There is a similar question here, but I think the answer is not correct.
Yahoo! Boss gives me the access to its entire search index, whereas Google Custom Search API allows you to search sites which you yourself provide.
So, I want to know if there is a Google Search API, which allows me to search its entire index like Yahoo! Boss.
I suspect you are mistaken, with this pdf searchengine
and they're using Google Custom Search.
I'd say that YBOSS is much more straightforward, but since v2 you have to pay for it, and there might be legal issues as to whether with Google you can re-order the results. I suspect you cannot.