Create a QSlider-like widget for inputting doubles

I have often wanted a slider widget for inputting floating-point values. Although it is possible to map the desired range to an integer set, this is inconvenient and limits the range of values that the widget can express. It would be extremely useful to have a properly implemented double slider, using double as its internal data representation.

(I have a partial implementation that I may be able to share. It is based on QWidget, as I do not see any other way to do it properly, and lacks some QSlider features, including tracking, orientation and ticks. However it works and is a fairly clean implementation, although it does not implement the QSlider/QAbstractSlider split, which may be desirable for a proper in-Qt implementation.)