Don't the SDKs take care of computing the multi-part checksum during upload?

> To create a trailing checksum when using an AWS SDK, populate the ChecksumAlgorithm parameter with your preferred algorithm. The SDK uses that algorithm to calculate the checksum for your object (or object parts) and automatically appends it to the end of your upload request. This behavior saves you time because Amazon S3 performs both the verification and upload of your data in a single pass. https://docs.aws.amazon.com/AmazonS3/latest/userguide/checki...

It does and has a good default. An issue I've come across though is you have the file locally and you want to check the e-tag value - you'll have to do this locally first and then compare the value to the S3 stored object.