AWS Official Documentation is Incorrect

I'm following this guide

https://aws.amazon.com/premiumsupport/knowledge-center/cognito-user-pool-remembered-devices/

to set up remembered devices and I'm doing most things from scratch because there is no Ruby library like Warrant.

First off, let me just say the PasswordVerifier formula in this doc is incorrect/lacks information (when calling ConfirmDevice). I had to look at js source code and warrant source code to reverse-engineer what it was actually looking for.

Next for, Call RespondToAuthChallenge for DEVICE_PASSWORD_VERIFIER it seems like the forumla given does not work at all. Is there any open source code

The formula for S_USER = (SRP_B - k * g^(x))^(a + ux) does not seem to be using modular exponentiation and is returning a number so large, that my code isn't able to deal with it without some extra libraries. That does not seem like it's expected if all the other S values in open source code is using modular exponentiation.

Please provide some client-side code where this final formula for DEVICE_PASSWORD_VERIFIER actually works. There does not seem to be a working example anywhere, and it seems like AWS is just posting incorrect guides.

Edit: I'm looking at the code in these places to respond to device password verifier and it's completely different from what is described in the blog post:

• https://github.com/aws-amplify/amplify-js/blob/master/packages/amazon-cognito-identity-js/src/CognitoUser.js#L643
• https://github.com/aws/aws-sdk-net-extensions-cognito/blob/e79202c2c622839e36e76659141b329c7a044251/src/Amazon.Extensions.CognitoAuthentication/Util/AuthenticationHelper.cs#L255