Gas Optimizations

[code423n4]

for loops can be optimized

1- For loop index increments can be made unchecked for solidity versions > 0.8.0. There is no risk of overflowing the index of the for loops. Therefore, they can be changed to unchecked to save gas. This would save more gas as iterations in the loop increases.
2- Postfix increments can be changed as prefix as it is cheaper.
3- There is no need to set uint256 variable to 0 since default value is already 0.

Lines of code

There are 32 lines some of which are below:
https://github.com/code-423n4/2022-06-connext/blob/main/contracts/contracts/core/connext/libraries/SwapUtils.sol#L254
https://github.com/code-423n4/2022-06-connext/blob/main/contracts/contracts/core/connext/libraries/SwapUtils.sol#L268
https://github.com/code-423n4/2022-06-connext/blob/main/contracts/contracts/core/connext/libraries/SwapUtils.sol#L289

Recommended Mitigation Steps

I suggest to change the original code from this

    for (uint256 i = 0; i < numTokens; i++) {
      s = s.add(xp[i]);
    }

to this

    for (uint256 i; i < numTokens; ) {
      s = s.add(xp[i]);
      unchecked { ++i; }
    }

Error string longer than 32 characters

Error reason strings take space in the deployed bytecode. Every reason string takes at least 32 bytes so make sure your string fits in 32 bytes or it will become more expensive.

Lines of code

There are many lines some of which are:
https://github.com/code-423n4/2022-06-connext/blob/main/contracts/contracts/core/connext/libraries/LibDiamond.sol#L121
https://github.com/code-423n4/2022-06-connext/blob/main/contracts/contracts/core/connext/libraries/LibDiamond.sol#L123
https://github.com/code-423n4/2022-06-connext/blob/main/contracts/contracts/core/connext/libraries/LibDiamond.sol#L132

Using != 0 is cheaper than > 0 when used on a uint in a require() statement with the optimizer enabled

Lines of code

There are many lines some of which are:
https://github.com/code-423n4/2022-06-connext/blob/main/contracts/contracts/core/connext/libraries/LibDiamond.sol#L121
https://github.com/code-423n4/2022-06-connext/blob/main/contracts/contracts/core/connext/libraries/LibDiamond.sol#L226
https://github.com/code-423n4/2022-06-connext/blob/main/contracts/contracts/core/connext/libraries/LibDiamond.sol#L247

Redundant initialisation with default value

Some variables are initialised with their default values which cause unnecessary gas consumption

Lines of code

All the for loop index inits to zero and additioanlly the lines below.
https://github.com/code-423n4/2022-06-connext/blob/main/contracts/contracts/core/connext/facets/BridgeFacet.sol#L68
https://github.com/code-423n4/2022-06-connext/blob/main/contracts/contracts/core/connext/facets/VersionFacet.sol#L16

Prefix increment/decrements are cheaper than postfix

Lines of code

https://github.com/code-423n4/2022-06-connext/blob/main/contracts/contracts/core/connext/facets/BridgeFacet.sol#L613
https://github.com/code-423n4/2022-06-connext/blob/main/contracts/contracts/core/connext/libraries/LibDiamond.sol#L134
https://github.com/code-423n4/2022-06-connext/blob/main/contracts/contracts/core/connext/libraries/LibDiamond.sol#L153