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In a day that saw injuries cut the programme short, Federer was joined in the final eight by second seed Tomas Berdych, who booked his place after Marcos Baghdatis retired hurt.
With Berdych up 3-0 in the first set, Baghdatis deemed his calf injury, which had severely hampered his play, to be too serious to continue.
But while Federer and Berdych had an easy time on things on Thursday others were made to work for their victories - although not too hard.
Fifth seed Richard Gasquet needed just 78 minutes to see off Alex Bogomolov Jr of Russia 6-3 6-2.
“I served well and hit good shots on my backhand,” said Gasquet. “I am happy to be in the quarter-finals. I am playing well and I am happy the way I am playing at the start of the season.”
Meanwhile, Juan Martin del Porto beat world number 105 Karol Beck 6-4 7-5 as he secured his third consecutive quarter-final berth of the year.
“I played better than the first round and the game was completely different,” del Potro told the ATP website. “I served well and was trying to hit winners with my forehand.
“When I got my chance I took it. I need to play better in my next round. I need to play 100 percent with my forehand and serve and then anything can happen.”
In other results, Andreas Seppi defeated Philipp Kohlschreiber 6-4 6-2 while Viktor Troicki was made to work for it by world number 232 Jesse Huta Galung, eventually claiming a 7-6 (2) 6-3 victory.