Stewart penned the script for "Rosewater," which is based on the book "Then They Came For Me: A Family's Story of Love, Captivity and Survival" by Maziar Bahari.
Bahari is the BBC journalist who left London in June 2009 to cover Iran's presidential elections for a week and instead spent 118 days in an Iranian prison being brutally interrogated, Deadline said.
Oliver is to tape eight weeks worth of "Daily Show" episodes while Stewart is making the film, the website said.
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