Multiply std::chrono timepoint by a scalar - c++

Question

How can one multiply a chrono timepoint by a scalar? It works for durations, but timepoints can't be multiplied by a scalar ("error: invalid operands to binary expression").
Context:
I have some code that in real life will run for a long time. For testing purposes, I want to be able to speed it up by a factor, so everything happens similarly, but just in fast forward.
I thought of making my own ScaledClock class, that returns values from chrono::steady_clock, but with a scaling parameter that can be set to something greater than 1 to achieve a speed up. Here is some code:
steady_clock::time_point ScaledClock::now() {
return steady_clock::now() * speedUp; // <--- error
}
void ScaledClock::sleep_for(steady_clock::duration duration) {
std::this_thread::sleep_for(duration / speedUp);
}
void ScaledClock::sleep_until(steady_clock::time_point time) {
std::this_thread::sleep_until(time / speedUp); // <--- error
}
If the speedUp is 2, for instance, then the program will always think that twice as much time has passed. It will also sleep for half as long. As long as I am disciplined about not using this class for all timing, I think it should work.
(Alternatively, if someone has a much better way of achieving this, I'd love to hear it).
Edit: copy of comment, because I think it is useful clarification:
en.cppreference.com/w/cpp/chrono/time_point:
Class template std::chrono::time_point represents a point in time. It
is implemented as if it stores a value of type Duration indicating the
time interval from the start of the Clock's epoch.
So I want all the times since the epoch doubled. If the epoch is not start of program execution, and my code happens to think that it is running in 4036, I'm not really bothered

Answer 1

You will need to store a starting point (now() e.g. at program start) and then determine the time passed since that starting point as a duration. You can then add this duration multiplied with your factor to the start point and return it as time point in your ScaledClock::now() function. Just like this:
#include <chrono>
#include <unistd.h>
int main() {
auto start = std::chrono::steady_clock::now();
sleep(1);
auto actualNow = std::chrono::steady_clock::now();
auto timePassed = actualNow - start;
auto timePassedScaled = timePassed * 2.0;
auto scaledNow = start + timePassedScaled;
return 0;
}