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Michele, Alessandro, thank you both for your work! And thank you Cheryl for managing this ticket.
I like mangrisano's design where the target time is passed as an argument to the ``autorange`` method, although I prefer the name "target_time". (But I'm open to alternatives.)
So I think a good approach might be a hybrid between mangrisano's design, and the design by Alessandro:
1. the constructor takes the target time and records it as an attribute;
def __init__(self, ..., target_time=default_target_time):
 self.target_time = target_time
2. when the ``timeit`` method is used, if number=0 the target time is taken from self.target_time and passed to ``autorange``;
- if the ``autorange`` method is called directly, the caller can override the target time by passing it as argument; otherwise the default value is looked up from the instance attribute.
So something like
def autorange(self, callback=None, target_time=None):
 if target_time is None:
 target_time = self.target_time
 ...
Please suggest alternatives or point out anything I may have missed, and thank you all again!
(I'm now going to be away from the keyboard for at least the next 18 hours so if I don't reply quickly, that's why.)