Here's a link to the Gyllenhaal Family Tree Project, which is built around a database of thousands of Gyllenhaal descendants in the U.S. and Sweden. The database includes lists of Gyllenhaals who are descended from a common ancestor who lived in Sweden in the 16th century. 

https://www.gyllenhaal.org/index.html

The database was assembled by Ed Gyllenhaal, son of Charles Gyllenhaal whose memoir is reproduced here and helped to prompt this look at the current Gyllenhaal family.