++`]]
:_unsafeAccess: pass:normal[xref:#Checkpoints-_unsafeAccess-struct-Checkpoints-Checkpoint---uint256-[`++_unsafeAccess++`]]
:Trace224: pass:normal[xref:#Checkpoints-Trace224[`++Trace224++`]]
:Checkpoint224: pass:normal[xref:#Checkpoints-Checkpoint224[`++Checkpoint224++`]]
:push: pass:normal[xref:#Checkpoints-push-struct-Checkpoints-Trace224-uint32-uint224-[`++push++`]]
:lowerLookup: pass:normal[xref:#Checkpoints-lowerLookup-struct-Checkpoints-Trace224-uint32-[`++lowerLookup++`]]
:upperLookup: pass:normal[xref:#Checkpoints-upperLookup-struct-Checkpoints-Trace224-uint32-[`++upperLookup++`]]
:latest: pass:normal[xref:#Checkpoints-latest-struct-Checkpoints-Trace224-[`++latest++`]]
:latestCheckpoint: pass:normal[xref:#Checkpoints-latestCheckpoint-struct-Checkpoints-Trace224-[`++latestCheckpoint++`]]
:length: pass:normal[xref:#Checkpoints-length-struct-Checkpoints-Trace224-[`++length++`]]
:_insert: pass:normal[xref:#Checkpoints-_insert-struct-Checkpoints-Checkpoint224---uint32-uint224-[`++_insert++`]]
:_upperBinaryLookup: pass:normal[xref:#Checkpoints-_upperBinaryLookup-struct-Checkpoints-Checkpoint224---uint32-uint256-uint256-[`++_upperBinaryLookup++`]]
:_lowerBinaryLookup: pass:normal[xref:#Checkpoints-_lowerBinaryLookup-struct-Checkpoints-Checkpoint224---uint32-uint256-uint256-[`++_lowerBinaryLookup++`]]
:_unsafeAccess: pass:normal[xref:#Checkpoints-_unsafeAccess-struct-Checkpoints-Checkpoint224---uint256-[`++_unsafeAccess++`]]
:Trace160: pass:normal[xref:#Checkpoints-Trace160[`++Trace160++`]]
:Checkpoint160: pass:normal[xref:#Checkpoints-Checkpoint160[`++Checkpoint160++`]]
:push: pass:normal[xref:#Checkpoints-push-struct-Checkpoints-Trace160-uint96-uint160-[`++push++`]]
:lowerLookup: pass:normal[xref:#Checkpoints-lowerLookup-struct-Checkpoints-Trace160-uint96-[`++lowerLookup++`]]
:upperLookup: pass:normal[xref:#Checkpoints-upperLookup-struct-Checkpoints-Trace160-uint96-[`++upperLookup++`]]
:latest: pass:normal[xref:#Checkpoints-latest-struct-Checkpoints-Trace160-[`++latest++`]]
:latestCheckpoint: pass:normal[xref:#Checkpoints-latestCheckpoint-struct-Checkpoints-Trace160-[`++latestCheckpoint++`]]
:length: pass:normal[xref:#Checkpoints-length-struct-Checkpoints-Trace160-[`++length++`]]
:_insert: pass:normal[xref:#Checkpoints-_insert-struct-Checkpoints-Checkpoint160---uint96-uint160-[`++_insert++`]]
:_upperBinaryLookup: pass:normal[xref:#Checkpoints-_upperBinaryLookup-struct-Checkpoints-Checkpoint160---uint96-uint256-uint256-[`++_upperBinaryLookup++`]]
:_lowerBinaryLookup: pass:normal[xref:#Checkpoints-_lowerBinaryLookup-struct-Checkpoints-Checkpoint160---uint96-uint256-uint256-[`++_lowerBinaryLookup++`]]
:_unsafeAccess: pass:normal[xref:#Checkpoints-_unsafeAccess-struct-Checkpoints-Checkpoint160---uint256-[`++_unsafeAccess++`]]

[.contract]
[[Checkpoints]]
=== `++Checkpoints++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/Checkpoints.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/Checkpoints.sol";
```

This library defines the `History` struct, for checkpointing values as they change at different points in
time, and later looking up past values by block number. See {Votes} as an example.

To create a history of checkpoints define a variable type `Checkpoints.History` in your contract, and store a new
checkpoint for the current transaction block using the {push} function.

_Available since v4.5._

[.contract-index]
.Functions
--
* {xref-Checkpoints-getAtBlock-struct-Checkpoints-History-uint256-}[`++getAtBlock(self, blockNumber)++`]
* {xref-Checkpoints-getAtProbablyRecentBlock-struct-Checkpoints-History-uint256-}[`++getAtProbablyRecentBlock(self, blockNumber)++`]
* {xref-Checkpoints-push-struct-Checkpoints-History-uint256-}[`++push(self, value)++`]
* {xref-Checkpoints-push-struct-Checkpoints-History-function--uint256-uint256--view-returns--uint256--uint256-}[`++push(self, op, delta)++`]
* {xref-Checkpoints-latest-struct-Checkpoints-History-}[`++latest(self)++`]
* {xref-Checkpoints-latestCheckpoint-struct-Checkpoints-History-}[`++latestCheckpoint(self)++`]
* {xref-Checkpoints-length-struct-Checkpoints-History-}[`++length(self)++`]
* {xref-Checkpoints-push-struct-Checkpoints-Trace224-uint32-uint224-}[`++push(self, key, value)++`]
* {xref-Checkpoints-lowerLookup-struct-Checkpoints-Trace224-uint32-}[`++lowerLookup(self, key)++`]
* {xref-Checkpoints-upperLookup-struct-Checkpoints-Trace224-uint32-}[`++upperLookup(self, key)++`]
* {xref-Checkpoints-latest-struct-Checkpoints-Trace224-}[`++latest(self)++`]
* {xref-Checkpoints-latestCheckpoint-struct-Checkpoints-Trace224-}[`++latestCheckpoint(self)++`]
* {xref-Checkpoints-length-struct-Checkpoints-Trace224-}[`++length(self)++`]
* {xref-Checkpoints-push-struct-Checkpoints-Trace160-uint96-uint160-}[`++push(self, key, value)++`]
* {xref-Checkpoints-lowerLookup-struct-Checkpoints-Trace160-uint96-}[`++lowerLookup(self, key)++`]
* {xref-Checkpoints-upperLookup-struct-Checkpoints-Trace160-uint96-}[`++upperLookup(self, key)++`]
* {xref-Checkpoints-latest-struct-Checkpoints-Trace160-}[`++latest(self)++`]
* {xref-Checkpoints-latestCheckpoint-struct-Checkpoints-Trace160-}[`++latestCheckpoint(self)++`]
* {xref-Checkpoints-length-struct-Checkpoints-Trace160-}[`++length(self)++`]

--

[.contract-item]
[[Checkpoints-getAtBlock-struct-Checkpoints-History-uint256-]]
==== `[.contract-item-name]#++getAtBlock++#++(struct Checkpoints.History self, uint256 blockNumber) → uint256++` [.item-kind]#internal#

Returns the value at a given block number. If a checkpoint is not available at that block, the closest one
before it is returned, or zero otherwise. Because the number returned corresponds to that at the end of the
block, the requested block number must be in the past, excluding the current block.

[.contract-item]
[[Checkpoints-getAtProbablyRecentBlock-struct-Checkpoints-History-uint256-]]
==== `[.contract-item-name]#++getAtProbablyRecentBlock++#++(struct Checkpoints.History self, uint256 blockNumber) → uint256++` [.item-kind]#internal#

Returns the value at a given block number. If a checkpoint is not available at that block, the closest one
before it is returned, or zero otherwise. Similar to {upperLookup} but optimized for the case when the searched
checkpoint is probably "recent", defined as being among the last sqrt(N) checkpoints where N is the number of
checkpoints.

[.contract-item]
[[Checkpoints-push-struct-Checkpoints-History-uint256-]]
==== `[.contract-item-name]#++push++#++(struct Checkpoints.History self, uint256 value) → uint256, uint256++` [.item-kind]#internal#

Pushes a value onto a History so that it is stored as the checkpoint for the current block.

Returns previous value and new value.

[.contract-item]
[[Checkpoints-push-struct-Checkpoints-History-function--uint256-uint256--view-returns--uint256--uint256-]]
==== `[.contract-item-name]#++push++#++(struct Checkpoints.History self, function (uint256,uint256) view returns (uint256) op, uint256 delta) → uint256, uint256++` [.item-kind]#internal#

Pushes a value onto a History, by updating the latest value using binary operation `op`. The new value will
be set to `op(latest, delta)`.

Returns previous value and new value.

[.contract-item]
[[Checkpoints-latest-struct-Checkpoints-History-]]
==== `[.contract-item-name]#++latest++#++(struct Checkpoints.History self) → uint224++` [.item-kind]#internal#

Returns the value in the most recent checkpoint, or zero if there are no checkpoints.

[.contract-item]
[[Checkpoints-latestCheckpoint-struct-Checkpoints-History-]]
==== `[.contract-item-name]#++latestCheckpoint++#++(struct Checkpoints.History self) → bool exists, uint32 _blockNumber, uint224 _value++` [.item-kind]#internal#

Returns whether there is a checkpoint in the structure (i.e. it is not empty), and if so the key and value
in the most recent checkpoint.

[.contract-item]
[[Checkpoints-length-struct-Checkpoints-History-]]
==== `[.contract-item-name]#++length++#++(struct Checkpoints.History self) → uint256++` [.item-kind]#internal#

Returns the number of checkpoint.

[.contract-item]
[[Checkpoints-push-struct-Checkpoints-Trace224-uint32-uint224-]]
==== `[.contract-item-name]#++push++#++(struct Checkpoints.Trace224 self, uint32 key, uint224 value) → uint224, uint224++` [.item-kind]#internal#

Pushes a (`key`, `value`) pair into a Trace224 so that it is stored as the checkpoint.

Returns previous value and new value.

[.contract-item]
[[Checkpoints-lowerLookup-struct-Checkpoints-Trace224-uint32-]]
==== `[.contract-item-name]#++lowerLookup++#++(struct Checkpoints.Trace224 self, uint32 key) → uint224++` [.item-kind]#internal#

Returns the value in the oldest checkpoint with key greater or equal than the search key, or zero if there is none.

[.contract-item]
[[Checkpoints-upperLookup-struct-Checkpoints-Trace224-uint32-]]
==== `[.contract-item-name]#++upperLookup++#++(struct Checkpoints.Trace224 self, uint32 key) → uint224++` [.item-kind]#internal#

Returns the value in the most recent checkpoint with key lower or equal than the search key.

[.contract-item]
[[Checkpoints-latest-struct-Checkpoints-Trace224-]]
==== `[.contract-item-name]#++latest++#++(struct Checkpoints.Trace224 self) → uint224++` [.item-kind]#internal#

Returns the value in the most recent checkpoint, or zero if there are no checkpoints.

[.contract-item]
[[Checkpoints-latestCheckpoint-struct-Checkpoints-Trace224-]]
==== `[.contract-item-name]#++latestCheckpoint++#++(struct Checkpoints.Trace224 self) → bool exists, uint32 _key, uint224 _value++` [.item-kind]#internal#

Returns whether there is a checkpoint in the structure (i.e. it is not empty), and if so the key and value
in the most recent checkpoint.

[.contract-item]
[[Checkpoints-length-struct-Checkpoints-Trace224-]]
==== `[.contract-item-name]#++length++#++(struct Checkpoints.Trace224 self) → uint256++` [.item-kind]#internal#

Returns the number of checkpoint.

[.contract-item]
[[Checkpoints-push-struct-Checkpoints-Trace160-uint96-uint160-]]
==== `[.contract-item-name]#++push++#++(struct Checkpoints.Trace160 self, uint96 key, uint160 value) → uint160, uint160++` [.item-kind]#internal#

Pushes a (`key`, `value`) pair into a Trace160 so that it is stored as the checkpoint.

Returns previous value and new value.

[.contract-item]
[[Checkpoints-lowerLookup-struct-Checkpoints-Trace160-uint96-]]
==== `[.contract-item-name]#++lowerLookup++#++(struct Checkpoints.Trace160 self, uint96 key) → uint160++` [.item-kind]#internal#

Returns the value in the oldest checkpoint with key greater or equal than the search key, or zero if there is none.

[.contract-item]
[[Checkpoints-upperLookup-struct-Checkpoints-Trace160-uint96-]]
==== `[.contract-item-name]#++upperLookup++#++(struct Checkpoints.Trace160 self, uint96 key) → uint160++` [.item-kind]#internal#

Returns the value in the most recent checkpoint with key lower or equal than the search key.

[.contract-item]
[[Checkpoints-latest-struct-Checkpoints-Trace160-]]
==== `[.contract-item-name]#++latest++#++(struct Checkpoints.Trace160 self) → uint160++` [.item-kind]#internal#

Returns the value in the most recent checkpoint, or zero if there are no checkpoints.

[.contract-item]
[[Checkpoints-latestCheckpoint-struct-Checkpoints-Trace160-]]
==== `[.contract-item-name]#++latestCheckpoint++#++(struct Checkpoints.Trace160 self) → bool exists, uint96 _key, uint160 _value++` [.item-kind]#internal#

Returns whether there is a checkpoint in the structure (i.e. it is not empty), and if so the key and value
in the most recent checkpoint.

[.contract-item]
[[Checkpoints-length-struct-Checkpoints-Trace160-]]
==== `[.contract-item-name]#++length++#++(struct Checkpoints.Trace160 self) → uint256++` [.item-kind]#internal#

Returns the number of checkpoint.

== Libraries

:deploy: pass:normal[xref:#Create2-deploy-uint256-bytes32-bytes-[`++deploy++`]]
:computeAddress: pass:normal[xref:#Create2-computeAddress-bytes32-bytes32-[`++computeAddress++`]]
:computeAddress: pass:normal[xref:#Create2-computeAddress-bytes32-bytes32-address-[`++computeAddress++`]]

[.contract]
[[Create2]]
=== `++Create2++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/Create2.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/Create2.sol";
```

Helper to make usage of the `CREATE2` EVM opcode easier and safer.
`CREATE2` can be used to compute in advance the address where a smart
contract will be deployed, which allows for interesting new mechanisms known
as 'counterfactual interactions'.

See the https://eips.ethereum.org/EIPS/eip-1014#motivation[EIP] for more
information.

[.contract-index]
.Functions
--
* {xref-Create2-deploy-uint256-bytes32-bytes-}[`++deploy(amount, salt, bytecode)++`]
* {xref-Create2-computeAddress-bytes32-bytes32-}[`++computeAddress(salt, bytecodeHash)++`]
* {xref-Create2-computeAddress-bytes32-bytes32-address-}[`++computeAddress(salt, bytecodeHash, deployer)++`]

--

[.contract-item]
[[Create2-deploy-uint256-bytes32-bytes-]]
==== `[.contract-item-name]#++deploy++#++(uint256 amount, bytes32 salt, bytes bytecode) → address addr++` [.item-kind]#internal#

Deploys a contract using `CREATE2`. The address where the contract
will be deployed can be known in advance via {computeAddress}.

The bytecode for a contract can be obtained from Solidity with
`type(contractName).creationCode`.

Requirements:

- `bytecode` must not be empty.
- `salt` must have not been used for `bytecode` already.
- the factory must have a balance of at least `amount`.
- if `amount` is non-zero, `bytecode` must have a `payable` constructor.

[.contract-item]
[[Create2-computeAddress-bytes32-bytes32-]]
==== `[.contract-item-name]#++computeAddress++#++(bytes32 salt, bytes32 bytecodeHash) → address++` [.item-kind]#internal#

Returns the address where a contract will be stored if deployed via {deploy}. Any change in the
`bytecodeHash` or `salt` will result in a new destination address.

[.contract-item]
[[Create2-computeAddress-bytes32-bytes32-address-]]
==== `[.contract-item-name]#++computeAddress++#++(bytes32 salt, bytes32 bytecodeHash, address deployer) → address addr++` [.item-kind]#internal#

Returns the address where a contract will be stored if deployed via {deploy} from a contract located at
`deployer`. If `deployer` is this contract's address, returns the same value as {computeAddress}.

:isContract: pass:normal[xref:#Address-isContract-address-[`++isContract++`]]
:sendValue: pass:normal[xref:#Address-sendValue-address-payable-uint256-[`++sendValue++`]]
:functionCall: pass:normal[xref:#Address-functionCall-address-bytes-[`++functionCall++`]]
:functionCall: pass:normal[xref:#Address-functionCall-address-bytes-string-[`++functionCall++`]]
:functionCallWithValue: pass:normal[xref:#Address-functionCallWithValue-address-bytes-uint256-[`++functionCallWithValue++`]]
:functionCallWithValue: pass:normal[xref:#Address-functionCallWithValue-address-bytes-uint256-string-[`++functionCallWithValue++`]]
:functionStaticCall: pass:normal[xref:#Address-functionStaticCall-address-bytes-[`++functionStaticCall++`]]
:functionStaticCall: pass:normal[xref:#Address-functionStaticCall-address-bytes-string-[`++functionStaticCall++`]]
:functionDelegateCall: pass:normal[xref:#Address-functionDelegateCall-address-bytes-[`++functionDelegateCall++`]]
:functionDelegateCall: pass:normal[xref:#Address-functionDelegateCall-address-bytes-string-[`++functionDelegateCall++`]]
:verifyCallResultFromTarget: pass:normal[xref:#Address-verifyCallResultFromTarget-address-bool-bytes-string-[`++verifyCallResultFromTarget++`]]
:verifyCallResult: pass:normal[xref:#Address-verifyCallResult-bool-bytes-string-[`++verifyCallResult++`]]
:_revert: pass:normal[xref:#Address-_revert-bytes-string-[`++_revert++`]]

[.contract]
[[Address]]
=== `++Address++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/Address.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/Address.sol";
```

Collection of functions related to the address type

[.contract-index]
.Functions
--
* {xref-Address-isContract-address-}[`++isContract(account)++`]
* {xref-Address-sendValue-address-payable-uint256-}[`++sendValue(recipient, amount)++`]
* {xref-Address-functionCall-address-bytes-}[`++functionCall(target, data)++`]
* {xref-Address-functionCall-address-bytes-string-}[`++functionCall(target, data, errorMessage)++`]
* {xref-Address-functionCallWithValue-address-bytes-uint256-}[`++functionCallWithValue(target, data, value)++`]
* {xref-Address-functionCallWithValue-address-bytes-uint256-string-}[`++functionCallWithValue(target, data, value, errorMessage)++`]
* {xref-Address-functionStaticCall-address-bytes-}[`++functionStaticCall(target, data)++`]
* {xref-Address-functionStaticCall-address-bytes-string-}[`++functionStaticCall(target, data, errorMessage)++`]
* {xref-Address-functionDelegateCall-address-bytes-}[`++functionDelegateCall(target, data)++`]
* {xref-Address-functionDelegateCall-address-bytes-string-}[`++functionDelegateCall(target, data, errorMessage)++`]
* {xref-Address-verifyCallResultFromTarget-address-bool-bytes-string-}[`++verifyCallResultFromTarget(target, success, returndata, errorMessage)++`]
* {xref-Address-verifyCallResult-bool-bytes-string-}[`++verifyCallResult(success, returndata, errorMessage)++`]

--

[.contract-item]
[[Address-isContract-address-]]
==== `[.contract-item-name]#++isContract++#++(address account) → bool++` [.item-kind]#internal#

Returns true if `account` is a contract.

[IMPORTANT]
====
It is unsafe to assume that an address for which this function returns
false is an externally-owned account (EOA) and not a contract.

Among others, `isContract` will return false for the following
types of addresses:

 - an externally-owned account
 - a contract in construction
 - an address where a contract will be created
 - an address where a contract lived, but was destroyed
====

[IMPORTANT]
====
You shouldn't rely on `isContract` to protect against flash loan attacks!

Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
constructor.
====

[.contract-item]
[[Address-sendValue-address-payable-uint256-]]
==== `[.contract-item-name]#++sendValue++#++(address payable recipient, uint256 amount)++` [.item-kind]#internal#

Replacement for Solidity's `transfer`: sends `amount` wei to
`recipient`, forwarding all available gas and reverting on errors.

https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
of certain opcodes, possibly making contracts go over the 2300 gas limit
imposed by `transfer`, making them unable to receive funds via
`transfer`. {sendValue} removes this limitation.

https://diligence.consensys.net/posts/2019/09/stop-using-soliditys-transfer-now/[Learn more].

IMPORTANT: because control is transferred to `recipient`, care must be
taken to not create reentrancy vulnerabilities. Consider using
{ReentrancyGuard} or the
https://solidity.readthedocs.io/en/v0.5.11/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].

[.contract-item]
[[Address-functionCall-address-bytes-]]
==== `[.contract-item-name]#++functionCall++#++(address target, bytes data) → bytes++` [.item-kind]#internal#

Performs a Solidity function call using a low level `call`. A
plain `call` is an unsafe replacement for a function call: use this
function instead.

If `target` reverts with a revert reason, it is bubbled up by this
function (like regular Solidity function calls).

Returns the raw returned data. To convert to the expected return value,
use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].

Requirements:

- `target` must be a contract.
- calling `target` with `data` must not revert.

_Available since v3.1._

[.contract-item]
[[Address-functionCall-address-bytes-string-]]
==== `[.contract-item-name]#++functionCall++#++(address target, bytes data, string errorMessage) → bytes++` [.item-kind]#internal#

Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
`errorMessage` as a fallback revert reason when `target` reverts.

_Available since v3.1._

[.contract-item]
[[Address-functionCallWithValue-address-bytes-uint256-]]
==== `[.contract-item-name]#++functionCallWithValue++#++(address target, bytes data, uint256 value) → bytes++` [.item-kind]#internal#

Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
but also transferring `value` wei to `target`.

Requirements:

- the calling contract must have an ETH balance of at least `value`.
- the called Solidity function must be `payable`.

_Available since v3.1._

[.contract-item]
[[Address-functionCallWithValue-address-bytes-uint256-string-]]
==== `[.contract-item-name]#++functionCallWithValue++#++(address target, bytes data, uint256 value, string errorMessage) → bytes++` [.item-kind]#internal#

Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
with `errorMessage` as a fallback revert reason when `target` reverts.

_Available since v3.1._

[.contract-item]
[[Address-functionStaticCall-address-bytes-]]
==== `[.contract-item-name]#++functionStaticCall++#++(address target, bytes data) → bytes++` [.item-kind]#internal#

Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
but performing a static call.

_Available since v3.3._

[.contract-item]
[[Address-functionStaticCall-address-bytes-string-]]
==== `[.contract-item-name]#++functionStaticCall++#++(address target, bytes data, string errorMessage) → bytes++` [.item-kind]#internal#

Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
but performing a static call.

_Available since v3.3._

[.contract-item]
[[Address-functionDelegateCall-address-bytes-]]
==== `[.contract-item-name]#++functionDelegateCall++#++(address target, bytes data) → bytes++` [.item-kind]#internal#

Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
but performing a delegate call.

_Available since v3.4._

[.contract-item]
[[Address-functionDelegateCall-address-bytes-string-]]
==== `[.contract-item-name]#++functionDelegateCall++#++(address target, bytes data, string errorMessage) → bytes++` [.item-kind]#internal#

Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
but performing a delegate call.

_Available since v3.4._

[.contract-item]
[[Address-verifyCallResultFromTarget-address-bool-bytes-string-]]
==== `[.contract-item-name]#++verifyCallResultFromTarget++#++(address target, bool success, bytes returndata, string errorMessage) → bytes++` [.item-kind]#internal#

Tool to verify that a low level call to smart-contract was successful, and revert (either by bubbling
the revert reason or using the provided one) in case of unsuccessful call or if target was not a contract.

_Available since v4.8._

[.contract-item]
[[Address-verifyCallResult-bool-bytes-string-]]
==== `[.contract-item-name]#++verifyCallResult++#++(bool success, bytes returndata, string errorMessage) → bytes++` [.item-kind]#internal#

Tool to verify that a low level call was successful, and revert if it wasn't, either by bubbling the
revert reason or using the provided one.

_Available since v4.3._

:findUpperBound: pass:normal[xref:#Arrays-findUpperBound-uint256---uint256-[`++findUpperBound++`]]
:unsafeAccess: pass:normal[xref:#Arrays-unsafeAccess-address---uint256-[`++unsafeAccess++`]]
:unsafeAccess: pass:normal[xref:#Arrays-unsafeAccess-bytes32---uint256-[`++unsafeAccess++`]]
:unsafeAccess: pass:normal[xref:#Arrays-unsafeAccess-uint256---uint256-[`++unsafeAccess++`]]

[.contract]
[[Arrays]]
=== `++Arrays++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/Arrays.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/Arrays.sol";
```

Collection of functions related to array types.

[.contract-index]
.Functions
--
* {xref-Arrays-findUpperBound-uint256---uint256-}[`++findUpperBound(array, element)++`]
* {xref-Arrays-unsafeAccess-address---uint256-}[`++unsafeAccess(arr, pos)++`]
* {xref-Arrays-unsafeAccess-bytes32---uint256-}[`++unsafeAccess(arr, pos)++`]
* {xref-Arrays-unsafeAccess-uint256---uint256-}[`++unsafeAccess(arr, pos)++`]

--

[.contract-item]
[[Arrays-findUpperBound-uint256---uint256-]]
==== `[.contract-item-name]#++findUpperBound++#++(uint256[] array, uint256 element) → uint256++` [.item-kind]#internal#

Searches a sorted `array` and returns the first index that contains
a value greater or equal to `element`. If no such index exists (i.e. all
values in the array are strictly less than `element`), the array length is
returned. Time complexity O(log n).

`array` is expected to be sorted in ascending order, and to contain no
repeated elements.

[.contract-item]
[[Arrays-unsafeAccess-address---uint256-]]
==== `[.contract-item-name]#++unsafeAccess++#++(address[] arr, uint256 pos) → struct StorageSlot.AddressSlot++` [.item-kind]#internal#

Access an array in an "unsafe" way. Skips solidity "index-out-of-range" check.

WARNING: Only use if you are certain `pos` is lower than the array length.

[.contract-item]
[[Arrays-unsafeAccess-bytes32---uint256-]]
==== `[.contract-item-name]#++unsafeAccess++#++(bytes32[] arr, uint256 pos) → struct StorageSlot.Bytes32Slot++` [.item-kind]#internal#

Access an array in an "unsafe" way. Skips solidity "index-out-of-range" check.

WARNING: Only use if you are certain `pos` is lower than the array length.

[.contract-item]
[[Arrays-unsafeAccess-uint256---uint256-]]
==== `[.contract-item-name]#++unsafeAccess++#++(uint256[] arr, uint256 pos) → struct StorageSlot.Uint256Slot++` [.item-kind]#internal#

Access an array in an "unsafe" way. Skips solidity "index-out-of-range" check.

WARNING: Only use if you are certain `pos` is lower than the array length.

:_TABLE: pass:normal[xref:#Base64-_TABLE-string[`++_TABLE++`]]
:encode: pass:normal[xref:#Base64-encode-bytes-[`++encode++`]]

[.contract]
[[Base64]]
=== `++Base64++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/Base64.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/Base64.sol";
```

Provides a set of functions to operate with Base64 strings.

_Available since v4.5._

[.contract-index]
.Functions
--
* {xref-Base64-encode-bytes-}[`++encode(data)++`]

--

[.contract-item]
[[Base64-encode-bytes-]]
==== `[.contract-item-name]#++encode++#++(bytes data) → string++` [.item-kind]#internal#

Converts a `bytes` to its Bytes64 `string` representation.

:Counter: pass:normal[xref:#Counters-Counter[`++Counter++`]]
:current: pass:normal[xref:#Counters-current-struct-Counters-Counter-[`++current++`]]
:increment: pass:normal[xref:#Counters-increment-struct-Counters-Counter-[`++increment++`]]
:decrement: pass:normal[xref:#Counters-decrement-struct-Counters-Counter-[`++decrement++`]]
:reset: pass:normal[xref:#Counters-reset-struct-Counters-Counter-[`++reset++`]]

[.contract]
[[Counters]]
=== `++Counters++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/Counters.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/Counters.sol";
```

Provides counters that can only be incremented, decremented or reset. This can be used e.g. to track the number
of elements in a mapping, issuing ERC721 ids, or counting request ids.

Include with `using Counters for Counters.Counter;`

[.contract-index]
.Functions
--
* {xref-Counters-current-struct-Counters-Counter-}[`++current(counter)++`]
* {xref-Counters-increment-struct-Counters-Counter-}[`++increment(counter)++`]
* {xref-Counters-decrement-struct-Counters-Counter-}[`++decrement(counter)++`]
* {xref-Counters-reset-struct-Counters-Counter-}[`++reset(counter)++`]

--

[.contract-item]
[[Counters-current-struct-Counters-Counter-]]
==== `[.contract-item-name]#++current++#++(struct Counters.Counter counter) → uint256++` [.item-kind]#internal#

[.contract-item]
[[Counters-increment-struct-Counters-Counter-]]
==== `[.contract-item-name]#++increment++#++(struct Counters.Counter counter)++` [.item-kind]#internal#

[.contract-item]
[[Counters-decrement-struct-Counters-Counter-]]
==== `[.contract-item-name]#++decrement++#++(struct Counters.Counter counter)++` [.item-kind]#internal#

[.contract-item]
[[Counters-reset-struct-Counters-Counter-]]
==== `[.contract-item-name]#++reset++#++(struct Counters.Counter counter)++` [.item-kind]#internal#

:_SYMBOLS: pass:normal[xref:#Strings-_SYMBOLS-bytes16[`++_SYMBOLS++`]]
:_ADDRESS_LENGTH: pass:normal[xref:#Strings-_ADDRESS_LENGTH-uint8[`++_ADDRESS_LENGTH++`]]
:toString: pass:normal[xref:#Strings-toString-uint256-[`++toString++`]]
:toHexString: pass:normal[xref:#Strings-toHexString-uint256-[`++toHexString++`]]
:toHexString: pass:normal[xref:#Strings-toHexString-uint256-uint256-[`++toHexString++`]]
:toHexString: pass:normal[xref:#Strings-toHexString-address-[`++toHexString++`]]

[.contract]
[[Strings]]
=== `++Strings++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/Strings.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/Strings.sol";
```

String operations.

[.contract-index]
.Functions
--
* {xref-Strings-toString-uint256-}[`++toString(value)++`]
* {xref-Strings-toHexString-uint256-}[`++toHexString(value)++`]
* {xref-Strings-toHexString-uint256-uint256-}[`++toHexString(value, length)++`]
* {xref-Strings-toHexString-address-}[`++toHexString(addr)++`]

--

[.contract-item]
[[Strings-toString-uint256-]]
==== `[.contract-item-name]#++toString++#++(uint256 value) → string++` [.item-kind]#internal#

Converts a `uint256` to its ASCII `string` decimal representation.

[.contract-item]
[[Strings-toHexString-uint256-]]
==== `[.contract-item-name]#++toHexString++#++(uint256 value) → string++` [.item-kind]#internal#

Converts a `uint256` to its ASCII `string` hexadecimal representation.

[.contract-item]
[[Strings-toHexString-uint256-uint256-]]
==== `[.contract-item-name]#++toHexString++#++(uint256 value, uint256 length) → string++` [.item-kind]#internal#

Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.

[.contract-item]
[[Strings-toHexString-address-]]
==== `[.contract-item-name]#++toHexString++#++(address addr) → string++` [.item-kind]#internal#

Converts an `address` with fixed length of 20 bytes to its not checksummed ASCII `string` hexadecimal representation.

:AddressSlot: pass:normal[xref:#StorageSlot-AddressSlot[`++AddressSlot++`]]
:BooleanSlot: pass:normal[xref:#StorageSlot-BooleanSlot[`++BooleanSlot++`]]
:Bytes32Slot: pass:normal[xref:#StorageSlot-Bytes32Slot[`++Bytes32Slot++`]]
:Uint256Slot: pass:normal[xref:#StorageSlot-Uint256Slot[`++Uint256Slot++`]]
:getAddressSlot: pass:normal[xref:#StorageSlot-getAddressSlot-bytes32-[`++getAddressSlot++`]]
:getBooleanSlot: pass:normal[xref:#StorageSlot-getBooleanSlot-bytes32-[`++getBooleanSlot++`]]
:getBytes32Slot: pass:normal[xref:#StorageSlot-getBytes32Slot-bytes32-[`++getBytes32Slot++`]]
:getUint256Slot: pass:normal[xref:#StorageSlot-getUint256Slot-bytes32-[`++getUint256Slot++`]]

[.contract]
[[StorageSlot]]
=== `++StorageSlot++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/StorageSlot.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/StorageSlot.sol";
```

Library for reading and writing primitive types to specific storage slots.

Storage slots are often used to avoid storage conflict when dealing with upgradeable contracts.
This library helps with reading and writing to such slots without the need for inline assembly.

The functions in this library return Slot structs that contain a `value` member that can be used to read or write.

Example usage to set ERC1967 implementation slot:
```
contract ERC1967 {
    bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;

    function _getImplementation() internal view returns (address) {
        return StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value;
    }

    function _setImplementation(address newImplementation) internal {
        require(Address.isContract(newImplementation), "ERC1967: new implementation is not a contract");
        StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation;
    }
}
```

_Available since v4.1 for `address`, `bool`, `bytes32`, and `uint256`._

[.contract-index]
.Functions
--
* {xref-StorageSlot-getAddressSlot-bytes32-}[`++getAddressSlot(slot)++`]
* {xref-StorageSlot-getBooleanSlot-bytes32-}[`++getBooleanSlot(slot)++`]
* {xref-StorageSlot-getBytes32Slot-bytes32-}[`++getBytes32Slot(slot)++`]
* {xref-StorageSlot-getUint256Slot-bytes32-}[`++getUint256Slot(slot)++`]

--

[.contract-item]
[[StorageSlot-getAddressSlot-bytes32-]]
==== `[.contract-item-name]#++getAddressSlot++#++(bytes32 slot) → struct StorageSlot.AddressSlot r++` [.item-kind]#internal#

Returns an `AddressSlot` with member `value` located at `slot`.

[.contract-item]
[[StorageSlot-getBooleanSlot-bytes32-]]
==== `[.contract-item-name]#++getBooleanSlot++#++(bytes32 slot) → struct StorageSlot.BooleanSlot r++` [.item-kind]#internal#

Returns an `BooleanSlot` with member `value` located at `slot`.

[.contract-item]
[[StorageSlot-getBytes32Slot-bytes32-]]
==== `[.contract-item-name]#++getBytes32Slot++#++(bytes32 slot) → struct StorageSlot.Bytes32Slot r++` [.item-kind]#internal#

Returns an `Bytes32Slot` with member `value` located at `slot`.

[.contract-item]
[[StorageSlot-getUint256Slot-bytes32-]]
==== `[.contract-item-name]#++getUint256Slot++#++(bytes32 slot) → struct StorageSlot.Uint256Slot r++` [.item-kind]#internal#

Returns an `Uint256Slot` with member `value` located at `slot`.

:multicall: pass:normal[xref:#Multicall-multicall-bytes---[`++multicall++`]]

[.contract]
[[Multicall]]
=== `++Multicall++` link:https://github.com/OpenZeppelin/openzeppelin-contracts/blob/v4.8.1/contracts/utils/Multicall.sol[{github-icon},role=heading-link]

[.hljs-theme-light.nopadding]
```solidity
import "@openzeppelin/contracts/utils/Multicall.sol";
```

Provides a function to batch together multiple calls in a single external call.

_Available since v4.1._

[.contract-index]
.Functions
--
* {xref-Multicall-multicall-bytes---}[`++multicall(data)++`]

--

[.contract-item]
[[Multicall-multicall-bytes---]]
==== `[.contract-item-name]#++multicall++#++(bytes[] data) → bytes[] results++` [.item-kind]#external#

Receives and executes a batch of function calls on this contract.