Is this capital loss carry over calculation by TurboTax correct?

I have read several articles about capital loss carry over and the $3000 deduction limit, I, however, still feel that TurboTax's calculation for me is wrong. Please help!

 

My situation:

* Capital loss carry over from 2018: $10,000 (hypothetically)

* 2019 capital gain: $3,100 (hypothetically, a number higher than 3000) 

 

My understanding of how capital carry over should be calculated:

* I can use $3000 from my carried over capital loss to offset my gain in 2019. 

* This means that I need to pay capital gain tax only for  $3100 - $3000 = $100 in 2019.

* My capital loss carry over will be $10,000 - $3,000 = $7,000 next year.

 

What TurboTax calculated:

* Capital loss carry over next year is : $3,900 (which seems to be $10,000 - $3,000 - $3,100.) 

* It doesn't seems like I'm taxed for the $3,100 - $3,000 = $100 portion. 

 

I'm scratching my head to try to make sense of the TurboTax calculation. I mainly have two questions:

* Is the $3,000 portion being deducted twice from the capital loss carry over? 

* Can I, like TurboTax did, offset the entirety of my $3,100 2019 capital gain? If so, what does the $3,000 limit mean?

 

Thanks in advanced!