When Roger Federer began his comeback here nine days ago, he knew he was capable of producing some good tennis but was unsure for how long he would be able to maintain it.

Yesterday, the 35-year-old answered his own question and with it, moved to within two wins of what would be one of the most remarkable grand slam victories in recent memory.

It is four and a half years since Federer won the most recent of his 17 grand slam titles and the odds against him adding to it are still strong, with Stan Wawrinka up first and then, perhaps, Rafael Nadal in the final.

Federer should have been playing Andy Murray in the quarter-finals, of course, a task that might have been too much for him so soon into his comeback after six months out with a knee injury.

But Murray’s defeat by Mischa Zverev opened a door for him and Federer duly dispatched the German 6-1, 7-5, 6-2 yesterday, winning the first five games in 12 minutes.

Despite going a break down early in the second set, Federer hit back quickly, moving sweetly and hammering numerous forehand winners past the on-rushing Zverev, who never really stood a chance.

“I think winning back-to-back matches in best-of-five sets against quality, great players, that was for me the big question mark, if I could do that so early in my comeback,” a relaxed Federer said.

“I felt I was always going to be dangerous on any given day in a match situation. But obviously as the tournament would progress, maybe I would fade away with energy, that kind of stuff.

“I think now that I'm in the semis, feeling as good as I am, playing as good as I am, that's a huge surprise to me. If someone would have told me I'd play in the semis against Stan, never would I have called that one for me. For Stan, yes, but not for me.”

Now he is, though, the mindset changes and he will take an 18-3 record into his semi-final with Wawrinka, who dispatched Jo-Wilfried Tsonga 7-6, 6-4, 6-2 yesterday.

Fourth seed Wawrinka has won a grand slam title in each of the past three years, passing Federer in the rankings after the seven-times Wimbledon champion cut his season short last summer.

The dynamic between the two may have changed, somewhat, but there is a gleam in Federer’s eye and he is excited about what he’s achieved and may go on to achieve before this fortnight is out.

And the faster conditions this year, both the court surface and lighter tennis balls, is also playing in his favour.

“The older generation, anything before 2005, are used to faster courts,” he said. “From that moment on, it was a switch but we had to grow up in faster conditions.

“Maybe there's less thinking going on (so) you just play with instinct. That's maybe what older guys can do very well because they don't get frustrated in faster conditions.

“Maybe it has helped me, too, in my comeback, no doubt about it.”

The last time they played each other, in the semi-finals of the 2015 US Open, Federer won in straight sets but the 31-year-old, who won the US Open last September, did win when they played at the 2015 French Open.

“For sure now I'm more confident with myself,” he said. “When I step on the court, doesn't matter who I play, I know what I have to do if I want to win.

“Against Roger, it's always special because he's so good. He's the best player of all time. He has answer for everything. But I managed to beat him in a grand slam so we'll see.”