xref:api:utils.adoc#ECDSA[`ECDSA`] provides functions for recovering and managing Ethereum account ECDSA signatures. These are often generated via https://web3js.readthedocs.io/en/v1.7.3/web3-eth.html#sign[`web3.eth.sign`], and are a 65 byte array (of type `bytes` in Solidity) arranged the following way: `[[v (1)], [r (32)], [s (32)]]`.
The data signer can be recovered with xref:api:utils.adoc#ECDSA-recover-bytes32-bytes-[`ECDSA.recover`], and its address compared to verify the signature. Most wallets will hash the data to sign and add the prefix '\x19Ethereum Signed Message:\n', so when attempting to recover the signer of an Ethereum signed message hash, you'll want to use xref:api:utils.adoc#MessageHashUtils-toEthSignedMessageHash-bytes32-[`toEthSignedMessageHash`].
WARNING: Getting signature verification right is not trivial: make sure you fully read and understand xref:api:utils.adoc#MessageHashUtils[`MessageHashUtils`]'s and xref:api:utils.adoc#ECDSA[`ECDSA`]'s documentation.
* xref:api:utils.adoc#MerkleProof-verify-bytes32---bytes32-bytes32-[`verify`] - can prove that some value is part of a https://en.wikipedia.org/wiki/Merkle_tree[Merkle tree].
* xref:api:utils.adoc#MerkleProof-multiProofVerify-bytes32-bytes32---bytes32---bool---[`multiProofVerify`] - can prove multiple values are part of a Merkle tree.
In Solidity, it's frequently helpful to know whether or not a contract supports an interface you'd like to use. ERC-165 is a standard that helps do runtime interface detection. Contracts provide helpers both for implementing ERC-165 in your contracts and querying other contracts:
* xref:api:utils.adoc#IERC165[`IERC165`] — this is the ERC-165 interface that defines xref:api:utils.adoc#IERC165-supportsInterface-bytes4-[`supportsInterface`]. When implementing ERC-165, you'll conform to this interface.
* xref:api:utils.adoc#ERC165[`ERC165`] — inherit this contract if you'd like to support interface detection using a lookup table in contract storage. You can register interfaces using xref:api:utils.adoc#ERC165-_registerInterface-bytes4-[`_registerInterface(bytes4)`]: check out example usage as part of the ERC-721 implementation.
* xref:api:utils.adoc#ERC165Checker[`ERC165Checker`] — ERC165Checker simplifies the process of checking whether or not a contract supports an interface you care about.
Although Solidity already provides math operators (i.e. `+`, `-`, etc.), Contracts includes xref:api:utils.adoc#Math[`Math`]; a set of utilities for dealing with mathematical operators, with support for extra operations (eg. xref:api:utils.adoc#Math-average-uint256-uint256-[`average`]) and xref:api:utils.adoc#SignedMath[`SignedMath`]; a library specialized in signed math operations.
Some use cases require more powerful data structures than arrays and mappings offered natively in Solidity. Contracts provides these libraries for enhanced data structure management:
The `Enumerable*` structures are similar to mappings in that they store and remove elements in constant time and don't allow for repeated entries, but they also support _enumeration_, which means you can easily query all stored entries both on and off-chain.
This is especially useful for building URL-safe tokenURIs for both xref:api:token/ERC721.adoc#IERC721Metadata-tokenURI-uint256-[`ERC-721`] or xref:api:token/ERC1155.adoc#IERC1155MetadataURI-uri-uint256-[`ERC-1155`]. This library provides a clever way to serve URL-safe https://developer.mozilla.org/docs/Web/HTTP/Basics_of_HTTP/Data_URIs/[Data URI] compliant strings to serve on-chain data structures.
The `Multicall` abstract contract comes with a `multicall` function that bundles together multiple calls in a single external call. With it, external accounts may perform atomic operations comprising several function calls. This is not only useful for EOAs to make multiple calls in a single transaction, it's also a way to revert a previous call if a later one fails.