Gas Optimizations

[code423n4]

[G01] Unchecked Increments in Loops

When incrementing i in for loops there is no chance of overflow so unchecked can be used to save gas. I ran a simple test in remix and found deployment savings of 31,653 gas and on each function call saved ~141 gas per iteration.

contract Test {
	function loopTest() external {
		for (uint256 i; i < 1; ++i) {
		Deployment Cost: 125,637, Cost on function call: 24,601
		vs
		for (uint256 i; i < 1; ) {
		// for loop body
		unchecked { ++i }
		Deployment Cost: 93,984, Cost on function call: 24,460
		}
	}
}

For loops that can use unchecked increments:
BytesUtils.sol#L266
BytesUtils.sol#L313
DNSSECImpl.sol#L93
ETHRegistrarController.sol#L256
ERC1155Fuse.sol#L92
ERC1155Fuse.sol#L205

[G02] Pre Increments in Loops

In for loops pre increments can be used to save a small amount of gas per iteration.
I ran a test in remix using a for loop and found the deployment savings of 497 gas and ~5 gas per iteration.

contract Test {
	function loopTest() external {
		for (uint256 i; i < 1; i++) {
		(Deployment cost: 118,408, Cost on function call: 24,532)
		vs
		for (uint256 i; i < 1; ++i) {
		(Deployment cost: 117,911, Cost on function call: 24,527)
		}
	}
}

For loops that can use pre increments:
BytesUtils.sol#L266
BytesUtils.sol#L313
DNSSECImpl.sol#L93
ETHRegistrarController.sol#L256

[G03] Custom Errors

As your using a solidity version > 0.8.4 you can replace revert strings with custom errors. This will save in deployment costs and runtime costs.
Based on a test in remix, replacing a single revert string with a custom error saved 12,404 gas in deployment cost and 86 gas on each function call.

contract Test {
	uint256 a;
	function check() external {
		require(a != 0, "check failed");
	}
}   (Deployment cost: 114,703, Cost on Function call: 23,392)
vs 
contract Test {
	uint256 a;
	error checkFailed();
	function check() external {
		if (a != 0) revert checkFailed();
	}
}   (Deployment cost: 102,299, Cost on Function call: 23,306)

Instances where custom errors can be implemented:
RRUtils.sol#L307
ETHRegistrarController.sol#L99-L102
ETHRegistrarController.sol#L137-L139
ETHRegistrarController.sol#L196-L199
ETHRegistrarController.sol#L232-L242
ETHRegistrarController.sol#L259-L261
ReverseRegistrar.sol#L41-L54
BytesUtil.sol#L28
BytesUtil.sol#L42
ERC1155Fuse.sol#L60-L62
ERC1155Fuse.sol#L85-L87
ERC1155Fuse.sol#L107-L109
ERC1155Fuse.sol#L176-L179
ERC1155Fuse.sol#L195-L203
ERC1155Fuse.sol#L215-L217
ERC1155Fuse.sol#L248-L252
ERC1155Fuse.sol#L290-L293
Controllable.sol#L17

[G04] Long Revert Strings

If you opt not to use custom errors keeping revert strings <= 32 bytes in length will save gas.
I ran a test in remix and found the savings for a single short revert string vs long string to be 9,377 gas in deployment cost and 18 gas on function call.

contract Test {
	uint256 a;
	function check() external {
		require(a != 0, "short error message"); 
		(Deployment cost: 114,799, Cost on function call: 23,392)	
		vs 
		require(a != 0, "A longer Error Message over 32 bytes in     
        length"); 
		(Deployment cost: 124,176, Cost on function call: 23,410)	
	}
}

I recommend shortenning the following revert strings to < 32 bytes in length:
ETHRegistrarController.sol#L99-L102
ETHRegistrarController.sol#L137-L139
ETHRegistrarController.sol#L198
ETHRegistrarController.sol#L232-L242
ETHRegistrarController.sol#L259-L261
ReverseRegistrar.sol#L41-L54
ERC1155Fuse.sol#L60-L62
ERC1155Fuse.sol#L85-L87
ERC1155Fuse.sol#L107-L109
ERC1155Fuse.sol#L176-L179
ERC1155Fuse.sol#L195-L203
ERC1155Fuse.sol#L215-L217
ERC1155Fuse.sol#L248-L252
ERC1155Fuse.sol#L290-L293
Controllable.sol#L17

[G05] && in Require Statements

If optimising for runtime costs over deployment costs you can seperate && in require functions into 2 parts. I ran a basic test in remix and it cost an extra 234 gas to deploy but will save ~9 gas everytime the require function is called. (note: If you upgrade to solidity version > 0.8.13 this is no longer true)

contract Test {
	uint256 a = 0;
	uint256 b = 1;

	function test() external {
		require(a == 0 && b > a) 
		(Deployment cost: 123,291, Cost on function call: 29,371)
		vs
		require(a == 0);
		require(b > a);
		(Deployment cost: 123,525, Cost on function call: 29,362)
	}
}

Require statements that can be split up:
BytesUtils.sol#L268
ERC1155Fuse.sol#L215-L218
ERC1155Fuse.sol#L290-L293